UNIVERSITY OF CALIFORNIA PUBLICATIONS IN AGRICULTURAL SCIENCES Vol. 4, No. 8, pp. 183-232, 1 1 figures in text May 20, 1921 THE TEMPERATURE RELATIONS OF GROWTH IN CERTAIN PARASITIC FUNGI* BY HOWAED S. FAWCETT CONTENTS PAGE Introduction 184 Methods 193 The culture medium 193 Stock cultures .. 195 The experimental cultures 195' Observations on growth 196 The maintained temperature chambers 198 Structural differences related to temperature 198 The experimental data 199 Discussion of results 204 General considerations ., 204 The growth temperature graphs 206 Changes in the growth temperature relations 210 Comparison of growth temperature relations of different organisms by means of graphs brought to the same height 211 Eelation of growth-rate to the time of exposure 214 Temperature coefficients 217 Introductory 217 Temperature coefficients in the present study 220 Conclusion 229 Literature cited 231 * Paper No. 62 from the University of California, Graduate School of Tropical Agriculture and Citrus Experiment Station, Eiverside, California. Manuscript submitted September 2, 1919. 184 University of California Publications in Agricultural Sciences [Vol.4 INTRODUCTION It is commonly recognized that, of the many different and varying conditions that affect life processes, temperature is one of the most important. The range of temperature at which certain important physiological processes may occur at all is relatively narrow, and comparatively slight temperature changes produce marked effects upon the velocity of other processes having more extended ranges. Although many biological investigators recognized the great importance of this subject, the more detailed study of the effects of maintained temper- atures on vital processes awaited the development of simple, adequate and inexpensive methods of artificial temperature control. In the earlier investigations of temperature effects upon organisms it was often impossible to maintain the desired constant temperature through- out sufficiently long periods of time to get results that might be con- sidered as related to maintained temperatures. In recent years a rapidly increasing number of papers reporting investigations on the effects of maintained temperatures upon different physiological pro- cesses is an indication that more attention is now being given to this subject. There is still, however, a great lack in our knowledge in this field, especially as regards plants. On certain animal processes some- what more work appears to have been done, though even in this field much remains to be accomplished. It should be remembered in this connection, also, that the subject of the temperature responses in living things involves problems more complicated than those just suggested as having to do with maintained temperatures. Most organisms (aside from warm-blooded animals) are never exposed, in nature, to maintained temperature for any con- siderable period of time; their temperature environment is practically always in a state of flux. From this it follows that a knowledge of the relation holding between maintained temperatures and vital pro- cesses, no matter how thorough such knowledge may be, can not be expected to be a complete basis for an interpretation of physiological processes going on under natural conditions. In order to obtain a more adequate basis for such an interpretation suitable methods need to be devised for dealing also with rate of temperature change as an environmental condition, aside from the degree of temperature itself. The experimental aspect of this phase of physiological and ecological 1921] Faivcett: Temperature Relations of Growth in Certain Parasitic Fungi 185 temperature relations remains practically untouched as yet. It is almost unmentioned in the literature as a serious consideration, al- though MacDougal (1914) has called attention to its great importance. It is clear, at any rate, that the problem of temperature influence upon organisms falls readily into two fundamentally related but super- ficially different portions, one dealing with maintained temperature and the other with fluctuating temperatures. Practically all the con- trolled experimental work hitherto published deals with the first por- tion of the problem, and it is in this same category that the present investigation lies. Indeed it seems unwise to attack the problems related to fluctuating temperature until a more thorough appreciation has been gained concerning the general principles underlying the influence of maintained temperatures upon vital processes. It was with the aim of throwing additional light on some of the principles underlying the effects of maintained temperatures on the growth of certain fungi that the investigation reported in this paper was under- taken. Filamentous fungi were used because they are comparatively simple organisms whose growth rate may be easily measured, because they lend themselves readily to culture in darkness and because, each cell being in direct contact with all features of its environment, their relation to their surroundings is simple and close. The four forms — Pytlnacijstis citrophthora Smith and Smith, Phytophthora terrestria Sherbakoff, Phomopsis citri Fawcett and Diplodia natalensis Evans — were used, all of them being parasitic on citrus trees. These were known to grow well on certain prepared media and some evidence was at hand showing that they differed from one another as regards their temperature relations. Another reason for selecting these four citrus parasites was the possibility that their pathogenic activities might be influenced by climatic temperature conditions. It was thus possible that a study of their temperature relations might throw some light upon their probable occurrence and upon methods of combating them. General observations in connection with many diseases due to plant parasites have indicated that temperature is a very important factor in their prevalence in any given season or in any given region. N. E. Stevens (1917) has shown that the rate of increase in diameter of chestnut blight cankers is closely related to temperature. Edgerton (1915) has emphasized the apparent relation of temperature conditions to the occurrence of certain plant diseases in subtropical climates. He 186 University of California Publications in Agricultural Sciences [Vol. 4 is convinced that the absence of anthracnose in beans grown at certain seasons in Louisiana is due to the fact that the average temperatures for the seasons when the disease is absent are too far above the opti- mum for the growth of the pathogenic fungus. The writer (1917) has previously referred to the limited geographical distribution of melanose due to Phomopsis citri, one of the fungi here studied, and has suggested that temperature conditions may be among the important factors limiting its distribution. Humphrey (1914) came to the con- clusion that temperature differences in various localities in the state of Washington largely determined the differences in distribution and severity of the tomato wilt induced by Fusarium oxysporum. Tisdale (1917) has shown for Fusarium wilt of flax that the temperature at which the host is most injured by the disease corresponds to that favoring the maximum growth of the parasite in cultures. For many parasitic organisms it is probable that the temperature range within which serious infection of their hosts may occur natur- ally is comparatively small. Temperature differences and differences in moisture conditions may largely account for many of the striking differences observed in the occurrence of many plant diseases from season to season and from one region to another. Many other obser- vations aside from those given above might be mentioned in this con- nection, but it seems to be clear enough that the pathological or agricultural point of view demands much more thorough knowledge than we yet have concerning the temperature relations of parasitic fungi. It was thus thought that the results obtained in the present study might ultimately be of value in pathological work. Considering the limited time available for this study, it appeared better to confine the experimentation to the four forms mentioned above and to subject the results to a critical study than to include a larger number of forms, with the accompanying necessity of treating the results in a more superficial manner. Our knowledge regarding the physiology of fungi, as well as that regarding plant temperature relations, may be increased first by intensive studies of a few forms. After the main principles have been worked out for certain selected forms it may become largely a matter of routine to compare a large number of organisms with respect to the principles previously worked out. The four fungi here to be considered seemed to offer oppor- tunities for intensive study, and they also furnish valuable material for comparisons. 1921] Fawcett : Temperature Relations of Growth in Certain Parasitic Fungi 187 As naturally follows from the general concept of conditional con- trol of physiological processes (Verworn, 1912), the relation of the process studied to any given condition is determined not only by the given condition but also by the remaining conditions. For example, if the temperature relations of a given organism are to be dealt with they must necessarily be stated together with as definite a description as possible of the non-temperature conditions that are supposed to be effective. To state that the mycelial mat of a given fungus was ob- served to enlarge more rapidly at one temperature than at another means little, unless it be also stated just what sort of medium was employed ; just what was the length of the time period ; just what relation this time period had to the beginning of the test ; just what the radiation conditions were, etc. By altering the non-temperature conditions the relations of a given process to different maintained temperatures may be profoundly altered. To illustrate still more concretely: Lehenbauer (1914) found that the optimum temperature for elongation of the shoots of maize seedlings in his experiments was 30° C. when the exposure period was 6 hours, and the corresponding optimum temperature for an exposure period of 12 hours was 32° C. If Lehenbauer 's twelve-hour period of exposure be divided into four periods of three hours each, and if the optimum temperature be calcu- lated from his data for each of these four successive periods separately, the optima are found to be 30°, 31°, 31°, and 32° C. respectively. Obviously, any physiological process must be regarded as controlled by all the effective conditions acting together. The conditions that influence the rate of growth of a fungus in a culture may be roughly classified in five groups as follows: (1) The nature of the fungus, which implies its internal condi- tions — everything that goes to make it the particular organism that it is. This set of internal conditions is vaguely and partially indi- cated by the name of the fungus, with an implied morphological con- cept of its form and development, to which the name refers. But it is well known that the same species of fungus may develop quite different complexes of internal characteristics under different sets of environmental conditions. For this reason it is of the greatest im- portance to include not merely a morphological description but defi- nite information concerning the previous history of the experimental organisms. (2) The nature of the medium, implying all the physical and chem- ical properties of the space about the hyphae, their environment. For 188 University of California Publications in Agricultural Sciences [Vol. 4 the most part, the conditions of the medium (aside from temperature and radiation) involve the concentration of numerous chemical sub- stances such as oxygen, carbon dioxide, starches, sugars, acids, inor- ganic salts, etc. (3) Temperature conditions. Since the temperature of the hyphae follows closely that of the medium and since the latter follows closely the temperature of the more distant surroundings of the culture, it is conventional to consider the temperature of these surroundings as constituting a condition in itself. After all, however, it is the tem- perature of the fungus hypha that directly influences its rate of growth, not that of the medium, culture dish or chamber about the dish, etc. But, since the temperature of all these spaces is practically the same, this last distinction has generally been ignored. The tem- perature conditions for two cultures may differ in several ways. If they are maintained temperatures, they may differ in degree or in- tensity alone, and we may express them in terms of degrees on some thermometer scale. If they are not maintained temperatures, they may differ (a) as to the particular temperatures with which the cul- tures were started, ( b ) as to the direction of variation during a given period (whether the temperature became higher or lower with time), and (c) as to the time rate of temperature variation. It is clear that this rate of change in temperature may itself be constant, or may vary throughout a given time period. When only maintained temperatures are to be considered, as in the present study, the only differences to be dealt with between any two cultures are those of degree or intensity as measured in terms of centigrade, etc., degrees. (4) Radiation conditions, involving the various groups of wave- lengths of radiation and the relative and absolute intensities of each group. Up to the present time most biological discussion has ignored most of the wave-lengths of radiation excepting the small group com- monly designated as light. Since the cultures of the present study were uniformly carried out in darkness and in chambers around which a mass of water was continuously circulating, radiation conditions will not require attention here. (5) The duration condition, implying the length of time during which the organism is subjected to the other conditions. From one point of view every condition has a duration factor, but when most of the conditions are maintained, or practically so, the duration factor is common to all, and we may regard it as a separate condition. More- over, as far as the presenl investigation is concerned, this duration 1921] Fawcett: Temperature Relations of Growth in Certain Parasitic Fungi 189 condition may be divided into two parts, each one of which may be considered as a separate condition: (a) the actual length of any interval of time considered, and (b) the location of this time interval in the entire culture period reckoned from its beginning. If the time period be always reckoned from the beginning, the second aspect of the duration condition may be neglected and only the length need be considered, as is done in the first part of the discussion of the present investigation. When, however, changes in rate of growth are studied with reference to the age of the culture, the location of the observation period within the culture period, as well as its length, come to be important, and these may be regarded as two different duration con- ditions, as is done in the latter part of the discussion to follow. To illustrate all these conditions in detail, a certain fungus, Pythi- acystis (condition 1) is surrounded by nutrient agar (condition 2), and subjected to a maintained temperature of 23° C. (condition 3), in darkness (condition 4), and it exhibits an average growth rate of 8.0 mm. per day for a period of three days after inoculation (con- dition 5). In the example just given, the observation period begins with the beginning of the culture period. An observation period, however, need not begin with the beginning of the culture period and may not be continued to the end of the culture period. Thus two observation periods may be alike in length, say two days, but they may still have entirely different relations to the beginning of the culture period, so as to constitute, in a sense, distinct duration conditions. Of course, this state of affairs is to be related to changes that go on within the organism, with the lapse of time, even though all physical and chem- ical environmental conditions are assumed to be maintained without alteration. The organism is generally not exactly the same at the moment of inoculation of a culture as it is a day later, four days later, etc. This consideration introduces one of the most perplexing features of the whole study of maintained temperatures as related to vital processes, and considerable attention will be devoted to it in the later sections of this paper. From the points mentioned in the preceding paragraphs it is, of course, clear that no very definite knowledge of the various environ- mental influences, as they act to control the physiological processes of any organism, may be expected from physiological tests in which any of the effective conditions are allowed either to vary or to differ in unknown ways. As long as the conditions differ only in known 190 University of California Publications in Agricultural Sciences [Vol. 4 ways from one culture to another, or as long as they vary only in known ways in the same culture, there is hope of advancing our knowledge of environmental influences. In order that the inoculum for each series should be as similar as possible to that of any other series, the four species were kept in the dark in stock tube cultures with ordinary corn-meal agar and at a temperature ranging from about 16° to 18° C. From these primary stock cultures inoculations were made at frequent intervals, on agar plates of the same kind of medium and kept at the above temperature range. These plates formed the secondary stock cultures. The mar- ginal region of a mycelial disk of a secondary stock culture (about five days after inoculation) furnished material for inoculating the experi- mental cultures of that fungus. The inocula for each species were fairly similar, therefore, with respect to parentage, age, vegetative activity, etc. Practically the same amount of inoculating material was always transferred to each experimental culture. It is conse- quently safe to suppose that all experimental cultures of the same fungus were practically alike at the beginning, no matter when they were made. The four fungi used furnish, for the whole study, four different sets of initial complexes of internal genetic conditions. Pro- gressive variation in the internal conditions of the fungus is one of the features taken into consideration and will receive attention in later sections. Although several different media were employed in certain aspects of the experimentation, only one (corn-meal agar) will be considered in the present paper. Special precautions were taken to have this medium as nearly as possible the same at the beginning of all cultures, no matter at what time they were started. The consistency of results obtained by repetition showed that this aim was practically attained. It was also shown by special tests on one of the fungi (Pythiacystis) that the unoccupied medium did not considerably alter during the period of any single culture. It therefore seems safe to suppose that the medium was always the same at the beginning of all cultures, and also that the medium remained practically unaltered during the pro- gress of any culture, at least until it was reached and passed by the enlarging weft of hyphae. Unquestionably the medium occupied by the mycelial disk suffered alterations in composition, but it was not apparenl that such changes influenced the rate of growth of marginal hyphae. 1921] Fawcett: Temperature Relations of Growth in Certain Parasitic Fungi 191 Since the elongating hyphae lie largely near the aerial surface of the agar plate, while some are partially in contact with the air space above, it is well to consider the aerial environmental conditions, as well as those within the agar medium itself. Aside from temperature, the air conditions in the culture dishes above the agar were sensibly the same in all cultures at the start, except that the pressure of water vapor was, of course, different for cultures exposed to different tem- peratures. Since the air space of the culture dish was always practi- cally saturated with water vapor, the pressure of the water vapor would nearly follow the equilibrium vapor pressure of water at the various temperatures. The unsealed dishes allowed a slow escape of water vapor and, consequently, a slow evaporation from the agar sur- faces during the culture period, the rate of water loss being somewhat greater at higher than at lower temperatures. Different maintained temperatures, therefore, were automatically accompanied by slightly different rates of variation in the water content of the yet unoccupied medium. Such variation may be neglected in this case, however, since it was shown by special tests that variations even larger than those that actually occurred in the experimental cultures had no appreciable influence on the rates of growth of the fungi. As has been said, the temperature conditions were always artifi- cially maintained, with a very small degree of fluctuation throughout any given culture period. The radiation conditions are regarded as nonexistent in these tests. Light (and radiation of still shorter wave- lengths) was always excluded and the stirring apparatus operated to prevent any one-sided action of long-wave radiation upon the cultures. The duration condition offers no particular difficulty in such work as this. Since the experimental cultures are all regarded as alike at the time of inoculation, the duration conditions may be regarded as beginning to operate from the beginning of this culture period, the time of inoculation being considered as zero time. If either the length of the culture period or the time between observations for any culture is different from that for another, this fact is, of course, quantitatively shown by the inoculation intervals between successive observations. From the preceding discussion it will be observed first that the research at hand was so planned as to involve the actual or assumed control, during the respective culture periods, of all the groups of effective conditions except internal ones, and second, that the only conditions considered as effectively different from culture to culture 192 University of California Publications in Agricultural Sciences [Vol.4 are: (1) the nature of the fungus used (initial internal conditions), (2) the rate and direction of physiological alteration within the organism, and (3) maintained temperature. The following scheme may serve to show the sorts of terms that enter into the interpretative comparisons that may be made for an investigation of this kind : A. COMPARISON OF CULTUEES OF THE SAME FUNGUS I. Internal conditions (genetic constitution and physiological state of fungus). 1. Initial conditions, alike for all cultures of same fungus. 2. Direction and rate of physiological alteration during culture period, may be different from one set of cultures to another. This alteration always to be stated as within the limits prescribed by: (a) The initial internal conditions, and (b) The external conditions. II. External conditions (environment). 1. Initial environmental conditions, except temperature, considered alike for all cultures of same fungus. 2. Initial temperature conditions different from one set of cultures to another set. 3. All environmental conditions assumed to be maintained at their initial values throughout the culture periods. B. COMPARISON OF CULTURES OF DIFFERENT FUNGI I. Internal conditions (genetic constitution and physiological state of fungus). 1. Initial internal conditions different for four different fungi. (a) As to genetic constitution (whose capabilities are roughly indi- cated by taxonomic description). (b) As to physiological state, because of different reaction of different fungi to essentially identical preliminary environmental conditions. 2. Direction and rate of physiological alteration during culture period, may be different from culture to culture. This variation always to be stated as within the given limits set by the initial internal conditions and the external conditions, as above. II. External conditions (environment). 1. Initial environmental conditions, except temperature, considered alike for all cultures. 2. Initial temperature conditions either alike or different from culture to culture. 3. All environmental conditions assumed to be maintained at their initial values throughout the culture periods. The study here reported is thus seen to comprise five different studies. The influence of maintained temperatures on the growth rate of i'i\c\\ of four fungi was measured, under the given non-temperature conditions, which are considered as initially alike, and under the given 1921 ] Fawcett: Temperature Belations of Growth in Certain Parasitic Fungi 193 initial internal conditions also considered as alike for all cultures of the same fungus. The fifth study comprises the comparison of the four fungi as to their temperature relations under the given set of non-temperature, external conditions. The investigation reported in the present paper was carried out during the period between October, 1916, and June, 1918, in the labor- atory of Plant Physiology of the Johns Hopkins University. The author wishes to express his thanks to Dr. H. .J. Webber and the University of California for arrangements that made it possible for him to be absent from the Citrus Experiment Station during the period just named. He also wishes to record his appreciation of the privileges and facilities accorded him by the Johns Hopkins University, including a Johnston scholarship in that institution. Finally, he desires to acknowledge his indebtedness to Professor B. E. Livingston and to Dr. H. E. Pulling, of the laboratory of Plant Physiology of the Johns Hopkins University, for much valued aid and criticism in connection with the planning and carrying out of the experimental part of this study and in the interpretation and presentation of the results. METHODS The Culture Medium The corn-meal agar employed in these experiments was prepared according to the procedure described by Shear and Wood (1912), using 20 gm. of corn meal and 15 gm. of agar shreds for each liter of water. More water was added before the final filtering, so that there was one liter of the medium for each 20 gm. of corn meal originally used. The exact chemical and physical nature of such a culture medium can not, of course, be stated. It undoubtedly contains a large number of inorganic salts and a still larger number of organic compounds, all in rather low concentration. It also contains various substances in a state of suspension, and, since it has more or less the nature of a gel, there is no marked tendency for these to precipitate out. Since the time available for this study was limited, it was decided to make no attempt to devise a nutrient medium of known composition or even to find out what any of the media commonly employed by mycologists 194 University of California Publications in Agricultural Sciences [Vol. 4 may contain. In order to be able to proceed immediately to the prob- lem of temperature influence, the whole matter of nutritional condi- tions — a very important one in itself — was ignored. All that was done in this connection was to be sure that the medium employed would support what appeared to be excellent growth of all four fungi, and to take precautions so that practically the same medium might always be used throughout the entire study. Since corn-meal agar is an infusion of corn meal and agar-agar shreds, both of them ex- ceedingly complicated, unknown, and variable materials, it was feared that different samples of the medium might be very different. And an attempt was made to avoid this danger by preparing enough medium at the beginning for the entire investigation, mixing it thoroughly in a single container and then preserving it in bottles for future use. That the infusion itself might alter with time was, of course, possible, but various repetitions of the experiments indicated clearly that such alteration — if it occurred — was not of such nature and magnitude as to alter the growth of the fungi when other conditions were the same. Since the amount of medium necessary for the entire study could not well be prepared in a single day, about eight liters *were made at a time, until about 48 liters were ready. The entire amount was then liquefied by heat, placed in a 20-gallon earthenware vessel and thor- oughly mixed, after which it was poured into liter bottles. The mouths of the bottles were then plugged with cotton in the usual way and the bottled medium was immediately subjected to a temperature of 115° C. for 15 minutes. This heating was repeated on the two following days, after which the tops of the cotton plugs were flamed and covered with several thicknesses of paraffined paper, tied tightly around the bottle neck. The bottles of medium were stored in dark- ness at a temperature of about 18° C. "When a lot of cultures were to be made the required number of bottles of medium were removed from storage, brought into the liquid condition by heating in the auto- clave, and used in the ordinary way for pouring the plates. About 15 c.c. of medium was used in each culture dish. It was found by test that this amount might be increased or diminished by as much as 3 c.c. or more without perceptibly influencing the growth of the fungi. 1921] Faircett : Temperature 'Relations of Growth in Certain Parasitic Fungi 195 STOCK CULTUEES The original sources of the fungus materials were as follows: Pythiacystis citrophthora, isolated by the author from the diseased bark of a lemon tree suffering from gummosis, at Whittier, California, in August, 1915 ; Phytophthora terrestria, also isolated by the author from the diseased bark of a citrus tree suffering from mal di gomma, at Palmetto, Florida, in January, 1914; Diplodia natalensis, isolated (by Mr. J. M. Rogers) from a citrus tree in the Isle of Pines, W. L, and received by the writer in the fall of 1916 ; and Phomopsis citri, received from H. E. Stevens, from Florida, in October, 1916. All four fungi had been cultivated under the same conditions, in tubes of corn-meal agar, in darkness at from 16° to 20° C, for at least nine months previous to the beginning of the experiment. During that time transfers to new tubes of media had been made at intervals of about six or eight weeks. These cultures may be termed the primary stock cultures in this study. The four fungi, therefore, had each been subjected for at least nine months, to the same environmental condi- tions. They had also been grown in the same kind of medium as that into which they were now to be introduced for the temperature ex- periments. THE EXPEEIMENTAL CULTUEES Approximately five days before the starting of each series of ex- periments several cultures of each fungus were started, by transferring small bits of medium containing mycelium from a primary stock cul- ture to the center of the agar plates. These were the secondary stock cultures, and were kept in darkness with a temperature of about 20° C. for about five days previous to the making of the experimental cultures. Little plugs or disks were cut out of the agar plate just behind the advancing margin of the circular growth area of one of these five-day secondary stock cultures. The disks were 2.5 mm. in diameter and about 1.5 mm. thick. They were cut out by means of a cylindrical platinum cutting device like that described by Keitt (1915) . Each disk was lifted on the flattened end of a platinum needle and was then inverted and placed centrally upon the surface of a new agar plate. The petri dishes used were 10 cm. in diameter and 1 cm. deep ; each contained approximately 15 c.c. of corn-meal agar, which had been poured hot and allowed to solidify before the transfers were made. After inoculation the experimental cultures were divided into 196 University of California Publications in Agricultural Sciences [Vol.4 seven similar groups, and one of these groups was placed in each of the seven chambers of the temperature-control apparatus. The cul- tures of any given species always occupied the same relative position in all the chambers and in all the series. This precaution was ob- served so that any possible difference in temperature between the upper and lower portions of the chamber would not render the mea- surements of the different lots of the same species incomparable. But such differences in temperature between different parts of any one of the seven chambers proved to be slight (less than 0.5° C. between the top and bottom of a chamber). The cultures of Pythiacystis citroph- thora and Phytophthora terrestria occupied a position, on the rack in the chamber, at nearly the same level as the bulb of the thermometer from which the temperature records were taken. The cultures of Phomopsis citri were about 15 cm. below and those of Diplodia nata- lensis were about 15 cm. above the thermometer bulb in each case. Observations on Growth As the hyphae grew out in all directions from the center of the plate a rounded mat or mycelial disk was formed on or near the surface of the medium. This disk remained practically circular, as it enlarged, for both Pythiacystis citroplithora and Phomopsis citri, forming a nearly perfect circle at all stages of enlargement. The mycelial disks of Diplodia natalensis and Phytophthora terrestria were often slightly irregular in form or rather evenly lobed, especially at the higher temperatures used. No irregularities in growth, such as bring about zonation in mycelial mats of many fungi, were observed in any of the cultures with maintained temperatures. In special tests, however, in which the fungi were grown for a certain time in one temperature and then transferred and grown in a markedly different temperature, such zonation was pronounced. Observations were made at daily intervals for a culture period of from four to six days. The chief matter of observation was the mean diameter of the disk, which was obtained by averaging two measure- ments of different diameters, selected to represent the disk as a whole. When the margin of the enlarging disk was clear and definite these measurements were made by menus of a thin millimeter scale applied on the bottom of the Petri disli outside. In other cases the Petri dishes were inverted and the length of the mycelial outgrowth was measured by means of a microscope with an ocular micrometer. 1921] Faivcett: Temperature Eelations of Growth in Certain Parasitic Fungi 197 Measurements with the millimeter scale were read to within 0.5 mm. This was deemed sufficiently precise for the purpose. Since none of these fungi produced anything but vegetative hyphae during the culture periods employed and the growth activities were not complicated by the formation of any reproductive bodies, these measurements of the mycelial disks and the daily increments of disk enlargement derived from them appear to furnish as satisfactory a criterion of physiological activity in general as might be found. The only other criterion for such comparisons as these, and that hitherto generally used by physiological workers, is the rate of production of mycelium measured on the basis of dry weight ; the employment of this criterion offers great practical difficulty when agar medium and short culture periods are used. At the time of observations, each chamber was opened for a frac- tion of a minute to remove just one group of cultures, all the cultures being alike. These dishes were immediately wrapped in cotton bat- ting, to exclude light and prevent very rapid temperature changes. Each dish was removed from the wrapping for a minute or less, while the observations were made, and was then returned to the wrapping. After all the cultures of the group had been observed the entire group was replaced in its temperature chamber and another group was taken out for observation. The time required for the entire operation of removing, measuring, and replacing a group of 10 cultures averaged less than 10 minutes. The opening of the chambers for removing and replacing the groups of cultures had very little effect upon the temperature of the chamber itself. The thermographs in the chambers usually showed the occur- rence of this series of momentary openings by a slight rise or fall of the pen tracing, producing short vertical lines, each representing a degree or less of practically momentary alteration in the temperature of the chamber. Several tests were carried out to determine whether the daily dis- turbance of the maintained temperature, caused by removing the cultures for observation, might exert any appreciable influence on the growth of the fungi. These tests showed that the amount of growth observed after several days was practically the same whether the cul- tures had been left in the chamber for the whole period or had been removed for daily observation in the regular way. These daily dis- turbances of the maintained temperature are considered negligible in the present study. 198 University of California Publications in Agricultural Sciences [Vol. 4 The Maintained Temperature Chambers The various temperatures employed in the experiments here consid- ered were maintained by means of an apparatus described by Livings- ton and Fawcett (1920) . This apparatus consisted essentially of seven experiment chambers about 33 cm. in diameter and 43 cm. deep, each one surrounded below and at the sides by a large mass of water. Light was excluded. The air of the chamber and the water around it were kept in constant circulation by mechanical stirrers. The seven cham- bers were built in a row, with the water jacket of each in contact with that of the next, except for a sheet-iron partition which kept the several masses of water entirely separate. A tank of mechanically stirred water having automatic temperature control was added at either end of the series of experiment chambers and the entire apparatus was well insulated from the surroundings. The two ends of the series were adjusted for any two desired temperatures. Between these, after equilibrium had been established, lay the maintained temper- atures to be studied, each of which differed from the next by a certain amount, depending on the position of the chamber in the series. The daily fluctuations in any chamber were only rarely more than 0.5° C. Access to the chambers was had from above, and, of course, the main- tained temperatures of the cultures were slightly disturbed by opening for observations, as has been noted. STRUCTURAL DIFFERENCES RELATED TO TEMPERATURE Microscopic observation of the fungus hyphae near the margin of the mycelial disk was made occasionally, at the time of measuring. Since no spores were produced in any of the experimental cultures in the time here recorded, vegetative growth alone can be considered. The only structural differences observed between different cultures of the same fungus consisted in more or less marked peculiarities in cultures that had been exposed to very high or very low temperatures. Within a range of maintained temperatures extending downward about 12 degrees or 15 degrees centigrade below a temperature slightly above the optimum temperature for enlargement no influence of temperature on structure was noticeable. Within this range the hyphae were of regular and simple form and the branching was regular. 1921] Fawcett: Temperature Relations of Growth in Certain Parasitic Fungi 199 With temperatures near the maximum point at which any enlarge- ment would occur, the outgrowing hyphae were of irregular shape, bent and twisted, with occasional swellings and usually with apical enlargements. The hyphal diameter was usually much larger than that of hyphae with more favorable temperatures for enlargement, and these thicker irregular hyphae showed contents that appeared dark colored and granular, in contrast to the smooth, clear appearance of the cell contents for cultures with the more favorable temperatures for enlargement. The granulation was frequently pronounced and refraction was such as to give the whole hypha a very dense appearance. With the lowest maintained temperature tested (7.5° C.) the hyphal diameter for Pythiacystis and Phytophthora was much greater than with temperatures within the favorable temperature range. The hyphal contents for these low-temperature cultures was only slightly granular. The low-temperature filaments of Pythiacystis were much swollen and were divided into many short, thick, club-shaped branches ; those of Phytophthora showed a series of swollen joints. These low- temperature cultures of Phomopsis showed filaments somewhat smaller in diameter, with less frequent branching, than those of cultures grown with favorable temperatures for rapid enlargement. In Diplodia the diameters of the hyphae were also somewhat smaller at 7.5° C. than at more favorable temperatures for enlargement. THE EXPERIMENTAL DATA As previously noted, the temperature apparatus contained a bat- tery of seven chambers, so that seven different maintained temperatures could be employed at one time for a given series of cultures. After preliminary tests the apparatus was so adjusted as to give the main- tained temperatures that promised to be most useful. Two diameters of each mycelial disk were measured at the end of each 24-hour period during the experiment. The average of these two measurements was taken to represent the average diameter for a given culture at the time of measurement. From this average diameter at the end of the first 24-hour period the diameter of the transplanted cutting (2.5 mm.) was subtracted and the remainder was taken as the value for the increment of enlargement for this first observation period. The difference between the average measurement for the end of the first and that for the end of the second 24-hour period represented the 200 University of California Publications in Agricultural Sciences [Vol. 4 increment of enlargement for the second 24-hour period. Increments for the subsequent periods were obtained in a similar way. All the culture averages for a group of like cultures in the same chamber were finally averaged to give the group mean. These group means were taken as relative measures of the rates of radial enlargement for the different fungi, different time periods, and different maintained temperatures. In tables I-IV are presented the group means for the four fungi, for the different maintained temperatures, and for the different 24- hour observation periods, as well as for the first 2-day and the first 3-day periods. In cases where a considerable number of data are at hand for culture periods longer than three days the group means are given for the first 4-day, first 5-day, etc., period after inoculation. The number of cultures employed in the derivation of these group means is also indicated in each case in parentheses. The rates given in tables I-IV do not always represent single series. In many cases the same maintained temperature was tested at different times for the same fungus, and all the measurements available for any fungus and tem- perature have been used in deriving the mean rate for that fungus and temperature, without reference to the particular series of tests in which any group of measurements may have occurred. Also, the data in any vertical column of these tables, representing the enlarge- ment rates for the respective maintained temperatures indicated in the first column, do not all represent the same series. Thus a test for a given maintained temperature may have been made in July and repeated in August and the two sets of data com- bined for the particular fungus and temperature in question. Many repetitions of this sort were made, involving the same maintained temperature in different experimental series, and the growth rates of similar cultures in different series usually agreed as closely as did those of duplicate cultures of the same series. This indicated that the initial fungus materials and nutrient medium used did not ap- preciably alter during the period of the investigation. It will be noticed that the number of cultures (shown in parentheses) after each rate in the first part of the tables usually decreases after the second or third consecutive exposure period. This is due to the fact that some of the cultures in each temperature chamber were trans- ferred to other chambers with a different temperature after the second or third day, and the subsequent growth increments measured. These data are intended for a later paper and are not included in the present discussion. 1921] Faivcett: Temperature Belations of Growth in Certain Parasitic Fungi 201 CM 00 oo t- : cm : iH : : oo : : oo : cm co ■ t^ • 00 ' OS "£ ci' O o CO 50 00 X ^ N >* .Jj^'S to (O H OS © CO r-J CO CM eo io" «o t>" oo' os" oi os fem : io cm co oo co cm oo ! ffl O O N •* H tJ( : os' OS* 00 t-" CO r-1 O w Fh ^ -J O ^3 £ .2 W d Eh rt a s t =3.2 £ Tj "B corHcot^xososos OS OS X t^ rH rH CO COCO COCO CO COCO IO CO iH rH lO CM LO iH O0 CO r-J r-J CO* co' go' oo' 00* oo os' os' os' 00* t>" IO* iH «!cjo m m m w io in io in w w .^T3"n CM CO rH CO CM CO 00 t>- 00 rH O CO r-J IO OS 00 rH CM CM "^ co'co*i>'t>'t>"t>'o6os'osodt>'io"cM* 05 .« fa -d w « d a 5 3^ o.2 ^ t>- : CO rH in : in GC os : os o in cd COmrHXrHrHOmO rH rH r-1 in rH x in in rH cm cm co : co' q « in ■* h in t> in q i-H* H* co' GO* os' os' OS* o o o co iq co io o o d os' o* co' o o j o - CD # — > ?H -1^ 5 3^ OC b- -H o -* rH c IO -j IO -t X t^ CO -v OJ CM 00 rH X Z ctS rH H rH rH s _^ w 3X m s a T3 d o ' i Eul ^ p< " CM 00 X CO iq CO iq 00* X oi OS OS iq d 04 d > OS Os' X o x" iq rH o o O o O o a .1-1 i— i rH u fe — 1 p -rj 3^ — o. 00 O) 00 CO H" CM r- h- CM X o o OS OS GO 1 — CM o rH o o rH rH rH i-H rH rH i— 1 rH rH rH I — rH d 5r'r ^— ' ^— ' v — ' N — ' "— ' v «^' N — ' v — ' ^>— ' y ^_^ ^^^ ^— ' v -— ' ^—s s — ' v — ' y ^^s v — ' s ^-' ■> ^s CO CM X — o OS a; OCi r - CM o CM c o s §J-s ^ i— 1 rH rH rH rH rH rH rH rH 1 — rH n ^2 ^5s rH CM IO CO X o IO ~ o o- IO CO OS rH IO t> o c o o o c O w 2 rH rH r^ h- OS os c 3 a O o X X in d rH rH r-\ rH CM £ to o ,° C 03 00 ci oa CO rH r^ o r^ CM X o o OS OS X r— CM o C] O rH rH i-H rH rH rH rH rH rH c rH c5 ^ o iq co o i>; cq rH hj t-; o co co co ocoososiqiqoooo cm" cm' h" rt* in co' in* in* o* t>* 06 i>* t-* co* tjh 03 cs v -' k^ m in in in 10 iq o in in o cq in iqooooiqiqotqoo qJ bh t>* CO* IO* X* oi tH* CO* CO rH LO* t>" t>* ai d rH CM* H* rH IO* CO CO O IO iHrHrHCMOlOlCMCMCMCM CMCOCOCOCOCOCOCOCOrHrH 202 University of California Publications in Agricultural Sciences [Vol.4 $2* CO 00 : co Tfl O : o cs : as fc»g. CO ■ t>- i>- ' OS &S t^ 00 00 CO CD ^ CO (M !:■- « iooto©!0«Doi co oq t-- : oq 1 41 'WTtH©t>C0010iHHH ' Oq ° ft rH rH rH ' © t^ Oq 01 Oq IO IO IO IO ■g OJ rH 00 00 CO CO CO N tJH Oq_ OS £ ' N M W l> 00 OJ 05 H H H Pi — i — i , — i 03 lo iq CO m b"o O] CO 5D © © CO O © COCO CO £,§■£ H N CO O l> 00 !D CO « (O « C| 00 O ^ S ec S ' H CO ic © t> oo oi d 6 H OO CO ■s ^"S oo to io io w m io io io io u3-~ O W H ■* 00 M CO H «D •* a O) O l> N S cq "W ' rl N il W td N M ffi 0> a N ^i s § J CD W H . CD 02 CD B 5? £5 OJ ft a o a w x S-O IO IO -w O O -w ^_^ CM ^ IO COO WWWWWWWWWWW rH OQ co co ^ "*? g oo t|h s h h x q oo a ■* o ^ ^ P " t}" ■* OS OS OS* rH* ©" © tH tH o o o o X. JH T) h- t- H- o OS H- CO h7 o oq H? rH oq 00 00 c rH rH ,r: 2 "« — ' ^— ' v — / '-— ' v — ' v — ' v ' ^-* v — ' ■> — ' V-' "»— ' s — ' ^s v — ' z -f 1) t^ 01 TjH CI o X TH o CI o © IO oq o o CO IO X as as rH rH re CO ^ oq l, oooooqosoooosocqoorHoqorHOO Tj 3-d rHrHrH rHrH rHrHrHrH 5-i o O v — " v — ' s — ' Ss — ' s — ' ^^ ^-^ s -- / v — ' s —' s — ' s — ' ^^ s ~"' s — ' y ~ ' N ~'' 3^'E rH Eh ^ p, oq co co Ttj co oq co t>- co rH t^ © cq co o o o Oq' IO* CO* 00* OS* rH rH CO CO* CO* rH Oq* rH rH rH rH rH rH _. u oooooqosoooaso^— sOOrHoqooqoo 12 pTj rHrH rH rH H O] rH rH rHrH |0,2 — ' ^ WWWWWWWWWWWW WW j^h p, p-j © oq cq r-j cq iq © oq rH cq cq oq iq cq o o * oq" cd co* od os* o th* co co* co" oo' 'cH rH rH rH rH rH *2rtf oooooqosoooasooqoorHoqooqoo ■^QOrHrH r-\ rH r-{ rH rH rHrH Ti^oOrHiocqooqcqiooococoooooooo ' rH rH* Oq" CO H* H* IO* IO* kO* CO* t>* H^' rH* oe g . iq iq iq iq iq o iq © o o o iq »q © iq © © C S 5* t>-' CO >d GO* rH* CO* H* !>" ©" rH oi TlH io* ©' co' ©" kO '3 2"^ rHiHrHOlOaOqOJCOCOCOCOCOCOCOH^T^ r-% ^ 1921] Fawcett : Temperature Relations of Growth in Certain Parasitic Fungi 203 CO : oo : co o co : io oo : (m co IO ' (O t> N ' UO rH •£ >^ 00 CM tH CM .^.2 io «o h co a g . S ' cm' co' n" th" CM CM CM ^ o iq oq io id co' cd co' i>" g£.2 fe^ s t~ io io io cm t- t-~ io t>- : io t)h t-j o o to oq h n ih io cm : as CM* CO tJh tJ* tjh" id id co' co' t>" : ^" cc c$ «2 o SI of J 3 (3 j g o ^ "g f?"o CO CO CO CO CO CO COCO CO CD CO ™r§-g co oq oq iq co iq as iq t>; oq oq as co o ^ S m S ' H N CO* "#" rj" rjn id id id CO* rt" -*" rH ^^ IO loioioioioioioio «.2 ooiOT-Host>-oocoascscMco H N O tO HNWMCO^^^lOtO^NH ^ CO CO ~ = 2 O IO oo' oo" CO 00 co' i-i fe4 « a © iq iq co os ih tj" co' id id O T}( ■* H ^ tJh os © © iq co' co' oo" oo" oo' ^ oq o id r-5 "2 3 "2 oo oo ^HH o ■HH 01 r ^ OS I— I ^ orT CM ^H CM I— 1 r— o ' a; ^ci a OS o cc -* IO 00 o IO IO IO IO t^ CO o O CO CO IO IO w SC cc t> X 00 CD CO & .a W cu -2 co 'j cu a "S ©©O0CMa0-rH©CMO0rHCM H< % CO n a co to co in to oq q s cm © © iq t>- cm cm o o cm' tj! tih" id id co' co' t>" t>° oo' co' t-' r-I (* J b3 M O d w T^ fH Ovl a; — £ ~ - 00 CM CO © © CM* CO* Tl* id id co' CO* CO* l>" 00* IO* CM* r-1 += 3^3 OOOOCMOOCDOOOrHrHOOrHOCMOOrHCM m q, O t- I r— I rH r-\ t—\ t— I pL| ^ ^ ,_{ w ft o t>. o o r^ iq iq cq co iq cq iq cq oq os o o r-1 rH CM* CM' CM* CO* CO* CO* TJH* CM* CM* gs lOlOlOLOlOlOOOlOlOlOlOOOOlOlO NCOIOGOOlHNCO^tON O rH CM t^ IQ 0]CMCMCMCMCMCMCOCOCOCOCO 204 University of California Publications in Agricultural Sciences [Vol. 4 TABLE IV Mean 24-Hourly Diameter Increments (mm.) of Mycelial Disks for dlplodia natalensis (Numbers in parentheses indicate number of cultures from which mean was obtained.) Maintained temperature, deg. C. First 24-hour period Second 24-hour period Third 24-hour period 7.5 .OS ► (10) 1.9 (10) 2.1 (10) 13.5 8.0 (10) 11.0 (10) 10.0 (10) 15.5 10.1 ( 6) 13.7 ( 6) 14.2 ( 6) 18.5 13.0 (12) 17.5 (12) 18.5 (12) 19.5 15.5 ( 8) 20.5 ( 8) 18.5 ( 8) 21.5 17.0 ( 8) 21.5 ( 7) 23.5 ( 7) 23.0 18.2 (22) 24.0 (22) 23.7 (22y 25.0 23.0 (10) 27.2 (17) 26.0 (17) 27.5 25.9 (18) 31.0 (18) 26.1 (18) 29.5 27.7 ( 9) 29.3 ( 9) 24.5 ( 9) 30.0 30.0 (12) 29.8 (12) 23.6 (12) 31.0 29.3 ( 7) 25.5 ( 9) 21.5 ( 9) 32.5 27.5 ( 7) 25.0 ( 7) 21.1 ( 7) 34.0 26.0 ( 8) 21.5 ( 8) 18.0 ( 8) 35.5 14.5 (10) 5.0 (10) 0(10) 36.5 9.1 (15) 1.0 (15) 0(15) 40.0 1.5 (15) 0(15) 0(13) 41.0 .7 ( 8) 0( 8) 0( 8) 45.0 .2 (10) 0(10) 0(10) First 2-day period First 3-day period .97 1.35 9.5 9.66 11.9 12.66 15.25 16.33 18.0 18.16 19.25 20.66 21.1 21.96 25.1 25.4 28.45 27.66 28.5 27.16 29.9 27.8 27.4 25.43 26.25 24.53 23.75 21.83 9.75 6.5 5.05 3.36 .7 .5 .35 .23 .1 .06 DISCUSSION OF RESULTS General Considerations It is obvious from an examination of the data in tables I-IV that the magnitude of the mean rate of enlargement of mycelial disks (here expressed for convenience in terms of the diameter increment per time period of 24 hours) is influenced by the variations in at least three conditions for any one organism, namely, (1) the degree of maintained temperature, (2) the length of the time period considered in deriving the mean rates, and (3) the time relation of any given observation period to the beginning of the entire culture period. As has been pointed out, each number in the first column represents a given temperature nearly constantly maintained over the entire period indicated in 1lie tables. The diameter increments given in the re- maining columns may be considered as rates, expressed in millimeters per 24 hours or one day. In the first part of the tables the rates of 1921] Faivcett: Temperature Relations of Growth in Certain Parasitic Fungi 205 diameter increment (mm. per 24 hours) for any one temperature are for consecutive exposure periods, also of 24 hours in length, the con- secutive columns representing the manner in which the increment rates change from one 24-hour period to the next, etc., with the lapse of time. In this case each exposure period has a different time relation to the initial moment of exposure to the given temperature, i.e., each exposure period began where the preceding period terminated. In the second part of the table the consecutive columns show the mean daily increments (mm. per 24 hours) for exposure periods of different length (2 to 6 days), but each having the same time relation to the beginning of the culture period, the time period always beginning with the beginning of the culture period. The rates derived in the manner shown in the second part of the tables are here included in order to show the manner in which the relation between growth and temperature has been worked out in some of the previous investigations with plants in which minimum, optimum, and maximum temperatures for growth have been considered. It was in connection with the em- ployment of such time periods as these that Lehenbauer (1914) dis- cusses the growth-temperature relations for shoots of maize seedlings. It is readily seen from an examination of these tables that because of the influence of the time factor the old conception of a definite optimum temperature for growth of a given organism is inadequate. Blackman (1905) pointed out that the term "optimum temperature" as commonly used had no definite meaning. Lehenbauer, in order to make the term "optimum temperature" usable, defined it as that temperature at which there is best growth during a given time period. In this sense a process may have, not one, but a large number of tem- perature optima. Blackman states in connection with his discussion of carbon dioxide assimilation that the time factor is important only at higher temperatures, the higher the temperature the more rapid the falling off of the rate with time. A new definition of optimum temperature, based on this idea, has been proposed by Leitch (1916), namely, the highest temperature at which no time factor enters. Since the time factor may be operative at all temperatures at which growth is possible for some organisms, the optimum so defined would have no important meaning for such organisms. For convenience of dis- cussion, Lehenbauer 's definition will be followed in this paper. An added restriction, however, is to be placed on this definition when the growth rates for consecutive observation periods are to be considered. An examination of the first part of tables I-IV shows that in order 206 University of California Publications in Agricultural Sciences [Vol. 4 to define the optimum for such data not only must the length of the observation period be stated but the relation of that time period to the beginning of the culture period must also be given. Lehenbauer 's observation periods, from which his rates were derived, all had the same relation to the beginning of the culture period. Turning again to the first part of table I-IV, it is evident that there are three variables to be considered. The growth rate, expressed in millimeters per 24 hours; temperature, expressed in centigrade de- grees, and time, expressed in number of days from the beginning of the culture period. The relation between these three varying quan- tities can best be discussed for our purpose by means of graphs and the graphs used will be of three kinds : ( 1 ) those showing the relation between growth rate and temperature at fixed time periods, (2) those showing the relation between growth rate and the march of time from the beginning at given maintained temperatures of the culture, and (3) those showing the relation of the magnitude of the temperature coefficient (Q10) to the shifting of the 10-degree temperature intervals from which the coefficients are derived. The relations of these three variables (rate of growth, temperature, and time) could, of course, all be represented graphically together by means of lines on a drawing showing three dimensions, as is done by Rahn (1916) for rate of development of bacteria with temperature and time. While this is the most complete manner of showing the relation existing between these three variables, making clear at once the uselessness of considering any growth-temperature relation with- out reference to the influence of time, it is not so convenient for our present discussion as is the use of a number of simple graphs. The Growth-Temperature Graphs The growth-temperature graphs were constructed in the ordinary way. For the given fungus and observation period the mean 24-hour rates (first part, table I-IV) were plotted as ordinates and the indices of maintained temperature were plotted as abcissas. After the points were in place a smoothed graph was drawn in the regular manner. To illustrate this process of smoothing, the four graphs for the second 24-hour period after inoculation are shown together in figure I. The points shown on or near each smoothed graph represent the mean rates taken from the table. It is at once seen that they arrange them- selves in a very satisfactory manner as regards the smoothed graph, 1921] Fawcett : Temperature Relations of Growth in Certain Parasitic Fungi 207 i.e., that the process of smoothing introduces only very slight alter- ations from any of the values derived directly from observations. These four second-day graphs are representative of the others. All are shown (without the points, the values for which may, however, be obtained from tables I-IV) in figures 2-5, each figure presenting i \ / \ / \ / • \. / \ /• \ Temperature 24 26 28 30 32 Fig. 1. Smoothed growth-temperature graphs for the second 24-hour period for each of the four fungi employed. The points represent the actual increments as given in tables I-IV. Phythiacystis citrophthora Phytophtliora terrestria Diplodia vatalensis — Phomopsis citri the several smoothed graphs for a single fungus. These graphs repre- sent the growth-temperature relations for each one of the successive 24-hour observation periods (within the exposure period) for which adequate data were available. In general form and shape the growth-temperature graphs of the four fungi are much alike. Beginning with the lowest temperature tested, the graphs all rise gradually, being slightly concave upward 208 University of California Publications in Agricultural Sciences [Vol. 4 at first, but becoming decidedly convex upward as the graph maximum is approached. Beyond this maximum region the graphs descend rap- idly to the graph minimum (maximum temperature for growth). It is clear that the growth optimum always lies far above (to the right of) the middle of the total temperature range and that the upward slope of every graph is much less steep than the downward slope. In these general characteristics these graphs resemble those of Ed- gerton (1915) for the growth of Glomerella, those of Lehenbauer (1914) for the growth of maize seedlings, those of Leitch (1916) for the growth of roots of Pisum sativum, and those of most other students 2. Smoothed growth-temperature graphs for each of the first five 24-hour observation periods, for 'Pythiacystis. First Second Third Fourth - Fifth I'i: W 8 10 12 14 16 18 Temperature 24 26 28 30 32 34 36 3. Smoothed growth-temperature graphs for each of the first five 24-hour observation periods, for Pythophthora. First Second — Third Fourth Fifth 1921] Fawcett : Temperature Eelations of Growth in Certain Parasitic Fungi 209 of life-process-temperature relations based on short time and temper- ature intervals. The graphs published by Brooks and Cooley (1917) showing the relations of growth of a number of apple rot fungi to temperature for 5-degree intervals also suggest the same general type of curve. 5 2 24 26 28 30 6 R 10 12 14 16 18 Temperature Fig. 4. Smoothed growth-temperature graphs for each of the first five 24-hour observation periods, for Phomopsis. First Second : Third Fourth Fifth 10 12 14 16 18 20 22 Temperature 28 30 32 34 36 38 40 42 Fig. 5. Smoothed growth-temperature graphs for each of the first three 24-hour observation periods, for Diplodia. First - Second Third 210 University of California Publications in Agricultural Sciences [Vol. 4 Changes in the Growth-Temperature Eelations The four fungi all show very different growth-temperature graphs for the successive observation periods. For the same fungus the mean growth rate for any one of the successive 24-hour periods within the entire exposure period is generally not the same as that for any other 24-hour period. It follows from this that the growth-temperature graph for each organism alters its shape as we proceed from one observation period to another in the continuous series, as is clear from a superficial inspection of figures 2-5. This progressive change in the form of the growth-temperature graph, of course, represents a corre- sponding progressive change in the growth-temperature relation of the fungus, as time elapses after inoculation. Since the external con- ditions of these experiments are considered as not altering with time, this apparently gradual change in the growth-temperature relation must be evidence of internal physiological changes occurring in the organism. When the curves for the successive 24-hour periods for each fungus (figs. 2-5) are compared certain general features can be noted. For every fungus there is a shifting of the apparent maximum temper- ature for growth downward (to the left in the graphs) with each successive observation period. This shifting is much more pronounced between the first and second 24-hour periods than between any other two consecutive periods, except in case of Phytophthora. For Pythia- cystis the maximum shifts from about 36° for the first 24-hour period to about 31° for the fifth period; for Phytopthora the corresponding displacement is from about 38° to about 35° ; for Diplodia the maxi- mum temperature changes from about 46° for the first 24-hour period to about 35° for the third period. The maximum temperatures for Phomopsis are more uncertain. A similar displacement of the apparent temperature optimum (graph maximum) is shown for all the fungi excepting Phomopsis. The apparent optimum temperature for Pythiacystis shifts from about 27.5° for the first day to about 24° for the fifth day, the corresponding change for Phytophthora is from about 34° to about 28°, and for Diplodia the optimum is displaced from about 31° for the first day to about 27° for the third day. Aside from the shifting of the apparent maximum and optimum temperature values just considered it should be noted that a similar 1921] Fawcett : Temperature Relations of Growth in Certain Parasitic Fungi 211 displacement is evident for growth rates lying within a large part of the suboptimal region of the growth-temperature graphs for each fun- gus. Throughout a large portion of this suboptimal region the ordi- nate value for any given maintained temperature is greater for every observation period after the first than it is for the immediately pre- ceding period. This statement is true for Pythiacystis for the first five 24-hour periods after inoculation and for maintained temperatures up to 21° C. It is true for Phytopthora and Phomopsis for the first Hive observation periods for maintained temperatures up to 23.5° and 26° C. respectively. For Diplodia it is true for the first three 24 -hour periods and for maintained temperatures up to about 21° C. In much of the supraoptimal region, on the other hand, the value of any given ordinate value is usually less than that for the next preceding period. The result of these shiftings in the specific relations of growth rate to maintained temperature is that the growth-temperature graph for each successive observation period intersects the next preceding graph. The only apparent exception to this statement is for two of the graphs for Phomopsis, for the third and fourth 24-hour periods. These rela- tions to time are brought out more clearly in graphs of figures 8 and 9. Growth-Temperature Relations of Different Organisms Compared by Means of Graphs of Equal Height To compare the curvatures of different graphs it is convenient to express all the ordinate values of each in terms of thje maximum and to replot the graphs using the values thus derived. This treatment removes apparent differences in curvature due to differences in the magnitudes of the maximum ordinates. Such relative graphs, for the second 24-hour observation period for each fungus, are presented in figures 6 and 7. The upward and downward slopes of these four graphs are strictly comparable as to direction or angle, always with reference, not to actual growth rates in millimeters, but to relative growth rates, in terms of the corresponding maximum rate. Referring to figures 6 and 7, the relative degrees of steepness of the four graphs are nearly the same for the suboptimal region and the same is true for the supraoptimal region, except that the graph for Diplodia is here somewhat less steep than are the other three. While the actual values are here hidden, the relative values as com- pared with the maximum growth may be compared for any process. The four graphs differ considerably in other details, however, mainly 212 University of California Publications in Agricultural Sciences [Vol. 4 in regard to total temperature range and in regard to minimum, optimum, and maximum temperature values. Since all the graphs are brought to the same height by this treat- ment, the growth-temperature relations as a whole for one organism may be compared more directly with another irrespective of differ- ences in actual growth increments. By this means the form of the growth-temperature graphs of a rapidly growing fungus, for example, 1.0- *•*■ - ■N \ 0.9- 0.8- 0.7. / / / / / y \ \ \ \ 0.6- 0.5. / / / / \ \ 0.4. / / / / \ 0.3- / / / / \ 0.2. \ 0.1. 0,0 / S /--" ' V 6 fl 10 12 14 16 18 Temperature 24 26 28 30 32 34 36 38 Fig. 6. Growth-temperature graphs for Phythiacystis and Phytophthora for the second 24-hour period after inoculation, the ordinate values being expressed in terms of the corresponding maximum growth rate taken as unity in each case. Pythiacystis citrophthora Phytophthora terrestria 1.0 0.9 0.8 s /, /, //* \ 0.7. /? \ \ \ \ \ \ 0.6- V // V \ \ 0.5. '/ / \ \ \ \ \ \ 0.4 y ' 0.3 / / s 0.2. / / / V \ \ 0.1 / ,, \ \ 0.0 \ \ 18 Temperature 24 28 30 Fig. 7. Growth-temperature graphs for Phomopsis and Diplodia for the second 24-hour period after inoculation, the ordinate values being expressed in terms of the corresponding maximum growth rate as unity in each case. Diplodia natalensis I'liomopsis citri 1921] Fawcett : Temperature Belations of Growth in Certain Parasitic Fungi 213 may be compared directly with those of a slow-growing one, or, further- more, the rate of one kind of a process as influenced by temperature may be compared with the rate of any other process no matter how diverse or in what units each may be expressed. It is to be noted that if the entire graph for Phytophthora were moved to the left through 4 degrees of temperature, e.g., if all the rates for this fungus were plotted at temperatures 4 degrees lower, this graph would follow closely the curve for Pythiacystis, except that the first part of the downward slope is a little steeper for .Phy- tophthora. The difference between the two curves is, therefore, mainly one of location of the temperature range and the actual values of the increments. The extent of the temperature range, in number of de- grees, and the values of the increments in relation to each other and to that for the optimum are nearly the same for these two fungi. The growth-temperature curves for the other two fungi, Phomopsis and Diplodia, show the optimum temperature close to the same point, 27° and 28° C. respectively. The maximum temperatures for these two, however, appear to be about 33° for Phomopsis and 37° for Diplodia, a difference of 4 degrees. TABLE V Characteristics of the Graphs of Figures 6 and 7 for Bates Equal to or Greater Than 0.1 of the Maximal Rate Name of fungus Extent of range in Deg. C. Lower limit of range Deg. C. Upper limit of range Deg. C. Approximate optimum temp. Deg. C. Per cent of range below optimum temp. Pythiacystis 23.2 8.7 31.9 26.5 77.7 Phytophthora 24.1 12.0 36.1 31.5 80.5 Phomopsis 22.3 9.1 31.4 27.0 80.2 Diplodia 27.6 8.4 36.0 28.0 72.0 The total ranges of temperature can not be satisfactorily read from these graphs, although they are indicated in a general way. Since the interest of this discussion centers mainly about the forms of the graphs for the regions where the mean 24-hour rates are con- siderable, the range between the two temperatures giving a relative rate of one-tenth of the maximum rate may be considered instead of the total temperature range. This range is expressed as the length of the horizontal line lying between the two sides of the graph and having the constant ordinate 0.1. The graphs may be compared with respect to the magnitude of this partial range and also with respect to the relative position of the optimum temperature within this range. The main characteristics of the four graphs of figures 6 and 7 are shown in table V. 214 University of California Publications in Agricultural Sciences [Vol. 4 The extent of the temperature ranges for rates equal to or greater than 0.1 of the maximum rate for the four fungi are all considerably different; Diplodia has the greatest range (27.6°) and Phomopsis the smallest (22.3°). This partial temperature range has its lower limit lowest (8.4°) for Diplodia, a little higher for Pythiacystis (8.7°) and Phomopsis (9.1°), and highest for Phytophthora (12°). But the four fungi do not stand in this relation in regard to the upper limit of this range, for Phytophthora and Diplodia show about the same limit (36.1° and 36°), while Pythiacystis and Phomopsis also nearly agree in this respect (31° and 31.4°), the value for the last two being markedly lower than for the first two. Roughly speaking, it may be said that from about 70 to about 80 per cent of the temperature range here considered lies below the optimal temperature, with from about 30 to about 20 per cent lying above. Of course, such comparisons as these might be instituted between different fungi with reference to any other time period than the one here employed ; only the mean rates of enlargement for the second 24-hour period after inoculation are here considered. Relation of Growth Rate to the Time of Exposure It has been emphasized that the growth rates as measured in the work here reported differ not only for different fungi with the same maintained temperature and for different maintained temperatures with the same fungus, but also for different consecutive observation periods with the same fungus and the same maintained temperature, and it has also been pointed out that these last differences in growth rate must be regarded as due to progressive alterations in the internal conditions of the fungus as the culture becomes older. This influence of time on rate of growth is best shown by the set of graphs shown in figures 8 and 9. Here the ordinates are in terms of diameter increase, but the abcissas represent successive 24-hour periods after exposure to a given temperature. Each graph shows growth on successive days at a given maintained temperature. Inspection of tables I-IV and the graphs (figures 8 and 9) shows that the mean rate of enlargement alters with the age of the culture in three general ways. (1) For lower temperatures the rate increases throughout the culture period, the rate of increase being generally greatest for the first two days and much more gradual afterwards. (2) For a small range of higher temperatures the rate first increases 1921] Fawcett : Temperature Belations of Growth in Certain Parasitic Fungi 215 Days 1 Fig. 8. Graphs showing relation of rate of enlargement to age of culture, for Pythiacystis grown with various maintained temperatures. Ordinates are 24-hour increments and abscissas are number of days from moment of inoculation. Days Fig. 9. Graphs showing relation of rate of enlargement to age of culture, for Phytophthora grown with various maintained temperatures. 216 University of California Publications in Agricultural Sciences [Vol. 4 and then remains constant or oscillates till the end of the culture period. (3) For the highest temperatures with which growth pro- ceeds the rate decreases throughout the culture period, this decrease soon bringing the value of the growth rate to zero. These graphs which indicate roughly the change of rate with time at various maintained temperatures suggest that we may have here a family of curves, which if the data were sufficient would be capable of mathematical treatment. It may be seen from tables I to IV and graphs of figures 8 and 9 that in general the rates increased with the time at temperatures below about 20° C. For example, with Pythia- cystis the upper limit was about 19.5° C. and with Phythophthora it was about 21.5° for the 6 days tested. The growth rate in general decreased with time from the second day and thereafter at, and above, about 30° C. With Pythiacystis it was at or above 27.5° C. and with Pythophthora at or above 30° C. These same effects are apparent in some of the graphs showing the relation of temperature to the growth of apple rot fungi published by Brooks and Cooley (1917). That the increase or decrease in growth rate with lapse of time in the present study was not due to the accumulation of products in the yet unused portions of the medium was shown, at least for Pythia- cystis, by special tests in which fresh medium was placed at the ad- vancing edges of parts of the mycelial disks after they had grown for two days. The subsequent rate of advance of the mycelial disk upon the fresh medium at the various maintained temperatures was the same as that upon the remainder of the unoccupied medium that had been in the dishes from the start. 1921] Fawcett: Temperature Belations of Growth in Certain Parasitic Fungi 217 TEMPERATURE COEFFICIENTS Introductory. — A temperature coefficient as here considered may be denned as the ratio of the rate of a given process at any given temperature to the rate at another temperature at a fixed interval below the first temperature. While the temperature interval consid- ered may have any magnitude desired, it has been usual to consider in most chemical and physiological studies an interval of 10 degrees centigrade. In some investigations, where the rate considered alters greatly for small differences of maintained temperature, temperature coefficients for smaller intervals have been used. The temperature coefficient for the rate of any process for a dif- ference of 10 degrees is frequently represented by the symbol Q10. When derived directly from experimental data showing rates for tem- perature intervals of 10 degrees this coefficient is, of course, the quo- tient obtained by dividing the rate for the higher temperature by the rate for the lower. It is, however, frequently calculated from data at irregular temperature intervals. The values obtained from such data by the employment of the usual formulae appear to be reliable only when the coefficient is constant, or nearly so, over a considerable range of temperature. Where the coefficient is changing rapidly with successive intervals of temperature, as is the case in many physio- logical processes, such derived coefficients are apt to be misleading. Temperature coefficients for physiological processes have been much discussed in the literature. The statement occurs in numerous papers that the rate of a certain process under consideration does, or does not, obey the ' ' Van 't Hoff-Arrhenius rule ' ' for chemical-reaction veloc- ities with change in temperature, this rule being commonly under- stood to mean that the reaction velocity is continuously doubled or trebled for each rise of 10 degrees centigrade. It has been usual for some biologists and chemists to use this rule, as thus understood, to decide whether a given process should be regarded as chemical or physical in its nature. If the rate of the process in question be found to have a 10-degree temperature coefficient lying between 2 and 3, this is often considered an indication that the process dealt with is a chemical one or is controlled by chemical reactions. If, on the other hand, the 10-degree temperature coefficient proves to be much below 2, 218 University of California Publications in Agricultural Sciences [Vol. 4 this is taken as an indication of a physical reaction. In many dis- cussions of temperature influence on process rates it has been assumed that if this coefficient appears to be more or less nearly constant for several 10-degree ranges and has a magnitude between 2 and 3 for the particular ranges studied, then the process follows the Van 't Hoff- Arrhenius rule. If, on the other hand, the coefficient be not constant with higher and lower 10-degree ranges, but varies greatly above 3 or below 2, it is considered that the rule does not hold. This common, narrow interpretation of the Van't Hoff-Arrhenius rule appears to have been based on a general misconception of the Van't Hoff formula. It has been clearly pointed out by Stuart (1912) that Van't Hoff's formula itself makes clear that a constant coefficient is not implied even for chemical reactions and that Van't Hoff (1896) himself recog- nized that the coefficient values of different 10-degree ranges are by no means to be taken as constant ; they are generally smaller with higher 10-degree ranges and larger with lower ones. All that Van't Hoff did was to make a very rough generalization and to point out that in many chemical reactions within the temperature usually dealt with in experimental observations it was interesting to note that the temperature coefficient was apt to fall between 2 and 3. If it is not usual for the temperature coefficient to be constant for simple chemical reactions, it is not to be expected that it would be constant for physio- logical processes, where much more complex reactions take place. An examination of the experimental data on the relation of a large number of life-processes to temperature shows that the temperature coefficients for such processes generally tend to diminish in value from lower to higher ranges of temperature. 1 Kanitz (1905) appears to have been one of the first to regard this feature as an essential in the analysis of the relationship between rates of life-processes and maintained temperatures. Trautz and Volkmann (1908) gave considerable attention to this variation in the magnitudes of the temperature-coefficients for certain chemical processes, and Snyder (1911) pointed out that since it is the rule for the temperature coefficients of chemical reactions to vary with temperature such variation should be expected in physiological pro- cesses. Livingston (1916) noted that the temperature coefficient of the growth rates of maize seedlings, as determined by Lehenbauer (1914), might be regarded as following the Van't Hoff rule, as com- monly understood, only for a very limited range of temperatures. i Data for a large number of life-process rates, with citations of 363 papers, have been collected and compiled in a monograph by Kanitz (1915). 1921] Faivcett : Temperature Relations of Growth in Certain Parasitic Fungi 219 Leitch (1916), using short exposure periods, found that for the growth of Pisum sativum the temperature coefficient (Q10) decreased grad- ually from 8.25 for the interval between 0° and 10° C. to 2.2 between 18° and 28° C. The coefficients given by Lehenbauer (1914) for maize seedlings decrease from 6.56 for the 10-degree interval between 12° and 22° C. to 1.88 for the interval between 22° and 32° C. Rahn (1916), taking his data from experiments of Marshall Ward (1895) on the rate of development of Bacillus ramosus and B. coli, constructed some curves of the temperature coefficients, showing how these decrease rapidly from high values for low temperature intervals to low values for higher temperature intervals. Matthaei's (1905) data for the rate of carbon assimilation with temperature, from which Blackman de- rived the temperature coefficient of 2.1, show that the coefficient varied greatly even at the lower ranges, where the time factor was least oper- ative, from a high value for the lowest intervals to a much lower value for higher intervals. Moore's (1918) work with the influence of tem- perature on the rate of heart beat of Fundulus embryo shows that the temperature coefficient decreases progressively from 7.6 at the temperature interval 2.5° to 12.5° C. to 1.4 for the interval 25° to 35° C. Denny (1916), reviewing the monograph by Kanitz (1915) on temperature and life processes, says : ' ' Many processes in living organisms show a temperature coefficient approximately that of the Van't Hoff law (2 to 3) within certain limits. Among the plant processes for which this has been found to be the case the following may be mentioned: C0 2 assimilation (Mat- thaei) between 0° and 37° C. ; respiration of seedlings (Kuijper) be- tween 0° and 35° C. ; geotropic presentation time (Rutgers) between 5° and 25° C. ; phototropic presentation time (M. S. De Vries) be- tween 5° and 25° C. ; protoplasmic streaming in Elodea (Velton) be- tween 2.5° and 35° C. ; permeability of plant cells and tissue (Ryssel- berghe) between 0° and 30° C. ; intake of water by barley grains (Brown and Worley) between 3.8° and 34.6° C." An examination of the data in most of these cases will 'show that while the coefficients are of the order of magnitude required by the so-called "Van't Hoff rule," in a majority of cases there is (even within the limited range to which the rule is supposed to apply) a marked tendency for them to decrease from lower to higher intervals of temperature ; so that one may conclude that even these coefficients form part of a coefficient-temperature curve which if extended to the left would approach infinity and if extended to the right would arrive 220 University of California Publications in Agricultural Sciences [Vol. 4 at zero. The temperature coefficients given by Loeb and Chamberlain (1915) for the rate of segmentation of Arbacia decrease from 6 for a temperature interval between 8° and 18° C. to 2.5 between 15° and 25° C. Temperature Coefficients in the Present Study. — The growth-tem- perature relations of the four fungi used in the work here reported were studied in certain aspects by means of such temperature co- efficients as have just been considered. Since unexplained fluctuations in growth rate as related to temperature are to be neglected, it being desired to obtain information of a general nature only, the mean 24- hour rates for the various 24-hour observation periods ( given in tables I-IV) were not employed in calculating the coefficients. Instead of TABLE VI Mean 24-Hour Bates of Enlargement for Consecutive 1-Day Observation Periods, for Pythiacystis, as Determined by Measuring the Ordinates of the Smoothed Graphs of Figure 2 Temperature deg. C. First day mm. Second day mm. Third day mm. Fourth day mm. Fifth day mm. 8 .3 .8 .9 1.1 1.4 9 .5 1.2 1.4 1.6 2.0 10 .7 1.7 1.9 2.2 2.4 11 1.0 2.3 2.5 2.8 3.1 12 1.3 2.9 3.0 3.4 3.7 13 1.6 3.5 3.6 4.0 4.2 14 2.0 4.1 4.3 4.7 5.0 15 2.4 4.8 5.0 5.4 5.8 16 2.8 5.5 5.7 6.2 6.5 17 3.3 6.2 6.5 6.8 7.2 18 3.7 6.8 7.1 7.5 8.0 19 4.2 7.4 8.0 8.3 8.7 20 4.7 8.0 8.7 8.9 9.2 21 5.1 8.6 9.3 9.5 9.7 22 5.7 9.1 9.8 9.9 10.0 23 6.1 9.6 10.2 10.3 10.2 24 6.6 9.9 10.4 10.5 10.3 25 7.1 10.2 10.4 10.4 10.1 26 7.6 10.4 10.3 10.2 9.9 27 8.0 10.4 10.1 9.8 9.5 28 8.1 10.2 9.6 9.3 8.8 29 7.8 9.4 8.7 8.3 7.9 30 7.1 7.8 7.4 6.9 6.4 31 6.1 5.3 3.5 1.5 .5 32 4.8 .7 33 2.6 34 .9 35 .4 36 1921] Fawcett: Temperature Belations of Growth in Certain Parasitic Fungi 221 these, the length of the ordinate for each degree on each of the smoothed graphs of figures 2-5 were used. These ordinate values are presented in tables VI-IX. The arrangement and notation of the first parts of tables I-IV are here followed. From these ordinate values of the smoothed growth-temperature graphs were calculated temperature coefficients for every 10-degree interval by whole degrees, between the lowest and highest maintained temperatures tested for each of the consecutive 24-hour observation periods represented in tables VI-IX. To illustrate the method fol- lowed, the mean 24-hour growth rate for Pythiacystis for the first day after inoculation is seen to be 0.3 mm. for a maintained temper- ature of 8° and 3.7 mm. for a maintained temperature of 18° C. The TABLE VII Mean 24-Hour Eates of Enlargement for Consecutive 1-Day Observation Periods, for Phytophthora, as Determined by Measuring the Ordinates of the Smoothed Graphs of Figure 3 Temperature deg. C. First day mm. Second day mm. Third day mm. Fourth day mm. Fifth day mm. 8 .07 .25 .4 1.0 1.1 9 .15 .4 .9 1.5 1.6 10 .2 .7 1.2 2.0 2.1 11 .3 1.0 1.7 2.5 2.7 12 .5 1.4 2.2 3.0 3.3 13 .7 1.9 2.7 3.5 3.9 14 .9 2.4 3.3 4.1 4.5 15 1.1 3.0 3.9 4.7 5.2 16 1.4 3.7 4.5 5.3 5.8 17 1.7 4.4 5.3 5.9 6.5 18 2.0 5.2 6.0 6.6 7.2 19 2.4 6.0 6.7 7.2 7.9 20 2.7 6.9 7.4 7.9 8.6 21 3.0 7.8 8.2 8.7 9.3 22 3.3 8.6 9.0 9.3 9.9 23 3.6 9.3 9.8 10.1 10.3 24 4.0 10.0 10.5 10.7 10.7 25 4.3 10.8 11.1 11.3 10.9 26 4.6 11.4 11.8 11.9 11.1 27 5.0 11.9 12.3 12.4 11.3 28 5.3 12.5 12.8 12.9 11.3 29 5.7 12.9 13.2 13.3 11.3 30 6.0 13.3 13.4 13.6 11.2 31 6.4 13.5 13.6 13.7 11.0 32 6.7 13.5 13.6 13.6 10.7 33 6.9 12.2 12.8 12.6 9.2 34 7.1 9.5 11.2 10.2 6.0 35 6.1 5.7 6.8 4.2 1.0 36 2.2 1.7 .5 .2 222 University of California Publications in Agricultural Sciences [Vol. 4 ratio 3.7 : 0.3 is 12.3, which is the 10-degree coefficient (Q10) for the 10-degree interval from 8° to 18° C. Now, since the value of Q10 varies with the maintained temperature, if its fluctuations are to be studied it is necessary to calculate the different values, not for suc- cessive 10-degree intervals (as 8°-18°, 18°-28°, 28°-38°), but for 10- degree ranges beginning with each successive whole degree for which data are available (as 8°-18°, 9°-19°, 10°-20°, etc.). If the value just obtained for the range 8°-18° C. be written Q10 (8°-18°) =12.3, then referring to table VI we may write Q10 (9°-19°) =8.4; Q10 (10°-20°) = 6.7 ; Q10 (11°-21°) = 5.1, etc. For convenience of ref- erence and for facility in plotting these temperature coefficients for various 10-degree temperature ranges as they are made to shift by single degrees, the middle point of each 10-degree range is taken to represent the range itself. Thus the coefficient value plotted at 13° stands for the 10-degree temperature coefficient for the range (8°-18°) whose middle point is 13° (figs. 10 and 11). TABLE VIII Mean 24-Hour Eates of Enlargement for Consecutive, 1-Day Observation Periods, for Phomopsis, as Determined by Measuring the Ordinates of the Smoothed Graphs of Figure 4 Temperature deg. C. First day mm. Second day mm. Third day mm. Fourth day mm. Fifth day mm. 8 .1 .4 1.1 1.2 1.3 9 .2 .7 1.4 1.5 1.6 10 .3 1.1 1.8 1.8 2.0 11 .4 1.4 2.1 2.1 2.4 12 .5 1.9 2.4 2.5 2.8 13 .6 2.2 2.8 2.9 3.2 14 .8 2.6 3.1 3.2 3.6 15 1.0 3.0 3.5 3.6 4.0 16 1.2 3.4 3.9 4.0 4.4 17 1.4 3.7 4.2 4.4 4.8 18 1.6 4.1 4.6 4.8 5.2 19 1.8 4.5 5.0 5.2 5.6 20 2.1 4.9 3.4 5.7 6.1 21 2.3 5.3 5.8 6.1 6.5 22 2.6 5.8 6.2 6.5 7.0 23 3.0 6.2 6.6 7.0 7.4 24 3.4 6.7 7.1 7.4 7.8 25 3.8 7.1 7.5 7.8 8.2' 26 4.1 7.5 7.8 8.2 8.4 27 4.4 7.7 7.9 8.5 8.3 28 4.2 7.4 7.8 8.2 8.0 29 3.4 6.0 7.0 7.6 7.3 30 2.4 3.0 5.0 6.6 5.8 31 1.5 1.2 1.2 3.3 1.8 32 .9 .3 .2 1921] Faivcett: Temperature Relations of Growth in Certain Parasitic Fungi 223 The 10-degree coefficient values for all whole intervals of 10 degrees for which data are at hand for all four fungi and for each of the successive 24-hour observation periods employed in this experimenta- tion are set forth in table X. The first column of this table presents the different temperature ranges, the second column shows the middle TABLE IX Mean 24-Hour Bates of Enlargement for Consecutive 1-Day Observation Periods, for Diplodia, as Determined by Measuring the Ordinates of the Smoothed Graphs of Figure 5 Temperature deg. C. First day mm. Second day' mm. Third day mm. 8 .7 2.7 3.0 9 2.0 4.1 4.5 10 3.2 5.6 5.8 11 4.4 7.0 7.2 12 5.7 8.4 8.7 13 6.8 9.9 10.1 14 8.1 11.3 11.7 15 9.3 12.7 13.1 16 10.5 14.1 14.6 17 11.8 15.7 16.1 18 13.1 17.0 17.6 19 14.3 18.5 18.9 20 15.6 20.0 20.5 21 17.0 21.6 22.2 22 18.4 23.0 23.5 23 19.8 24.5 24.7 24 21.2 26.1 25.4 25 22.7 27.6 26.0 26 24.2 29.1 26.3 27 25.8 30.5 26.3 28 27.2 30.8 25.8 29 28.8 30.5 24.9 30 29.7 29.2 23.8 31 29.7 27.4 22.6 32 29.0 25.6 21.0 33 27.4 23.0 19.0 34 24.9 12.0 15.9 35 19.9 11.0 9.3 36 11.4 2.7 37 7.4 38 5.0 39 3.0 40 1.5 41 .8 42 .5 43 .4 44 .3 45 .2 224 University of California Publications in Agricultural Sciences [Vol. 4 ^^aOOqiOOt-^OqOOSCOlOCOOqOOSt^CDcO lO^«m(MO](MiM tH CO H Ol N (O^MMNIMONMHHHHHH l> S OO OO H lO ^ ^ !>; i—l 03 OO Oq OS CD tH CO Oq O O OS t>; lO rtf Oq 00 "^ Oq j* cs d n tj5 co co* oq* oq' oq" cm" oq" oq" oq' i-h* rA iH t-h th" X >» O CO rH OS tjH tJH CO iH O OS l> Ttj iH IO ^^ -si* cd co* oq* oq" oq" oq* oq* Oq' r-i rH rH* iH ^ i>, ■* w q s iq m w h q a n ^ q n TOr§ tJH CO CO » © tjh tjh oq © oq iq co oq © oq co cq oq ^4* d © ■*' W CO w. oq* Ol* Oq* CM* rA i-i _^ © o o © oq © oq oq tH i-h cd oq oq cq i? c3 CD O* t> d lO lO ^' CO* CO W N H H 1-1 -a rH ,3 :*> co oq os tjh rH os CD ■>* oq h a co t> io ■* oq ^^ CD tjh co* co cd cq' oq' oq* oq* oq' i-h* i-h* i-h* i-h* i-h* i-h* co r^j © ^H r-i IO* t>* CD oq # © oq rH oq oq HJ il co co oq* oq' rH os oq cd iq co © Oq* r-i i-H* rH* rA rA rA 'o >> © © oq oq ^ cd* id os* t-' Oq r-i CD © t>; TtJ rM OS t>; co" cd oq' oq* oq* rA rH* © © O © CD rH rjH OS CO OS CD CO 03 r-i © OS 00 -^ xH o cd cd o cd id ^" cd cd oq" oq* oq* oq' oq* oq" rH* t-h" i-h* t- 10 -g ^» oq oq © tJh os cq oq os cd tjh oq © «>; r-i •5t3 CO IO* •*' CO* Oq' Oq' Oq' rH rA rA rA rA to t>- ^^ost^cot^oqooTHOoqiocorHoqcq cor§ t>* io* ^* cd cd oq* oq* oq* rA rA rA rA t^ r-i O. 'g >. iq r-i b- t> oq oq tJh i-h os t>- iq cq os cd © CJ-S 00* CD TJH* CO* CO* Oq' Oq* Oq' rA rA rA rA J2_3 oqoocoio'TjHcocdcooqoqoqrHrHrH "V r-i bJJQ g>Q O0 OS O r-i ™ r-i r-i OJ O] TH LO CD t^ 00 OS O rH Oq CO r^ IO CI oq oq oq oq oq CO CO CO CO CO CO (OSOOaOHOlCOilOCDSOOOJO WNCicicocococococomcococo^ I I I I I I I I I I I I I I I COt-OOOSOrHOqcO^lOCOt^OOOSO rHrHrHrHOjoqoqoqoqoqoqoioqojco 1921] Fawcett: Temperature Relations of Growth in Certain Parasitic Fungi 225 points of these ranges, which are to be taken as representing the various ranges themselves. The rest of the table falls into four parts, each part giving the data for a single fungus. Each single column gives the coefficients for a single one of the consecutive 24-hour ob- servation periods. Inspection of the coefficient values given in table X brings out the fact that, for every one of the four fungi and for each of the consecutive 24-hour observation periods, the 10-degree temperature coefficient for mycelial enlargement is greatest for the lowest temper- ature shown and regularly decreases toward higher temperatures, be- coming smallest for the highest temperatures. The highest coefficient value here encountered (30) is that for 13° C. (range from 8° to 18°), for the first 24 hours after inoculation, for Phytophthora. This value is progressively smaller for progressively higher temperatures, becom- ing 0.47 for the temperature 31° (range from 26° to 36°). For the temperature 13° (range from 8° to 18°) the lowest coefficient value shown (4.0) is for the fourth 24-hour period for Phomopsis, and this value is progressively smaller for progressively higher temperatures, becoming 0.5 for the temperature 26° (range from 21° to 31°). The lowest coefficient value of the whole table is 0.01, for the temperature 31° (range from 26° to 36°) for the fourth 24-hour period for Phy- tophthora, this value being progressively larger with progressively lower temperatures and becoming 6.6 for the temperature 13° (range from 8° to 18°). Aside from the regular falling off in the coefficient value for each observation period and fungus, as we pass from lower to higher tem- peratures, as just pointed out, the value for any temperature and fungus is always largest for the first 24-hour period after inoculation and generally tends to become smaller with each successive period after the first, although this last statement is not always strictly true for all temperature ranges. The relation of the value of this temper- ature coefficient to the maintained temperature representing the middle point of the 10-degree temperature range from which each coefficient value is derived is shown graphically for the second 24-hour period after inoculation, for three of the fungi in figure 10. Abscissas rep- resent these middle points, while ordinates are the corresponding co- efficient values. These graphs have not been smoothed. These three graphs of 10-degree temperature coefficients are seen to be alike in their general form. Every one begins with a relatively very high value at the left (lowest temperature range tested) and 226 University of California Publications in Agricultural Sciences [Vol. 4 descends, rapidly at first and then less rapidly, with higher temper- atures. From the nature of the temperature coefficient it is clear that its value for any range of maintained temperatures having its lower limit just below the minimum temperature for enlargement must be infinite, since the ratio of any positive quantity to zero is, of course, infinity. On the other hand, as the temperature range for which the co- efficient value is calculated has its upper limit approaching the maxi- mum temperature for enlargement the coefficient value approaches zero. No matter what range of temperature is employed, a change of 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31 32 Fig. 10. Graphs of the 10-degree temperature coefficient, as related to temperature, for Phytophthora, Pythiacystis and Diplodia, for the second 24-hour period after inoculation. 1921] Faiccett : Temperature Relations of Growth in Certain Parasitic Fungi 227 maintained temperature from some value below the maximum temper- ature to some value above that cardinal point must be accompanied by a corresponding change in the rate of enlargement from a positive value to zero, and the ratio of zero to any positive quantity is, of course, zero. For graphs such as those here considered it follows (from the points brought out above) that the slope of the graph at the point of maximum ordinate value (left end) appears to furnish a criterion by which it may be judged, at least in a general way, how nearly the abscissa of this point approaches the minimum temperature. An inspection of the curves at the lowest temperature range here consid- ered (8°-18° C.) indicates that its lower limit (8° C.) is much more nearly the minimum temperature for enlargement for Phytophthora than it is for the other fungi. The curves also indicate that 8° is nearer the temperature minimum for Pythiacystis than for Diplodia. Since the graph of temperature coefficient as related to temperature shows ordinates that decrease in magnitude from infinity to zero, it follows that there must be some point on every such graph at which the ordinate value is unity. This point at which the temperature co- efficient value is unity will represent the middle point of a range within which lies the optimum temperature. The temperature value corresponding to this abscissa is, therefore, near the temperature optimum for the process considered. For lower temperatures the co- efficient values are all greater than unity, for higher ones they are all smaller than unity. A point that needs emphasis in studying the general nature of the temperature coefficients of most processes showing temperature minima and maxima is this, that every such process must show a certain tem- perature range for which the temperature coefficient has values be- tween 2.0 and 3.0, etc. It is, therefore, quite without any definite meaning to state that the temperature coefficient for any process has a certain value, unless the corresponding temperature range is simul- taneously stated. The coefficient value may be everything between zero and infinity, depending on the temperature range considered and upon the position of that range within the total temperature range of the process. The so-called Van't Hoff rule, stating that the temper- ature coefficients of many chemical reaction velocities have values between 2.0 and 3.0 is obviously true, therefore, if the proper temper- ature ranges are considered. It appears to be true that many simple chemical reactions and many physiological processes show temperature 228 University of California Publications in Agricultural Sciences [Vol. 4 coefficient values between 2.0 and 3.0 for certain temperature ranges within the ordinary range of weather temperatures on the earth, and it is perhaps this fact that has led to so much inadequate discussion about these coefficients, especially in physiological literature. Great emphasis should be placed upon the fact that the temperature co- efficient for most processes having temperature limits is a continuously varying value, the variation proceeding from infinity to zero. From this point of view the temperature relations of different processes under stated non-temperature conditions and with stated exposure periods are clearly comparable, not by means of single tem- perature coefficient values, but by means of the coefficient-temperature relation as a whole. Practically, the simplest way to present this re- lation for a given process is to construct such coefficient-temperature graphs as those shown in figures 10 and 11. The form and position of these graphs completely describe the rate-temperature relation. If two processes are to be compared in respect to this temperature relation, the comparison should be instituted between the two coefficient-temperature graphs, constructed on the same scale. If the two graphs coincide throughout, then the temperature relations of the two processes are alike; they have approximately the same temperature minima, op- tima, and maxima, and the two rates change from one temperature to another in just the same way. If the two graphs fail to coincide throughout, the two rate-temperature relations differ, and just how they differ is apparent from an inspection of the graphs. Further- more, the different values of the temperature coefficient for the same process, etc., may readily be compared for different temperatures and the coefficient values for different processes may be compared for the same temperatures. Some of the points brought out by inspection of the group of three coefficient-temperature graphs shown in figure 10 have been mentioned, but many others not here considered may be noted. The three graphs thus far dealt with show the relation of temper- ature coefficients to temperature for three of the fungi employed in this study and for the second 24-hour period after inoculation. The four coefficient graphs for Pythiacystis, for the first, second, third, and fourth 24-hour periods after inoculation, are shown in figure 11. These graphs are constructed from the data given in table X in the manner employed for figure 10; they have not been smoothed. The graph for each successive period after the first lies below the one for the preceding period. The progressive lowering (already mentioned) 1921] Fawcett: Temperature Eelations of Growth in Certain Parasitic Fungi 229 of minimum, maximum, and optimum temperatures with the succes- sive periods is clearly shown ; also the difference between the growth- temperature relation for the first period and that for the second is shown to be far more pronounced than all the differences between these relations for successive periods. 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Fig. 11. Graphs of the 10-degree temperature coefficient, as related to temperature, for Pythiacystis, for four consecutive 24-hour observation periods within the 4-day exposure period. CONCLUSION From the results of the investigation of the temperature relations of growth in pure cultures of four fungi (Pythiacystis citrophthora, Pliytophthora terrestria, Phomopsis citri, and Diplodia natalensis) , discussed in detail in the preceding pages, the following generalizations may now be brought together. It was indicated that there is the usual optimum temperature above and below which the rate of enlargement was smaller with higher or lower maintained temperatures. Growth-temperature graphs (with temperatures as abscissas and growth rates as ordinates) rise from left to right (from lower to higher temperatures) , being at first slightly concave upward, then becoming convex till the optimum is passed, and then falling rapidly toward the temperature axis. The fact is to be emphasized that the optimum temperature for the average rate of growth of a given fungus with a given medium is 230 University of California Publications in Agricultural Sciences [Vol.4 not always the same for different lengths of observation periods, or when periods of equal length have different time relations to the be- ginning of the culture period. With culture periods of from three to six days and an observation period of 24 hours in length, it was found that in general the optimum temperature for growth shifted to lower temperatures for each suc- cessive observation period. There was also corresponding displacement of the apparent maximum temperature downward (from higher to lower temperatures) with each successive observation period. A comparative study of the growth-temperature graphs of the four fungi for the second 24-hour period shows that the total range of temperature within which growth rate values are one-tenth or more of the maximum rate includes from 32.5 to 37 centigrade degrees of the temperature scale. Of this range, from 70 to 80 per cent is below the optimum temperature for growth. With comparatively low temperatures the growth rate increases with the age of the culture throughout the culture period and with the highest temperatures it decreases throughout the culture period, this decrease soon bringing the value to zero. With a small range of intermediate temperatures, the rate first increases with time and then remains constant, oscillates or decreases. The 10-degree temperature coefficient (Q10) for each of the four fungi has a high value at the lowest range studied and decreases pro- gressively through lower values to zero. The form of the graphs repre- senting the value of the temperature coefficient as related to different ranges of maintained temperature shows that the value of the temper- ature coefficient must begin with infinity for some low range, must pass through all finite values and then must reach zero for some higher range. For growth-temperature relations of this type the range for which the coefficient is unity will include the optimum temperature, the range for which the coefficient is infinity will include the minimum temperature, and the range for which the coefficient is zero will include the maximum temperature. The use of the coefficient-temperature graphs furnishes a direct method of comparing the growth-temperature relations of different organisms, no matter in what units the rates have been expressed. If the graphs of two different processes coincide throughout, the growth- Icinperature relations must be considered to be the same. On the other hand, if the two graphs fail to coincide throughout, their lack of coincidence furnishes evidence of the particular manner in which the temperature relations of the two processes differ. 1921] Fawcett : Temperature Relations of Growth in Certain Parasitic Fungi 231 LITERATURE CITED Blackman, F. F. 1905. Optima and limiting factors. Ann. 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