but I I ll WMffl BBH fB«119 BBS vv J ^v v-cy 5 5>^ 'bK ■b, **rrr^ j> J t> '•^r°* .«*■'' "o, "-;r 1 ' c • • . * 4 o * A ^ ^ «... ^ .0> A v ^^ ^ ^ v^ .0' » H o & -w o v *b ♦7?77* a rt^ o - c *^ A *A V ** t -UL% ^ "o^ t>^ A. . . 5 < > 0^ ,v*% ^ aV^, Issued April 24, 1913. U. S. DEPARTMENT OF AGRICULTURE. BUREAU OF PLANT INDUSTRY— BULLETIN NO. 269. B. T. GALLOWAY, Chief of Bureau. EXPERIMENTS IN WHEAT BREEDING EXPERIMENTAL ERROR IN THE NURSERY AND VARIATION IN NITROGEN AND YIELD. BY E. G. MONTGOMERY, Experimental Agronomist of the Nebraska Agricultural Experiment Station and Collaborator of the Office of Cereal Investigations, Bureau of Plant Industry. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1913. , ^ BUREAU OF PLANT INDUSTRY. Chief of Bureau, Beverly T. Galloway. Assistant Chief of Bureau, William A. Tayxor. Editor, J. E. Rockwell. Chief Clerk, James E. Jones. Cereal Investigations. scientific staff. Carleton R. Ball, A ding Cerealist in Charge. Charles E. Chambliss, H. B. Derr, H. V. Harlan, and C. W. Warburton, Agronomists. E. L. Adams, Assistant Agronomist. Clyde E. Leighty, Expert. Cecil Salmon, Physiologist. John F. Ross, Farm Superintendent. A. A. Potter, Assistant Pathologist. L. C. Aicher, P. V. Cardon, Manley Champlin, J. A. Clark, N. C. Donaldson, J. Mitchell Jenkins, E. M. Johnston, Jenkin W. Jones, F. A. Kiene, jr., Clyde McKee, J. D. Morrison, B. E. Rothgeb, T. R. Stanton, and L. Wermelskirchen, Scientific Assistants. F. R. Babcock, Assistant. L. R. Breithaupt, L. C. Burnett, and H. H. Love, Agents. D. E. Stephens, Executive Assistant. i D, OF D, *PK 3J 1913 LETTER OF TRANSMITTAL U. S. Department of Agriculture, Bureau of Plant Industry, Office of the Chief, Washington, D. C, October 16, 1912. Sir: I have the honor to transmit herewith and to recommend for publication as Bulletin No. 269 of the series of this Bureau the accompanying paper entitled "Experiments in Wheat Breeding: Experimental Error in the Nursery and Variation in Nitrogen and Yield," by Prof. E. G. Montgomery. This paper contains the results of special experiments in wheat breeding conducted by the Nebraska Agricultural Experiment Station in cooperation with the Office of Cereal Investigations of this Bureau, during the years 1905 to 1910, inclusive. In part, the work is a continuation of that recorded in Bureau of Plant Industry Bulletin No. 78, by Dr. T. L. Lyon, under whose direction the experiments were conducted from 1902 to 1906, inclusive. From 1907 to 1910, inclusive, the work was under the charge of Prof. Montgomery, experimental agronomist of the Ne- braska experiment station, who has since become professor of farm crops in the College of Agriculture at Cornell University. The paper is concerned chiefly with the nature and extent of experimental error in the wheat nursery in connection with breeding experiments in the inheritance of nitrogen content and yield in wheat plants. The standardization of agronomic experiments has been receiving much attention in recent years and is regarded as of fun- damental importance in agronomic research. The results contained in this paper are presented as a contribution to this subject as well as to the improvement of wheat. Respectfully, B. T. Galloway, Chief of Bureau. Hon. James Wilson, Secretary of Agriculture. 269 CONTENTS. Page. I. Experimental error in the nursery and variation in nitrogen content 9 Introduction , 9 Relation of yield of grain to nitrogen content 19 Reducing the experimental error 22 Replication of single plants 22 Replication of 2-foot rows 24 Replication of 16- foot rows ■ 25 The small-block test 27 Increasing the size of plat 29 The limit of experimental error 30 Summary 31 II. Experimental error in the nursery and variation in yield 33 Introduction 33 Variation in yield from check rows 33 Variation in yield from repeated rows 34 Variation in yield from small blocks 37 Effect of repetition in reducing error 38 Relation of size of plat to variation 39 Constancy of variation on the same plats 41 Variation in yields from centgener plats 41 Alternating check rows as a means of obtaining comparative yields. . . 42 Effect of increasing length of row 42 Influence of rate of planting on yield 45 Effect of competition between adjacent rows 47 Variation in pure strains and relation of data in centgener nursery and in field plats 48 Isolation of pure strains 48 Percentage of nitrogen 52 Strength of straw : 52 Yield per plant 53 Yield per centgener 53 Size of kernel 53 Quality of kernel 53 Superiority of strain 54 Comparison of rows, centgeners, blocks, and field plats 55 Cost of planting and harvesting centgeners, rows, and blocks 56 Use of check plats 58 Error in check plats 59 Other precautions against error 60 Accidental injury to plats 60 Unequal drainage 60 Summary 60 269 5 TABLES. Page. Table I. Results of a study of transmission of nitrogen content in wheat ker- nels in 1902 and 190:5 10 II. Nitrogen content of 57 wheat plants in 1903 and of their progeny in 1904 and 1905 11 III. Data from six wheat plants, showing irregular variation in yield and in nitrogen content of grain 12 IV. Nitrogen content and yield of grain from families Nos. 42 and 48, from ] 902 to 1905, inclusive 1 G V. Nitrogen content of 29 centgeners and corresponding rows from family No. 831 in 1908 19 VI. Nitrogen content and yield of grain from 180 wheat plants, arranged in inverse order of percentage of nitrogen, in groups of 10 20 VII. Nitrogen content of 90 plants of Turkey wheat from 1 centgener and of 840 plants variously combined into groups to show devia- tion from mean 23 VIII. Nitrogen content of 110 2-foot sections of drill row of Turkey wheat. . 24 IX. Nitrogen content of 100 16-foot rows of Turkey wheat 25 X. Summary showing degree of error due to variation in environment, according to several methods of comparison 26 XI. Nitrogen content of Turkey wheat grown in 224 block plats in 1909 and 1910 27 XII. Yield of 47 14-foot check plats of Turkey wheat in 1909 34 XIII. Yield of thrashed grain from 100 rows of Kherson oats 35 XLV. Yield of grain from 500 16-foot rows of Turkey wheat, systematically repeated in various ways to show experimental error 36 XV. Yield of Turkey wheat grown in 224 block plats in 1909 and 1910. . . 39 XVI. Yield, in grams, of Turkey wheat grown during the season of 1910 in 500 rows, each 16 feet in length 43 XVII. Summary showing coefficients of variability under various systems of arranging block plats and row plats 45 XVIII. Results of rate-of-seeding test on 100 16-foot rows of Red Rustproof oats .• 46 XIX. Results of rate-of-seeding test on 60 block plats of Kherson oats 47 XX. Relations of certain characters of 24 strains of Turkey wheat grown in nursery and in field and tested during 4-year periods 48 XXI. Yields of grain from 11 varieties of oats grown in field plats, cent- geners, rows, and blocks 56 XXII. Comparative number of plats of different types that can be planted or harvested in 10 hours 57 269 6 ILLUSTRATIONS. PLATES. Page. Plate I. Fig. 1. — Head-to-row nursery, in which 25 grains from a single head are planted in a row 20 inches long. Fig. 2. — Row-plat nursery, in which the rows are 16 feet in length with a 4-foot alley between beds, thus making the beds 20 feet in width 42 II. Fig. 1. — Increase plats of one-thirtieth acre each. Fig. 2. — Increase plats harvested and ready to thrash 42 III. Fig. 1. — Type of road grader or drag used in grading a nursery into beds. Fig. 2. — Grains of Turkey wheat, showing variation in appearance 52 IV. Fig. 1. — Representative kernels from four strains of Turkey wheat, selected to show variation in appearance. Fig. 2. — Representa^ tive kernels from four strains of Turkey wheat, selected from a series of 80 strains to show variation in quality 52 TEXT FIGURES. Fig. 1. Diagram showing the transmission of nitrogen content in 57 wheat plants of 1903 to progeny in 1904 and 1905 10 2. Centgener nursery, Nebraska Agricultural Experiment Station 12 3. Wheat centgener just after growth has started in spring, showing about 40 per cent of the plants winterkilled 13 4. Wheat centgener of 100 plants, showing variations in yield of grain and of nitrogen in 1907 14 5. Diagram of a portion of the wheat nursery in 1907, showing variations in nitrogen content in centgeners and families 15 6. Diagram of 10 centgeners and 10 corresponding rows, showing varia- tions in nitrogen content for individual plants, for each centgener, for each corresponding row, and also for their parents 18 7. Diagram of plat of Turkey wheat containing 224 blocks, showing the location of each block and variations in the percentage of nitrogen in the grain ' 22 8. Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks when combined in groups of adjacent blocks, with average nitrogen content for each group 22 9. Diagram showing the method of selection for nitrogen content when the experimental error is known 31 10. Diagram of plats of Turkey wheat, showing the arrangement of 224 blocks and the yield of grain for each block 37 11. Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks when combined in groups of adjacent blocks, with the aver- age yield for each group 38 269 7 ILLUSTRATIONS. Page. 12. Diagrams showing Turkey wheat grown in 224 blocks, combined in four groups of 56 adjacent blocks to show variations in yield and nitrogen content 41 13. Field plats of pure strains and check plats of original seed of Turkey wheat, 1910 50 14. Wheat nursery plats, showing variations in winterkilling 50 15. Field plats, showing variations in winterkilling between two pure strains of Turkey wheat 51 16. Increase rows of Turkey wheat, showing variations in the time of head- ing in different strains 52 17. Field plats of Turkey wheat, showing variations in stiffness of straw in two strains 53 18. Cereal laboratory, showing the method of taking notes on quality 54 19. Block nursery, showing blocks 4.2 by 16 feet in size . .' 55 20. Five-row nursery drill used for planting row plats and block plats 57 21. Row plats at harvest time 58 22. Diagram showing the method of selection for yield when the experi- mental error is known 59 269 B. P. I.— 785. EXPERIMENTS IN WHEAT BREEDING: EXPERI- MENTAL ERROR IN THE NURSERY AND VARIA- TION IN NITROGEN AND YIELD. I -EXPERIMENTAL ERROR IN THE NURSERY AND VARIATION IN NITROGEN CONTENT. INTRODUCTION. The investigation of the variation of plants of winter wheat in relative nitrogen content when grown under field or nursery condi- tions was begun by Dr. T. L. Lyon, formerly agronomist of the Nebraska Agricultural Experiment Station, in collaboration with the Bureau of Plant Industry of the United States Department of Agri- culture. His results were published as a bulletin of that bureau. 1 Since 1907 the investigation has been continued by the writer and his assistants. 2 One of the striking features of the data obtained by Dr. Lyon was the variation in nitrogen content of the kernels from different plants of wheat grown under apparently similar conditions. For example, 800 spikes of Turkey wheat were selected and half of each spike analyzed for proteid nitrogen, the lowest having only 1.12 per cent while the highest contained 4.95 per cent. In 1903, 288 plants which were the progeny from 119 of the spikes analyzing above 3 per cent proteid nitrogen in 1902 were analyzed and found to vary from 1.20 per cent to 5.85 per cent in nitrogen content. In most of the families only a single plant was selected for analysis, but in the remainder two to six plants were selected. Even where all the plants were grown from a single parent the varia- tion was quite as great. 1 Lyon, T. L. Improving the Quality of Wheat. Bulletin 78, Bureau of Plant Industry. 1905. 2 The writer wishes to acknowledge with thanks the assistance of a number of men who have contrib- uted to the production of these data. Dr. T. L. Lyon, now of Cornell University, planted the first wheat nursery in 1902 and conducted the work until 1906, being assisted by Prof. Alvin Keyser, now of the Colo- rado Agricultural Experiment Station. They left an excellent set of records, from which data previous to 1906 have been prepared (Table II). Mr. L. L. Zook, now of the Bureau of Plant Industry, assisted with the work in 1907 and 1908, as did Mr. Erwin Hopt in 1908 and 1909. Prof. T. A. Kiesselbach had charge of the records during the seasons of 1909 and 1910 and has prepared much of the tabular matter for publication. The chemical analysis has been under the direction of Dr. F. J. Alway, who devised a rapid method especially for this work. 69826°— bul. 269—13 2 . 9 10 EXPERIMENTS IN WHEAT BREEDING. Dr. Lyon noted this variation, as follows: For instance, the plants numbered 21205 to 21212, all of which come from the same parent, vary from 2.16 to 5.23 per cent in proteid nitrogen content, while plants 69805 and 69806 vary from 5.82 to 1.66 per cent in this constituent. 1 In addition to the 119 "highs" preserved in 1903, progeny were analyzed also from 20 "mediums" and "lows." When these data were summarized it seemed that there had been some tendency to transmit the character, as shown in Table I. Table I.— Results of a study of transmission of nitrogen content in wheat kernels in 1902 and 190 J 2 Llange in percentage of proteid nitrogen. Number of analy- ses aver- Pro teid nitrogen in kernels. lto3 3 and over. Per cent. 20 j L85 119 3.39 Number of analy- ses ave'r- 70 288 Proteid nitrogen in kernels. Per cent. 2.59 2.92 Fig. 1. — Diagram showing the transmission of nitrogen content in 57 wheat plants of 1903 to progeny in 1904 and 1905. The vertical lines represent successive years. The horizontal lines represent the percentage of nitrogen found, and the figures in parentheses show the number of plants in each group analyzed for nitrogen content in 1903. 269 Summaries of the results obtained in 1904 and 1905 show very little tendency to transmit this charac- ter. In 1906, after four years of selec- tion of extremely high fluctuates, and later, after two more years of selection, by taking a composite sample of all the progeny of a plant it was found that no gain had been made in the nitrogen content of the crop. In Table II is a summary of data obtained in the years 1903 to 1905 from 57 of the original plants. Fig- ure 1 is a graphic presentation of the same data, in which the hori- zontal lines represent the percent- age of nitrogen, the vertical lines represent successive years, and the figures in parentheses show the num- bers of plants in each of the seven groups analyzed for nitrogen content in 1903. i Lyon, T. L. 2 Lyon, T. L. Op. cit., p. 99. Op. cit., table 26, p. 98. EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 11 Table II. — Nitrogen content of 57 wheat plants in 190,3 and of their progeny in 1904 and 1905, arranged in groups according to the percentage of nitrogen. Record of 57 plants 1903. harvested in Record of progeny plants in 1904. Record of progeny plants in 1905. Kernels per Nitrogen in Kernels per Nitrogen in Kernels per Nitrogen in plant. kernels. w plant. kernels. >> plant. kernels. M u a a a S3 a § .a a 3 3 o a a a +^ bl. 2 a £ ,fi be |S a 2 £i M 3 a .a E o £ o a M a < * Pm jg: ^ Ph Gms. Gms. Gms. Gms. Gms. Gms. 7 555 10.82 1.68 0. 1709 35.... 641 9.12 2.69 0. 2491 112... 1,052 17.71 2.68 0. 4606 6 654 14.66 2.20 .3040 35.... 790 12.63 2.63 .3262 99.... 1,040 19. 13 2. S4 .5207 18.... 601 11.26 2.74 .3068 90. . . . 745 11.42 2.64 . 2985 285... 1,165 21.44 2.69 .5716 10 338 5.87 3.27 .1919 53.... 694 10. 59 2.74 .2947 180... 1,057 19.49 2.82 .5486 5 306 6.44 3. 68 . 2431 23.... 723 10.56 2.74 . 2875 51.... 1,093 23.16 2.71 .6154 6 366 6.62 4.25 . 2837 30. . . . 779 11.54 2.65 . 3137 98. . . . 1,245 22.02 2.80 .6153 5 274 5.68 5.13 .2773 25. . . . 716 10. 56 2.59 .2710 81.... 1,1S3 20.12 2.64 .5317 It is difficult to explain why such great variations exist when there seems to be little or no tendency to transmit them. It seems ap- parent that the variations must be due to differences in environment. Since the ordinary factors of environment, as sunlight, warmth, moisture, and apparent fertility of the soil, are constant for all plants under our nursery conditions, we must conclude that there are factors profoundly influencing the growth of plants beyond the ordinary range of observation. Figure 2 shows the general appearance of the centgener nursery, each centgener containing 100 plants 6 inches apart each way. Figure 3 shows a single centgener just after growth has started in the spring, about 40 per cent of the plants having winterkilled. The great variation in the size of the remaining plants is probably due to the effect of environment and is not hereditary. This environmental variation is usually noted even in centgeners where most plants have survived and is often interpreted as indicating real hereditary differences. A number of interesting problems are suggested. Why should one plant, growing under practically the same environment as another, collect from the soil two or three times as much nitrogen ? Or why should two plants yielding different quantities of grain collect the same quantities of nitrogen ? Table III illustrates these variations. 269 12 EXPERIMENTS IN WHEAT BREEDING. Table III. — Data from six wheat plants, showing irregular variation in yield and in nitrogen content of grain. Plant No. Kernels. Nitrogen in kernels. Plant No. Kernels. Nitrogen in kernels. Number. Weight. Per cent. Total weight. Number. Weight. Per cent. Total weight. 21107 21108 21109 1,058 1,030 927 Grams. 22. 879 16. 679 16. 026 2.45 2.59 1.74 Grams. 0. 5605 . 4324 .2789 23905 23907 24005 776 1,167 1,495 Grams. 18.507 23. 01S 30.064 3.57 2.86 2.19 Grams. 0.6607 .6583 .6584 The three plants, Xos. 21107 to 21109, are from the same mother growing in a single centgener, probably less than 2 feet apart, yet the actual grams of nitrogen gathered differ more than 100 per Fig. 2. — Centgener nursery, Nebraska Agricultural Experiment Station. Each centgener contains 100 plants. cent. This difference is not inherited, as these plants rarely trans- mit this quality. It therefore seems hard to explain on a difference in the root development or in the functioning parts of the plant. As plants growing only 6 inches apart commonly exhibit such differ- ences, it can not be ascribed to a difference in soil solution. Differ- ence in vigor of growth is not a satisfactory explanation, as plants Xos. 23905, 23907, and 24005 illustrate. These three plants under uniform conditions yielded different quantities of grain, yet the heaviest yielder produced no more nitrogen than the lowest. Such differences are not only common among plants from the same cent- gener, but quite marked variations are also noted between cent- geners from the same mother plant. 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 13 Some of the results obtained from the study of this problem are shown in figures 4 and 5. Figure 4 is a plat of a single centgener (1907), with the plants 6 inches apart each way, making the entire area 5 feet square. All plants in this centgener are from the same parent. Each square represents a plant. Where no figures occur the plant was missing. The upper number shows the percentage of nitrogen, the central number represents the kernels borne by the plant, and the lower number the weight in grams of the good kernels. Each plant was harvested separately, the kernels counted and weighed, and the percentage of nitrogen determined. Two wave lines indicate plants analyzing above 3 per cent nitrogen and one wave line those Fig. 3.— Wheat centgener just after growth has started in spring, showing about 40 per cent of the plants winterkilled. Note the great variation in size of the remaining plants. analyzing between 2.8 and 3 per cent. A tendency to group is noted. Those containing between 2.56 and 2.80 per cent are not marked. One straight line indicates plants with between 2.55 and 2.40 per cent of nitrogen; two straight lines, less than 2.40 per cent. Figure 5 shows a section of the wheat nursery in 1907. The small squares represent centgeners 5 feet square and the heavy lines out- line family groups; that is, all the plants and centgeners within a heavy line came from the same original plant. The percentage of nitrogen was obtained by taking a composite sample from all plants on the centgener. Variation is quite marked, although there is some tendency for certain families to run high or low; as, for example, family 339. 269 14 EXPERIMENTS IN WHEAT BREEDING. An illustration of the irregularities in number and weight of ker- nels, in percentage of nitrogen, and in total yield of nitrogen per plant is afforded in Table IV, pedigree records of two families. The wide variations were supposed at first to represent natural fluctua- tions which would be in some degree transmitted, but the selection of these high fluctuations has had no apparent effect in modifying the g.gi 247 6.80 2.32 299 8.8G 2.52 SO/ 13.4- 252 36/ IO. o 2.55 446 15.7 2.60 S07 13.8 2.60 40/ 2.6Q 347 e.a 2.63 £49 15.0 2.52 4// 1 1. a 2.72 6/3 12.5 2.53 409 9.8 2.5Q 4/7 10. 1 2.56 227 5.3 2.75 S43 14.3 2.56 60/ 17.5 2.23 4/0 I I.O 2.56 284 a.o 2.63 390 9.4- 2.66 370 9.3 466 10.4- 2.45 322 8.9 275 406 9.7 2.69 392 9.5 J^J6. ~2^6 3.8 3. IO 362 7.6 2.8 2.42 8.5 3. OS 3.20 9.5 2.71 467 5.3 2.60 379 7.4- 2.66 470 II. I 2.76 277 362 4.8 10.8 2.52 66/ 16.8 2.58 ^■7(? 14.4 2.60 S/O 12.1 2.58 8.1 3.M 7.5 Fig. 4. — Wheat centgener of 100 plants, showing variations in yield of grain and of nitrogen in 1907. Upper figures, percentage of nitrogen content; middle figures, number of kernels produced; lower figures, weight of good kernels in grams. The various underscorings of the upper figures indicate five groups having successively higher nitrogen content as follows: (1) Figures underscored with two straight lines lie between 2.15 and 2.40 per cent; (2) those underscored with one straight line lie between 2.41 and 2.55 per cent; (3) those not underscored lie between 2.56 and 2.59 per cent; (4) those underscored with one wave line lie between 2. SO and 3 per cent; (5) those underscored with two wave lines lie above 3 per cent. nitrogen content of plants in a family, as there always seemed to be a mean content for each family, to which the types returned. As examples of variation, note that No. 35809 in family 42 has a low yield of nitrogen, yet the yield of nitrogen found in its progeny is practically equal to that of other members of the family. In family 48 (Table IV) note that in 1903 the three plants selected analyzed 3.82, 4.43, and 5.48 per cent of nitrogen, respectively, 2G9 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 15 while the family as a whole contained 3.53 per cent. The progeny of these plants returned to normal in percentage and total yield of nitrogen, except No. 21909, in which the yield of grain was above the average. Just why these wide fluctuations occur when every precaution is taken to grow the plants under uniform conditions is not very apparent. In 1908 a more thorough investigation of this point was made. Twenty-nine plants from the 1907 crop were all selected from a single centgener, and therefore all came from a single plant in 1906. From each of these 29 plants a centgener was planted, and also a row 14 feet long. The 29 centgeners were planted side by side, also the 29 rows. At harvest time all the plants in each of the 10 adjacent 2. 35 313 314 2 65 314- 2.93 32 8 3 04 3 as 2.89 SSI 2.73 3SI 2 56 38S 259 335 2.89 405 2.77 405 a.62 417 2.55 417 277 S22 2.71 522 2.55 556 289 556 2.43 3 277 3 2.46 313 2.60 3I4 2 72 3)4 3O0 328 2. 45 32S 2.72 3SI 2.75 3SI 2.71 385 272 385 2.50 391 2.83 405 2.63 4^7 2.58 417 293 522 2.99 522 2 52. E56 2.5 2 5 56 2.68 3 3.02 3 2.56 313 2. «.e 314 2.69 314 2.93 317 2.92 338 2.57 381 2.82 3B5 253 385 262 385 2.53 39/ 3.00 4-OS 2.53 417 2.49 4-17 2.93 522 3.11 522 2.59 556 2.68 £56 2S0 3 2.36 3 2.58 313 2.60 314 2.63 316 2.73 317 3.17 339 2.83 381 2 53 385 2.S3 38 5 2.76 385 249 391 2.89 40S 2.59 417 2 63 4-17 2.66 S22 2.95 522 2.S5 556 2.66 556 2. 55 632 3.03 3 2 34 313 2.69 314 2.84 316 z.s>o 317 3.16 339 2.80 381 3.02 38J 2.66 385 2.93 390 3.06 391 2.87 407 2.75 417 2 71 .417 2.69 522 2 92 555 2.39 556 2.63 55"6 2.62 632 2.96 3 2.72 313 £.76 314 2.87 316 2.87 317 3.17 333 289 381 2.43 385 2. SO 335 2.71 390 2.46 391 2.89 407 2 60 4-17 2.68 4-17 2 .89 522 268 555 2.92. 556 2.63 SSb 2.68 632 2.95 3 2.46 313 2.95 314 2.93 316 2.SO 317 3.09 339 2.79 381 2.60 385 2.89 385 275 390 277 391 2.82 4-07 3.00 4 OS 2.77 3.00 522. 2 83 555 2.83 556 £ 63 556 256 632 2.83 3 2 62, 313 2.80 314 2.89 3IS 2 73 317 3.13 332 2.45 379 2.63 385 2.56 3S5 2.76 390 2.68 391 292 4-08 Z.&4 40S 2.71 4 25 3.03 522 2 ©7 555 2 59 555 2.79 55-6 2 62 .556 2.89 3 2 35 313 2.59 314- 2.76 316 2.63 317 2.58 377 2.87 379 2.73 385 2.68 385 2.60 390 2.68 391 269 468 289 •408 2.66 425 2.72 425 3.02 555 2.73 sss 2.76 556 2.6 9 2 68 3 set •314- 2.44 314 2.66 316 2.63 317 2.46 377 2.S2 379 2.73 385 2.63 38S see, 390 2 66 391 2.59 4-08 283 4-oe 2.52 4-2 5 263 421 2.77 555 273 555 2.68 556 2.7( 55-6 266 3 2.87 314- 2.80 314 3.00 316 2.71 317 2.7S 377 234 379 2 66 385 2.49 385 2.65 390 ate 391 2.V9 408 2 87 4-oe 290 2.62 ■425 3 16 555 2 84 555 2.72 556 1.76 556 2.68 3 a. 77 3)4 258 314 2.9fc 316 2.72 317 2.63 377 3.20 377 2.73 385 2.73 385 2.72 3 90 2.77 390 2.84 4-OS 3.02. 4 OS 2.6 6 4-25 2.65 42.5 2.79 55S 2.90 555 2.62 556 2.11 556 2.73 3 Fig. 5.— Diagram of a portion of the wheat nursery in 1907, showing variations in nitrogen content in cent- geners and families. Each square represents a single centgener, and each area within heavy lines shows the centgeners belonging to a single family. The upper figures represent the percentage of nitrogen; the lower figures are the family numbers. centgeners were harvested in order and analyzed. The 10 dupli- cate rows were grown in a manner similar to field conditions; that is, sown at the rate of 5 pecks to the acre and the rows 8 inches apart. The plan was to see whether the same sort of variation would be found among plants under field conditions. To secure a uniform sample from the rows, 7 plants were harvested from each foot of row, 98 plants being harvested and analyzed from each row. In the centgeners the results were similar to those obtained in 1907. The plants in the rows, being planted close together, yielded only about one-tenth as much grain per plant, but the variation in yield and in percentage of nitrogen per plant was even greater than in the centgeners. 269 16 EXPERIMENTS IN WHEAT BREEDING. CCWOX"* >o hhO«3(N •*f igocco^M CO . CO CM ~* t^ CM 5 CM CO -*< »-H 00 CM O CO to 10 to O CO O Ol 01 CO *:■ iC X *f C. ■* g cc cm «c a: ^5 t , x x 1 - -r t^. c-t M »o ^cooooo ■O CD^COON -c 00 a S tS &3 OOJHHIO ■ O CM -^ Tf -* ^H rt MNtCCMN 00 O0 CO CO CO rt V- 4J CO CO oc 01 1-- r* r^r* 05 00 00 X t>. .5 .-_; £| CM CM CM CM CM CM CM CM CM CM CM BH CNCN CNCN CM c-i IS Z 1 CO X ft ■B £ 450©0500 c: 01 1 - ~ — ■ 3 C0«i"0»0 »C O? 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"a S °£ % •So ^ o >^ t3 O 03 ^ ft -3 i2 S S a ft a C c^ c3 o a Figure 6 is a graphic illus- tration of the centgener and row plats. The soil on which these plats were located was thought to be very uniform, and the appearance of the crop on the various plats was also uniform. The average per cent of nitrogen in the 10 centgeners varied from 2.27 (No. 41301) to 3.04 (No. 42001). To show the loca- tion of high and low ni- trogen plants in each cent- gener the method of plotting shown in the figure was used. Where plants were missing the space is left blank; where a plant analyzed less than 2.20 per cent in nitrogen a dot (.) is used; from 2.20 to 2.80 per cent the circle is employed, denoting interme- diates; from 2.80 to 3 per cent a dash ( — ) is used; and all plants analyzing above 3 per cent are marked by a cross ( + ) . The ' ' highs ' ' and "lows" tend to segregate, as in 1907. Also there is a pro- gressive increase toward one end of the series. The 10 duplicate rows are plotted in a similar manner. The rows were more uniform in com- position than the centgeners, but they show a variation in composition from 2.58 to 2.84 per cent of nitrogen. Also there seems to be no con- sistent relation between the rows and the corresponding centgeners, or the parent 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 19 plants. The variation in both centgeners and rows seems to be due to local effects, and does not appear to be hereditary. We may eliminate any possibility of hereditary effect by adding to- gether the short rows in the centgeners which come end to end, thus making 10 long rows with each centgener equally represented. The results of such composite analyses are shown at the right of the centgener plat, indicating a variation ranging from 2.40 to 2.81 in percentage of nitrogen in the 10 rows. In the same way we may divide the 10 original rows into blocks having each row equally represented. Variation in the 10 blocks thus formed is shown, at the bottom of figure 6, to be from 2.47 to 2.85 per cent of nitrogen. RELATION OF YIELD OF GRAIN TO NITROGEN CONTENT. Since some centgeners yield more grain than others, the 29 cent- geners from the same parent plant, of which the 10 centgeners just considered were a part, were arranged according to percentage of nitrogen and summarized in groups of 5 centgeners. This summary (Table V) shows some relation between yield of grain per centgener and nitrogen content, the yield varying inversely with the nitrogen content, but when the 29 corresponding rows were arranged in the same way no such relation was shown. Table V. — Nitrogen content of 29 centgeners and corresponding rows from family No 831 in 1908. Arranged according to nitrogen in centgeners. Arranged according to nitrogen in rows. CD a CD a 3 a CD 60 o 2 »>. "3 o Average yield per plant. a o o CD ">. o a to £ 2 'P. o a a> so o M 2 « O Eh 2 ■pVa v | > ft s-8 •- a aft CD bo o 5. , 5 5 5 , 5 4 P. ct. 2.83 2.63 2.56 2.52 2.-14 2.34 Grams, 616 614 851 767 799 916 Grams. 7.19 7.13 9.60 9.01 9.01 10.50 P.ct. 2.67 2.66 2.65 2.57 2.52 2.64 Grams. 194 200 173 179 189 209 Per cent. 2.69 2.68 2.63 2.66 2.71 2.68 5 5 5 5 5 4 P.ct. 2.78 2.72 2.65 2.60 2.55 2.35 Grms. 189 196 194 195 188 176 P. ct. 2.63 2.57 2.52 2.57 2.55 2.50 Grms. 652 763 817 789 777 729 Grms. 7.52 9.03 9.14 11.13 8.72 8.50 P. cf. 2.65 2.73 2.72 2.62 2.64 2.68 269 20 EXPERIMENTS IN WHEAT BREEDING. Table VI. — Nitrogen content and yield of grain from ISO wheat plants, arranged in inverse order of percentage of nitrogen, in groups of 10. Ninety Plants from Centgenek No. 41801. I'lunt No. Nitro- gen. Yield. Plant No. Nitro- gen. Yield. Plant No. Nitro- gen. Yield. 52 Per ct. 3.44 3.22 3.21 3.19 3.19 3.17 3.13 3.00 2.98 2.98 Grams. 1.55 . 60 7.86 4.36 6.45 7.92 4.89 13.42 10.6.5 7.54 64 Per ct. 2.62 2.62 2.62 2.61 2.61 2.60 2.60* 2.58 2.58 2.58 Grams. 11.11 16.23 19.49 9.16 1.20 7.00 3.11 8.22 6.45 6.76 27 Per ct. 2.43 2.43 2. 43 2. 43 2.41 2.41 2.40 2.39 2.39 2.39 Grams. 7.49 79 83 47 7.11 01 93 59 78 26 63 6.60 81 9 7.39 91 51 7.48 41 31 14.83 22 67 20 10.37 L2 8 8.82 6 16 48 1.44 01 54 69 8.40 Average. 56 60 73 76 32 95 14 18 Average. . . . 68 3.15 6.52 2.60 8.87 2.41 7.99 71 2.92 2.92 2. 89 2.85 2.82 2.82 2.79 2. 78 2.77 2.77 2.46 10.52 9.14 7.69 11.75 .45 11.46 6.82 7.59 4.44 2.58 2.57 2.57 2.56 2.53 2.51 2. 50 2.48 2.48 2.48 6.61 10.56 15.31 1.34 8.42 12. 25 17.52 11.22 6.15 4.69 2.37 2.37 2.36 2.34 2.30 2.29 2. 29 2.27 2.27 2.27 8.00 90 96 6.07 80 55 8.30 33 24 11.07 72 45 9.59 87 25 13. 16 23 58 8.19 42 28 7.90 75 49 50 86 34 43 70 98 36 8.60 97 44 6.85 Average 39 Average 2.83 7.43 2.52 9.41 2.31 8.77 ll 2.71 2.70 2.68 2.68 2.65 2.65 2.65 2. 65 2.65 2.62 11.47 6.83 10. 52 6.32 5.55 14.26 7.45 5.21" 16.94 9.17 2.48 2.47 2.47 2.47 2.47 2.46 2.46 2.46 2.44 2.43 10.01 21.10 11.18 13.25 6.83 12.08 8.27 12.81 2. 93 16.20 2.26 2.25 2. 23 2.22 2.20 2.20 2. 20 2.11 2.11 2.09 8.66 74 29 9.85 21 30 9.17 85 46 7.24 15 37 10.01 53 40 77 57 14.78 84 89 13.50 88 99 10.. ..r 17 10.31 94 19 10.40 7 5 38 6.90 Average Average 2.66 9.47 2.46 11.47 2.19 10.08 Ninety Plants from Row No. 141801. 79 3.31 3.29 3.25 3.20 3.19 3.18 3.18 3.17 3.10 3.09 0.84 .26 .30 .35 .77 .44 .79 1.94 .33 .96 88 2.77 2.76 2.76 2.76 2.75 2.74 2.74 2.71 2.69 2.67 0.56 1.69 1.08 3.41 1.29 2.51 1.30 .53 .63 .18 25 31 2.54 2.54 2.54 2.53 2.53 2. 52 2.51 2.48 2.48 2. 47 0.87 8 1.54 18 99 40 72 1.07 11 1.72 49 46 89 2. 42 76 77 62 .10 .66 5 15 38 10 Average. 50 32 64 93 97 47 78 50 70 51 Vverage. . . . 74 26 54 63 34 56 86 1.62 87 4.32 U 69 2. 00 81 3.20 .70 2.73 1.32 2.51 1.63 S3 3.09 3.08 3.07 3.05 3.02 3.00 2. 09 2.96 2.90 2.88 .30 .65 .79 .69 2.37 .77 2. 27 1.59 1.28 2.02 2.67 2. 66 2.66 2.66 2.65 2.64 2. 64 2.63 2.62 2.61 .65 1.01 1.21 1.29 7.76 .70 .45 .74 .57 2.01 2.47 2. 47 2. 45 2. 45 2.44 2.43 2.39 2.39 2.39 2.35 1.46 16 2.07 17 37 39 .60 20 .81 23 98 7.10 12 41 2.33 21 42 2. 74 27 44 2.22 85 58 .86 90 52 1.12 Average.. . 71 Average.. .. 3.00 1.27 2.64 1.64 2.42 2.13 68 2.87 2.84 2.82 2.80 2.80 2.79 2.79 2.77 2.77 2.77 1.42 2.34 1.61 .52 .24 .88 1.48 .65 1.92 .52 2.61 2.60 2.60 2.60 2.58 2.58 2.58 2.58 2.57 2.56 1.07 1.18 .10 .94 .99 .38 .90 2.50 2.16 2.31 2.33 2.30 2.29 2.25 2.18 2.14 1.99 1.87 1.37 1.33 1.39 30 91 .81 29 61 .20 6 48 1.17 60 .. 24 .21 55 .. 43 1.31 84 36 1.13 22 96 28 67 Average. . 45 1.07 53 94 .79 75 .. 19 .47 Average . . Average 2.80 1.14 2.59 1.25 2.00 .85 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 21 Table VI. — Nitrogen content and yield of grain from ISO wheat plants, arranged in in vene order of percentage of nitrogen, in groups of 10 — Continued. Summary of Averages. Group Croups from cent- gener No. 41801. Groups from row No. 141801. Group No. Groups from cent- gener No. 41801. Groups from row No. 141801. No. Nitrogen. Grain per plant. Nitrogen. Grain per plant. Nitrogen. Grain per plant. Nitrogen. Grain per plant. 1 Per cent. 3. 15 2. S3 2. 66 2.60 2.52 Grams. 6.52 7.43 9.47 s. 87 9.41 Per cent. 3.20 3.00 2.80 2.73 2.64 Grams. 0.70 1.27 1.14 1.32 1.64 6 Per cent. 2. 40 2.41 2.31 2. 19 Grams. 11.47 7.99 8.77 10. OS Per ct m. 2.59 2.51 2.42 2.00 Grams. 1. 25 2 7 1.63 3 8 2.13 4 9 . 85 .5 The fluctuation in yield between plants within a centgener or row commonly varies as much as 500 per cent. To note whether this wide variation bore any relation to nitrogen content, the results from all the plants in centgener No. 41801 and from its corresponding row were tabulated according to nitrogen content (Table VI). While the summary shows a marked variation in nitrogen content, there is no corresponding change in yield, although there is a slight irregular tendency for yield to increase as nitrogen decreases. While the foregoing data deal almost entirely with variations under nursery conditions, it would be interesting to know whether such local variations also occur under field conditions. That individual plants vary in this way is without doubt true, as the records of the row plats just cited show. To determine whether local variations were found in field plats, two sets of data were secured in the following manner: In one of the field plats a drill row 224 feet long was selected and divided into 2-foot sections. The soil was of average fertility and uniformity. . The results are shown in Table VIII. Also a plat of land 77 by 88 feet with a 5-foot margin outside of this was sown to Turkey winter wheat, using a drill 5.5 feet wide. A very uniform stand and quite uniform growth were secured. The plat would have yielded about 30 bushels per acre. At harvest time it was divided into blocks 5.5 feet square, making 224 such blocks. A composite sample was made from the harvest of each block and each sample was analyzed for total nitrogen. Figure 7 is a diagram of this plat, showing the yield of grain and percentage of nitrogen in each block. The same variation is here found that has been noted hereto- fore in the centgeners and nursery rows. For example, in the first series of 16 blocks, Nos. 2 and 13 average 1.74 per cent of nitrogen, while Nos. 3 and 8 average 2.07 per cent. This variation seems large in view of the fact that each block has an average of 600 to 800 plants. In this case the variation must be due to some local soil condition. When different numbers of blocks are grouped, the resulting areas are of considerable size, as illustrated by figure 8. The plats shown at B are 11 by 22 feet in area and each was sampled 8 times, yet they show a variation in nitrogen content ranging from 1.81 to 1.97 percent. 269 22 EXPERIMENTS IN WHEAT BREEDING. REDUCING THE EXPERIMENTAL ERROR. So great is the fluctuation in individual plants, due to variation in environment, that there would seem to be no hope of improving the percentage of nitrogen /eo /.&3 £80 221 /.93 222 £.89 ggi 2 00 220 £96 219 £89 218 2.03 217 z/o 210 £93 209 207 /56 206 £96 205 204 203 2.// 202 200 £.94 198 £87 £83 194 £.86 £.83 190 /#7 182 £.82 £87 167 £96 162 /73 /.. 93 a /.- 90 /. te /. 92 A 92 A 9/ / 94 A. 9? i X2 / 94 a w A 95 / 90 A 99 /.. IS A IS /.. 90 A 90 A *? A 9/ a 92 A 94 /.'. 93 Fig. 8. — Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) when combined in groups of adjacent blocks, with average nitrogen content for each group: A , Groups of 4; B, groups of 8; C, groups of 16. REPLICATION OF SINGLE PLANTS. In the first case the 840 centgener plants from the same parent, heretofore referred to (fig. 6), were grouped in various ways. Starting 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 23 with the first plant and taking every forty-second plant thereafter gave a composite group of 20 plants. Taking the second and every forty-second thereafter in the same way gave a second group, and so on in the same manner until 42 groups of 20 plants each had been made. In a similar manner 21 groups of 40 plants each were formed. Also, each of the 10 centgeners, being 10 plants square, was formed into 10 rows and the rows numbered 1 to 10. Each row would have 10 plants if the stand were perfect, but in this case it averaged only 8.4 plants per row. By combining the first rows, second rows, etc., in the 10 centgeners, 10 groups were made of 10 rows, or 84 plants each. The results of the above combinations are shown in Table VII. Where 20 plants, uniformly distributed, were combined, the variation in nitrogen content was from 2.40 to 2.67 per cent. Where 40 plants were combined, the variation ranged from 2.47 tro 2.60 per cent, but the 10 groups of 10 rows each varied only from 2.49 to 2.59 per cent. Just what should constitute the limits of error in any case will depend on the minimum limit of the variations which are to be detected. In this case 0.1 per cent of nitrogen might be considered such a limit. Table VII. — Nitrogen content of 90 -plants of Turkey wheat from 1 centgener and of 840 plants variotisly combined into groups to show deviation from mean. 840 single plants variously combined into groups. Com bination Com bination 90 single plants in 1 centgener (united when having same nitro- gen content). Combination 1.— Four groups, each composed of every 42d plant in 10 centgeners, or 20 plants. 2. — T w groups , each composed of every 21st plant in 10 3. — A group composed of every 10th row in 10 cent geners or 10 rows, — centgeners, or 40 plants. equaling 84 plants. >> c >. c a p c a a a a - a d a 0> M O s a a a — n H — > U. "> M '> h "> £ "> i~ © © 03 £ fe Q k £ O Sz; S k Sz; n fc fi P.ct. Per ct. Per ct. Per ct. Per ct. Per ct. 2.09 1 -0. 482 2.58 4 +0.CC 2.47 -0.04 2.44 -0.08S 2.48 -0.044 2.49 -0.042 2.11 2 - .462 2.60 3 + .028 2.47 — .043 2.51 _ .019 2.49 - .034 2.51 - .022 2.20 3 - .372 2.61 2 + .038 2.48 — .033 2.51 _ .019 2.50 - .024 2.52 - .012 2.22 1 - .352 2.62 4 + .048 2.50 — .013 2.51 ^_ .019 2.52 - .004 2.52 - .012 2.23 1 - .342 2.65 5 + .078 2.51 — .003 2.51 - .019 2.52 - .004 2.53 - .002 2.25 1 - .322 2.68 2 + .108 2.51 — .003 2.51 _ .019 2.53 + .006 2.53 - .002 2.26 1 - .312 2.70 1 + .128 2.53 + .017 2.52 + .009 2.53 + .006 2.53 - .002 2.27 3 - .302 2.71 1 + .138 2.54 + .027 2.59 + .061 2.53 + -006 2.54 + .008 2.29 2 - .282 2.77 2 + .198 2.54 + .027 2.59 + .061 2.55 + .036 2.56 + .028 2.30 1 - .272 2.78 1 + . 20S 2.58 + .067 2.60 + .071 2.59 + .066 2.59 + .058 2.34 1 1 3 - .232 - .212 - .202 2.79 2.82 2.85 2.89 1 2 1 + + + + .218 .248 .278 .318 2.36 2.37 2.513 .0276 2.529 .0386 2.524 .023 2. 532 .0188 2.39 3 - ! 182 1 2.46 _ .092 2.40 .128 2.47 - .07 2.40 1 - .172 2.92 2 + .348 2.51 — .042 2.48 _ .048 2.48 - .06 2.41 2 - .162 2.98 2 + .408 2.52 — .032 2.50 _ .C28 2.48 - .06 2.43 5 - .142 3.00 1 + .428 2.52 — .032 2.52 -008 2.50 - .04 2.44 1 - .132 3.13 1 + .558 2.54 — .012 2.53 + .002 2.53 - .01 2.46 3 - .112 3.17 1 + .598 2.54 — .012 2.54 + .012 2.53 - .01 2.47 4 - .102 3.19 2 +- .618 2.54 — .012 2.54 + .012 2.54 00 2.48 2 - .092 3.21 1 + .638 2.58 + .028 2.56 + .032 2.54 .00 2.50 1 - .072 3.22 1 4- .648 2.64 + .088 2.56 4. !o32 2.56 + .02 2.51 1 - .062 3.44 1 + .868 2.67 + .118 2.57 -j- .042 2.60 4- .06 2.53 1 - .042 2.57 + !042 2.61 + .07 2.56 1 — .012 2.572 .214 2.552 .0468 2.58 2.528 2?57 2 - .002 - + .052 2.54 .0364 .0365 269 24 EXPERIMENTS IN WHEAT BREEDING. Where the plants were repeated 20 and 40 times the error was almost what we might reasonably expect the actual variation in pure strains to be, but where 10 centgener rows, or 84 plants, were combined the extreme error was within bounds. The data would indicate that single plants would have to be replicated nearly 100 times to bring: the variation within the limits of error. REPLICATION OF 2-FOOT ROWS. Table VIII illustrates the variation to be expected by replicating 2-foot rows. For these data a single 220-foot drill row in the general wheat field was divided into 2-foot sections and a composite sample made of each section. The sections were combined in two different ways. The first combination was composed of every twenty-second section, making 22 groups of 5 sections each, and the second com- bination was composed of every eleventh section, making 11 groups of 10 sections each. Here, again, the extremes are rather wide, but if these are excluded the results would be called satisfactory. If a comparison of pure strains of wheat was being made under similar conditions, it would be necessary to take for further trial the entire best half of the strains tested in order to be within the limit of error. (See p. 30 and fig. 9.) Table VIII. — Nitrogen content of 110 2-foot sections of drill row of Turkey wheat, arranged in order of -percentage of nitrogen and also in groups of 5 and 10, to show devia- tion from mean. Five rows in a Ten rows in a group Single 2-foot rows (those with same nitrogen contenl united). group composed compos 3d of every of every 22d row. 11th row. Nitro- Fre- Devia- Nitro- Fre- Devia- Nitro- Devia- Nitro- Devia- gen. quency. tion. gen. quency. tion. gen. tion. gen. tion. Per cent. Per cent. Per cent. Per cent. 1. 76 -0. 271 2.04 5 +0.009 1.91 -0. 109 1.96 -0. 069 1.79 - .241 2.05 2 + .019 1.96 - .059 1.98 - .049 1.81 - .221 2.06 4 + .029 2.01 - .009 1.98 - .049 1.85 - .181 2.07 5 + .039 2.01 - .009 2.00 - .029 1.86 - .171 2.08 4 + .049 2.01 - .009 2.02 - .009 1.87 - .161 2.09 3 + .059 2.02 + .001 2.03 + .001 1.88 - .151 2.10 6 + .069 2.02 + .001 2.04 + .011 1.89 - .141 2.11 1 + .079 2.03 + .011 2. 06 + .031 1.90 - .131 2.12 2 + .089 2.06 + .041 2.06 + .031 1.91 - .121 2.13 2 + .099 2.09 + .071 2.06 + .031 1.92 - .111 2.14 3 + .109 2.09 + .071 2.13 + .101 1.93 5 - .101 2.15 1 + .119 1.95 5 - .081 2.16 1 + .129 2.019 .0355 2.029 . 0374 1.96 1.97 3 2 - .071 - .061 2.17 2.19 1 2 + .139 + .159 1.96 - .077 1.98 5 - .051 2.20 3 + .1C9 1.98 - .057 1.99 2 - .041 2.26 4 + .229 1.99 - .047 2.00 4 - .031 2.28 1 + .249 1.99 - .047 2.01 7 - .021 2.37 1 + .339 2.03 - .007 2.02 2.03 2 6 - .011 - .001 2.03 2.04 - .007 + .003 2.031 + .093 2.05 + .013 2.08 + .043 2.09 + .053 2.17 + .133 2.037 .0443 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 25 REPLICATION OF 16-FOOT ROWS. Since 16-foot rows are frequently used as test plats, a determina- tion was made of the variation in a series of these. One hundred check plats from the 1909 field nursery were grouped by fives and tens in the same manner as in the two cases just cited. The results are shown hi Table IX. The coefficient of variability and also the extreme variation are less than in the cases just considered. Table IX. — Nitrogen content of 100 16-foot rows of Turkey wheat, all from the same seed, arranged singly in order of percentage of nitrogen and also in groups of 5 and 10, to show deviation from mean. Five rows in a Ten rows in a group Single 16-foot rows (those with same nitrogen content united). group composed composed of every of every 20th row. 10th row. Nitro- Fre- Devia- Nitro- Fre- Devia- Nitro- Devia- Nitro- Devia- gen. quency. tion. gen. quency. tion. gen. tion. gen. tion. Per cent. Per cent. Per cent. Per cent. 1.82 1 -0.316 2.18 6 +0.044 2.09 -0.050 2.10 -0. 037 1.86 2 - .276 2.20 1 + .064 2.11 - .036 2.11 - .027 1.87 1 - .266 2.21 1 + .074 2.13 - .016 2.12 - .017 1.89 1 - .246 2.22 4 + .084 2.13 - .016 2.13 - .007 1.92 2 - .216 2.23 1 + .094 2.13 - .010 2.14 + .003 1.93 2 - .200 2.25 2 + .114 2.14 - .000 2.14 + .003 1.94 1 - .196 2.27 2 + .134 2.16 i + .014 2.15 + .013 1.96 3 - .176 2.28 2 + .144 2.17 + .024 2.15 + .013 1.97 2 - .166 2.29 3 + .154 2.19 1 + .044 2.15 + .013 1.99 1 - .140 2.31 3 + .174 2.21 + .064 2.18 + .043 2.00 2.01 3 1 - .136 - .126 2.34 2.35 2 1 + .204 + .214 2.146 1 .0292 2.137 .0176 2.03 2.04 5 3 - .100 - .096 2.36 2.38 1 1 + .224 + .244 2.07 i - .058 2.06 6 - .076 2.42 1 + .284 2.08 - .048 2.07 2 - .086 2.43 1 + .294 2.09 1 - .038 2.08 6 - .056 2.45 1 + .314 2.09 - .038 2.10 3 - .036 2.48 1 + .344 2.10 - .028 2.11 2 - .026 2.50 1 + .364 2.13 + .002 2.13 7 - .006 2.52 1 + .384 2.17 + .042 2.14 2.15 2 4 + .004 + .014 2.18 2.18 + .052 + .052 2.136 .1178 2.17 4 + .034 2.19 + .062 2.128 .0420 Where the 16-foot rows were repeated 10 times the extreme dif- ference in nitrogen content was only 0.08 per cent. To further test this question, 500 rows, each 16 feet in length, were planted in the fall of 1909 under quite uniform conditions. These rows were har- vested and combined in groups of 5, 10, 15, and 20, as in the previous case. The results are summarized at the bottom of Table X. When the rows are repeated only 5 times the error is too wide for satisfac- tory results, but when repeated 10 times the error is small enough for experimental purposes. Repeating 15 and 20 times gave only a small further reduction in variation. A point of interest is the fact that in 1909, where rows were repeated 5 or 10 times, the experimental error was less than it was hi 1910. In fact, there is no way of establishing a set rule as to the number of repetitions necessary, since the experimental error is influenced by 69826°— Bui. 269—13 4 26 EXPERIMENTS IN WHEAT BREEDING. all the factors affecting the growth of plants, such as soil fertility, climate, or insects. In order to know what this error is in a par- ticular case it would be advisable to grow a sufficient number of check plats in each system of plats to determine the error by actual test. Table X is a summary of results with the systematic repetition of plants and rows. The column under "Coefficient of variability" shows that repeating 20 single plants in a systematic way has given about as great accuracy in determining nitrogen content as 2-foot rows repeated 10 times or 16-foot rows repeated 5 times. For deter- mining comparative nitrogen content, repeating single plants 20 to 40 times in a systematic method seems to give quite satisfactory results. Table X. — Summary showing degree of error due to variation in environment, according to several methods of comparison. Classification. Number of groups. Mean nitrogen content. Extreme variation. Average devia- tion. Standard devia- tion. Coeffi- cient of varia- bility. 90 single plants (Table VII) 90 Per cent. 2.572 2. 09-3. 44 0. 2140 0.279 Per cent. 10.85 840 single plants (Table VII): Every 42d plant, 20 plants in a f a 10 1 blO 1 c 10 I dl2 2.513 2.552 2.529 2.528 2.47-2.58 2. 46-2. 67 2. 44-2. 60 2. 40-2. 58 .0276 .0468 .0386 .0365 .0335 .0592 .0473 .0484 1.33 2.32 1.87 1.91 10.5 2.531 2. 44-2. 61 .0374 .0471 1.86 Every 21st plant, 40 plants in a / a 10 \ bll 2.524 2.540 2. 48-2. 59 2. 47-2. 61 .0230 .0364 .0307 .0455 1.22 1.17 10.5 2.532 2. 47-2. 60 .0297 .0381 1.50 As 10 centgeners, every 10th cent- gener row, 10 rows in a group 10 110 2. 532 2. 49-2. 59 .0188 .0260 1.03 110 2-foot rows, single rows (Table VIII). 2.031 1.76-2.37 .093 .1087 5.35 Every 22d row, 5 rows in a group 1 all \ bll 2.019 2.037 1.91-2.09 1.96-2.17 .0355 .0443 .0499 .0574 2.47 2.82 11 11 100 2.028 1.94-2.13 .0399 .0537 2.65 Every 11th row, 10 rows in a group.. 2.029 1.96-2.13 . 0374 .0464 2.28 100 16-foot rows (Table IX) 2.136 1.82-2.52 .1178 .1492 6.98 Every 20th row, 5 rows in a group.. . / a 10 \ blO 2.146 2.128 2. 09-2. 21 2. 07-2. 19 .0292 .0420 . 0347 .0451 1.62 2.12 10 2.137 2. 08-2. 20 .0356 .0399 1.87 Every 10th row, 10 rows in a group. . 500 16-foot rows (in 1910): 10 2.137 1.905 1.904 1.917 1.908 1.890 2. 10-2. 18 1.68-2. 28 1.81-1.99 1.84-2.02 1.81-2.03 1.81-1.98 .0176 .0859 .0393 .0376 .0403 .0388 .0219 .1080 .0469 .0469 .0502 .0488 1.02 5.67 Every 100th row, 5 rows in a group.. f a 25 1 b25 1 c 25 1 d25 2.46 2.45 2.63 2.42 1.905 1.82-2.00 .0379 .0474 2.49 / a 25 \ b25 Every 50th row, 10 rows in a group. . Every 33d row, 15 rows in a group ... 1.908 1.902 1.905 1.905 1.S3-1.96 1.83-1.96 1.86-1.96 1.85-1.96 .0273 .0286 . 0235 .0190 .0329 . 0343 .0276 .0242 1.72 1.80 1.45 1.27 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 27 THE SMALL-BLOCK TEST. Figure 7 (p. 22) illustrates the method of making the small-block test and also shows the percentage of nitrogen in the grain from each block. Table XI shows the result of repeating these blocks 4, 8, and 16 times in a systematic method, i. e., taking every fifty-sixth, twenty-eighth, or fourteenth block (fig. 8). The experimental error varied inversely with the number of repetitions, but was only within the limit of error when the repetition was 16 times. Table XI. — Nitrogen am i '.ent of Turkey wheat grovm in 224 block plats {each 5 .5 feet square) in 1909 and 1910. Systematically Repeated to Form Groups of 4, S, and l(i Blocks. Four blocks in a group composed of 3very 56th Eight blocks in a group composed of every Sixteen blocks in a group composed of every 28th block. 14th block. Nitrogen. Deviation. Nitrogen. Deviation. Nitrogen. Deviation. Nitrogen. Deviation. Per cent. Per cent. Per cent. Per cent. 1.78 -0. 128 LSI -0.115 1.S2 -0. 096 1.84 -0.06 1.84 - .068 1.85 - .075 1.87 - .046 1.86 - .04 1.85 - .058 1.87 - .055 1.88 - .036 1.87 - .03 1.88 - .028 1.87 - .055 1.90 - .016 1.87 - .03 1.89 - .018 1.90 - .025 1.90 - .016 1.89 - .01 1.90 - .008 1.93 + .005 1.90 - .016 1.90 + .00 1.91 + -002 1.93 + .005 1.92 + .004 1.90 + .00 1.91 + .002 1.96 + .035 1.92 + .004 1.91 + .01 1.93 + .022 1.96 + .035 1.94 + .024 1.91 + .01 1.93 + .022 1.96 + .035 1.94 + .024 1.92 + .02 1.94 + .032 1.96 + .035 1.94 + .024 1.92 + .02 1.95 + .042 1.97 + .045 1.95 + .034 1.93 + .03 1.98 + .072 1.97 + .045 1.95 + .034 1.94 + .04 2.02 + .112 2.01 + .085 1.99 + .074 1.94 + .04 Av'ge.. 1.908 .0439 1.925 .0464 1.916 .032 1.90 .024 1.83 - .041 1.80 - .094 1.83 - .051 1.83 - .041 1 . 86 - .034 1.85 - .031 1.83 - .041 1.87 - .024 1.86 - .021 1.84 - .031 1.87 - .024 1.86 - .021 1.84 - .031 1.87 - .024 L.86 - .021 1.85 - .021 1.88 . - .014 1.S7 - .011 1.85 - .021 1.89 - .004 1.88 - .001 1.86 - .011 1.90 + .006 1.88 - .001 1.87 - .001 1.90 + .006 1.88 - .001 1.87 - .001 1.90 + .006 L.89 4- .011 1.88 + .009 1 . 90 + .006 1.90 4- .021 1.94 + .069 1.90 4- .006 1.92 + .041 1.95 + .079 1.94 + .046 1.92 + .041 1.95 + .079 2.04 + .146 1.93 + .051 Av'ge. .1.871 .034 1.894 .0314 1.881 .0231 269 28 EXPERIMENTS IN WHEAT BREEDING. Table XI. — Nitrogen content of Turkey wheat grown in 224 block plats {each 5.5 feet square) in 1909 and 1910 — Continued. Combined in* Groups of 4, 8, and v> Adjacent Blocks, to Show the Effect of Size of Plat on Variability. Two sets of 14 groups, Four sets of 14 groups, with 4 adjacent blocks in each with 8 adjacent group. blocks in each group. One set of 14 groups, with 16 adjacent blocks in each group. Nitrogen. I >evia- tion. Stand- arc t devia- tion. Nitro- gen. Devia- tion. Stand- ard , Nitro- devia- gen. tion. Devia- tion. Stand- ard devia- tion. Nitro- gen. Devia- tion. Stand- ard devia- tion. Per cent. 1.79 1.84 1.86 1.88 1.91 1.91 1.92 1.92 1.93 1.93 1.93 1. 94 1.96 1.98 -0.117 - .0(17 - .047 - .027 + .003 + .003 + .013 + .013 -f .023 + .023 + -023 + .033 + .053 + .073 Per ct. 1.86 1.87 1.87 1.88 1.88 1.89 1.90 1.90 1.91 1.91 1.95 1.95 1.97 1.98 -0. 05 - .04 - .04 - .03 - .03 - .02 - .01 - .01 + .04 + .04 + .06 + .07 Per ct. 1.81 1.83 1.87 1.88 1.89 1.89 1.90 1.92 1.92 1.92 1.92 1.93 1.93 1.94 -0. 0S6 - .066 - .026 - .016 - .006 - .006 + .004 + .024 + .024 + .024 + .024 + .034 + .034 + .044 Perct. 1.82 1.85 1.85 1.88 1.89 1.90 1.90 1.90 1.90 1.91 1.93 1.94 1.94 1.95 -0. 077 - .047 - .047 - .017 - .007 + .003 + .003 + .003 + .003 + .013 + .033 + .043 + .043 + .053 Average.. 1.907 .037 0.048 1.91 .0311 0. 0376 1.896 .0299 0. 0372 1.897 .028 0.0363 1.82 - .072 - .052 - .052 - .042 - .042 - .012 1.81 1.81 1.87 1.87 1.88 1.88 - .081 - .081 - .021 - .021 - .011 - .011 1.84 1.84 1.85 1.85 1.88 1.81 1.81 1.81 1.82 1.84 1.S7 1.87 1.88 1.89 1.90 1.91 1.93 1.98 2.03 - .072 - .072 - .072 - .062 - .042 - .012 - .012 - .002 + .008 + .018 + .028 + .048 + .098 + .148 1.91 1.91 1.91 1.91 1.92 1.94 1.95 1.96 + .018 -t- .018 + .018 + .018 + .028 + .048 + .058 + .068 1.88 1.88 1.90 1.90 1.91 1.92 1.97 2.00 - .011 - .011 + .009 + .009 + .019 + .029 + .079 + .109 Average.. 1.892 .0390 . 0436 1.882 .0496 .0636 1.891 .0358 .0492 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 29 Table XI. — Nitrogen content of Turkey icheat grown in 224 block plats (each 5.5 feet square) in 1909 and 1910 — Continued. Summary Showing Experimental Error when Blocks are Assembled in Various Ways.. o Ml O H V ,o B 3 Season of 1909. Season of 1910. Classification. c o +J b c |l § 8 a X 2 a o . .2 2 0} S3 o > O a 9 t a ZZ a) 5 ° 5 03 - - fa * _ a T) O s- — . a > OS o . S'S O > O Systematically repeated . . Every 56th block, 4 blocks in a group . . . 1 f a 14 I b 14 1 c 14 I d 14 P. ct. 1.898 1.90S 1.871 1.925 1.894 1. 68-2. 18 1. 78-2. 02 1. S3-1. 95 1. 81-2. 01 1. 80-2. 04 0. 0786 .0439 .0340 . 0464 .0314 0. 0981 .0579 .0425 .0546 .0503 P.ct. 5.17 3.03 2.27 2.84 2.61 P.ct. 1.866 1.852 1.850 1.871 1.885 1. 66-2. 24 1. 81-1. 89 1. 79-1. 91 1. 81-1. 92 1. 82-2. 04 0. 0692 .0250 .0300 . 0259 .0386 0. 8987 .0278 .0342 . 0316 .0532 P.ct. 4.81 1.50 1.85 1.69 2.82 14 1.90 1. 80-2. 00 .0389 .0513 2.69 1.865 1. 81-1. 94 .0299 .0347 1.96 Every 28th block, S blocks in a group . . . 1 a 14 \bl4 14 14 1.916 1.S81 l'.90 1. 82-1. 99 1.83-1.93 .0320 .0231 .0438 .0287 2.29 1.53 1.863 1.869 1. 83-1. 89 1.83-1.91 . 0143 . 0184 .0167 .0226 .89 1.21 1. 82-1. 96 .0275 .0362 1.91 1.866 1. 83-1. 90 .0163 .0196 1.05 Every 14th block, 16 blocks in a group. .. 1.90 1.84-1.94 .0240 .0295 1.55 1.864 1.84-1.8S . 0123 .013; .72 Adjacent groups: Four blocks in a group f a 14 bl4 1 C 14 | dl4 1.907 1.892 1.910 1.882 1. 79-1. 98 1. 82-1. 96 1.86-1.98 1.81-2.03 .0370 .0390 . 0314 .0496 .0480 .0436 .0376 .0636 2.52 2.31 1.93 3.31 1.929 1.871 1.841 1.817 1.80-2.02 1. 79-1. 96 1. 78-1. 92 1. 77-1. 89 .0503 .0400 . 0301 .0261 .0612 .0484 .0363 .0319 3.17 2.59 2.00 1.76 14 1.894 1. 82-1. 99 .0442 .0482 2.54 1.865 1. 78-1. 95 .0366 .04-^6 2.38 Eightblocksinagroup / a 14 \ b 14 1.896 1.891 1. 81-1. 94 1. 81-2. 00 .0299 . 0358 .0372 .0492 1.96 2.60 1.901 1.829 1. 82-1. 98 1. 79-1. 89 .0444 .0263 . 0504 . 0299 2.65 1.63 14 14 1.894 1. 81-1. 97 .0328 .0432 2.28 1.865 1. 80-1. 93 .0353 .0401 2.14 Sixteen blocks in a 1.897 1. 82-1. 95 .028 .0363 1.91 1.866 1.80-1.96 . 0403 .0464 2.49 In 1910 the same set of blocks was again in wheat, and they w r ere again grouped in the same way, exactly the same plats being com- bined each year. The experimental error was less in 1910 than in 1909, and repeating the blocks 8 times gave total variations ranging from 1.83 to 1.90 per cent, which is weW within the experimental limit. It appears that repeating the plats in this particular case 8 times in 1910 gave as good results as repeating 16 times in 1909; in fact, repeating 4 times would have been almost as satisfactory. In the case of the 16-foot rows just described the error was least in 1909, while the reverse was true in regard to the error in the blocks. This result again illustrates the point, made in discussing the row tests, that sufficient check plats must be used in order to know die experi- mental error in any particular case. INCREASING THE SIZE OF PLAT. Table XI also illustrates the effect of increasing the size of the plat. While such increase ought theoretically to reduce error from the standpoint of increasing the number of plants and including a larger 269 30 EXPERIMENTS IN WHEAT BREEDING. number of local soil variations, yet an equal number of large plats reach over into new territory and include new causes for variation. To secure a practical illustration the 224 small blocks were combined into several series of larger plats by adding together adjacent plats. This method is illustrated in figure 8 (p. 22), and the statistical data are given in Table XI, a study of which shows that increasing the size above four adjacent blocks does not decrease the variability. In comparing systematic replication (Table X) with increase in size of plat it will be seen that the former constantly decreases variation, and would so continue to infinity, while the latter would not be con- trolled by such a law. It has been noted that the degree of variability was not the same when similar data were collected from different fields or in different years. Variation is not a constant factor even where conditions are quite uniform, as is illustrated by the four sets of 14 groups composed of four adjacent plats. The fluctuation of extremes is almost twice as great in the fourth set as in the third. The foregoing data can not be taken as a strict comparison of the different methods, as the data in each case were secured under some- what different conditions. They are mainly valuable in illustrating the expected variation when different methods of comparison are used. It is evident that, whatever the method used, a single plat or duplicate plats can not be relied on for determining the actual nitro- gen content of a strain or variety of wheat. The plats must be repeated 5 to 15 times, depending on uniformity of conditions and accuracy of results desired. In addition, at least a few series of check plats should be included in order to determine the experimental error as a guide to accuracy of results. Our experience so far indicates that the simplest and most accurate method is to use 16-foot rows, replicated 10 tunes, with a check plat every 5 or 10 rows. THE LIMIT OF EXPERIMENTAL ERROR. The above examples give some indication of the experimental error to be expected by the different methods. Since the experi- mental error depends upon the variation in environmental condi- tions, it is possible that conditions might be found so ideal that there would be practically no experimental error; also that under other conditions it might be greater than in the cases just cited. In all cases the experimental error should be determined by the use of check plats. With this factor known it will be possible to decide on some plan of selection. Figure 9 illustrates an ideal case where the experimental error is known. Suppose that in 10 strains of wheat being tested by the row method with check plats, the highest should 269 EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 31 average 3 per cent of nitrogen and the lowest 2 per cent of nitrogen, the remainder being distributed between. Suppose a series of checks, repeated in the same way as the tested strains, showed a variation of 2.2 per cent to 2.6 per cent, with a mean of 2.4 per cent. This would give an experimental error of 0.2 per cent; that is, a certain strain might be 0.2 per cent higher than it should be or 0.2 per cent lower than it should be. Let the line ab indicate the variation in nitrogen content obtained in the 10 strains under test. If the experi- mental error equaled 0.2 per cent, then No. 1 might equal either 3.2 per cent or 2.8 per cent, and in the same way a strain analyzing 2.6 per cent might possibly be either 2.8 per cent or 2.4 per cent. In other words, the strain analyzing 2.6 per cent might be just as good as the one analyzing 3 per cent. Therefore, if the experimental error has been determined, the rule would be to double the error and subtract this sum from the highest variant. The remainder after subtraction would rep- resent the nitrogen content below which all strains could be dis- carded without danger of discarding a high- nitrogen strain. (The same method applies to the use of experi- mental error in select- ing for yield.) In the case illustrated in fig- ure 9, all strains ana- lyzing above 2.6 per cent must be selected best is not being; left. e &n a \&6 , --_, r^l ""■----___ 1 '—— . ----- ""--- "~— ~ pvS < $ /.0 d \ X /234-567B9/0 Fig. 9. — Diagram showing the method of selection for nitrogen con- tent when the experimental error is known. for further test to be sure that one of the If the experimental error equals one-half the real variations in strains compared, then no selection can be made, but all the strains must be re tested. SUMMARY. ^ (1) Wheat plants growing under field conditions or nursery con- ditions show great variation in nitrogen content. This variation, however, does not seem to be inherited but is apparently due to local variation in environment and is therefore not capable of transmission. (2) Centgeners, rows, and small plats vary almost as much as individual plants, owing to local variation in environment. (3) The most practical way of overcoming this variation is by replicating the plats a sufficient number of times to reduce the error to less than one-half the real variation. 269 32 EXPERIMENTS IN WHEAT BREEDING. (4) To bring the experimental error within proper bounds, single plants should be repeated 4/) or more times, 16-foot rows 5 to 10 times, and blocks 5.5 feet square 8 to 16 times. No data are given for centgeners, but the variation in centgeners is about the same as in the blocks. (5) In order to eliminate the undesirable strains, the experimental error must be less than one-half the real or expected variation. (6) The easiest and most practical method of growing strains to compare for nitrogen content is to plant in rows 12 to 16 feet in length and repeat 10 times in different parts of the field. Several series of check plats should a(lso be inserted. 269 II— EXPERIMENTAL ERROR IN THE NURSERY AND VARIATION IN: YIELD INTRODUCTION. A very large share of cereal breeding to-day consists in the separa- tion of pure strains from what we call our ordinary varieties of cereals. In dealing with new hybrids the separation involves the selection of the most desirable strains after types have been fixed. We are mainly concerned for the present in finding the best-yielding strains. This necessitates the finding of a method by which com- parative field tests can be made rapidly in large numbers. The method of comparing strains in "centgeners" first came into general use some 10 years ago, and later the "row" method was evolved. At present the Nebraska Agricultural Experiment Station is experimenting with a small block similar in size to the centgener, but sown at the ordinary rate of seeding. A number of sources of error in all these methods are due to unex- pected variations in soil and climate. It is the purpose of this paper to discuss some of these sources of error and to suggest methods of correction. VARIATION IN YIELD FROM CHECK ROWS. In our row-breeding work we use every fifth row as a check plat. All check plats are from the same seed and sown in the same way. A great variation is found in these check rows even when conditions appear quite uniform. Table XII shows the yield of 47 consecutive check rows in one of the 1909 series. These rows were 14 feet long and each was hand planted with 400 seeds of Turkey wheat. They were not quite as uniform as we sometimes have them, owing to dry weather in the spring, although the appearance of the plats was uniform enough at harvest time. One object in presenting the data here, however, is to illustrate the effect of repeating check plats on correction of error. All things being equal, the yields of the 47 plats should have been the same. But all factors can never be equal, so in row-breeding work, owing to unequal environment, we must expect a wide degree of error. The only practical way so far suggested to overcome this error is to repeat the plats, according to some sys- tematic method, enough times to equalize variations in soil or climatic effects. If the plats are repeated only a few times there is 269 33 34 EXPERIMENTS IN WHEAT BREEDING. still danger of a large error due to the chance combination of plats unduly high or low. This is illustrated by data given in the lower half of Table XII, where all the above check rows have been brought together in groups of six each (except group Ti), taking every eighth plat to form a group, to show the chance of error in repeating a series of strains six times. Table XII. — Yield of 47 14-foot check plats of Turkey wheat in 1909. Check Plats in Consecutive Order. Grams. Grams. Grams. Grams. Grams. Grams. Grams. Grams. 205 239 162 165 182 205 216 230 170 240 204 279 205 270 278 310 202 167 200 238 285 265 222 238 247 216 225 284 255 265 279 155 304 272 226 237 245 150 268 186 209 310 278 347 168 306 239 Check Plats Systematically Repeated to Form Eight Groups. Group a. Group 6. Group c. Group d . Group e. Group/. Group g. Group h. Grams. Grams. Grams. Grams. Grams. Grams. Grams. Grams. 205 170 202 247 304 209 239 240 167 216 272 310 162 204 200 225 226 278 165 280 238 284 237 347 182 265 285 255 245 168 205 270 265 265 150 306 216 278 222 280 268 239 230 310 238 155 186 219 239 217 285 234 216 215 272 Groups arranged in order of average yield of included plats: g, 215; /, 21G; c, 217; a, 219; e, 234; b, 239; h, 272; d, 285. Average, 237. Groups a and d illustrate the chance grouping of high-yielding and low-yielding plats. With only 5 plats out of the 47 yielding above 300 grams, three of them by chance fell into group d while a r num- ber below normal fell into group a. The average yields of the 8 groups varied from 215 grams to 285 grams. This variation indi- cates the amount of experimental error to be expected under similar conditions. Since the experimental error is larger than the real variation expected in different strains of wheat, results obtained under such circumstances would not be reliable. Until our system of testing will show actual differences of 10 per cent in yield, it can not be of much value in comparing the yielding value of different strains. VARIATION IN YIELD FROM REPEATED ROWS. In order to make a more careful test of the accuracy of replicating row tests, 100 rows of Kherson oats were planted, each row being 12.5 feet in length and containing 500 seeds. The plat chosen for this test was quite uniform and the appearance of the plat at harvest was very satisfactory. Three-fourths of the rows yielded from 225 to 275 grams each, with a few much higher and a few very low. Table XIII shows these rows arranged hi consecutive order as they were 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 35 in the nursery, with the yield of each row and the average yield of groups of five adjacent rows. We may get some idea of how replication corrects error by assem- bling these rows into series as in the comparative test of strains. These data are shown and also summarized in Table XIII. In series 1 the yields of 5 adjacent rows are averaged (as rows 1 to 5, 6 to 10, etc.). In series 2 every twentieth row is taken (as rows 1-21-41-61- 81, etc.) and averaged. In series 3 every tenth row is taken, making 10 repetitions; and in series 4 every fifth row, making 20 repetitions. Table XIII. — Yield of thrashed grain from 100 rows of Kherson oats. By Rows and Groups of Five Adjacent Rows in Consecutive Order. Yield of grain . Yield of grain. Yield of grain. Yield of grain. Row No. Row No. Row No. Row No. Actual. Mean of 5 rows. Actual 1 Mean of Actual. 5 rowg Actual. Mean of 5 rows. Actual. Mean of .5 rows. Grams. Grams. Grams. ! Grams. Grams. Grams. Grams. Grams. 1 228 ] 26 252 51 244 ■. 76 233 | 2 273 27 248 52 261 77 247 3 255 } 236 28 206 [ 246 53 258 } 2.50 78 211 } 225 4 224 29 2S0 54 244 79 237 5 204 J 30 247, 55 245 J 80 200 6 205 1 31 2.57 56 248 1 si 248 l 7 230 32 240 57 229 82 200 8 260 I 224 33 233 | 235 58 211 \ 221 83 227 } 222 9 195 34 230 59 227 84 220 10 233 J 35 217 60 188 85 214 11 257 1 36 226 61 248 86 1S4 l 12 243 37 190 62 257 87 233 13 250 \ 248 38 222 [ 220 63 270 \ 263 88 244 [ 234 14 230 39 261 64 264 89 241 15 261 40 200 65 275 90 270 16 235 | 41 246 66 300 1 91 241 1 17 273 42 249 67 151 92 174 18 273 \ 255 43 276 I 254 68 153 \ 216 93 247 \ 242 19 263 44 237 69 205 94 266 20 230 45 261 70 272 95 281 1 21 244 1 46 267 71 194 96 240 ) 22 245 47 259 72 274 97 232 23 209 \ 234 48 252 \ 249 73 242 \ 235 98 228 247 24 247 49 251 74 235 99 290 25 224 J 50 218 J 75 229 J 100 245 1 Systematically Grouped in Various Ways to Show Effect of Replication on Reduction of Varia- tion in Yiele. Series 1. — Groups of 5 adjacent rows. Series 2.— Groups of 5 rows, tak- ing every 20th row. Series 3.— Groups of 10 rows, taking every 10th row. Series 4.— Groups of 20 rows, taking every 5th row. Yield. Devia- tion. Yield. Devia- tion. Yield. Devia- tion. Yield. Devia- tion. Yield. Devia- tion. Yield. Devia- tion. Grams. 216 220 221 222 224 225 234 234 235 235 Grams. -21.8 -17.8 -16.8 -15.8 -13.8 -12.8 - 3.8 - 3.8 - 2.8 - 2.8 erage Grams. 236 242 246 247 248 249 250 254 255 263 Grams - 1.8 + 4.2 + 8.2 + 9.2 + 10.2 + 11.2 + 12.2 + 16.2 + 17.2 +25.2 Grams. 212 223 224 229 234 234 234 236 237 238 Grams. -25.8 -14.8 -13.8 - 8.8 - 3.8 - 3.8 - 3.8 - 1.8 - .8 + .2 Grams. 239 231 242 242 243 246 246 248 245 256 Grams. + 1.2 + 3.2 + 4.2 + 4.2 + 5.2 + 8.2 + 8.2 + 10.2 + 17.2 + 18.2 Grams. 226 229 230 237 238 239 241 243 245 250 Grams. -11.8 - 8.8 - 7.8 - .8 + .2 + 1.2 + 3.2 + 5.2 + 7.2 + 12.2 Grams. 234 235 238 241 241 Grams. -3.8 -2.S + .2 +3.2 +3.2 Av 237.8 11.4 237.8 7.9 237.8 5.8 237.8 2 6 269 36 EXPERIMENTS IN WHEAT BREEPTNfl. Table XIII. — Yield of thrashed grain from 100 rows of Kherson oats — Continued. Summary Showing Comparison of Groupings. Number of rows in a group. Average deviation from mean yield when rows are — Coefficient of varia- bility when rows are- Variation of extremes in yield when rows are^- Adjacent. Distrib- uted. Adjacent. Distrib- uted. Adjacent. Distrib- uted. 1 Grams. 21.26 11.38 7.60 3.46 Grams. 21.26 7.87 5.84 2.60 Per cent. 11.5 5.50 3.66 1.56 Per cent. 11.5 4.8 3.0 1.7 Grams. 151 to 300 216 to 263 227 to 251 234 to 243 Grams. 151 to 300 212 to 256 10 226 to 260 20 234 to 241 There is less variation when the five rows are distributed through- out the plat than when adjacent; also the variation decreases as the number of repetitions increases. Evidently in the case under con- sideration it would be necessary to repeat about 20 times in order to obtain comparable data. To secure more data on this point, 500 row plats of Turkey wheat were planted in the autumn of 1909. The rows were each 16 feet in length, all planted uniformly and with the same seed in soil of average fertility and in good tilth. At harvest the rows appeared to be uni- form in character and would have yielded about 30 bushels to the acre. Table XIV summarizes the results. Table XIV. — Yield of grain from 500 16-foot rows of Turkey wheat, systematically repeated in various ways to show experimental error. Classification. Number of groups. Mean yield. Extreme variation. Average deviation. Standard deviation. Coeffi- cient of varia- bility. 500 f a 25 1 b25 1 c25 I d25 Grams. 250. 7 242.0 256.0 247.3 256.6 Grams. 156 -403 219. 6-277. 8 233.6-281.4 226. 4-272. 6 228. 4-282. 4 Grams. 28.67 13.3 11.7 11.9 11.8 Grams. 35. 85 15.76 14.11 13.03 14.85 Per cent. 14.34 Every 100th row, 5 rows in a group 6.51 5.51 5.27 5.79 250.5 227. 0-278. 5 12.17 14.44 5.77 1 a 25 \ b25 Every 50th row, 10 rows in a group 245.1 256.3 224. 1-270. 7 242. 0-276. 6 10 8 12. 18 9.69 4.97 3.78 • 250. 7 233. 0-273. 6 9 10.93 4.37 33 25 Every 33d row, 15 rows in a group Every 25th row, 20 rows in a group 250.2 250.7 235. 5-273. 9 234. 3-269. <> 6.2 7.4 7.95 9.28 3.18 3.70 In this case the experimental error was much higher than with the 100 rows of oats (Table XIII) and did not reduce so rapidly by repetition. This may be due to the fact that the 500 rows of wheat covered a greater area than the 100 rows of oats, thus having more causes for variation. It is probable that the greater the number of strains to be compared the more replications will be necessary 269 EXPEKIMENTAL ERROR AND VARIATION IN YIELD. 37 because of the larger area they will cover. However, when repeated 15 times, the average deviation is about half as much as when repeated 5 times, but replicating 20 times did not make a further improvement. It will be seen that the extreme variation is rather wide. It would be impossible to make a direct comparison of yield between strains or varieties tested under conditions where the variation of extremes is so large. It would be necessary in such case to select a rather large percentage of the high-yielding varieties and continue the test with them for some years. The method of selection will be hereafter explained. 671 657 210 703 2M 755 2|£ 760 213 686 214 592 215 739 216 732 217 710 210 753 219 680 220 680 221 677 zzz 795 223 723 224 658 193 713 194 613 195 632 196 667 197 645 660 199 768 ZOO 786 20I 768 aoz. 666 203 843 204 795 zos 763 ZOb 716 207 74/ 208 657 177 671 |78 623 179 715 160 543 isi 613 laz '640 163 798 IS4 750 185 76+ 186 995 187 793 I8S 936 189 755 190 792 191 838 192. 642 161 68 O 162. 654 163 673 164 760 165 709 166 682 167 7Z4 168 774 169 S60 170 787 171 725" 172 664 173 851 174 690 175 770 176 735 145 380 146 620 14-7 675 I4g 765 149 742 ISO 772 i5i G98 U2 652 153 661 154 768 155 777 IS6 745 15 7 768 158 851 159 719 IbO SIS 12 9 598 130 705 >3l 642 132 704 133 643 134 650 135 572 136 752 |37 740 138 863 139 eeo IAO 722 141 723 142 703 143 756 144 izn H3 633 ii4 615 M5 116 662 117 639 H6 657 119 &oe 120 62.0 121 6 2,4 122 74-5 123 764 124 703 125 752 126 788 127 682 128 572 97 373 96 St>0 99 645 too 692 644 102. 632 103 574 104 606 io5 648 |06 806 107 791 108 629 109 &SO no 679 hi 588 112 58o Bl 4-25 0Z 732 S3 730 84 706 8S 732 ee 736 87 655" 80 673 89 793 9o 765 91 576 92 609 93 568 94 728 95 620 96 see C5 5Zb 66 506 67 777 776 69 779 10 72/ 71 720 72 604 73 742 74 665 75 62/ 76 Gil m 623 78 64fc 79 fe/7 BO 6)7 49 683 SO 726 51 835 52 663 53 664 34 691 ss 770 56 775 57 685 5« 723 59 583 to 580 61 395 62 511 63 653 64 602 33 662 34 640 35 700 36 650 655 563 39 60O 40 730 41 690 42 713 43 530 44 5"68 AS 4-IO 46 478 47 636 48 665 736 16 630 19 see 2.0 <995 2.1 S9Z 22 5-93 23 659 Z4 713 25 705" at 667 27 585 zs 560 29 655 so 633 31 733 32 609 706 2. 790 3 6 78 4 695 716 622 i 658 S 597 9 632 7/3 535 657 ;3 495 14 6IS 15" 652 16 Fig. 10.— Diagram of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) and the yield of grain (in grams) for each block. VARIATION IN YIELD FROM SMALL BLOCKS. For this experiment 224 blocks, each 5.5 feet square, were laid out in a plat 14 blocks one way by 16 the other. The blocks were all sown to Turkey winter wheat in the fall of 1908. To sow these the drill, 5.5 feet wide, was driven straight across the first series of 14 blocks, the boundaries of the blocks being later established. Each series was sown in the same way and no path or space was allowed between the blocks. Figure 10 is a diagram of the blocks, the yield in grams being marked in each block. A large variation in yield was found in the different blocks, amounting to 100 per 269 38 EXPEKIMENTS IN WHEAT BREEDING. cent in the extreme cases, although the appearance at harvest time was fairly uniform. These plats have been combined in various ways in order to study the yields. The results are shown in Table XV. EFFECT OF REPETITION IN REDUCING ERROR. The first part of Table XV shows the 224 blocks combined in various ways, namely, 56 groups of 4 blocks each when every fifty- sixth block was taken, 28 groups of 8 blocks each when every twenty-eighth block was taken, and 14 groups of 16 blocks each when every fourteenth block was taken. The 56 groups of 4 blocks each were divided into 4 sets of 14 each and the 28 groups of 8 into 2 sets of 14 each. This division into sets was for the purpose of having an equal number of blocks for comparison in each case. We find illustrations of a combination of high-yielding plats and low-yielding plats such as were noted in Table XII. For example, 7*2 $90 748 TPO 7. K 7l> 16 74 13 6 \ 13 6i '8 S. '8 6\ •s ■& 7- 1-2 e 77 7. ?6 7< 12 6' >/ 6 * 6c \3 6. <7 6i. 32 6 '3 6 57 e, s 6 ?4 6 TO 6 '7 Fig. 11.— Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) when combined in groups of adjacent blocks, with the average yield for each group: A, Groups of 4; B, groups of 8; C, groups of 10. when the blocks are repealed 4 times the range in yield varies from an average of 595.2 grams per block to an average of 786.5 grams per block, a difference of 32 per cent. If varieties were being tested by the same system, this variation would be more than we might expect in the yields of different kinds. When the blocks are repeated 8 times the average variation ranges from 627.5 to 717.8 grams, a difference of 90 grams, or 14 per cent. By repeating 16 times the extreme variation is reduced to 47 grams, or 7 per cent. However, with the exception of the extremes, the variation here is small. The question now to consider is the mini- mum number of blocks which will insure comparable results. If comparable results are to be secured the first season, the blocks should be repeated 15 to 20 times. If it were desirable to carry the strains for a period of 3 years, repeating 8 to 10 times would probably be sufficient, since this would give a total of 24 to 30 blocks for the 3 years. 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 39 RELATION OF SIZE OF PLAT TO VARIATION. It is veiy desirable in plant-breeding work to determine the minimum size of plat that it is practicable to use, since with hundreds of strains to try each year it would be impossible to handle them in large plats. Taking the above series of 224 small blocks, the adjacent blocks could be combined to give a continuous series of larger and larger blocks. Figure 11 shows how these combinations were made and Table XV gives statistical results, showing also in a summary for two years the comparative effect of increasing the size of the bLock and of repeating small blocks. Table XV. Yield of Turkey wheat grown in 224 block plats (each 5.5 feet square) in 1909 and 1910. Systematically Repeated to Form Groups of 4, 8, and 16 Blocks. g. S be B Season of 1909. Season of 1910. Classification. 2 a t, £ ft > . 2 a B.2 S3 •a . a a> o bcfl > > "Ho "2.5 OS 2 O u a. 2 a » o g c3 pv *4 'O . ■a o3 1^ Every 56th block, 4 blocks in a group. 224 f all J bl4 1 c 14 1 dl4 680. 38 66S. 82 I ISO. (Hi 680. 95 683.36 373 -995 613. 25-721. 25 645. 75-786. 50 595. 25-728. 00 627 -744. 75 67. 23 29.33 32. 99 21.71 24.36 81.98 35.79 39.80 30.09 32.09 P.ct. 13 5.35 5.77 4.42 4.69 463.71 468. 23 467. 09 450. 59 468. 93 300 -809 441.75-502.75 412. 25-504. 25 3E7. 50-490. 50 403.75-581.50 47.62 15.80 15.36 21.52 35.12 62.62 17.88 21.87 26.34 44.23 P.ct. 13.50 3.82 4.68 5.84 9.43 Average 680. 77 620.32-745.12 27.09 34.44 5.05 463. 71 413. 81-515. SO 21.95 27. 58 5.94 1 a 14 \ bl4 Every 28th block, 8 blocks in a group. . 674. 20 686. 66 627. 50-704. 88 660. 38-717. 88 18.04 16. 45 21.63 18.62 3.21 2.71 459. 41 468. 01 441. 3S-472. 50 433.38-515.38 8.46 15.28 9.65 19.34 2.10 4.13 680.43 643.94-211.38 17.25 20.13 2.96 463.71 437.38-493.94 11.87 6.47 14.43 3.11 14 Every 14th block, 16 blocks in a group. . 680. 43 653. 25-700. 38 7.24 10.41 1.53 463. 72 450. 86-490. 56 9.60 2.07 Combined in Groups of 4, 8, and 16 Adjacent Blocks, to Show the Effect of Size of Plat on Variability. Four adjacent blocks in a group . f a 14 1 b!4 1 cl4 I dl4 / a 14 \ bl4 14 652 681.48 713.61 676. 78 680.97 529. 75-725. 25 617. 75-748. 25 624. 50-825 4S8.25-S01.50 37. 36 30. 84 53.14 70.96 V.). OS 35. 75 61.46 85.80 7.53 5.25 S.47 12.67 443.18 465. 30 504.64 441.71 387. 25-497 389. 50-576 413.75-587.50 386. 75-493. 25 26.76 45.62 31.84 26.37 30.93 33.86 41.90 31.49 6.98 11.57 8.30 7.13 Average 565.06-775.00 48.07 58.02 8.48 463.71 394. 31-538. 44 32.65 39.34 8.49 Eight adjacent blocks in a group. . 666 695 636. 13-S29 586. 50-706. 75 24.57 55.93 31.57 70.30 4.74 10.11 454. 21 473. 18 398. 62-510. 25 S94. 12-545 27.86 31.55 37.97 40.01 8.36 8.45 Average 6S0 611.31-767.87 40.25 50.93 7.42 463. 69 396. 37-527. 62 29.70 38.99 8.40 Sixteen adjacent blocks in a group. . 680 603. 75-797. 06 35.43 48.87 7.20 463.71 406. 69-509. 38 21.67 26.43 5.70 269 40 EXPERIMENTS IN WHEAT BREEDING. Table XV. — Yield of Turkey teheat grown in 224 block plats (each 5.5 jcct square) in 1909 and 1910— Continued. Summary Based on this Average of Both Seasons, Showing the Effect on Coefficient of Vari- ability of Increasing the Size of Plat as Compared with Distributing the Same Area by a Systematic Method. Number of groups averaged. Coefficient of variability. Number of blocks combined in each group. Plats increased in size, blocks adjacent. Plats distributed systemati- cally. Four adja- cent blocks combined and combi- nation dis- tributed 4 times=16 blocks. 1 224 56 28 14 13.25 8.48 7.91 6.45 13.25 5.44 3.03 1.80 1 4 8 \ 3.42 16 j Summary Based on the Yields of 1909, Arranged to Show the Relation Between Size of Plat and Average Deviation. Shape of plat. 1 lby 2 lby 4 2 by 2 2 by 4 lby 8 2 by 8 4 by 8 7 by 8 Number of blocks in plat. Total number of plats. 224 112 56 56 28 28 14 Average deviation. Per cent. 9.76 8.57 7.16 7.38 6.05 6.08 5.30 5.37 5.29 Average deviation when plats are made up by systematic method. Every- 56th block. J2Xth block. 14th block. Per cent. 5.05 2.96 1.53 Starting with a coefficient of variability of 13.25 per cent, it is decreased to 8.48 when the block is made 4 times as large, to 7.91 per cent when 8 times as large, and to 6.45 per cent when increased 16 times in size. Table XV gives the result of repeating the same num- ber of plats equal distances apart. Here we see that where the plats are repeated 16 times the average variability for the two years rapidly decreases to 1.8 per cent. It might appear from a study of the first part of this table that if the size of the plat were constantly increased the variability would be constantly reduced. However, increasing the size of the plat beyond a certain point does not continue to remove the cause of variability, namely, variation in soil. The last part of the table, which contains the data for 1909, is arranged to show the effect of increasing the size of the plat. It indicates a rapid decrease in variability up to plats 16 blocks in size, but no decrease in the next two cases. While acre plats are probably less variable than tenth-acre plats and tenth-acre plats less variable than hundredth-acre plats, yet plats of this size are too variable for direct comparison and they are much too large 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 41 /909. Y/£~LQ /V/r/?06£W //V Gfi/fMS. P£# C&vr. /s/o. Y/£L£> M/r/?OG£M WGfiH/fS. £&?C£Wr. ^.'■T-'Z- -,L&£> Z r - > 77i?G ^(-,4 ££-U2 77^? /.--t' jZ,tZ5' -,<-£lQ. C^™' T- c^ /J^CiL /-Chi CXjC >. u't' 4aL(- _^G^> V ^•V^n 7^?c: f< A'uX't ^£-,fiUt > tt H r yttlt-T ) "-"*] ^W^-7- Alt-7- \ <£tT.^ /? ? t-C\il \ 'TtttT y'T^Z. ( " ) c/ coErnc/e/vr or t//i/?/^B/L/7-y. for practical plant-breeding work. On the other hand, repeating the plats in a systematic way constantly removes the Cause of varia- tion as the number of repetitions increases. It then appears that the most practical method of removing error is to repeat series of small blocks a rather large number of times. CONSTANCY OF VARIATION ON THE SAME PLATS. Table XV gives statistical data for 1909 and 1910 on the same blocks arranged in the same way both years. Figure 12 shows the average yield of each section and the average percentage of nitrogen in the two years for sections a, b, c, and d. The yield per block varied about the same for the two years, be- ing highest in section c in both seasons. The variation in nitrogen was not as regular, section c being highest in nitrogen in 1909, while in 1910 there was a small but regular increase in nitrogen from d to a. The second part of figure 12 shows the coefficient of variability in both yield and percentage of nitrogen when the small blocks are com- bined in sets of four (Table XV). Section a was highest in varia- bility of both yield and nitrogen content in 1909 and low in 1910. Section 6 was low in variation in yield in 1909 and high in 1910. This would indicate that different seasons do not affect equally all parts of the plat, and illustrates the difficulty of "standardizing" plats by the system of sowing all plats to one crop for a season in order to determine relative yield. VARIATION IN YIELDS FROM CENTGENER PLATS. The centgener method consists of planting 100 plants in a centgener, 6 inches apart each way, making blocks 5 feet square. In 1908, 178 centgener blocks were compared for variability with an equal number 269 pert cs/vr P£/?c£/vr P£/?ce^t P£tfCfA/K L/2LjC3' 2 '£,£- ^ r (-1 t-^Ur > fitTirr *.f. XT J. 7TT [ -Lt-^±~Z l-CWi- St-CtAt- '3-/&3 ? -tr.^r -jYcfcF- ZKyO L.X^r [ ^~ >LC O 'It- J-t-A'^,f- P-'PJS iTZk7 ,Z «.£ fi7iD? 4**11 ±— "7-CSl. "2-iZll £.'X$sk 3~^t \ /.OC iV.tM- Z.Kt.70 «7v? f I a w ya Fig. 12.— Diagrams showing Turkey wheat grown in 224 blocks, combined in four groups (Table XV, a, b, c, d) of 56 adjacent blocks to show variations in yield and nitrogen content in 1909 pud 1910. 42 EXPERIMENTS IN WHEAT BREEDING. of duplicate row plats 16 feet in length. The variability was found to be practically the same. Other data confirm this conclusion, although under unfavorable conditions centgener plats are quite variable, owing to the fact that the individual plants are so far apart that the missing plants are not compensated for by the tillering of neighbors, as is the case where the planting is at the normal rate. ALTERNATING CHECK ROWS AS A MEANS OF OBTAINING COM- PARATIVE YIELDS. In order to test the value of the method of alternating check rows, the 500 rows before referred to (pp. 36-37) were used as a basis for data. It was assumed that every odd-numbered row would repre- sent a check row, while every even-numbered row would represent a strain being compared with a check row. Thus, row No. 2 would be considered a strain to compare with rows 1 and 3 as checks. It is apparent from data heretofore presented that the error would be too great if only a single row were compared with its adjacent checks. For example, there are numerous cases in the 500-row plats where the even-numbered row would be 20 to 30 per cent higher or lower in yield than the average of the adjacent odd-numbered row plats. Table XVI shows the result of averaging five odd rows and the adjacent five even rows, i. e., rows 1, 3, 5, 7, and 9 are averaged to compare with rows 2, 4, 6, 8, and 10. In the first 10 rows, for example, the five odd rows averaged 235.6 grams per row and the five even rows 226.4 grams per row, or 9.2 grams less than their checks. In the next block the even rows yielded 9 grams more than the checks. Out of the 50 cases here cited the extremes vary from —26.6 to + 32.8, with an average deviation of 10.14 grams or 4 per cent. In selective work it is the unusually high variants that are sought after, but with an experimental error greater than the expected variation they would be difficult to locate. Table XVI also shows the result of dividing the 500 rows into blocks of 20 and 40 rows and comparing the yield of odd and even rows in each case. While in most cases the average deviation is small, yet there are a number of quite wide variations. For example, when 50 series of five odd rows are com- pared with five even rows, 17 series, or about one-third, show a deviation greater than 5 per cent of the mean; when 25 series of 10 odd rows are compared with 10 even rows, 6 series, or about one- fourth, show greater than 5 per cent average deviation; and when 12 series of 20 odd rows are compared with 20 even rows, none show 5 per cent deviation. EFFECT OF INCREASING LENGTH OF ROW. To increase the length of the row will decrease the error in about the same way as to increase the size of the block. In the 500-row plats just discussed most of the rows were in series and end to end, 269 Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. Plate I. - Fig. 1 .— Head-to-Row Nursery, in which 25 Grains from a Single Head are Planted in a Row 20 Inches Long. The second year the seed from each 20-inch row is planted in a lG-foot row. Fig. 2.— Row-Plat Nursery, in which the Rows are 16 Feet in Length with a 4-Foot Alley Adjacent, thus Making the Beds 20 Feet in Width. These beds are slightly rounded, to give perfect drainage. Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. Plate II. - f.i %■, r ' j: "••"" IHBi- Fig. 1.— Increase Plats of One-Thirtieth Acre Each. Selected strains from the nursery are tested in these plats for 3 years. Fig. 2.— Increase Plats Harvested and Ready to Thrash. The plats in this field averaged 60 bushels per acre. EXPERIMENTAL ERROR AND VARIATION IN YIELD. 43 with only a narrow alley a few inches in width between the ends. By adding together the rows end to end, longer rows could be made. (PL I.) A total of 84 rows 64 feet in length was made in this man- ner, and the yields calculated. Table XVI gives the variability in the original 500 rows, each 16 feet long, in comparison with the same rows when combined into lengths of 64 feet. By increasing the length four times the deviation and variability are reduced not quite one-half. The longer rows are also less variable than blocks of five adjacent 16-foot rows, but more variable than five rows dis- tributed in a systematic way throughout the plat. The best length of row to use must be determined by circum- stances. If sufficient uniform land is available and it is more con- venient to make long rows, to do so would lessen the number of repetitions of plats necessary to reduce the error within proper limits, but it would always take a larger area to secure the same degree of accuracy with the long rows. Table XVI. — Yield, in grams, of Turkey wheat grown during the season of 1910 in 500 rows, each 16 feet in length. Arranged by Odd and Even Rows and Averaged in Groups of Ten. 1 Rows 1 to 100. Rows 101 to 200. Rows 201 to 300. Rows 301 to 400. Rows 401 to 500. Odd. Even. Differ- ence. Odd. Even. Differ- ence. Odd. Even. Differ- ence. Odd. Even. Differ- ence. Odd. Even. Differ- ence. 205 212 246 244 258 253 259 292 27S 230 226 222 235 298 233 241 317 340 278 238 245 231 230 245 262 219 314 285 277 280 262 238 248 226 182 220 223 219 307 300 240 229 - 9.2 266 231 3.8 246 239 - 1.8 238 262 9.4 283 295 235.6 226. 4 245 24S.8 236.2 234.4 270.2 279.6 284.6 278.6 - 6 180 183 228 226 224 218 198 223 268 250 214 255 242 266 222 261 251 287 258 250 256 220 220 227 256 231 223 204 253 250 216 234 213 235 229 241 209 223 242 239 237 256 9 225 245 14.2 292 198 -14.2 229 194 4.2 189 2S7 220.6 229.6 225.6 239. 8 244.6 230.4 222 226.2 242 255.2 13.2 214 231 271 212 235 229 216 216 284 276 235 208 235 238 235 271 222 204 200 217 284 316 247 227 235 212 245 236 316 285 275 240 247 255 221 242 231 194 194 243 272 228 -11.4 267 296 - 7.8 273 269 4.8 200 218 - 9.2 363 343 256 244.6 253.4 245.6 239. 8 244.6 222.8 213.6 271.4 272.8 1.4 272 239 269 259 219 255 228 200 248 294 275 215 250 289 270 280 227 228 380 338 224 237 278 246 275 191 218 208 326 287 220 240 222 256 282 249 242 257 265 315 182 263 4.2 308 276 - .2 268 237 -20.4 221 230 - 2.6 314 290 234.6 238.8 265.4 265.2 262.8 242.1 227.2 224.6 306.6 304.8 - 1.8 156 252 297 280 213 246 215 252 328 273 227 263 230 310 255 269 269 210 324 315 254 224 323 263 235 242 171 228 300 279 226 188 317 261 247 268 230 207 252 240 246 255 14.6 305 268 -18 303 242 2.8 222 200 — "2 331 273 221. 8 236.4 294.4 276.4 250. 6 253.4 221.4 219.4 307 277.8 -29.2 Average difference in yield between odd and even rows, grams, 10.4; per cent, 4. 269 44 EXPERIMENTS IN WHEAT BREEDING. Table XVI. — Yield, in grams, of Turkey wheat grown during the season of 1910 in 500 rows, each 16 feet in length — Continued. Arranged by Odd and Even Rows and Averaged in Groups of Ten— Continued. Rows 1 to 100. Rows 101 to 200. Rows 201 to 300. Rows 301 to 400. Rows 401 to 500. Odd. Even. Differ- ence. Odd. Even. Differ- ence. Odd. Kven. differ- ence. Odd. Even. ' Differ - ence. Odd. Kven. Differ- ence. 227 247 275 249 257 225 282 246 224 303 230 285 241 269 190 204 269 240 349 320 263 281 285 245 227 250 250 230 272 283 255 255 249 222 222 174 233 268 291 331 280 280 18.6 246 223 -17.6 208 216 - 7 213 249. 1 200 236. N -12.6 208 271 251 269.6 259.2 241.6 220.8 213.8 268. S 301.6 32. 8 275 237 232 228 229 187 200 207 269 293 264 277 200 228 200 215 219 233 293 327 268 227 282 242 238 238 225 207 257 263 204 218 227 239 242 202 205 230 254 244 237 202 -17.4 246 ' 222 - 5.6 190 245 - 6.4 243 216 .2 250 311 249.6 232.2 237.4 231.8 223.8 217.4 218.4 218.6 264.6 287.6 23 235 229 266 287 218 212 250 208 286 243 204 210 351 312 212 184 276 254 297 403 257 312 265 300 234 267 235 245 316 285 294 295 322 313 211 213 243 255 297 239 313 315 11.6 293 285 232 284 10.6 257 252.2 281 248.6 - 3.6 211 247 260.6 272.2 299.4 299.4 221.4 232 281.4 283. 4 2 233 265 248 273 230 219 298 316 208 219 276 214 233 243 236 228 261 208 255 255 327 300 280 261 290 314 225 24S 243 289 312 316 259 263 208 195 233 226 247 275 370 290 -26.6 248 272 8.8 225 219 - 2.8 205 214 _ 2 249 266 303.6 277 253.6 262.4 237.8 235 244.4 242.4 240.4 260.8 20.4 271 236 241 250 232 211 250 230 217 215 251 246 266 254 185 257 254 211 235 285 269 251 310 263 242 242 205 269 252 235 217 242 245 245 279 270 237 216 222 289 298 308 - 4.6 275 269 —11.2 265 270 9.4 242 192 -14 271 288 261.2 256.6 267.4 256.2 240.6 250 237.6 223.6 239.4 262.4 23 Summary of Odd and Even Rows Arranged in Blocks of 20 and 40 Rows to Show Deviation. The 20 odd and 20 even rows from The 10 odd and 10 even rows from each adjacent 20 grouped together. each adjacent 40 grouped to- gether. Odd. Even. Difference. Odd. Even. Difference. Odd. Even. Difference. 228.1 228.0 - 0.1 222.6 224. 7 + 2.1 236.7 234.8 - 1.9 245.3 241.7 - 3.6 239.2 242. 5 + 3.3 245.7 252.6 + 6.9 236.4 253.0 + 16.6 246.1 252.9 + 6.8 25S. 8 255.5 -3.3 255. 1 252.2 - 2.9 225.0 219.1 - 5.9 268.1 257. 2 -10.9 282. 4 266.8 -15.6 235.4 228.1 - 7.3 264.4 263.9 — . 235.3 244. 3 + 9.0 235.3 233. 6 - 1.7 245.8 237.9 - 7.9 259.4 255. 4 - 4.0 241.0 233.0 - 8.0 229.1 229.1 276. 8 259.0 -17.8 263.3 266.9 + 3.6 242.6 247.7 + 5.1 268.4 268.6 + .2 271.0 288.8 + 17.8 230. 2 223. 6 - 6.6 260.5 259.3 - 1.2 287.9 289. 7 + 1.8 238. 1 233.3 - 4.8 240.4 232.4 - 8.0 273.0 285. 5 + 12.5 267.1 277.8 + 10.7 251.3 243.5 - 7.8 239.9 261.6 +21.7 280.4 287.6 + 7.2 235.7 233. 6 - 2.1 Average difference. 7.256 Average difference. 5.483 Summary Showing Result of Combining 16-Foot Rows in Various Ways. Classification. Extreme varia- tion. Standard devia- tion. Coeffi- cient of variabil- ity. Classification. Extreme varia- tion. Standard devia- tion. Coeffi- cient of variabil- ity. 500 single rows 16 feet 156-103 196-284 35.85 21.43 Per cent. 14.33 8.8 5 adjacent rows 16 212-317 227-278 26.11 14.44 Per cent. 10.38 84 rows 64 feet long (4 times length of 5 rows 16 feet long distributed (ev- ery 100 rows) 5.77 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 45 Table XVII shows a comparative summary, based on the data herein reviewed, from which it appears that to repeat the 5.5-foot square blocks, in series, will reduce the error at the greatest rate, while to repeat the 16-foot rows will give the next most rapid reduc- tion. However, the method of alternating 5 odd rows with 5 even rows gave about as good results as to repeat 10 rows, and the system of alternate planting with check rows would sometimes be desirable. Table XVII. — Summary shotving coefficients of variability under various systems of arranging block plats and row plats. , Kind of plats and Number of plats combined. Remarks. arrangemeni . 1 5 10 15 20 Blocks 5.5 feet square (Table XV):. 13 13 14 14 14 8 5 11 5 7 2.5 7 4 4 6.4 1.8 5 3.2 3.6 3.5 3.7 3 Variation will not continue to decrease. Rows 16 feet long (Table XVI): Variation does not continue to decrease. Do. To correct by check plats is sometimes uncertain, as pointed out hereafter, and therefore the advantage seems to be with the method of systematic repetition of rows or blocks. The repetition of the square blocks 10 times gave a higher degree of accuracy than repeat- ing rows even 15 and 20 times, and it seems probable that further experimenting is likely to show the block system to be the most accu- rate for close comparisons. It also does away with the competition which no doubt takes place between adjacent rows, and also makes note taking easier by giving a mass effect, such as is secured under field conditions. To increase the size of plat will also reduce error, as shown by Table XV, and on the basis of these data a plat, about three times the size of the 5.5-foot blocks reported on, is being tested. This block is 4.2 by 16 feet in size, and indications are that with this block the variation will be reduced about one-half, as compared with the 5.5-foot block. INFLUENCE OF RATE OF PLANTING ON YIELD. For several years in planting our row plats care was taken to plant the same number of seeds in each row. In case of wheat, 400 kernels usually were planted to the 16-foot row, which was equivalent to the normal rate of seeding, or 5 pecks per acre. However, in 1908 and 1909 counts of the number of plants harvested were made of many rows at harvest time. In the row plats of wheat where the rate of seeding was about normal it was found that only about 60 to 80 plants 269 46 EXPERIMENTS IN WHEAT BREEDING. were harvested to every 100 kernels planted. A variation of 20 per cent in stand was not apparent to the observer because all plats would appear to have an equally good stand at harvest time. This loss of plants was due to many causes, such as winterkilling, insects, and accidents, but chief among the causes appeared to be the normal competition of plants. For example, certain plants were weak or were slow in starting spring growth; the stronger plants would quickly outdistance them, causing at least a certain percentage of the weaker plants to perish as a result of competition. It seemed doubtful, how- ever, whether this difference in plants harvested had a marked effect on yield. For example, here and at many experiment stations tests have been made with sowing wheat at various rates, from 4 pecks to 10 pecks per acre. The difference in yield is never large. Doubling the amount of seed sown, from 4 to 8 pecks per acre, does not double the yield, and in many cases does not affect it at all. This is due to the tillering power of the plant, which is able in this way to compen- sate for the difference in number of plants. To make a test of the rate of planting under row-plat conditions, a series of plats was planted with Red Rustproof oats in the spring of 1910. Each row plat was 16 feet in length. There were 5 plats in the series, planted at the rate of 400, 500, 600, 700, and 800 grains per plat. The series was repeated 20 times, making 100 rows in all. The results are shown in Table XVIII. Table XVIII. — Results of r a te-of -seeding test on 100 16-foot rows of Red Rustproof oats. Statement < f averages. N umber of grains sown per row. 400 500 600 700 800 20 197 20 213 20 215 19 215 20 Average yield per row grams.. 234 The normal rate of seeding would have been about 600 grains per row. It appears from the data that a slight variation in rate of planting, as 25 or 50 grains more or less than normal, would not affect the results. To further test the effect of rate of seeding, a series of 60 blocks was laid out, each block being 5 drill rows wide and 16 feet in length. As the drill rows were 10 inches apart, this made the plats each 4.2 by 16 feet. The blocks were planted with a small drill devised for the puqjose. Five rates of seeding were used, namely, 42.6,' 49.1, 55.9, 65.4, and 73.3 grams per block. The series was repeated 12 times, giving 12 blocks of each rate for averaging. The results are shown in Table XIX. 269 EXPEKIMENTAL ERROR AND VARIATION IN YIELD. 47 Table XIX. — Results of rate-of-seeding test on 60 block plats of Kherson oats. Statement of averages. Weight of seed sown (grams). 42.6 49.1 55.9 65. 4 ; 73. 3 12 1,069 12 1,101 12 1,151 12 12 1,149 1 1,156 The normal rate of seeding would be about 60 grams per block, and it is apparent from the data that a variation of 10 or even 20 per cent above or below normal in the weight of seed used would not have a marked effect on the yield. In view of the data just presented, it would seem not to be necessary to actually count the number of seeds to be planted in each small plat, providing some other quicker means can be found of obtaining approximate accuracy. If the seed is first carefully fanned, scoured, and screened to one size, equal volumes will usually not vary more than a small percentage in number of kernels^^AIso equal weights will have approximately the same number of kernels, provided the seed has first been carefully prepared by fanning and screening to a uniform size. EFFECT OF COMPETITION BETWEEN ADJACENT ROWS. In 1908 it was observed that a certain strain of early wheat in a series of row plats made a very poor appearance at harvest time, while the same strain planted in centgeners made a much better comparative showing. Apparently the larger and faster growing strains on each side, the rows being only 8 inches apart, exercised some competitive effect. This effect of competition has been noted for two years since. Also in certain variety tests of oats, grown in row plats 10 inches apart, the same effect was noted. Exact data can not be given on this point, as the results from the series of plats planted in 1909 and in 1910 for this purpose were seriously impaired by unfavorable conditions; but Table XVIII, giving results from adjacent row plats sown at different rates, shows that the 800-seed rate made a marked increase over the 700-seed rate, while in a similar series of blocks (Table XIX), sown at the same rate, this marked increase was not noted. Since the 800-seed row was always adjacent to the 400-seed row, it may have had some advantage on this account. Danger from this source can probably be avoided if care is taken to plant only similar varieties in adjacent rows. Where the block plat is used this source of error is eliminated. 269 48 EXPERIMENTS IN WHEAT BREEDING. VARIATION IN PURE STRAINS AND RELATION OF DATA IN CENTGENER NURSERY AND IN FIELD PLATS ISOLATION OF PURE STRAINS. In 1902, Dr. T. L. Lyon, now of Cornell University, planted 800 heads of Turkey winter wheat in a centgener nursery, arranging to keep a record of the progeny of each head. The heads were num- bered from 1 to 800 and these original numbers are still retained as family numbers. The original plan was to select for increased nitrogen content and yield, discarding those families which did not show high averages in both these respects, and to practice con- tinuous selection of individual plants from among those families that were promising. A considerable number of the families were discarded each year, until at the end of harvest in 1906 only 47 of the original 800 were retained for further work. At this time the writer took up the work and the practice of continuous selection was discontinued as it began to be apparent that the isolation of pure strains was a more promising way of obtaining results. The 47 pure strains were put in field plats to test for yield. Complete records, however, can be given on only 24 pure strains, as all but 26 were dropped in 1908 for lack of space, and the nursery data are incomplete on 2 strains out of the 26. These strains are shown in field plats in Plate II. Table XX gives the average results for four years, both in the centgener nursery and in the field plats. By "centgener" is meant the method of planting 100 seeds from a single plant in a square plat, the plants 6 inches apart each way. Table XX. — Relations of certain characters of 24 strains of Turkey wheat grown in nursery and in field and tested during 4-year periods. Ranked in Groups of Five in Order of Yield in the Field. Data from centgener nursery (average for four vears, 1906-1909). Family No. (The numbersinitalicindieate the five highest yielders.) Total or average. 556. 225. 215. 47.. /'. ct. 2.66 2.52 2.68 2.61 2.70 2.63 2.72 2.53 2.63 2.60 2.70 Yield per- Grams. 13. 38 12.38 11.58 12.27 9.83 11.89 12.36 11.12 11.14 12.26 11.01 P ~ Gins. 764 704 622 646 612 670 593 623 605 664 620 *2 Grams. 0. 02192 . 01864 . 02105 . 02344 . 01824 . 02058 . 02267 .01984 . 02064 . 02013 . 02168 /■. a. 80 81 63 68 67 72 Days. 36 35 35 36 35 35 Data from field plats (average for four vears, 1907-1910). " P. ct. 2.60 2.49 2.48 2.55 2.56 134 38 29 48 123 18 2.54 2.54 2.55 2.54 2.51 2.53 Bush. 40. 7.5 40.59 39.90 39.21 39.18 39.93 38.86 38.78 38.64 38.50 38.48 >tal or average 2.64 11.58 621 .02099 63 35 256 2.53 1 Averages of check plats: Nitrogen content, 2.61 per cent; yield. 35.18 bushels 269 38.65 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 49 Table XX. — Relations of certain characters of 24 strains of Turkey wTieat grown in nursery and infield and tested during 4-year ■periods — Continued. Ranked in Groups of Five in Order of Yield in the Field— Continued. Family No. numbers in italic indicate e Ave highest yielders.) Data from centgener nurserv (average for four years, 1906-1909). Data from field plats (average for four years, 1907-1910). G g a o o CI 0) BO o u, % Yield per — o +J OS a - G > a> i O bo G s ■d _o 'C CO P, so g ! G a u . o o I- > ■9 « G *-< s * a 3 a o o a s 2 2 5 Pi (The th 5 00 JfJ. f- cr. O i-H O •a O M a> > 391 P.ct. 2.70 2.63 2.50 2.81 2.59 Grams. 10.93 12.46 11.95 11.05 11.08 Gms. 510 647 597 563 558 Grams. . 02185 . 02295 .02118 . 02016 . 01889 P. ct. 64 64 68 60 65 Days. 34 34 36 34 34 28 59 114 20 26 P.ct. 2.51 2.59 2.53 2.70 2.58 Push. 37.96 36.57 36.27 36. 13 36.12 5 221 12 313 5 377 5 206.. - 5 2.65 11.49 575 .02111 64 34 247 2.58 36.61 32 314.. 2.68 2.63 2.76 2.84 2.52 9.70 10.70 10.03 10.79 12.11 560 512 614 620 594 . 02020 . 02247 . 02029 . 02057 . 02108 66 63 66 62 66 34 34 34 24 35 52 23 18 20 43 2.63 2.60 2.73 2.71 2.48 35.22 34.84 34.20 33.56 33.46 8 108 8 526 5 379 216. 8 2.69 10.67 580 . 02089 65 34 156 2.63 34.26 34 20'.).. 2.49 2.87 2.56 2.62 11.38 11.27 9.S6 11.89 570 526 548 508 .01915 . 02270 . 02180 . 02522 82 54 58 62 34 34 36 33 37 48 33 30 2.45 2.75 2.55 2.73 32.93 32.58 31.88 28.88 8 37 5 2 . 8 32S . . 5 2.63 11.10 538 . 02228 64 34 148 2.62 31.56 26 Summary of Results, Arranged in Groups of Five Strains and Ranked in Various Ways. CENTGENER TESTS. In order of nitrogen content: 37,379,377,526,556 ^5,391,3,314,^ 45,221,168,215,328 SIS, 47, 206, 2, 225 257,216,313,209 In order of strength of straw: 209,287,48,215,313 313,425,314,526,216 206,225,391,221,3 42,168,47,379,328 377,2,556,37 In order of vield per plant: 48, 221, 257,556, 312 47,216,313,328,42 209,37,215,225,206 377,526,3,391,379 168,2,425,314 In order of vield per centgener 48,287,47,221,312 225,42,3,379,526 425,215,313,216,556 209,377,314,206,2 37,168,391,328 FIELD-PLAT TESTS. In order of nitrogen content: 37, 526, 32S, 379, 377 314,45,168,221,206 425,2,225,3; 2, 556 215,3,313,391,47 257,42,216,209 In order of yield per acre: 48,287,42,312,425 556,225,215,47,3 391,221,313,377,206 314,168,526,379,216 209,37,2,328 209 2.80 11.10 583 2.69 10.61 585 2.63 11.91 607 2.58 11.32 608 2.51 11.95 616 2.58 12.11 658 2.63 10.72 595 2.63 11.32 592 2.67 11.44 585 2.74 11.13 558 2.63 12.57 671 2.58 11.96 597 2.62 11.20 576 2.76 10.76 585 2.64 10.02 558 2.60 12.55 685 2.70 10. 91 620 2.61 11.48 600 2.63 10.61 560 2.70 11.20 514 2.78 11.01 566 2.64 11.46 608 2.62 11.09 604 2.63 11.46 604 2.55 11.86 622 2.63 11.89 670 2.64 11.58 621 2.65 11.49 575 2.69 10.67 580 2.63 11.10 538 0. 02128 59 34 144 2.69 35.07 . 02060 65 34 156 2.54 38.15 . 02224 68 34 182 2.61 35. 94 . 02082 64 35 242 2.55 36.90 . 02001 74 35 217 2.49 35.81 . 02076 76 35 161 2.53 38.42 . 02020 67 35 262 2.59 35.67 . 02104 64 34 160 2.55 37.58 .02189 63 34 219 2.61 35.14 . 02183 57 35 139 2.63 34. 86 . 02192 70 35 173 2.55 39.20 .02173 64 35 333 2.55 35.40 . 02024 67 34 188 2.57 35. 81 . 02091 63 34 104 2.64 36.07 . 02068 63 35 143 2.58 35.28 . 02041 71 35 258 2.55 39.12 . 02068 64 34 108 2.60 36.98 . 02076 65 35 278 2.53 37.28 . 02040 66 34 168 2.58 34.46 . 02306 61 34 129 2.65 33.56 .02179 61 34 136 2.72 33.07 . 02129 68 34 182 2.60 36.70 .02120 63 36 166 2.55 37.58 .02120 66 35 331 2.52 37.97 .01998 73 35 126 2.47 36.72 .02058 72 35 134 2.54 39.93 . 02099 63 35 256 2.53 38. 65 .02111 64 34 247 2.58 36.61 . 02089 65 34 156 2.63 34.26 . 02228 64 34 148 2.62 31.56 50 EXPERIMENTS IN WHEAT BREEDING. To sum up, the 24 pure strains have varied in the centgeners from 2.49 to 2.87 in per cent of nitrogen, from 54 to 82 per cent in strength of straw, from 9.70 to 13.38 grams in yield per plant, and from 508 to 764 grams in yield per centgener. They also have showi^ a variation , ■> Fig. 13.— Field plats of pure strains and check plats of original seed of Turkey wheat, 1910. The upper numerals are family numbers: the lower, 4-year average yields. Two of the poorest yielders out of 20 strains came adjacent to two of the best. The difference in yield would not have been suspected from the appearance of the plats. Fig. 14.— Wheat nursery plats, showing variations in winterkilling. Pure strains were alternated with the original Turkey wheat from which the strains were isolated. The original was mostly winterkilled while many of the select strains withstood the winter well. in average weight of kernel ranging from 0.01824 to 0.02522 gram. In the field plats the percentage of nitrogen varied from 2.45 to 2.75 and the yield per acre from 28.8 to 40.7 bushels — -a difference of about 12 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 51 bushels. Some of these plats and the check plats noted below are shown in figure 13. It is interesting to note that the check plats of original unselected Turkey winter wheat averaged 35.18 bushels per acre, or about halfway between the highest and lowest pure strains. More strains surpass the check in yield than fall below it, but this is probably because a large percentage of the poor-yielding strains were discarded after the first field test in 1907. It appears that neither the original selection of the 800 heads, nor the discarding of centgeners in the nursery, nor the continuous selection of high-yielding plants within the centgeners had any effect on eliminating the poor yielders. There was a marked difference in the appearance of the pure strains, some Fig. 1.5.— Field plats, showing variations in winterkilling between two pure strains of Turkey wheat. Strain No. 377 is shown at the right and No. 102 at the left; No. 377 withstood the winter almost perfectly. having short grains and others long grains. They also varied in color, lodging, and general appearance in the field, both in fall growth and spring growth. Figures 14, 15, 16, and 17 illustrate these variations better than they can be described. Table XX also shows the data from Table XV grouped in series of 5, and arranged hi various ways to illustrate relationships. The principal considerations in this work were the improvement of wheat in nitrogen and yield. Records were kept of many characters of the plant in the nursery, but evidence points to six that are of interest, namely, (1) nitrogen content, (2) yield per plant, (3) yield per cent- gener, (4) weight of kernel, (5) strength of straw, and (6) length of fruiting period. 269 52 EXPERIMENTS IN WHEAT BREEDING. PERCENTAGE OF NITROGEN. The percentage of nitrogen is in inverse ratio to strength of straw and length of fruiting period, but has no direct relation to other char- acters. It is transmit ted in the field plats as indicated in the summary of Table XX. A striking example of this conclusion is seen in a com- parison of families Nos. 209 and 37, Table XX. These families represent the two extremes in percentage of nitrogen and strength of straw, with an inverse relation, but are nearly the same in all other characters. From 1903 to 1906, records were kept of individual plants selected from the nursery. When these plants were classified according to Fig. lG.— Increase rows of Turkey wheat, showing variations in the time of heading in different strains, each from a single plant. Four rows of each strain are grown. percentage of nitrogen or size of kernel, regardless of the family from which they came, there was a marked inverse relation, the percentage of nitrogen increasing as the size of kernel decreased. It seems prob- able, however, that the individual plants having small kernels may have suffered some degree of arrested development, since this relation disappears when the pure strains are so classified. Percentage of nitrogen and yield per acre in field plats vary inversely. STRENGTH OF STRAW. Strength of straw varies inversely with percentage of nitrogen and directly with yield per acre and yield per centgener. 269 Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. Plate III. &JL iMmn^^ -. /Kq -■•j 0M **'*' - PP*:"*" ':-■'"". HHBjjEJfljjffigfr^ScMBIfc msn BIWWrEB^^^S^^ SW^f?^i^^SjB Fig. 1.— Type of Road Grader or Drag Used in Grading a Nursery into Beds 20 Feet Wide to Afford Uniform Drainage. Fig. 2.— Grains of Turkey Wheat, Showing Variation in Appearance. Nos. 51 and 60 are typical kernels from two pure strains and represent the shortest and longest kerneled types out of 80 strains. No. 76 is a hard, vitreous kernel, somewhat approaching the durum wheat in type. No. 75 is a soft wheat. The plants of this strain are typical Turkey in appearance but the grain is larger and almost white. Notwithstanding the white color, this strain was the highest in nitrogen content of 80 strains in 1910. Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. Plate IV. Fig. 1.— Representative Kernels from 4 Strains of Turkey Wheat, Selected to Show Variation in Appearance. No 48 is a large plump-kerneled strain, while No. 287 has a rather small kernel. No. 328 has a large dark-colored kernel, while No. 313 hasa decided yellow color and is long and pointed. Fig. 2.— Representative Kernels from 4 Strains of Turkey Wheat, Selected from a Series of 80 Strains to Show Variation in Quality. On the basis of a perfect wheat, grading 100, these strains grade as follows: No. 77 grades 50, No. 51 grades 70, No. 27 grades 80, and No. 42 grades 95. EXPERIMENTAL ERROR AND VARIATION IN YIELD. 53 YIELD PER PLANT. The yield per plant shows some correlation to yield per acre and yield per centgener, but this correlation is not high, as it is only in the first class that the correlation is marked. One of the best-yielding strains (No. 425) had a small plant yield in the nursery. YIELD PER CENTGENER. The yield per centgener shows a high correlation with yield per acre and strength of straw, but not a close relation to other characters. SIZE OF KERNEL. The size of kernel (PL III, fig. 2) appears to have no fixed relation- ships; as a character of a pure strain it seems to be independent of other characters. An example of this is shown in Table XX. Families Fig. 17.— Field plats of Turkey wheat, showing variations in stiffness of straw in two strains. Each strain originated from a single plant. Nos. 287 (PI. IV, fig. 1) and 425 have small kernels, but they are among the best in yield, while No. 328 (PL IV, fig. 1) is poorest in yield, but has the largest kernel. Nos. 48 and 287 are the best yielders out of the 26 strains (Table XX), averaging 40.7 and 40.6 bushels per acre, respectively, in a four-year test. No. 48 has a large, plump kernel, while No. 287 has a rather small kernel. No. 328 has averaged 28.9 bushels under the same conditions, yet tins strahi has a large, dark-colored kernel. Our records do not seem to show a rela- tion between the appearance of the berry and the yield. No. 313 has averaged 36.3 bushels per acre, but the kernel has a decided yellow color, and is long and pointed in shape, approaching a rye grain in type. QUALITY OF KERNEL. As already noted, there does not seem to be a definite relation between the appearance of the berry and the yield of the strains. 269 54 EXPERIMENTS IN WHEAT BEEEDING. Plate IV, figure 2, illustrates four strains of Turkey wheat selected from a series of eight strains to show variation in quality. On the basis of a perfect wheat grading 100 these strains grade as follows: No. 77 grades 50, No. 51 grades 70, No. 27 grades 80, and No. 42 grades 95. These grades indicate the variation in quality found in pure strains and show the great possibility of improving quality (fig. 18). To sum up, high yield in the field is associated with high yield per centgener and strong straw, has a slight relation to size of plant, no relation to size of berry, and varies inversely with percentage of Fig. 18.— Cereal laboratory, showing the method of taking notes on quality. Comparisons of 80 strains of Turkey wheat are being made. There were 10 plats of each strain, making 800 in all, but the 10 samples of each strain are arranged together. Notes are taken on each sample separately, then an average is made of the results. To facilitate note taking, a set of "standard samples" representing different qualities is kept in long, 2-ounce vials. A set of these vials is plunged into the sample, and by comparison very accurate data are obtained. nitrogen. A high or a low nitrogen content as indicated in the nursery gives correlated results in the field. High nitrogen content is antag- onistic to high yield. However, an occasional strain, such as No. 48, combines a fair percentage of nitrogen with high yield. SUPERIORITY OF STRAIN. From the point of view of yield per acre there would seem to be little choice among the five best strains (Table XX), but in some ways No. 48 is outstanding in desirable qualities. With a high yield 269 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 55 per acre, it still is above the average in nitrogen content, has a strong straw and a large berry of good appearance. It is also very winter resistant, as was shown in the severe winter of 1909-10, when it came through with much less winterkilling than standard varieties, such as Big Frame and ordinary Turkey wheat. COMPARISON OF ROWS, CENTGENERS, BLOCKS, AND FIELD PLATS. In 1909-10 the 26 strains of Turkey wheat were sown in field plats and duplicated in rows, centgeners, and blocks, but this portion of the nursery was winterkilled. However, very good results were obtained with 11 varieties of oats sown in the spring of 1910 in all four ways. The field plats were one-fifteenth of an acre in size and Fig. 19.— Block nursery, showing blocks 4.2 by 16 feet in size. The beds are slightly elevated, as In the row nursery. were repeated three times. Each variety was repeated 10 times in centgeners, rows, and blocks. The centgeners were each 5 feet square and contained 100 plants 6 inches apart each way. The rows were 12 feet in length and the grain sown in them at the rate of 10 pecks per acre, the usual rate of seeding in this region. The blocks were each 4.2 by 16 feet, or 5 drill rows wide (fig. 19), and sown at the usual rate of seeding. The results summarized in Table XXI show a high degree of correlation between the yield of the field plats and the rows and blocks, but practically no correlation in the case of cent- geners. Except for the Lincoln oat, which yielded exceptionally high in the nursery, the correlation in the rows and blocks would be very high. 269 * 56 EXPERIMENTS IN WHEAT BREEDING. Table XXI. — Yields of grain from 11 varieties of oats grown in field plats, centgeners, rows, and blocks. [The field plats were repeated 3 times, the others 10 times.] Average yield of thrashed grain. Variety. Field plats, per acre. Cent- geners. Rows. Blocks. Bushels. 60.7 60.6 Grams. 729.2 622.9 Grams. 238. 2 206.9 Grams. 1,196.8 1,047.2 60.65 676. 05 222. 55 1.122.0 55.8 55.3- 55.2 584.3 572.8 473.7 213.5 178.0 167.0 865.8 867.1 809.8 54.77 543.6 186.16 847. 56 51.9 51.8 51.0 550.9 654.4 601.3 170.4 207. 3 184.2 800.8 1,071.5 842. 5 51.56 602.2 576.1 187.3 177.3 904. 93 821.6 Swedish Select (09) 50.3 49.8 49.3 560.4 581.1 470.3 170.8 174.3 159.6 791.1 760. 4 776.7 49.83 537. 26 168.23 776. 26 1 It is possible that the lack of correlation with the centgeners in the last three groups is due to the fact that the lower yielding ones were rather late, coarse-strawed, and rank-growing strains. Under the thin planting of the centgeners every plant had opportunity to develop to full size, which probably gave a slight advantage to the later and coarser types, which was not apparent under the usual rate of seeding. Table XX, giving results for 24 strains of Turkey wheat, shows a perfect correlation between yield of centgener and field plats, wherein the wheat strains were all similar, there being no great difference in time of maturity or habit of growth. This sug- gests that when similar strains are being compared data on the average yield of centgeners would be reliable, but that in the case of dissimilar varieties, especially of large ones and small ones, the results would not be comparable with those obtained under field con- ditions. COST OF PLANTING AND HARVESTING CENTGENERS, ROWS, AND BLOCKS. When a large number of strains is being tested in rows or blocks and the series is repeated ten to twenty times, the question of time and relative cost becomes one of importance. Rapidity of planting and harvesting is probably the matter of first consideration, as it is desirable to have these operations performed in the shortest possible time in order to secure comparable conditions. 269 EXPERIMENTAL EKEOR AND VARIATION IN YIELD. 57 Table XXII is a summary showing the relative number of plats of each kind that can be planted in a day by one gang of men, based on our experience. All preliminary work, such as preparing the land, sorting and labeling the seed, preparing stakes, etc., is done before- hand. However, there is usually time for preliminary work, so that Fig. 20.— Five-row nursery drill used for planting row plats and block plats. Four or five men with this drill will easily plant 500 row plats in a day, where not more than 100 row plats could be planted by hand. The work of the drill is also more uniform and satisfactory than planting by hand. the method of planting that permits the greatest rapidity has some advantage. The planting is done with a nursery drill (fig. 20), the harvesting with hand sickles (fig. 21), and the thrashing with a small power machine. Table XXII. -Comparative number of plats of different types that can be planted or harvested in 10 hours. Men in gang. Number of plats covered in 10 hours. Kind of plat. Planted. Harvested. Thrashed, weighed, etc. Centgener, using centgener planter 16-foot row plat, row made with hoe or spade and planted 5 5 5 5 100 100 500 150 250 500 500 200 500 750 750 Block 4.2 by 16 feet, planted with nursery row drill 250 L'G9 58 EXPERIMENTS IN WHEAT BREEDING. USE OF CHECK PLATS. In nursery work where plats are repeated 10 or more times the checks will not be needed as a means of correcting error. Their principal use here is to determine the degree of experimental error. For example, in 1910 we had in one series 80 strains of Turkey wheat. The series was repeated 10 times, making 800 rows in all, but every fifth row was a check, making 200 check rows. To deter- mine the experimental error, the 200 check plats are grouped in sets of 10, taking 1 plat from each series, the same as in grouping the strains. This method gives 20 sets of 10 checks each, and the range of experimental error to be allowed for is at once apparent. Fig. 21.— Row plats at harvest time. Each plat is harvested with a hand sickle and the stake tied into the bundle. The bundles from the row plats that are to be kept pure for seed should be covered with cheese cloth or paper bags. Another important use of checks is as a standard by which to judge progress, and this judgment can be formed very well if the original stock from which selections were made is used for checks. Figure 22 illustrates the method of selection when the experimental error is determined by the use of checks. Let the figure illustrate an ideal case where any number of strains are being compared for yield, the yield varying from 200 to 320 pounds. Let line eh represent this variation. A series of check plats shows a variation ranging from 240 to 280, represented by line cj. The mean yield of the checks is 260 EXPERIMENTAL ERROR AND VARIATION IN YIELD. 59 260, with an extreme error of 20 above or below the mean. The limits of error for the line eh are shown by the lines dg and fi. To be sure that a certain strain was better than the check plats its yield must fall outside the line cl or be better than 280. In the same way two strains can not be compared without making an allowance of 40. For example, 320 is not surely better than 280, since they both might equal 300, but we are sure 320 is better than anything less than 280. If the extreme variation of checks should equal the variation in strains or varieties, then selection would not be possible. On the other hand, if the error in checks is zero, direct comparison between strains could be made, and small differences would be significant. This illustration emphasizes the importance of knowing the probable experimental error and having it well within the limits of expected variation if results are to be secured bv selection. Y/£LD 32Q 240 260 280 300 3ZO 320 ">*' A VV «** 1,% &, A, *V-\ % ,A^ C, vT * y ■ . \s> £ cv . L ' • . o »$• c ° " ° * ■** • l ' * •» o a*^ "\ '* ^0* ^0* C, vP %/ -Mix \S -m&\ ^/ » ^ ■\ % # -Stifef- ^ ^ C, vP in. ,o- ' * • * «G A <\ *'7VT' &* \a -o.»* A r o^ > ^ •: 4 0^ * , ^ '**• /" 0° c, *p ^ 4 » ^ '•' *> '+