with age to a certain point followed by a decline. An empirical curve following these plotted points shows a type familiar to us from other biological problems. It is in fact a logarithmic curve. Pearl" has shown that the changes in milk flow with age in dairy cattle follow such a logarithmic curve and he has determined its equation. The writer has now proceeded to form the equation relating fertility to to age in the material at hand, and has in the calculations used the method of moments (Miner13). The general form of the equation is y= a + bx + cx2 + d log x where y denotes the size of litter and x the ordinal litter number. In this special case the equation has been calculated to be the following y=8.414+0.915x -0.078x2 + 1.627 log x. By solving the equation for the values of x ranging from 1 to 10 the theoretical average size of the successive litters has been determined. These values are given in the third column of table 1 and they are used in plotting the curve in figure 1. This curve shows a satisfactory agreement with the empirical figures plotted out. By putting dy/dx = 0 and solving for x the litter of maximum size is found to be 6.56th in order. Summary.-1. Records from 134 sows of native Danish breed all having ten litters to their credit show an increase in fertility up to the 6.56 point in litter order followed by a decrease. 2. The curve relating fertility to age is logarithmic, its equation is calculated, and the curve fitted. 'Papers from the Department of Biometry and Vital Statistics, School of Hygiene and Public Health, Johns Hopkins University, No. 35. "The native Danish breed is a white, fertile and hardy hog of bacon type, producing sometimes crossed with Yorkshire boars-the great proportion of the choice bacon exported from Denmark to England. 3Bell, A. G. 1904. The multi-nippled sheep of Beinn Bhreagh. Science, N. S., 19. 'Bell, A. G. 1912. Sheep breeding experiments on Beinn Bhreagh. Ibid., 34. "Carmichael, W. J. and John B. Rice. 1920. Variation in farrow: With special reference to birth weight of pigs. Univ. Illinois, Agric. Exp. Sta., Bull. 226. "Carlyle, W. L. and T. F. Mc Connell. 1902. Some observations on sheep breeding from the Experiment Stations flock records. Univ. Wisconsin, Agric. Exp. Sta., Bull. 95. "Frölich und Georgs. 1911. Fruchtbarkeit und Geschlechtverhältnis beim weissen Edelschwein. Jahrbuch für wissenschaftliche und praktische Tierzucht, 6. Hammond, John. 1914. On some factors controlling fertility in domestic animals. J. Agric. Sci., 6. 'Humphrey, G. C. and F. Kleinheinz. 1907. Observations on sheep breeding from records of the university flock. 24th Ann. Rep. Wisconsin Agric. Exp. Sta. 10Jones, S. N. H. and J. E. Rouse. 1920. The relation of dam to observed fecundity in domestic animals. I. Multiple birth in cattle and sheep. J. Dairy Sci., 3. 11King, H. D. 1916. 12Machens, A. 1915. The relation of age to fertility in rat. Anat. Rec., 11. Fruchtbarkeit und Geschlechtsverhältnisse beim vereddelten Landschwein. Berliner Tierärtzliche Wochenschrift, 31. 13Miner, J. R. 1915. Fitting logarithmic curves by the method of moments. J. Agric. Res., 3. 14 Minot, C. S. 1891. Senescence and rejuvenescence. First paper: On the weight of guinea pigs. J. Physiol., 12. 15 Mumford, F. B. 16 Pearl, R. 1913. 17Pearl, R. 1914. Exp. Biol. Med., 12. 18 Rommel, G. M. Breeders Report 3. 1917. The Breeding of Animals. Note regarding the relation of age to fecundity. Science, N. S., 37. 1907. Inheritance of litter size in Poland China sows. American VARIATION AND INHERITANCE IN SIZE IN TRYPANOSOMA LEWISI1 1. LIFE-CYCLE IN THE RAT AND A STUDY OF SIZE AND VARIATION IN "PURE LINE" INFECTIONS2 BY W. H. TALIAFERRO DEPARTMENT of Medical ZOOLOGY OF THE SCHOOL OF HYGIENE AND PUBLIC Communicated by R. Pearl, MAY 2, 1921 The flagellate, Trypanosoma lewisi, is a non-pathogenic blood parasite occurring in various species of rats all over the world. It is known to be transmitted from rat to rat by the rat flea. This trypanosome was selected for the present work because it occurs in the latitude of Baltimore and the vertebrate and invertebrate hosts can easily be reared in the laboratory. The general plan of the present work on size in T. lewisi is to make a careful study of size and variability in a pure line and then with this background to attempt to explain the facts observed in infections occurring in nature. After a pure line infection was obtained the following questions were attacked: (1) What are the mean and the coefficient of variation? (2) Does growing the same "pure line" in different vertebrate hosts cause significant differences in the mean size or in the coefficient of variation? (3) Does passage of the "pure line" through the invertebrate host cause significant differences in the mean or coefficient of variation? This question gives us a chance to test the possibility that passage of the "pure line" through the invertebrate host may cause a splitting up of the "pure line" into heritably diverse lines. After a study is made of these questions we can attack the final one: (4) Does an infection occurring in nature consist of a large number of "pure lines" such as has been described by Jennings3 and others in free-living protozoa which differ among themselves but are per se constant in size? As will be seen later, these questions cannot be approached with any degree of exactness until a thorough study is made of the changes in mean size and variability throughout the course of an infection. The present paper deals with these changes in size and variability and with the first of the questions enumerated above. The other three questions are to be taken up in a later report. A study of inheritance in a parasitic protozoon such as T. lewisi is of interest from several points of view. In the first place the results are of interest from a comparative standpoint when considered in the light of recent advances in our knowledge of the genetics of free-living species. In the second place, the results may be of value in the interpretation of the results of the many studies on the production of strains of parasitic organisms which exhibit new characteristics. Finally the work is the first of a program of investigations, the ultimate object of which is a study of the mechanism of the formation of new lines exhibiting such characters as arsenic-fastness and the inheritance of these characters after passage through both the vertebrate and the invertebrate hosts. While lack of space prevents a discussion of technique in detail, it may be noted that every precaution was taken to use microscopical technique such that the trypanosomes would be free from shrinkage and distortion. All measurements were made from camera lucida outlines drawn at a magnification of X3000. The unit used in measuring the drawings was 3 mm.; consequently all of the determinations given in this paper are in actual microns. In making the determinations 100 specimens, taken at random without selection, were drawn in each case. In isolating single organisms with which to start "pure line" infections, a sensitive mercury pipette was used in conjunction with a Barber pipette holder. Figure 1 is a diagram of a trypanosome indicating the various parts of the organism and the distances measured in this work. The names of the parts of the trypanosome run vertically and the abbreviations of the six distances run horizontally. Size and Variation throughout a "pure line" Infection.-The infection in the rat can be divided into three periods: (1) the incubation period lasts from 1-7 days and is the time which elapses between inoculation and the first appearance of the trypanosomes in the blood. (2) The multiplication period starts with the first appearance of the trypanosomes in the blood and lasts for 10-25 days. This period is characterized by the great variations in size due to the growth and the multiplication of the trypanosomes. (3) The period of "adult" infection follows the second period and is characterized by the absence of all growth and multiplication. This period lasts from one to many weeks at the end of which time the trypanosomes disappear from the blood and the rat is immune to another infection with T. lewisi. It is apparent that in an organism which shows a cycle of growth and division such as characterizes T. lewisi, we must make all comparisons of size and variability at the same stage in the cycle, and that if there is a period in which there is no growth and division comparisons should be made during this period. A study of the changes in the means and in the coefficients of variation of the different parts of the trypanosome throughout the course of a "pure line" infection demonstrates very clearly that there are different periods of the infection and indicates the stage at which to make comparisons of size and variability between different infections. Let us take, for example, the coefficients of variation and the means for total length in rats 116 and 105 which are shown in figure 2. The infection in rat 116 was started from a single trypanosome and rat 105 was inoculated from rat 116. In other words, although the infection in the first rat started from a single specimen and in the second rat from many specimens, all of the trypanosomes in both rats are descendants of the single organism injected into rat 116. We can make no determinations during the incubation period since no one knows where the organisms are at this time. Let us consider first the constants for rat 105. On the first day of the blood infection the mean length was 24.785.423. This rose rapidly until the 5th day when it reached 30.108.280. This rise continued gradually until it reached 31.412.065 by the 19th day. From the 19th until the 32nd day, at which time the infection disappeared from the blood, there was no significant change in the mean. The coefficient of variation behaved in much the same manner as the mean. On the first day of the infection it was 26.521.35%. It dropped very rapidly for the first seven days and then much slower for the next twelve days. By the 19th day it reached the low value of 3.11.14% and it showed no significant change from this value throughout the remainder of the infection. It is well to compare the conditions found in rat 116 with those in rat 105. Rat 116 is given here because a longer time elapsed before the infection reached the adult stage than was the case in any of the other infections studied. This is due probably to the fact stated above, viz., that the infection in rat 116 started from a single trypanosome while the others although they were "pure lines" were sub-inoculated from 116, and in consequence were started with a large number of specimens. As these curves are probably expressions of the resistance of the host to the parasite, we would expect that this resistance would increase more rapidly when the infection is started with a large number of trypanosomes than when it is started with only one. We cannot compare the shape of the curves in the two rats very well because there are not enough points in the curve for rat 116. One thing is probably true, however, and that is that both the mean and the coefficient of variation reach a constant value by the 25th day. At first it looks as if the mean tends to rise even until the 32nd day. That this is not the case, however, is shown by the fact that the value on the 25th day does not vary appreciably from that of the 72nd day. The same type of result was obtained for all of the six distances shown in figure 1, namely, for the distances posterior end to parabasal body, parabasal body to nucleus, nucleus to anterior end, anterior end to end of Undulating Membrane Diagram of T. lewisi showing the parts of the organism and the distances measured in this work. The parts of the organism are placed vertically while the distances are placed horizontally. The latter consist of the distance from (1) posterior end to parabasal body, (2) parabasal body to nucleus, (3) nucleus to anterior end, (4) anterior end to end of flagellum, (5) total length, and (6) width. flagellum, and width, although most of the constants do not reach as low a level as is the case with those for total length (see table 1). Curves of this nature were obtained in four rats. These results prove, what we had been led to believe from cytological evidence, viz., that there is practically no division or growth in T. lewisi after the 25th day of the blood infection. After it was determined that there was no significant change in the mean or coefficient of variation after the 25th day we decided to make all measurements after this day. Most of the measurements which will be given in a later report were made on the 30th day of the blood infection. The fact that the trypanosomes in the blood of the rat reach what we can consider an adult stage makes size a very favorable character with Anterior End .End of flagellum |