ABSTRACT INTERACTIONS OF SIRE WITH MATERNAL GRANDSIRE IN MICHIGAN HOLSTEINS by Basil Ralph Eastwood First available Michigan DHIA lactations from 3798 Holstein- Friesian cows whose sire and maternal grandsire were in artifi- cial service were studied to measure interactions between sire and maternal grandsire for productive traits. Records used were deviations of 305 day-ZX-mature equivalent lactations from the 305-2X-ME lactation herd average. There were represented 225 sires and 229 maternal grandsires. Components of variance were calculated from the model: Y. = +.+f+ f.+Y.+9.+T.+. J£m~ P cJ 1 “”31 J11 J! 32 €ka where c is sire, f is maternal grandsire, (cf) is the interaction of sire with maternal grandsire,7'is a reciprocal interaction effect, 9 is a specific inbreeding effect, T is a general effect of inbreeding, and e is an error term. All components are un- correlated random variables. Components were also calculated for a model which eliminated the inbreds (ejx and zj) and for a model with only simple interaction. LMA.._ -: r q .1" 1'! ET . 2 Basil Ralph Eastwood The standard deviations for milk and fat production were 2,100 and 77 lbs. Sire and maternal grandsire effects accounted for 5.7 and 1.9 percent of the variation in milk production and 5.9 and 2:5 percent of the variation in fat production. Negative components of variance were obtained for recipro- cal effect and for both inbreeding effects. A large positive estimate was obtained for the interaction of sire with maternal grandsire. This component became negative, however, when the three negative components were set equal to zero and the sire, maternal grandsire, and interaction components were re-estimated. The best estimate of the contribution of the variance components ‘Y: 9,'T, and (cf) to the overall variation in these data is zero. The unbalanced nature of these data with only 5 percent of the subclasses filled has apparently prevented an interaction from being detected if one truly exists. INTERACTIONS OF SIRE WITH MATERNAL GRANDSIRE IN MICHIGAN HOLSTEINS By Basil Ralph Eastwood A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Dairy 1967 4 5,11%; ACKNOWLEDGMENTS Appreciation is expressed to Dr. Clinton E. Meadows and Dr. Lon D. McGilliard for their patient and helpful guidance throughout the course of this work and to Mr. A. J. Thelan and associates at the Michigan DHIA Computing Center for their many hours of assistance. Appreciation is also extended to Dr. Charles Lassiter for the research assistantship, to my wife, Barbara, for her help and en- couragement, and to Mrs. C. L. Kern for typing the manu- script. ii TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . The Genetic Basis of Specific The Present Study . . . . . . REVIEW OF LITERATURE . . . . . . . . Research with Plants . . . . Recurrent Selection . . Laboratory Experiments . . . Poultry Breeding Experiments Research with Swine . . . . . Beef Cattle Research . . . . Research with Dairy Cattle . SOURCE OF DATA . . . . . . . . . . . MODEL AND ANALYSIS . . . . . . . . RESULTS AND DISCUSSION . . . . . . . SWRY O O O O O O O O O O O O O 0 REFERENCES 0 O O O O O O O O O O O 0 iii Combining Ability 11 12 17 20 21 25 27 33 62 65 . '41. —-.-._.-—u- . Table 10. 11. 12. 13. LIST OF TABLES Fractions of genetic variance contained . . . . . A generalized representation of the data . . . . Expected coefficients of variances from the complete model in uncorrected sums of squares for milk . . Expected coefficients of variances from the complete model in corrected sums of squares for milk . . . . Expected coefficients of variances from the complete model in mean squares for milk . . . . . . . . . Expected coefficients of variances from the complete model in mean squares for fat . . . . . . . . . . . Variance components for milk (10 lbs.) from the com- plete model . . . . . . . . . . . . . . . . . . . . Variance components for fat (in lbs.) from the com- plete model 0 C C O O 0 O O O O O C O I O O O O 0 Expected coefficients of variances from the off-dia- gonal model in uncorrected sums of squares for milk Expected coefficients of variances from the off-dia- gonal model in corrected sums of squares for milk . Expected coefficients of variances from the off- diagonal model in mean squares for milk . . . . . . Expected coefficients of variances from the off- diagonal model in mean squares for fat . . . . . Variance components for milk (10 lbs.) with inbreds eliminated O O I O O C O O O O O O I O O O O O O 0 iv Page 16 26 29 3O 31 32 33 34 35 37 38 38 Table 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Variance components for fat (in lbs.) with inbreds e liminated O O O O O O O O O O O O O O O O O O O O 0 Expected coefficients of variances from the simple interaction model in uncorrected sums of squares for mi 1k 0 C O I O O O I I O I O O O O O D O O O O O O 0 Expected coefficients of variances from the simple interaction model in corrected sums of squares for mi 1k 0 C O O O I C O O O C C O O O O O C O O I O O 0 Expected coefficients of variances from the simple interaction model in mean squares for milk . . . . . Expected coefficients of variances from the simple interaction model in mean squares for fat. . . . . . Variance component estimates for milk (10 lbs.) using the simple interaction model . . . . . . . . . Variance components for fat (in lbs.) from the simple interaction model C O O O O C O C C C C O O C C O 0 Comparison of fat production variance components for three mOdels C O O O O O O O O O O O O O O O O O O 0 Expected coefficients of variances in corrected sums of squares for milk and fat from the complete model with r, 6, and T assigned zero values . . . . . . . Expected coefficients of variances in mean squares for milk and fat from the complete model with'r, 6, and T assigned zero values . . . . . . . . . . . . . Variance components for milk (10 lbs.) from the com- plete model with r, 6, and T set equal to zero . . . Variance components for fat (in lbs.) from the com- plete model with Y3 6, and T set equal to zero . . . Variance components for milk (10 lbs.) from the off- diagonal model with7*set equal to zero . . . . . . . Variance components for fat (in lbs.) from the off- diagonal model withflrset equal to zero . . . . . . Page 39 4O 41 41 42 42 43 44 47 48 49 49 so 50 Table 28. 29. 30. 31. 32. 33. 34. Page Variance components for milk (10 lbs.) from the complete model with r, G, T, and (cf) set equal to zero . . . . . . . . . . . . . . . . . . . . . . 51 Variance components for fat (in lbs.) from the com- plete model with'r, 9, T, and (cf) set equal to Zero . C C C O C O C O O O O . C C . . O I C O O O 51 Variance components for milk (10 lbs.) from the off- diagonal model withycand (cf) set equal to zero . . 52 Variance component estimates for fat (in lbs.) from the off-diagonal model withd'and (cf) set equal to zero . . . . . . . . . . . . . . . . . . . . . . . 52 Comparison of fat production variance components for the complete model with those of the complete model after‘r, 9, and T, and r, 9, T, and (cf) have been set equal to zero . . . . . . . . . . . . . . . . . 53 Comparison of fat production variance components for the off-diagonal model with those of the off-diagonal model after r, andflrand (cf) have been set equal to zero . . . . . . . . . . . . . . . . . . . . . . . 54 Distribution of the degrees of freedom for each model used in this StUdy O O O O O O O O O O O O O O O O 55 vi LIST OF FIGURES Figure 1. Diagram showing reciprocal offspring groups 2. Heritability of milk production based on the sire component of variance . . . . . . . . . vii Page 56 59 INTRODUCTION The genetic contribution to the variation in any trait may be divided into additive and non-additive fractions. Sprague and Tatum (43) suggested in 1942 that in any previously unselected pop- ulation the genes with additive effects are more common or produce greater effects than genes with dominance or epistatic effects. After many generations of selection, however, the relative importance of the non-additive fraction increases. As differences in additive effects are eliminated, dominance and epistatic effects become relatively more important. It is doubtful that any measurable decrease in the additive genetic variation for productive traits of dairy cattle will occur for many generations. Although selection procedures are becoming constantly improved, the long generation interval and small selec- tion differential hold the average rate of genetic improvement at a rather low level. If non-additive genetic effects are important, however, maximum progress may be obtained only through use of specific combinations of individuals or lines. Present sire evaluation procedures are more effective if the mates of a sire are a random sample of the cow population for that breed. It is improbable that many dairymen select their sires at random, and most dairymen use only one or a few sires each year. Therefore, the mates of some sires could be highly related to each other and very atypical of the population. A genetic correlation of the sire with his mates could greatly bias the evaluation of that sire and lead to an incorrect decision regarding his future use. Such correlations may be referred to as Specific combining ability or nicking. If these correlations are important, sire evaluations would need to consider the genetic make-up of the group of mates that produced the progeny, and recommendations for future use of that sire would need to specify the relative groups to which he should be mated. The Genetic Basis of Specific Combining Ability Sprague and Tatum (43) first used the term "Specific combining ability" in 1942 in their discussion of single crosses of corn. These workers used specific combining ability to designate "those cases in which certain combinations do relatively better or worse than would be expected on the basis of the average performance of the lines involved”. The term "general combining ability" was used to designate the "average performance of a line in hybrid combinations”. The observed differences in specific combining abilities between individuals or lines may come from several sources. Dominance devia- tions are one source. If the favored gene is dominant, the heterozygote AA will produce better offspring when mated to AA than when mated to A3 and much better than when mated to AA. Larger differences in specific combining ability may be caused by overdominance. The AA individuals will then appear superior when used on AA mates, but inferior when used on AA mates. The contribution to specific combining ability due to overdominance may become more extreme as the number of genes increases. Another source of differences in specific combining abilities is epistasis. Epistasis has been defined as interaction between non-allelic genes. Examples of non-additive combinations of the effects of genes such as inhibiting genes, threshold effects, and the case in which the phenotypic optimum is a genetic intermediate may contribute to Specific combining ability. (31) When specific combining ability is estimated in small populations confusion may arise due to other causes of variation contributing to the estimate. Chance at Mendelian segregation does not cause differences in specific combining ability, however it may contribute to the estimate of Specific combining ability. Since the effects of chance at Mendelian segregation would be reduced with greater numbers of observations, chance has less effect on estimates of general combining ability than on estimates of Specific combining ability. The estimate of Specific combining ability can also include differences caused by uncontrolled variations in the environment. These environmental variations may cause the phenotypes of the off- spring from a cross to average higher or lower than that which corresponds to their average genetic values. Both genotype-environ- ment interactions and random environmental variations may contribute to an estimate of Specific combining ability. The Present Study This study was undertaken to ascertain whether a sire produces superior offspring when mated to daughters of certain other sires than would be expected from the average performance of daughters of the sires involved. More Specifically, a good estimate of specific combining ability was sought from the component of variance for interaction of sire by maternal grandsire in production of milk and fat. REVIEW OF LITERATURE Much of the research on Specific combining ability has been with plants. Some laboratory work with rats, mice, Tribolium, and Drosophila has been done to evaluate combining abilities. Only relatively recently, however, have breeding experiments with dairy cattle been attempted to estimate the Size of the "specific” effects commonly known as "nicking". General and specific combining ability among inbred lines of dairy cattle are being studied at the Ohio and Minnesota stations in cooperation with the United States Department of Agriculture. The South Dakota and Wisconsin stations are studying the effects of in- breeding on economic traits in eight inbred lines of Holstein cattle. These inbred lines will be crossed and combining abilities measured. Crossbreeding experiments are being engaged in at Illinois, Indiana, and the Beltsville, Maryland, Station of the United States Department of Agriculture. Each of these studies should provide needed data on specific com- bining ability for productive traits in dairy cattle in addition to other breeding information. Each is closely controlled but must nec- essarily deal with relatively few animals. Larger numbers of dairy cattle may be utilized to study specific combining ability by using existing records. Several studies, in- cluding the present one, are of this nature. Research with Plants Many workers have studied Specific combining ability in various Species of plants. In general, they have found varying (but presum- ably real in many cases) amounts of Specific effects. Carnahan gt_§l. (8) in studying combining abilities in alfalfa for seedling vigor and fall growth habit in the year of establishment found the variance from general combining ability was much higher than variance from Specific combining ability. They concluded that evaluation for interactions of genotype with location for these traits Should receive as much or more attention than that devoted to determining specific combining ability. Morley g£_§l. (38) found the component of variance for specific combining ability was approximately equal to that for general combin- ing ability in their study of summer production of hybrids between 10 alfalfa varieties. For winter production, however, the variance for general was considerably greater than that for Specific. In a study of orchard grass, Oldemeyer and Hansen (40) noted considerable variation among the Single crosses for the reSpective parents and suggested that this indicated the expression of specific combining ability. Allard (1) has described four general types of tests for combin- ing ability in plants: the Open-pollinated progeny test, tOp-cross test, polycross test, and the single-cross test. The first three of these measure general combining ability while the single-cross test measures the combining ability of particular pairs of parents (clones, lines, etc.). The single-cross is the most SOphisticated of the four and also lends itself to animal breeding experiments. If all of the possible single crosses among 2 selected parents are made, the resulting set of crosses is called a diallel cross. The average combining ability of any parent may be calculated from single-cross data as the mean performance of that parent in its crosses. Average combining ability becomes more and more similar to general combining ability as the number of single crosses involving that parent is increased. Recurrent Selection. - Hybrid varieties of cross pollinated crOps have been universally developed by selection of desirable plants from heterozygous sources, inbreeding the progenies of these plants to in- crease homozygosity, and producing F1 hybrids by crossing the most productive of these inbreds. The early maize hybrids were produced by isolating inbred lines directly from the old open-pollinated varieties. Later, "second-cycle"'hybrids were produced which utilized inbreds isolated from crosses between superior inbred lines. This eventually led to development in the 1940's of the breeding system commonly referred to as recurrent selection. In recurrent selection in maize, plants from a heterozygous source are self-pollinated and are evaluated for some trait. Superior plants are selected, all possible intercrosses are made, and the resulting intercross pOpula- tion serves as source material for recurrent cycles of selection and intercrossing. Four types of recurrent selection generally recognized are: simple recurrent selection, recurrent selection for general combining ability, recurrent selection for Specific combining ability, and reciprocal recurrent selection. In simple recurrent selection no test crosses are made; the plants are discarded or propagated on the basis of their phenotypes or phenotypic scores on their selfed progeny. This system is not effective in selecting for combining ability for yield. The other three types of recurrent selection utilize test crosses to measure combining ability. In recurrent selection for general combining ability a tester with a broad genetic base is used to rate the plants on their general combining ability. A tester with a narrow genetic base (an inbred line) is employed to rate a group of plants on specific combining ability in recurrent selection for specific combining ability. Reciprocal recurrent selection allows for selection for both general and specific combining abilities and utilizes two heterozygous source populations -- each being the tester for the other. An excellent discussion of these systems is given by Allard (l). Recurrent selection for specific combining ability was proposed in 1945 by Hull (22) to take advantage of that part of heterosis resulting from nonlinear interactions of both allelic and non-allelic genes, i.e. dominance and epistasis. The outcome of this selection program would presumably be to develop a line which approaches the opposite extreme in gene frequency from the inbred line used as a tester. The line thus produced would then be crossed with the tester to produce com- mercial hybrids. The other recurrent selection system which places some emphasis on specific combining ability is reciprocal recurrent selection, pro- posed by Comstock et al. in 1949 (9). These workers compared the efficiency of reciprocal recurrent selection with that of recurrent selection for general combining ability and recurrent selection for specific combining ability on a theoretical basis. The assumptions were that only two alleles per locus were possible, that no epistasis was present, and that the relative frequencies of genotypes at linked loci were at equilibrium. In general, the conclusion reached from this theoretical analysis of efficiencies was that reciprocal recurrent selection is at least as effective as recurrent selection for general combining ability and recurrent selection for specific combining ability for all situa- tions considered. Where overdominance is important, reciprocal re- current selection and recurrent selection for Specific combining ability are clearly superior to recurrent selection for general com- bining ability. In the case of partial or incomplete dominance, re- ciprocal recurrent selection and recurrent selection for general com- bining ability are superior to recurrent selection for specific com- bining ability._ The presence of epistatic interaction, multiple lO alleles, or linkage disequilibrium would favor reciprocal recurrent selection and recurrent selection for Specific combining ability (9). From this study reciprocal recurrent selection is superior to the other recurrent selection methods for use on pOpulations where both general and Specific effects are expected to be present. In a population of lines previously unselected for combining abilities, genes with additive effects may be more common or produce larger effects than genes with dominance or epistatic effects. In material previously selected for genes having additive effects, genes with dominance and epistatic effects become relatively more important as differences in additive effects are eliminated (43). Lonnquist and Rumbaugh (30) presented data in 1958 from their work with corn to support the common practice of testing new lines first for general combining ability and following this with tests for specific combining ability. Population improvement was greater when selection was based on a tester having a broad genetic base. Laboratory Experiments Several experiments with rats and mice have provided information from diallel crosses on the relative importance of general and specific effects for growth characteristics in these animals. Using four inbred lines of rats, Kidwell g£_§l. (28) made all sixteen possible mating combinations including inbreds and reciprocal crosses. The effects of sex, lines, and maternal ability on body weight were highly significant at 70 days but not at 90. There was no 11 evidence of Specific combining ability or sex linkage effects; how- ever, an interaction between maternal effects and mating system was indicated for 28 day weight. Differences in general combining ability were highly significant at 28 days but not significant at 70 days. The authors concluded that preweaning differences in maternal ability and a post weaning compensating effect might also account for these results. In a somewhat similar experiment with mice, Carmon (7) used weights of 1824 individuals from 312 first litters of all possible crosses among 4 lines of mice. Heterosis measured as a comparison between linebreds and crossbreds was highly significant. General com- bining ability, maternal effects, and sex linkage effects were signifi- cant, but specific combining ability was not. The 72 possible single crosses among nine inbred lines of mice were made and studied by Eaton.g£_§l. (12). They found that Specific combining ability effects were important though not significant for total litter weight but unimportant for individual mouse weights. Line differences were important only for mouse weight. Line differ- ences in maternal influence were important for both litter size and mouse weight but because of a -.85 correlation between these com- ponents, were non-existent for total litter weight at 45 days. Ratios of variances from specific and general cross performance, assuming epistasis negligible, suggested superiority of the heterozygote for 12 viability and total litter weight but little dominance for genes influencing mouse weights. Regressions of F1 on inbred parent with- in common parent lines indicated much dominance for 45 day weight, however. Poultry Breeding Experiments Many experiments have been conducted with poultry to determine the relative importance of general and Specific effects and also to Study the effectiveness of various Systems of selection. Bell and co-workers (3) in their discussion of poultry breeding systems concluded that recurrent selection for nicking would increase the frequencies of desirable genes more rapidly than would reciprocal selection but would have a somewhat lower theoretical limit of im- provement. Reciprocal selection would probably be more practical since superior strain and breed crosses could be utilized as foundation Stocks. A number of experiments crossing inbred and non-inbred lines have been carried out with poultry. Goto and Nordskog (15) estimated variances of general and specific combining abilities, maternal effects, and reciprocal effects for inbred linecrosses. General combining ability was more important than specific effects for all nine charac- ters studied with the possible exceptions of percent brooder house mortality, percent hatch of all eggs, and percent laying house mortality. Hill and Nordskog (21) studied nine factors in linecrosses and found an appreciable amount of Specific combining ability present only for March body weight and broodiness. 13 Another Study of linecrosses in poultry, conducted by Hutt and Cole (23), utilized two strains of Leghorns with low inbreeding coefficients of thirteen and eight percent. The resulting crosses consistently excelled both parent strains in hatchability, early maturity, egg production, size of eggs, and size of birds. The reciprocal crosses were equally as good. These workers suggested that enough heterosis might be achieved from crosses between lines of low inbreeding to eliminate the necessity of develOping highly inbred lines. Wyatt (47) found little relationship between topcross performance and inbred performance for the five traits studied. Since the rela- tionship between topcross and inbred performance is a function of heritability, this indicates a relatively small contribution by addi- tive genes to the variance between lines. The different testers used failed to rank the inbred lines in the same order as measured by the average performance of the topcross progeny. This was further evidence that genes with additive effects contributed little to the variance between lines. Evidence of an important contribution by dominance and non-linear gene interactions was given by a significant line x tester interaction for hatchability and weight at six weeks. Since inbreeding decline is evidence of some kind of genetic variance, Wyatt concluded that non-additive genetic variance was probably important in these lines. 14 If heritability of individual differences is one hundred per- cent, the linear regression of t0pcross on inbred parents would be five-tenths. Glazener and Blow (14) found a regression value of three-tenths for weight in broiler production and reasoned that this difference between five-tenths and three-tenths could be due to interline non-additive genetic variance and intraline genetic and environmental variance. With large numbers of chicks in each line, the differences would reflect largely interline non-additive genetic effects. They concluded that since heritability of weight was high, a large portion of the variance between line means was the result of genes acting in an additive manner. However, since the inbred line x tester interaction was significant, dominance and gene interactions may also play an important role. An analysis of variance to determine the types of gene action involved in the inheritance of ten-week body weight and breast angle in broilers was carried out by Brunson g£_gl. (5). Approximately 43 percent of the total variance in body weight was due to genetic differences. This was subdivided into 41 percent for additive and 2 percent for non-additive genes. Sex linked genes accounted for 10 percent of the total variance and maternal effects for 2 percent. Maw (35) found that the crossing of unrelated inbred lines for seeming lower mortality and increased egg production appeared superior to topcrosses, related inbred crosses, and random-bred leghorns kept as controls. 15 To separate the total phenotypic variance into additive genetic, non-additive genetic, and environmental variance, Kan E£_il° (27) utilized an analysis of variance components on six broiler traits from a series of diallel matings. The non-additive genetic effects were then studied by a test of significance of the interaction mean square and by estimating the interaction component. Of the six traits studied, non-additive gene effects contributed to the varia- tion in shank length, heel length, body depth, and possibly gain in weight but had no apparent influence on 4 and 9 week body weight. Another study of diallel matings using eight week body weight was made by Kan g£_gl. (26). A significant interaction component was found but was overestimated due to small families of 12 hens per pen. Jerome.gg_§l. (24) utilized Henderson's method I for variance component analysis with the following model: = + + + + + )1 a 31 dj (Sd)ij e Yhijk h hijk where "a" is hatch; "s" is Sire; "d" is dam; and ”e" is a random error term. A large amount of dominance variance was found for total egg production and fall body weight. The portions of genetic variance in the different components were as follows where "10" signifies additive, "01" -- dominance, "20" -- additive by additive, "ll" -- additive by dominance, and "02" -- dominance by dominance: 16 TABLE 1. Fractions of Genetic Variance Contained (Jerome et al., 24) 02 62 02 02 62 Components 10 Ol 20 ll 02 Between Sire l/4 1/16 full sib Dam 1/4 1/16 groups Sire x Dam 1/4 1/8 1/8 1/16 Within Full SibS 1/2 3/4 3/4 7/8 15/16 full sibs l l l 1 1 Hazel and Lamoreux (17) studied three sets of diallel matings to estimate the importance of nicking. About five percent of the varia- tion in body weight was due to maternal effects; however, sexual maturity was not influenced at all by maternal effects. Nicking was a minor factor in this study and seemed likely to be unimportant generally in non-inbred matings. The method used in this study was an analysis of variance to separate the total variation in each series of matings into three parts: I. differences within families, II. differences between dams mated to the same sire, and III. differences between Sires. To examine the importance of the three sources of variation as they relate to differences between individual birds, the mean squares from the combined data were reduced to components of varia- tion. The variance among unrelated birds was W + D + I + S, and the variance among paternal half-sisters which have different dams but the same sire was W + D +'I where W is the variance expected between 17 full sisters, D is the variance associated directly with the dams, I is the variance attributed to nicking between sires and dams, and S is the contribution from sires. In a group of birds some of which are related, correction must be made for the average number of full sibs or half sibs. Research with Swine A large volume of information is available on crossbreeding of swine and heterosis and its converse, inbreeding degeneration. A considerable amount of commercial application has been made of the general principles elucidated by these reports. The research report- ed here, however, will be limited to studies of line crosses within breeds and attempts to study Specific combining ability. Some of the early work in this area of investigation was done by Henderson (19) in 1949. Single crosses among 12 inbred lines of Poland China swine were studied for litter number and weight at O, 21, 56, and 154 days. Specific effects (dominance and epistasis) accounted for five to fifteen percent of the variation among the crosses. The relative efficiencies of line cross and topcross tests for estimating general combining ability were studied. The line cross not only estimates general combining ability more efficiently, but it also furnishes information concerning maternal, specific, and sex-linked effects. Bradford g£_§l. (4) studied two-line crosses of inbred lines of swine and found maternal effects were more important than general l8 combining ability for 56-day pig weights. The Opposite was true, however, for five-month pig weights. Specific combining ability was not important for either 56-day or 5-month pig weights. If maternal effects are present, certain lines should be used only as female parents and certain others as male parents. There appear- ed to be a negative genetic association between the additive effects in the pig and maternal effects of the lines. This type of associa- tion could explain the ineffectiveness of selection for overall per- formance and would give support to the practice of selecting for cross performance. Magee and Hazel (32) in 1959 estimated differences in the general combining abilities and the general maternal effects from 2137 three-line cross pigs of 12 Poland China inbred lines. Dif- ferences in general combining ability were statistically significant and accounted for 4 percent of the variation among pigs of the same season and farm. The maternal effects of the lines and the inter- actions involving specific effects were not statistically significant. The ratio ____§a___. = 27 = .04 indicated that pigs E + L + G 450 + 228 + 27 from the same three-way cross (but from different litters) will vary 4 percent less in their weights than unrelated pigs of the same season- farm group. In this ratio G = general combining ability; L = litters within subclasses; and E = pigs within litters. 19 Two hundred eighteen litters from crosses among six inbred lines of swine were studied by Hetzer g£_gl. (20) to determine differences in general and Specific combining abilities. Dif- ferences in general combining ability were significant for only one pre-weaning trait, litter weight at 56 days. They were signi- ficant, however, for all post-weaning growth traits and for all carcass traits measured except dressing percentages, accounting for from 5 to 7 and 6 to 16 percent of the variation in these two sets of traits. Maternal effects were not significant for litter and pig weight at 56 days, pig weight at 140 days, daily gain, dressing percentage, yield of bacon, and yield of fat cuts, account- ing for 7 to 21 percent of the variation in the latter five character- istics. Specific combining ability was significant only for yield of bacon. Wilson g£_§l. (46) obtained a significant line x season inter- action in their study of the influence of sire and line of breeding on sow productivity but attributed this to the small number (2.8 to 3.5) of daughters per sire. Beef Cattle Research The long generation interval and the expense involved in breed- ing experiments with beef cattle greatly limit the volume of infor- mation available on Specific combining ability. O'Bleness et al. (39) 20 studied the weaning weights of single cross animals from 13 inbred lines crossed with each other and crossed with an outbred control group. The differences between lines of sire and between lines of dam were significant at the 0.01 level. Least square estimates were used to rank the lines used as sires and as dams. The low rank correlation coefficient of 0.11 showed that some lines in this study performed better as sire lines than they did as dam lines and vice versa. Damon g£_§l. (10) studied beef crossbreeding data with a rather sophisticated model. The data studied were 180 day weight, slaughter calf grade, slaughter grade, rate of gain on feed, and weight per day of age. General combining ability was significant for all five traits (1.3 to 18.7 percent). Heterosis and Specific combining ability effects were significant for all but slaughter calf grade. Specific combining ability was especially important for rate of gain on feed and weight per day of age accounting for 21.0 percent and 27.4 percent of the variance among crosses. Maternal effects were significant for all except slaughter grade; however, sex-linked effects appeared to have little influence on these traits. Another detailed model was used by Beal and Martin (2) in their study of crossbreeding dual purpose cattle. These workers used Red Dane, Red Poll, and Milking Shorthorn Sires and dams. Breed of dam and breed of sire were highly significant for total milk 21 production, persistency, and part-lactation production. The sire x dam (breeds) interaction was highly significant for total milk, persistency, and the early months of the lactation but tailed off to no significance the last two months of lactation. Research with Dairy Cattle An early study of Specific combining ability in dairy cattle in this country was made in 1933 by Fohrman and Graves (13). These workers used Ayrshire A. R. records from daughters of 51 different sires that had each been used in at least two herds. Only one bull had daughters significantly higher in one herd than in the other, leading to the conclusion that there was essen- tially no ”nicking" present. Heizer g£_§l. (18) in 1938 studied records of two Holstein- Friesian sires used in one herd and three Guernsey sires used in another. Daughter-dam comparisons were calculated for each sire x maternal grandsire group to determine whether any nicking had occurred. Since considerable differences were found in the apparent success of the matings, it was concluded that some nicking had occurred in the sires and herds used in this study. Since some sires appeared to work best on closely related families, it was concluded that the results were probably the effect of complementary effects of genes (epistasis) rather than heterosis. 22 In 1940, Johnson g£_§l. (25), using Register of Merit records of daughters of 17 Jersey sires having daughters in more than one herd, studied both daughter-dam comparisons and daughter averages to get at the question of nicking in dairy cattle. These workers found four sires to have large differences in production between herds, but after studying the situation further, they concluded that these differences were largely environmental. Seath and Lush (41), also in 1940, used an analysis of variance on daughters of Kansas DHIA proven sires to determine whether nicking had occurred between sire and maternal grandsire. It was concluded that with the kind of data usually found in proving sires, nicking is not often important enough that the pedigrees of the daughters need consideration if the records of the dams are taken into account. Wisconsin workers (37) using data from 187 Holstein heifers representing six Sire lines and four systems of mating, found that sire line and system of mating significantly affected the age at which an animal reached puberty. The interaction of sire line with systems of mating, however, was not significant. In another study (33), these same workers found conception rate was significantly affected by the interaction of sire line with system of mating, suggesting the presence of non-additive gene action among the lines on conception rate. 23 A third study by these same workers, (34) using an analysis of variance of the first estrual-cycle length following calving in outbred and inbred cows, showed a significant interaction of sire line and system of mating, again indicating non-additive genetic effects. Dickinson and Touchberry (11), in a study of the broader aspect of non-additive genetic effects involved in crossbreeding, found a considerable influence of heterosis on livability and concluded that crossbreeding dairy cattle may provide a means for immediate and marked improvement in herd health and longevity. Verley and Touchberry (44), however, in the same year, Studied seven measures of reproductive performance and found no significant differences between the purebred and crossbred animals for any of the seven. 'These measures of reproductive performance, therefore, did not seem to be greatly affected by non-additive gene action. An authors' summary on Swedish research by Hansson.g£;§l. (16), using data from 12,897 Swedish Red and White and 10,926 Swedish Friesian heifers sired by 939 and 764 bulls, respectively, reported that nicking had no significant effect on the genetic improvement of first lactation milk yield. Shreffler and Touchberry (42), in a study of the effects of crossbreeding on rate of growth in dairy cattle, found little evidence to suggest that the effects of crossbreeding on Size 24 are dependent on mating a specific sire of one breed to dams of another breed. Since the effects of system of mating, breed of sire, and breed of dam were relatively large, additive genetic factors were the predominant genetic influences upon rate of growth. Several studies have been conducted to ascertain the impor- tance of genotype -- environment interactions in dairy cattle. These studies have concentrated mainly on attempting to measure any sire by herd or sire by type of herd environment interaction that may have been present (6, 29, 45). The component for this interaction was nearly zero or negative in all cases. It was con- cluded that sires will be ranked about the same regardless of the herds or environments in which their daughters are located. Although these studies with dairy cattle Show results which vary from no interaction between sire and maternal grandsire to significant interaction, no evidence of a conclusive nature has been presented. Each study was hampered by lack of a sufficient number of animals or a definitive technique for measuring a Sire by maternal grandsire interaction. Non-additive genetic effects have been demonstrated for cer- tain traits in many different plants and animals. In some cases breeding schemes have been devised to take advantage of this varia- tion. The inconclusive results, high cost, relatively small num- bers available, and long generation interval inherent in cattle breeding have made it generally unfeasible to develop a scheme for utilizing non-additive genetic effects. SOURCE OF DATA First available lactations from the Michigan Dairy Herd Improvement Association on 3798 Holstein-Friesian cows sired by bulls in artificial service and from dams who were also sired by A. I. bulls were utilized. The records were on a 305 day, twice-a-day milking, mature equivalent basis and were deviations from the 305-2X-ME lactation herd average. A total of 225 sires and 229 maternal grandsires was involved in the study with the average number of daughters per sire being 16.88 (ranging from 1 to 268), and the average number of granddaughters per maternal grandsire being 16.58 (ranging from 1 to 176). There were 2555 sire by maternal grandsire subclasses filled, the average number of animals in each being 1.49 with a range of l to 19. A generalized representation of the data may be seen in Table 2. 25 26 u «o EdwamE ... H u E Amumuswamppcmuwv mumuswamv mum w 6 mo Eaefixme ... a u N mmuwmpsmum Hmsumume mum «m a mo ESEmeE ... H u a mmuwm one F.e .. H .~U.M. "W ... .N.» "w ... .N.>.flw .H.>flw o oqv o v QHU I: WWWHW Nflw NMHW Vlw . v v w v v v v v v a u yeas...msss ass» ayes...~q s Ha s um s...- s Hm s us s...NH s as s o . . . H .HH .usuW :qu .6.qu wnw . v v Um n a u y as...w as a .s “4“»...Nxfls Ham» uNaS...-fis Haas ssh»...uans as.» an ”:6 ..vmwww v ...uwQquW ...u .wauw u .3qu .N u . my...N.~» H.~w N»...Nw~w Hum» NNV...NNNM Hum» Haw...~H~» Ham» No v ..UHMWW .3.qu .NkuW .3qu . u H u . a»...m as seas “was...~xas Hus» uwa»...-H» HNH» “HHS...~HH» Haas #0 MW .0 o. H u . «m . mm m .mump use we cowumucmmwuamu pmnwfimumcom < .N mum¢a MODEL AND ANALYSIS The method used to calculate the components of variance was a modification of Henderson's method I described by McGilliard (36). The components of variance were calculated from the data in this study using the following model: = + c, + f + cf , + y: + e. + T, + e P J l ( >11 11 Y. . Jim J1 31 Jim p is the overall population mean. c is the amount the jth sire causes the average of his daughters to deviate from the average of daughters of all sires. j = l °°° q fl is the amount the,Xth maternal grandsire causes the average of his granddaughters to deviate from the average of granddaughters of all grandsires. 1 = 1 --- q (Cf)jl is the amount the particular combination of sire j(1) and maternal grandsire‘£(j) causes the average of their daughters (granddaughters) to deviate from the average of all daughters (granddaughters) of c (cf)j and fl and is 1 such that (Cf)j1 = (cf) = 0 for j = I. 13- 1 27 T32 .11 ii e. Jlm 28 is the amount the particular combination of sire j and maternal grandsire] causes the average of their daugh- ters (granddaughters) to deviate from the average of all daughters (granddaughters) of the combinations jg and [j and is such thatygz = -7}j° = 0 for j #X and for j =,( is the amount that inbreeding to sire j (maternal grandsire,() causes the average of these inbreds to deviate from the average of inbreds from all sires (maternal grandsires). = 0 for j f,(and for j =,( is the amount that inbreeding (sire x daughter matings) causes the average of all in- breds to deviate from p. T11 - T22 = qu, is a random effect assumed to be normally and indepen- dently distributed with a mean of zero and variance, 6%. m=looot All components of the model are uncorrelated random variables 2 222, 2 with ze 0 ex ‘ d w‘ h ‘ r pectation an it variances a; , 0% , déf , d},, 66 OT 2 2 . , and 0’ , respectively. 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