THE GENETICS OF SQUAREHEADEDNESS AND OF DENSITY IN WHEAT, AND THE RELATION OF THESE TO OTHER CHARACTERS SABKIS BOSHNAKIAN, M. S. in Agr. A Thesis Presented to the Faculty of the Gmduate School of Cornell University, March 1920, in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Reprint of Memoir 53, (May 1922), Cornell University Agricultural Experiment Station MAY, 1922 MEMOIR 53 CORNELL UNIVERSITY AGRICULTURAL EXPERIMENT STATION THE GENETICS OF SQUAREHEADEDNESS AND OF DENSITY IN WHEAT, AND THE RELATION OF THESE TO OTHER CHARACTERS SARKIS BOSHNAKIAN t ITHACA, NEW YORK PUBLISHED BY THE UNIVERSITY \^ ^a- CONTENTS PAGE Physiological conditions affecting rachis internode length 802 Determination of density and of squareheadedness 803 Development of the whaat plant with reference to squareheadedness 804 The mechanics of squareheadedness 806 Effects of crossing on squareheadedness 807 Effects of nutrition 809 Summary 812 The genetics of squareheadedness 813 Inheritance of squareheadedness in crosses within the sativum group. . .. 814 Relation of the degree of squareheadedness of the vulgare parent in vulgarc x squarehead crosses, to the squareheadedness of their progem- 824 False dominance of squareheadedness 826 Relation of width of culm to squareheadedness 827 Inheritance of squareheadedness in spelt x sativum crosses 829 Effect of the spelt factor on squarehe;idedness 831 Inheritance of squareheadedness in specific crosses 833 Summary 834 The genetics of density 835 Inheritance of density in crosses betw"een Triticutn compactum and other forms of the sativum group 836 Inflence of the density of the lax parent in a lax x compactum cross on the density of succeeding generations 843 Relation of density of F2 plants to that of their progeny 844 Relation of density of dense and lax segregates of heterozygous F2 plants 845 General consideration on the frequency distributions of compact x lax crosses 846 The nature of density factors 854 Factors producing squareheadedness as comprising one of the group of factors modifjnng degree of density 856 Relation of squareheadedness to density in F2 -generation plants 858 Relation of length of rachis to density in hybrid plants 865 Relation of length of culm to rachis length and density 866 Correlation between average internode length and length of sterile glumes 870 Correlation between average internode length and length of kernels 871 Relation of density of rachis to density of racliilla 872 The factor for spelting acting as a modifier for the density factor 874 The synthetic production of 7 riticum compactum 876 Summary : 879 Literature cited 881 THE GENETICS OF SQUAREHEADEDNESS AND OF DENSITY IN WHEAT, AND THE RELATION OF THESE TO OTHER CHARACTERS THE GENETICS OF SQUAREHEADEDNESS AND OF DENSITY IN WHEAT, AND THE RELATION OF THESE To OTHER CHARACTERS' Sarkis Boshnakian- The niendelian inheritance of each of the more striking characters in wheat, such as beardedness, color, fehing, density, and so forth, has heen determined quaHtativel}- by various workers. Much remains to be done, however, if the genetics of these characters is to be analyzed from a quantitative point of view, as there are numerous lesser inherited varia- tions within their simple gross segregations. Practically all of these characters show certain degrees and types of interrelations with other characters. Some of thenv show complete or liartial linkage. Others, when analyzed quantitatively, appear to have been affected by one or another character but not necessarily linked with it, so that if one of these characters appears in an intense or a dilute form the others vary also in the same direction and more or less in the same degree. Besides the above-mentioned type of interrelation, in which the ap- pearance and the intensity of appearance of a group of characters are due to the presence or the absence of the same factor or factors, there is another type embracing a set of characters that appear as an indirect effect of the presence of another character. In a sense these characters are acquired, but they seem to be inherited simply because the causal character is inherited ; and whenever the latter is present it gradually causes the modification of the former characters during the lifetime of the individual. The subject of the inheritance of types of internode length presented in this paper has been treated from the following three viewp>oints : (i) the analyses of minor segregations within gross (3:1, i :2: i, or the like) segregations; (2) the determination of the interrelations of varied ' Paper No. 93, Department of Plant Breeding, Cornell University, Ithaca, New York. Also presented to the Faculty of the Graduate School of Cornell University, March, 1920, as a major thesis in partial fulfillment of the requirements for the degree of doctor of philosophy. -In cooperation with the Office of Cereal Investigations, United States Departmeni of Agriculture. 801 8o2 Sarkis Boshnakian characters; and (3) the determination of characters that were found to be the resultant of other characters. Since the characters studied were confined to those that were not distinctly contrasting in the usual niendelian sense but represented dif- ferent gradations on a scale between two extreme cjuantitative charac- ters, it was not possible to classify them into genetic classes or to express the results always- in terms of ratios. The analyses were made according to such biometrical methods as seemed best suited to bring out the direc- tions and tendencies of the variations. Factorial explanations, however, have been given wherever the tacts obtained warranted the formulation of such hypotheses. The material on which observations were made consisted, exclusive of interspecific crosses, of more than sixty F, progenies, fourteen of which were carried through the F3. To avoid duplications of similar results it is not considered necessary to present here the results of all the crosses, but sufficient data are given to serve as illustrations and to show the general trend of the various modes of inheritance. For many valuable suggestions and criticisms during the progress of this work the writer fully acknowledges his indebtedness to Professor H. H. Love, of the Department of Plant Breeding at Cornell University, under whose direction the studies were made. Most of the Fj and F3 progenies studied were furnished by Dr. C. E. Leighty, of the United States Department of Agriculture. The writer wishes to express his appreciation of Dr. Leighty's generosity in supplying these and also carefully numbered hybrid progenies, which made possible the tracing of each back to the F, and parental material, all of which had been saved. Thanks are due also to the Office of Cereal Investigations, United States Department of Agriculture, through whose courtesy the writer was enabled to enjoy the field and laboratory facilities at the Arlington Experimental Grounds during the summers of 1916 and 1917. PHYSIOLOGICAL CONDITIONS AFFECTING RACHIS INTERNODE LENGTH Like many tiuantitative characters, density and squareheadedness are afi'ected to a greater or less extent by a number of environmental condi- tions which tend to change the normal course of development of the plant, thereby suppressing or accelerating the growth of certain of its Squareheadedness and Density in Wheat 803 parts. A brief discussion of the effect of environmental factors on the production of these internode characters will serve to show to what extent nongenetic variations may take place. In the first part of this paper the main object is to explain the phenomena of density and square- headedness on a purely mechanical basis. DETERMINATION OF DENSITY AND OF SQUAREHEADEDNESS The terms density and squareheadedness are used in this paper to designate two different phenomena of rachis internode length. The differences between these two characters are discussed elsewhere (Bosh- nakian, 1917)', but they may be briefly redescribed here. Density is expressed in terms of average rachis internode length, which is found by dividing the length of the rachis by the number of rachis internodes. The average internode length, or density, of a head 90 milliineters long with 20 rachis internodes, is thus 90 -^ 20, or 4.5 millimeters. The average internode length in wheat varies from about 1.3 to about 8 millimeters. In vulgar e wheat it usually does not extend beyond 5 millimeters. Density is comparative. The average internode length usually varies in dense wheats from 1.2 to 2.5 millimeters, and in lax forms from 3 to 5-|- millimeters. There are intennediate gradations, but, in a general way, by dense or lax forms are meant, respectively, forms varying in density between the two ranges specified. Although the word club refers to a capitate type of head, following the present usage of this term it is here applied to dense wheats of the sativum group (that is, Tt-iticum conipactutn) whether capitate or not. Squareheadedness, on the other hand, refers to the ratio between the average internode length of the central third of the rachis and that of the terminal third. The density of the middle and upper thirds of the rachis is equal to the ratio of the number of internodes in these two sections of the rachis. The coefficient of squareheadedness is found by divid- ing the number of rachis internodes in the terminal third of the rachis by the number of internodes in the middle third. Thus, if the terminal third has 9.5 internodes and the central third has 5.6 internodes, the degree of squareheadedness is equal to 9.5 H- 5 .6, or i .69. The forms ^Dates in parenthesis refer to Liieruiure Ciinl. page 881. S04 SaRKIS P.nSMNAKiAN that are usually called squarelieads have a coefficient of about 1.33 or more; and in this paper, by vulgare or non-squarehead forms are meant types with coefficients of less than i .33, and by squareheads, forms hav- ing coefficients of more than 1.33. This division is entirely arbitrary and is made for convenience. It is seen, then, that squareheadedness has no reference to density. Squareheads may be dense or lax. This divides the wheat tyjies into tlie following four classes with respect to their rachis internodes: non- squarehead, lax {Triticum vidyurc, Plate L,XVII, upper, 12) ; square- head, lax (Tr. capitattim, Plate LXVII, upper, 11) ; non-squarehead, club {Tr. compactuin, Plate LXV'II, lower, 13); squarehead, club (Tr. coin- pacto-capitaluiH Plate LXVII, upper, 9). These varietal names apply to the wheats of the sativum group only. According to these classifications, the semi-dense forms • having a squareheadedness of less than i . 33 are named seini-dense vulgare — not squareheads, a name too often applied for such forms, and perhaps with some justification as such semi-dense forms when well developed may appear square in cross section. Since the discussions in this paper center solely upon squareheadedness and density, it is necessary for the reader to bear in mind the sense in which these two terms are used. i df,ve;i,opment oi-' the wheat plant with reference TO squareheadedness The head of the wheat plant is found in an embryonic stage when the plant starts a new growth after a short or a long period of rest. When the head is about 10 millimeters long it is covered with concentric rings of sheaths, each sheath being attached to the culm at its respective node. The different parts of the plant do not all grow at the same rate. When the spike is about 15 millimeters long, the enveloping sheaths and blades are fairly well developed, but the culm internodes are only a few millimeters in length, the terminal ones being the shortest. After the sheaths have gone through their chief period of growth, the develop- ment of the internodes is accelerated. During this period the head also begins to develop. From this time on, the increase in the height of the Mf.moir S3 Pj.atf. I.Wll W- 0'^ W'4 A"^ 1+ ■^ly \ VARIOI'S FORMS OF GROWTH Upper: 1, Aegilops ovala: 2, Fl {Aegilops x Silver Club); 3, Silver Club. 4, White Spell; 5. Dale Gloria; 6 lo 12, F^' types (Whire Spelt x Dale Gloria, series 13255a) — 6. homozygous lax spelt; 7, heterozygous dense spelt; 8. homozygous dense itpell; 9, homozygous dense sativum (club); 10. heterozygous dense sativum; 11, homozygous lax sativum., squarehead; 12, homozygous lax sativum., vulgare Lower: Dense forms of different species: 1, durum: 2 and 3. rapitarc and den^e harley heads (lateral florets of 2 re- moved); 4. capitate sativum: 5, dense -ipelt; ti, den^e potontcnm: 7 and ft. rliib wheals; 9, titrf^idum: 10, club; 11 and 12. capitate dicoccums; 13. club pyramidal; 14. capitate spelt; 15, dense po^tinirum; 16, club Memoir 53 Plate LXVIII f' r 1 "I VARIOUS FORMS OF GROWTH I'pper: 1 lo 5, 6 to 10. Heads of two hybrid plants showing lack of harmony of growth characters. 11 and 12, Heads of spelts eubjecled to longitudinal pressure; zigzagging of internodes produced instead of Hqiiareheadedneas Lower; 1 to 4, 5 lo 8, Heads of two plants showing vaiialiona in density on same plant; plants grown in greeDliouse; long spikes headed out about four weeks earlier than dense epikes SqUAREHEADEDNESS" AND DENSITY IN WlIEAT 8oS plant is due primarily to the increasing length of each culm internode. During the first period of the development of the culm, the basal inter- nodes, except a few near tlie ground, begin to develop, and successive internodes undergo their chief period of growth as the growth of the internode below is beginning to decline. The terminal section of the culm, which carries the spike, during its development has to push the spike up all along the length of the terminal sheath, which envelops the head in such a way that occasionally, and especially among plants of hybrid origin, the culm cannot exert sufficient pressure to unfold the .-heath. In such cases the spike fails to head out; or, if it finally does head out, the head appears in an abnormal condition and the tip spikelets very often remain undeveloped (Plate LX\'III, upper, i to lo). The factors that seem to produce a strain on the terminal culm inter- node during its growth are the following: the rapid growth of the culm; the spread, width, shape, and texture of the spikelets; the stiffness of the enveloping sheath and its resistance to unfolding. It seems that as the rate of growth of the tenninal culm increases, the movement of the spike through the sheath should encounter a greater de- gree of resistance in an opposite direction. The spread of the spikelets is probably one of the most important factors. The glumes of the spikelets are pointed upward and outward. This in itself tends to increase resistance. If the contact of the glumes with the sheath increases their spread, the resistance will in(iiease many fold. In species such as the spelt or the emmer, in which the spikes are very narrow and the spikelets are very close to the rachis, the resistance is decidedly decreased because the spikelets themselves assume a wedge shape, the glumes being drawn together tightly ; and also because the spikelets, lying flat against the rachis, are not likely to spread out. The third factor, which is not so important as the other two, is the texture of the sheath and its habit of development. The sheath that normally unfolds at the proper time, or is easily unfolded by the move- ment of the spike, sometimes fails to open completely or opens under difficulty. Sheaths of this type produce a considerable longitudinal pres- sure on the culm. So6 Sarkis Boshnakian THE MECHANICS OF SQUAREHEADEDNESS In order to understand the mechanics of the production of squarehead- edness, it is necessary to know the effect that is produced by pressure along the cuhii axis. The presence of longitudinal pressure is evident from the undulations of the culms often observed in square or dense forms (Plate LXVII, lower, 9 and 16.) The part of the spike that most reacts to the effect of pressure is the terminal part, because it is directly in contact with the sheath. The pressure produces a compressing effect, and this in turn checks the development of the terminal part of the head, especially the development of the rachis internodes, and produces the eft'ect known as squareheadedness. This character of squareheadedness is mainly evidenced by the gradual shortening of the terminal rachis internodes (Plate LXVII, lower, 4, 11, and 12). But there are also other characters which accompany this short- ening of the internodes and which are the direct or indirect results of the same cause. One of the most prominent of these is the so-called clubbing, or capitate form, produced by the spreading of the spikelets away from the rachis in those regions of the head where the internodes are short. Because of the pressure exerted, the normal elongation of the internodes is inhibited but the spikelets in most cases continue to develop. Since the space between the spikelets is not sufficient, they are forced mechani- cally to spread out to make more room for development. This process is on the principle of the isosceles trapezoid, in which, the base being constant, the distance between the sides increases as the latter take a position toward a right angle with the base. In the plant the rachis internode is represented by the base, and the axes of the spikelets by the sides, of the trapezoid. In squareheads the spikelets of only the upper part of the spike (ex- cept the terminal two or three spikelets) thus diverge. In most coin- pactum forms all spikelets diverge as a result of the shortness of all the internodes. This is seen on comparing the divergence of spikelets of dense heads 5 and 9, in Plate LXVII (upper), with that of lax heads 2, 4, and 6. In wheat, as well as in barley, the opposite condition exists also in some cases ; that is, the shortening of the internodes does not occur near the upper part, but near the basal region. In such cases the ear, in- Squareheadedness and Density in Wheat 807 stead of being capitate in form, assumes a pyramidal or conical form, as shown by heads 13, Plate LXVII (lower), and 8, Plate LXVII (upper). Another phenomenon of squareheadedness is the drawing of the ter- minal spikelets toward one side so that when the head is viewed along one of the directions of the plane of symmetry, which separates the spikelets of one side from those of the other, the rachis appears exposed (Plate LXVII, upper, 11). Viewed from the opposite side the rachis is covered by glumes and awns which are outdrawn and gathered in that direction. With the receding of the glumes the part of the side where the rachis is exposed appears flat (Plate LXVII, upper, 11), and to a person not viewing the head from the opposite side also it gives the im- pression that the spike is square in cross section. This impression, which has been left on the popular mind, has given to this form the name squarehead. The character of squareheadedness is not confined to the whea: known by this name but may appear also in the dense forms known as club wheats {Triiicum com pactum). The total shortening of rachis internodes in these forms is primarily due to the presence of a genetic factor which produces also a general shortening of many parts of the plant. But in most forms a certain degree of squareheadedness may be found. This may be inherent — that is, transmissible — or it may have been produced mechanically. When the spikelets spread out as a result of the short- ness of the internodes, as described above, the increased width of the head and the projections of the tips of the glumes are likely to offer consider- able resistance, thus producing squareheadedness in the manner already explained. EFFECTS OF CROSSING ON SQUAREHEADEDNESS Squareheadedness, and shortening of all the rachis internodes, are two ditiferent phenomena. As shown in the preceding discussion, square- headedness is a postnatal character, as it were, being dependent on the combined effect of certain vegetative growth characters. Density of the compactiim wheats, on the other hand, is predetermined and is due to the presence of one or more genetic factors which cause dwarfing of a number of plant parts, including incidentally the shortening of all rachis internodes. Squareheadedness is dependent on a certain balance of the rate of 8o8 Sarkis Boshnakian b rowth of the parts concerned. An unfavorable balance produced through hybridization may result in certain hereditary anomalies. A few such forms are shown in Plate LXVIII (upper). Heads i to 5 were produced on a single F, plant derived from a cross between a durum and a common wheat. In these cases the curling of the awns all along the length of the heads shows that the latter were partly prevented from moving up the sheaths by the tightenmg of the sheaths. The illustrations show also the rudimentary condition of the terminal 5 to 7 spikelets, which represent the region whose growth was checked altogether by being subjected to pressure. Heads 6 to 10 in the same plate represent another condition of lack of harmony of growth iietween different parts of the plant. The spiral ionn of the awns of head 7 shows that this head was forced to make a corkscrew movement while making its way up the sheath. Heads 8 and 10 show the failure of the sheath to open at the proper time. Heads 6 and 9 represent heads that were finally released. Heads 11 and 12 represent a single spelt plant whose sheaths were evidently wrapped too tightly around the heads. The pressure which the tight sheath exerted on the head by the growth of the culm produced a zigzagging of the rachis. The internodes of the spelts, being compara- tively stifif, are not so likely to remain short as a result of pressure. These two spelt heads are interesting because they show the relative tendency of the different internodes to be affected by pressure. The basal internodes are thick and are very slightly affected by the induced zigzagging eft'ect. Each successive internode is weaker than the one below, and more and more likely to show the effect of pressure. The conditions to which these heads were subjected are identical with those to which squareheads of sativum or other soft-glumed species are sub- jected, but the effect is somewhat different because of the differences of texture and ear form of the spelt as compared with those of some other forms. These cases show that there are a number of growth characters to which the production of squareheadedness is due, and that the factors producing these characters seem to segregate and recombine like any other factors. H the combination is such as will produce a pressure of Squaeeheadedness and Density in Wheat 809 the head in a certain rate and intensity, various degrees of squareliead- edness may result. If the head encounters httle or ho presstu"e the in- temodes may be more or less uniform, and if the growth of parts is unbalanced certain abnormalities of the spike may result. Since a number of morphological factors are concerned in the pro- duction of squareheadedness, logically it would be expected, and experi- mentally it would be found, that the segregates of a cross between a squarehead and a non-squarehead do not appear in a definite ratio but give a distribution approaching the normal curve of error. EFFECTS OF NUTRITION In one of the preliminary experiments to determine the effect of nu- trition under field conditions, seeds from a pure variety of a squarehead were grown at varying distances. In one case the seeds were drilled rather closely; in the second case they were planted 7.5 centimeters apart; in the third case they were planted 15 centimeters apart. The frequency distribution of squareheadedness of these three sets of plant- ings is given in table I. The set that was drilled in had a mean degree of squareheadedness of 1.325 dz 0.012; the seeds planted 7.5 centimeters TABLE 1. V.\Ri.\TioNs OF Squareheadedness in Plants Grown at V.^rying Distances (Variety, Giant Squarehead) Seeds drilled Seeds planted 7.5 cm. apart Seeds plgntt-d 1.5 cm. apart Siluareheadedness 1,00 I-IO 1.20 1.30 I 40il 3011 bO 1,70 1 80 1,90 2.00 2,10 2,20 14 18 25 6 3 2 Number of plants 94 1 32o±,012 42 1 fl7S± 025 II I 1 2.M± 027 apart gave a higher mean, 1.678 dz 0.025; 3"^ those planted 15 centi- meters apart gave a mean of but 1.254 ± 0.027. The plants from the drilled rows made a fair growth but were inferior to those of the second set. The plants of the third set were mostly win- terkilled, and such as survived had a poor stand with heads of varying length and degrees of development. The poor condition of the last- named was due to the wide distances between the plants, which made them unable to protect themselves from winter conditions. In the case of the other sets there was enough foliage developed during the fall for winter protection. 8io Sarkis Boshnakian Disregarding the third set, it is apparent that the high degree of square- headedness of the second set was due to the greater feeding allotted to these plants ; for there was also a corresponding general development. Another experiment was made with potted plants growing under greenhouse conditions. It consisted of four sets of nine pots. One set was grown m a cool house, the second under moderate greenhouse con- ditions, the third in a damp chamber, and the fourth in a rather warm place. Each set consisted of triplicate pots containing, respectively, soils of a very poor sandy mixture, of fair fertility, and of higher fer- tility. In the sets grown in cool and moderate temperature conditions, the pots containing poor soil produced heads of a low degree of squarehead- edness, while the heads of plants grown in moderately fertile soils showed a higher degree of squareheadedness.* There is no question that in these cases the high degree of squarehead- edness was produced by the fertility of the soil. That fertility in- creases squareheadedness has been noted by Edler (1903), Preul (1908), Ohlmer (1908), and Meyer (1909). Aleyer found in addition that ni- trogen was the causative factor, as neither calcium, potassium, nor phosphorus, alone or in combination, had any noticeable effect on the production of this character. It is not so difficult to explain how high fertility increases square- headedness, in the light of the causes of squareheadedness given in the preceding discussions. If rapid growth of the culm subjects the head to higher pressure, the spike takes the squarehead form. By increasing the nitrogen content of the soil, the rate of growth of the culm is acceler- "atcd and the tissues of the parts of the head are softened. The first of these conditions increases the pressure to which the head is subjected, and the second renders the head more sensitive to the effect of pressure. In the absence of sufficient nitrogenous food, the rate of growth is re- tarded and the parts of the head become fibrous. Due to the first con- dition suflirient pressure is not developed, and with the hardening of the tissues the spike offers a greater resistance to whatever pressure niay be developed. *The sets grown in the damp cliamher and in the warm place did not do well. Squareheadedness and Density in Wheat Sii The effect of the rate of growth on squareheadedness maj' be deter- mined also by ascertaining the degree of squareheadedness of the leading culm and of those that develop later. Practically in every case the leader, which is by far the most vigorously growing culm, has a higher degree of squareheadedness than the others. Often the smaller culms of squarehead plants will have z'ldgare-Vike: heads. In cases in which squareheading is increased by the rapid growth of the culm, the plants having longer spikes are more squareheaded than those with shorter spikes. The relative degree of squareheadedness of short and of long spikes of the same plant is shown in table 2. From four to six well-developed heads w^ere measured from each plant in connection with another experiment. Here the shortest and the longest of these, respectively, are shown. Out of twelve cases taken at random there was but one case in which the short head had a higher degree of squareheadedness. The average of the summation of the differences was o. 0.021 in favor of the long heads. TABLE 2. Differences in Degree of Squareheadedness of Long and of Short Heads of the Same Plant Short heads Long heads Length (centimeters) Squareheadedness Length (centimeters) Squareheadedness Difference in squareheadedness 10 1.23 13.5 1 47 -i-0.24 11,6 1.41 13.2 1.51 +0.10 104 1 50 13.8 1.50 00 10 3 1.24 12 1.51 +0.27 10.7 1.21 14 1.37 +0.15 10 5 1 24 13.6 1.48 +0 24 8.0 1 39 10.5 1.60 +0 21 7.6 1.31 10 1.65 +0.34 8 7 1.51 10.1 1.65 +0.14 8.4 1 33 11.2 1.57 +0.24 8 3 1 39 12 5 1.58 +0.19 7 9 1 29 10 3 1 17 -0 12 Mean and average error 12 0± 40 1 .50± 026 +n 17± 021 When vigor is induced by soil fertility, the plants with longer heads will be more squareheaded than the others; and when vigor is induced by crossing certain zndgarc forms, the long heads of each plant will be found to be more of a squareheaded type. The increase of squarehead- edness of the Fj plants, as shown later, will serve as exaanples. If, on the other hand, squareheadedness is caused, not so much by the 8i2 Sarkts Boshnakian vigorous development of the culm, but by the failure of the sheath to unfold at the proper time, then the plants that are more squareheaded will be found to have shorter heads that the non-squarehead forms. Figures illustrating this type of squareheadedness are given in connection with the discussion of that subject. Before concluding the discussion of the effects of nutrition, it may be well to make a few remarks regarding its effect on the density of the cotnpactum form. As already mentioned, the density of this form is not the result of pressure. But by increasing the fertility of the soil it is possible to change markedl} the degree of density. Four heads from each of two coiupactniii plants are shown in Plate LXVIII (lower). These two plants were grown in 4-inch pots in a greenhouse. The soil was highly fertilized. The heads tirst developed (2, 4, and 5) were almost like vulgare, but as the season advanced, and more spikes began to head out, the heads became more and more dense. There was an interval of about four weeks between the time of heading-out of the first and of the last head. When the last spike headed out, the first one was almost ripe — that is to say, the nutrients in the plant or those in the soil were already used up; hence the spikes heading out later obtained very little food. From the difference in thickness of the culms of dense and lax heads an idea may be formed of the relative amount of nourish- ment obtained by the different heads. This experiment was conducted under abnormal environmental con- ditions, and it is not likely that variations as great as these will be found on plants growing under field conditions. But it points out the fact that increased fertility in the soil tends to increase the length of the rachis internodes. SUMMARY The wheat plant during its development undergoes two more or less distinct periods of growth. In the first period the sheaths and the blades develop. In the second period the rate of growth of the sheaths diminishes and the culms begin to develop, and during this period the spike carried at the end of the terminal culm internode is pushed up through the enveloping sheath. Squareheadedness is the combination of a number of characters which Squarehe.m^edne^s and Density in Wheat 813 are produced by the shortening of the terminal rachis internodes. It is expressed by the coefficient found by dividing the number of internodes in the terminal third of the rachis by the number of internodes in the central third. Density is the shortening of all the rachis internodes. It is determined by dividing the length of th.e rachis in millimeters by the nunaher of internodes. There are numerous gradations of squareheadedness and of density. Squareheadedness is the result of pressure developed by differential growth of culm and sheath. Rapid growth of the culm, failure of the sheath to unfcld, and ears with soft-spreading glumes, tend to increase squareheadedness. Any factor, genetic or environmental, which affects principally the development of the above-named characters, will affect the degree of squareheadedness. Fertilit}- of the soil or access of the root system to sufficient available nitrogenous matter increases squareheadedness. Density is purely an inherited character, but favorable growth con- ditions may somewhat increase average internode length. Under ab- normally favorable or unfavorable conditions, the increase or the de- crease of densitv even on the same plant may be considerable. THE GENETICS OF SQUAREHEADEDNESS Investigations on the genetics of scjuareheadedness have given many confusing results, chiefly because no definite standards have been used for measuring this character. There are many instances in which this word has been used for designating a moderate degree of density. One of the earliest studies of the subject was made by Rimpau (1891), who crossed lax vidgare types with lax and moderately dense square- heads. The Fj hybrids were intermediate and the types of the F, populations varied within respective parental ranges. Von Riimker (1909) obtained from squarehead x vulgare crosses, Fj populations, some of which yielded more and others fewer square- heads. The squareheads varied also in degree. Nilsson-Ehle (1911) found the vulgare type to be dominant over the 814 Sakkis Boshnakian squarehead form. The ratio of vttlgare to squarehead was between 3:1 and 15:1. Further work" has been done, but because of the different meanings given to the word squarehead it is not possible to compare the resuhs with those that are here presented. INHERITANCE OF SQUAREHEADEDNESS IN CROSSES WITHIN THE SATIVUM GROUP Squareheadedness is a quantitative character. Crosses in which it is involved do not show a clear-cut segregation into mendelian classes and ratios. Physiological experiments have shown that the character is the result of the interaction of a number of growth factors, certain combinations of which cause the compacting of the terminal part of the spike. The character is very variable, for any environmental con- dition that affects these growth factors in one way or the other indirectly increases or decreases the degree of compactness of the terminal part of the rachis. Before considering tlie inheritance of the character in squarehead x non-squarehead crosses, it may be well to illustrate the mode of inheri- TABLE 3. Degree of Squareheadedness in Vui.gare X VULGARE Crosses Gener- ation Degree of squareheadedness Mean Number ot g s »c ° ^ 10 10 s S § S plantB Parent plants Mealy Jones Longberry Pride of Genesee. Dawson Golden Chaff.. , Crosses 13158a Mealy X Jones Longberry. . . . 13158a Mealy X Jones Longberry. . . 13178a Jones Longberry X Mealv. 13178a Jones Longberry Fi F2 Fi F2 Fi F2 Fi F2 '2 1 1 1 ■3 6 2 3 3 2 1 4 6 7 3 13 1 _25 6 2 2 2 13 8 17 1 14 6 4 14 9 15 3 _9 7 3 6 9 5 17 2 _6 4 2 1 5 6 .. 10 _6 4 1 1 6 1 4 4 2 1 1 3 4 9 4 _i_ 1 1 1 2 1 2 _2 1 3 1 1 2 2 1 ■■ 2 1 1.14 1 12 1.08 98 1.35 1.12 1.50 1.17 1.42 1.11 1.09 1 06 28 15 23 17 6 61 6 55 13179a Jones Longberry 3 13179a Jones Longberry 90 13177a Dawson Golden Chaff X Pride of Genesee 13177a Dawson Golden Chaff X Pride of Genesee 7 70 Sqcareheadedness and Density in Wheat Si 5 tance of squareheadedness when either the squareheads or the. vulgare type (non-squareheads) are crossed among themselves. The degree of squareheadedness in Fi and F„ generations of vulgare X vulgare crosses is shown in table 3. The first three crosses here (series 13158a, 13178a, and 131793) are between Mealy and Jones Longberry, both of which have practically the same degree of squareheadedness, i . 14 and 1 . 12, respectively. The mean degree of squareheadedness of the F; generation fluctuated around the means of their parental forms, being, respectively, 1.12, 1.17, and i.ii. The fourth cross, 13177a, was made between plants of lower coeffi- cient; that of Pride of Genesee was 1.08 and that of Dawson Golden Chaff was 0.98. The F, generation from this cross were all non-square- heads and had a mean squareheadedness of i .06, these also somewhat ap- proaching the average of their parents. The degree of squareheadedness in crosses between squareheads is shown in table "4. The F.. of the first cross, 13201a, has a range with- TABLE 4. Decree of Squareheadedness iw Squarehead x Squarehead Crosses Gener- ation Degree of squareheadedness Mean Xumber of 1 W3 2 4 _2 2 4 '2 11 _7 "2 8 1 _4 1 2 12 7 2 '2 7 fi '3 4 10 _4 3 2 2 1 _5 CO 1 2 _7 3 5 1 6 1 3 •0 2 4 1 1 _2 2 4 2 _2 .0 1 1 1 2 4 2 i 1 S ■3 2 1 1 plants Parent plants New Soules Fi F2 Fi F2 1.71 1.77 1.49 1.87 1.46 1.55 I.IJS 15 33 Jones Mammoth Amber Crosses 13201a New Soules x Giant Squarehead 13201a New Soules x Giant Squarehead 13203a Jones Mammoth Amber X Giant Squarehead 132fl3a Jones Mammoth Amber X Giant Squarehead 15 5 72 3 52 in the squarehead classes with a mean of 1.46. Compared with the averages of the parental forms — Xew Soules, 1.71, and Giant Square- head, 1.77 — the mean of the F„ is lower. The second cross, 13203a, has an F^ mean squareheadedness within the means of the parents. There are two points of interest in connection with these two sets of crosses : first, as a rule, when vulgare forms are crossed among them- .>elves or squareheads are crossed among themselves, the Fn generation 8i6 Sarkis Boshnakian TABLE 5. Decree of Squareheadedness in Squarehead x Vulgare Crosses Gener- ation Degree of squareheadedness Mean Number o 1 Nc N o 1 t r 1 nt T o 1 ceo 1 o 1 1 1 2 4 1 rde 1 § o 1 1 3 3 2 1 8 2 d I 1 3 'd § 11 3 6 2 14 8 I i 3 4 i 6 4 3 4 6 6 3 5 2 2 6 11 3 4 '4 6 13 13 2 S 7 '4 '3 io '4 '2 w 4 s 2 3 4 6 2 11 3 6 11 1 '9 11 '3 16 5 6 6 '4 is 6 14 _3 '8 7 2 5 6 3 2 17 5 6 9 7 8 4 ■3 io 7 '2 9 '9 '5 8 14 10 S 4 2 1 2 I 21 7 9 '7 11 11 8 6 6 8 9 io S 13 14 ■9 18 18 1 4 11 11 6 '7 io i3 10 8 ii 13 ■9 11 '7 \2 2 1 1 1 17 9 8 9 11 S 1 7 8 '5 7 6 '4 ■3 ii 12 's 2 '2 1 1 4 2 6 1 8 8 12 7 8 i4 6 '7 '7 '4 2 7 10 7 4 6 2 8 3 9 '7 9 4 1 3 12 '7 3 i2 '3 '3 '7 2 6 1 3 _5 in 1 3 2 5 1 5 5 2 11 1 4 6 10 1 2 6 4 3 2 16 '3 1 4 5 s 2 4 2 ■ 3 1 4 2 2 2 1 12 1 3 1 I 9 2 4 2 i ■2 1 5 1 ■3 2 S 3 4 4 1 2 5 3 8 6 1 1 ■7 1 1 2 g 1 3 1 2 I 1 4 1 6 1 5 1 2 1 1 '7 1 3 2 1 g 1 1 ■ 4 2 i 1 2 2 2 2 '4 1 2 I 1 1 1 1 J 5 3 2 1 3 1 2 1 1 1 4 2 1 1 i ■3 '4 1 2 1 1 1 ^ 4 2 1 i 1 2 1 1 2 i 1 1 1 ' i 2 1 1 as 4 2 1 1 1 1 1 1 3 ° 2 1 of pLints Parent plants Giant Squarehead.. . New Soules Extra Early Windsor Jones Mammoth Fi Fa F. Fa Fi F2 Fi Fa F, F2 Fi Fa Fi Fa Fi Fa Fi Fa Fi Fa Fi Fa Fi Fa Fi Fa F, Fa Fi Fa Fi Fa Fi Fa 1.77 1 71 1 57 1 49 1 15 1 14 1 04 1 12 1 08 1 12 1 08 1 35 1 24 1 41 1,31 1 40 1 33 1.62 1.29 1.62 1 36 1 51 1 21 1 47 1 22 1 77 1 40 1 55 1.22 1 28 1.68 1.30 1.32 1.24 1,75 1.25 1.40 1.25 1 46 1 24 1 42 1 22 1,27 33 15 24 15 Minnesota 169 Mealy Fultz FultzrvMedit Pride of Genesee Jones Lungberry Rural New Yorker, - Crosses 13131a Giant Square- head X Minn. 169 . Ditto 13150a Minn. 169 X Giant Squarehead Ditto ISlotia Minn. 169 X Giant iSquarehead Ditto 13134a Giant Square- head X Mealy Ditto 13135a Giant Square- head X Mealy Ditto 13137a GiantSquare- head x Fultz Ditto 13138a Fultz x Giant Squarehead Ditto 13140a Giant Square- head X Fultzo- Mediterranean Ditto 13141a Giant Sq. X Pride of Genesee . Ditto 13200a Pride of Gen- esee X Giant Square- 41 28 13 13 23 15 12 1 135 4 75 4 74 2 95 5 121 3 111 5 89 2 101 3 71 Ditto 76 4 74 6 6.-1 1 76 3 85 4 73 2 95 13202a Jones Long- berry X Giant Sq.. . Ditto 13194a Pride of Gen- esee X New Soules. Ditto 13144a New Soules X Pride of Genesee. . Ditto 13176a New Soules X Rural New Yorker Ditto 13196a Pride of Gen- esee X Extra Early Windsor 13193a Junes Mam- moth Amber x Meaty Ditto 13143a Extra Early Windsor x Pride of Genesee . . . Ditto _ _ _ _ J_ 64 Squareiieadedne^s and Density in Wheat 817 consists of practically only vulgarc or only squareheads, respectively ; secondly, the mean of the F, generation approaches the average of the parental forms. Regarding the inheritance of squareheadedness among squarehead x vulgare crosses, an idea can be obtained by comparing the Fj-genera- tion distributions with the parental distribution (table 5). Special attention might be called to the comparatively high degree of square- headedness of the Fj generations; in most of the cases the F^ plants are almost as squareheaded as the squarehead parents. On a theoretical basis the means of the F^ would be expected to coincide with thoie of the Fn. The departure here is too wide. This increase in squarehead- edness of the F, is attributed both to heterosis and to greater care taken in growing and spacing the plants (jf this generatiim. The F„-generation distribution, even when the number of individuals of which they are composed is considered, shows certain characteristics with respect to range of distribution and mean. If the F. distributions of squarehead and non-squarehead. crosses are compared with those of the crosses in which the parents were either both squareheads or both vulgare, it is seen that so far as the mode of inheritance is concerned there is no essential difference between them. The means of the F,- generation plants shift toward or away from the more squarehead classes, but show a constant tendency to regress toward the means of the parental forms; and the range of the F2 also spreads or contracts, depending on the extent to which the parents vary in degree of squareheadedness. Although several of these crosses were carried through the F3 genera- tion because of the similarities of the results, only two series are con- sidered here, tp illustrate the behavior of the F„ plants in F.^. The results of Giant Squarehead -x Fultzo-Mediterranean (series 13140a) are shown in table 6, and those of Giant Squarehead x Mealy (series 13135a) are shown in table 7. 8i8 Sarkis Boshnakian 3 a m ■< c a ?, c: < H fc tl. ;^ a 1/2 CQ a lOZ'Z 00 ; 06- 1 Si'I 69' I SS I O^I OS I sit 00' I — > - ro-^ ro — • CO O -^ M ro - eo'Vr^c-i-«'t~c> -^^O-H^-^j. iM CO -co CJ -O - M CI tr-3roc>iT'i:5-^'V-*(£)eOM'*-* - O'O'V— - -Oic^fSt^^M ua-^-W^«-^TH — -Hco-^t^ • c^OJ «3 eceo J-^ZSC^Tl-O^— •'— — ^cou ■■■>»<-* C-) inc-sco ci — CJiO>0 OCiJicC — tOTOOC^C^Sl — ■> ^-r *■' V. r^ "' -J '^ «MM^ "* 0-J'--;)CO'«"tCCO-*T^CO-^tOCCO^CCC^t— Tt"Com^Dr-MrC 05 I 1 :' ;=; — ■ — c^e-s -PI — — t-«re Wco-^f-^iftrt-HTj-co ■ t^ eo 1^ :© i^ c^ 1^ — c^ c^ to r-. ■« sri I ;•" i'^ r-ca CO — 00 ^- 51 r?«^c^^-c^iooo •*•»« ^H -^ r-c^ eoto — ootfi^ ■^-ocro ort| :^ :- lOfC-l — O^T'O '»■— -co— ■■—1 -!£) -lO— I ■ ■— '-HCOCO •CO'J'CJ^^ClCOT'l^ soi| ;'■= : = c-)5=>— ^^roc^ii^ — — — ■ . — ITS 01 — — —J- ■ - — .0 ..o™— - . ™oj 00 I i :" :'' -JO— _H — CO-— — — ._-.-.^.c-l— --.c^ — — 56 ' - ;- 06 0| . . .^' !""" . "" . ! "" ! "" l'^ ! *" " .'..'.'.'.'.'. S8 0| : .— '.'.'..'..'...'.'... '.~' ''.'.'.'.'.'.'.'..'.','.'.'.'.'.]'.'. '. 3 — > uTc^.' .2 "s -5 sfe5^No^c^c^cococococo'9''*-^^-^^Ti'TrTtr>.t--ao ^S — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — » — Mn_ to i i ~. i i 3-. ri r; 5 ^ QO ^2 A CI ■^ i I 00 Si ^^ - i coen ct ^ — 820 Sarkis Boshnakian That a segregation of forms is taking place is (iuite evident. The F3 distributions shown in table are arranged in the order in which they were planted, so that the differences may not be ascribed to environmental conditions. Cultures 24-S, 25-3, and 25-4 show notable differences in distribution and mean from the cultures growing next tu them. Simi- larly, in table 7, where the F, distributions are arranged according to the degree of squareheadedness of the F„ plants, the difference in square- headedness of cultures 19-17, 19-18. and 19-19, and many others, is to be noted. The progeny of plant ig-17, representing a line in which none of the plants were squareheads, grew immediately next to a row, 19-18, which produced only squareheads, thirty in all. In order to show that the variations noted in the F3 are not chance variations but are hereditary, the curves shown in figure 78 were plotted, l&) if /^ pro^eoy 1 2.0 1 2 7 6 2 1 2.8 3 1 2 ra — ' r=0.405±0.033 The writer considers this correlation as not due to any form of link- age but as a direct result of squareheadedness, which is caused in turn by the shortening, or rather ham])ering of the development, of the terminal part of the spike due to pressure produced b_\' rapid development of the culm inlern(j(le immediately at the base of the head, and to the failure of the sheath enveloping the spike to grow at a corresponding rate. When the longitudinal growth of the culm internode is checked or retarded, growth naturally takes place in other directions, often causing a thick- ening of the culm wall. A similar thickening of the wall of the culm occurs also in non-squarehead dense plants and more pronouncedly in squarehead dense plants. In these cases, however, the thickening seems to be due to the presence of the density factor, which shortens the culm internode length as well as the length of the rachis internode. Due to dwarfing, the plant cannot grow in height. The food produced con- stantly by the plant is stored partly in the culm, thus increasing the thick- ness of its walls. Squarehe.\dedness and Density in Wheat 829 The club wheat owes its abiUty to stand erect in the presence of strong winds to the presence of the density factor, which, as mentioned above, produces thickening of the culm and incidentally of other j>arts. This factor, which is later considered at length, causes the shortening of the culm also, without affecting the number of nodes. The shortening of the culm internodes increases the number of nodes to each unit of length, thereby giving the culm added strength ; moreover, the shortening of the culm lowers the leverage. These three conditions, direct or indirect results of the presence of the density factor, are the chief causes of the non-lodging quality of dense wheat. INHERITANCE OF SQUARE!! EADEHN ESS IN SPELT X SATIVUM CROSSES In crosses wherein the spelt character has been introduced, the curve of the F„ generation is very distinctly skewed near the extreme of the range on the side of the non-squarehead classes (table 11). True spelts TABLE 11. Squarehe.\dedness im Spelt x S.\tivum Crosses Degree of squareheadedness Mean Number 5 s 12 7 12 IC 11 2 4 - 14 11 17 = N N 5 4 4 s s 3 6 6 10 qua qua 2 4 3 S re! re! I 2 2 lea ea 1 1 ds is 7 3 1 5 2 2 -*• 3 1 S 1 1 •0 m 1 2 2 2 in to 1 2 1 00 ^ 1 « s 2 1 1 W5 1 of plants 13121ja Crimean X White Spelt . . 13260a White Spelt X Turkey . 13216a Giant Squarehead x White Spelt... 13255a White Spelt X Dale Gloria 3085a Black Bearded Spelt X Jones Long- 1 01 1 10 1 24 73 71 50 differ in their ability to carry the factors producing squareheadedness. It cannot be determined from the appearance of the spelt plants whether or not they carry the squareheading factors, as the spelt character acts as an inhibitor for squareheadedness. In fact, the presence of a large number of individuals in the non-squarehead classes of spelt x sativum crosses is the result of the presence of a large number of spelts, which, although carrying the squareheadedness factors, were themselves non- 830 Sarkis Boshnakian squareheads because they carried also the spelt factor, which, as stated above, acts as an inhibitor for the squarehead character. Five crosses between spelts and sativums are shown in table 11.^ Series 13125a and 13260a, which were crosses hetwecnvulgarc and White Spelt, produced F, generations composed of non-squareheads only. When this same spelt form was crossed with Giant Squarehead (series 13216a), a number of squareheads were produced in F^. The White Spelt X Dale Gloria cross (13255a) also showed a fair number of square- heads (Plate LXVII, upper, 6 to 12). From these results it is seen that the White Spelt does not carry the necessary factors for squareheadedness, since when it was crossed with vulgare it produced no squareheads. Squareheads appeared only when a squarehead form was used as the sativum parent. These four crosses were carried through F.,. The first two crosses produced practically no squareheads ; a few were obtained, but they were not tested to ascertain their stability. The remaining crosses produced F3 progen}- which were composed of forms of various degrees of square- headedness. .Since the spelt factor acted as an inhibitor, the spelts of the F3 showed no squareheadedness. The non-spelts produced curves similar to those shown in tables 6 and 7. That there was no so-called repulsion between the spelt and square- headedness factors was evident from the reappearance of squareheads among the progeny of some F, spelts, and from the absence of square- heads among the offspring of other F, spelts. Another spelt form, known as Black Bearded Spelt, when crossed with a vulgare, Jones Longberry (series 3085a), produced a large number of squareheads. These forms were more intensely squareheaded than those produced by the White Spelt x Giant Squarehead cross (13216a). About ten spelt x vnlgarc crosses, with Black Bearded Spelt as one of the parents, were examined by the writer, and in every case there were a large number of squareheads in the progeny, most of which were semi-dense. The progeny of cross 3085a were not carried through F,, but another ^The F2 segregations. of these crosses were in the proportion of 3 spelts or spelt- like forms to 1 sainum. Squareheadedness and Density in Wheat 831 cross between this same Black Bearded Spelt and a viilgare showed that most of the squareheads bred true. If it is recalled that some of the F^ spelts of the squarehead x White Spelt cross produced squareheads in F3 while others that were phenotyp- ically like the former did not, it will not be difficult to understand how the Black Bearded Spelt could have produced different results from those of the White Spelt. It appears, from these examples, that spelts may carry the squareheadedness factors the same as do squarehead sativums themselves, but due to the presence of the spelt factor, which acts as an inhibitor, such spelts do not appear squareheaded. This leads to the consideration of another condition. Since the pres- ence of squareheadedness cannot be detected without a genetic analysis, one may come across a spelt form which, crossed with vulgarc, may sometimes yield squareheads and sometimes not. Either such a spelt is heterozygous with respect to squareheadedness, or the variety to which it belongs has not been stabilized with respect to this character. As the investigator is guided by apparent characters in purifying a line or in calling it a pure line, he cannot detect the segregation of non-detectable factors which is going on within his selected line. EFFECT OF THE SPELT FACTOR ON SQUAKEHEADEDXESS In the discussion of the inheritance of squareheadedness in spelt x satiznini crosses, it was mentioned that the spelt factor inhibited scjuare- TABLE 12. ReL-\TION of SoU.'kREHEADEDXESS TO SpELTIXG (Series 13216a, Giant Squarehead x White Spelt) Degree of squareheailedness 00 o a o o " — a Q 1 .3 .3 3 2 1 *:> 1 2 1 1 2 1 1 2 1 3 2 1 1 2 1 3 2 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 2 1 2 1 83^ Sarkis Boshnakian a; a TABLE 13. Relation of Squareheadedness to Spelting (Series 1325Sa, White Spelt x Dale Gloria) Degree of squareheadedness O too »CO >0 lOO »00 OO too lOO »oo»o 00 00O3 OSO O-^ ^CJ C^CC CC-*** -^O lO^ CJDt^t^ o o o o — ' '-' --1 —I — ' — — ( rt — 1 -< — ' -■ rt -H 1 3 3 6 2 1 1 ?. 2 1 3 2 2 3 1 1 3 2 1 1 4 1 1 2 5 2 1 1 1 6 1 7 1 1 2 8 . 9 1 1 10 3 1 1 1 4 2 2 1 1 2 1 1 TABLE 14. Relation of Squareheadedness to Spelting (Series 308Sa, Black Bearded Spelt x Jones Longberry) Degree of squareheadedness + o ioo>oo moo t^ t^OOQOOS OiOO o — — -< -' •^ rt . -1 -H _ -H -, -H — -. _ -. -. -. — - H C^ 04 1 2 5 1 1 hn2 1 2 2 2 1 .= 3 4 - 4 1 1 a , m h y, •^ o H fi 7 3 1 S?S '} "9 1 1 1 10 1 1 1 1 2 2 1 1 1 3 headedness. The object here is to show to what extent this inhibition takes place. To illustrate this, three types of crosses are used. The first is the Giant Squarehead x Wiiite Spelt cross (table 12) ; the second is White Spelt x Dale Gloria (table 13) ; and the third is Black Bearded Spelt X Jones Longberry (table 14). In the first two crosses, square- headedness is introduced by a lax squarehead and a dense squarehead, re- spectively, and in the last cross it is introduced by the spelt. Squareheadedness and Density jn Wheat 833 The F2 plants in these tables are classified into ten arbitrary classes of spelting. The spelts in such crosses exhibit the spelt character in various degrees. Those showing it in an intense form are placed in class I ; classes 2, 3, 4, and so on up to 9, show various degrees of dilu- tion of the character; the plants in class 10 are all sativum forms, and lack the spelt altogether.*^ The distribution of the plants with respect to spelting and squarehead- edness, as shown in tables 12 to 14, seems to depend to a great extent on the types used as parents. Different spelts crossed widi different sativums show different modifications. All crosses, however, show the following general distribution : Spelts of classes i to 5 inclusive arrange themselves more or less within the non-squarehead classes 0.80 to 1.15- There is a slight tendency in spelt classes 3 to 5 to move the mean toward 1.15. As the classes approach the sativum type, the shifting of the mean toward the more squareheaded classes is accelerated in geometri- cal proportion. The spelt factor, then, does not prevent squareheadedness altogether, but plants that are heterozygous spelts or those that carry modifiers tending to dilute .this spelt character are very much more likely to be squareheaded than plants that are intensely spelted. Squareheadedness in spelts, however, is always of a low degree. INHERITANCE OF SQUAEEHE.\DEDNESS IN SPECIFIC CROSSES It has already been shown (page 829) that v.hen Black Bearded Spelt is crossed with a sativum of a uniform rachis internode length, an ap- preciable number of squareheaded forms appear in the F„. Square- heads may be obtained also when a vulgare is crossed with other species. In table 15 the progeny of a number of interspecific crosses are classi- fied into two groups, the first containing forms resembling the sativum type and the second including all the other forms. Their degree of squareheadedness is represented in the usual manner. In all series a large proportion of the sativum or sativiim-Wkt forms were squareheads. The segregates belonging to other species were prac- tically all non-squareheads. *The genetics of the spelt character with reference to the crosses under consideration has been fully discussed in a recent paper (Leighty and Boshnakian, 19:il). 834 Sarkis Boshnakian TABLE IS. Degree OF Squareheadedness in- Species Crosses. F2 Data 3032 Salt Lake Club x Kahle (Triiicum durum) 3034 Gharnovka {T. durum) x Black Bearded Spelt (T. stelta) 1312a Poole IT. vulgare) x Alaska {T. turgidum) 1328a Satisfaction (T. vulgare) x Alaska (T. turgidum) 1360a Jones Paris Prize (.T. vulgare) x Kubanka (T. durum) Fa generation Degree of squareheadedness Mean Number of plants results » » d 4 3 7 2 8 S '2 24 I 13 2 i '3 2 8 2 1 '4 1 1 1 '2 2 1 1 5 ° 4 2 '2 1 2 2 1 3 '2 6 i 5 2 1 1 2 2 1 i 1 2 I 1 !0 2 1 1 1 _2 1 i 2 1 2 » » § 2 2 1 4 3032— Sativum and sativum-like forms 1.32 1.04 1.81 99 1.38 1,08 1 69 1.10 1.33 1.5 35 1 '2 11 3034— 5fl(tru»i-like forms * 5 36 1312a— Sativum and sa(mm-Iike 22 4 13 58 1328a— Sativum and sa(iiium-like 8 All other forms 3 3 5 4 7 5 1 _5 41 13ti0a— Sativum and sad'vum-like 9 All other forms _\_ _2 15 "^Series 3034 did not produce true sativums in tile F2. t-.OO or over. Squareheadedness is not confined, however, to the sativum form. Other species, with the exception of the wild wheat, may show this character, particularly the segregates of the durum, the turgidum, and the polonicum types and even the diccccum type. But squareheaded- ness in these forms is of low degree and is comparatively rare (Plate LXVII, lower). The analysis of the F, forms in specific crosses presents a difficult task because a large number of specific forms appear, of which some are developed and others are very mediocre or sterile with different tendencies toward squareheadedness. SUMMARY Squareheadedness, being the result of a combination of growth charac- ters, shows a complex mode of inheritance. Simple mendelian segre- gations were not obtained in these experiments. Squareheadedness and Density in Wheat 835 In the F3 generation there were obtained plants of different degrees of squareheadedness, ranging from forms which were distinctly com- pacted at the tip to forms which were denser near the base of the ear. As a rule the range of variation in F., depended on the differences be- tween the extremes of the parental ranges. The means of the F„ ap- proached the parental means. The Fj generation usually had a higher coefficient than the parental mean. Some Fj progeny of two non-squarehead parems were even dis- tinctly squareheads, but in Fj none of these forms were obtained. These variations from normal expectations are ascribed to heterosis and to greater feeding area. A coefficient of correlation of 0.465 ± 0.033 was found between width of culms and squareheadedness. The purely spelt forms were found not to be affected by the factors producing squareheadedness. The more the spelts approached the sativum type, the more they were found to be affected. Speltoid forms did carry these factors, as is shown by the fact that among their sativum progenv a large number of squareheads of varying intensities were found. Certain spelts when crossed with a vulgare fonn will produce a large number of squareheads in F„. Others will produce only non-square- headed sativum forms. Squarehead forms may be produced by crossing Triticum vulgare with other wheat species. THE GENETICS OF DENSITY The discussion in the following pages deals with the genetics of com- pactness of the dense forms of wheat, and especially of Triticum com- pactum, the club wheat. The name club zvlieat seems to have been originally given to tlie squareheads, but at present it is applied almost exclusively to the compactum form. The index of compactness used in this paper is the average rachi.s internode length. The index is found by dividing the length of the rachis in millimeters by the number of rachis internodes. The denser or more compact the head, the shorter is the length of the rachis inter- node. 836 Sarkis Boshnakian Although there are numerous grades of compactness, the rachis inter- node length of what is usually called a club wheat does not exceed 2.25 millimeter.-. The mean density of the club used in the studies present- ed in this paper was about 1 .4 millimeters. INHERITANCE OF DENSITY IN CROSSES BETWEEN TRITICUM COMPACTUM AND OTHER FORMS OF THE SATIVUM GROUP The studies of density herein discussed were made on crosses be- tween Dale Gloria (Plate LXVII, upper, 5) and a number of lax forms consisting of both squarehead and vulgare types. The mean density of the Dale Gloria parent was i .41 millimeters; the means of the lax parents were in the neighborhood of 4.50 millimetA^s. The Fj hybrids were all dense, but not quite as dense as Dale Gloria (table 16). They varied from 1.80 to 2.40, depending on the cross. TABLE 16. Segregation of Density in Crosses between D.^le Gloria (Com- paltum) and Lax Forms 13174a Extra Early Windsor x Dale Gloria 13173a New Soules x Dale Gloria 13172a Mealy x Dale Gloria 13214a Turkey x Dale Gloria 1321Sa Seneca Chief x Dale Gloria 1337a Turkish Amber x Dale Gloria 13213a Red Wave x Dale Gloria Degree of squareheadedness Mean Nusnber 1.3 15 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3 1 3.3 3.5 3.7 39 4 1 4.3 4 5 4 7 4.9 5.1 5.3 55 of plants Parent plants Dale Gloria Extra Early Windsor . . New Soules Mealy Turkey Seneca Chief Turkish Amber ... Red Wave. Fi plants 13174a 13173a 13172a 13214a 13215a 1337a 6 9 Not 3 2 rec 2 4 jrde 1 2 ;; I I 5 '7 7 5 8 11 i 'i 9 12 1 6 8 '3 6 1 2 4 i 4 '6 4 ■3 3 .. 1 1 2 '4 1 " 5 3 1 i '8 3 1 4 '5 1 3 5 2 2 2 4 ■3 9 7 \ 1 3 5 1 2 3 1 4 2 5 4 3 4 3 ■ 2 2 1 2 2 2 4 3 4 1 3 3 3 4 2 '2 4 2 5 2 3 '7 2 4 3 3 1 '4 1 1 2 2 i 8 2 1 '2 'i 2 7 5 i I 3 1 i 3 1 '2 2 1 41* 4 25 3 89 4 53 4 34 4 48 4.82 4 94 1 80 1.90 2.10 1.90 2.30 2.40 2 59 2 33 2.64 2.74 2.40 3 04 2 87 18 24 30 14 15 11 . 34 14 13213a F2 plants 13174a 13173a 13172a 132Ha .... 13215a .... 1337a 13213a . 1 4 i 6 7 5 1 7 1 2 10 13 7 9 5 1 2 7 8 7 5 8 9 5 11 6 16 7 26 7 8 61 48 76 67 67 65 *This figure represents the arithmetical average, not the mean of the frequency distribution. Squareheadedness and Density in Wheat 837 The density curves of the Fj-generation plants, tniHke those of the squarehead x non-squarehead crosses, were all discontinuous, consisting of two well-defined curves. In each case the curve of the dense cbsses contained about three times as many individuals as that of the lax classes. The proportions of these forms are given in table 17. In five cases the TABLE 17. Proportioxs of Dense and Lax Segregates of the F-j Gener.\tions OF Crosses between Dale Gloria (Comp.a.ctum 1 anp other Lax Forms Dense forms Lax forms Prob- Dev. Mean of Mean of Mean of number of indi- viduals Series Devia- able dense lax all Number Number Number Number tion error plants plants plants obtained expected obtained expected 13n4a 40 45,7 21 13.2 --(-5.8 ±2.28 2.54 1.88 3.95 2 59 61 13173a 39 36 9 12.0 +-3,0 ±2.02 1.48 1.74 3.74 2 33 48 13172a 55 57,0 21 19.0 —1-2.0 ±2 55 0.78 2.11 4,04 2 64 76 13214a 54 50,2 13 16,7 4—3.7 ±2 39 1 55 2.30 4,51 2 74 67 13215a 54 50,2 13 16,7 +-3.7 ±2.39 1.55 1.98 4,12 40 67 1337a 43 48,7 22 16,2 -+5.S ±2.36 2.46 2.34 4 40 3 04 65 13213a 47 45.7 14 15.2 +-1.2 ±2.28 53 2 33 4 67 2 87 61 Total 332 3.33 7 113 111 2 -+l.f ±6 16 29 2 09 4 20 2 66 445 deviations from the calculated ratios exceeded somewhat their probable errors, and in two cases the deviations were well within the probable errors. Summing up the results of these seven crosses, of 445 plants obtained in the F, generation ^2i~ were dense and 113 were lax; the deviation from the calculated proportions on the 3 :i basis was — -j- 1.8, which is about one-third of its probable error. These results show that so far as these crosses are concerned the F, plants segregate into dense and lax forms in 3:1 ratio, the density being dominant. Four of these crosses, of which two were with squareheads and the other two with vulgare, were carried through the F3 generation in order to test whether the assumption of the presence of one factor was cor- rect. The results obtained are condensed and given in table 18. Of the 125 F„ plants tested, 30 were homozygous dense, 67 produced both dense and lax forms, and 28 were homozygous lax. These figures, com- pared with the calculated proportions — 31.2 zt 3.3, 62.5 ± 3.9, and 31.2 ± 3.3, respectively — show a very close agreement with the 1:2:1 ratio. The proportion of plants obtained in each cross taken separately agrees also with the theoretical expectancy, the largest departure being but 25 per cent more than its probable error. 838 Sarkis Boshnakian < t3 o u >• n ■ a: N o ?^ S Isi c :1 ffi ei h to O u a f; o H o BS to PQ < ■«J ="S gi-5| r* to CJ M CO Cl (M =•0-^ 1 SN Cl C-' CO m ~ Oi qIcu — - a- 3 - QO "5 •.-s to CO 1 S 2 CO ofe -H -H -H -H -H (£ i a .Sc cq in 01 Cl M £.2 1 + + 1 1 >i i--o If Ci [^ CO 00 d 3 a CO Z£ — ij £ -a_c r- 00 t^ eo 00 Z-5 £1^" « i."5 W 10 C^ L-3 lO Qio: — - 0^ J 3^ 00 t- 01 01 ^2 CI — — _H CO -H -H -H -H ■H (X Q 01 - 10 •n -0 ■> 3 C-J — -f Q ^.^ + + + + VI? ^2 'O lO 1 Si oc *-•; j,- 'JS CI 3 a to w z2 i-"3 0, d/ J2 = S"5 ^- (2 rc f^ J^ C-) — ' — c !^; r^ (O — C-- --3 e^ q'o. — 4^ 1 •S fe 00 1/: •0 <£> CO S s CO i r^ -H -H -H -H -H i R 01 L-5 »o ■ CI -0 > ^- i Q- 1 1 1 4- + OB s-l! CI ^ u~ CI 01 r- fC W z g CO 1.-D X g E'a O) «; to OS 3 *^ Zo "li ~ij — ~" — "Sjg^ --si rt : iL ° E^ Q : *^.2 i ^'S 3 t._o^ >.o S2 X c^ 't; M W So^ ^0 H Squareheadedness and Densfty in Wheat «39 The behavior of each individual F. plant of the four crosses under consideration is shown respectively m tables 19, 20, 21, and 22. Of the TABLE 19. Behavior of F2 Plants in Fs- -Series 13172a, Mealy (Vulgare) x D.\LE Gloria Mean Mean Dense plants Lax plants Prob- n... F2 density density Total Devia- able - ycv. F:; pedigree density of dense F3 plants of lax F3 plants Number obtained Number calcu- lated Number obtained Numbfer calcu- lated F3 plants •tion error * .E. 30-n 1.50 1.35 29 29 30-21 1.53 1,66 22 22 .... 29-9 1.57 1,18 6 6 29-8 1.65 1.46 20 20 30-2 1.71 1.37 22 22 30-U 1.73 1.52 24 24 30-5 1.76 1.54 24 24 30-13 1,81 1.43 28 28 29-4 1.89 1.71 18 18 30-7 1.84 1.47 3.08 24 22.5 6 7,5 30 + - 15 ±1,63 ) 92 30-6 1.85 1,72 3 41 33 32 2 10 10 7 43 + - 0,7 ±1,92 ) 36 30-9 1.90 1 52 3.01 34 33 7 11 11 2 45 + - 2 ±1,96 00 30-8 1.95 1,69 3.56 31 30 7 10 10 2 41 H — 0,2 ±1 87 ) 11 29-6 2.00 1,44 3.06 18 18.7 7 6 2 25 — 1- 8 ±1 46 ) .55 30-19 2 00 I 65 3.00 23 21 5 7.0 28 + - 2,0 ±1.55 29 29-10 2.06 1 80 3 70 25 24.7 8 8,2 33 -1— 0.2 ±1 68 ) 12 30-3 2.10 1,67 3.53 28 27,0 8 9.0 36 +- 1,0 ±1,78 ) 56 29-3 2.11 2 08 3 30 19 15 7 2 5,2 • 21 -1 — 3 2 ±1 34 ; 39 30-13 2.14 1 70 3 33 34 36,0 14 12 48 —1-2 ±2 02 ) 99 29-12 2,19 2.04 4.03 92 18 7 3 6 2 25 H — 3 2 ±1.46 M9 30-20 2,25 1 83 3.64 22 24 7 11 8 2 33 -+ 2,8 ±1.68 1 67 29-1 2 39 1 90 3.15 18 16,5 4 5 5 22 +- 15 ±1 37 1 09 29-11 2 42 1.72 3,69 30 29,2 9 9 7 39 + - 0,7 ±1.82 3 38 30-10 2.43 1 93 3 52 32 27,7 5 9 2 37 4— 4,2 ±1.78 2 36 30-1 2.50 2.22 4 23 37 35.2 10 11,7 47 + - 17 ±2 00 3 85 30-15 2.52 1.85 3 47 28 25 5 6 8,5 34 -t— 2,5 ±1 70 1,47 29-2 2 53 2.00 3 64 19 19 5 7 6 5 26 — h 0,5 ±1.49 3 33 30-4 2 58 1 81 3,56 27 23 5 11 9 5 38 -+ 1,5 ±1 80 3 83 29-14 2 84 1.78 4 26 13 13 5 5 4 5 18 — 1- 0,5 ±1 24 3 40 Total hete rozygoua pii ints .... 517 501 7 1.52 167 2 669 -1—15 2 ±7 55 1 2 01 30-16 3.28 3.39 16 16 30-12 3.55 3 36 23 23 30-22 3 75 3.12 20 20 30-17 3.84 3,43 17 17 29-13 4,16 3,88 20 20 29-5 4.27 .8.65 17 17 29-7 4 44 4 08 5 5 Total F3 plants , . , , 1 1 1 980 1 1 ^=^1= 669 heterozygous plants obtained in series 13172a (table 19), 517 were dense and 152 were lax, the deviation from the calculated ratio being about twice its probable error. In series 13173a (table 20), the ratio between the probable error and the deviation from expectation is i : 5 . 22, which is rather high. In series 13174a (table 21) this ratio is 1:5.62, and in series 13214a (table 22) it is only i :o.46. All these results, in spite of the differences between observed and calculated ratios which 840 Sarkis Boshnakian TABLE 20. Behavior of Fo Plants in F3. Series lol74a, New Soules (Capitatum) X Dale Gloria Dense plants Lax plants Fa F2 Total F3 plants Deviation Probable Dev. pedigree density error p_ jj_ Number Number Number Number obtained calculated obtained calculated 32-7 1 31 37 37 31-11 1.52 23 23 32-6 1,52 • 60 .'. . . 60 31-3 1 55 40 40 31-9 1 55 35 35 32-8 1 62 41 41 31-8 I 64 24 27 8 13 9 2 37 —1- 3.8 ±1.78 2 13 32-13 I 65 52 58 5 26 19 5 78 — f 6.5 ±2.58 2 52 32-14 1 68 51 54.0 21 18 72 — h 3.0 ±2 48 1 21 31-7 1 71 29 31 5 13 10 5 42 -+2.5 ±1 89 1 32 32-15 1.71 93 99 8 40 33 2 133 — f 6 8 ±3 37 2 02 32-9 1.78 67 67 5 23 22 5 90- -+ 5 ±2 77 18 32-16 1.81 59 63 25 21 84 —1-4 ±2 68 1 49 31-12 1.88 35 32 3 8 10 7 43 +- 2 7 ±1 92 1 41 32-5 1 91 46 46 5 16 15 5 62 — t- 0.5 ±2 30 22 32-10 1 95 62 63 22 21 84 -+ 10 ±2 68 37 31-1 1 95 30 43 5 28 14 5 58 -+13. 5 ±2 22 6 08 32-2 2.00 42 39.0 10 13 52 +-3 ±2 11 1 42 31-2 2.06 40 39 8 13 13 2 53 H — 0.2 ±2 13 09 31-4 2 09 30 33.0 14 11 44 -+ 3 ±1 94 1 55 32-12 2.15 83 87.8 34 29 2 117 -+ 4 8 ±3 16 1 52 32-17 62 69 8 31 23 2 93 -+ 7 8 ±2 82 2 76 Total heterc zygous plan ts 805 . 856 5 337 286 5 1.142 -+5 5 ±9 87 1 5 22 31-10 3 40 37 37 .... 1 31-6 3 43 21 21 32-4 3 45 56 56 32-3 3.80 69 69 32-1 3 87 31 31 31-5 3.95 33 33 31-13 4 19 24 24 32-11 4 28 71 71 Total F3 plants they exhibit occa.sionally, show, that so far as these crosses are concerned only one factor is involved in the production of density. Referring to tables 19, 20, 21, and 22, it will be noticed that while in series 13172a and 13214a the proportion of dense and lax forms agreed rather closely, in series 13173a and 13174a an excess of lax forms was recorded in practically every case. In series 13173a, out of 16 heter- ozygous plants tested all but three yielded an excess of lax forms, while in series 13174a all but one plant yielded an excess of lax forms. When wheat plants are grown closely together, the roots occasionally tend to intertwine, and unless the heads show variations of segregating gross characters it is not usually possible to determine whether there are two plants or only one. In crosses between dense and lax plants, in which the segregation is 3:1, out of 16 possibilities there are 9 chances Squareheadedness and Density in Wheat 841 TABLE 21. Behavior of Fo Plants in Fa. Series 13174a Extra Early Windsor CCapitatum) x Dale Gloria Dense plants Lax plants Mean Mean Prob- Dev. F2 density density Devia- P.E. pedigree density of dense of lax Number Number Number F3 plants tion error F3 plants F3 plants obtained calcu- lated obtained calcu- lated 3t-3 1 31 1,29 29 29 34-8 1 40 1.28 25 25 34-11 1 55 1 36 22 22 33-5 1 55 1.28 46 46 33-1.5 1,85 1.30 46 46 33-9 2 00 1 28 1,37 39 39 33-4 1,70 3,09 59 64 5 27 21 5 86 -+ 5,5 ±2 70 2 04 33-2 1 74 1,57 3.77 56 63 7 29 21.2 85 -+ 7 8 ±2 69 2 90 34-4 1 86 1,57 3 69 31 32,2 12 10.7 43 -+ 13 ±1 92 68 34-6 1 95 1,54 3 31 23 24,0 9 8.0 32 -+ 1,0 ±1,65 61 Itf 1 95 1,69 3 33 23 24 9 8 32 — 1- 10 ±1 65 61 2 00 1,39 3 32 18 17 2 5 5.7 23 + - 7 ±1.40 50 33-6 2 00 1 54 3 59 49 51 7 20 17 2 69 — t- 2,8 ±2 43 1 15 33-7 2 00 1 60 3 34 45 48 19 16.0 64 -+ 3 ±2.32 1 29 33-3 2 00 1 60 3 42 45 50.2 22 16 7 67 — f 5 3 ±2 39 2 22 33-13 2 05 1 60 3 80 47 48,7 18 16 2 65 -+ 1,8 ±2 36 76 34-10 2,11 1.69 3.48 23 24 9 8,0 32 — f 10 ±1 65 61 33-17 2 20 1,57 3 53 48 52 5 22 17,5 70 -+ 4,5 ±2 44 1 84 33-11 2 21 1 65 3.50 51 . 57 25 19,0 76 -4-6 ±2 55 2 35 Total heterozygous plants . I 518 I 5.58 I 226 I 186.0 1 — H40 01 ±7 ' 33-10 34-1 33-1 34-9 34-7 33-16 33-12 3 30 3 20 22 22 3 50 3 35 34 34 3.71 3 35 35 35 3 95 3 36 18 18 3 96 .... 3,62 24 24 4 05 3 33 .. 42 42 4 42 3.77 51 51 •■ ■ Total F3 plants 1.177 I that a dense plant will grow next to a dense plant, 6 chances that it will grow ne.xt to a lax plant (or that a lax plant will grow next to a dense plant), and i chance that a lax plant will grow next to a lax plant. In other words, where entangling exists due to close planting, there will be six cases in which this condition will be detected and lax and dense plants separated, and nine cases in which it will be overlooked because the heads will all be dense and will show no visible difference. If this factor of entanglement is present whereby some dense plants are over- looked, theoretically there will be fewer dense plants than are expected. If the degree of experimental error introduced by this factor is cal- culated, it will be found that if, among 50 plants forming a segregating population, there are two or three cases in which a dense plant has been interlaced with its neighbor and is not separated, the differences between recorded and theoretical ratios will be about as great as those shown in tables 20 and 21. 84:; Sarkis Boshnakian TABLE 21. Behavior of F2 Plants in Fs. Series 13214a, Turkey (Vulgase) X Dale Gloria Dense plants | Lax plants Mean \ lean Prob- Dev. F2 F- density df nsitv — Total Devia- able P.E. pedigree density of dense o flax" Number Number ^^ [,ljjr Number F3 plants tion error Fs plants F3 plants obtained c"'™- obtJ lated ined ra'™- lated 38-8 1.72 1.46 68 68 .... 39-9 1.91 1,76 45 45 38-12 1.95 1 41 97 97 38-14 1.95 1 49 85 83 39-4 2.06 I 66 33 33 38-11 2 16 1.51 59 59 38-9 2 33 1 61 83 83 38-13 2.39 I 58 57 57 38-4 2 75 1 49 44 44 40-3 1.57 1.37 IS 73 57 8 4 19 77 H — 15.2 ±2,56 5 94 40-6 2 11 1 65 (23 47 41 3 8 13, 55 -H- 5.7 ±2 17 2 63 38-15 2. II 1.58 i 20 35 40 5 9 13 > 54 — i- 5.5 ±2,15 2,56 40-1 2.28 1.64 i.l5 42 48 !2 16 ( ) 64 — V 6,0 ±2.34 2,56 39-3 2.35 1.67 ! 28 29 31,5 3 10 . > 42 — f 2.5 ±1.89 1 32 40-2 2,35 1,91 !.51 53 54 8 !0 18 > 73 -- 1- 1.8 ±2 50 0,72 39-2 2.53 I "6 ) 44 52 51 7 7 17. > 69 — 1- 0,2 ±2.39 08 38-2 2.53 2,08 1 30 10 12 8 7 4 17 — 1- 2.8 ±1 20 2 33 40-7 2 57 1,92 i.77 46 42 14 ) 56 -1— 4.0 ±2.19 1.83 38-10 2.61 1 96 ! 51 30 30 10 ( ) 40 0.0 ±1,85 39-5 2.75 1.87 ).32 24 23 3 7 7 1 31 -h- 0.7 ±1 63 043 40-8 2.79 2.13 !.78 48 58 5 iO 19 ) 78 --H0.5 ±2 58 4 07 38-5 2.89 2.16 1.09 23 24 9 8 ( ) 32 — H 1.0 ±1 65 61 38-7 2,90 2.23 i.72 47 45 3 15 ( ) 60 H — 2.0 ±2 26 0.88 40-4 2 94 2.18 i.59 48 45 8 3 15 ! 61 -f- 2.2 ±2 28 96 40-10 3.00 2 20 i.83 51 48,8 4 16 ! 65 -1 — 2.2 ±2 36 93 39-6 3 06 2.28 i,89 73 71 3 !2 23 1 95 + - 1.7 ±2 85 60 Total heterozygous plants I 731 I 726 7 I 238 1 242 2 I 960 |-h- 4 21 ±9 09 I 38-3 38-1 38-6 39-1 38-16 40-5 4.06 3,94 37 37 4.11 4 57 12 12 4.14 3 75 41 • • . . 41 4.21 3 41 32 32 4,59 3,78 58 58 1 5 29 3 64 91 91 . , , , , , , , 1 Total F3 plants In crosses 13173a and 13174a, density was the only visible dift'eren- tiating character; hence the separation of the entangling plants depended merely on that character. In series 13172a and 13214a, in which the experimental errors were practically as much on one side as on the other, the error due to entangling was reduced, respectively, bv the introduction of the pubescent glume character through the Alealy jiarent, and by the color of chaff and the beardedness introduced by the Turkey parent. The introduction and consequent segregation of these characters enabled the author to detect the presence of more than one plant, and through their separation the degree of experimental error in these two sets of crosses was greatly lowered. Squaeeheadedness and Density in Wheat 843 INFLUENCE OF THE DENSITY OF THE LAX PARENT IN A LAX X COMPACTUM CROSS OX THE DENSITY OF SUCCEEDING GENERATIONS In connection with table 16 (page 836) the reader perhaps noticed that there was a tendency- on the part of some Fj and Fg generation fre- quencies to be shifted somewhat toward the laxer classes while others tended to shift toward the denser classes. Since the dense parent (Dale Gloria) was the same in all seven cases, these variations, if hereditary to any extent, should be ascribed to the influence of lax parents which represent the variable factors. The mean densities of parent and offspring are represented graphically in figure 80. The curves are arranged in the ascending order of the /^eeJn densiTy of - lax p>i^rents "1 /V(?^/3 dens'iTy of ^■J7i-'^°\./^e?j/2 c/easify of , /Ve^/2 dens/fy of V - ' --L-^^^ ^e^fa densJ/y of Fig. 80. influence of density of lax parent on density of fi- and fs- gexeration plants 844 Sarkis Boshnakian densities of the lax parents. The straight Hnes fitted to the curves show a general rise; that is, with the increase of the average internode length of the lax parent, the averat^e internode length of the Fj and the Fj increase more or less in the same proportion. The slopes of the fitted lines for the F,, the total Fj, and the dense Fj segregate, are practically the same, being 0.089, 0.086, and 0.090, re- spectively. Those for the lax parents and the lax F, segregates show- also a general rise but of a higher degree. It should be borne in mind that the higher the class values, the greater is the tendency of the curve toward a higher inclination. The curves representing the densities of the Fj and the dense F, segregates follow each other very closely. The other curves also follow the same general course. Evidently the material representing the cross with Mealy was somewhat denser, because both the Fj and the F^. curve show a similar rise at that point. The rise of the Mealy parent is not in the same proportion. Aside from these differences, it should be noted that the values of Pi and Fj are higher because they represent crops grown in different years and also because they were spaced more widely than the F„ plants. Be- sides, the Fi perhaps shows vigor due to heterozygosis, which, together with increased food supply due to the wide distances between plants, tends to increase the size of the spike without increasing the number of spikelets, which in turn tends to increase the average internode length. RELATION OF DENSITY OF F, PLANTS TO THAT OF THEIR PROGENY The comparison of the density of F, and of F., plants leads to the decision as to whether the variations in density, especially of the F^ heterozygous plants, are hereditary or represent mere fluctuations due to external conditions. To be sure, environmental conditions, as is pointed out in the first part of this paper, have a great mfluence on the degree of density. The plants used in this experiment were grown on a small area, and consequently the environmental factors had practically as much opportunity to affect the density of one plant as that of another. In comparing the density of the F, plants with that of their progeny, series 13214a may be taken as an example. Deductions based on this cross will apply as well as for the other crosses. The mean densities of Squareheadedness and Density in Wheat «45 the F; parent and the offspring, as shown in table 22, are represented graphically in figure 81. Comparison of the density curves of the F, plants with the mean density curves of their progeny shows that, espe- cially in the case of the heterozygous F„ plants, there is a correlation between the density of the F, and that of their F3 segregates. Since there is such a correlation between F. and F., ihese apparent fluctuations are s.z 50 ■ 1 1 1 \ i -> 1 1 1 \, / / 1 ' / \ \ ^ -7.6 /-- 1 \ 1 N ' lnjf k / 5> ■09 532 ^ "'1 A 'lux /^ />roye V , H^r^r, izy^u us ^ ,- 'deasi 1 — •• ftomoi -' L--- /"" /\ A — -^ r 7.^ /^ y ■/ens t r fomo - and /ieti!ro7j/(jou5 K dense broken 1 1 1 1 ■ 1 ' , ■ y »0 ^ ^ ^ vfi l^ i < J3A0 JO O'S - -^ -." - _- 6 i -." ■ 8 » "' M « ■ ■ i «• ■^ -- »-ra - ■— -co— ■ ■ — coco -.c- co^- S E . CO — — tDCl ■ — — CM - — -0 — _-:M ^t^uo-£;l| t E TC--w(r^ . -(N CM — CM TO J — EI ^ t~ t^ — c^ -^ -^ P7 1^ as to "C -w c^ CO ?^ — e I C^ 40 ■OO'lJ- CO — — 00 — — w -— ■ 11 eo -co — ■" ;"- — ■ — ' w — . 01 :"" ; '^ .2 c 5 & 1 iZ fa 1 s Density of F2 1.72 • 1.91 1 95 1 95 2 06 2.16 2 33 2 39 2.75 1 57 2 11 2 11 2 28 2 35 2 35 2 53 2 53 2 57 2 61 2 75 2 79 2 89 2 90 2 94 3.00 3 06 4 06 •4 U 4 14 4 21 4 59 5 29 "■5oc 5 oc CO i CO aoQC CO CO a QC co^ lO i d- ^■i C-i 1^ coeo^ "? CO 00 lO c c a 38-3 38-1 38-6 39-1 38-16 40-5 8so Sarkis Boshnakian C! •J < X 2 fe. u Q CQ w < J3A0 JO O'S ■ - 6H 8f i ~ :H ~ - "" , . 9 t\ M , ■ S-* . — . »■» ■* - " ■^ en ^ - : ."^ ■ ■ 'W Z-i\ - w .-H^ . « - -co r» 1 CM ») .""■ ^^ -Oi^-- ..«..« * t~ n fic^ '^ : :^ — —..—■« 6 8 1 n - .oc^ 0^ c^ — — — - C>1 — ■« 8 Si - w - — -0 „!VI .-.— — »— CO i'8 N .^-, -Ol-^CO ■*»■ C-1 CO -M TJ- ^ ro 3> 9 81 - — 01 — roc^ i«co(M'MN »o d<.0'>-romm te S-81 ^ -oirc ■ CO - COC^ •— C0«0 — ^ CO — CO Tf -:0 a «■ SI - CCM ■ -M C-lWC-i ■C-l-'TQ — 'J-t^ — -^O-M ESI - TO -^^^^ .coco - — CO-OC-l'-OtO^iMOOC^II ? S M CCCOC^CJ— ■V — C-lTf — --iO"«< t— ^^ t S CO C-» ■ CJ -^ t^ ■V c SI US •- ■^■^ItCJ ■ ■ — CO -^ ;'^ : 6 51 -^ «-.— - :"■ s 8 Si ■* e^ ---1 LZ\ — — ■§ 9 51 -• > S"6 1 {■■5 — So 55 1 'n " : :■"■ IZl ^ ;"■" — - C^l - -If ■ - 51 as ■c^ca "^ to — ■cico-^-* 61 1 — « ■ .— ■ — »n (Mr~ — io-4=-o — -v-T^Mcot^^-CM-rMaiac S'l 1 ■" : m — •o•o^^rc — ^i>CCv ^tocoaoocT^?OfC>o til'' : " c^ — -j';r:c:ir:r^L';c-)>^— ■^itO^o^*''^'— >020 S li-' : - O lO 3-. r^ — M t^ CC ^t ?t C'l Ol r^ -^ t- .O to CO 511^ : ^■lao?^^^-'''^"''"^'^'"^'*'^'" ;" Ml ^■o.-^ro-j-io — ^1 — o-il : " — : :|| 1 c i 1 -a ,1 cS .1 a (fa Density of F2 1 31 1 40 1 55 1 55 1 85 2 00 1 70 1 74 1 86 1 95 1 95 2 00 2 00 2 00 2 00 2 05 2 11 2 20 2 21 3 30 3 50 3 71 3 95 3 96 4 06 4 42 acc- P M30^ 11- 3COCOC :2c coc 3 c- 3C c coc r- CO — — CO CO CO -^ cocoeoc 3C 4- CO;; COCl CO CO CO ii Squareheadedness and Density in Wheat 851 Average internode length (in millimeters) Sf - II LH - .- 9f\ — CO .■ ■ s-^ ^ « ^ MC^ — if] — M — "^ -• 8* cc — — cq - Zi\ - -" - TfM PI - I i '- 0.J -- - : (M - Of\ ■^ : " — -M n 6 8 — - M -M - -- --- ^ ^^ CO 8 8 CO ^ - : - - - -- ■CO ■ IS\ " - : — — "- -* M CO C-1 ■ — - II 9 8 "" (N — M - — — — ^ — Tf — CO CI- ?-I - S8 -^ -cj - ) — C^J — 18 ec — 3^^t~»OC4C4-M rs '^ — — (Tl C^) — — C^J— ■ [-- CO -P — t-. CO "O ra— 'COCO — -j'-f'Tco^'Oc-jtD ■ 6 1 CO " - C-J— . . — — rOtDt^rO-»"M'*'MCOCO'MiO — Ol-T-I- -^T->C-1 I- t^ -N CO M ^1 c^ sii-" s— -I- z com ir5-«!or-'.j>t*30oro»rafo;-3M-.oca — c^^jric-) CO- M c^i- til " coco -«" t^iOiOO »0^^0(^^co^^^o ^i ^ — — M — 81 !" •iO -HC^ Oi^«»0 m-*r~cot:o-« lO CO — - :" j; II'' eo-^-*— — CO ■"■ -^ , 1^ Gl s s ■a s "0 S s S /-2 + 4- + /.4 + + + + ++ + 1- ++ + !.& + ■i- + ' i.e LEGEno + Z?.7/e 6r/or/el /^e\^5ou/es • Turkey X Tui-Mish /Imbe-t Po 2.2 ^.-f S.6 S.Q ■3.0 3.2 A-f X 3.6 3.8 • 0° -* I 2.1 1 1 1 1 2 2.3 2.5 1 2.7 2.9 1 3.1 3.3 1 1 3.5 1 1 1 b.7 3.9 1 4.1 1 4.3 1 crosses in which one parent is the same, not all vulgare nor all square- heads nor all dense forms produce a frequency distribution of square- headedness or of density of the same type and within the same range. Whether the range will remain approximately in the same location, or will shift one way or the other, is determined to a great extent by the degree of squareheadedness or of density of the different forms of vulgare or squareheads, as the case may be, which are involved in the cross. 3. There are exceptions to the general rule stated above. In series 1337a there was a visible segregation of density but not of squarehead- edness. In this case there was evidently interference by another factor. Nilsson-Ehle (1911) considers the inheritance of squareheadedness and gives a factorial explanation to account for the apparent proportion in which it appeared in some of his crosses. But, while Nilsson-Ehle used the term squar*ehead for la.x forms — which have a comparatively shorter average internode length than the vulgare forms — that term is applied in the present paper to forms showing a relative density of the Squarehe.'Ujedkess and Density in Wheat 865 middle and the upper third of the spike of about 1.33 or over, irrespec- tive of the average inteniode length. It is not possible to compare Xils- son-Ehle's results and hypothesis with those from this study. RELATION OF LENGTH OF RACHIS TO DENSITY IN HY'BRID PLANTS Lengtli of rachis is dependent on two factors, namely, the number ot internodes and their length. If the number of internodes in a popula- tion is more or less constant, as has been the case in all the crosses be- tween Dale Gloria and other forms considered herein, the length of the rachis is directly proportional to the average internode length. This is so obvious that it needs no illustration. If both factors are made variable by the selection of parents which var}' both in number and in length of internodes, then there is no cor- relation between length and density. As an illustration a cross may be cited which was made by the writer for this purpose. This cross was Silver Club x Aegilnps ovata. Silver Club (Plate LXVII, upper, 3) is a club wheat from four to five centimeters long, with about seventeen to twenty internodes. The Aegilops (Plate LXVII, upper, i) also was short, like the cliib wheat, but had only six internodes of an average length of about six to seven millimeters. The basal internodes were the shorter, their spikelets being rudimentary. ' Unlike the parents, the Fj plants all had long heads, resembling the spelt wheat. Three plants obtained in the F, also were lax. The point of interest in this cross was that the F, and F„ plants did not inherit length of rachis from their parents, but number and length of internodes. The Fj heads usually had from twelve to fourteen internodes from six- to seven millimeters in length. The three F. plants showed some varia- tion in length. In the Fj 'plants, both characters being intermediate, the heads were necessarily much longer than in either parent. It would be expected, if sufficient Fj plants were obtainable, that the plants would segregate with respect to both characters into short heads dense and lax, that is, with many and with few internodes, and also comparatively long heads dense and lax, with possible intermediate forms. In this connection it may be pointed out that what has been called vigor due to heterosis in wheat is. often the appearance of unusually long heads in Fj or later generations in crosses with certain emmers. 866 Sarkis Bosiinakian These are, as a rule, somewhat dense and bear some thirty internodes to the spike. Hence the question is rather one of number of internodes and internode length. The plants that combine the internode length of the vulgare parent with the number of internodes of the emmer must necessarily be unusually long. In actual practice, in a cross such as the above a considerable number of synthetic spelts appear. These spelts have the peculiarity, as is shown later, of producing internodes longer than those of the lax parent. The appearance of this new type helps to increase the proportion of un- usually long heads. RELATION OF LE-NGTH OF CUI.M TO EACH IS LENGTH AND DENSITY In a pure line of wheat there is practically no correlation between culm length and density, but there is a correlatioii between culm length and length of rachis. The plant that prodvices a short culm due to un- favorable environmental conditions naturally produces a small head ; but such a head as a rule has fewer rachis internodes than the mean of the line, and therefore, although the undeveloped head is short, its density has not been affected to any extent because the number of rachis internodes has decreased more or less proportionately. The writer's studies of the relation of culm length to density were made on series 13214a, because this line produced practically no square- heads. Squareheading, it has been shown, unless it is due to favorable growth conditions, has a tendency to shorten the average rachis internode length. There being no squareheads in the material used, that factor was eliminated. The question of the relation of culm length to other characters of the head is of interest from both the economic and the genetic viewpoint. Because of the many phases to which this problem of density has led, it was not possible in this investigation to study the relation of culm characters as intensively and extensively as the subject deserves. Suffi- cient data have been obtained, however, to give an idea of the general liehavior of this character. Due to the great variability of culm length, the preliminary studies were made with a number of progenies of F„ plants each of which had yielded on an average about 60 individuals. The frequencies of the u o ■«: K Id > ^;-S < U ^: Id Id I w m < S 87 44 8 14 4 01 69 52 3 03 1 52 79 53 4 91 C-J CO 00 CO 81 16 5 36 2 61 75 53 3 05 1 51 77 59 3 47 -0 31 — a> ■= 3i-0 r— ^ ^1 00 93 77 7 97 3 83 93 59 5 06 2 52 92 59 7 05 3 69 CO ova: lOCO — 00 -WCI •S-rrK oor^ ]'^JO t^r-«j -*-»•— so-*— -xnoo t^urto HOm -t*^co -^Tr-^ rococo •j-'vi- tocoeci t— r^to oooooo ^-t--** omt-o tooo oioioi iqiqio ira>oio Ill "iot "zoT ^ loT ~66 ~ii ~S6 ~S6 ~T6 ~68 IS ~si "~E8 ~Ti Ti ~Ti ~Tl ~Tl ~69 "li S9 89 ~I9 6S 5 51 Fn TT\ on roT 19 TI Ts Ti =^ : : . . : " : Cl ■ ■ — ■ : ~ : . M— — : ^ : :"" " W — CO : =^ : " Nt-« '^ : -- - CO , tzi ■ 5 01 IS «« -co iM coc-i ■ t- . ffl^« 8 6! 6 » M"M -" : ■""■ : ■ — "■ «U3« : " — -^ CO CO — — — : "" ^1 10 to 01 oc ■ ■<»■ cq CO c^ri — uitnin M — 1.0 ■* fM — : — ■n tO-^'OO t^ . 01 — t>. "w — "" : M05 30 ;■ " to CO -.o CO f — . — ; — lO so lO lO C^ (M (M *iO r.- CO — ^) — — -I- W3 ^ — ■ - N - « — oo -w - o> '^ CO co-roo -j-c-jc-i -^^^ CT"- — -.»• f^ cccows - CO —. CS'^'f C4M— CO ■ >« c^esc^ t— "ooo 'j-coc-J t-oi^r ^r co cic^i— • OS w3m ■ ■ ■ OllM -.»• M3 -^fi -J> -co i« . Ci H,^ « — ooc co-*^ t-icco 00 • ■ 0— ■ 9 9 8E 00-HM -H ■ . •<}• . ^ Tj" CO tOCMCJ »0 ■ CO ^ — CO f -US C-l— "M ^COiO r- — M 10 — CO 5 9 Ti Ts IE 6 5 i-5 I"^ ■ "^CO — coiM M-^-^.r- • 00 — ■— coco— — C^l— OOOjcO-* —CD- ■ - ■ c^coco i*-^— oc«e"» »o. ■ 00 „^ . -.^w ■ ;- ;l-- COCvj - t- .- ■"- - C4 ■ - -^ t^ ■f -»• C>) — 1 ■ Cv)«; .... ^t~_ eo — — -OC^- -0 — OS TT Tf Ts Ts Ts Ti I's Tt 1 1 c & J 03 55 Ti 15 Ti TT ; '^ ; - lOlOCO OJ ■ '^'t^'Z ''~ ■ = — ro— ... -O"* - — :■) — CO ^- CO ^ ~m UO - ■ co"*«: -a> - oavc^ — t — t- Ci . . - d w ci — ■ c-i CO — -r 10 1-- - o - . W5U5-*- -H . »o — ■* c^ , «00 — CO— •Ct^ --■— OJOO - 1^ Lo r^ - CI m CJ -^ •«■ 4Q C^ ■ — ■ ^ «o as — ■ -f L- ■ CO ... • =-. t~ ■ — . -1 _ t^ lO ^ ■ CO 00 — coco — I Tj- »o to lO -r — a: t— — CO 1^ - - ■ ■ iTO »-o ■ ■ C-J — M CO ... - Oj to Tf 00 ^ SI Ti ~n To 1 i s > :"2S .^ . lOi^ac -faoc^j ■- »■ co . . ■ •— - M CO — ci ■ ■ ooo coc^r* ■ eg^r^ " : - . - — CO ci ■ •« t- r.- c-i ^ - eo - ■ -■■CM4CCO— — -H ;•; '.'.'. '^ . . ■ c-i ■ - -;:":: . •" " ; e i o OS o s > 3 ■-0 34 i -- 6 '. '. ii » 3 el > = ■ ai 3i 3 Q. C c s : :g ; ;g : 3:5> 3C1> 3C 1 Nl : :| : :| 3 :s > 3 > Si 3 2 1 00 Qi 1 ■3 C c 5 5 -.0 CO -^ 1 868 SaRKIS BtiSHNAKIAN tliree characters, culm length, rachis length, and rachis internode length, are shown in table 31, together with then- means. The F3 lines included m this table are arranged according to the order in which they were planted— 38-3, 38-4, 38-5, and so on, representing successive rows of plantings. An inspection of the table shows that these three characters — length of culm, length of rachis, and average internode length--are more or less closely correlated. As a rule the lines with long culms pro- duced lax plants and those with short culms yielded dense plants. It is seen from the curves in figure 84, prepared from the data in table 31, that Culm Rifchls Pcdiqree ryfi^ Fig. 84. average culm, rachis, and internode length of some F3 FAMILIES OF SERIES 13214a '^''^ nrlilf„f,1''' i'^^.V^'a'ion of culm length to rachis and u.ternode length, order of the families corresponds to the order in which they were planted The Squareheadedness and Density in Wheat 869 when the mean of one of the characters decreases or increases, the others vary as a rule in the same direction. There being no inherited variation in number of internodes (which averages about 20 to the spike) in the F3 hnes, the curves of rachis length and average internode length follow each other very closely. The curve of the culm length, although in a general way varying with density, shows certain irregularities, especially in the case of lines 38-6 and 40-4. The former is a homozygous lax type and the latter is heterozy- gous; yet the mean culm length of the former is considerably less than that of the latter, although theoretically it should have been greater. The possibility of the effect of environmental conditions being out of the question, it appears that there is a segregation of culm length inde- pendent of the dwarfing caused by the presence of the C factor. This statement is made as a suggestion only, since at the present time no def- inite explanation can be given. A fact which seems rather interesting is that the C factor does not shorten the culm length in the same proportion as it shortens the rachis length. The averages of the rachis and culm lengths of the homozygous lax (cc) plants were about 7.7 centimeters and 89 centimeters, respec- tively. The presence of the double dose of the C factor (in 38-4, 38-8, and 38-9) shortened the rachis length to an average of 3.2 centimeters and the culm length to about 74 centimeters, a shortening of 58 and 17 per cent, respectively, from the general average. In other words, while the rachis length was shortened by the C factor by more than one-half, the culm length was shortened but one-sixth. Studies of the characters of dense and lax segregates ha\^ led the author to believe that the C factor is a dwarfing factor, shortening, be- sides the culm length, the rachis length, and the rachis internode length, a number of other characters such as length of gkimes, length of kernels, length of awns, and length of culm internodes. These two last-named characters have not been studied carefulh- by the author. Sapehin (1916) and his collaborators, who studied the correlation between density and culm internode length, claim that there is a significant positive cor- relation between these two characters. From the present studies it seems apparent that the shortening of the culm as a result of the pres- 8/0 Sarkis Boshnakian ence of the factor for density, is due not to the reduction in number of culm internodes, but to the reduction in length of the cuhii internodes, the number of these , internodes remaining more or less constant. In this respect the phenomenon of the shortening of the culm is similar to that of the shortening of the rachis. It has been demonstrated by vari- ous workers that in maize also dwarfing causes the shortening of the internodes of the stalk without necessarily affecting their number. In a general statement such as is made here regarding the presence of a correlation between density of the head and shortness of the culm, it is not intended to convey the idea that dense plants or varieties are all to be short, and lax plants tall. The cardinal points brought out are (i) that when the factor of density or its absence has been introduced in a progeny through hybridization, provided there are no interfering factors, the dense plants will be more likely to have short culms than the laxer plants; and (2) that this shortening of the plant is caused, not by the reduction in number of culm internodes, but by the reduction in their length. It should be borne in mind, however, that these charac- ters are affected by environment. From a genetic viewpoint the exhi- bition of a quantitative character in an individual plant is of little value especially if this is affected by environment. The comparative height of a plant is determined by the behavior of its progeny. CORRELATION BETWEEN AVER.\GE INTERNODE LENGTH AND LENGTH OF STERU.E GLL'MES One of the proofs that the density factor is a dwarfing factor is found in the high degree of correlation existing between the average internode length and the length of the sterile glumes. The material for the study of this correlation consisted of the spelt plants of series 132553-15, rep- resenting a cross between Dale Gloria and White Spelt. This F, line seg- regated into dense and lax sdfk'uiiis and spelts. In the data here only the spelts are represented. The spelts were selected primarily because the glumes could be readily removed from the spikelets, as they break off uniformly at the base of the glume at a definite region just below the heel. With vuU/are forms the taking of measurements is somewhat more laborious. The measurements of the glumes recorded here rep- Squareheadedness and Density in Wheat 871 resent the average of the length of opposing sterile glumes on the same spikelet at a distance from the base of the spike of about one-third the length of the rachis. This precaution was taken because the glumes shorten as they approach the distal or the basal part of the head. The correlation between average internode length and glimie length is represented in table 32. The correlation coefficient here is 0.838 ± TABLE 32. Correlation between Density and Length of Sterile Glumes (Series 13255a-15, Dale Gloria x White Spelt; only the spelts measured) Length of glumes (in millimeters) 6.5 7.0 7.5 8.0 8.5 9 9 5 10.0 10 5 a_ 0} CD a a > < 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1 1 3 3 1 1 6 1 3 2 1 2 • 1 2 1 1 1 1 1 1 2 1 1 1 1 r = 0.83S±0.039 0.039, which shows significantly that in this particular cross the factor decreasing rachis internode length is the one causing the shortening of glumes. The relation of density to glume length may be readily seen on heads 6, ~, and 8 in Plate LXV'II (upper), which show the grades of density and consequently of glume length. CORRELATION BETWEEN AVERAGE INTERNODE LENGTH AND LENGTH OK KERNELS The same degree of correlation exists between density and length of kernels as between density and glume length. The measurements of the length of the kernel as here recorded represent the average length of the first and second kernels developed on the basal florets. Of these two kernels the first was very often longer than the second. In cases in which either the first or the second basal floret had not produced seed, the third seed was not measured in its stead because the third seed is always likely 872 Sarkis Bosiinakian to be smaller. In such cases a different spikelet was chosen, the samples being taken always at a distance from the base of the head of about one-third the length of the rachis. Correlating these two characters as shown in table 33, a correlation TABLE 33. Correlation between Density and Length of Kernels (Series 1325Sa-15, Dale Gloria x White Spelt; only the spelts measured) Length of kernels (in milHrneters) 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 :g 1-5 ^ 2.0 1 1 1 1 1 1 -?2.5 ■il 3.0 E e 3.5 1 2 3 5 1 1 1 1 2 ■Zl 4.5 2 5 2 g— 5.0 1 5.5 1 1 1 1 1 < 6.0 1 1 1 coefficient of 0.747 it 0.024 \- r = 0.747±0.024 obtained. Compared in terms of the respective probable errors, this is as high as or slightly higher than the correlation between density and glume length. The width of the kernels was not atfected by the length of the kernels or by density. This density factor does not seem to produce diminu- tiveness but to shorten along one axis only. The width of the kernels, whether taken laterally or dorsi-ventrally, remaining practically the same, the shape of the kernels assumes a spheroid form among the dense seg- regates and a long spindle form among the lax plants. Since density is correlated with length of glume and length of kernel, it is obvious that in this material there is also a direct correlation between length of glume and length of kernel. KELATION OF DENSITY OF RACHIS TO DENSITY OF RACHILLA A rachilla is the rachis of a spikelet, and branches out from the main rachis. A spikelet may have three or more rachilla internodes ; the basal one is very short, but toward the terminal part of the spikelet the internodes elongate and then shorten again. Squarehe.\dedi\ess and Density in Wheat 873 It is practically impossible to measure the average rachilla internode length. For comparative purposes, however, the relation of density to average rachilla internode length can be determined indirectly by noting the extent of the protrusion of the fertile glumes of the florets. The relative distance between the fertile glumes of the first and the third floret on different wheat heads indicates their relative rachilla inter- node length, as is illustrated in figure 85. Fig. 85. spikelets of spelts of v.^rying degrees of density, showing relation of INTERNODE LENGTH (.X, -X'. AND x") TO LENGTH OF STERILE GLUMES ( Y, y', AND y" ) AND REL.\TIVE R.\CHILLA INTERNODE LENGTH AS DETERMINED BY DISTANCE BETWEEN THE TIPS OF THE FERTILE GLUMES OF THE FIRST ."iND THIRD FLORETS (z, z', .^ND z") To l:>ring out the correlation between rachis and rachilla internode length it is necessary to find a population comprising wheat plants of the same species which are segregating into dense and lax forms. Dense and lax spelt plants of series 132553-15 are reprersented, respec- tively, in A and B of figure 85. The illustration shows that the laxer was the form, the more did the florets protrude above the two sterile glumes. In figure 85, C, is represented the appearance of a synthetic spelt of un- 8/4 Sarkis Boshnaktan usual length derived from a durum x lulgare cross. It shows a further increase in rachis internode length, together with a relative increase in glume length. These observations, which unfortunately cannot be presented in the usual form of a correlation table, indicate that C, the factor for com- pactness, shortens also the length of the rachillae or that of their inter- nodes. THE FACTOR FOR SPELTIXG ACTING AS A MODIFJER FOR THE DENSITY FACTOR Density, like squareheadedness, is affected to a large extent by the presence of the spelt factor. In series 13255a, which represents a cross between White Spelt and Dale Gloria ( I'late LXVII, upper, 4 to 12), there is but one spelt factor. Spelts and sativums segregate in this cross in the simple monohybrid ratio of 3 spelts of all grades (heads 6, 7, and 8) to I sativum (which includes compactum [heads 9 and lol, square- heads [head 11], and rulgarc [head 12]). In a cross in which one of the parents is a spelt, the inheritance of density cannot be studied if all the plants are classified according to density alone, for, as will be seen, in the presence of the factor for spelting the factor for density does not produce compactness in the same degree as it does in the ab- sence of the spelt factor. Therefore, in determining the mode of in- heritance in such cases, it is necessary to take into consideration both the degree of spelting and the density, and in interpreting the data the density curves of the spelt and those of the sativums should be examined separately. The difference in density of the spelt and the Sativum form may be best illustrated by the density curves of the progeny of the two F^ plants, one of which was homozygous dense and the other was homozygous lax, but both of which segregated into spelts and sativums. The relatiVe density of spelts and satimwis is shown in table 34. The plants of 132553-26 are segregates from the Dale Gloria x White Spelt cross. They are all homozygous dense, but are derived from F„ plants heter- ozygous for the spelting character. If S stands for the spelting factor and C for compactness, the F, progeny of line 132553-28 consists of SScc, Sscc, and sscc individuals, while 132553-26 consists of SSCC, Squareheadedness and Density in Wheat 875 o < in N u; X CO S tx < W m 0^ Q 2 hi . -W LO z £; u D > 2 < a. X hJQ < 0} 1 « c s » ™ cc «o ^ -^ pi ^ L. ^ S i^J Tf- irq 10 r* M — ec — z - 1 ^ 01^ ^1, tr cc a H >=— -S ra" S c."S a,a E'jit^ g-jico c as K V i lU bC 1 to 00 ^ 1 "1* 7 V 1 ' a. [ 8/6 SaRKIS BoSHNAKrAN SsCC, and ssCC plants. The mean internode length of the lax spelts, as shown in table 34, was 4.22 millimeters; that of the sativunis was 2.76 millimeters, showing a difference of 1.46. Of the plants homio- zygous for the density factor, the dense spelts had a mean internode length of 2.00 millimeters and the dense safh'iiins one of 1.57, showing a difference of 0.43 millimeter. From these results it is seen that, although the internode length of the spelts can be shortened by the introduction of the C factor, the presence of the ,S" factor tends to interfere with the effect which a known C fac- tor would otherwise produce. The relation of the 5 factor to density is the same as the relation of this same factor to squareheadedness. It has already been shown that the presence of factors for squareheading have a very slight effect on the heads that carry the factor for spelting. THE SYNTHETrC PRODUCTION OF TRITICUM COilPACTUM Triticiim compactum, as has already been shown, is but a fonn of Tr. sativnin, which carries an additional factor or factors for compact- ness. The results of crosses between different species show that this same factor can be carried as well by any of the other species of Triticum. In fact, there will be found in commercial strains species that carry density factors, though not necessarily the same factor. Many forms of durum, and especially of dicoccum, carry a density factor. When these are crossed with a lax I'ulgare form, compact forms invari- ably appear in varying proportions, and, depending on the genotypic forms of the plant, some of these compact forms l)reed true while others segregate. In order to produce compact forms, it is not necessary that one of the parents should be a dense form. If the plant is carrving an inhib- iting factor besides the factor for density, it may appear lax although it has the potentiality of producing dense forms. Thus, Black Bearded Spelt, which has been used by the author, is perfectly lax, but when cross- ed with vulgare it produces lax spelts in the F,, and in the F„ an appre- ciable number of perfectly dense forms. The White Winter Spelt, on the other hand, produces no compact forms. The Black Bearded Spelt, then, carries a factor for compactness and also an inhibiting factor. Certain Squareheadedness and Density in Wheat 877 forms of turgidum, durum, and even polonicuiu also have the abihty to produce dense types in the F„. The writer has had no experience with vulgare crosses which liave produced compact forms in the F, ; and unless the inhibiting factor is closely linked with the factors producing a certain specific form, it seems possible that certain vulgare forms will be met with which, although carrying the density factor, will be lax because of the presence of an inhibiting factor. The mode of inheritance of density in some species crosses is very complex, because new specific forms arise in such crosses, each of which is affected in a peculiar way by the density factor. Besides factors for inhibition, many inodiliers also may be involved. Often irregulari- lies are produced by the failure of development or maturation of some forms which seem to carry combinations of growth factors that restrict growth or cause various anomalies. Before being able to analyze from a factorial point of view the inheritance of density in such crosses, it is necessary to know in what proportions the various specific forms segre- gate. There are two cases which suggest that compact or semi-compact vulgare forms have been obtained through crossing two vulgare forms. De Vilmorin (1913) cites two instances in which lax forms produced dwarf forms. The dwarf plant, a photograph of which accompanies the text, appears to be a compact form much denser than the plant from which it mutated. It may also be possible that these cases were natural crosses with a com pactum pollen, since segregation of other characters occurred also. Another case is that mentioned by Neethling (1918), in which tall vulgare forms crossed among themselves yielded dwarf forms. The latter behaved as recessives. The statement is made that the dwarf plants had short ears, but nothing is said about density. If these were compactum forms, the fact that these dwarf forms appeared in a pro- portion somewhat less than 25 per cent tends to lend support to the possibility that the parent which carried the density factor carried also a factor inhibiting the production of dense forms. Until more is learn- ed about the behavior of the F. in the F,, no definite explanation can be given to account for its mode of inheritance. 8/8 Sarkis Boshnakian In Plate LXVII (lower) are shown a number of dense forms of dif- ferent wheat species, most of these being synthetically produced in inter- specific crosses. Some show both compactness and squareheadedness; others show one of these characters in the absence of tlie other. Korn- icke (1885) has observed dense and squarehead varieties in other wheat species. He gives the following botanical varieties : Triticum durum Desf. var. compactum Ser., Tr. polonicum L. var. compactum Link., Tr. polonicum L. var. qiiadraium Ser., and Tr. turgidiim L. var. quad- ratum Ser. Density, or the excessive shortening of the rachis internodes, is not confined to the genus Triticum. Dense forms are common both in barley and in rye. The question of the origin of Tr. compactum becomes simplified if it is recalled that this form may be produced when a sativum form is crossed with another wheat species, and also that natural crossing occurs not infrequently. Such being the case, one would expect Tr. compactum to be practically as old a form as any of the other species, and, so far as archaeological evidences go, cultivation of Tr. compac- tum has been traced as far back as the Stone Age. Buschan (1895) states that this compact form has been found in the remains of caves and lake dwellings and among other prehistoric relics in regions extending from Egypt to central Europe and to Sweden. According to Unger (i860), the culture of wheat has been traced back to the year 3623 B. C, and hence its origin must be older still. If interspecific crosses between vulgare and other forms are able to produce compact forms, it seems that the first origin of Tr. compactum should have followed that of Tr. vulgare. Undoubtedly Tr. compactum has reappeared many times in the same manner, for the appearance of this form in interspecific crosses is rather common. Tt'. compactum may be a mutational form of vulgare, although there is no dependable evidence regarding this possibility for vulgare wheats. There is a par- allel example in the case of the rye known as "Heinrich-Roggen" (Hill- mann, 1910:579). This is a very compact form of rye which is said to have appeared in 1880 as a mutation on a single ear. Squareheadedxess and Density in Wheat 879 SUMMARY The density studies reported herein were made primarily on the prog- eny of a number of crosses in which the dense parent was Dale Gloria {Triticuiii com pactum), with an average internode length of about 1.41 millimeters. Density was found to be dominant over laxness. The ratios obtained approached 3:1. The heterozygous forms were somewhat laxer than the homozygous dense forms, but by no means intermediate between the dense and the lax parents. The V„ curves were bi-modal and discontin- uous. The F3 plants showed various degrees of density within the dense and the lax classes. Proofs are given in the text showing that these varia- tions are hereditary and are the result of the segregation of modifiers or of additional density factors capable of producing density only with- in short ranges. Experimental evidence is cited suggesting that different density fac- tors form allelomorphic series, and other evidence that they belong to multiple series. Squareheadedness and density were found to represent two different characters. Hybrid progenies showed all types and grades of combina- tions between these two characters. The process of squareheading was found to shorten the average in- ternode length. The effect on density thus produced, however, is slight. The phenotypic transmission of the squareheadedness of Dale Gloria is dependent on the type of the lax non-squarehead parent. In some crosses there was a large proportion of lax squarehead forms in the ¥„, while in others there were none of these forms. Although in F„ progenies resulting from dense and lax crosses an almost perfect correlation exists between rachis length and density, these two characters are not necessarily correlated. Rachis length is- the indirect product of average internode length and number of inter- nodes. The correlation between density and rachis length becomes less and less as the difference between tJie numlier of internodes of the parental forms increases. High degrees of correlation were found between average internode 88o Sarkis Boshnakian length and length of culm, length of sterile glumes, and length of ker- nels, and average rachilla internode length. These, together with other observations, show that density and the shortening of these other length characters are the result of a single dwarfing factor. Plants exhibiting the spelt character are not as much affected by the density factor as are those that show sativiiiii characters. Compact forms may be produced by crossing a lax sativum with lax forms of other species. Dense fonns may also appear occasionally in crosses where neither parent is a sativum. Compactness is not a char- acteristic of sativum forms; other species also may exhibit this charac- ter. Squareheadedness and Density in Wheat 88i LITERATURE CITED Bateson, W. Mendel's principles of heredity, p. 1-396. 1909. BiFFEN, R. H. Mendel's laws of inheritance and w heat breeding. Jotirn. agr. sci. I : 4-48. 1905. Boshnakian, S. The comparative efficiency of indexes of density, and a new coefficient for measuring scjuareheadedness in wheat. Anier. Soc. Agron. Journ. 9 : 231-247. 1917. Buschan, Georg. Triticum. In Vorgeschichtliche Botanik der Cultur- imd Xutzpflanzen der alten \Ve\t auf Grand prahistorischer Funde, p. 1-34. 1895. Edler, W. Die Aehrenform des Squarehead in ihrer Beziehung zur Ertragsfahigkeit verschiedener Zuchten. Illus. landw. Ztg. (Cited in Die deutsche landwirtschaftliche Pflanzenzucht [Hillmann].) 1903. Hillmann, Paul (Editor). Die deutsche landwirtschaftliche Pflanzen- zucht, p. 1-603. 1910. KoRNiCKE, FriEdr. Der Weizen. /;; Die Arten und Yarietaten des Getreides. Handbuch des Getreidebaues 1:22-114. 1885. Leighty, Clyde E., and Boshnakian, Sarkis. Genetic behavior of the spelt form in crosses between Triticum spelfa and Triticum sati- vum. Journ. agr. research 22 1335-364. 1921. Mall, W. Die Ergebnisse verschiedener Getreidebastardierungen. Deut. landw. Presse 39:164. 1912. Meyer, Karl. Uber den Einfluss verschieden hohen Wassergehalts des Bodens in den einzelnen Vegetationsstadien bei verschiedener N- Diingung auf die Entwicklung des Gottinger begrannten Square- head- Winterweizens. Journ. Landw. 57:351-384. 1909. Neethling. J. H. A preliminary note on dwarfs appearing in Gluyas Earlv (wheat) hybrids. South African journ. sci. 14:540-547. 1918. Nilsson-Ehle, H. Kreuzungsuntersuchungen an Hafer und Weizen. II. Lunds Univ. Arsskr. 2: 7*': 1-84. 1911. Ohlmer, W. tjber den Einfluss der Diingung und der Bodenfeuchtig- keit bei gleichem Standraum auf die Anlage und Ausbildung der Aehre und die Ausbildung der Kolbenform beim Gottinger begrann- ten Squarehead-Wintervveizen. Journ. Landw. 56:153-171. 1908. Parker, W. H. Lax and dense-eared wheats. Journ. agr. sci. 6:371- 386. 1914. 882 Sarkis Boshnakian I'reul, Franz. Untersuchungen iiber den Einfluss verschieden hohen Wassergehaltes des Bodens in den einzelnen. Vegetationsstadien bei verschiedenem Bodenreichtum auf die Entwickelung der Sonimer- vveizenpflanze. Journ. Landw. 56:229-271. 1908. RiMPAU, W. Kreuzungsprodukte landwirtschaftlicher Kulturpflanzen. Landw. Jahrb. 20 :335-369. 1891. RuEMKER, K. VON. Methoden der Pflanzenziichtung in e.xperimenteller Priifung. Landw. Inst. Breslau. Mitteil. 5:1-322. 1909. Sapehin, a., and others. Analyse hybridologique des caracteres cor- relatives chez le froment. L (In Russian. Summary in French.) Imp. Agr. Inst. Southern Russia 86- : 455-544. 1916. Spillman, W. J. Quantitative studies on the transmission of parental characters to hybrid offspring. In Proceedings of the fifteenth annual convention of the Association of American Agricultural Colleges and Experiment Stations. U. S. Dept. Agr., Office Exp. Sta. Bui. 115:88-98. 1902. StrampEli,!, NazarEno. Alia ricerca e creazione di nuove varieta di frumenti a mezzo dell' ibridazione. R. Staz. Sper Granicolt. Rieti 1907:74. 1907. TscherjN[ak, E. \'0N. Bastardierung. In Die Ziichtung der landwirt- schaftlichen Kulturpflanzen, by C. Fruvvirth, 4: 164-187. 1910. Unger, F. Botanische Streifziige auf dem Gebiete der Culturgeschich- te. K. Akad. Wiss. [Vienna], Math-Natur. CI. Sitzber. 38:69-140. i860. ViLMORiN, PhillippE de. Sur une race de ble nain infixable. Journ. gen. 3:67-76. 1913. AV^iLSON, John H. The hvbridisation of cereals. Journ. agr. sci. 2:68- 88. "1907. Memoir 46. A Classification of the Cultivated Varieties of Barley, the eeventh preceding number in this aeries of publications, was mailed on March 16, 1922. Memoir 47. Typha Insects: Their Ecological Relationships, waa mailed on Dereniber 30, 1921. Memoir 48, The Inheritance of Salmon Silk Color in Maize, was mailed 00 January 30. 1922. Memoir 49. The Biology of Ephydra subopaca I.oeiv, waa mailed on February 16. 1922. t > LIBRftRv OF CONGRESS 000 935 672 1 I