REMOTE STORAGE PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE 2/17 20:: Blue FORN S/DateDueForrns_2OI7.undd - 09.5 GENETIC AND ENVIHONMLNTAL CONTRIBUTIONS TO THE ECONOMIC CHARACTERISTIOS OF THE RICHIGAN STATE COLLLGE DAIRY HERD ‘ By BEERAPPA CHANDRASHAKER w—-—\ A THmSIS Submitted to the School of Graduate Studies of Richigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Animal Husbandry 1951 .. ‘1 CV? CHAPTER TABLE OF CONTENTS A INTRODUCTIONOOOOOOOOOOOOOOOOOOOOO-OOOOOO. Basis Defined........................... Variations: Historical Background And Their Synthesis................... Biometrics............................... Path Coefficient....................... Analysis of Variance, Its Derivatives And Use in Biometrics................ Correlation and Regression Compared.... HERITABILITY............................. Mathematical Derivations of Heritability, Importance of Heritability............... Sources of Error in Heritability Estimates.............................. REVIEW OF LITERATURE..................... Methods of Estimating Heritability....... Methods Used in the Present Study........ Heritability and Repeatability Estimates For Traits in Dairy Cattle............. SOURCES OF DATA.......................,.. Need For Standardization of Records...... ANALYSIS OF DELTA...OOOOOOOOOOOOOOOOOOOOOO <¥£a1 Fxsx>) a“... '4 ; ' .'.‘V ‘ . PAGE 12 12 17 20 2h 25 28 30 31 31 #3 45 50 51 65 CHAPTER . PAGE Calculation of Heritability of Milk Production............................ 71 Calculation of Heritability of Butter- Fat Production........................ 102 Calculation of Heritability of Percentage of Butterfat............... 120 II REPEATABILITY OF PRODUCTION CHARACTERISTICS: MILK AND BUTTERFAT...................... lhO Introduction............................ 140 What is Repeatability................... 1A1 Repeatability and its Place in Aids to Selection.............................. lhl Relationship of Heritability to Repeatability.......................... lh5 Method of Analysis of Data for Repeatability.......................... 146 Butterfat............................ 1&9 Milk................................. 155 III INFLUENCE OF THE MONTH OF CALVING ON BUTTERFAT PRODUCTION.................... 162 Analysis of Data........................ 168 IV SEX RATIO AMONG DAIRY CATTLE-----------~-- 172 Twinning in Dairy Cattle.................. 177 v GENERAL CONCLUSIONS AND SUMMARY........... 186 VI BIBLIoGRAPHY...;........................... 196 ACKNOWLEDGELE NT S The author is deeply indebted to the Government of mysore (India) and in particular to the Department of Animal Husbandry (NWsore) for the financial support during the three and one half years of stay and study in the United States of America which made it possible for him to complete this investigation. The writer wishes to express his sincerest appre- ciation to Dr. Ronald H. Nelson, Head of the Department of Animal Husbandry and Professon of Animal Breeding, under whose inSpiration, guidance and constant encouragement it was possible to carry out the work and the preparation of this thesis. He also express sincere thanks for providing all the facilities and extending the warmest courtesy by the Department during the course of work here. He is also grateful to the members of the guidance committee: Dr. Harrison R. Hunt, Head of the Department of Zoology and Dr. Nbel P. Ralston, Associate Professor of Dairy Husbandry, for their aid, helpful suggestions and constructive criticisms, and to Dr. William.D. Eaten, Research Professor of Statistics, for his help in statistical procedures. He is especially grateful to Dr. Earl weaver, Head of the Department of Dairy, and to Dr. Carl F. Huffman, Research Professor, Department of Dairy, for placing at his disposal all the production records and data of the Michigan State College dairy herd. To his wife, Nagamma, and to his two children, he is much indebted for their loving sacrifice, which was a source of great encouragement in the present under- taking. INTRODUCTION ASIS DEFINED Fundamentally, genetical investigations, whether through biometrics or through Mendelian experimentation depend primarily on variation. There could be no selection if the population were homozygous and it con- tinued to remain so, because of no mutations. By variation is meant the differences between individuals in any given related population. While dealing with quanti- tative characteristics, such as milk, butterfat or wool production, one is actually thinking of a continuous variation, whose visible "average effect" could be changed by the substitution of a "good" or a "bad" gene by selection. Whereas in case of qualitative characteristics such as color, polled and horned conditions, would con- stitute a discontinuous variation, based on the effect of the "unit" or discrete nature of a gene. And any problem of genetics that attempts to unravel the complex mechanism of inheritance must proceed to do so either on the basic assumption of one or the other form of variation. While Galtonian approach provides a basis to solve continuous variations, the solution for discontinuous variation should be sought from Mendelian concept of hereditary transmission. No matter whatever approach one takes, a knowledge of the 2 historical develOpment of these variations, whose differ- ences at present have largely disappeared, would be essential to visualise them in their proper perspective-- the rich and ever unfolding science of Genetics. VARIATIONS: HISTORICAL BACKGROUND AND THEIR SYNTHESIS The first formulation of the fundamental theory of evolution by Darwin in 1859 based on the one hand to enormous facts from which he induced evolutionary process and on the other hand starting from few principles he deduced further the principle of natural selection. By logical thinking based on these facts he presented three observations, from which he drew two deductions: the facts are l) the tendency of all organisms to increase in a geometrical ratio, due to the fact that in the early stages offSpring are always more numerous than parents, 2) that in Spite of the tendency to progressive increase, the numbers of a given Species remain more or less approximately constant, and 3) variation; that all organ- isms vary appreciably. From the first two facts he deduced the struggle for existence or survival, since a larger number of younger ones are competing always against their older ones for survival. And from the first and the third fact he deduced the theory of natural selection of favourable variations against unfavourable variations. He believed that favourable variations which are minute and continuous are transmitted by heredity and the unfavourable variations die and fail to reproduce. This phenomenon came to be known as the differential transmission of inherited variation. While he was willing to subscribe to some extent to the earlier La- marckian theory of inheritance of acquired characters through use and disuse of them, he on the other hand went to the length of dismissing as "unimportant" any variation which was not inherited. Amplifying on his theory of natural selection and domestication, namely, the accumulative selection and correlated variation, Darwin further proposed, among others, two outstanding conceptions, which even today not only stood the test of time but also have contributed in no small measure to our knowledge and thinking of . genetics. He pointed out in his treatise on "Variations of Animals and Plants," (1868, p. 14) the principle of accumulative selection thus: Man may select and preserve each successive variation, with the distinct intention of improving and altering a breed, in accordance with a precon- ceived idea; and by thus adding up variation, often so slight as to be imperceptible by an uneducated eye, he has effected wonderful changes and improvements. It can, also, be clearly shown that man . . . b preserving in each successive generation the individ- uals which he prizes most, . . . slowly, though surely, induce great changes. Continuing his inquiry further, he observed the importance of correlated variation in precise terms in "Origin of Species" (1875, p. It) as: Hence, if man goes on selecting, and thus augmenting, any peculiarity, he will almost certainly modify unintentionally other parts of the structure, owing to the mysterious laws of correlation. These concepts provide ample thought for multi- factorial inheritance, which was not fully understood at that time, besides, it strengthened the theory of con- tinuous variation in the papulation. Fbllowing Darwin's formulation of evolution, a tremendous force of scientific exploration ensued, with ‘Weisman seeking to clarify variation with his somatic and germplasm theory, wherein which the variations in the germ plasm.were alone transmitted. This theory is generally known as the Continuity of Germ Plasm Theory, which later on formed the basis of two fundamentally distinct categories, viz., modification in the soma and mutation in the germ plasm. Another highly significant contribution which drew its inspiration from the fbuntain head of Darwinian con- ception, was the application and development of statistical mathematics to the problems of biology-~called biometrics, by Galton and later by Karl Pearson and his school. They conceived their method on the basis of a continuous variation but shortly after it suffered a set back in its avowed purpose because of the material Galton chose to express the mode of hereditary transmission. The material selected for his study was the stature of the man, which is a quantitative character. These characters show continuous variation as they are governed by several genes. Since he attempted to explain a continuous variation on the basis of particulate or discontinuous 5 nature of hereditary transmission, he did not at first succeed though he and later Pearson were able to show the variation to be at least partially heritable. Thus biometrics had to go fer a time into recluse and its full acceptance as a mode of genetical study had to be delayed until a later date. In the wake of these developments, Bateson in 189A, threw a challenge and attacked the whole foundation of the Darwinian edifice, which was threatened to be razed and replaced by a new theory. He contended that the whole basis of evolution was due to discontinuous variation and sought to substitute it in place of Dar- win's. Without going into the merits or the demerits of the theory advanced by Bateson, it would suffice to note that it marked a new era of mutation theory, which postu- lated that large mutations and not the small "continuous variations" were the cause of evolution. The theory was later formulated by de Vries in 1901 and 1905 and was adopted by several other workers notably Mbrgan, T.8. in 1926. ' In 1900, shortly after Bateson's work, the re- discovery of Mendel's breedinngxperiment with peas carried on from.185T to 1865, revealed some of the basic principles of hereditary transmission. Mendel, the father of systematic experimental genetics, was successful 6 to a large extent because he reduced his problem to its simplest form consisting of two contrasting characters. From.his work it was shown that recombination of existing genetic units will produce and modify new heritable variations, which lead to the establishment of the two basic laws of inheritance, viz., segregation and inde- pendent assortment. In essence Mendelian heredity is based on the inheritance of particulate or discrete units. The units are the.Mendelian factors or genes, and their different ferms are called alleles or allelomorphs. These genes are located on chromosomes as seen under the microscope, and due to the particulate nature of inheri- tance, the type and the proportion of these units could be calculated in the offspring after a cross. In the study of’Mendelian factors, which implies unit inheritance, one would thus, be dealing with a discontinuous or dis- crete variation, generally known as the inheritance of qualitative characters. Post-Mendelian additions, such as linkage, corrosing over, etc., added further proof on the discontinuity of the variation, thereby drawing sharper differences between the two types of variations. Thus, these two conflicting theories of variations;, one, that of Darwin's continuous variation which formed the basis of biometrics of Galton and his school and the other the discontinuous theory of Mendel based on his 7 unique experimentation with unit characters, clearer in their own approaches to genetical laws, came therefore, face to face. Since, the workers on each side of these theories refused to acknowledge the others merit, a compromise and blending of these theories had to be brought about before biometrics could be accepted as an important method in genetical research. The biometricians thought that the continuity in phenotypic expression should correspond to the continuity in genotype, while the Men- delians considered that any phenotypic continuation was incompatible with the discontinuous genetic material. Gradually the one gene-one character theory of Mendel became enlarged into the phenomenon of pleotropism. At the same time the existence of multiple factors as casual agents of a single character, advanced by Nilsson- Ehle in 1909, came more and more into the favour. Addi- tional light thrown by these helped a good deal to narrow down the differences between the two theories. But it was not until the work of Johannsen, W. (1926) who, while experimenting with beans in 1909, formulated the pure line theory and showed that a character is the product of non- heritable environment and the heritable genotype, and that both contribute to the phenotypic variation. He expressed in his book "Elements Der Exakten Erblichkeitslehre” (1926, 3rd. Edn. p. 202) thusé - Und innerhalb der reinen Linie sind die oft so grossen individuellen phanotypischen Variationen auch Ausdrucke der modifizierenden Einflusse ausserer Verhaltnisse. *The unique resultant contributory effect of these findings and theories in the post-Mendelian period was the smoothing of discontinuous theory, which finally came to be regarded basically same as the continuous theory: the discontinuity observed in the genotype due to.Men- delian factors (genes), was rendered continuous in pheno- type due to the effects of environment. And as Huxley (l9h3) expressed it more clearly that it is possible theoretically for a gene to alter its character by ”mutating step by small step" from one member of allelo- morph series to another and that discontinuous germinal changes are perfectly capable of producing continuous changes in somatic characters. Thus, the synthesis of the biometrical and Men- delian approaches to genetical problems marked a great step in the advancement of this particular branch of science: the farmer provided a method to handle contin- uous variations and the latter showed the principles on which the analysis of genetical problems must be based. The only fundamental difference between the two as pointed out by Pearl (1915) is that biometrics deals I$Since then one refers to a character as a product of both heredity §gg_environment and not as a case of whether heredity g; environment. 9 primarily with the ancestry, while Mendelism deals pri- marily with the progeny or the filial generations, hence, both are essentially statistical and also essentially biological. In any animal genetical investigation, therefbre, biometrics occupies a very important place and its appli- cation depends fundamentally on continuous variation in the attributes of a pepulation. One should not consider it, however, as being superior to the methods of actual experimentation. BIOMETRICS In biometrical studies one attempts to accomplish two things, namely, on the one hand to furnish a description of a group of objects or events in terms of the group's attributes rather than in terms of the individuals composing the group, and on the other hand the prediction of the individual case on the basis of’mathematical theory of probability, from a precise knowledge of the group or mass. 7 --Pearl (1915) In essence one will be measuring quantitative characteristics or the continuous variations observed in the phenotype of a group, and then establish a genetical relationship; both in type and degree, by discounting or attempting to discount the influences of environment and that of nonaddative hereditary variations; such as dominance and interaction. Following the methods of Galton and his school (correlation), notable contributions to biometrics for lO correlating quantitative characteristics have been the development of analysis of variance and its extension; covariance and correlation by Fisher (1925) and the method of path coefficient by wright (1921, 1934). These methods, as discussed befbre, primarily aim at establish- ing the type and the degree of genetical relationship. While the approaches advanced by Fisher have been profusely used in the present study, which will be explained under the respective methods for estimating heritability etc., it was thought pertinent and important to include in the present discussion a brief description of the basic concepts on which the path coefficient method has been developed. A working knowledge of the methods supplied by these outstanding workers have become powerful tools in the study of any mathematical genetics. The principle of path coefficient has been employed to determine the relative importance of heredity and environment, both of which constitute the "observable" characteristic of an animal. Here again the hereditary variance is further made up of the variance due to additive genetic fraction and the variance resulting from dominace and interaction, which act in a nonadditive or nonlinear pattern. The additively genetic variance resembles more closely the transmitting ability of an (P) 11 individual; meaning closer resemblance to its "expected" value. In most of the genetical studies one is inter- . ested inseparating this effect from a complex nature of a characteristic to determine genetical correlation. The variances due to dominace and interaction in an animal, though they contribute to the variability in a population, are not transmitted due to the Mendelian laws of segrega- tion and recombination. Similarly, the environmental influences are non-transmissable. While the "observed" value of a characteristic is the result of the combined effect of all of these variances, the "expected" value is mostly the result of the additive genetic variance only. The figure (1) will illustrate the relationship of various factors that enter in the making of an "observable" characteristic based on path coefficient method. C; LEI _ - Phenotype or 5 Character ? - Heredity 4 :9 - Environment e”””’a—,a” - Genetic or the H \ "an E3 GINO: 'U breeding value of an individ- ual in a popu- lation 1 D - Dominance I - Interaction or . Epistasis rEH- Correlation between environ- ment and heredity / '\ FIGURE (1) 12 PATH COEFFICIENT: The,method has been developed on the main basis of cause and effect between variables; the cause being the independent variable and the effect being the depend- ent variable. The relationship that might exist between these variables has been attempted to be measured by this method. 0ne proceeds, however, on the assumption that there exists a linear relationship between the variables and that the influence of the causes combine approximately by addition. The path coefficient has been defined as: The ratio of the standard deviation of the effect when all causes are constant except the one in question, the variability of which is kept unchan ed, to the total standard deviation. (wright,1921§. Seeking further clarification of the method, he has stated a few of the most important principles involved thus: 1) The path coefficient differs from a coefficient of correlation in having a direction or ggth, which is represented by straight line. e straight lines have arrows at one end indicating the direction from an independent variable to a dependent variable. In case of residual correlation between variables, it is represented by double-headed arrow; 2) variability between cause and effect measured . by standard deviation. 3) The path coefficient squared measures the degree of determination by each cause and is called the coefficient of determination. It is h) 13 convenient to represent path coefficient by single small letters. If the causes are independent of each other, a the sum of the squared path coefficient is 5) 6) unity. If the causes are correlated, terms representing Joint determination must be recognized. The squared path coefficient and the expres- sion fer Joint determination measure the por- tion of the squared standard deviation (variance) of the effect due to the causes singly and jointly, respectively. The correlation between two variables can be shown to equal the sum of the products of the chains of path coefficients along all of the paths by which the variables are connected. From these statements, two equations have been developed, namely, 1) expressing the complete determin- ation of each variable by others, and 2) expressing the correlation in terms of path coefficients. The fellowing figure (2) and the equations will ”B X c illustrate the basic concept of the path coefficient: A a. fqgc FIGURE (2) 1h The X and I represent the effects (dependent variables) and A, B, C, D, represent the causes (inde- pendent variables). a, b, c, d, and a', b', c', d' are the respective paths leading to X and I; The correlation between causes B and C are represented by r Since BC“ variable X is dependent on A, B, C, it could be equated as: u l x: A + B + c (1) By simple algebra, if'X is squared, the yhglg term on the right hand side must be squared which reduces it to .8 trinomial expansion. Thus the variance of X, which is the sum of squared deviations divided by "n" can be shown to be equal to the sum of the variances plus any Joint terms resulting from the existence of correlation between the variables. The fermula (1), expressed in terms of variances reduces itself thus: 62x ' §A+§B+§G + zras‘Aab + 21.300305 + 21.110410?) (2) A If no relationship exists between A and B or A and C, the formula simplifies into (3): _ _ . : 0' 0’ 0’2]: -62A+£B+0;C+2rBC-BC (3) Dividing throughout by ng (3) becomes, 15 d’ , ,2 2 2r ‘fB C (4) (A-Jh/6- BC i' +- + 1e0 1' 2 2 2 2 .0711 o’xo’x fl By definition of path coefficient a 54; , b =‘B , c .60 , - 6X if 4’2 therefore, the complete measure of determination of X in terms of the other variables becomes: 1.0 : a2 + b2 + c2 + 2rBCbc (5) In other words the variance of the X, the effect, is completely determined and is equal to the squared path coefficients leading to it plus any terms resulting from the effects of Joint causes. Similarly, a relation could be established for I or for any other effects. The correlation between two variables (X and I) can be shown to be equal to the sum of the products of all the; path coefficients connecting the two variables, thus: rXI : bbi + set + b chci + chCbi (6) Path coefficients can be measured by use of the least square method--linear. Nelson (l9h3) has pointed out that the least square method, to determine the path coefficients from each of the causes to a single effect would result in a more complete estimate of the corre- lation coefficients. 16 By path coefficients the following formula could be derived from the figure (1) on page 9. 0’2? ' 62H * 6:: * 2rHEJH (E (7) But: 2 {'. 2 2 2 - (8) JH JG JD 61 . The formula (7) can thus be written as: 2 (H013 (9) 2 2 2 2 fp=dg+6D+fI*KE erS By dividing throughout by 03? : 2 2 2 E 0’? :60 0'1) (1 (E farm (10) w definition of path coefficient 6% .. hg from figure (1): Thus formula 10 becomes: 1.0 : h2g2 h2d2 h2i2 e2 2er eh * (11) J4 If no correlation exists between H and E, 2r HEeh becomes equal to zero. Thus it could he seen that an ohservalle character- istic or phenotype is the product of several factors, and HE “’ * 2r eh is also written.as 2 cov. or 2 " . HE (HE ' 17 the greater the accuracy one develops in eliminating the non-transmissable variances from the total, the more precise will be the prediction of the genetic merit or correlation. ‘ This useful knowledge of path coefficient has been utilised in the present study for the ensuing dis- cussion on heritability, which is an important tool in the hands of a breeder. Thus, any heritability estimate of characteristics would be fundamentally an extension of the path coefficient principle. ANALYSIS 9;; VARIANCE, Ilé DERIVATIVES, THEIR gsE IF. BIOMETRI08: ' 2' ' A A Since the time it was first presented by Fisher in 1925, it has become one of the most useful tools in the field of biometrics. It has provided the workers with a very powerful and effective means of breaking down the "causation complex” into its elements. The analysis of covariance and intraclass correlation are all extensions of this fundamental concept. Under path coefficient it was considered that the variance of Q’sample with "n" variates could be used to estimate the variance of the population. But when one is dealing with "N" variates in a large sample, whose constituent parts are made up of "k" sub-samples with "n" variates in each (N: nk) of them, the estimate of 18 the population variance would then consist of two inde- pendent variances, namely, the variance of the sub- samples drawn at random and the variance of the means of these sub-samples (the variance of all the sub-samples put together is better estimate than the variance of one sample). Either of these variances could be used to estimate the population variance. The variance of the sub-samples is termed as the variance within group or zandom variance or error term, and the variance between the subesample means as the between the group variance or the systematic variance. While the variance within the group is the best estimate of the variance of the population, which is always true under any condition, the variance between the groups depends upon whether or not the sub-samples are under any systematic influence. For example daughters of different sire groups or as a result of different treatment of sub-samples, in other words, whether or not the sub-samples came from the same parent pOpulation or from different populations. The differences between these two variances are then tested by means of "F"-test, which is a ratio between the variance over that of the within the variance. If F-test proves to be insignificant, one would conclude that no significant difference exists between the two 19 variances and that any one of them would be a good esti- mate of the population. If F-test turns out to be sig- nificant, it indicates that the differences between the sub-samples are real and not due to any chance in random sampling. It cannot, therefore, be used as an estimate of the population variance. And where one is interested in obtaining a measure of population variance, as in the different methods of heritability estimates, this system- atic difference, if significant by F-test, must be removed from the total variance. If not significant either of these two variances might be used to estimate the popula- tion variance. The following is the fundamental indentity of analysis of variance:2 - 2 5(x-ggz 3(x s'Xh)2 S(X-X8) nk-i k-l k(n—1) where nk: N, Xm. grand mean of the whole sample, and X5 . the mean of the sub-sample. The factors in the denominators represent the degrees of freedom. The first term on the right hand side is the variance between the means of the sub-samples and the second term is the variance within the group (error term).. The analysis of covariance is an extension of this principle used fer two or more sets of variables. The 20 error term in this is corrected not only by the analysis of variance method but also by multiplying-it with the coefficient of regression of the dependent variable on the independent variable. The regression coefficient is given by the ratio of the covariance to the variance of the independent variate, which tells in actual units the nature of relationship existing between two things. In the ratio, the unit of the independent variable is one and is understood when expressed in terms of the regression coefficient. "The regression coefficient which results from the use of two or more sets of variables in the analysis of covariance, has been used in the present study to obtain correlation coefficients and heritability estimates. Thus, it could be seen that the concept of analysis of variance is an important addition in solving genetical problems. DIFFERENCE BETWEEN REGRESSION COEFFICIENT _A_N_1_)_ CORRELATION COEFFICIENT: 6 r 'w " Since these two terms are used so often in bio- metrical studies, one is cften asked to express the differences between them: Correlation is an attempt to summarise in one number the degree of relationship existing between two 21 things. The method used to obtain it is essentially an averaging process by which an average relationship is established. The primary use of it is to show in one number the relationship existing between two variables. Regression coefficient summarises in one number the ngtugg of relationship existing between two variables. '.The relationship between these two statistics expressed mathematically would thus be: xy' Tbyx . bxy_ - Geometric average of the two regression coefficients. where r = correlation coefficient, b a regression coefficient and x and y are the independent and dependent variables. Also: bx.y e r% The value of correlation coefficient can range from -1.0 to + 1.0. When the correlation coefficient is +1 or - 1, there is perfect positive or negative relation- ship between the two variables. The primary disadvantage of correlation is that it always assumes linear relation- ship, whether that assumption is correct or not. The square of the correlation coefficient r2, as pointed out in path coefficient, is the coefficient of determination, which gives a measure of the percentage of the variance of dependent variable (I) that has been accounted for by the relationship with the independent variable (X). 22 The regression coefficient doesr not assume any linear relationship. Since tle main purpose of the regression coefficient is to describe the nature of relationship and to hhow the rate of change in one factor in terms of another, it is found both in linear and non-linear functions. In a linear function, as the increment is constant the "b" Tecomes constant, while in a non-linear function since the increment is variable, tle Tb" also becomes vorialle with (X). As "r" approaches 1, the value of "b" is a more accurate estimate of the genetic variance of daughtéh on dams, tut as "r" becames zero, the value of "h" loses much of its significance. Lush (1940) pointing out tle differences between these two statistical terms as applied in genetics, reported that while selection of dams would reduce the parent- Offspring correlation coefficient, it would not hiaskthe regression coefficient of these related animals. In a population where no selection has been practiced, either of these statistics i.e3 "b? or,!r",i could.be used with.advantage to determine genetical relationship. But where selection has been done the regression coefficient is a better measure than corre- lation coefficient particularly in heritahility estimates. However, while selection of dams would reduce the "r“, the selection of offspring.would 23 impair both the statistics. One of the chief differences between the intra- breed daughter-dam correlation and regression, and the intra-herd intro-sire correlation and regression of daughter on dam, is that in the case of the former the environmental damnonent is not removed, while it is discounted in the latter. Thus a genetic correlation which to some extent also includes a fraction of envirsonmental influences is obtained by the latter method, which is the basis in the present heritability estimates. As Lush (1942) pointed out, the intra-breed daughter-dam correlations are usually 2 to 3 times larger than the intra-sire daughter-dam correlation._ This difference is due to the fact that breed is not an homogeneous popu- lation and that a certain amount of Teterogeneity exists from animal to animal, herd to herd, and the progenies of one sire with the other. PART I HERITABILITY Lush (19A9) has defined heritability as: that fraction of the observed or phenotypic variance which is caused by differences between genes or the genotypes of the individuals in a particular population. It is used both in broad and narrow sense. In a broad sense it refers to the functioning of the whole genotype as a unit in contrast to the environment. According to the laws of Mendelian heredity of segregation and recombina- tion of genes, it is impossible that the genotype as a unit would be transmitted. Instead some of the genes may interact with others in such a way as to produce a non-additive effect, which in certain combinations have effects quite different from their average effects in a given population. The differ- ences between the actual effects in each combination and their average effects in the whole population are called dominace deviations and epistatic devi- ations, which are seldom, if at all, transmitted. Since, they would not materially add to ones estimate of heritability of characteristics, these non- additive influences are generally discounted. The heritability in its narrow sense would then include only the average effects of the genes i.e. the additive genic differences. The breeder is mainly interested in heritability in its narrow sense, since it expresses the fraction of the phenotype that one could recover in the offsprings. Theoretically, heritability could range from O to 1, though these extremes rarely occur. High or low herita- bility would indicate high or low heredity of a character- istic. In deriving the mathematics of heritability by path coefficient, the following terms have been used, 25 which signify thus: ,3, fin N I {D‘ Z Phenotypic variance, also called observed, to- tal, or actual variance. Hereditary variance (in the broad sense). Also called the genetic or the genotypic variance. _ Environmental variance, which includes both temporary and permanent effects of environ- ment. variance due to the interaction between heredity and environment. _ Genie variance. Also called genetic, addi- tively genetic, or hereditary variance in the narrow sense. variance due to dominance. variance due to epistasis. Also called non- linear interaction. Ngte: In biometrics, particularly in heritability esti- mates, since one is interested in the study of the differ- ences between individuals rather than actual values i.e. variations, it would be best to express these differ- ences in terms of their squares or variances. While working with actual data, these differences are expressed in terms of regression and correlation. MATHEMATICAL DERIVATIONS Qfi HERITABILITY: As has been already pointed out an observed characteristic or phenotype is the product of the com- bined effects of environment and Wit; in their broadest 2.6. sense. By heredity in the present context is meant the whole combination of the genes in an individual. Some characteristics may be affected more by the one than the other. Mathematically a phenotype could be a function of heredity and environment, thus: P : f(H,E) ‘ (12) To determine P the best way would be to combine the differences in heredity and environment, which could be expressed as figure (1): P : H + E ‘ (13) According to path coefficient, H and E are the causes and P is the effect. The effect and the causes stated in terms of variances could thus be expressed as in formula (7) on page 16. Since theéfi could be subdivided into 3 variances, 1) due to additively genetic, 2) due to dominance, and 3) due to interaction, formula (7) could be expanded as referred to in formula (9) on page 16. Due to the linear_. ; nature of the relationship between the variables G, D, T, no correlation exists, except in the case of two related individuals, which may show some correlation in any one or all of these variances. Further, if heredity and environment-are uncorrelated, the covariance term nggahah would be equal to zero, which would then reduce the fermula (9) to its simplest form showing more clearly the relationship that exists between phenotype, 27 heredity and environment, thus 2 2 2 ' 2 2 JP "' 6c; ‘5 6D " 61 + 62-3 (14) Ey using the formula (9), one could then express herita- hility in terms of mathematics, thus: 1) In the troad sense: 6g 6'2 6+ 6'2 I + 2 Heritalsility = H g G D 6 I 2 + 2 ,_ 2 + 2 .. 5?... a“; go 6'3 61 63 H1 By path coefficient h.i 02$. Therefore heritatility P in the broad sense a h . 2) In the narrow sense: I-Ieritaizility 02G .3 3G 2 2 2 2 .+ 2 + 6 6 * 6 + 6 0; gm P a, G D I a By path coeficient hg : G . Therefore heritatility in the narrow sense 3 h2g2 . Thus, expressed mathematically, heritability repre- sents a ratio, which could be altered hy change in values in the nuemrator or denominator. Since tie denominator includes tie numerator, any change in values in the 28 numerator automatically affect the denominator. Further, since these values refer to a particular characteristic in a given population, heritability estimates would also therefore apply only to the characteristic in the popu- lation under study. IMPORTANCE 9;: HERITABILITY: In any planned breeding program through selection a breeder is most interested in knowing what fraction of the total variation observed in a population for a given characteristic could be recovered in the progeny. Thus, an estimate of heritability in that particular characterp istic would be important and useful to him, since it would indicate the improvement he can effect per generation, on an average, through selected parents. Any improvement in the genetic material credited to his herd by the breeder would be permanent. As Briquet, Jr. and Lush (1947) have concluded that when heritability is high, there is less room to influence a characteristic by the dominance, epistasis, and environmental effects to any appreciable extent. In such instances, mass selection (phenotypic selection) without any attention to progeny, pedigree, etc. is most effective in producing the desired effect. If heritability in its narrow sense is low the breeder must lay less 29 emphasis on mass selection and more attention to progeny selection, pedigree estimates, sib relations etc., since there is considerable room for the non-additive variations including the effects of environment on the genotypic expression of the individuals. In other words, the various aids in mass selection have been advanced,to solve selection problems where heritability is low; If epistasis forms a large fraction of the total variance, the selection should be practiced between families and the linebreeding type of inbreeding followed in order to create new lines distinct from each other. If overdominance is important, Lush (1949) Points to the develOpment of inbred lines, then testing these in crosses with each other, and then multiplying the ones which cross most favourably so as to develop them on a commercial scale. .If variance due to the interaction between heredity and environment is large, Lush (l9h9) suggests producing a separate variety fer each ecological niche, if it is large enough to justify the cost. Estimates of heritability could be used profitably as genetic constants in setting up selection indexes. Finally, heritability estimates provide an important source of information in measuring the relative importance of characteristics for developing culling programs and 30 selection of breeding animals One of the principal purposes of the study is to determine the estimates of heritability of some economic characteristics, such as milk production, butterfat production, and butterfat test, in the Michigan State College dairy herd, which consists of all the five common breeds. SOURCES QE ERROR lfl.HERITABILITY ESTIMATES: Errors due to sampling may bias heritability estimates. To overcome such errors one should increase the volume of the data.' Certain kinds of relatives, such as sibs developed in the same uterus, or animals raised under similar conditions may show environmental correlations, which would result in poor estimates. Errors may be introduced into the estimates as a result of mating systems practised in the herd which might be different from random. In such instances corrections should be made for the particular system of breeding, Hazel et al (l9h5). If the genotype as a whole function in a way different from the additive effects of all the genes, it may result in producing small or large deviations between genotype and phenotype of the individuals. 31 REVIEW OF LITERATURE 5. METHODS QE ESTIMATING HERITABILITY: Lush (l9h0, 1945, and 1949) has proposed sev- eral methods of estimating heritability, and one or several of these methods have since been used in large numbers of investigations to estimate heritability. Fundamentally these methods depend upon the similarity of related individuals. The closer the relationship the more accurate one could predict the genetic relationship and thereby the more reliable will be the heritability estimate. In other words, with the help of these methods one tries to find to what extent phenotypic likeness parallels the genotypic likeness. Or in terms of sta- tistics it is the regression of the genotypic differences on phenotypic differences. Estimating heritability among unrelated animals would be most unprofitable because of the existence of very little genetic correlation. Generally the methods for estimating heritability include: the study of isogenic lines, parent-offspring correlation, and regression, developing high and low ,lines by selecting in the opposite directions from the same initial population, full sib and half sib resem- lances (correlation). Since these methods have been dealt with in detail 32 by Lush (1940, 19h5, and l9h9) it was thought to summarise very briefly the various methods separately. Isogenic Line Method: Egg 9; Identical Twins and Homozygpus Lines. In view of the very rare occurrence of the iso- genic lines, particularly in dairy cattle it has not much practical importance. The only examples of isogenic lines are identical twins (homozygous). In a later study on twins it will be shown that these very seldom occur. Any variation within an isogenic line is wholly environmental The relationship between two individuals of same genotype or between identical twins is 1.00 or 100 per cent, hence the ratio of the variance or the correlation coefficient is the estimate of heritability. This method is the only method which will measure in animals both the additively genetic variance as well as the non-additive variance due to dominance and epistasis. The heritability estimate could be obtained in two ways, 1) the method of intraclass correlation as outlined by Snedecor (1946), where the variance between the iso- genic lines is compared with the variance within the population under study, and thus, obtain directly an estimate of heritability. The variance within the iso- genic line is wholly environmental; 2) the method of 33 single classification of analysis of variance method. If (T) is equal to total observed variance, (H) the variance between the members of same isogenic line which is environmental and (E) the variance within the randomly chosen population under study, which is genetic, one can write the relationship as: T u H + E or E g T - H Then heritability could be expressed and obtained directly thus: Heritability g_%_ u T - H Some of the disadvantages of this method besides being rarely applicable to farm animals, are 1) that environment under which the individuals of an isogenic line are raised may be entirely different from those in the general population. Consequently it might result in an overestimate of heritability of a given characteristic; 2) the variance between the lines might include some interaction between environment and heredity, which might also increase the heritability estimates; 3) identical twins in farm animals are so rare and even if they do occur it is immensely difficult to identify them. However, if one could develop by intense inbreeding, homogenous lines with q a 1.0, one might probably overcome this problem, since any variance within a homozygous line is entirely environmental. But the expense and the time 3h involved for such an undertaking in farm animals does not warrant such a costly venture. Besides, mutation pressure might upset the homozygosity by changing the frequency of "q". Selection Experiment Method: Several workers have used this method in their investigations. One of the classical examples of this method was presented by "Student" (l93h) on his analysis of Illinois selection experiment for high and low oil content in corn. By using the contrasting lines and their progenies of the succeeding generations, he was able to determine the genetic variance from the differ- ences between these lines. The method depends on seeking to develop a high and a low line by mass selection in the opposite directions, from an initial population so that a regression (slope) of offSpring on parents might be obtained. Since any phenotypic characteristic is the product of joint effects of both environment and heredity, the heredity alone being transmitted, the offspring therefore show a ten- dency to regress to the herd average in a random popu- lation. The principle involved in the method is that differ- ences produced between two lines are divided by the total 35 amount by which phenotypes of the parent in all the generations exceeded the mean of the generation in which they were born, Lush (19h9). By path coefficient, as the correlation between parent and offspring, is 0.50 of the hereditary variance; (rOP . 1/2 h2), it should be multiplied by 2 to obtain an estimate of heritability. Since correlation is the geometric aver- age of two regressions b0? and bPO’ the same factor 2 is used to multiply the regression coefficient to get an estimate of heritability. Besides genetic, some of the epistatic variance might be included in the estimate, but the effect of dominance would be excluded from it. After the lst. and 2nd. generation of selection the epistatic effect becomes so diluted that it would not effect the heritability estimates in its narrow sense. Thus to obtain a more reliable estimate of heritability, one would do well to discard the first two generations. The differences between the first two generations and the later genera- tions could be used to estimate the variance due to epistasis. The method has its greatest advantage where selection has been practiced for only one characteristic. But where more than one characteristic is involved, which would be the case generally, one might obtain an erroneous estimate of heritability. Further, it is rarely to be 36 expected that a breeder could afford to practice se- lection in the opposite direction, besides selection for more than one generation poses problems of replace- ments which must be made within each line itself. And finally, for an adequate control of environment for both the lines it becomes necessary for selection in the opposite direction to be practiced in a contemporary control line. Intra-Sire Daughter-Dam Regression 2;,Correlation Methodh It is one of the most frequently used methods. The principle is fundamentally based on path coefficient and coefficient of relationship between the parent and off- spring. It could be shown by path coefficients that the correlation between parent and offspring is half the heritability estimate (rOP : 1/2 hz), hence the corre- lation or regression is multiplied by 2 to give an esti- mate of heritability. In other words, since each parent contributes, on the average, only half of the inheritance to its offspring the "r" or "b" must be doubled in esti- mating heritability. A . l The correlation between parent and offspring includes half of genic variance and somewhat less than one fourth of epistatic variance but does not include the variance due to dominance. Further, the correlation 37 might include some of the environmental variance, which could be reduced to zero by proper experimental design. Hence, the main object of setting up the analysis of parent-offspring data on an intra-sire basis is to elim- inate this environmental variance and also to discount for any non-randomness in breeding system. In the case of environmental correlation it is offset by this method because, 1) the daughters and the mates of a sire are kept nearly always in the same herd. And therefore the differences in the management from herd to herd would be removed along with the differences between sires instead of contributing to the daughter-dam correlation; 2) the offspring of a sire are nearly contemporary, which elim- inates any deviations in management contributing to daughter-dam comparison. Since heritability by this method expresses the fraction of the variance which existed among the females mated to the same sire, any deviations from random mating are eliminated. The main procedure in the method involves estimating how much difference could be expected between their off- spring per unit of phenotypic differences between those dams. In term of statistics, it seeks to determine the regression of genic differences among those dams on the phenotypic differences among them. The use of offspring 38 in the method is, thus, merely to indicate genic values of their dams. Broadly the steps in the calculation, which also apply to other methods involving parent-offspring and sib comparisons, are: 1) discount the environmental variance, 2) multiply the resultant correlation by the appropriate factor to change it to heritability estimate, and 3) cor- rect for any non-randomness in mating system. If the population is breeding at random no correction is needed, otherwise, divide by l+m if the population was inbred, or by 1+rSD, if it was phenotypic assortive mating. Here "n” is the relationship between mates and "r"3D is the phenotypic correlation between mates. Intraedam regres- sion of offspring on sire could also be done similarly, but is rarely done due to meager data because of fewer offspring produced by dams as contrasted to sires. Full-Sib Correlation Method: It is very similar to parent-offsPring correlation method.. The coefficient of genetic relationship between full sibsin a randomly bred population is 0.50, i.e. they inherited half of the genic variance from their parents. Therefore, as in the ease of parent-offspring correlation, the regression or correlation is multiplied by 2. But the phenotypic resemblance, besides contain- ing half of the genic variance, also contains about one 39 fourth of epistatic variance, a little less than one fourth of'dominande variance, and the variance due to common environment between full sibs. Since the estimate contains the fraction of the dominance as stated above and some amount of environmental variance, it would be somewhat higher than the estimate by the parent offspring method. It is important in this method, therefore, to dis- count for environmental variances, otherwise the estimate would be biased. Any error of sampling would automatically be multiplied by 2. The best way to overcome this short- coming is to analyse the data on a intra-herd basis. The procedure in calculating is similar to the one enumerated in parent-offspring method. Half-81b Correlation Method: Unless very large amounts of data are available, which would substantially reduce the errors of sampling, this method is not as accurate as other methods described so far. The coefficient of genetic relationship between half sibs, if randomly bred, being 0.25, the correlation should be multiplied by k to get an estimate of herita- bility. Generally, the method is worked out on the basis #0 of parental hal£ sib and the data analysed by intra-class correlation by analysis of variance method as outlined by Snedecor (1946). The estimate includes genic variance, a small fraction of epistatic variance but does not include any dominance. As regards the environmental variance, if the data were analyzed on paternal half sib basis, it would not include any of the maternal environment. But if they were analysed on a maternal basis, the estimate would include 4 times the maternal environment and nothing from the paternal if the differences in half sibs are as large as those of the non-sibs. Further, it exaggerates samplingg error when multiplied by 4, which is a distinct disadvantage inherent in the method. To discount these environmental influences would be to run the analysis on intra-herd and intra-seasonal basis. Intra-seasonal analysis would correct for any differences between seasons which are apt to occur in old herds. Since the method primarily concerns the comparison of sibs and does not take into account parental phenotypes it could be used with advantage in those animals whose traits are measured by destroying them, such as the car- cass of meat animals. The procedures in calculating are similar to those noted in parent-offspring method. yfid-Parent-Offspring Correlation 9;_Regression Method: The method is similar to the parent-offspring method, except that in the place of one parent, the average of both the parents are included in the study. The estimate under this method includes genetic variance and somewhat less than half of the epistatic variance as was the case in the parent offspring method. Dominance is excluded and if the population has been properly randomized environmental variance also would be eliminated. By the theory of path coefficient as shown in Figure (3) the correlation between parental averages (mid-parent) must be multiplied by 1.41 to obtain an ‘ estimate of heritability. This method cannot be applied for characteristics if expressed in one sex only. Also it cannot be used for estimating such traits which one could only measure by destroying the animals as in the case of meat stock. The procedure is similar to intra-sire offspring- dam method. Derivation of the factor 1.41 by path 42 coefficient method: I b ‘5'. .\'9~e5'"— ) LX)\$ °’ an-anE NT orrfpflmg‘k t G / , O 3 ‘Da” )5 °\'.\G KOO (Pam ) A Sim... HtD-pgar/ (X) A Data- (X) X and X' 3 Observed characters in sire and dam. FIGURE (3) The degree of determination for Figure (1,b) is: 1 . 82+ 82 2 ' 83W The correlation between mid-parent and offspring from Figure (1,a) would be: or 1 g 2 s rGM : 2 x hgabhgs Since ab by path coefficient is equal to i, the fermula becomes: 2 2 r M = 2 x i xv; h g 43 rOM : \l: 11252 h2g2: rOM /\/—{ or 1.41 x rOM Heritability : 1.41 x rOM . Qigllgl ngssi g Methgd: This method consists of breeding two sires to the same females at two different times and then analysing the differences in full sibs, maternal or paternal half sibs. (The resultant regression or correlation is then multiplied by the appropriate factor to get an eestimate of heritability. If the data used were from full sibs, the estimate would contain some fraction of dominance, epistatic and environmental variance as pointed out in the discussion under full sibs. But, if the estimate was determined from the half sibs, the dominance would be excluded. The method was originally used to measure the breeding merit of the sires and it could be used with advantage in meat animals or in those where the traits could be measured in both the male and female progeny. It, therefore, has no practical value as a method for heritability estimates in dairy cattle. A. METHODS USED IN THE PRESENT STUDY: For a best estimate of heritability of all the Ah three economic characteristics: milk production, butterfat production, and percentage of butterfat in the M.S.C. dairy herd, the following three methods were chosen for the present study: 1) Intra-sire regression of daughters on dam method, 2) Intra-sire daughter-dam correlation method, and p 3) Paternal half-sib correlation method Finally, to obtain a best aggregate estimate, the weighted average of these methods, the weighted average of five breeds and the weighted average of three methods and five breeds have been calculated. The methods, procedures, calculations and discussions are presented on the following pages. The data was further made use of, in addition to the heritability estimates, to a study of the following factors which have important bearing in dairy cattle breeding enterprises: l. Repeatability of milk yield 2. Repeatability of butterfat production 3. The effect of the month of calving on the fellowing lactation 4. Sex ratio 5 Twin ratio 45 g. HERITABILITY AND REPEATABILITT ESTIMATES FOR Tails; IN DAIRY CATTLE The heritability estimates for the economic characteristics in dairy cattle, investigated in the present study are the milk production, butterfat pro- duction, and butterfat test. The repeatability estimates are confined only to the milk and butterfat. Due to the very slight variation in butterfat test that exists between one lactation and another of the same cow, it could be considered for all practical purposes to be close to 100 per cent. Hence, the calculation of the repeatability of the test was thought to be unnecessary. Only the literature pertaining to milk production, butterfat production, and butterfat test have been reviewed here. A general review of the heritability of these traits previous to 1941 was presented by Lush (1941), while the review on repeatability previous to 1940 was made by Dickerson (1940). To these have been added those estimates not included in the above reviews as well as those investigations published subsequent to them. The reviews on these topics have been set out for the sake of brevity in a tabular form, Table I below: TABLE I 46 ESTIMATES OF HERITABILITY AND REPEATABILITY FOR VARIOUS CHARACTERISTICS IN DAIRY CATTLE .I_. HERITABILITY: 5. MILK ‘ ‘ Herita- Method used to Reference bility determine (percent) heritability I 41 Regression of Daughter Edwards 1932 on Dam 57 Regression of Daughter Rice 1933 on Dam . 53 or 56 Full sib Gowen 1934 38 Regression of Daughter "Brain Truster" on Dam 1936 33 Regression of Daughter Lush and Arnold 1937 on Dam 38 Regression of Daughter Lush et a1 1942 on Dam (dams' lst. (Iowa D.H.I.A. record with daughters) records) 68 Regression of Daughter ” " " on Dam (dams' later records with daughters) I. HERITABILITI: B. BUTTERFAT 23 Regression of Daughter on Dam 51 I! I! R n ,3 .. . . .‘. 12 Intra-herd daughter- dam correlation 25 (about) .Intra-sire daughter- dam correlation Gifford 1930 Gifford 1930 Copeland 1932 Plum 1935 Lush and Shultz 1936 47 TABLE I I. HERITABILITY: B. BUTTERFAT (Continued) 28 Regression of Daughter Lush and Arnold on Dam 1937 27.5 Regression of Daughter Lush 1940 (Iowa on Dam (dams' 1st DHIA records) record with daughters) - 28 Intra-sire regression Lush 1940 " 25 Regression of Daughter Lush et a1 1942 on Dam (dams' lst (Holstein HIR record with daughters) records) 62 Regression of Daughter " " " on Dam (dams' later records—with-daughters) 30 Regression of Daughter " " " on Dam (dams' 2nd. record with daughters) 75 Regression of Daughter " " " on Dam (dams' other records-except 1st and 2nd-with daughters) 26.8 *Intra-sire regression Lush and Straus 1942 26.8 *Intra-sire correlation Lush and Straus 1942 17.4 #Intra-sire regression Lush and Straus 1942 27.4 Intra-sire linear Beardsley et a1 1950 regression 31.0 *Intra-sire regression Chai 1951 17.0 #Intra-sire regression Chai 1951 ;. gERITABILIggz g. BUTTERFAT TEST 86 Regression of Daughter Rice 1933 on Dam 83 Full sibs Gowen 1934 #8 TABLE I ;. HERITABILITY: Q. BUTTERFAT TEST (Continued) 50(about) Intra-sire correlation Lush 1936 1L REPEATABILITY: ,5. MILK 65 66 73 37 32 48 Intra-breed Correlation Intra-breed correlation Within-herd correlation All sires correlation (uncorrected records) A11 sires correlation (corrected) First'record-over'later records of dams (Jerseys-all herds) Gowen 1920 (Holsteins-all herds) Gowen 1924 Sanders 1930 Gaines 1935 Gaines 1935 Lush et a1 1942 I_I_. REPEATABILITY: g. BUTTERFAT 69 71 54.7 54 60 40 Intra-breed correlation Intra-breed correlation Intra-herd analysis of variance (Lactation records) Intra-herd analysis of variance (C.T.A. records Intra-breed correlation (All herds) Intra-herd analysis of variance (Jerseys-all herds) Gowen 1920 (Holsteins-all herds) Gowen 1924 Harrish et a1 1934 Harrish et a1 1934' Plum 1935 Plum 1935 49 TABLE I II. - BREATAQILITY: a. BUITERT‘AT (continued) 45 75 88 43 43, 4O 34 First record over later Lush and Arnold records of dams 1957 Intra-breed correlation COpeland 1938 (Jersey R. of M; Cows) Intra-breed correlation Copeland 1958 (Jersey Herd Test cows) Intra-breed correlation Berry and Lush (Holstein HIR records) 1939 First record over later Lush 1940 records of dams First record over later Lush et a1 records of dams (Iowa DHIA 1942 records) First record over-later Lush et a1 records of dams(Holstein 1942 HIR records) Analysis of variance Chai 1951 the: The repeatability estimates on Intra-breed corre- lations based on all herds in the above review show markedly high values. This is due to not discount- ing the effects of temporary enviornment or to differences in herd enviornment. * Expressed in terms of the average of all records. # Expressed in terms of what it would be if each cow had only one record. The formula used to transform the heritability estimate based on the average of all the records to bani one record is as follows, Lush (1942): [1 + (:1 - 1)rdd] , if all the dams had the same number of records (m). 2 b - .. [1 + h - on. . on - an 1'11 n3 The estimate on single record is generally lower than that on average records. 50 where m is the average of lactation records of all dams when they are variable, b is the regression of daughter on dam when single records of/each are used, b' is the regression when lifetime averages are used, rdd is the repeatability within herds; i.e. the average correlation between successive lactations of the same dam, and (3m is the variance of the (m) lactation records of dams. SOURCE 9}; DATA The data used in the present study are the pro-'\ duction records of the dairy herd of Michigan State College at East Lansing, accumulated over a period of several years. The earliest production records date as far back as 1919. The college, a part of the State Agricultural Experiment Station, intended mainly for teaching and demonstrational purposes to the farmers of the state of Michigan, is comprised of all the five com- mon dairy breeds viz. Holsteins, Jerseys, Ayrshires, Guernseys, and Brown Swiss. All of these animals have been registered in the reapective Pure Breed Associations. Records of cows transferred from time to time for experi- mental purposes such as nutrition etc. have been excluded from the study so as to keep down the influence of environment as low as possible. A total of 473 cows from all five breeds were 51 available for a preliminary study. Cows that were sold or disposed of otherwise or such of those with lactation periods less than 275 days were not included in the study. It was thought that any cow with less than 275 days of lactation period might have been under a dominating influence of environment such as, state of health, age, etc. Generally under normal conditions of heredity the occurrence of such low periods of lactation are rare, if not completely absent. In the present analysis, inclu- sion and study of such extreme values of production would not serve any useful purpose. Further by adjusting these incomplete records to mature equivalent one would be only giving far considerable weightage which might not exist, thus introducing inaccuracies. NEED FOR STANDARDIZATION 92 RECORDS: To provide a basis of comparison between cows and also to predict the relative breeding efficiency of sires, it would be necessary to adjust or standardise the records for environmental variations. The interplay of physiolog- ical factors, the effect of age, the climatic influences within and between years, management, number of times milked per day, and length of lactation period are some of the environmental factors which have a definite bear- ing on the expression of an animal's productive 52 characteristic-phenotype. To correct for all factors, however, would be impossible as good deal of effort and time is involved but by adjusting at least for two or three most important environmental conditions a compara- tive reliability could be attained on the average to a whole or part of the population. Finally, it is of utmost importance that correction factors should not be subject- ive. 1. Cows born as identical twins which have the ability toreact alike to changes in environment would produce differently under different management conditions, Lush , (1937). 2. Cows with larger body size have greater feed capacity and thus production of more milk. Turner (1929) reported that when age was held constant there was on the average an increase of 20 pounds of butter fat for an increase of 100 pounds of body weight. He further stated that about 25 per cent of the total increase in fat is due to live weight of animal and 75 per cent of increase is due to the development of udder. 3. Breed differences also influence production; breeds which produce a milk of high fat content give less milk than those which are lower testers, for example, Holsteins and Jerseys, Gaines (1931). He also pointed out that efficiency of production in dairy cattle decreases 53 with increasing body weight of the cow. 'Within the breeds, heifers are more persistent than cows, because a heifer is increasing in size and in the amount of secretory tissue in the udder. But as regards the efficiency, Edwards (1936) reported that cows are more efficient producers than heifers. He also reported that stage of lactation in dairy cattle gener- ally effects the gross efficiency, i.e. steady decline in efficiency from 38.75 to 29.25 per cent with the advance- ment of lactation. 4. Kendrick (1941), has concluded that a cow milked 4 times a day increases her production by 35 per cent and when milked 3 times a day the increase is about 20 per cent over what it would have been on a 2 times a day milking basis. Likewise more milk is produced in a 365-day period than in 305-day period. Edwards (1936) also found that 3-X milking is better than 2-X milking. 5. On the effects of management on production, a classical study was made by Eckles (1939), who compared the milk and fat production of the same cows under differ- ent conditions. Forty one cows under farm conditions produced an average of 8395 pounds of milk and 343 pounds of butterfat but under official test conditions this was raised to 14331 pounds of milk and 564 pounds of butter- fat, an increase of 70.7 per cent in milk and 64.9 per cent in butterfat respectively. 5h 6. As regards the relationship between age and production, several notable contributions have been made, all of which agree as to the non-linear relationship between these two factors. The classical work in this field was reported by Pearl (1914), who derived the non- linear formula between age and production as follows: I c A + BX + CX + D log X, where Y is the pro- duction and X is age. He brought this relationship in more precise terms and stated: The amount of milk produced by a cow in a given unit of time (7 days, 1 year etc.) is a logarithmic function of the age of the cow. . . . Milk flow increases with increasing age but at a constantly diminishing rate (the increase in any given time being inversely pr0portiona1 to the total amount of flow already attained) until a maximum flow is reached. After the age of maximum flow is passed the flow diminishes with advancing age and at an increasing rate. The rate of decrease after a maximum, on the whole, is much slower than the rate of increase preceding the maximum. The above law applies both to the absolute amount of fat produced as well as to milk. Drop in the rate of secretion is not as pronounced because the size of the cow does not change greatly after maturity. Later, Pearl and Patterson (1917) working with 5821 Jersey 7-day records and Pearl, Gowen, and Miner (1919) working with 2153 yearly-records in the Register of Merit of Jersey Breed, also showed the logarithmic form of the curves, which most closely fitted a non-linear second degrees 55 equation as that of the above. ‘They also reported that the maximum yield was attained about the age of 8 years and 7 months. Gowen (1920) in his Studies with Jersey breed, whose records extended as far back as 1897, independently reached similar conclusions. Brody et a1 (1923) studying nearly 50,000 records of different breeds not only agreed with the findings of the early workers, but also concluded further, that milk and fat production gradually increase as the dairy cow becomes mature and then gradually decrease with the onset of old age; thus under similar conditions of feeding and manage- ment a heifer is expected to increase her yearly production at each succeeding lactation period until she reaches maturity. Thus, production gradually increases up until between seven and eight years of age and then gradually decreases with the onset of old age. This is in essence similar to the conclusions of Pearl (1914). The Figure (4) on page 56 illustrates the relationship of age with the various traits in dairy cattle. From the foregoing discussions, it can be seen that an animal's characteristic is a complex combination of both genetic and environmental factors, both of which have varying effects on the phenotypic expression. 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Nam annoy asflas.o naua.s swam oaumsm ma.u~o~ mm ”.moama mo chasm nsoem m manna.o oamm.s mused candor m ”mos as.” «new on osonoeono a emauon.o omno.s cums muses oa.u~o~ mm.” mmaoa on methadone m oeaumo.o seam.“ nMOm humus oa_umma as.” some one encodes a maaumm.o mm.ur.m oumaa muses am ”can rm.” «Hess («ma nonopoaom a an an an ad , an an “hon .opm. coo .>o . moo .bo . . omofil ozoo Mo coma pmmnoppsm commoppom saws sonssz ocean .oz a _ .ona _ , .ena .. . . mammmm.m>Hh was and mom.amma 94m Immasbm 92¢ Bahamaaam MAHE mo ZOHB¢H>MQ QmNHN mnmds 113 The above correlations and regression were then multiplied by the apprOpriate factors, as indicated on page 84. TABLE XXXIX ESTIMATES OF HERITABILITY AND STANDARD ERRORS FOR THE ADJUSTED BUTTERFAT PRODUCTION OF COWS Breed Paternal Intra-sire Intra-sire half-sib regression correlation method method method Herit- Standard Herit- Standard Herit- Standard ability error ability error ability error rI x 4 SI x 4 6 x 2 so x 2 r x 2 SO x 2 Holsteins 0.664 0.412 0.168 0.247 0.143 0.211 Jerseys 1.273 0.472 0.374 0.327 0.297 0.257 Guernseys 0.405 0.584 0.052 0.254 0.060 0.292 Ayrshires 0.546 0.654 0.209 0.287 0.241 0.328 Brown Swiss 1.673 0.583 -0.262 0.278 -0.329 0.344 Just as in the case of milk production, the weighted average of heritability and that of the standard error of butterfat production for all five breeds and three differ- ent methods was obtained by use of the formula suggested by Hazel and Terrill (1945). The desired statistics, such as the squares of the standard errors and their reciprocals required in the use of the above formulae were calculated and shown separately 114 in Table XL. These values were then used along with the heritability estimates in the formulae and the weighted average was thus obtained for five breeds and three methods, which in turn were pooled and a final weighted average for the Michigan State College herd was presented. TABLE XL SQUARED STANDARD ERRORS AND THEIR RECIPROCALS OF THE HERITABILITY 0F BUTTERFAT PRODUCTION. Breed Half-sib Intra-sire Intra-sire Reciprocal method regression correlation sum of 3 method method methods 2 . 3 Shl 1/312,l sfiz 1/sfi2 sh3 1/sfi3 S(i/sfin) Holsteins 0.170 5.88 0.061;16.37 0.045.22.47 44.72 Jerseys 0.223 4.49 0.107 9.34 0.066 15.15 28.98 Guernseys 0.341 2.93 0.064 15.53 0.086 11.70 30.16 Ayrshires 0.428 2.34 0.082 12.14 0.108_ 9.27 23.75 Brown Swiss 0.340 2.94 0.077 12.94 0.118 8.45 24.33 Reciprocal 18.58 66.32 67.04 151.94 Sum of 5 Breeds 115 TABLE XLI 'WEIGHTED AVERAGE OF THREE METHODS (BUTTERFAT PRODUCTION) Breed Heritability Standard error Holsteins 0.212 0.149 Jerseys 0.473 0.186 Guernseys 0.090 0.182 Ayrshires 0.255 0.205 Brown Swiss -0.052 0.203 TABLE XLII WEIGHTED AVERAGE OF FIVE BREEDS (BUTTERFAT PRODUCTION) Method Heritability Standard error Paternal half-sib correlation 0.846 0.081 Intra-sire regression 0.093 0.123 Intra-sire correlation 0.117 0.122 TABLE XLIII WEIGHTED AVERAGE OF THREE METHODS AND FIVE - BREEDS - I . Trait Heritability Standard error Butterfat Production 0.20 0.081 Thus, the final estimate of heritability of butterfat production of the Michigan State College dairy herd, which is the weighted average of all the five breeds and three methods is 0.20 1 0.081. 116 HOLSTEIN HERD TABLE XLIV ANALYSIS OF COVARIANCE 0F BUTTERFAT PRO; DUCTION OF DAMS AND THEIR DAUGHTERS FOR HOL- STEIN HERD 0N INTRA-SIRE BASIS Source of . Degrees of Sums of Squares and Products Variation Freedom 5x2 Sxy Sy2 Total 90 1112470 262644 1145677 Between Sires 20 561534 216503 393243 Within Sires 70 ‘ 550936 46141 752434 (or ERROR) TABLE XLV ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAMS (X) IN HOLSTEIN HERD Source of Degrees of Freedom Sum of Mean Square F-value Variation Squares ' Total 90 1112470 Between Sires 20 561534 28077 3.57** Within Sires 70 550936 7871 (or ERROR) ** F-test highly significant at 1% level TABLE XLVI ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAUGHTERS (Y) IN HOLSTEIN HERD Source of Degrees of Freedom Sum of Mean Square F;value Variation Squares Total 90 1145677 Between Sires 20 393243 19662 1.83* Within Sires 0 gggéERROR’ 7 752434 10749 ;_F-test significant at 5% level 117 JERSEY HERD TABLE XLVII ANALYSIS OF COVARIANCE 0F BUTTERFAT PRO- DUCTION 0F DAMS AND THEIR DAUGHTERS FOR JERSEY HERD 0N INTRA-SIRE BASIS Source of Degrees of Sums of Squares and Products Variation Freedom 8x2 Sxy sy2 Total 59 269496 86679 373 817 Between Sires 19 157827 65828 196973 Within Sires 40 111669 20851 176844 (or ERROR) TABLE XLVIII ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAMS (X) IN JERSEY HERD Source of Degrees of Sum of Mean Squares F-value variation Freedom Squares Total 59 269496 Between Sires 19 157827 8307 2.98** Within Sires 40 111669 2791 (or ERROR) ** F-test highly significant at 1% level TABLE XIL ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAUGHTERS (Y) IN JERSEY HERD . Source of Degrees of Sum of Mean Square F—value variation Freedom Squares Total 59 373817 Between Sires 19 196973 10367 2.34* Within Sires 40 1 68 21 (or ERROR) 7 A“ h“ * F-test significant at 5% level. 118 AYRSHIRE HERD TABLE L ANALYSIS OF COVARIANCE 0F BUTTERFAT PRODUCTION OF DAMS AND THEIR DAUGHTERS FOR AYRSHIRE HERD 0N INTRA-SIRE BASIS Source of Degrees of Sums of Squares and Products variation Freedom 8x2 Sxy 5;,2 Total 37 273154 50338 151100 Between Sires 7 130001 35360 43395 Within Sires 30 143153 14978 107705 (or ERROR) TABLE LI ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAMS (X) IN AYRSHIRE HERD Source of Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 37 273154 Between Sires 7 130001 18572 3.89** Within Sires 30 143153 4772 (or ERROR) ** F-test was highly significant at 1% level. TABLE LII ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAUGHTERS (Y) IN AYRSHIRE HERD Source of Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 37 151100 Between Sires 7 #3395 6199 1.73 Within Sires 30 (or ERROR) 107705 3590 F-test was found to be not significant. 119 BROWN SWISS HERD TABLE LIII ANALYSIS OF COVARIANCE 0F BUTTERFAT PRO- DUCTION 0F DAMS AND THEIR DAUGHTERS FOR BROWN SWISS HERD ON INTRA-SIRE BASIS Source of Degrees of Sums of Squares and Products variation Freedom 2 2 Sx Sxy Sy Total 33 298524 -31306 197778 Between Sires 6 70556 -l424 52836 Within Sires 27 227968 -29882 144942 (or ERROR) TABLE LIV ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAMS (X) IN BROWN SWISS HERD Source of Degrees of Sum of . .Mean Square F-value Variation Freedom Squares Total 33 298524 Between Sires 6 70556 11759 1.39 Within Sires 27 227968 8443 (or ERROR) FCtest was found_to be not significant TABLE LV ANALYSIS OF VARIANCE 0F BUTTERFAT PRODUCTION OF DAUGHTERS (Y) IN BROWN SWISS HERD Source of Degrees of Sum of Mean Square F-value variation Freedom Squares , Total 33 197778 Between Sires 6 52836 8806 1.64 Within Sires 27 1 68 (or ERROR) 4494 53 F-test was found to be not significant. 120 HERITABILITY 0F BUTTERFAT PERCENTAGE One could express the percentage butterfat in milk as merely the ratio of fat to milk from which the amount of butterfat that a cow yields is calculated. In other words butterfat can be expressed as the multiple of milk production and butterfat percentage. While considering the inheritance of milk and fat production it is nearly impossible to separate the two factors, since one who aims at increasing the yield of milk also increases the fat. But certain definite relationships do exist between milk and fat percentage, between fat percentage and age of the cow, fat percentage and the effect of environment such_as nutrition and the seasons, that it deserves to be studied from the point of heritability estimates as a definite and distinct characteristic of a dairy cow. While it is generally agreed that the milk yield has a logarithmic curve in relation to age, Pearl (1914), Gowen (1920) and Turner (1927), it was shown by Gowen (1924) in a study of the associationship of age to percentage of fat of a large number of Holstein-Friesian cows, that a clearly linear relationship exists between the two. He found a correlation coefficient between butterfat and age to be one of negative; -0.075 ;,0.0133, indicating that butterfat percentage has but a slight 121 relation to the age of the cow. During the whole life of a cow, from two years to fifteen years of age the difference in test was, on the average, 0.13 per cent. Eckles (1939), while working with Official Test records of all the five breeds and also the ordinary records of Jersey and Holstein cows made under ordinary conditions, also reached similar conclusions and pointed out that there is no variation in the butterfat percentage of any consequence due to age. A cow of a high-testing breed averaging 5 per cent of fat as a young aminal will decline to about 4.5 per cent if she continues to produce to 14 years of age, Figure (4). The percentage of fat in milk is generally higher in colder months than in the hot months of the year. During the lactation period the percentage of fat in milk varies inversely with the amount of milk secreted, although not in direct proportion. The decline in butterfat percentage usually occurs during the first month, although in some breeds it is in the second month of lactation. From the second and third month there is a gradual but consistent increase in the per cent fat. These increases, however, are not significant enough to justify the use of correction factors, Figure (4). As regards the relationship between milk and the 122 percentage of fat several workers have reported that the relationship generally is one of negative correlation. Gaines (1927), while analysing the Holstein records reported an inverse correlation of -0.229 ;.012. At the same time work carried out on the continent by Bonnier (1927) with 79 cows of Swedish Ayrshire breed also showed a negative correlation between milk and the butterfat test. His cOrrelation figures varied between 0.0169 and -0.8337. A similar analysis by Copeland (1927) of the Jerseys in the Jersey Consolidated Volume resulted in a negative correlation of -0.33 1 0.03. It was also shown by Gaines (1927) that the relationship between these two variable factors was not linear. How- ever, it should be noted that although there exists a negative correlation between milk yield and the percentage of fat, the milk yields do not decrease in the same ratio as the fat percentage increases, otherwise there would be no justification for breeding of higher testing cows. As to the nature of inheritance, COpeland (1927) further pointed out that the high testing sires and dams produce offspring which generally continue to test higher than the breed average, while the offSpring from low testing sires and dams show performances below the herd average. These results could be explained on the basis of Galton's Law of equal inheritance from sire and 123 dam. The methods used in estimating the heritability of butterfat test where similar to those used for milk and butterfat production, namely: 1. Intra-sire correlation coefficient method. 2. Intra-sire regression coefficient method. 3. Intraclass paternal half-sib correlation method. In the method 1 and 2 the "r" and "b" were derived from the intra-sire analysis of covariance Tables, and in the method 3, the "rI" was obtained from the Tables of the analysis of variance of intra-sire paternal half- sibs in each breed. While use of correction factors for adjusting the environmental differences in the case of milk and butter fat production were made for each lactation record, the percentages of butterfat performance of the daughters and dams were not corrected. The reason was that environ- mental factors, such as age, nutrition and managemental practices etc., have little or no significant effects on the test, which thus, do not justify the use of correction factors. For calculation purposes the butterfat test of each record of daughter and dam were pooled together and a lifetime average was obtained. The lifetime averages of butterfat test for dams 124 and daughters were classified for each breed on an intra-sire group basis for the purpose of carrying out the usual analysis of covariance and variance, as outlined by Snedecor (1946). The dams were treated as the independ- ent variable, X, and the daughters as the dependent var- iable, Y, in a given population. The calculation proce- dures were very similar to those followed in the previous sections for milk and butterfat production. However, for completeness of presentation of the methods, the Brown Swiss breed was selected for calculation details. Table LVI summarizes the preliminary statistics; the sums, sums of squares and products of these two variables. TABLE LVI PRELIMINARY DATA FOR THE STATISTICS OF BUTTER- FAT TEST OF BROWN SWISS HERD Sire NumberPairs Sum Sum of Sum of Sum of Sum of of Dam- of X Squares Y Squares Products Daughters of X of Y of X and Y I 8 33.6 141.34 30.3 115.07 127.29 II 10 42.9 184.59 41.6 173.46 178.79 III 10 41.2 170.06 42.3 179.37 174.24 IV 1 4.4 19.36 3.8 14.44 16.73 V 1 3.7 13.69 4.2 17.64 15.54 VI 2 8.5 36.13 8.1 32.85 34.41 VII 2 7.4 27.38 8.1 32.81 29.97 Total 34 141.7 592.55 138.4 565.64 576.97 125 CALCULATION PROCEDURE FROM TABLE LIII A. Correction Term: For x - (SX)2/N = (141.7)2/34 e 590.56 For Y _ (5112/4 . (138.4)2/34 : 563.37 For XYJSXHSYVN = (141.7) (138.4)/34 : 576.80 B. Total Sum 22 Squares: For X - 8X2 - C.Tx 592055 - 590056 1099 y 565.6h - 563037 2.27 For H: SKY "' O'Txy : 576.96 "' 576.80 : 0.16 For Y = 512 - C.T 9. Between Siggg §EQ g; Squares: For x : S(SX)2/N - 0.7x : (33.6)2/8 + (42.9)2/10 + . . .+(7.4)2/2 - C.Tx = 591.46 - 0.Tx : 0.90 For Y : S(SY)2/N - 0.Ty = (30.3)2/8 + (41.6)2/10 + . . . +(8.1)2/2 — cury : 564.45 - 0.7 : 1.08 For XI = S(sx) (SY)/N - CoTxy : (33.6) (30.3)/8 + ' . . . +(7.4) (8.1)/2 - c.Txy 3 576,66 - c. T = —0.14 Y xy These data are set forth in the Table LIV, of analysis of covariance and by using the within sire line values the desired statistics, namely, correlation and regression coefficients, were calculated. Further, these 126 data were grouped and tabulated separately in Tables LV and LVI or analysis of variance to test fer the significance of the "F"—value. TABLE LVII ANALYSIS OF COVARIANCE OF PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS AND DAUGHTERS FOR BROWN SWISS HERD 0N INTRA-SIRE BASIS Source of Degrees of Sum 0f Squares and Products variation Freedom 8x2 Sxy sy2 Total 33 1.99 0.16 2.27 Between Sires 6 0.90 -0.14 1.08 Within Sires 27 1.09 0.30 1.19 (or ERROR) TABLE LVIII ANALYSIS OF VARIANCE 0F PERCENTAGE OF BUTTER- FAT PRODUCTION OF DAMS (X) IN BROWN SWISS HERD Source of Degrees of Sum of Squares Mean Square Fevalue Variation Freedom Total 33 1099 Between Sires 6 0.90 0.150 3.75** Within Sires 27 1.09 0.040 (or ERROR) **F-value highly significant at 1% level. 127 TABLE LIX ANALYSIS OF VARIANCE 0F PERCENTAGE OF BUTTER- . FAT PRODUCTION OF DAUGHTERS (Y) IN BROWN SWISS HERD . Source of Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 33 2.27 Between Sires 6 1.08 0.188 A.09** Within Sires 27 1.19 0.04A (or ERROR) ** F-value highly significant at 1% level. The "F" tests in both dams and daughters showed a high degree of significance at 1% level, which could be interpreted as indicating that the variance between the sire groups i.e. systemic or group variance, was signif- icantly different from one another in respect of percent- age of butterfat production. In a study involving genetic relationship one must remove this group variance as it would constitute one of the sources of errors. A. INTRA-SIRE CORRELATION AND REGRESSION METHOD: The within sires values in the analysis of co- variance Table XXXV, which is the best estimate of the population parameters, were used to calculate the "b" and "r". In order to avoid repetition, direct calculation of "b" and "r" from individual sires by breaking down the 128 values in the error line, the average of which gives identical results, was not employed. a) Correlation coefficient: ry.x : Sxy/\)Sx ?.Vg;;—; of daughters and dams 0.30/41.09V1.19 : 0.2636 b) Standard error of the correlation coefficient: senor : '(1-r2) Nn—Z g 1—(o.26z.)2/\I 31,-2 ._- 0.1645 multiplying the correlation coefficient by 2, the estimate of heritability for the percentage of butterfat production was obtained, which is found to be equal to, 0.264 x 2 = 0.5272. Likewise, the standard error of heritability was obtained by multiplying the standard error by 2, which is equal to, 0.1645 x 2 g 0.329. Thus, the heritability estimate of the percentage ofbutterfat production of the Brown Swiss herd of the Michigan State College by intra-sire correlation method is --0.527 1 0.329. = by.x = SXY/sz c) Regression coefficient of daughters on dams d) Standard error of the regression coefficient: 2 S error = Standard error of estimate of the error term/n-Z Sum of squares of "x" of the error term 129 Sy2 - (Sxy)2/Sx2 {1.2 OR 5x2 5y2 - b(Sxy)/n-2 3x2 «03175 Serrori U003175 : 0.178 The regression coefficient and the standard error were multiplied by 2 to get an estimate of heritability and its standard error, which are equal to, 0.2752 x 2 = 0.550h and 0.56t0 x 2 a 1.1280, reSpectively. Thus, another estimate of heritability of the percentage of butterfat production in Brown Swiss herd of the Michigan State College, by intra-sire regression coefficient method is 0.550k11.1280. g. HALF-SIB CORRELATION METHOD: The intra-class correlation as the basis for this method was worked out from Table LIX in exactly similar manner as in milk and butterfat productions. As the method was explained in detail in previous sections, only the direct calculations have been presented here. 130 Formula for intra-class correlation coefficient: SE/(SZ+S§) r1 l/(n—l).(Sk2/Sk) z l/(6-1).(34-(82+102+102 +12+22+22)34 = u.3 K O 82 between sires = 0.180 82 within sires g 0.04u 8% = (S2 between sires - 82 within sires)/4.3 : 0.03163 r: : 0.03163/(0.03163 + 0.0hA) = 0.L182 Standard error for intra-class correlation is: SI(error) = (1 - rfi) V335 = (1 - o..132)2/ 34-2 = 0.1459 Heritability = r1 x A = 0.u182 x 4 = 1.6728 Standard error of heritability X k = 0.5836 SI(ERR0R)X h = 0.1h59 Hence, the heritability estimate of percentage of butterfat production of Brown Swiss herd of the Michigan State College, by paternal half-sib method using the intra- class correlation is found to be 1.6728 i 0.5836. I FOr the remaining four breeds, Holsteins, Jerseys, Guernseys, and Ayrshires, tables have been presented separately in the following pages, which explain the procedural sequance in heritability estimates. 131 Breed Tables Pages Holsteins LXVII, LXVIII, LXIX 136 Jerseys LXX, LXXI, LXXII 137 Guernseys LXXIII, LXXIV, LXXV 138 Ayrshires LXXVI, LXXVII, LXXVIII 139 TABLE LX CORRELATION, REGRESSION AND STANDARD ERRORS OF THE ADJUSTED PERCENTAGE OF BUTTERFAT PRODUCTION OF COWS Breed No. No. Paternal half- Intra-Sire Intra-Sire Sires Pairs Sib correlation Regression Correlation D- D ams rI SI(err0r) b Sb r Sr Hols. 21 91 0.3808 0.0906 0.2625 0.1037 0.2591 0.0989 Jers. 20 60 0.2575 0.1226 0.0638 0.1672 0.0501 0.1307 Guern. 16 48 -0.0207 0.1475 0.2393 0.0307 0.3414 0.0630 Ayrs. 8 38 0.4816 0.1445 0.2540 0.1924 0.2153 0.1589 Br. 3w. 6 34 0.4182 0.1459 0.2752 0.1780 0.2636 0.1645 Total 72 271 By multiplying the above correlation and regression coefficients by the apprOpriate factors, the desired heri- tability estimates were obtained and set forth in Table LXI. 132 TABLE LXI ESTIMATES OF HERITABILITY AND STANDARD ERRORS FOR THE ADJUSTED PERCENTAGE OF BUTTERFAT PRODUCTION OF COWS Breed Paternal Intra-sire Intra-sire half-sib regression correlation method method ' fiethod h h 2 HeriS- Standard Herit- Standard Heth- Standard ability error ability error ability error rI I 4 SI x h b x 2 Se x 2 r x 2 Se x 2 H018. 1.5232 0.3624 0.5250 0.2074 0.5182 0.1978 Jers. 1.0292 0.4904 0.1276 0.33h4 0.1002 0.2618 Guern. -0.0828 0.5900 0.4786 0.0614 0.6828 0.1260 Ayrs. 1.9264 0.5780 0.5080 0.3848 0.4306 0.3178 Br. Sw. 1.6728 0.5836 0.5504 0.3560 0.5272 0.3290 These estimates were pooled together and a final weight- ed average of heritability and its standard error was cal- culated in the same manner as was done in the case of milk and butterfat productions. The desired statistics, such as the squares of the standard errors and their reciprocals, which are an integral part in the application of the two formulae, were calculated and summarized in Table LXII. 133 TABLE LXII SQUARED STANDARD ERRORS AND THEIR RECIP- ROCALS OF THE HERITABILITY OF PERCENTAGE OF BUTTERFAT PRODUCTION Breed Half-sib Intra-sire Intra-sire Reciprocal method regression correlation sum of 3 method method methods 2 2 2 .2 2 2 1 S 1 S 1 S 18 Hols. 0.1313 7.62 0.0430 23.26 0.0391 25.57 56.45 Jers. 0.2405 4.16 0.1118 8.94 0.0685 14.60 27.70 Guern. 0.3481 2.87 0.0038 255.17 0.0159 62.89 328.93 Ayrs. 0.3341 2.99 0.1481 6.75 0.1010 9.90 19.64 Br. Sw. 0.3406 2.94 0.1267 7.80 0.1082 9.24 19.98 Reciprocal 20.58 0.1267 309.92 122.20 452.70 sum of 5 breeds TABLE LXIII WEIGHTED AVERAGE OF THREE METHODS (PERCENT- AGE OF BUTTERFAT PRODUCTION) Breed Heritability Standard Error Holsteins 0.657 0.133 Jerseys 0.248 0.190 Guernseys 0.512 0.055 Ayrshires 0.685 0.226 Brown Swiss 0.706 0.224 13h TABLE LIV 'WEIGHTED AVERAGE OF FIVE BREEDS (PERCENTAGE OF BUTTERFAT PRODUCTION) Method Heritability Standard error Paternal half-sib correlation 1.27 0.220 Intra-sire regression 0.474 0.057 Intra-sire correlation 0.654 0.090 TABLE LV WEIGHTED AVERAGE OF THREE METHODS AND FIVE BREEDS Trait Heritability Standard . error Percentage of butterfat 0.56 0.047 production (Butterfat test) Thus, the final heritability estimate of the percentage of butterfat production (butterfat test), which is the weighted average of all five breeds and three methods, of the Michigan State College herd is, 0.56 1 0.047. 135 TABLE LVI HERITABILITY ESTIMATES OF THE THREE MAIN ECONOMIC CHARACTERISTICS OF THE MICHIGAN STATE COLLEGE DAIRY HERD, WHICH CONSISTS OF THE FIVE MAIN BREEDS--HOLSTEINS, JERSEYS GUERNSEYS, AYRSHIRES, AND BROWN SWISS Traits Heritability Standard , error Milk production -0.01 0.08 Butterfat production 0.20 0.08 Percentage of butterfat 0.56 0.05 production (butterfat test) [ll i ll...“ 136 HOLSTEIN HERD TABLE LXVII ANALYSIS OF COVARIANCE 0F PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS AND THEIR DAUGHTERS FOR HOLSTEIN BREED 0N INTRA- SIRE BASIS Source of Degrees of Sums of Squares and Products variation Freedom 3x2 fixy Sy2 Total 90 9.16 2.73? 11.60 Between Sires 20 3.56 1,25 I 5.85 Within Sires 70 5.60 1.47 5.75 (or ERROR) TABLE LXVIII ANALYSIS OF VARIANCE OF PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS (X) IN HOL- STEIN HERD Source of Degrees of Freedom Sum of Mean Fbvalue Variation . Squares Square Between Sires 20 3.56 0.168 2.1* Within Sires 70 5.60 0.08 (or ERROR) *F-test significant at 5% level. TABLE LXIX ANALYSIS OF VARIANCE 0F PERCENTAGE OF BUTTER FAT PRODUCTION OF DAUGHTERS (Y) IN HOLSTEIN HERD Source of Degrees of Freedom Sum of Mean F-value variation Squares Square Total 90 11.60 Between Sires 20 5.85 0.293 3.56** Within Sires 70 5.75 0.082 (or ERROR) ** F-test highly significant at 1% level. 137 JERSEY HERD TABLE LXX ANALYSIS OF COVARIANCE 0F PERCENTAGE OF BUTTER- FAT PRODUCTION OF DAMS AND THEIR DAUGHTERS FOR JERSEY BREED 0N INTRA-SIRE BASIS Source of Degrees of Sums of Squares and Products variation Freedom Sx 2 Sxy 5Y2 Total 59 8.60 1.43 16.90 Between Sires 19 3.27 1.09 8.23 Within Sires 40 5.33 0.34 8.67 (or ERROR) TABLE LXII ANALYSIS OF VARIANCE OF PERCENTAGE OF BUTTER-V FAT PRODUCTION OF DAMS (X) IN JERSEY HERD Source of 'Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 59 8.60 Between Sires 19 3.27 0.172 1.29 Within Sires 40 5.33 0.133 (orERROR) F-test not significant. TABLE LXXII ANALYSIS OF VARIANCE 0F PERCENTAGE OF BUTTER- FAT PRODUCTION OF DAUGHTERS (Y) IN JERSEY HERD Source of Degrees of Sum of Mean Square F-value variation Freedom Squares TOTAL 59 16.90 Between Sires 19 8.23 0.433 2.00* Within Sires 40 8.6 0.21 (or ERROR) 7 7 * F-test significant at 5% level. 138 GUERNSEY HERD TABLE LXXIII ANALYSIS OF COVARIANCE 0F PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS AND THEIR DAUGHTERS FOR GUERNSEY BREED 0N INTRA- SIRE BASIS Source of Degreed of Sums of Squares and Products Variation Freedom 2 2 Sx Sxy Sy Total 47 11.00 6.65 6.28 Between Sires 15 2.14 4.50 1.92 Within Sires 32 8.86 2.12 4.36 (or ERROR) TABLE LXXIV ANALYSIS OF VARIANCE 0F PERCENTAGE OF BUTTER- FAT PRODUCTION OF DAMS (X) IN GUERNSEY HERD Source of Degrees of Sum of Mean Square F-value variation Freedom Squares Total 47 11.00 Between Sires 15 2.14 0.143 0.52 Within Sires 32 8.86 0.277 (or ERROR) F-test not significant. TABLE LXXV ANALYSIS OF VARIANCE OF PERCENTAGE OF BUTTER- FAT PRODUCTION OF DAUGHTERS (Y) IN GUERNSEY HERD Source of Degrees of Sum of [Mean Square F-value variation Freedom Squares Total #7 6.28 Between Sires 15 1.92 0.128 0.94 Within Sires 32 4.36 0.136 (orERROR) F-test not significant. 139 AYRSHIRE HERD TABLE LXXVI ANALYSIS OF COVARIANCE OF PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS AND THEIR DAUGHTERS FOR AYRSHIRE BREED ON INTRA- SIRE BASIS Source of Degrees of Sums of Squares and Products Variation Freedom 3x2 Sxy syZ Total 37 5.71 3.50 5.87 Between Sires 7 3.82 3.02 3.23 Within Sires 30 1.89_ 0.48 2.64 (or ERROR) TABLE LXXVII ANALYSIS OF VARIANCE OF PERCENTAGE OF BUTTERFAT PRODUCTION OF DAMS (X) IN AYRSHIRE HERD. Source of Degrees of Sum of .Mean Square F-value Variation Freedom Squares Total 37 5.71 Between Sires 7 3.82 0.546 8.67** Within Sires 30 1.89 0.063 (or ERROR) ** Fbtest highly significant at 1% level. TABLE LXXVIII ANALYSIS OF VARIANCE OF PERCENTAGE OF BUTTERFAT PRODUCTION OF DAUGHTERS (Y) IN AYRSHIRE HERD Source of Degrees of Sum of Mean Square F-value variation Freedomg Squares Total 37 5.87 Between Sires 7 3.23 0.464 5.27** Within Sires 20 2,64 0,033 (or ERROR) ** F-test highly significant at 1% level. PART II REPEATABILITY_OF PRODUCTION CHARACTERISTICS: MILK AND BUTTERFAT 1. INTRODUCTION: A knowledge of repeatability of economic character- istics in modern animal breeding and selection techniques, has become a tool of considerable value: 1. To predict the probable future producing ability or performance of an animal, such as, a) production in cows, b) prolificacy in sows, c) fleece weight in sheep and d) sire performance in beef cattle. 2. To obtain an estimate of the upper limit of heritability. 3. Where subjective estimates are made of characters, such as coat color, which change but little from year to year repeatability tests the accuracy of Such estimates, Briquet and Lush (1947). 4. To estimate progress made per generation in selection on the basis of an average of "n" records. 5. To study repeatability of type ratings in dairy cows, Johnson and Lush (1942). While very little correlation exists between type and production in dairy cows, purebred associations do insist on excellent types and conformation as one of the means in the improvement 141 of purebreds. 2. WHAT TS REPEATABILITY: Repeatability is the coefficient of correlation (r) between recurrent expressions of a characteristic by the same animal within its herd. Since all of the genetic variance is contributed to repeatability estimates, one could consider it as an expression of its genetic merit repeated from one lactation to the other in the same animal. This relationship that exists among the production records of the same cow has been p0pularly termed as "repeatability." As indicated by Lush (1945), it is, therefore, not a basic biological constant but a description of a given pOpulation. 3. REPEATABILITY AND ITS PLACE EN AIDS 1Q SELECTION: To the breeder, while the estimates of heritability of economic characteristics serve as a definite guide in planning a breeding program, not infrequently he is confronted with another problem. That is, the problem of culling and selection of individual animals, partic- ularly the breeding females in order that he might ultimately increase the frequency of the "good" genes in his herd. Depending on the genetic composition of a certain 142 characteristic to which the breeder looks forward in his selection, he could be aided by three different methods, namely, 1) phenotypic selection, 2) pedigree estimates, 3) progeny test. However, it would profit one to be aware of some of the inherent limitations in selection. First, as pointed out by Stewart (1945), that selection for one or several characters basically depends on not only the genetic variability of the population from which selections are made but also on the proportion of available animals that are required for breeding purposes, and that progress through selection is equal to that of the selection differential, that is due to heritable differences in the genotypes of females. Second, that though selection alters the type, it does not greatly reduce the variability in the population, Lush (1945). Culling or selection among several cows on the average of the adjusted records for each cow would be generally misleading, since the cow with the least number of records will have the greatest error and would be far from providing a true picture of its merit. Whereas if one could obtain a measure which would express the correlation among the records of individual cows, then they could be easily reduced to a comparable basis. Where the repeatability of a characteristic, which is "r" is very high, that is, nearer to 1.0, the most probable 143 future producing ability of the could be estimated from its first record alone just as well as from her any or all of the records. For characteristics where "r" is small the first record is not reliable and for relia- bility an average of several records, at least four, should be taken in order to reduce the environmental variations. In cases where a cow has not made any records, the herd average should be used for estimating the producing ability, because of the tendency of the cows to regress towards herd average. The formula often employed for predicting the probable future producing ability of a cow is: Y s Herd Average + nr' x (Her average-Herd average) 1 -r+nr where n = the number of records made, r : repeatability, which is the fraction of the total variance among the corrected records which is due to permanent differences between cows, and l — r is the fraction of the variance caused by temporary environmental conditions which vary from one record to another of the same cow. As shown by Lush et a1 (1941) that the fraction nr would test I=F‘an the real ability of the cow for "n" number of completed records in comparison to the average of the population. As "n" increases the percentage of the real ability of the cow also increases and where "n" is equal to 5 and "r" is equal to 0.4, the real ability would be equal to lhh 77 per cent, of the cows actual average. Again if one desires to estimate a cow's breeding value instead of the real producing ability, the "r" in the numerator must be replaced by the heritability fraction (h), which would be somewhat less. The measure of repeatability could also be used for correlating for purposes of comparison a non-consec- utive record with the average of the consecutive records or another non-consecutive record or vice versa. As for example one cOuld correlate the first record with the average of the next four records. The formula generally used for such correlation and comparison is, Berry and Lush (1939): R: n I-r+nr Although the phenotypic selection based on production records of an animal is the most effective method for selection for breeding purposes or for culling in a herd, it is sharply limited by conditions which vary from lactation to lactation for the same cow. An attempt has been made in the foregoing to present the methods to over- come these sources of error, i.e. the fraction of the total variance due to environmental conditions; 1) by use of larger number of "n" records, and 2) by obtaining an estimate of "repeatabilitY’of the same cow. 145 Therefore, a measure of repeatability has a defin- ite and important place in phenotypic selection or cul- ling. It is also inexpensive except what it costs to postpone culling until two or more observations are made, Lush (l9h5). 4. RELATIONSHIP OF HERITABILITY IQ REPEATABILITY: 1. Heritability is the study of a genotype in a given population, whereas the repeatability concerns with the study of a characteristic (phenotype), which is variable in a particular population and is expressed in 'an individual severally at different times during its life. 2. Heritability is the fraction of the total variance in a given trait which is due to the additive ef- fects of genes, Hazel (1942), whereas, repeatability is the fraction of total variance among the corrected records of the same cow, which is due to permanent non-trans- missable differences between the cows. The permanent differences include the differences due to dominance, epistasis, and also such effects of environment which are permanent, such as poor management of calves at birth which might result in stunted growth, etc. While these are not heritable, they differ from one animal to the other. 146 3. Since repeatability includes both the effects of permanent non-transmissable differences and genetic variance, the estimate could be used generally as an upper limit of heritability at least in the broad sense, Stewart (1945). It could be larger than heritability but it could hardly be less. 5. METHODS OF ANALYSIS OF DATA FOR REPEATABILITY: The method employed in estimating repeatability is that of single way classification of analysis of variance, where k = the number of observations (records) corrected for temporary environmental conditions, and n . the number of cows. Different methods are employed for estimate of repeatability. Lush (1940) has shown that repeatability can be determined by regression of daughter on dam, while Dickerson (1940) and Briquet (1947) have reported the use of analysis of variance method. Stewart (1945) has also recommended the use of partial correlation method for estimating repeatability. In the present study the estimates of repeat- ability were obtained from analysis of variance by using the following formula: The formula-- Repeatability : 52 within cows 82 within cows + 82 between cows 147 In order to arrive at the above statistics for use in the formula, the mean square or the variance in the table of analysis of variance should be split into their reapective component parts for the sub-samples. Table LXXIX shows the mean squares and their component parts that make up the total variance. TABLE LXXIX BREAK UP OF MEAN SQUARES IN ANALYSIS OF VARIANCE TO THEIR COMPONENT PARTS Source of Degrees of .Mean Squares Components of variation Freedom Mean Squares Total nk - 1 I T - 2 2 Between Cows n 1 C S + S between cows Within Cows n(k - 1) E 52 (or ERROR) Each record of a cow was corrected for three main environmental conditions: 1) age, 2) length of lactation period - 305 days, 3) times of-milking per day - 3X. Unlike the daughter-dam comparison on intra-sire basis in heritability estimates, all animals of a breed with more than one record were pooled together. Since the use of correction factors in repeatability estimates has been a subject of much controversy, it is not within the scope of the present study to go into the merit or demerit on this subject. It has been however, agreed by Sanders (1930) and later on by Dickerson (1940) that 148 age-corrected 305-day records are most satisfactory for selection purposes, since they are easily available and easier to compute. Table LXXX shows the number of cows in each breed, the average number of records per cow etc., as a prelim- inary step in the analysis of the data. TABLE-LXXX PRELIMINARY DATA SHOWING THE NUMBER OF COWS . . AND AVERAGE NUMBER.OF.RECORDS FOR EACH BREED Breed Number Average number Average Average of Wof Records per Pounds of Pounds of Cow . .., Hulk per Butterfat . A Cow per Cow Holstein 279 3.4 15,096 509 Jersey 186 3.6 8,229 432 Guernsey 155 h-B 9,415 455 Ayrshire 52 2.7 11,071 #35; Brown Swiss 117 3.6 12,923 . 530 A. CALCULATION OF REPEATABILITY OF MILK AND BUTTERFAT PRODUCTION Repeatability estimates were made for two char- acteristics, namely, milk and butterfat separately for each breed. And in case of the percentage of butterfat-- BFtest-- since the variations from one record to the other 149 in the same animal are generally so small, if any, the repeatability estimates were not calculated. Since the methods for both milk and butterfat production are identical, only one of them was chosen for a detailed explanation of the procedures. B. ESTIMATES_QP REPEATABILITY_QF BUTTERFAT PRODUCTION: Separate estimates for each breed were made and the Holstein herd was selected for illustrating the method in detail. The statistics necessary for setting up an analysis of variance table were obtained as follows: CALCULATION PROCEDURE: I. Correction Term : (SX)2/N = (142123)2/279 = 72397660 - 5x2 - C.T. - 75702823 — C.T. II. Total Sum of Squares - _ 3304163 III. Between Cows Sum of Squares : S(SX)2/N - C.T. : (3902)2/7+(6122)2/10+~-+(2560)2/N - c.T. ._. 74451354 - c.T. : 2053694 These data were set forth in Table LXXXI below and further statistics desired for calculating repeata- bility were obtained therefrom. 150 TABLE LXXXI ANALYSIS OF VARIANCE OF BUTTERFAT PRO- DUCTION OF COWS OF HOLSTEIN HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean Components F-value 'Variation Freedom Squares Square of Mean Square Total 278 3304163 , 2 2 Between Lows 81 2053694 25354 S +KS between 3,99** within Cows 197 1250467 6348 52 °°W$ (or ERROR) ** F-test highly significant at 1% level. KO = l/n-l (Sk - SkZ/Sk) l/82-l(279 - 1191/279) l/8l(279 - 4.27) = 3.4 2 2 S + K sbetween cows ' 2535“ 32 = 6348 82 = 19007 between cows Sgetween COWS = 19007/K = 19007/3"." : 5590 Substituting the values in the formula: RGPIataVilitY : 52/(52*Sgetween cows) r = 6348/ (6348+5590) = 0.53 Standard error of repeatability: 1 — rZ/ n - 2 : 1-532/ 279-2 : 0.7191/16.6 0.43 151 Thus, the repeatability of the records of the butter- .fat production in Holstein herd of the Michigan State College was found to be equal to 0.53 ;_0.43. Since the methods for estimating repeatability of butterfat production for the other four breeds, namely, Jerseys, Guernseys, Ayrshires, and Brown Swiss, were exactly similar, only the analysis of variance tables for each of these breeds have been given below. TABLE LXXXII ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION OF COWS OF JERSEY HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of {Mean Components F-value Variation Freedom Squares Square oanean Square Total 185 1317174 2 Between Cows 51 763913 14979 S +K SEet 3,63# . . s 2 cows Within Cows 134 553261 4129 S (or ERROR) * F-test highly significant at 1% level. 152 TABLE LXXXIII ANALYSIS OF VARIANCE OF BUTTERFAT PRO- DUCTION OF COWS OF GUERNSEY HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean Components F-value Variation Freedom Squares Square of Mean Square Total 154 879002 Between Cows 35 422051 12059 S2+K sfigt. 3.l4* OWS Within Cows 119 456951 3840 52 (or ERROR) * F-test highly significant at 1%leve1. TABLE LXXXIV ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION OF COWS OF AYRSHIRE HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean Components F-value variation Freedom Squares Square of Mean Square Total 51 574350 Between Cows 18 431233 23957 82+K sget. 5.52* . cows Within Cows 33 143117 4337 52 (or ERROR) * F-test highly significant at 1% level. TABLE LXXXV ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION OF COWS OF BROWN SWISS HERD BASED ON THE NUMBER OF RECORDS Total 116 1182623 Between Cows 31 779919 25159 SZ+K SEet. 5.31* COWS Within Cows 85 402704 4738 52 (or ERROR) * FLtest highly significant at 1% level. 153 In all the five breeds the F-test was found to be highly significant indicating that the permanent environ- mental differences and probably the genotypes between the cows were different and significant, and that values as large as or larger than the F-values would be expected to occur by chance alone less than one per cent of the time. These permanent environmental differences are not transmissable and may be due to dominance, epis- tasis, or management practices when the animals were young which resulted in permanent effect on them, for example, stunted growth, differences in nourishment while young, etc. From these tables the desired statistic, such as the components of mean square-within cows and between cows variances were calculated for the remaining four breeds in exactly the same manner as that of Holstein breed. The final repeatability estimates of butterfat production in the different breeds of Michigan State College dairy herd have been summarized in the Table LXXXVI below. 15h TABLE LXXXVI ESTIMATES OF REPEATABILITY OF BUTTERFAT r PRODUCTION IN JERSEYS, GUERNSEYS, AYR- SHIRES, HOLSTEINS AND BROWN SWISS Breed Number 82 sgetween . . R -. ow 8882815211” 3133;. S /($ +Sbet. cows) Hols. 279 63h8 5590 0.53 O.h3 ' Jers. 186 #129 3014 0.59 '0.h8 Guern. 155 BSAO 1911 0.67 O.hh Ayrs. 52 #337 7267 0.37 0.12 Br. Sw. 117 , 4738 5626 0.46 0.74 TOTAL 789 23392 23h08 In order to obtain one statistic as an estimate of all the five breeds,.the respective calculated variances of each breed was combined by the following formula: 2 a) b) Re eatability Estimate - is within cows (R - All five breeds ' 2 :E(Swi thin cows+S2 between cows) : 23322 = 0.499 or 0.50 A 00 Standard error for the combined repeatability g l - r2 / n - 2k where n is equal to the total number of animals from all the five breeds and k is the total number of breeds included in estimating combined repeat- ability. 155 . 1 - (0.50)2V789 —10 3 0.750/27.9 g 0.269 Thus, the combined repeatability estimate for butterfat production in all the five breeds of the Michigan State College dairy herd was found to be 0.50 ;_O.269. E. CALCULATION OF REPEATABILITY OF MILK PRODUCTION: Gowen (l92h) has shown very high degree of positive correlation between milk yield and butterfat production, both by direct correlation and by partial correlation coeffiCient methods. By direct correlation he found that "r" was 0.8927 ;,0.0075 and by partial correlation method where age was held constant the "r" was 0.863 ‘1 0.009. It does show, therefore, that environmental conditions including the permanent differences that af- fect the production of butterfat also influence the milk yield. Gaines (1936) while working with 10,307 365-day records of Jersey Registry of Merit also concluded that size and age have substantial influences on milk yield and butterfat production: With regards to size Edwards (1936) in England, studying 2400 records accumulated over a period of 12 years between 1922 and 1930, has reported that hereditary environmental conditions being equal, larger cows produce 156 more milk than smaller cows. Earlier work by Turner et a1 (1924), in their attempt to analyse the records of all the breeds, had also reached similar conclusions as regards size. It was pointed out by them with particular reference to Jersey cows that after the animal reaches 470 pounds of body weight, there is an increase of 20 pounds of fat for each 100 pounds of body weight with age held constant. The increase in body weight contributes about 20 per cent to the total increased fat yield with age, while the other 80 per cent increased fat yield with age is due to other factors accompanying increased maturity. Swett et al (1937) in a comparative study of con- formation, anatomy and udder Characteristics between the beef and dairy breeds, i.e. the Herefords and H01- steins respectively, observed that specialized beef breeds, which have more compact body conformation do not inherit mammary development sufficient to become liberal milkers. With regards to age in relation to milk production, Pearl and Patterson (1917) investigating the change in milk flow with age on 5821 seven-day records of Jersey cattle showed the correlation coefficient between age and milk production to be + 0.1925 ;,.0085. In a study of the variations and correlations in milk secretion with age by Gowen (1920) on 1741, 8-month milk yield 157 records of Jersey cows concluded that the correlation coefficient between age and milk yield to be +0.2596 I. .0151. Since several other factors influencing production have already been dealt with in detail in earlier sections, their repetition here has been avoided. In spite of the high correlation that exists between milk yield and butterfat production, the main object of determining the repeatability of milk yield has been to provide a source of guidance to the breeder for culling or for selection in places where no system of butterfat testing is practiced and has to depend upon milk yields. To save the repetition of the methods and procedures used in develOping the repeatability of milk yield, which is identically the same as in butterfat, it was considered to be enough to present tables of analysis of variance separately for each breed in the following pages. These tables however, provide the basis for estimating repeatability of milk yield. 158 TABLE LXXXVII ANALYSIS OF VARIANCE OF MILK YIELD OF COWS OF HOLSTEIN HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean Components F-value variation Freedom Squares Square of Mean Square Total 278 30298259 Between Cows 81 19563824 241529 32+K 3% t 4.43* ows within Cows 197 10734435 54490 52 (or ERROR) * F-test highly significant at 1% level. TABLE LXXXVIII ANALYSIS OF VARIANCE OF MILK YIELD OF COWS OF JERSEY HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean ComponentS‘ F-value variation Freedom ‘ Squares Square of Mean Square Total 185 5655630 Between Cows 51 3639070 71354 82+K Sget 4.748 Within Cows 134 2016560 15049 52 °°Ws (or ERROR) A * F-test highly significant at 1% level. TABLE LXXXIX ANALYSIS OF VARIANCE 0F MILK YIELD OF CONS . 0F GUERNSEY HERD BASED ON THE NUMBER OF RECORDS Source 5? Degrees onSum of Mean COmponents F;vaIfie Variation Freedom Squares Square ,of Mean Square Total 154 3842221 Between Cows 35 1949390 55697 82+K SEet 3,50 * Within Cows 119 1892831 1 06 32 COWS (or ERROR) 59 * F-test highly significant at 1% level. 159 TABLE XC ANALYSIS OF VARIANCE OF MILK YIELD OF COWS OF AYRSHIRE HERD BASED ON THE NUMBER OF RECORDS Source of Degrees of Sum of Mean Components F-value variation Freedom Squares Square of Mean Square Total 51 2770847 Between Cows 18 2057170 114287 32+K SEet 5.28s S cows Within Cows 33 713677 21627 or ERROR F-test highly significant at 1% level. TABLE XCI ANALYSIS OF VARIANCE OF MILK YIELD OF COWS OF BROWN SWISS HERD BASED ON THE NUMBER OF RECORDS . Source of Degrees of Sum of Mean Components F-value Variation Freedom Squares Square of Mean Square Total 116 6188339 Between Cows 31 3870742 124863 52+K3Eet. 4.58* cows Within Cows 85 2317597 27266 52 (or ERROR) * F-test highly significant at 1% level. NOTE: The milk yield of individual records in all five breeds liters reduced by a constant 0.10 i.e. 10 76, to facilitate calculation of analysis of variance in the above tables, which does not alter the variances. 160 The desired statistics from these tables, such as, the components of mean square and the respective repeatability estimates were calculated as similar to butterfat and summarized in Table XCII that follows. TABLE XCII ESTIMATES OF REPEATABILITY OF MILK YIELD IN ALL THE FIVE BREEDS OF DAIRY HERD .-. «nu—QI- . 2 2 Breed 12111111116? 4,8 sbetggig Repeatability : Std. 2 2 2 Error 8 /(S +sbet. cows) Hols.‘ 279 54490 55012 0.50 0.45 Jers. 186 15049 15640 0.49 0.56 Guern. 155“ 15906 9254 0.63 0.49 Ayrs. 52 21627 34319 0.39 0.12 Br. Sw. 117 27266 26886 0.50 0.70 TCTAL 789 134338 141111 A single estimate of repeatability for all the five breeds was then obtained and the standard error calculated in a manner similar to that of butterfat. Thus: a) Re eatability Estimate . (R? - All five breeds : 134338/275449 : 0.49 b) Standard error of the combined repeatability : l - rz/‘ln - 2k : 0.2599 : 0.272 27.9 161 Where n is the total number of animals from all the five breeds and k is the total number of breeds included in estimating combined repeatability. Thus, the combined repeatability estimate for milk yield in all the five breeds of the Michigan State College dairy herd was found to be 0.49:0.272. From these studies, it could be concluded that repeatability estimates, 0.50 3.0.269 for butterfat and 0.49 1 0.272 for milk Show what fraction of the total variance among the records of the cows was due to the permanent differences between the cows which made those records. The rest of the variance was caused by the temporary environmental influences, which have so much effect on the size of the records. In view of the high correlation between milk and butterfat, the repeatability estimate for both these characteristics from the present study seems to Show very little difference between them. Therefore, it could be said that either of these estimates might be used with certain advantage depending upon the circum- stances and the nature of the records available (milk or BF) for culling or for selection. PART III INFLUENCE OF THE MONTH OF CALVING ON BUTTERFAT PRODUCTION 0f value to the breeder for efficient planning and production, it was thought pertinent to include in the scope of the present study the effects of the month of freshening (calving) on the yearly production of butter- fat. In view of the high significant correlation of +0.863;,0.009 reported by Gowen (1924), between milk and butterfat yields, only the effects on butterfat production were studied. Turner (1927) has shown that a rapid increase in butterfat production occurs immed- iately following freshening and remains at a peak level during the first three to four months of lactation. It would seem reasonable to assume that a breeder would be most interested to get the maximum benefit of the yield without being adversely affected by environ- mental influences. It is thus a study of an aspect of environmental influences with particular reference to the degree of heat tolerance that an animal possesses. From manage- ment and economic considerations, there are reasons for having cows freshen in different seasons; particular- ly either in fall or Spring, but the main object of the 163 present study has been to test statistically whether or not there is any significant relation between the month of calving and the production in the lactation period following it. In range herds and in animals subjected to extreme temperatures one would observe a good deal more fluctu- ation in their production than those kept under barn conditions where the temperature is cooler and in some places is controlled. The higher the heat tolerance among the dairy cattle the smaller the variation in the yield. Rhoad (1938) has reported that animals adapted to tropical climates have better heat tolerance than the European breeds of cattle. While genetic material is not generally affected by the environment, it does influence the expression of the phenotype. Seath (1947) studying the rectal temperatures of Jerseys and Holsteins during the years 1944 and 1945, reported that heritability of heat tolerance to be about 15.1 to 30 per cent, which would thus explain the greater susceptibility of dairy cattle for large variations in temperature. Experimenting under controlled conditions, Ragsdale and Brody (1922) on the effect of temperature on the percentage of fat in milk reported that the per cent of fat increased almost 0.2 per cent for every 10° F 164 decrease in temperature between the limits of 30° F to 700 F. In a more exhaustive investigation Ragsdale et a1 (1948) have again Shown that the critical temper- ature for Holsteins is about 75° F to 80° F and for Jerseys 80° F to 85° F. Any increase in temperature above these levels would depress feed consumption and milk production. At 105° F both virtually stopped. 0n reducing the temperature to a level of 50° F - 60° F feed consumption and milk yield returned to normal. The effects of temperature are more pronounced as is generally true in tropical countries such as some parts of India where the yield becomes reduced during the hot summer months and gradually returns to normal with the approaching coOler seasons. Studies on the effect of month of freshening on milk production by Arnold and Becker (1935) using analysis of variance method on 319 lactation records of Jersey cows accumulated over a period between 1917 - 1933 found no significant difference under the climatic conditions of Florida. A similar experiment by Morrow et a1 (1945) on 4030 lactation records of grades and all breeds of purebreds also concluded that there is not only no effect on the length of lactation but also there is no significant relationship between month of freshening and milk yield, under New Hampshire conditions. 165 While studying under Western Oregon conditions, 2690 re- cords of all breeds following calving, Oloufa and Jones (1948) also arrived at similar results. But Sanders (1927) in England, in his studies on the variations in milk yield after freshening in rela- tion to seasons of the year, pointed out that best months for calving would be October, November and Decem- ber, which would result in highest yields. Cannon (1933) analysing 68,000 Cow Testing Association records for 1925-1930 belonging to all breeds reported that those freshened in November had highest milk yield and those in June had the least. Earlier work by wylie (1925) on 2900 Jerseys Registry of Merit records completedin 1921, showed that freshenings occurring in July, October, November, December, January, February and March had highest milk yield. Those that freshened in August had the lowest milk yield. Since some of these works gener- ally suffer from statistical analysis it would be dif- ficult to conclude whether or not they were statistic- ally significant. Even if they had proved to be signif— icant by statistical tests, they would have only provided further proofs on the modifying effects of environmental (seasonal) conditions, which vary from one locality to another. From these considerations, it seems therefore, that 166 any external factor or factors that would influence the first few months of production following calving, would to a great extent affect the total production of an animal during that year. Thus, it was thought desirable to study the relationship, if any, between the month of calving on yearly butterfat production on the Michigan State College dairy herd. The total number of births from the five breeds with lactation records following freshening have been summar- ized in Table XCIII below on a monthly basis. The average monthly production of cows in each breed following freshening has also been shown in Table XCIV. TABLE XCIII NUMBER OF CALVES BORN T0 CONS wITH RECORDS FOLLOWING FRESHENING DURING THE VARIOUS MONTHS OF A YEAR Breed No. of ' 1 Cows - - 'Months TotalNo. of $4 1’: gh$gRecords 53,... 88822 : L. <1 H ° ’2 5 *3 O a, m 88528532051553 *7 R. #4 '¢ 2. *3 ’3 q: a) CD :3 C) Hols. 123 13 8 7 10 14 ° 2° 7 11 8 ll 8 "123 Jers. 75 9 4 7 6 9 5 h 3 7 5 ll 5 75 Guern. 55 4 5 7 5 2 2 4 2 4 4 8 8 55 Ayrs. 42 2 3 3 3 7 5 2 2 3 2 5 5 42 Br.SW-37 4 33 34 323 2°6437 Total 32 23 27 27 36 21 32 17 27 19 “1 3° 332 167 TABLE XCIV MONTHLY AVERAGE PRODUCTION OF COWS IN ALL FIVE BREEDS FRESHENING IN THE DIFFERENT METHODS Breed. #1 Months Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Hols. 577 530 539 #73 581 550 490 533 A77 #35 48h 526 Jers. #01 385 #22 #36 #58 450 397 hh3 #23 39h AAA #81 AYrs. 384 L80 #08 #67 38h 4&8 hlh #12 #91. #97 #25 #26 Guern. #78 #83 All 4h0 375 38h #23 A66 A83 43h #14 #78 Br. Sw.588 530 #72 488 502 511 586 531 E83 0 563 582 Weighted AverageSOE 488 E53 E61 498 E80 #68 495 466 A31 h6h #97 It could be observed from the above table that the births have been fairly well distributed in all the twelve months of a year, and that no definite system of calving seems to have been followed in the Michigan State College dairy herd. As a helpful adjunct to the present study, the mean annual temperature and rainfall and the range at East Lansing, where the college herd is located, covering the period of study from 1919 to 1950 both inclusive, has been shmm1in.the following Table XCV. 7 Whit-Ii??? 2"! 168 TABLE XCV THE MEAN AND THE RANGE IN TEMPERATURE AND RAIN- FALL BETWEEN 1919 - 1950 AT EAST LANSING Nature of a Mean Range Environmental (yearly) (yearly) Condition Temperature £47.29 F 50.6 - M...6° F * Rainfall 31.0 inches 39.7 - 18.5 inches * Range of temperature within a year was 13.2 - 74.19 “ I." on 0 th avera e. ANALYISIIS 9_ THE DA A: To study the effects of month of freshening on the yields of butterfat, the usual method of analysis of variance as outlined by Snedecor (1946) was used. Each breed was considered separately. The main object of run- ning analysis of variance has been to separate from the total variance, the variance due to the effects of month and that due to random variance and test the former by the latter by means of "F"-test. Before subjecting the data for analysis of variance, the yearly butterfat records following each calving were classified and then adjusted for three main environmental influences, namely, 1) age, 2) length of lactation period- 305-day, and 3) times of milking per day - 3X. Since the methods and calculation procedures were exactly similar to those already outlined in the previous sections, the repetition here has been avoided, and only 169 the final tables of analysis of variance for each breed and the correSponding "F"-tests have been given in the following tables. TABLE XCVI ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION FOLLOWING FRESHENING IN HOLSTEIN HERD Source of Degrees of Sum of Mean Square F-value Variance Freedom Squares Total 122 1E62333 Between Months 11 175E02 15946 1.38 Within Mbnths 111 1286931 11595 (or ERROR) F-test for between months was not significant. TABLE XCVII ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION FOLLOWING FRESHENING IN JERSEY HERD Source of Degrees of Sum of Mean Square F—value Variation Freedom Squares Total 7h 617822 Between Months .11 5195b E723 0.53 Within Months 63 565868 8982 (or ERROR) F-test for between months was not significant. 170 TABLE XCVIII ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION FOLLOWING FRESHENING IN GUERNSEY HERD Source of Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 5h 36607h Between Months 11 62617 5693 0.81 ‘Within Months 43 303457 7057 (or ERROR) F-test for between months was not significant. TABLE XCIX ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION FOLLOWING FRESHENING IN AYRSHIRE HERD Source of Degrees of Sum of Mean Square F—value Variation Freedom Squares Total #1 252876 Between Months 11 55562 5051 0.77 Within Months 30 19731h 6577 (or ERROR) F:test fgr‘between months was not significant. TABLE 0 ANALYSIS OF VARIANCE OF BUTTERFAT PRODUCTION FOLLOWING FRESHENING IN BROWN SWISS HERD Source of Degrees of Sum of Mean Square F-value Variation Freedom Squares Total 36 329781 Between Months 10 5691.1 5694 o . 51, Within Mbnths 26 272840 10E9E (or ERROR) F-test for between months was not significant. 171 F-test in all the five breeds was found to be insignificant. It would be of value to run a "t"-test :if the Extest had been significant, to determine in ‘which ummth or months the significant increase in pro- duction occurred. But since there was no significant F-test, it was thought that no useful purpose would be served by carrying out "t"-test. From this study, it was thus concluded that the month of freshening has no appreciable and significant influence on the yearly butterfat production following it, in the several breeds of Michigan State College dairy herd. As pointed out by Olson (1938) the planning of breeding and freshening times in dairy herds are generally matters of management practices and marketing economics for the dairy products. Those closer to cities, where there would be an all the year round demand for the dairy products, breeders would have to gear up their production to meet these demands by a program of calving system throughout the year. In rural farming, one plans calving seasons on the basis of availability and the time of pasture, labor facilities, and the local demands. PART IV SEX RATIO AMONG DAIRY CATTLE Differentiation of the living organism from its unicellular state of development to two different and distinct sexes embedded within the mosaic of the complex multicellular organism is the greatest contribution of evolution to the world. With increase in the quest for knowledge, man's attention was turned to measure the relationship and the frequency of the male and female sexes. ‘Work in this field has been very voluminous and covers almost all phases of it, extending anywhere from control of sexes, to sex determination and development in the extra-uterine stages. Among animals, studies in sex ratio generally relate to either statistical analysis of available data or to various attempts to control or modify by experi- mental means. Gowen (1917) and again in (1942) analysing a large number of births among cattle showed the sex ratio to be 50.5 for male and 49.5 for females. He also con- cluded that age of the sire or the dam has no material effect on the sex ratio. works on the continent have alSo been fairly close to Gowen's work. Among the investigators who attempted to control sex ratio, mention should be made (If some of the outstanding works to illustrate the trend in this particular field. These workers have generally lised rats, rabbits, and swine for their work. Lush (1925) 173 attempted by utilizing dimorphism in sperms, that is, the XY type of sex inheritance, to separate them by centrif- ugation, as a possible method to control sex in artificial insemination. He worked on both rabbits and swine, though the results were not of any significance. Later, with Unterberger (1930) in Germany, while in the course of human medical practice accidnetally found that use of 5% sodium bicarbonate solution as a vaginal douche would result in male births and use of about 3% lactic acid solution as acid douche would result in female births. However, in all 53 cases he treated, he reported the birth of boys. Later works by others on humans have not supported his theory. This rather astounding work was replicated in animals notably in rats and rabbits by Roberts (1940), Cole et a1 (1940), Quisenberry and Chandiramani (1940, 1945) McPhee and Eaton (1942) and Casida and Murphree (1942). In all these works the results have failed to show any significant modification of the normal sex ratio. While the dairy cattle breeder is primarily inter- ested in sex ratio from an economic point of view, that is, 'whether or not it would open a new avenue if the frequency of the male or female stock is controlled, the above works point out the inherent limitations in this adventure. Sex ratio could be expressed as the number of males 174 per hundred females or the percentage of male births among all the births studied. Gardner (1950) studying sex ratio resulting from artificial insemination reported his results on the basis of the former, that is, 100 females to 105.89 males. The disadvantage of this method is that it magnifies any source of error that would affect any one sex. The latter method, which has been generally used by workers, has been, therefore, applied in the present study. While one regards sex ratio to be equal-~50 - 50, any effects of lethal genes, and environmental influences during the intra-uterine development resulting in embryonic mortality would affect considerably the sex ratio at birth. For any study involving sex ratio at birth, it is necessary therefore, to possess large number of data on births. During the life span of an animal, sex ratio could be studied at three different stages, namely, 1) at con- ception - primary, 2) at birth - secondary, and 3) at matur- ity - tertiary. Gowen (1942) while reporting on sex ratio in cattle, reviewed the work of Jewell, who had reported the intra-uterine sex ratio or also called the sex ratio at the primary stage to be 55.2% in cattle. But the study of sex ratio at conception is commonly limited to laboratory animals. In dairy cattle and other larger mammals, the 175 study has been generally based on the number of offSpring born i.e. at secondary stage. Since the present study relates to the secondary sex.ratio, it will be referred to hereafter as merely sex ratio. Still-born calves have also been included in the study. All the male and female calves born in the Mich- ;J igan State College dairy herd irrespective whether born single or in twins have been summarized in the Table CI as a basis of preliminary study. TABLE CALVES BORN IN THE MICHIGAN STATE COLLEGE DAIRY CI HERD FROM 1919 - 1950 Breed Under Twins Under Singles Total Grand Total Male Female Male Female Male Female Holstein! 41 41 367 368 408 409 817 Jersey 5 5 222 215 227 220 447 Guernsey 3 5 224 173 227 178 405 Ayrshire 1 7 87 94 88 101 189 Brown Swi SS 0 0 104 101 104 101 205 Total 50 58 1004 951 1054 1009 2063 176 TABLE CII CALCULATION OF SEX RATIO - ALL FIVE BREEDS Sex Number Percentage Percentage Standard Observed Expected Error Male 1054 51.1 50.00 1.1 Female , 1009 48.9 50.00 1.1 Total 2063 100.00 100.00 Standard error was calculated by the use of the formula: _ Standard error of percentage : PQ/N Where N is the total births =VI0.511 ¥ 0.489/2063 It means that if samplesare drawn at random two-thirds of the time one would get the percentage of the male to be between the range of 52.1% to 50.0%. To test the significance of the frequency of the male percentage Chi-Square test (X2) was applied: Chi-Square : S (0-0)2 with (n - 1) degrees of freedom, where 0 is the observed and C is the expected percentage of male and female births. Chi-Square : (1054 - 1031 - 5)2 + (1009 — 1031.5)2 1031.5 1031.5 177 : 0.962 -- not significant. DOF. : 2-1 = 1 Thus, from a total of 2063 births of dairy calves in all the five breeds of the Michigan State College dairy herd, the percentage of male calves was found to be 0.511 10,01 which by Chi-Square test was found to be not significantly different from .5. TWINNING IN DAIRY CATTLE Twins in dairy cattle are a special case of fer-' tility. As a supplement to the study of sex ratio in the present work it was thought to be valuable to include a discussion on the frequency of twins in dairy cattle. Twinning is very rare and its occurrence has evoked inter- est mostly among scientists from a research point of view but has little or no importance to the average dairy cattle breeder. Lush (1925) reported that twinning was more common among Holstein breed than other dairy breeds at Kansas State College and that there was some tendency to occur more frequently in particular families in the breed than the others. This indicates the inheritance of the char- acteristic. He reported the frequency of the twins to be 0.98%»of the births of dairy cattle and 8.84% among the Holstein breed. 178 Hewitt (1934) an Australian worker, observed the incidence of twins among Red P011 to be 2.1% and among Friesians to be 2.6% of the total births. The gestation period was shorter by 8 - 10 days and the twins and their dams showed to be heavier producers. {e concluded that a close genetic relationship exists between twinning, high milk and butterfat yields and longevity of life and fer- tility. Pfau (1948) reported twins to be 3.95% in dairy cattle. In regards to relationship of age of the dam to twinning, Jones and Rouse (1920), Hewitt (1934) and Pfau et a1 (1948), all agreed that it is rare in the first parturition, rises to a peak in the fifth to the seventh parturition and then declines with the advancing age. As to the general nature of the inheritance there is considerable lack of agreement among the workers. Pfau et a1 (1948) agreeing with the findings of Hewitt (1934) stated that the twinning exhibits Mendelian segregation and that it seems to be under the control of genes. Some workers believe that it is a simple Mendelian recessive factor. Apart from the genetic factors, environment does play a part in the causation of twinning, such as, age, size, physiological conditions, amangement and nutritional practices. While Hewitt (1934) agreed with the effect of 179 age on twinning, he pointed out that season has no influ- ence on twinning. Since dairy cattle, are classed as strictly uni- parous animals, according to the develOpment of their reproductive organs, the incidence of twins among them could be regarded as cases of atavism or reversion. It is considered as an undesirable character in dairy cattle. Twins are generally classified into two groups on the basis of fertilization and embryonic differentiation, namely: 1) Monozygotic - Twins resulting from the split- ting of a single fertilized ovum in the blastodermic stage and development. These are commonly referred to as "identical" twins. As they are genotypically the same, any variation within the identical twins must be consid- ered to be wholly environmental. Genetically their coefficient of relationship is 100 per cent. They are of more common occurrence in humans than in farm animals. Scientists are particularly on the lookout for them as they contribute an important source of information on the study of environmental effects, particularly in nutritional investigations, etc. 2) Dizygotic - Twins that result from independent but nearly simultaneous fertilization of two separate ova, and they are the same as ordinary full sibs in genetic 180 variability, except that they develop at the same time under identical intra-uterine environment. It could also be said that the extra-uterine conditions to some extent would be similar. The coefficient of relationship is 50% in dizygotic twins, as it would be in full-sib relationships. The first and the classical study on the diagnosis of monozygotic twins in domestic animals on the same methods as those applied to humans was done by Kronacher (1932), who based the diagnosis on the correlation of, a) physical characteristics, b) physiological character- istics, and c) on the concordance or otherwise of psychic properties. Kronacher later (1936), proposed a new approach to identify monozygotic twins in cattle. The method was based on similarity quotients on growth, production and physical characteristics, the post—mortem measurements of stature, and analysis of blood and hormonal secretions. Lush, 1937, while reviewing the work of Kro- nacher (1936) further elucidated that diagnosis of the identical (monozygotic) twins, which are of the same genotype, depends upon the similarity of long series of characteristics. Whereas in the case of fraternal (dizygotic) twins, who although they are similar in one or few characteristics, become more and more divergent as the number of comparisons of the characteristics increase. 181 With the help of the available data, the present study has been directed to determine the frequency of the different sex combinations of twins and to test the sig- nificance from the expected frequencies. As the data from all the five breeds of Michigan State College dairy herd were small, it was thought desir- able to include the data that were available on the State J Institution herds, which are primarily composed of the 3 Holstein breed. Table CIII shows the number of twins in different breeds. TABLE CIII TWIN SEX RATIO IN DIFFERENT BREEDS Breed Twin Combination Both Males Male and Female Both Females MICHIGAN STATE COLLEGE DAIRY HERD Holstein' 10 21 10 Jersey 1 3 l Ayrshire o 3 1 Guernsey O 1 3 Brown Swiss 0 0 0 STATE (GOVERN- MENT) HERD Holstein 35 94 53 Total 46 122 68 236 182 The total number of twins born in the College herd from all five breeds was 5A, which was found to be 2.62% of the total number of calves born. This figure compares favourably with those reported by Kronacher (1932) and Hewitt (193A), which were 2.7% and 2.1% to 2.6% respect- ively. Further statistical treatment consisted in testing _( whether or not the frequency of twin combinations was to a large extent a phenomenon of dizygotic nature; the tests were made under two different hypotheses. 1. It was assumed that the sex ratio was equal to 50 male calves to 50 female calves or in other words the frequency of male calves (q) to be 0.50. The total number of twins of all combinations being 236, the expected numbers were calculated by use of the formula, N [Efflrqi)2 as suggested by Johansson (1932), where N is the total number of all twins and (q) and(l-q) is the frequency of the males and females. The (q) having been assumed to be 0.50, the expected values were calculated and shown in Table CIV, along with the observed (actual) values. 183 TABLE CIV OBSERVED (ACTUAL) AND EXPECTED (CALCULATED) NUMBER OF TWINS OF DIFFERENT SEX COMBINATIONS Twin Combinations Total Both Males Male and Female Both Females Observed L6 122 68 236 Expected 59 118 59 236 Deviation ~13 +4 +9 The Chi-Square test on the above values was found to be insignificant, indicating the hypothesis to be cor- rect. That is, the observed twin combinations do not significantly deviate from those expected combinations under the hypothesis in which q was equal to 0.50. 2. Under the second hypothesis the sex ratio of 51.1% male and 48.9% female obtained from the data under study was assumed to be the frequency in the population. The expected number of different twin combinations was calculated by the same bionomial formula, NEq + (l-Qfl2 , where N is the total number of all twins which is 236 and(lis equal to 0.511 and l-q is equal to O.A89. The calmflated expected values and the observed values have been shown in Table CV. M ' I .:.:k 184 TABLE CV OBSERVED AND EXPECTED NUMBER OF TWINS OF DIF- FERENT SEX COMBINATIONS TWIN COMBINATIONS ' Total .4 Both Males Male and Females Both Females Observed 46.0 122.0 68.0 236 Expected 61.6 117.9 56.4 235.9 or 236 Deviation -15.6 +4.1 +11.6 Again the Chi-Square test for the above values was carried out and was found to be not significant. The hypothesis that they do not deviate from expected is correct. Thus, it could be concluded that if there was pre- ponderance of the monozygotic twins, there should have been a noticeable frequency of the same-sexed twins. Instead there is a slight increase in the opposite-sexed twins, which is not only not significant but also similar to the binomial distribution of q = 0.5. From this it could‘be concluded that the twins born in the Michigan State College dairy herd and that of the State (Govern- ment) herd, were mostly dizygotic twins, though one would not rule out the possibility of the occurrence of 185 few monozygotic (identical) twins. From the present study, tie twin sex ratio among the dairy cattle was found to be: 466.331.2259 :68 99 PART V ' GENERAL CONCLUSIONS AND SUMEARY GENERAL DISCUSSION OF RESULTS The present study covers a range of varied char- acteristics, which have been dealt with as independent economic factors in the dairy herd of the Michigan State College at East Lansing. While discussions concerning these Specific characteristics have been examined at length in the respective sections, only overall con- sideration of the resulting effects on the dairy cattle breeding has been stated here. , The heritability estimates are all based on the lifetime averages, which was 2.6 lactation records per cow for the whole herd. In view of the relatively smaller number of samples in some of the breeds, no attempt was made to transform and express these findings in terms of what they would be if each cow had only one record. The heritability values in the present study, on an intra-sire basis for the whole herd was found to be, -0.01 1 .08 for milk, 0.20 1 .08 for butterfat, and 0.56 1 .047 for butterfat test. These are the weighted averages of 3 methods and 5 breeds in the herd. The corresponding estimates based only on intra-sire regression method were, -0.08 1 .12 for milk, 0.09 1 0.123 for 187 butterfat and 0.47 1 .06 for the butterfat test. In comparing;the results by the former method with that of 'the latter method it could be seen that in the case of milk and.butterfat, the sampling errors (standard errors of heritability) have been partly reduced by weighting the average estimates of the different methods, which could be considered.al of Some advantage. Further, the sampling errors by the regression method in the case of milk and butterfat show values greater than the heri- tability estimates themselves, which was discounted in part by the weighted average. The occurrence of nega- 1tive values of heritability in some of the individual breeds and methods, the weighted averages have been obviously smaller than weighted averages of the five breeds, as well as those of the three methods. Under the hypothesis that there is a population difference which obviously presupposes that the differ- ence must vary between certain limits, the fiducial limits at 99 per cent were calculated. These limits, how- ever, provide one with the amount of confidence that one can place in these various heritability estimates: Limitghlt .lesh The "t" value at l per cent level should be taken for (n-2) degrees of freedom, where "n" is equal to the Inmmer of pairs of daughter-dams. ‘Here, n 3 271, and 188 the "t" value at 1 per cent level is 2.592. By use of the above formula the confidence limits were found to be, -0.01 1 .21 for milk, 0.20 1 .21 for butterfat and 0.56 1,047 for butterfat test. Therefore the 99 per cent confidence limits are: Milk : +0.20 and -0.22 Butterfat a 0.41 and -0.01 Butterfat test : +0.69 and + 0.43 These figures indicate that the heritability esti- mates under the present study in 99 out of 100 could lie within these limits. Since a negative heritability estimate is meaningless, the negative values and limits have thus been rejected from consideration. It seems, therefore, the peculiarities in these estimates, includ- ing negative values could be due to sampling variations. The heritability estimate of milk yield by regression of daughter on dam method was found to be 0.11 which value is within the above fiducial limits of milk and closely approaches the positive limit. According to the Galton's law of inheritance, the sire and the dam contribute almost equally to the genetic make up of the offSpring. Therefore, the expected gain per generation in each of the traits, milk, butterfat, and butterfat test would be proportional to half the product of the percentage of heritability” the standard deviation and the total selection differential. The standard deviation for the whole herd inclusive of all breeds for 189 each of these traits was calculated by use of the following formula: A 6 : Ill-SE + {1283+ o o o +I].}(S]:2c 111+ 112+ o o o +nk-k where n1 . . . nk is equal to the number of animals in each breed, sf . . . sfi is the variance of each of the component breeds, and k is equal to the number of breeds. Thus the combined standard deviation in each instance was: Milk . 232 pounds Butterfat = 92 pounds Butterfat test = 0.5 per cent According to Lush (1945), if one considers the percentage of replacements needed in a static population are about 55 per cent in the case of dairy cows and about 5 per cent in the case of dairy bulls, the correSponding maximum selection differential in terms of the standard deviations would be 0.70 and 2.06 respectively, in a normally distributed population. If the heritability estimate for milk is considered to be 0.11 (regression of daughter on dam method) and the standard deviation to be 232 pounds, then the expected average gain per gener- ation would be (0.11) (232) (0.70 + 2.06)/2 : 35.2 pounds, provided the selection is directed only towards 190 increasing the milk yield. Similarly, for the butterfat, with the heritability factor (intra-sire method) and the standard deviation being 0.20 and 92 pounds respectively, theexpected average gain per generation would be (0.20) (92) (O.70+2.06)/2 = 25.4 pounds, granting that the selection is directed only towards improving the butterfat production. In the case of butterfat test, the expected average gain per generation would be (0.56) (0.5) (0.70+2.06)/2 : 0.39 per cent or 0.004, assuming that the selection would be practiced only in one direction, i.e. butterfat test. Judging from these various expected values that could be attained under the conditions stated above, the improvement that one would make in respect of butterfat yield seems to secure for the breeder a greater source of income in comparison to the other two traits. Since the average gains are expressed in terms of each generation, the maximum improvement or gain that could be attained in any one year would be one over the aver- age of the cows times the average gain per generation. Lush (1945) has estimated that the average age of cows ‘when their offSpring are born (i.e. average interval 'between generations) is between 4 and 4% years. On the basis of this estimate the average gain per year would be about 7.6 pounds of milk, 6 pounds of butterfat and about O.lJ+ per cent or 0.001 of butterfat test. When selection 191 is practiced for more than one character and when those characters (n) are such that no correlation exists, while being equally important, the possible gain in any one character would be only l/J—H'times as great as if all selection were directed towards improving one char- acteristic alone. Thus, in any balanced breeding program where the breeder attempts to improve several traits at one time and where allowances must be made for any intensity of selection in one of these, the actual gain would evidently be much lower than the expected values obtained above. REPEATABILITY: The repeatability for the whole herd, for milk and butterfat was found to be 0.49 and 0.50 reSpectively, which values compare favourably with the figures of other investigators. Since the greatest advantage of these estimates to a breeder is that they serve him as an import- ant tool in practicing culling in his herd they could be ‘profitably used in predicting the most probable future ;producing ability of a cow from the formula: Y : Herd average t nr 1 x (X - Herd average). 1+(n - 1)r where Y s a cow's most probable future producing ability X 3 a cow's actual production, 192 n = number of lactation records of the cow, r z the repeatability. The formula nr gives the real ability 1+(n-1)r of the cow. Repeatability estimates in combination with the heritability estimates could also be used to predict most probable breeding value of an animal in a given herd, if one practices culling on this basis, instead of on the producing ability. The breeding value could be obtained from the formula: Y - hn as far above or below the average 1+(n-1)r of the other members of the herd as the animals own actual records average. where Y the expected breeding value h heritability estimate. The formula is similar to the one stated above, except that the "r" has been replaced by "h". EFFECT OF MONTH OF CALVING ON MILK AND BUTTERFAT PRODUCTION: Since no significant relation between these two factors and the month of calving was fbund, it could be concluded that the planning of any system of freshening of cows in one or the other month or months is one that mostly concerns management and production practices in a 193 herd. The results found in this study compare well with several other similar studies. SEX RATIO AND TWIN RATIO: The sex ratio shows no significant deviation from the normal proportion of 50 males to 50 females in the general population. The twins among dairy cattle are extremely rare and no useful purpose would be served by practicing selection for them.. Many workers consider the occur- rence as an undesirable character in dairy cattle, which in several instances has been reported to have been attended with untoward effects on the cows as well as on the twins themselves. Therefore breeders should attempt to eliminate such of those animals which are capable of potentially transmitting these undesirable genes. 19h SUIVEV’LARY 1. A statistical study was made on the lactation records from 1919 through 1950 of milk yield, butterfat production and the percentage of butterfat (or butterfat test) of the Michigan State College dairy herd, which comprises of all the five breeds, namely, Holsteins, Jerseys, Guernseys, Ayrshires, and Brown Swiss. The herd is a part of the Michigan Agricultural Experiment Station. 2. The estimates of heritability on an intra-sire basis for the 3 most important economic characteristics of the dairy herd as a whole was found to be, -0.0l‘; .08 for milk,.0.20 _+_ .08 for butterfat and 0.56 1 .051!» BF test, which are the weighted averages of three methods and five breeds. 3. The estimate of heritability for milk yield by regression of daughter on dam method was found to be 0.11. 4. Repeatability estimates for milk and butterfat production were shown to be 0.49 1 .272 for milk and 0.50 1 .269 for butterfat. 5. The study of the effect of the month of calving on the production of butterfat showed no significant dif- ference between the two under the climatic conditions 195 that exist at East Lansing, Michigan. 6. The analysis of the calving records covering the above period of study showed that there were a total of 2063 births and the percentage of male calves was found to be 0.511 1 0.0; which was not significantly different from the normal ratio of 50 male births to 50 female births. 7. The study, which included the data from the Michigan State Institution dairy herd on the frequency of the twins in dairy cattle showed that there was a ratio of 4650,5122 59:6899. The nature of the binomial distribution of these twins appears to indicate that the occurrence of identical twins in dairy cattle is a rare phenomenon. 8. The frequency of twins in the Michigan State College dairy herd was 2.62% of the total number of calves born. BIBLIOGRAPHY Arnold, P. T. Dix, and Becker, T.B. 1935 The Effect of Season of the Year and Advancing Lactation Upon Milk Yield of Jersey Cows. Jour. 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