{.5 v... 4.. A .14.... 8.4.. .mm . . A464...“ 4 . .111 "4.4%. 43...... 4........w. ...r ,. 114%.?4ww who ...?!J. 430.1.Wkaé .. «awry . 1.4.4.41. 4.4011“..11..1.IJJ11.1 4 fuaurw.w.. w... 45? “MW.” 4T 1 4 é F INBR' RAITS 1N ‘ A HER n. .f.’~krr1!¢.w4. 4 firrfi. .1244.» 14/451110! 2m..4..5._1. 1.969» 4 ’0 . .. ..4... [Harrwiuw’m .. .. .... ........ . ....... .. Wm. ..... . . . .. .. ... ... .... ., (R. infill-1...... (”WWW ” . ... D. F , 4m...” V .0, a 4 . ... 1 o y 4 .01: T~ _ M S ers- ARTHU‘R :D I 551.8 EFFE . THE. T ‘BL‘E ‘ I Th Mll‘GHiGAN} ERITA H a . .-4 . . .. . .. - m 4 . .. ..4. 4 , .... .. ‘ . - ” ....-.» I W . . .. m V .. _ . . 4 _ . ‘4 .. . . I. l . . 1 . T. o. .4. . . : . .3. . . .114. .1. 4 . 54...“: 11.1 12.13.11... .4453"... .. m z -. .... .Z - J-. .3L...£}l..: 3... . :3... ..h...... . - .. 4 .. . . 4. 4.. .5 i I I I LIBRARY Michigan State University 1-H ESIS This is to certify that the thesis entitled THE EFFECTS OF INBREEDING ON HERITABLE TRAITS IN A HERD OF JERSEY CATTLE presented by ARTHUR D. DAYTON has been accepted towards fulfillment of the requirements for Ph.D. degree in Dairy 6572) Q mafia/WA, Major professor Date 30 November 3.ng IMWHWWWIUIW 31293 010051161 . ‘ '. N, ( -'~ . xv ‘3’ iii: if” E? - ‘ P C OK ABSTRACT THE EFFETS 0F DQBREEDING ON HERITABLE TRAITS IN A HERD 0F JERSEY CATTLE By Arthur1D.iDayton Inbreeding is a system of mating that the animal breeder may use to change the genetic preperties of a papulation. Inbreeding is defined as the mating of individuals more closely related than the average of the pOpulation from which they came. The purpose of this study was to determine the effects of inbreed- ing on seven growth characteristics, milk and fat production and body conformation. Foundation animals, including twenty-one females and five males, were purchased in California and brought to Michigan State University in 1951 to establish an inbred herd. Data used in this study were collected over a 15-year period with inbreeding ranging from zero to 50 per cent and averaging about 30 per cent. The number of animals used varied but at most, 265 animals were available for birth weight analysis. The regression coefficients of body‘ measurements on inbreeding were generally negative although only a few were statistically signifi- Arthur D 0 Dayton cant indicating that inbreeding has a depressing effect on growth. The rate of growth was slower for inbreds than non-inbreds from birth to 18 months and then tended to increase after 18 months. Intra-sire regressions, using the average of each cow's records, were ~.7§1.7h pounds of fat, 41:13 pounds of milk, and .OOSt.OOh per cent milk fat for each increase of l per cent in breeding. Maximum likelihood method was used to estimate simultaneously the effect of years, changes in average real producing ability of the herd, and the effects of inbreeding. The maximum likelihood estimates of inbreeding effects indicated a decline in production up to inbreed- ing coefficients of 12 and then an increase in production for animals inbred from 16 to 30 per cent and large negative estimates for animals inbred geater than 30 per cent. THE EFF'ESTS OF DVBREEDDJG 0N HERITABLE TRAITS IN A HERD 0F JERSEY CATTLE By Arthm' 1). Dayton A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR 0F PHIIDSOPHI Department of Dairy 1969 0 Av- ' ' EASCJ; fully ac}: AC KNOWLEDGI-EN T3 The author is grateful to Dr. Lon D. McGilliard for his interest and advice in handling the problem and for his critical reading of this manuscript. The financial assistance of Michigan State University is grate- fully acknowledged . 1*;1 t 9' run- run- v':n 5-6. V. ,ol‘o A.- . s ‘f‘.—. a fi' .qud ‘15.?“ - .1 , filo-ill I‘" A. \"3 5¥~.~. V‘rw-_. “ Q TABLE OF CONTENTS ACKNOWLEDGEMELTS . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . INTRODIBTION............. REVIEW OF LITERATURE . . . . . . . . . Introduction Method of computing the coefficient Mean and variability of an inbred pepulation of inbreeding EXperience from inbreeding dairy cattle . . . . . Effects of inbreeding on growth and body measurements Effects of inbreeding and outbreeding Summary............... SOURCE.AND DESCRIPTION OF DATA . . . . Foundation animals . . Project modifications . Selection procedures . Management procedures . Feeding o o 0 o o o c o ReprOdUOtim o PrOdUCtion o o o o o 0 ts General practices . . Weights and measuremen METHODS AND RESULTS on production Regression of weight and body measurements on Regression of production on inbreeding Effectl of inbreeding by multiple regression Effects of inbreeding on type rating Maximum likelihood method for estimating the effects inbreeding o Losses of females between birth and first parturition 0f inbreeding o c o o c c o o o o o o o c c o o o o 0 Estimates of repeatability" . . Maximum.likelihood estimates . DmUSSIONOOOOOOCOOOOOO. Mean and variation . . . . . . Bodyweight......... iii Page viii Uitrtrku \n t4 10 25 25 26 26 28 29 30 30 31 33 33 145 62 62 82 87 87 105 iv TABLE OF CONTENTS (Continued) Wither height 0 o o Other measurements 0 o o 0 L053 Of females 0 o o o o 0 Type rating 0 o o o o o o o PrOdUCtim o o o o o o o o S WHY O O O O O O O O O O O O O IITERATURE CITED . . . . . . . . . APPMIX O O O O O O O O O O O O O 0000. O O O O O Page 107 107 108 109 116 Anne 6“. 1. 53:15 inhr 2. IDLE veil (LI? 3. IL‘. wei KT: 1 ~. 4. LI". we 7. S i R n .. C i usr or TABLES Table l. 2. 3. h. 5. 7. 8. 9. 10. ll. Sums of squares and products of weight at birth and inbreeding . o o o o o o o o o o o o o o o o o o o o 0.0 0-0 Intra-sire regression coefficients and standard errors of weight and body measurements at different ages on inbreeding (Inbred herd) o o o o o o o o o c o o o o o o o o o o o o o Intra-aire regression coefficients and standard errors of 'weight and body measurements at different ages on inbreeding (Type herd). . o o o o o o o o o o o o o o o o o o o o o o o Intra-sire regression coefficients and standard errors of weight and body measurements at different ages on inbreeding (Combined herds) o o o o o o o o o o o o o o o o o o o o o O Sums of squares and products of milk yield and inbreeding (Combined herds) o o o o o o o o o o o o o o o o o o o o o o Sums of squares and products of fat production and inbreeding (Combined herds) o o o o o o o o o o o o o o o o Sums of squares and products of fat per cent and inbreeding (Combined herds) o o o o o o o o c o o o o c o o o o o o o o Sums of squares and cross products of milk yield and inbreeding (Inbred hard) 0 c o o o o o o o o o o o o o o o o Sums of squares and cross products of fat production and inbreeding (Inbred herd) o o o o o o o o o o o c o o o o o o Sums of squares and cross products of fat per cent and inbreeding (Inbred herd) o o c o o o o o o o o o o o o o o o Sums of squares and products of milk yield and inbreeding (Type herd). o o o o o o o o o o o o o o o o o o o o o o o o Sums of squares and cross products of fat production and inbreeding (Type herd) o o o o o o o o o o o o o o o o o o O Sums of squares and cross products of fat per cent and inbreeding (Type herd) o o o o o o o o o o o c o o o o o o o Intra-sire regression coefficients and standard errors of milk, fat, and fat test on inbreeding (Combined herds) . . . V’ Page 37 38 39 ho b1 h3 h3 h3 hh hS ii} A 1"] s“... l .1" J! 95 IIST OF TABLES (Continued) Table Page 15. 'Within sire partial regression coefficients of weights (1b) frombirthtoleonthsofage............... 148 16. ‘Within sire partial regression coefficients of weights (1b) 3monthsaftercalvings.................. ’49 17. ‘Within sire partial regression coefficients of wither height (cm) frotholeonths ofage... co. co. oo 50 18. ‘Within sire partial regression coefficients of wither height (0M) 3 months after C81Ving o o o o o c o o o o o o o 51 19. ‘Within sire partial regression coefficients of chest cir- cumference (in) at 3 to 18 months of age . . . . . . . . . . 52 20. ‘Within sire partial regression coefficients of chest cir— cumference (in) 3 months after calving . . . . . . . . . . . 53 21. ‘Within sire partial regression coefficients of chest depth (cm)from3t018montmofage.............. Sh 22. 'Within sire partial regression coefficients of chest depth (cm)3monthsaftercalving................ SS 23. Within sire partial regression coefficients of withers to hips (cm) from.3 to 18 months of age . . . . . . . . . . . . 56 2h. ‘Within sire partial regression coefficients of withers to hips(cm)3monthsaftercalving.............o 57 25. ‘Within sire partial regression coefficients of withers to pins (cm) from.3 to 18 months of age . . . . . . . . . . . . 58 26. 'Within sire partial regression coefficients of withers to pins (cm)3monthsafterca1ving.............. S9 27. Within sire partial regression coefficients of hips to pins (cm)from3t018monthsofage.............. 6O 28. 'Within sire partial regression coefficients of hips to pins (cm)3montmaftercalving................ 61 29. Inbreeding of females losses between birth and first parturition(Inbredherd).................. 63 30. Inbreeding of females losses between birth and first parturition(TypelBrd)................... 6h vi "-H -v— i J- . s“ .... e . Cru'- «I Y A) U) 4.4. A1, - . u‘ G h- 5'4 .. I u. a a! if ' J4. 4 IIST OF TABLES (Continued) Table 31. Intra-sire regression coefficients (10-1) of type rating oninbreeding....................... 32. Sample of records to illustrate method of maximum likelihood. 33. Cow equations for illustrative sample . . . . . . . . . . . 3h. Group, year, and inbreeding equations for illustrative Sample...oooooooooooooooooooooooo 35. Factors for absorption of the ckl equations into the (“+gk)andfjequations................ 36. Factors for absorption of the ck1 equations into the a. equations......................a'.. 37. Reduced equations, with okl's absorbed . . . . . . . . . . 38. Analfiis 0f variance for repeatability .0 o o o o o o o o o 39. iMaximum.1ikelihood estimates of group constants using repeatabilities Of .50 and .hOo o o o o o o o o o o 0'. o 0 ho. Yearly environmental deviations from maximum likelihood with repeatabilities Of .5 and 0,4 0 o o o o o o o o o o o o o 0.. bl. Maximum likelihood estimates of inbreeding constants using repeatability values Of .50 and 0140'. o o c o o o'o‘o o o o o h2. Means, standard deviations, and coefficients of variation for each characteristic at each age . . . . . . . . . . . . . . vii Page 65 73 75 76 77 79 80 83 8h 85 86 89 (7‘ o 5‘ . 'n ‘ I . —§M LIST OF FIGURES Figure l. 2. 3. h. 5. 6. 7. Graph of average weight, standard deviation and coefficient of variation from birth to fourth lactation . . . . . . .° . . Graph of average wither height, standard deviation, and coefficient of variation from three months to fourth lactation o o o o o o o o o o o o o o o e o o o o o o o o o 0 Graph of average chest circumference, standard deviation, and coefficient of variation from.three months to fourth lactation o o o o o o o o o o o o o o o o o o o o o o o o o 0 Graph of average chest depth, standard deviation, and coef- ficient of variation from three months to fourth.lactation. . Graph of average length (withers to hips), standard deviation, and coefficient of variation from three months to fourth lactation o o o o o o o o o c o o o o o o c o o o o o o o o 0 Graph of average length (withers to.pins), standard deviation, and coefficient of variation from three months to fourth lactation o o o o o o o o o o o o o o o o o o o o o o o o 0 0 Graph of average length (hips to pins), standard deviation, and coefficient of variation from three months to fourth IBCtEtiOD o o o o o o o o o o o o o e o o o o o o o e o o o 0 Page 93 97 99 101 103 “Yr-F -. ‘ Aai". a: :. .1 AA.‘ .o .3: a 7:3 .INTRODUCTIDN For a pepulation there exists a theoretical average level of con- saguinity. Inbreeding, one of two mating systems which can be used to change the genetic prOperties of a pepulation, is defined as the mating of individuals more closely related than the average relationship in the population. Types of inbreeding include closebreeding (mating between such closely related individuals as full sibs or parent and offspring), line- breeding (mating of related individuals -—usually'less closely'related than with close inbreeding -- to maintain high relationship to a favored ancestor), and inbreeding by isolation of small segments of a papulation. Pedigree isolation mayrhave had an important‘role in forming the dairy breeds as we know them today since they have been genetically isolated from the rest of their species for aslong as breeding has been strictly' pure. Dairy cattle breeders have long discussed the merits of inbreeding, with extreme and continued inbreeding being described for'a century or more by such terms as "breeding in" and "in”. A knowledge of the effects of mating systems on economically important characters is important in formulating breeding programs for improvement. Generally, there has been a decline in levels of performance as inbreeding progresses, but the mag- nitude of these effects differ from one study to another. .Although existing information about the effects of mating systems on such economi- cally important traits as milk yield, body weight, and heart girth in dairy cattle is fairly'extensive, genetic progress from using this infor- l I v: e5)? I‘m.) " 51“ u 2 mation has been hindered by several confounding factors. In most cases the level of inbreeding has not been high, different intensities of artificial selection have been operating simultaneously, the environmental conditions under which the experimental data were collected have not been comparable, and the genetics of the foundation animals were unknown. Other factors such as environmental fluctuations cannot be ignored, par- ticularly'in experiments with dairy cattle where the generation interval is long. Some deductive approaches to quantitative inheritance have been developed from the basic assumptions that (1) each trait is a result of a large number of loci which interact with one another and with the environment in complex ways, and (2) that for these traits individual genes or blocks of genes segregate and recombine in a Mendelian pattern. The total phenotypic variation of a character can be partitioned into components of genotypic and environmental differences. Further separa- tion of genotypic differences into variances due to the additive effects of the genes and the cominant and epistatic deviations from the additive scheme can be made on data collected from.specially designed eXperiments. The relative importance can be determined by separating genetic differences into the additive and nonadditive effects of genes. Since inbreeding causes a change in genotypic frequencies in a population, eXperimental evidence relative to effects of inbreeding on the variance of heritable traits is needed. The object of this study was to determine the effects of inbreeding on body size and type at different ages and on production in a herd of inbred Jersey cattle. b'v' '- ’1 use 4 30 Li: H I 3 ‘,U .G FL I - \- ..+ \J REVIEW OF LITERATURE Introduction. "The primary effect of inbreeding is to make more loci homozygous. This is a result of mates being alike in more of their genes than would two individuals chosen at random from that population. Consequently, the uniting gametes will be alike in more of their genes and the resulting offspring will.be homozygous in more loci than if their parents were unrelated. All.the other effects of inbreeding, such as uncovering recessive genes, increasing the resemblance between rela- tives, and splitting the pepulation into distinct families or lines, flow from this primary one of increasing homozygosis.", Lush (l9h8). Computing the coefficient of inbreeding (F) is to determine the probable increase in homozygosity caused by mating individuals which.are related to each other more closely than the average relationship within that population. The most widely known concept of the coefficient of inbreeding is the result of work by Sewall Wright (1922). ‘Wright pro- posed to use the coefficient of correlation between uniting gametes to measure the intensity of inbreeding. This correlation measures only the effects of consanguinity between mates and does not include any additional increase or decrease in homozygosis which may result from.se1ection or mutation. This omission is not serious, since the changes which selection and mutation can make in homozygosis within the Space of a few genera- tions are nearly always small. ForIF to express accurately the changes in homozygcsis requires that the gene frequency'remain constant. 3 him of was ham been: , mm for cm; were 1 of {km thong retion pond in 1; Method 2; conguting the coefficient 2; inbreeding. The compu- tation of the inbreeding coefficient for regular systems of inbreeding was known before Wright's method of path coefficient was develcped; however, most of the inbreeding which occurred in livestock was irregular, and prior to wright's method no logical technique was known for comparing the inbreeding from irregular systems of mating. Wright's pr0posal for E is based on the relation F '[Rad (1 ” Pepi (1 “ ngj/z - (Covariance SD)/ 2 where _S_ and 2 refer to the sire and dam, respectively. For compu- tation this equation reduces to: F'-'%{E1§ ”+”’ (1 +‘Eai1 where the term within the brackets is computed separately for each line of descent through which § and Q are related, 5 is the cannon ancestor through which they are related in that line, 2 is the number of gene- rations intervening between § and A in that line, and n' is the corres— ponding number of generations between 2 and _L_. The 2 thus computed measures the fraction of the heterozygosis in the foundation animals (those of the date to which the pedigree was traced for computing 2) which has probably been turned into homozygosis by the inbreeding. Mean and variability 2f _a_n inbred population. The effects of in- breeding on the mean and variance of the population are pointed out by Lush (19h8). In the main if the effects of the genes are additive, the mean will remain unchanged with increased inbreeding, but the mean will decrease with inbreeding if the effects of the genes are dominant. So far as epistatic effects are concerned, inbreeding will decrease the mean if the genes are dominant in their epistatic effects but will tend to effects manta it will Ha leer o lemme 0—5! Mitre: ficie: 5 tend to raise the mean of the population if the desireable epistatic effects are recessive. If the epistasis consists of a genetic inter- mediate being preferred, inbreeding will tend to lower the mean because it will spread the papulation toward both extremes and will produce a lower frequency of intermediate zygotes and more of the undesirable extremes in both directions. The genic variance of the population will be increased by in- breeding over what the variance would be, had the population been mating at random. Variance due to dominance tends to decrease as heterozygosis disappears, and epistatic variance is shifted from variance within inbred lines to variance between inbred lines. Experience from inbreeding 9322 23111-20 EXperiments have been carried out and are underway to explore the possibilities of herd improve- ment by a combination of mild inbreeding and selection. In addition, analyses have been made of herds and breeds in which inbreeding has been practiced to study the effects it has had on various characters. These analyses were mainly on three types of data. (1) Records from closed herds. These herds have been mildly inbred or linebred to a particular sire. The animals have descended from one or several related or unrelated foundation bulls. The average coef- ficient of inbreeding has been low and selection has been practiced. (2) Hardback data. The amount of inbreeding in pedigree matings has been calculated. The data generally have represented a wide sanpling of bulls in the population. However, since both sires and progency have been subject to selection, the data have represented intensely selected animals. (3) Inbreeding experiments. Due to limitations in experimentation with 12 O rents] Differ: has be! Select ten; or thoust v fella 6 with large animals, this type of data is relatively rare. The experi- ments have generally been started with one or few foundation bulls. Different sire-lines have been developed by systematic mating. Inbreeding has been more intense than that found in the previous two types of data. Selection has usually been within or between lines. In some cases, con- temporary control outbred animals from the same sire have been available, though the numbers of both outbred and inbred animals have been rela- tively small. A brief review of inbreeding eXperiments with dairy cattle follows. An experiment to study the effects of intense linebreeding with 16 cows of mixed breeding and a Guernsey hull was started in 1912 at ‘ Beltsville by the USDA, (Woodward and Graves, 1933). In the next year 11 Jersey cows and a registered Holstein bull were added. The female offspring were mated to their own sire for successive generations. The Guernsey group was discontinued after a few years due to severe incidence of brucellosis. In the major part of the experiment a Holstein bull for as long as he lived, was used on the grade cows and their offspring. When he died, he was replaced by an inbred son, and the inbred son was replaced by his inbred son, etc. The plan was to select for service those bulls most highly inbred. The progress of inbreeding was rapid at the beginning, reaching 50 per cent in the second generation of bulls, but few animals were produced with higher inbreeding coefficients than 60 per cent due to sterility and lack of vigor in the more inbred bulls. At the California Agricultural Experiment Station in 1928 (Rollins et al., 1919) the primary objective of inbreeding in one Jersey and one Holstein herd was to study the inheritance of milk and fat yields within tbred and one sees. proge aniia were three dicet ihbr 7 inbred lines and in crosses between the inbred lines. Five Jersey aims and one Holstein sire were selected for high production in their pedi- grees. The foundation cows came from two station herds. Sire-daughter matings were employed whenever possible, but there were many irregu- larities in the matings. The original plan called for the development of three inbred lines in the Holstein herd through sire-daughter matings, with each sire to be followed by progency tested inbred sons descended from a succession of high producing females. Sires were selected for their ability to transmit high milk yield. During the 1930's one line was discontinued because of variable milk yield, and the two remaining lines were merged. Within sire groups there was no disposing of female progency unless a heifer failed to breed after repeated matings. Few animals were inbred more than to per cent. In the Jersey herd, four lines were started, but two were merged to form a single closed line. In 19h6, three bulls related to each other but unrelated to the herd were intro- duced. Their outcross progency were used to start a second line. The inbreeding coefficients averaged 19 per cent. An apartment was initiated at the New Jersey Station in 1931 to establish genetic factors for high milk production and high fat test in the Holstein-Friesian breed (Bartlett et al., 1939). The foundation animals included 1:5 Holstein cows selected for normal size, good type, mature equivalent fat production of at least 1:80 lb, and with milk testing at least 3.6 per cent butterfat. Four bulls were selected as foundation sires on pedigrees which contained high producing ancestors. Progency of the foundation animals were mated by one of the following schemes: (1) sire-daughter matings 3 (2) brother-sister matings; (3) matings with less than 50 per cent of the same blood; and (h) outbreeding. The last system I he rat w'fin The ave discan made . mall‘s: iecaus ‘ J»: 0' Vii Iowa, EI‘osi the l the I 3 an USES bPEe 8 system of mating was used as a control for the inbreeding eXperiment. The rate of inbreeding was not high. The relationship of living animals to the foundation sire was slightly closer than a sire to daughter. The average inbreeding was very low. Three lines of the four were discarded, but genetic analysis of the defects which occurred was not made. In one line, the bulldog condition appeared, as well as various malformations of the reproductive organs. Another line was discarded because the sire was heterozygous for red, and the animals were of undesirable type. The third line was discarded because of low pro- duction. In 1930 a project with Holstein cattle was inaugurated by the Iowa Agriculture Eacperiment Station to determine the consequence of mild inbreeding acconpanied by selection for high production (von Krosigk and Lush, 1958). All bulls used since 19314 have been bred in the herd, and no females outside the herd have entered since 1937. In the closed herd the effect of inbreeding which automatically occurred in a small finite population could be measured in the herd under selection. Usually about 35 to 50 females of breeding age were in the herd. The breeding system was to use sons of the best producing cows and to keep than in service until sufficient cows (30 or more) were bred to each one so as to give a high probability of at least eight tested daughters per sire. This resulted in most of the bulls being used for slightly over one year each. This breeding system would be expected to increase the inbreeding about 2 to 3 per cent per generation or a little under 1 per cent per year. The inbreeding coefficients ranged up to 314 per cent with the majority in the lower part of the range. in experiment was initiated with Guernseys at Iowa State as a t . “3518 0 sam- ‘ 9 replicate of the Holstein closed herd (Hillers and Freeman, 1961:). The Guernsey herd was considerably smaller but was maintained in the same barn and under the same general management as the Holstein herd. The females came from within the Guernsey herd after 1913 except 12 females which left 10 daughters and 2 sons in the herd were purchased from four herds to broaden the genetic base in 1952. No bulls were brought into the herd from outside after 19116. Inbreeding in the herd ranged from O to 31 per cent with an average of 6.1: per cent. The average inbreeding of the cows calving in 1961 was 9.1 per cent. The herd was linebred to one superior cow born in 191:2. An inbreeding project with Holstein cattle was initiated by the University of Wisconsin in c00peration with two institutional herds in 1938 (Tyler et al., 19h9). One of the first two herds had been a closed breeding herd since 1937. Most of the foundation cows were daughters of two sires. The herd maintained a high relationship to these two foun- dation sires through their sons and grandsons. Five unrelated sire lines were available for inbreeding in the second herd. In 19141 a third herd was added to the project. A sire and his 17 daughters formed the basis of one line and after 191:1 two other lines were developed in the same herd. The plan of breeding in each herd was to mate the herd sires to their daughters or close collateral relatives and during the sam period to mate them to unrelated cows to produce outbred offspring as control animals by the same sire. The inbreeding coefficients ranged up to 38 per cent. The average inbreeding of the offspring by each sire ranged from 3 to 17 per cent. A cooperative study between the Wisconsin Agricultural EXperiment Station and the USDA designed to study the effect of various mating system of and Tyler, Solstein g daughters each sire of two at crossing coefficie 0t: cattle we Hanan, j herd at, - the sum “313313 al., 196 A: Rent. 5 “Ulstei; 10 systems of dairy cattle was started in l9h8 (Mi et al., 1965; Holtman and Tyler, 1966). In this herd, foundation animals consisted of six Holstein proven sires, one or two outbred sons of each, and twenty daughters by each sire. Matings were to produce inbred daughters within each sire line and outbred daughters for each sire line sired by bulls of two other lines. Close inbreeding within each sire line and line- crossing was followed after the first generation. The average inbreeding coefficient of all inbreds was 25.3 per cent. Other published information on effects of inbreeding in dairy cattle were investigations of the University of Missouri herd (Laben and amen, 1950), the Winterthur herd, (Davis et al., 1953), the Holstein hard at the North Platte Experiment Station (Plum and Rumery, 1956), the survey of herdbook data in Great Britain (Robertson, 19Sh), and the analysis of data on field progeny testing bulls in Sweden (Hansson et al., 1961). Another experiment on inbreeding is in an early stage of develOp- ment. At the South.Dakota EXperiment Station two inbred lines of Holsteins are to be used for reciprocal crossing when inbreeding of individual animals within the lines exceeds 30 per cent. .Another group of animals randomly sired by'A. I. bulls is maintained for control (Voelker et al., 1958). Effects-g; inbreeding gn_ggowth and body'measurements. In the Beltsville experiment,'Woodward and Graves (1933)found that inbreeding decreased birth weight and retarded growth of the calves. Mature weight was reduced but not preportionately as much as birthrweight. Some heteresis in birth weight and rate of growth of the calves was indicated by comparisons of offspring from.inbred cows and unrelated bulls with stir in} effects « ahcve 25 had an a for outt II of very? Svett e‘ approxi skeleta 11 their inbred dams. Later, Woodward and Graves (l9h6) reported that effects of inbreeding became marked when coefficients of inbreeding above 25 per cent were reached. Calves inbred more than 50 per cent had an average birth weight of only 65.9 1b as compared with 81.5 lb for outbred calves. The differences diminished with increasing age. In a study of body size and internal anatomy of outbreds and cows of varying intensities of inbreeding from the Beltsville experiment, Swett et al. (191:9) found that inbreeding resulted in a decline of approximately'IS per cent in body'weight or'mass but did not affect skeletal size as represented by measures of such as wither height, hip width, body length, and chest depth. Outbred compared to highly inbred cows showed a superiority of 10 per cent in live weight, taken about three months after first calving. Inbreeding did not decrease varia- bility'in body size or skeletal dimensions; there was some indication that as inbreeding became more intense, variability increased slightly for some of the dimensions such as hip width, body length, and chest depth. In a preliminary report of the New Jersey experiment, Bartlett et al. (1939) studied the body'measurements of 3125h outbred and 60 inbred animals at birth, 5 and 10 months of age with inbreeding ranging from 5 to 15 per cent. Measurements included weight, height at withers, and heart girth. There were no significant differences in measurements associated with inbreeding at 5 and 10 months of age. However, inbred females were significantly less than outbreds in birth weight. They- stated that daughters of different sires could be inbred successfully provided a rigid system.of selection was followed. If inbreeding resulted in inferior animals, they considered this to be due to mating ... V 3.9 dlcal hmloua enerilex Ir 01‘ over umii 12 genetically inferior animals and not to the system of mating used. Additional data were presented by Bartlett et al. (19142) from the same experiment supporting the earlier observations. They failed to discern any significant difference between inbred and outbred heifers at every age. However, at this stage, three of the four lines had been more or less discontinued. {A majority of inbred animals in the herd were des- cendants of one of the foundation sires. In a later report, Bartlett and Margolin (l9hh) found that at two years of age, inbred animals were considerably less in body weight and heart girth than outbred animals. Inbred animals showed more variation. Only animals with a coefficient of inbreeding of 20 per cent or over showed detrimental effects in all measurements. These animals were lighter in weight and less in height and heart girth.measurements than other groups. The inbred animals with lower coefficients of in- breeding were equal in size of frame to the outbred animals, although.they tended to weigh less. Maturity of inbred groups tended to be late. Margolin and Bartlett (1915) presented further evidence that in- breeding did not necessarily cause a decrease in body weight or size at any age from birth to maturity provided the coefficients of inbreeding did not exceed 20 per cent. Rigid selection for size, type, production, and vigor had been practiced for all outbred and inbred matings in their experilents. The incidence of culling for the inbred animals of the blood line Ormsby’Sensaticn hSth had not differed in the selection pro- cess from that of outbreds of the same blood line at any stage of their development. Females with an inbreeding coefficient higher than 20 per cent developed normally to the age of their first calving but showed a marked decrease in develOpment thereafter as compared to outbred controls. if] 13 This suggested a relationship between gestation or parturition and the failure of these animals to follow a normal growth pattern to maturity. From the California experiment, Baker et al. (19145) analyzed growth in height at withers, body weight, and heart girth of 88 daughters of one Holstein bull. Coefficients of inbreeding ranged up to about 1:2 per cent. Measmements were made monthly from six months to 115 months of age. Inbreeding caused a significant decrease in size throughout the period studied. Body measurements of 322 Jersey females sired by 15 bulls were analyzed by Rollins et al. (19119). The number at a given age ranged from 2711 at birth to 63 at 56 months of age. Regression analyses of height, weight, and heart girth on the per cent of inbreeding indicated that inbreeding caused a decrease in each of these characteristics. The magnitude of the effect varied with age and characteristic. Weight was most affected. The variation with age was the same for each charac- teristic with the maximum effect occurring at six months of age. At that age, an increase of l per cent in inbreeding caused a decrease of 0.117 per cent in weight, 0.15 per cent in heart girth, and 0.16 per cent in height. The corresponding figures at 11.5 years of age were a decrease of 0.10 per cent in weight, 0.01 per cent in heart girth, and 0.01 per cent in height. For birth weight the decrease was 0.28 per cent. Inbreeding appeared to affect the prenatal and postnatal rate of growth. The inbred animals were smaller at birth and grew more slowly up to about six months of age than the outcrossed animals, but at some time between six and twelve months of age the inbreds began to grow more rapidly than the outcrossed and continued to do so for the remainder of the period under study. Later, using records of 680 Jersey calves of bulls , E 10". recti Q H ‘43. ne ‘ I In ‘ V-.. .11.. ft: 313? so. 3‘ 61 Ar! ‘14 C «k 96 ‘1'. 1h 13 bulls, Rollins et al. (1956) reported a regression of birth weight on inbreeding of calf within sire and herd of ~0.06110.028 with length of gestation period held constant. Dickerson (l9h0) made a preliminary analysis of the effects of inbreeding among the progeny of different sires on birth weight and body measurements at six months of age in the Wisconsin breeding pro- ject. There were 171 arfi 131 calves available at the two ages. Calves With an average inbreeding coefficient of 16 per cent were nearly 10 per cent lighter at birth than non-inbred calves by the same sires after correction for differences in weight due to sex and to age of dam. This decline in birth weight occurred in both sexes and for six of the eight sires. He explained further that birth weight was determined to an important degree by the calf's own inheritance of size since the dams of the inbred calves were not inbred animals themselves. The difference in size in favor of the outbreds became proportionately smaller rather than larger up to six months of age. In a later study, Tyler et a1. (19h?) studied birth weight of 65h calves of 21 bulls from three Holstein herds in the thsconsin pro- ject. The birth weight of the calves decreased 0.28 lb for each 1 per cent increase in inbreeding within sire and adjusted for dam's mature heart girth measurement. Considerable variation‘was found between sires in the influence of inbreeding on the birth weight of their calves. The partial regression coefficients differed significantly betWeen sires, ranging from -0.823 to 1.090 1b. This was assumed to be due to differences in.the average birth weight transmitted by different sires. The inbred calves of sires transmitting heavy birth weights tended to be heavier than the outbred calves because of having more of their sires' genes, tae ave dam co: 15 which cancel, at least in part, the reduction in birth weight from increased homozygosity. In a second report, Tyler et al. (19119), used the average intrasire partial regression anaJySis holding size of the dam constant to study effects of inbreeding on body dimensions at six and 18 months of age and at maturity. The number of animals varied from 111 to 193 in the different analyses. The depressing effects of inbreeding were slight except on heart girth at 18 months of age. The partial regression coefficient of heart girth on per cent inbreeding was -O.17 on (p (.01). In the Wisconsin study started in 191:8, Mi et a1. (1965) found an increase in age of 0.03 3?. and a decrease in weight of -2.2 lb at first calving for each 1 per cent increase in inbreeding. They found no curvilinearity of inbreeding effects within sire lines. From the Iowa experiment, Nelson and Lush (1950) reported intra-sire regressions of birth weight in pounds on inbreeding per cent of calf of -0.09 and -0.16 for 179 male and 191 female calves. The weighted average of these two regressions was a decrease of about one-eighth of a pound in birth weight for each increase of l per cent in inbreeding. 0n the basis of this regression a first generation of mating parent with offspring or full sibs would be expected to lower average birth weight of the calf by about 3 lb. There was a decrease of approximately one-eleventh of a pound in birth weight for each increase of l per cent in inbreeding of the dam. For the five body measurements and weight at six months of age and over, an increase of 1 per cent in inbreeding resulted in a decrease of no more than 0.5 per cent and usually only about 0.1 per cent of the average of the respective measurement. The results indicated that the growth curve was changed by intensity of inbreeding. Inbreeding slowed the rate of growth (U 0') f0 16 at early ages as shown in smaller calves at birth and slower gains during the first two years of life. After that age, the inbred animals apparently gained faster than the non-inbreds and by five years of age approached or exceeded the non-inbreds in weight. In a more recent study of the Iowa data, Sutherland and Lush (1962) analyzed additional data with 808 calves of hl sires from the same experiment. They reported that birth weight decreased with inbreeding of both calf and dam by approximately 0.2 to 0.3 lb for each per cent of inbreeding. At later ages, body size was negatively correlated with inbreeding. The declines were maximum at approximately three years of age and tended to diminish at later ages. They indicated that inbred animals tended to grow more slowly than outbreds at each age from six months to three years. At later ages, they appeared to grow more rapidly than the outbreds and tended to reach similar body size. Killers and Freeman (1961;) using the Guernsey data from the Iowa herd found that as inbreeding increased, weight was depressed at all ages. They reported inbreeding appeared to exert its maximum effect at four years of age. From a preliminary analysis of growth of 103 calves at the South Dakota station, Voelker and Bartle (1958) reported that birth weight was not significantly affected by inbreeding. From birth to three months inbred calves (F - 0.10) gained 19 per cent more in body weight than did calves with higher inbreeding-«a significant effect. Iiighly inbred calves grew less rapidly in other body measurements than did calves with less inbreeding. There appeared to be more variation in growth rates of the more inbred group. Effects 2f inbreeding and outbreeding 313 production. In their cectege cows we: matings in fat results gen rec per ce: I‘Ef‘é‘ine limited l7 preliminary report, Woodward and Graves (1933) pointed out that there was no definite evidence that the moderate amount of inbreeding was detrimental to the production of milk and fat. Two successive matings to the Guernsey sire in the experiment increased the amount and per- centage of fat and decreased milk production, though only five of the cows were inbred. In the Holstein group, two generations of sire-daughter matings appeared to cause an increase in milk production and a decrease in fat percentage. 'Woodward and Graves (lshé) reported further on the results of the Holstein experiment, including animals up to the sixth generation. In the groups with.inbreeding coefficients higher than 30 per cent, the milk and fat production decreased and the fat percentage remained the same. The effect of outbreeding was also studied on a limited amount of data. By comparing daughters from the same inbred dams and sired by either inbred bulls or unrelated registered bulls, the outbred maternal half-sisters were better in average milk yield. Ebwever, the authors pointed out the possibility of differences in transmitting ability for level of production of the inbred and outbred sires. Another comparison of production of daughters of four sires which were out of inbred grade cows in the experiment and out of registered cows in the Beltsville herd, failed to show heterosis in production traits. Swett et al. (19h9) analyzed records of hS cows with inbreeding coefficients ranging from 12.5 to 6h.6 per cent from the Holstein experiment. Simple correlations between intensity of inbreeding and milk, fat, and fat per cent were -0.26i0.09, -0.3ht0.09, and -0.3110.09. Variability in milk, fat production and in fat per cent did not decrease significantly“with.inbreeding. 18 Bartlett and Nargolin (191424) compared the production records of 39 inbred and to outbred animals from the New Jersey experiment. Total milk and fat production were significantly less for inbred animals. Fat tests of inbred animals, however, were slightly but not significantly higher in groups by the same sires. Preliminary results from the California experiment showed that females with inbreeding coefficients of 38 per cent and above produced 199 lb less fat than first-generation daughters or 206 lb less than the foundation females (Ralston et al., 19138). Crossing two inbred lines produced offSpring which yielded 203 1b more fat than their dams and 52 1b more than the foundation cows. These Were considered to be indications of heterosis. An analysis by Laben et al. (1955) of the production records (BOS-day, 2x, 2-year-olds) of 161; cows, daughters of 22 sires, in the California Holstein herd showed significant intra-sire regressions of lactation yield on the coefficient of inbreeding amounting to -209.8 lb of milk, 44.9 lb of fat and 431.0 lb of FCM. There was a significant increase in fat test of 0.008 per cent for increase in each degree in inbreeding, but the authors reported this was probably due to negative correlation between milk yield and fat content rather than to inbreeding p33; 32. There was some evidence that inbreeding might have less effect on production for inbreeding levels below 20 per cent than for those above 25 per cent. Significant differences were found between sires in the reaponse of their daughters to inbreeding. Nasty-two inbred daugh— ters of one sire, averaging only 5366 lb of FCM (fat corrected milk), were outcrossed to a third unrelated sire, and 26 daughters from these matings averaged 10,910 lb of FCM. This yield was significantly greater m that l attrib uted F4 D ‘0' proiuction daughters held cons: of an: ar of intreec' siderable duction we indicated iDCI‘EdS ft 5813mm t In of ”Mum 19 than that of any group of the hard; this increased yield was, therefore, attributed, at least in part, to heterosis. In the Wisconsin experiment, the effect of inbreeding on milk production was studied by Tyler et al. (l9h9) on L7 outbred and h2 inbred daughters of five sires. ‘With the corresponding performance of dam held constant, the 305-2xAME lactation yield decreased within sire 7h lb of milk and 2.3 lb of fat for each per cent increase in the coefficient of inbreeding. The fat percentage of the milk was not affected. Con- siderable variation between sires in the effect of inbreeding on pro- duction was also Observed. Later results from.the‘Wisconsin study' indicated in general that line crosses were 15 per cent superior to inbreds for the production characteristics studied: yield of milk, solids-not-fat, and fat, and per cent solids-not-fat and fat (Holtmann and Tyler, 1966). The changes in actual yield of milk, actual fat, fat test, M. E. milk, and M. E. fat per 1 per cent inbreeding were 752 1b, -1.h lb, + 0.005 per cent, .70 lb, and -1.9 lb (Mi at al., 1965). The lifetime average fat production (BUS-EXAME) of 156 cows sired by 26 bulls during the early part of the Iowa project was analyzed by’ Nelson and Lush.(l950). The average production‘was h77 1b fat and average inbreeding coefficient was h per cent ranging from zero to 28 per cent. The intra-sire regression was -h.5 lb per 1 per cent increase in inbreeding (P (0.01). They concluded that if a breeding plan was followed in which the increase in intensity of inbreeding was less than 2 per cent per generation, enough selection should be possible to counter- balance the decline in production.expected from inbreeding. In a later report von Krosigk and Lush (1958) reported analyses of production of 53h cows, daughters of 69 bulls in the Iowa herd. The 355.21.;E re averaging 7« a: i breediz mined diction tin: by the dif: breeding H sion of pr Lactation the depres inbreeding attaining U51] (1961;), r, Obtained ‘ “3395310 ill-brawn and .001: T. e: I'D ca 20 305-2xAME records were used. Inbreeding ranged from zero to 3h per cent averaging 7.h per cent. For each increase of l per cent in the coefficient of inbreeding, there was a decrease of 51.117 lb, 1.71.+ .57 lb, and 0.003:0.003 per cent for milk, fat, and fat test. There was no evidence of curvilinearity in the effect of inbreeding on production, and dif- ferences among the individual sires' regressions were not significant. The production of the dams did not have a significant effect on the effects of inbreeding. That inbreeding caused some decrease in pro- duction through its detrimental effects on general body size was indicated by the differences in the regressions of first lactation record on in- breeding with and without heart girth held constant. The negative regres- sion of production on inbreeding was more pronounced for the first lactation than for following lactations. This was assumed to be due to the depressing effect of inbreeding on rate of growth. The effect of inbreeding on the ultimate size of the animals was less than that of attaining this size. Using the Guernsey data in the Iowa herd, Hillers and Freeman (196k), found the intra-sire regressions of production on inbreeding obtained from the analysis of covariance and the weighted average regressions, respectively, were -36118 and ~51tlh lb of milk per 1 per cent inbreeding, -l.6610.83 and -2.2310.66 lb of fat per 1 per cent inbreeding, and .0011.005 and .0021.00h per cent of test per 1 per cent inbreeding. The small size of the Guernsey herd prevented the results from.being con- elusive. Laben and Herman (1950) studied the effects of inbreeding on pro- duction in the Holstein herd at the Missouri station. The 305-2xFME lifetime averages of hard test records of 299 cows representing the pmgeny cf 3 had been the ml; 20 cows flute-fourth or inbred 16 decreased :1 immacfi not affected noticeable : on producti: ’Ifnen all ave average, the f" lilk, fa -0.881b (1: HM “Efficient the inbreedi Dada the “intent dauélters a W “breech: fat. None c °°n¢1uded th there was gr MQHEbm per “5‘“ fat Flu]- 21 progew of 3!; since were used. The anount of inbreeding was anal]. and had been the result of a general linebreeding program to the Onsby family. Only 20 cows had coefficients of inbreeding above 20 per cent. three-fourths of the cows with lactation records were either outbreds or inbred less than 6 per cent. On an intra-sire basis, ndik production decreased significantly about 66 lb and fat production 2 lb for each increase of 1 per cent in inbreeding. The percentage of butterfat was not affected. The effect of inbreeding on average production was not noticeable up to F - 0.15. While the general trend of inbreeding effects on production was downward, considerable variation between sires existed. When all averages of production were regressed to a contemporary herd average, the intra-sire regressions of the nost probable producing ability for milk, fat and fat test on per cent inbreeding were -30.7b 1b, (P( 0.01), -0.88 lb (P‘( 0.05), and 0.002 per cent. Plun (1931;) found a negative intra-sire correlation between the coefficient of inbreeding and fat production in one Jersey herd in which the inbreeding coefficients ranged up to 22 per cent. Davis et al. (1953) analyzed production of the Orlsby family of the Winterthur Holstein herd. Tienty bulls were involved and their 630 daughters averaged 8 per cent of inbreeding. The regression within sire on inbreeding was 40.8 lb of milk, -0.66 lb of fat, and 0.026 per cent fat. None of these regressions was statistically significant. The authors concluded that inbreeding did not depress production in this herd. However, there was great variation in effects of inbreeding along individml sires ranging fru 4:0). to 635 lb lilk, 45.2 to 27.7 lb fat, and -0.09 to 0.02 per cent fat for eachl per cent increase in inbreeding. Plum and Runery (1956) analyzed production at one of the Hebrasb. rations line. A on inte Eroducti each pez ( nimn Eerd. 1 cows Hi loved b Has 5 ; signifi (P (.05 sions I .51.9’ aVEPag1 were - accoun tation Variat 1&th first the 83 n. m; nth“ incite 22 stations Ihere inbreeding had been incidental to selection in a closed 11m. A total of 1.18 offspring of 12 sires was used. Inbreeding was not intense and about one-tenth of the animals had if: greater than .13. Production of fat in first lactation within sire decreased by .5 lb for each per cent increase in inbreedilg. Gaalaas et al. (1962) estimted the regression of milk and fat on inbreeding in different lactations of the same cows in an institutional herd. Data consisted of 305 day-2:413 records of 111 grade Holstein cows with four successive .lactations each. The yearly effects weze re- noved by maxim likelihood methods. The average inbreeding of the cm was 5 per cent and of their dans, 3 per cent. The latter did not have significant effect on production, while the former was significant (P (.05) for milk and fat in first lactation only. Intra-sire regres- sions of pounds milk per 1 per cent inbreeding of cows were «105.3, -h1.9, 48.0, -26.2, and -h7.9 for first, second, third, fourth, and average records, respectively. Corresponding regressions of pounds fat were -3.62, 4.06, «1.32, -0.86, and 4.69. The linear regressions accounted fa- about 1 per cent of the total variation in the first lac- tation but less than 1 per cent in the other three lactations. The variation in regression coefficients for the individual sires within lactations was not statistically significant. In Great Britain, Robertson (1951:) comared the yield during the first lactation of 82 cows fro- sire-daughter tastings with the yield from the sale actor of non-inbred daughters in the cane herds and years. 1b. :11]: yield of the inbred daughters was 7h gal less than that of the outbreds, corresponding to a yield of 0.32 per cent for each per cent increase in inbmeding. Fan an colle hedsh is 12,897 Get two nespec by the re] bout 2 pg Oi SL3 hac Tm yield first car Yield of : lactation being «11 held "an Partial r. E ficm 8e (humble ‘59 eifec ““86 Vii (1 a; 31.1% (2 bhecfing (3 is subject “1118, p 23 Hansson et a1. (1961) amlyzed first lactation records of field data collected in connection with the progeny testing of bulls of the kedish Bed and White breed and the Swedish Friesian breed. There were 12,897 daughters of 165 sires and 10,926 daughters of 111 sites for the two respective breeds. The degree of inbreeding of the daughters caused by the relationship of the sire to the maternal grandsire was calculated. About 2 per cent of the daughters of SRB and 5 per cent of the daughters of 8L3 had coefficients of inbreeding in the range of 11 to 29 per cent. Tns yield was converted to F0)! and corrected for differences in age at first calving. Inbreeding had a significant depressing effect on the yield of fat-corrected milk in both breeds, the regression of the first lactation yield on inbreeding betwaen sin within mterml grandsire being 41.5 kg (r (.01) and .10.? kg (P(.05) for the two breeds. With herd average and the general breeding value of the sire adjusted, the partial regressions of yield on inbreeding were 41:3 and 40.1, kg. m. Intensity of inbreeding was relatively low and arti- ficial selection was usually practiced for high production or other desirable perfornsnce traits. Several lines of evidence concermm the effects of inbreeding and outbreeding in dairy cattle appear to agree with findings in other species of animls. (1) Inbreeding increases the proportion of hcnosygous loci as shun by increased incidence of recessive lethals in inbred groups. (2) There is a general decline in level of performance as in- breeding progresses. (3) The closer the character is related to fitness, the more it is subject to inbreeding depression as shown by high mortality in inbred aninls, particularly at early ages, (Johansson, 1961). (h) I! show b (5) directly ; of non-lit (63 processes and outbn at (h) There are genetic differences in reaponse to inbreeding as shown by variation among sires or lines in inbreeding effects. (5) The change of performnce with inbreeding tends to be directly proportional to the coefficient of inbreeding as shown by lack of non-linearity of inbreeding effects of various quantitative traits. (6) Inbreeding appears to delay the develqment of physiological processes in animals as shown by a decrease in difference between inbred and outbred anilals with advance of age. I'_’_o_ Jersey he series of. dairy cai brought 1 cattle in records I '1': dfimdi cattle 11 mm F environs “131611 av caeffici. amber Pecans . latter g have 1mGer on of .27, him In. the in inbree sound: AND DESCRIPTION OF DATA Foundation animals. Foundation aninals to establish an inbred Jersey herd wen purchased from three dairymen who had been using a series of Jersey bulls from the long-tine breeding experiments with dairy cattle at the University of California. These animals were brought to Michigan State University in August, 1951. Because the cattle were housed in undesirable quarters prior to October, 1952, the records of tilt and fat production during the first year were not usable. The lethodmr coqyuting the coefficient of inbreeding, E, as defined by Wright (1922) was used in this study. The registered Jersey cattle in the United States about 1915 - 1920 was considered the base population. Four cows of mture age were from one California herd in which environ-ental conditions were poor. These four cows had eight records which averaged 6838 lb will: and 1108 lb fat (305-21443), and their average coefficient of inbreeding was .113. Seventeen femles were obtained from another California herd, five of which had eleven coqleted lactation records that averaged 9218 lb milk and 538 lb of fat (305-21418). ‘mis latter group included one nature cow, two four-year-olds, three three-year-olds, three two-year-olds, two senior yearlings, six fenles under one year of age, and three bulls which had inbreeding coefficients of .27, .28, and .03. he bulls purchased from a third cooperating dairy-an had inbreeding coefficients of .22 and .23. Sires produced fro. the foundation animls were used thereafter, the rate of increase in imreeding and the degree of inbreeding being determined by the smallness 25 smh a and co paeses 26 of the herd, by chance, and by selection. The purpose of the project was to investigate characteristics such as vigor and longevity, reproduction, growth, development, yield and composition of milk, and physiology and/or biochemistry of certain phases of the previously mentioned characteristics. Project modifications. In 19514 the herd was divided into two mating groups according to the closeness of each animal's relationship to each of two sets of full brothers available for service. These sets of full brothers were sons and grandsons of full sisters and were sired by the same sire. They were also paternal brothers of most of the females in the herd excluding the foundation cows purchased in California in 1951. Each of the females was mated with the bull most closely related to her. In 1955 the breeding plans were altered slightly to increase the information coming from the project while still retaining the original inbred structure of the experiment. Members of the groups were shifted to place animals with closest genetic covariances with one of the dams of the sires into one group and those most closely related to her full sister, the dam of the other set of brothers, into the other group. One group was chosen by chance to be selected for production of milk and the other group was designated as the control herd. The two groups were kept together as one herd under like conditions with the size of each herd being maintained at about 15 cows in milk. A third group of Jerseys unrelated to the original project herds and housed until August 1961 in a different location was incorporated into the plans in 1955. This third group was selected for type. Selection procedures. (McGilliard, 1956) I. II. 27 Removal of cows from herds. A. B. Control herd . l. 2. 3. Retain all females until one record complete. Maintain herd size at about 15 cows in milk. When it is necessary to eliminate cows to maintain herd size, excess cows shall be removed at random from among cows which have completed at least one lactation. Selected herd . l. 2. Maintain herd size at 15 cows in milk. When it is necessary to eliminate animals to maintain herd size, the animals ranking lowest in index value based on the milk production of the individual and of her relatives shall be removed from the herd. Both control and selected herds. l. 2. 3. 14. Any heifer which has not conceived after 8 services or by 214 months of age shall be removed from the herd. Any cow which has not conceived within 10 months from the previous calving date shall be removed from the herd. Females which cannot be milked by machine because of udder structure, injury, etc., shall be removed from the herd. Animals shall be removed from the herds for any disease or injury for which removal is the recommended veteri- nary control. Choice and removal of bulls. A. Control herd . 28 1. After the birth of each bull, determine by chance whether he shall be retained or discarded. 2. When the number of bulls 6 months to 12 months of age exceeds three or the number over 12 months of age, exclusive of the herd sire, exceeds two, discard excess bulls from each age group at random. 3. Choose herd sire by chance from bulls of breeding age which have not previously served as hard sire. B. Selected herd. l. Designate periodically the best cows from which to save bulls on the basis of milk production of them and their close relatives. 2. When it is necessary to discard young bulls to main- tain proper numbers for replacement, discard the bulls scoring lowest in index value based on milk production of close relatives. 3. Use the hull with the highest index value as herd sire. 0. Both control and selected herds. 1. When a bull is chosen to be herd sire, use him as soon as he is able to serve. Retain the previous herd sire or a substitute until the fertility of the new herd sire is ascertained. 2. Discard infertile bulls as well as those unable or unwilling to serve. Management procedures. Every effort was made to conform to approved standardized procedures which were in keeping with good herd management and for which facilities were available. These procedures were: I;"'_: by»)... 29 were: Feeding. In the main, efforts have been made to keep environ- mental conditions as constant as possible. However, the feeding regime has been altered slightly'from time to time to utilize the animals and facilities in nutritional and managerial eXperiments. Calves were allowed to remain with.their dams until b8 hours following freshening counting the day of birth.as the first day. They“were fed whole milk at the rate of 10 per cent of body weight until four months of age or longer if individual calves were small or unthrifty. Hay-was fed.gd libitum and calves were given sufficient grain to maintain good condition. The basic grain mixture contained approximately lb per cent crude protein. Heifers from.3 to 10 months of age were fed silage, grain, and hay at a rate designed to provide near maximum.growth and development. Heifers were provided with pasture, when possible, from ten months to calving and were given silage, hay, and grain in sufficient amounts to bring them up to calving in good flesh but not carrying excessive fat. For lactating cows, summer pasture, when available and practical, was given and supplemented with grass silage. In winter, feeding corn silage and a good quality legume hay was the standard procedure. Grain was fed in amounts according to milk production and in quantities to insure a sufficient nutrient intake to meet growth.requirements of the young cows. Reproduction. Detailed observations have been made routinely on the herd regarding various aspects of physiology of reproduction. Records of heat were kept beginning at 12 months of age, and prebreeding exami- nations of heifers not previously observed in heat were made at 1h.months. Heifers were bred at first regular heat after they reached approximately' weight: were de CEICul; 0n the 0’3 the than GI and 60 belgw E 10813, and vet pOSSibl health 30 550 1b of body weight or 15 months of age whichever came earlier. A heifer not pregnant by two years of age was discarded as a non-breeder. Cows were rebred at heat nearest 60 days after calving. Cows not in calf by 10 months after calving were removed from the herd. Manual palpations of the genital organs were made before breeding, 60 to 90 days past breeding, at post-partum, and at any time irregularities were reported. Production. All cows were milked twice daily and the daily milk weights were recorded. However, annual milk yield and fat production were determined monthly from the DHIA testing program. All records were calculated to 305-224th? basis using the extension factors developed by Lamb and McGilliard (1960) and the age conversion factors developed by the American Jersey Cattle Club. Until March 1956 the policy was to begin the dry period at least 60 days prior to the due date. After that date, the policy was altered slightly in order to give cows with calving intervals of less than a year a milking period of at least 305 days and reduce the dry period. That is, the primary emphasis was put on the length of the lactation period and secondary emphasis was placed on the length of the dry period. For cows with calving intervals longer than one year the dry period was started after 305 days of lactation and 60 days before calving. However, cows with daily milk production below 6 1b were turned dry regardless of days in milk. General practices. The herds were tested regularly for Brucel- losis, TB; preventive care was exercised in the control of mastitis, and veterinary treatment followed when needed. All abnormal conditions possibly having a bearing upon the experiment were recorded in the herd health b 00k e 9".- . R“."IC“ L‘uv. m kins, €17;+: eke.» 31 Most of the milking cows were classified at least once by an official classifier. An unofficial evaluation of body conformation was done at the time of each measurement. Alterations in the procedures listed were made in accordance With suggestions and recormendations by the North Central Regional Dairy Cattle Breeding Technical Committee to insure greater standardization among all research projects. weights and Measurements. The data were records on the Michigan State University Jersey herd from 1951 to 1966. Seven characteristics, weight, chest circumference, wither’height, chest depth, length from withers to hips, length from‘Withers to pins, and length from hips to pins, were measured at ages three months, six months, twelve months, eighteen months, and three months after each calving. Birth weights were recorded for all births and recorded to the nearest pound. Chest circumferences were recorded to the nearest one-quarter inch, and.all measurements of length and depth were recorded to the nearest one-quarter centimeter. The chest circumference measurements were taken With a steel tape in a plane perpendicular to the body axis immediately back of the elbows at the smallest part of the chest. 'Hither height, chest depth, and the three body length measurements were taken with calipers. 'Wither height was the vertical distance from the highest point over the Withers to the ground. Chest depth was the vertical distance from the back to the floor of the chest at its shallowest part. The three body lengths Were the horizontal distances from a point just in front of the withers to the middle of the hip bone, from the withers to the end of the pin bones, and from the middle of the hip bone to the end of the pin bones. Care was taken at each measurement to have the animal on a flat surface 32 in a nat ural positi on sta nd' ing rather square ly o n all four legs 0 genera cam: t time I econo: trane. METHODS AND RESULTS Regressionlgf'weight and body'measurements'gn inbreeding. An inbreeding experiment concerned with.dairy cattle is necessarily a long-term.project. This is especially so when there is no special effort to increase the inbreeding rapidly; The main reason is that the generation interval for dairy'cattle is of the order of five years. One cannot hape to hold environmental conditions entirely constant during the time needed for inbreeding to accumulate. Even if it were possible economically to control feeding and management conditions, other ex- traneous factors such as temperature, quality of pasture, and incidence of disease are impossible to control wholly and some important effects of these even may be unknown. Furthermore, the mean genetic composition of the herd can scarcely remain constant during the experiment. Besides any general effects of inbreeding, natural selection may have changed the composition in unknown ways, and the very nature of inbreeding per- mits gene frequency to drift randomly; These sources of change are in addition to any general effects of inbreeding having lowered the average amount of heterozygosityt That more of the less inbred cows are alive in the earlier part of the experiment while the more highly'inbred cows are more frequent in the later years confounds trends in average in- breeding with.time trends in other factors. .A dependable analysis must consider the possibilities which can arise from the confounding of these sources of variation. Making the analysis within sire would bypass most of the effects of both genetic and environmental time trends by removing the variance 33 are me: of the inbree are me there: render varia‘ 9x913 3h they caused and leaving it unanalyzed. The comparisons are then only between daughters of the same sire. Since the sires in this experiment were nearly always used for few years, their daughters are likely to have lived nearly contemporarily. The pooled intra-sire regression of weight and body meastn‘ements on inbreeding is a average of the indi- vidual regressions for the daughters of the several sires weighted by the inverse of the variance of the measurement. The assumption usual in regression that the independent variables are measured without error need not be fulfilled for complete validity of the analysis. The independent variables in the calculations are inbreeding coefficients calculated according to Wright (1922). These are merely expectations of the probable loss in heterozygosis and, therefore, differ from the actual loss for any one animal because of the random chance in Mendelian segregation and recombination. Provided that the only reason for there being any regression at all of weight and body measurements on inbreeding is the inbreeding itself, the dependent variable is correlated with these errors in the independent variable. This introduces a term in the nmnerator of ny/ £12 (ac-independent variable, y-dependent variable) which cancels the effects of the denomi- nator being too large. Berkson (1950) has advanced a more comprehensive eXplanation of the reason the regression is unbiased in such cases. Some error in the independent variable could arise if different mortality caused the more heterozygous animls to be more likely to live than the less heterozygous ones which had the same inbreeding coefficients. This would tend to make the regression coefficient a bit nearer zero than it should be. Since the type herd was incorporated into the plans in 1955 and 35 since the type herd was unrelated to the original project herds, the analysis was done for each herd separately'and BISO‘With the herds combined as one herd. Birth weights and weights and body measurements at 3, 6, l2, and 18 months and 3 months after calving at first, second, third, and fourth and greater parities were analyzed. The number of females decreased from 265 at birth to 79 at third lactation. Table 1 shows the partitioning of the corrected sum of squares and products for weight at birth for the inbred herd, type herd, and the combined herds. Tables 2, 3, and h give the intra-sire regression coefficients and standard errors of the regression coefficients for the weights and measurements of the inbred, type, and combined herds, re- Spectively. Regression gf_productionign inbreeding. For the analysis 607 mature-equivalent records were used. The data were inbreeding to the nearest per cent, fat production to the nearest pound, milk yield to the nearest hundred pounds, and fat per cent to the nearest one-tenth of one per cent. Tables 5, 6, and 7 show the partitioning of the corrected sums of squares and products . The standard deviations within sire of hundred pounds milk yield, fat production, and fat per cent were 17.6, 95, and .h?, respectively. That there was a difference among sires in inbreeding and also in milk and fat yield and fat per cent of their daughters is shown by'F test. For milk yield F - 7.9, for fat production F - 8.5, fat test F - 3.2, and for inbreeding F - 31.2; all of these F values have probabilities less than one per cent. ‘Where F is the ratio of mean squares. (1‘ (.4 36 The intra-sire regression of milk yield on inbreeding was -.121.07 hundreds of pounds of milk per one per cent of inbreeding. Decoded, this regression becomes -12t7 1b of milk. The intra-sire regression of fat production on inbreeding was -.SIt.h2 lb of fat for each increase of one per cent in inbreeding. The intra-sire regression of fat test on inbreeding was .003:.002 per cent of test per one per cent of inbreeding. None of these regressions was statistically significant from zero, but the regressions for milk and fat production approach significance. The correlations with.per cent inbreeding were -.07 for milk, -.05 for fat, and .05 for fat test. These indicate that inbreeding actually accounted for only a small part of the total variance of the production traits. Ta‘rle 1 Some < variatie Table 1 Source of variation (Inbred herd) Total Among sires Within sires (Type herd) Total Among sires Within sires (Combined herd) Total Among sires Within sires df 199 19 180 58 26h 26 238 37 weight ,Products 9873 -663 13h5 -981 8528 318 b .. £261.06 lb 311:9 -123o 576 -397 2573 -833 b . -.215t.ll lb 13830 1005 2727 1520 11102 .515 b - -.o32:‘..05 lb Sum of squares and products of weight at birth and inbreeding. Inbreeding 211470 9380 12090 5132 12514 3877 3702h 21056 15968 Tab 18 11 weight 1513118: Lalgh‘ ‘v. 1“.‘ .‘Ur.e + ... U0 Ll Table 2 n Weight (lb) Wither height (cm) Chest 011'. (in) Chest depth (cm) Withers to hips (cm) Withers to pins(cm) Hips to pins (cm) n Weight (1b) Wither height (cm) Chest Ciro (in) Chest depth (cm) Withers to hips (cm) Withers to pins (cm) Hips to pins (on) * Weight and '3 Me. 138 .o3t.18 -.01t.ch .oo .oo .00 «011.07 -.Olt.05 lst cal.* 106 -.5ht88 -.03i.03 .03t.03 -.01.+..02 -.01:..05 -.061.06 -.05*.’..02 meas urements 38 6M0. 13h -.2ht.33 -.Oht.03 -0011'002 “501:002 .o2t.oh -.lOt-.07 .0h:.07 2nd cal.* 73 "1 05 T11 035 -0061001‘» -.03t.0h ”0021003 .01:.06 "e 02:006 “MOI-31.02 12 Mo. 12h -1.16t.56 -.oht.0h -.01t.02 ’0021002 .Olt.oh " 0012-005 -.0h"_',.02 3rd cal.* h? "'1 025.11 05 7 -.oht.oS "oOZteOh .01:.03 .ohi.o7 -.01’:..07 -002?- 003 Intra-sire regression coefficients and standard errors of weight and body measurements at different ages on inbreeding (Inbred herd) \ 18 Me. 126 -10621069 -010t00h - 001‘: .03 -.02t..03 -.o9t.oh ”013.2005 -.014t.02 hth cal.* 30 -l.h6+.1.76 -002:.% “00110014. .01:.0h .151.08 .09t..08 -.03t.03 taken three months after calving am.“ i I. ....1. r‘ Title 3 39 inbreeding (Type herd) :1 Weight (1b) Wither height (on) at“ air. (in) Chest depth . (on) mthers to hips(cm) Withers to pins(cn) ' t :3: 0(a) n Weight (lb) Wither height (on) Chest C11... (in) Chest depth (cm) Withers to hips(cn) Withers to pins(cn) t 3:: 0(all) 3 no. to -.25:.35 .02:.05 ...021.03 .OILOB .03305 .0330? '0023002 18‘ 6810* u. -2.86.n.65 .012.06 “0032.05 4332.05 -.05."’..07 ”093$ «053.03 a Weight and measurements 6 M0. 39 «061.56 £82.06 .03t.03 .02303 -.m.t.05 -.02.’:.o7 27 "'3 061:2 03 8 «$1.07 .00 .03:.o6 «011.08 «0111.10 -.06:'.’.05 12 M0. 141 -ol‘ue66 .02:.05 -.03t.03 .00 -.lz:.06 “122.06 -.023.03 3rd 3810* 13 43012.10 .0530? .122.07 .09:.06 «163.12 «211.13 -0 0101.005 Intre-sire regression coefficients and standard errors of weight and body measurements at different ages on 18 H00 10 421.68 -. 091.07 . ..02 .02:.o3 -.07t.0h “063.05 «031.02 hth cal.* 11 .83n.h1 .o3t.08 .06:.o9 .o9t..06 -.oet.lo «181.11 - e 07:. 05 taken three months after calving a s— I ' _. I >_ p I" e»— s t ._. '- 9 "' O t A o a _. _ 9 V C ~ 7 Q ' 0* 1 0“ hole h Che st depth iithe to hi} Withe to pi Hips pins “913: Fithe neigi Chest Cir. Chest “apt: “the to hi lithe Pips Pins to Table I: Intra-sire regression coefficients and standard errors of'weight and body measurements at different ages on inbreeding (Combined herds) 3 MO. 6 MO. 12 MO. 18 Mo. n 178 173 165 169 Weight (1b) «053.16 -.19..+..29 -.9l::.hh «1.103.523 'Wither height (3.) emf-003 «00!..03 -002503 no .001; Chest cir. (in) «001.02 .001.02 «01502 -.02t.02 Chest depth (03) 000 ““002 “0012.02 “001:002 iflthers to hips(cn) 0011003 .01303 -.O3t.03 “ewteOB Hfithers to P1n3(°‘) .00 ~083.05 «0111.05 «123.01; Hips to pins (en) «013.01.: .053.05 -.Oh‘."..02 -.Oht..02 1“ 0810* 2nd 0810* 3rd ca1.* hth (3310* n 150 100 62 la Weight (1b) «373.81 4.053.151 4.353132 4.02:1.50 Wither height (CI) '0012003 “00620014 -002:eoh .015“! Chest 311'. (in) 002:.03 n.0a.03 «(113.03 OMOOB Chest depth (6.) 001302 £13.05 “0013006 0033003 Withers to hip-(cl) -.03t.0h .Ol‘.'.’..O5 «013.06 403.07 hflthars to pins(cn) -0073005 -0033005 «063.06 003:.“ Hips to pin. (OI) «0142.02 -.Oll.".. 02 -002; 02 “OdJLOB afihight and measurements taken three months after calving 141 Table 5 Sun of squares and products of milk yield and inbreeding (Combined herds) Source of variation df Milk Products Inbreeding Total 606 2104709 18739 121123 Along sires 2? 662111: 214760 71731 Within sires 579 178,465 ~6021 119391 b-.l2.'.‘..07 1b (102) per 1 per cent inbreeding Table 6 Sun of squares and products of fat production and inbreeding (Combined herds) Source of variation df Fat Products Inbreeding Total 606 7258980 1311196 121123 Alone sires 27 2055520 159203 71731 Within sires 579 5203160 .2500? W391 b-.51."'..h2 lb per 1 per cent inbreeding Table 7 an of squares and products of fat per cent and inbreeding (Combined herds) Source of variation df Fat test Products Inbreeding Total 606 152.9 502.1 121123 Along sires 27 19.7 357.5 71731 Within sires 579 133.3 1th 19391 b-.003'£.002 per cent of test per 1 per cent inbreeding of aqua give it sions f atatist of inbr the reg signifi among 1 ‘o% fc held a: dilcti 0: 152 Tables 8, 9, and 10 show the partitioning of the corrected sums of squares and products for the inbred herd and Tables 11, 12 and 13 give the same information for the type herd. In both herds the regres- sions for production on inbreeding per cent were negative but not statistically significant. The regression of fat per cent on per cent of inbreeding was negative for the inbred herd, and for the type herd the regression of fat per cent on inbreeding per cent was .0121.006, significant at the one per cent level of probability. in F test for each herd indicated that there were differences among sires in inbreeding, milk yield, fat production, and fat per cent. The correlations between per cent inbreeding and production were «m for milk, -.08 for fat, and -.Oh for fat per cent in the inbred herd and -.13, -.09, and -17, respectively, for milk yield, fat pro- duction, and fat per cent in the type herd. Inbreeding decreased production of both milk and fat; however, the decrease per one per cent increase in inbreeding was less than most of the other reports. hen the Iowa data (Von Krosigk and Lush, 1958, and Fraenan and Hillers, 1961;), the decrease in production frm in- breeding was about four tines greater in the Holstein herd and about three tines greater in the Guernsey herd than in this herd. In the Iowa study the average life time production was used rather than sirgle records. Regressions calculated from an average could differ. hh Table 11 Sun of squares and products of milk yield and inbreeding (Type ’mrd) Source of variatiul df Milk Products Inbreeding Total 180 75291; 11629 11306 Among sires 9 111168 47112 3818 Within sires 171 63826 -2887 71188 b-.391.22 lb (102) per 1 per cent inbreeding Table 12 Sun of squares and cross products of fat production and inbreeding (Type herd) Source of variation df Fat Products Inbreeding Total 180 2351807 112118 11306 Among sires 9 370611 ~669 3818 Within sires 171 1981196 4.0579 71.88 b--l.h1.‘.1.2h lb per 1 per cent inbreeding Table 13 Sun of squares and cross products of fat per cent and inbreeding (Type herd) Source of variation df Fat test Products Inbreeding Total ‘ 180 52.1 231.8 11306 “008 811‘" 9 10.2 139.5 3818 Within sires 171 hi.8 92.2 7h88 b-.012‘.'..006 per cent of test per 1 per cent inbreeding 15 from those estimated from single records since random errors tend to cancel out of an average. That the regressions calculated from an average were different can be seen from Table 1h,which shows the regressions for the inbred herd, the type herd, and also the combined herds. This table also gives the regression coefficients for each lactation for the combined herds. Table 1b Intra—sire regression coefficients and standard errors of milk, fat, and fat test on inbreeding (Combined herds) Number of 2 Average in~ Parity observations Milk (10 ) Fat % Fat breeding Z lst 212 -.2oi.1s «562.83 .oo6i.ooh 18 2nd 138 ”021:017 ~100me96 0001100011 19 3rd 93 -.22:.17 -1.0lt.92 .003t.005 19 Iron 60 «10.226 -.h8.’:1.o .0031.006 18 Average production 211 mat-.13 ~.7Si.7b .0051.ooh 18 Average production + + (inbred) 132 -.26i.1u -1.1h-.78 .002—.00h 26 Average production (type) 79 -.2ht..35 «5811.9 .0112”..008 1: Effects of inbreeding by_multiple regression. The methods of statistical analyses used in this phase were also based on the prin» ciple of least-squares. The method of analysis of data with unequal subclass numbers involving direct matrix arithmetic was illustrated by Harvey (1960). 116 A Isthemtioal model was: 113 -30 +81 + B]. rot + 32m: + BBTDJ 4- 311(50):, +311 there In was the observation on the 31:2 daughter of the 11:2 sire 3 Be, the constant term; 81 was the effect of the it_h_ sire; and Bl, 32, B3 and BI: were partial regression coefficients of I“ on the independent variables, ro , FD , TD , and (Fo)§. The independent variables were: 3 FOR - the inbreeding coefficient of the 131:3 individual FD - the inbreeding coefficient of the 13311 individual's dam TD - the measurement of the dam [If Yij - was birth weight, ID was birth weight of the individual's dam] (F0): - square of the individual's inbreeding coefficient. To be estimated were partial regression coefficients on the independent variable in question adjusted for variation in all other variables. The relative importance of each variable can be determined by the magnitude of the standard partial regression coefficient. The other models were: I” - 13° + 51+ 31 F0k + BZFDJ + Bh (1mg +313 r13 -30 +31 + BlFOk ”331(1) +13,4 (so): +313 Iii-30+Si+31FOk+BZFDJ+B3ID34-Eij 1:1J - so + Si . Black + aha-‘0)?c + a” 113 'Bo*51+31F°k*32FDi ”313 113 '30-'81 +BlFOk + B31113 +313 I1,1”KW”*Bil'fi"1:"3i.‘) The terns in the models have been defined above. The models with the independent variable (FO)2 were to indicate non-linear effect of in- breeding on the dependent variable. h? For this phase of the analysis data for type and inbred herds were combined, and only those individuals where the measurement on the dam was available were used. Hence, the number of observations varied from 166 at birth.to 32 at the third lactation. The partial and standard partial regression coefficients are in Tables 15 through 28 for each trait at the different ages of measurement. h8 Table 15 'Within sires partial regression coefficients of weights Age :1 OJ ’fli4ig (1b) from birth to 18 months of age Birth 17 166 52 31 B B' -010 - ell .07 .06 e06 009 .00 .07 “012 -0114- .06 .09 .00 .09 '012 'elh .07 .06 .01 .12 'e05 '005 .07 .06 .06 .09 'elh “016 .01 at “e05 -005 .06 .08 -.02 -.02 .06 .06 -.02 -e03 3 Months 18 120 133 31 B B' ‘e52 “e23 .0h .03 .21 .1h .01 .03 ’06]. -027 .21 .13 .01. .22 “002 ”001 .03 .03 .01 .03 -e08 -003 .Oh .Oh 020 e13 -.06 -003 .01 .08 “cos 'e02 .19 .12 ”e12 ’006 .03 .03 “elb -006 NS-number 0f sire groups NDanumber of daughter-dam pairs Thaverage weight of offspring Faaverage inbreeding of offSpring F0-inbreeding of offspring YDsweight (birth, 3, 6, 12, and 18 months) of dam FD=inbreeding of dam F2-square of inbreeding of offspring Bapartial regression coefficient 6 18 120 2b? 31 B B‘ 3.01 .66 .12 .13 .0h .01 '00“ “057 3.13 .69 .06 .02 -.Oh ’e60 3.13 .69 .12 .13 “e014. 059 .11 .02 .12 .1h .15 .05 3.31 .73 -0 'e63 .12 .03 .17 .05 .18 .0h .12 .13 .21 .05 12 20 112 tho 31 B B' -e23 -.0h .11 .12 'ehz “010 -.01 -.12 'elB “e03 'eh3 -.10 'eOl -e09 -1e19 '019 .11 .11 -000 -.00 '1e00 'e16 .11 .12 ‘039 “.09 -1e1h “e19 .00 .03 -071 ’012 “0’11 -009 .1020 -019 .11 .11 -091 '01; B'-standard partial regression coefficient 20 126 619 .25 -1007 El -016 .31 -.10 -021 “e33 -.02 .18 .09 .28 -.16 -.06 .30 -.O9 -.33 .18 -.02 -.08 .28 -.1h WEBB. New? . r e e v e e i . . c y e . v a e e p v h 9 1 e I c n I o . a o 4 e a e v e e a 4 u _ _ a a O 0 A A A e e A s .q a 9 o e e v .e .e e .I A Q 1 D s a “H. a»... 9 O C o a e O h I a .. A D J A A \ a e A O I 4. e c I .r a e I wk .1.. m at: he. memo ”was I I I e .v e. e a t C t I r 9 I D n A Q Q n V I t O 0 .0 O 0 Table 16 L801). NS Edi-4% see 388 3398 88 $8 868 68 'e 0 Int 15 106 800 B '10e6 .26 1.20 .17 “'8 e51 .98 .15 -9018 .26 .16 -2.23 .27 .91 “7063 -2 .116 .92 fi3e01 .28 -l.92 26 -.19 2nd 13 66 981 26 B “'11 063 .27 1.119 .18 -9 062 1.35 -10 957 .25 .15 -2.83 .22 1.01 -8.7h .13 -2 .119 .98 -2 .95 .22 -2 .62 119 B! -1015 .2 8 .20 .91 .18 .75 -1.0h .27 .79 “.28 .22 .1h -.86 .611 -.25 .13 -029 .22 -.26 NS-number of sire groups bin-umber of daughter-dam pairs leaverage weight of offspring 3rd 10 32 1032 19 B .15072 -e10 1.03 .26 -1S.h3 .66 .3h ~1h.69 «ch .33 -2 1:6 -.07 .31 41h.73 .23 -2.h7 .12 -2 .50 .06 -2 .h9 F's-average inbreeding of offspring FOacffspring inbreeding B8 ~1.29 -.10 .09 1.09 -1.28 .06 1.07 -l.22 -.07 1.00 -020 -.05 .03 -1.22 1.00 “e21 .01 -021 .03 .02]- Within sire partial regression coefficients of weight (1b) 3 months after calvings hth 11 611 1071 19 B B' '6055 ”096 -019 “e18 1.9h .29 .16 .96 'h039 -.65 1.95 .29 .11 .69 -7 .79 4.15 'e19 -019 .18 1.21 -010 'e01 -013 '012 2 .36 .36 '5063 -083 .15 .9h .19 .02 2.28 .3h .h7 .0? ”e11 “e11 .70 .10 ID-weight (lat, wnd, 3rd, and hth lactation) of dam FDainbreeding of dam F2=square of inbreeding of offspring Bapartial regression coefficient Bit-standard partial regression coefficient ".a‘ 1 ~19 Nb 1‘ . I a Y “ft. 1.1,. 9 0 I 0 e s v e l . a o o e e _ e a I e e o e p a n e . . v NEW. NEW. 3310.. Now/n WW... 0 e v I A o I O O s 9 O 1 v v v n o I D C . . C a J W. E .m. 50 Table 17 Within sire partial regressions cceffic ients of wither height (cm) from 3 to 18 months of age Age 3 Months 6 12 18 NS 18 18 20 20 ND 120 120 112 126 Y 79 91 105 115 F 31 31 31 30 B B' B B' B B' B B' F0 -008 " 019 001 002 -03 0 " 057 006 012 ID ’008 '006 018 016 017 0 02 8 027 FD .02 .08 .03 .09 .07 .20 .01 . F2 000 025 -000 -002 000 052 -000 “027 F0 -0014 -010 -002 -001]. “028 -053 “007 .0114 FD '003 '009 003 007 006 018 003 008 F2 .00 .16 .00 .06 .00 .53 -.00 -.07 F0 003 008 011 021 "' 013 " 026 00? 0114 m -007 -005 017 015 01!!- 012 029 028 F2 000 018 000 00,4 000 009 '000 -027 F0 003 008 001 001 “001 “001 " 008 “017 ID -.06 -005 017 016 017 01,4 028 026 FD .03 .07 .03 .09 .06 .17 .01 .011 F0 .03 .08 006 012 '0124 -027 -.05 "011 F2 000 006 000 007 000 030 "' 000 “'008 F0 003 007 001 002 .02 003 -011 '02]. FD .03 .09 .03 .07 .05 .15 .03 .08 F0 005 013 002 001-!- 003 006 “008 "' 015 m “008 " 006 017 015 015 012 028 027 F0 005 013 003 005 0014 008 " 010 -' 019 NEE-number of sire groups ND-number of daughter-dam pairs Yaaverage wither height (cm) of offSpring Faaverage inbreeding of offspring FO-inbreeding of offSpring YD-wither height (cm) (3, 6, l2, and 18 months) FBI-inbreeding of dam F2-square of inbreeding of offspring Bnpartial regression coefficient B's-standard partial regression coefficient of dam Table 1 -Cte TO 1h 7. 9: MW Emmy. Mn. 0 o 0 l 0 0 0 a t 0 n 1 . 0 0 A 0 C 0 u n 0 4 a A 0 e A l p 0 a 0 U H0 2 and. mum”. NEH... \IV AIL l0 ‘1. ...,u D «1.1.. 5: Ned an. E «U w.k Table 18 'Within sire partial regression coefficients of wither 51 height (cm) 3 months after calving L80t0 lflt NS 18 ND 120 ‘I 123 F 26 B B' F0 '001 -005 ID .27 .29 FD .01 .01 F2 .00 .29 F0 -002 -009 FD .02 .02 F2 .00 .38 F0 -.03 -.13 TD .28 .29 F2 .00 .31 F0 ’00; -031 10 .29 .31 FD .01 .02 F0 -.01 "0% F2 .00 .27 F0 -.01 -.05 FD .02 .02 F0 -009 -0h3 YD .25 .28 F0 -011 '132 “002 .28 "010 .02 '010 .29' -.10 2nd 13 66 125 26 BI '005 .29 ..05 '031 '008 .09 '0h2 .08 .29 -028 -003 .30 -.03 .03 -.36 ...32 .07 '03h .30 -.32 NSanumber of sire groups NDanumber of daughter-dam pairs “001 .05 .00 .10 .05 .06 .hz -000 .01 .05 .15 -.00 .01 .05 .83 -.01 leaverage wither height of offspring Fsaverage inbreeding of offspring F0=offspring inbreeding IDswither height (lat, 2nd, 3rd, and hth lactation) of FD-inbreeding of dam. F2=square of inbreeding of offspring Bapartial regression coefficient B'sstandard partial regression coefficient 3rd 10 32 127 26 B. '002 .38 .22 .0h .33 .19 -.3h .20 .36 '019 .02 .38 .22 hth 11 6h 127 19 B B' “005 '026 .h7 .h7 .08 .hi .00 .00 .13 .72 .07 .37 .00 .57 -008 “0&1 .h2 .L2 .00 .29 -.05 -.25 .h7 .h7 .07 . .09 .149 -000 -026 .03 .17 .06 .33 -002 ‘010 .39 .39 .05 .2h dam 52 Table 19 Within sire partial regression coefficients of chest cir- cumference (in) at 3 to 18 months of age Age 3 Months 6 12 18 N3 18 18 20 20 ND 120 120 112 126 Y 3h ’42 53 60 P 31 31 31 30 B B' B B' B B' B 3' F0 -006 .022 .21 063 -.03 -010 007 021 ID .00 .00 .18 .18 .15 .15 .29 .31 FD 002 0m -0m. -003 .00 .00 -000 -002 F2 .00 010 '000 -0110 000 0m- -000 '02? F0 -006 -03. 0214 I 072 -002 -005 -005 -017 FD 002 008 -001 -002 000 000 .01 006 F2 .00 .10 -.01 -._61 .00 .02 .00 .07 F0 -002 -0“ 019 058 -003 -010 006 020 ID .00 .00 .19 .18 .15 .15 .29 .30 F2 .00 .01 -000 -031 .00 001 -.00 -027 F0 -.03 --.11 .03 .07 -.03 -.09 -.02 -.O7 ID .00 .00 .19 .19 .15 .15 .28 .29 ED 002 0W .00 000 .00 000 -.00 -001 F0 '002 -006 023 067 -001 I'003 -005 -015 F2 .00 .01 -.01 «315 .00 .01 -.OO -.06 F0 -003 -011 003 .08 -.01 -002 -003 -010 FD 002 009 001 002 .00 000 .(II. .06 F0 -001 -005 003 .03 -003 -008 -002 -007 ID .00 .00 .19 .19 .15 .15 .28 .29 F0 -001 -05 003 009 -001 -002 -003 -009 RS-nuflaer of sire groups IID-tmsber of daughter-dam pairs I-average chest circumference of offspring (in) F-average inbreeding of offspring Fo-inbreeding of offspring ID-chest circumference (in) (3, 6, 12, and 18 months) of dam I'D-inbreeding of dam F2-square of inbreeding of offspring B-partial regression coefficient B'-standard partial regression coefficient le 2 L mnn men men mm Lact. p. 13' 30 TD F0 Table 20 Vithin sire partial regression coefficients “3“ 0 HS ND I F 2'53 353 73233 338 3393‘ 33 £33 a; O 53 cumference (in) 3 months after calving -.16 .23 .Cfl. .00 -.17 .02 .00 -;15 .23 .00 -.09 .2h .01 -.17 .01 -.08 .02 ..08 .21. -.07 let B. ”058 .25 .119 -.6h .15 .hB t.’ -040 .26 .38 1 -.25 .27 .07 -.61 .60 -.25 .18 -.26 .27 -.2h -.26 .25 .03 .00 -. 21 .03 .00 -.2h .28 .00 -.06 .21 .02 -.19 .00 -.0h .02 -.06 .21 -.05 2nd 13 66 69 26 BI -082 .22 .13 .68 -.65 .11 .55 -.76 .59 -.17 .18 .08 ...60 .88 -41h .07 -.18 .18 -.lh NS-mmber of sire groups ND-number of daughter-dam pairs -.32 .15 .08 .01 -.28 .09 .01 -.27 .31 .01 -.01 .08 .07 -.19 .00 -.01 .08 -.02 .25 -.01 3rd 10 32 71 26 BI .1.05 .12 .32 1.02 --93 .36 .93 -.91 .25 .83 -010 .07 029 -.60 .56 -.20 .32 -.17 .20 -.0h I-average chest cir. (in) of offspring F-average inbreeding of offspring EDI-offspring inbreeding ID-chest circumference (inches) (1st, 2nd, 3rd, lactation) of dam I‘D-inbreeding of dam F2-Iquare of inbreeding of offspring B-partial regression coefficient B'I-standard partial regression coefficient of chest cir- hth ll 61; 72 19 B B' .11 .51 -.07 -. . .30 -.00 -.23 .08 .111 .06 .29 -000 ”016 .06 .31 -.05 -.0h .00 .034 .06 .28 -.05 -.Oh .05 .28 005 023 .00 .09 .05 .25 .05 .29 .07 .35 .06 .32 and hth m1 NDbfl NEH NEH ENE %H mm mm m 0 O t O O I O I I O i O O o I o I 0 l O , g Q _ H e t e e l a o a u v v v e o I n D Q o 1 i w _ l i D C O Q Q I I I D O I O O U I O D V D O i i i H I a I I O b. I I Y e u I o O 0 I I u . .. _ n v o v o u n b o O o v a . I v i 9 l O _ . a y 0 y I o 1 o o A e e r v 9 O I I o O I i _ m . l I D D O o I D e I O t n U I C C o I C Sh Table 2!. Within sire partial regression coefficients of chest E e MHaa figgg 3 68 33 33 333 398 333 depth (cm) from 3 to 18 months of age 3 Months 18 120 35 31 B B' .03 .12 .07 .06 .CH. .03 -.00 -.11 .02 .06 001 .03 -.00 «014 .05 .18 .08 .06 -.00 -.15 .00 .01 .07 .06 .01 .011 .03 .11 -.00 «w ' .(Il .01 .01 .03 .01 .02 .07 .06 .m .03 18 120 .18 .17 .00 -.00 .17 -.01 -.00 .17 .17 -.m .03 .17 .00 .15 -.00 .03 .00 .03 .17 .03 31 .18 .00 -. 51 .61 -.oh -.51 .59 .18 -.38 .09 .18 .00 .52 -.h1 .12 .00 .09 .18 .12 NS-nnmber of sire groups ND-nmlber of daughter-dam pa I-average chest depth (on) of offspring 112 .05 .22 .00 .05 .oo ..00 .oh‘ .22 -.00 -.01 .22 .00 -.00 .02 .01 -.Ol .22 .02 F-average inbreeding of offspring POI-inbreeding of offspring YD-chest depth (cm) (3, 6, 12, and 18 months) of dam I'D-inbreeding of can F2-square of inbreeding of offspring B'partial regression coefficient BI .15 .22 -.16 .18 -012 .16 . 22 -.16 -.02 .22 .00 .25 -.15 .05 .03 -.02 .22 .06 B'-standard partial regression coefficient 18 20 126 60 30 B B' .06 .21 .37 .39 -001 -006 ”000 ‘019 “.11 ‘03? .01 .05 .00 .29 .05 .16 035 037 -000 -e16 .01 .01 .36 .38 -001 -.06 -.10 -.3h .00 .29 -.02 «05 .01 .05 -.0]. «GI. .31: .37 -.01 -.0h q ‘ 330'- NDEMM O I I I _ O I D I I I l I A O I U . O I I I a e s o u . u I I I I _ _ t I I mmumu I I I < v O O C I I I 1 I I v e I 7 O I I I 0 NEW. . I I a _ C I ’ D O . ' t . 9 A I I I h b a NEW... . U I a s e c s I o o u e I D MD. mm mm .mu. 0 e I I 6 o I v ‘ I O c . a e 7 v o e A I I I I a . i I I o e .. _ I I I I Table 22 55 Within sire partial regression coefficients of chest depth (on) 3 months after calving Lact . lat N3 15 ND 106 Y 66 F 26 B 3' F0 -.07 -.29 ID .29 .36 ED .01 .05 F2 .00 .18 F0 -.12 -.h7 FD .01 .06 F2 .00 .23 F0 -.07 -.29 ID .29 .36 22 .00 .15 F0 -.01 -.0h YD .31 .37 FD .00 .00 F0 -.12 -.h7 F2 .00 .21 F0 -.01 -.05 FD .01 .oh F0 -.03 -.1h ID .28 .29 F0 -.01 -.05 -.1h .hh -.01 .00 -.11 -.01 .00 -015 .hh .00 -002 -.11 .00 -.03 -.02 ...os O -.03 2nd 13 66 69 26 BI -.5h .38 -.06 .37 -.h2 -.07 .30 -.57 .37 .19 .37 -.09 -.hh .35 -013 -.09 -018 .37 -012 NS-nunber of sire groups BID-number of daughter-dam pairs I-average chest depth on of offspring -017 .20 .03 .00 -.1h .05 .00 -.15 .32 .00 -.03 .17 .02 -.09 .00 ..0’4 .03 .27 .03 F-average inbreeding of offspring Fo-offspring inbreeding ID-chest depth on (let, 2nd, 3rd, and hth lactation) of dam FD=inbreedi ng of da- FZ-square of inbreeding of offspring B-partial regression coefficient Bur-standard partial regression coefficient 3rd 10 32 71 26 B! -.76 .19 .19 .92 -.65 .8h -.70 .31 .83 -016 .16 .16 -.h0 .55 .17 .224 .13 . 26 .15 hth 11 6h 72 19 B B' .16 .91 -.16 -.18 .05 .29 -000 -036 .12 .68 .014 .22 -.OO -. 27 .08 .h6 .08 .09 -.00 ~07 .09 .52 -011 “-013 00,4 .25 .10 .55 .00 .08 007 .113 .03 .21 .07 .89 .08 em .08 .h7 Table 23 NS ND F0 'Within sire partial regression coefficients 56 to hips (cm) from 3 to 18 months of age 3 Months 18 120 h9 31 B B' ”032 “079 “012 ”.11 .03 .09 001 I75 -033 'e80 .03 .11 001 073 -026 -062 "013 -012 .00 .66 .02 .05 “012 'eIl .02 .06 ”025 “061 .01 .61 .Ol .01 .02 .09 .08 .09 "012 -011 .03 .07 B -011 .15 .03 .00 '010 .03 .00 '003 .15 .00 .00 .15 .02 .01 .00 *001 .03 .01 .15 .01 18 120 60 31 BI -.23 .1h .07 .21 -.20 .09 .16 “006 .15 .08 .00 .1h .06 .01 .01 “002 .08 .03 .15 .02 NSanuMber of sire groups ND=number of daughter-dam.pairs .17 .05 -001 -.00 .16 .01 -.00 .0h -.00 -.02 .00 .1h .00 “001 .00 -.02 .00 -.01 BI .32 .08 -.03 -032 .31 .02 “030 .27 .0h “.28 Yéaverage withers to hips (cm) of offspring Faaverage inbreeding of offSpring F0=inbreeding of offspring ID=withers to hips (cm) (3, 6,12, and 18 months) of dam FD-inbreeding of dam F2-square of inbreeding of offspring Bapartial regression coefficient B'=standard partial regression coefficient of withers 18 20 126 81 30 B B' “037 “.87 .1h .15 ”003 ”010 .01 .75 “oh? '095 -002 “I08 .01 .83 -eh0 -091 .13 .1h .01 .77 “003 “007 .16 .17 -003 -310 "ehB ‘098 .01.8h ‘eOh ‘008 ’002 -008 -.0h -.09 .15 .15 -005 ’010 Table 2b Lact. NS ND 57 Within sire partial regression coefficients of withers to hips (cm) 3 months after calving lst 15 106 89 26 B '011 .20 ‘003 .00 -.07 -.CS .00 -.O8 .26 .00 -.Oh .2h “.03 -011 .00 -.02 “.02 ‘eOh .26 -.QS BI ‘022 .2h -010 .18 -.15 “e16 .12 “015 .25 .10 ‘009 .23 -IJO ”.22 .18 “ooh ..C6 “008 .25 -011 ”elk .00 .00 2nd 13 66 9h 26 BI "' 031 .18 -007 .22 -.13 .oh -.3h .18 .26 ”010 .17 -.08 “016 .07 "009 ‘006 -.09 .16 -009 NS=number of sire groups NDcnumber of daughter-dam pairs 3rd 59 .15 -007 .01 -.b5 ".06 .01 .12 -.01 '00]. 10 32 96 26 Yéaverage withers to hips of offspring F=average inbreeding of offSpring FO=offspring inbreeding ID=withers to hips (cm) (lst, 2nd, 3rd, of dam FDsinbreeding of dam F2=squsre of inbreeding of offspring B=partial regression coefficient BI 'lezh .18 -018 1.18 -.95 ‘elh .89 '1032 .1h 1 .28 “.06 . .08 -.21 “1008 1.08 -.05 “018 ”003 ‘003 hth 11 6h 97 19 -.3h .03 .Ol ‘032 .00 BI -l.10 .05 -035 1.18 -1.0h 1.10 ”1001 .05 1.06 .00 -.O7 -.09 “-9h .97 .00 -007 .00 .00 and bth lactation) B'=standard partial regression coefficient 58 Table 25 Within sire partial regression coefficients of withers to pins (cm) from 3 to 18 months of age Age 3 Months 6 12 .18 NS 18 18 20 20 ND 120 120 112 126 Y 71 87 108 119 F 31 31 31 30 B B' B B' B B ' B B ' F0 -086 -1015 -.10 -.11 .JJ. .16 “0’47 "oBh ID -005 -e05 “ell ”.10 .08 .07 02h .22 FD 000 000 007 010 -002 “001} ‘003 '00? F2 .01 097 -000 “all -000 -018 001 068 F0 '079 “1.07 -009 “009 -009 015 'OSh: “e96 FD “.01 -001 .08 011 -001 -001 -002 ”003 F2 001 091 -000 -013 -.00 “016 .01 077 PO '086 '1016 012 01.3 007 .11 “.50 ”086 11) .05 -.O7 - .11 -.11 .08 .07 .21: .21 F2 .01 .97 -.00 '029 “000 'elh 001 069 F0 -005 -007 -021 “022 “002 ‘003 “.07 .-oll ID “ooh “.06 -011 'elo .08 007 .25 02h FD ”.02 “00,4 .0]- cl]. -001 “002 “003 “.07 F0 -081 ‘1009 015 .15 008 .12 -055 “.90 F2 “.01 -092 -000 -032 -.OO ".13 001 I78 F0 -.05 -.06 -.22 '023 -002 "“002 “009 “015 m -.02 -.d-I .08 013 ”I01 -001 -001 -0018 F0 “007 -006 -017 -018 -003 “00,4 “.08 '01}! ID -.05 -.07 ~612 -.11 008 007 025 023 F0 ’005 '00? -017 -018 .02 “003 -010 ‘016 NS-nmnber of sire groups ND-number of daughter-dam pairs Iaaverage withers to pins (on) of offspring F-average inbreeding of offspring FO-inbreeding of offspring ID-withers to pins (cm) (3, 6, 12, and 18 months) of dam FBI-inbreeding of dam FZ-square of inbreeding of offspring Bapartial regression coefficient B'nstandard partial regression coefficient Table 26 Last. NS wag 5’63 5’38 232393 a as as as sea 59 'Uithin sire partial regression coefficients of withers to pins (cm) 3 months after calving lat 15 106 130 26 B B' “019 “038 .21; .211 .01 .02 .00 .21 -.12 -.2h 008 009 .00 .18 -011 ‘022 .25 .25 .00 .17 - 008 ' 017 025 02b .00 .00 ‘008 -016 .00 .09 “-.08 "' 01,4 .00 .00 '00? '01h .25 .25 '00h “007 -.11 .01 4.10 .21 '011 2nd 13 66 137 26 -022 .01 -020 .21 -022 NS-number of sire groups ND-number of daughter-dam.pairs 3rd 10 32 um 26 Ihaverage withers to pins of offspring F-average inbreeding of offspring FO-offspring inbreed ID-withers to pins ( of dam FD-inbreeding of dam F2-square of inbreeding of offspring Bapartial regression coefficient hth 11 6h 1h2 19 B B' “035 “1011 ‘002 '00h -.07 —.23 .01 1.21 “036 “1015 '006 -022 .01 1.25 “032 '1002 .00 .01 .01 1.07 .01 .Oh “007 -013 '005 ‘018 ‘032 .1001 .01 1.07 .02 .06 -.0h -013 .01 .02 .00h -009 .01 .01. 83% (let, 2nd, 3rd, and hth lactation) B'ustandard partial regression coefficient 60 Table 27 Within sire partial regression coefficients of hips to pins (cm) from 3 to 18 months of age Age 3 Months 6 12 18 NS 18 18 20 20 ND 120 120 112 126 I 23 28 3h 38 F 31 31 31 30 B B' B B' B B' B B' F0 032 061‘ 015 018 “008 “036 002 .09 ID 000 000 007 007 025 023 027 025 ED 002 006 “007 “011 002 011 “000 “001 F2 “000 “05h 000 005 000 012 “000 “023 F0 .32 .63 .13 .16 -.05 -.25 -.01 -.0h ED 002 006 “006 “010 002 009 001 00h F2 -.01 -.5h .00 .06 .00 .0h -.00 -.19 F0 038 075 “006 “007 “00h “019 002 009 1D .00 .00 .06 .05 .25 .22 .27 .25 F2 “000 “061 000 02h “000 “001 “000 “023 F0 .03 .03 .20 .2h -.05 -.2h -.03 -.1h in 000 000 007 007 025 023 027 025 FD 003 008 “007 “011 002 010 “000 “001 F0 037 075 “006 “007 “002 “011 “001 “002 F2 “001 “061 000 023 “000 “006 “000 “019 F0 00h 008 018 022 “00h “020 “005 “02h ED 000 000 “006 “011 001 008 001 00k F0 00b 008 016 019 “00h. “020 “003 “01h 1D .00 .00 .06 .06 .214 .22 .27 .25 F0 00h 008 015 018 “00h “017 “005 “023 NS=number of sire groups NDanumber of daughter-dam Yul-average hips to pins (cm of offspring airs Fan-average inbreeding of offspring F0=inbreeding of offspring YDahips to pins (on) (3, 6, 12, and 18 months) of dam FD-Iinbreeding of dam F2-square of inbreeding of offspring Bupartial regression coefficient B'-standard partial regression coefficient Table 28 Lact. NS ND F0 F2 F0 F2 F0 F2 ‘Within sire partial regression coefficients 61 pins (cm) 3 months after calving lat 15 106 h2 26 “0111» .20 .03 .00 -.15 .03 .00 “ 012 -.31 .20 --37 -.08 2nd 13 66 uh 26 B! -.L9 .13 -.19 .ll -.57 -.22 .16 .,56 .1? .21 “-39 .1h -.20 -.67 .30 “0’41 -.23 -.36 .18 -.39 NS=number of sire groups NDanuMber of daughter-dam.pairs .02 -.12 .00 -.CO .07 .01 -.OO .00 “012 -.01 -.12 .00 .02 .01 .01 -.01 “012 .00 Yéaverage hips to pins of offspring Fcaverage inbreeding of offspring Fanffspring inbreeding YDahips to pins (cm) (1st, 2nd, 3rd, and hth lactation) of dam FDcinbreeding of dam F2=square of inbreeding of offspring B=partia1 regression coefficient 3rd 10 32 ha. 26 .08 “005 “013 .01 B'sstandard partial regression coefficient of hips to hth 11 6h DS 19 B B' “001 “010 .15 .1h .01 .01 .00 .02 “002 “012 “001 “007 000 005 “002 “011 .15 .13 .OO .03 “001 “008 .15 .1h .00 .02 “001 “007 .00 .01 “001 “00? .01 .07 “001 “00? .1h .13 “001 “009 62 _I_._g_s_s.§_s_ of females between birth and first parturition. During the last several years mortality and reproductive failures almost completely destroyed the effectiveness of selection because female replacements were too few to maintain the size of the herds. Most of the calf losses were due to death shortly after birth or during the first month of life. If the females survived, failure to breed was the major reason for heifers not going into the producing herd. 0n. the average, the inbreeding of the inbred calves which died at birth or during the first three months of life was three per cent higher than their contemporaries. However, the average inbreeding of heifers leased between 12 months of age and first calving was five per cent higher. Tables 29 and 30 give yearly for female births, the average in- breeding coefficient, and the number of calves lost between birth and three months, and the females lost from the herd between twelve months of age and first parity. This latter group was primarily females failing to breed. Effects g'lnhreeding in me rating. An unofficial type classi- fication was made each time the animals were measured, beginning at 6 months of age. Each of five classes ”poor“, "fail”, "good“, "good pllB', "very good", and "excellent” were divided into three sub-classes, 10w, middle, high. The numerical values assigned ranged from zero for low poor through 17 for high excellent. The results reported in Table 31 are for the inbred herd, the type herd, and the combined herds for three different ages and four parities. The regression coefficients are for dairy character, mammary system, and overall rating and are coded by 10.1. 63 Table 29 Inbreeding of female losses between birth and first parturition (Inbred herd) Deaths or removals Number Average 3 Months 12 Mo. to 1st calving Year of births inbreeding Number Average _1f Number Average E 1951 1 3 52 h 6 2 0 l 214 53 12 19 Sh 5 20 l 18 SS 12 2h 1 2h 56 21 21 S 18 2 33 57 19 28 3 33 58 1h 32 2 25 3 35 59 1h 32 2 37 l 33 1960 1h 32 2 3h 7 31 61 12 32 2 35 h 38 62 20 3h 6 37 1 39 63 11 36 7 35 7 39 6h 15 36 7 3h 2 36 65 1h 36 2 39 66 __§ 38 __3 38 193 29 37 31 32 3h 6h Table 30 Inbreeding of females losses between birth and first parturition (Type herd) Deaths or removals Year Number Average 3 Months 12 Mo. to lat calving of births inbreeding Number Average _F_' Number Average 2 1957 3 8 58 9 9 h 9 S9 8 12 l 16 1960 10 1h 5 16 61 7 1h S 13 62 6 15 3 l6 2 17 63 2 28 6h 11 18 5 19 1 18 65 3 2o 1 22 66 6 21 5 21 "25' "I; '21 '1? “"5 '33 Table 31 on inbreeding (Months) Age Inbred herd 6 12 18 let Parity 2nd 3rd hth Type herd 6 12 18 let Parity 2nd 3rd hth Combined herds 6 12 18 let Parity 2nd 3rd hth Number Observed inbreeding 121: 121 123 68 16 71 72 142 h? h? L? 29 17 33 166 168 170 88 105 Average 31 31 30 28 26 22 20 11 10 C'\O 0‘ 0‘ 26 25 25 22 22 22 16 65 Dairy character «051.05 .00 «151.05 «281.10 .oht.02 .16t.l3 .151.12 «0111.06 .lct..09 .02t.01 «0721.08 .01t.01 «0111.01 -03—9:011 «051.01; .OSt.05 .01t.Ol «2111.06 «1822.08 .03t.03 .08i.09 mammary system .00 -.07t.07 «101.05 «091.10 «11.21.11: «1111.09 “010:008 «0721.07 .00 .061.06 .26t.11 £72.13 .2631? 411.10 .02t.0h «0131.01: «091.01. .09:.07 .03:.0h. .00 - 002:003 -1 Intra-sire regression coefficients (10 ) of type rating Over-all rating «261.15 .081.08 «171.11 «362.23 «35:32 «211.31 “018:017 .16t.16 £131.13 .00 331.26 371.35 .60i.h3 .2lt.2s -.11'.'.'..11 401.10 «101.11 «022.03 «131.13 -.03".;.03 .05i.02 66 Maximum likelihood_method for estimating the effect§_g§.i§- .EEEEQEEB‘ There is always some question of whether regressions within sires actually are free of environmental.and genetic trends. This question may not be completely answerable, but Henderson (1959) pro- posed to estimate these time trends by maximum.1ikelihood. A term.can be added to the model to estimate the effect of inbreeding on production independently of changes in general yearly environment and producing ability of the herd. Of course, like all statistical methods, the vali- dity'of this method rests on assumptions which may or may not be ful- filled. If records of production are correctly adjusted for varying ages of the cows at calving, the average differences between the records of the same cows made in different years should be the differences due to environmental things which changed between those years. Then, if the average production of the herd is corrected for these yearly environ- mental changes, the rest of the change in the mean must be changes in the producing ability of the herd. But not all cows have an equal num- bers of records, and the question arises as to how to weight them properly. Of course, this is an over-simplified situation because the effects of sampling errors and selection have been left out for brevity. Nelson (19b3) presented a least squares solution to the prdblem and used the method to estimate the genetic change in the Iowa State hard. The method of least squares would probably'be effective if the cows were not selected for production. However, when a herd has been under selection, each year cows with best records are saved and those with the poorest are culled. ‘When those cows saved make records the following year, they generally produce less than they did the year they 67 were selected because of the incanplete repeatability of records. This makes the environment appear to be getting worse in successive years. Consequently, the producing ability of the herd appears wrongly to in- crease more or decrease less than it actually does. The main difference between methods of least squares and maximum likelihood is that the latter takes into account the incomplete repeat- ability of records. As with least squares, either an overall regression of production on inbreeding or a constant for each inbreeding level can be fitted with the maximum likelihood method. Fitting a constant for levels of inbreeding was chosen for these data to indicate whether the effect of inbreeding tended to be curvilinear. Maximum likelihood estimates the parameters of the Specified population which males the likelihood of the observed frequency in this supposedly random sample as large as possible. The model for this prob- lem was: Iijkl uu+ai+fj+gk+ckl+eijkl where Yijkl designates a 305 day-ZX-M.E. production record made in the th th th 1 year by the 1 cow with inbreeding in the 3 class and belonging th to the 1: time group, “is the p0pulation mean, ai is the amount the h environment of the it year raised or lowered production from the average of all years, I: is the deviation associated with the 3th inbreeding class, 31: is the deviation of the average producing ability of the cows th in the k group and eijkl is a random error of measurement. 1;; this. analysis the groups were made on the basis of the year in which the cows were born. on is the deviation of the 1th cow's producing ability from the mean producing ability of her group, the kth group. 68 To estimate by maximum likelihood some assmnptions of distri- bution are needed. Those assumed were that the ckl's are normally and independently distributed about a particular g1C with a variance 6:32, that the eijkl‘s are normally and independently distributed with mean zero and variance, 5'62, and that temporary environment, inbreeding, and real producing ability are independent and additive. F'I‘om the above asstmtptions, the joint frequency function f(ck1’eijkl) can be written. when it is multiplied by the number of observations in the sample, we have L, the likelihood function. This is merely the joint frequency distribution of two independent nomal distributions with the parameters given. L- [W (2152 > exp wk, (es-i > JET.” more? e - (262)..1 (Y - (H+ a + )2 XP 6 ijkl i + £3 1 8]: °k1> J - (2176:)‘nk1exp - (252) 1 Z. :19 Rafi-”131:1 . 2 ..l 2 6111’ " (268) 1&1 [11311 "(M ‘* 11 + 1'3 * 8}“ °k1J° The estimators which maximize the likelihood for the sample at hand are obtained by partially differentiating log (L) with respect to each parameter, setting the partial derivatives equal to zero, and solving the resulting equations simultaneously. log (L) -_ nkl log 2"; “kl 1° 62 '2'— ‘T g a 1 0 Tam 11- O n n ' 2 [Yijkl - ( M-I- 81 + £3 + gk + 61(1)] 69 Let summation over a particular subscript be denoted by'a dot. The general equations to be solved are: 31%;}; - 1 e [1,... - puny-{111... Si -§n.3.. fj- into}: 03k uh. .klc leji 0 or 11.... fi+§ni .00 $1 + Enojooif‘j + E coke gk + A kiln..kl ckl '1 Yo... '31 L - 1 [ - ...“- ...A - co '- fish) 75%" I‘mni ““1 31 ’3113 13' €111. 1:. E1: " kzlnistl an] - 0 A A 2 Q X A or nice.“ +111... 81 '1' jnij.. £3 + 1311.15. gk + Zn .Yi... k1 ni.kl °kl 810(1) ' 1 Y. 00 - a... A“: 00A " 0 00A '- '-ef-y R[1 “1 “ inn ai ”3 f3 an.jk. gr " gums an] " ° ‘ A 01‘ no 0 +§no o. f r . O A z ’5 I: I ° kln.jkl k]. .300 Owl. 310 L II 70 1 [Y..ko -n..k.};-Zn .3 A ———-3-U ——-2 i i 1 €131.“ fj- A or n..k’4*z a in i. 12.3 n’ ' A 1+ :1]! ti "' nook. gk ‘1' {in kl iikl 1+ on A L3 nuklgk+ or 6.2 . El 3; or . . "' 69 II 13k]. lYijkl (”‘1' Bi "' f 1 g ' 0 J 71 . . 6' 2 . . The coefflclent 6: of ckl 1n the ckl equation is closely related to repeatability as defined by r - 6‘02 c 2. e 2 Then £2... " 6.92 602 - (1:3)/r. For 0.1; the 502 6624-632 e + 60 general value of r for fat production, 1:; - 1.5. r The work of writing and solving the equations is sinplified somewhat if Hand gk are combined into a single parameter, Ul+gk). The general equations then become: A A [4* gk:n (Afg)+zn a «tin. f+ o.ko k i i.k. i j 3k. j 21111 61:1 ° 1'12 A A : Z A at kni.k. (14+ gk) + ni...ai +zjnijufj+ Z A . klni.klck1 Yi... A A Z A 18' fi'jk' ("1 gk) 1 11113.. ‘11 1 11.3.33" 2n 3 Y. kl °jk1 Id" j )+2 " A 3 A 4-: f + °k1 n..kl (u + g ini.kl ai jn'jkl :1 k A 2 n 'I' 6.6 6‘ Y 00k]. W R]. ookl The mechanics of the maximum likelihood method are illustrated by a sample of 15 cows. The mature equivalent records and other necessary information are in Table 32 from which the ckl equations can be written. For instance, the 0 equation is 11 72 3(j4+ g1) + 31+ a2 + a3 + 3H4 + 14.5 on - 11125, where (It? g1) stands for the group of cows born in 191:9, 81 for the year of freshening 1951, on for the first cow of group 1 by year of birth. The coefficient, 3, of (IAN 31) because 011 had three records and be- longed to the group g1. The coefficient, 1, of a 2, and a3 comes 1’“ fr c on: 11 having one 73 Table 32 Sample of records to illustrate method of’maximwm likelihood Lb of.fat in freshening Sum of Year of Cow Inbreeding 1951 1952 1953 records birth number per cent a1 a2 a3 or ck1 19149 °11 h h96 516 1:13 11:25 012 b 353 382 735 °13 0 Mo hos 31:0 1185 c15 8 376 376 1950 021 8 hh9 371 820 c22 8 303 20h 507 C23 0 381 381 02h 0 586 566 1152 025 h h36 hOO 836 1951 c.31 h US? h59 032 8 hBS b85 033 h 320 320 Sum of records of ai 1992 3895 hhél ‘ 103h8 7h record in each of those years. She had three records, and her inbreeding coefficient was I; per cent; therefore, the coefficient of fl; is 3. The coefficient of all other ckl's is zero. The coefficient, 1:5, 0f 011 . 2 is (n Gie ) or the total number of records for the first cow 00k]: + ...—T ’ 0 plus 1.5. The right hand side is 11:25, the sum of the three records of all. Table 33 shows the 15 °kl equations. The rest of the necessary equations can be formed by summing the appropriate terms in Table 33. The ( fl+ g1) equation then is 11(fl + g1) +30 +20 +1c 12 13 3J4 15 + . . . . + 0c35 - M85. The coefficient of (14+ 31) is 11 + Sa1+ ha, + 2a3 + 5f0+ 5:1” 118+ 3011+ 2c * O°21 because the cows belonging to this group made a total of 11 records; of the 11 records five were made in the year a1, five by cows with an in- breeding coefficient of h per cent, and three of them by 011’ etc. The right hand side is the sum of the 11 records. The (14+ gk), 31, and fj equations are given in Table 3h. Since the necessary terms for the Okl's in these equations can be read by going down the correSponding columns in Table 3, they will not be written down again. It is not necessary to solve all 214 of the equations because the and (11+ gk) equations can be absorbed into the a1 and f equations. °k1 The absorption of the c 3 kl equations can be facilitated if two new tables are prepared. Table 35 is formed by taking each number, n, except the en's, in Table 33 and replacing it by (n) n,, 1:]. noon 4. 6.;2 602 Cow equations for illustrative sample Table 33 R.H.S 1b25 °k1 h.5 3.5 h.5 3.5 .fi‘2-sal ll'* g2 .fit+ 33 Cow 735 1185 76h 376 820 507 2.5 3.5 3.5 75 381 1l52 2.5 3.5 3.5 836 LS9 hBS 2.5 2.5 0 320 2.5 2.5 héh h39 2.5 Table 314 Group, year, and inbreeding equations for illustrative sample ROHOS 141185 14+ 33 ... M82 14+ 81 1 3696 2167 1992 3895 76 HH 13% .30 .30 max gm 0:: ON Ins-l AIM Nm MO 3775 2652 O 7 8. m: 09mm: 8.8a oo.4ma 8. 3H m0.-a magma 3. «ma o~.mmm $.03 3.0mm $.03 8.02. om.maz mo. 0mm OmomOm 0004.0 0004.0 0003.0 0004.0 802.0 amen...” awed”; 0002.0 amen...” mquefi 0003.0 «mama 008.~ m~afl.fi 0000. N on AM on n 83.0 823 826 o8:.o 82.0 sums .Eme Emé fipmé ~80. 0 508.0 1:56 fipmé 0004.0 4Em.o 5”me 42mg. $8.0 fiemé 58.0 N 0003.0 0004.0 coo—.70 0003.0 0003.0 0N5”; mNJH.H 80:00 amen...” mNJH.H 0001.10 fibmé 580.0 finhmé ~000.0 Hm mm ..v.‘ N» +3. 000:.0 madden 0000. N mmfi..n 0000. N 28.3300 H the Axm ..va on» one.“ 39.3900 .30 on» Mo 53983.. no.“ unopomh h2.5.0 mm 0.33. 78 The quantity of n..n is the total number oi‘ records made by each can in the corresponding on column. Table 35 is used for absorption of the 01:1 equations into the (Hf 31‘) and the 1‘ equations. Table 36 J is used to absorb the ch 1 by replacing each number, n, except the cki's, in Table 33 by equations into the a equations and is formed n n 1 ..k1 + £2, The reduced equation for ( ’4. 3i) with the cki equations ab- sorbed is h.31h2 (14+ g1) + 2.1238 81 + 1.5238 8.2 + 0.6666 9.3 + 1.8571 :0 + 1.8571 £1; + 0.6000 f8 " 1737.98. The coefficient of (y. g1), h.31h2, is 11 (the element of (14+ g1) in Table 314) minus the sun of the elements of Table 35 for the cows in the ( [4+ gl) column. The coefficient of 9.2, 1.5238, is calculated by taking the element, )4, of 9.2 in the (”i 81) equation of Table 31; and subtracting the sun of the terms in column 82‘ for the cows which had records in the year :12 and also belorged to the (14+ 31) group. The right hand side, 1737.98, is calculated by summing the right hand sides in Table 35 for those cows belonging to the (14+ 31) group and subtracting this sum from the right hand side of the ( M + g1) equation in Table 31;. The £3 equations in Table 37 arefornied similarly. The 111 equations in Table 37 are calculated the same way, except that Table 36 is used instead of Table 35. The equations in Table 37 do not have a unique solution. However, diifemnces among the years and among the classes of inbreeding can be estimated. In this case a3 and to were the bases of comparison. Then, the constants obtained are the differences between 151.3 and each or the 79 0005 00.m00 00.000 00.00H o0.mma m0.0m0 ma.m0m 00.0m0 m0.000 00.0M0 00.0ma 0.0.000 Hm.m00 00.000 00.000 .mOmOm 0000.0 0000.0 0000.0 0000.0 000m.0 000m.0 005m.0 0000.0 000m.0 ~000.0 00 00 0004.0 000m.0 0000.0 000000500 000m.0 0000.0 0000.0 0000.0 0000.0 0m00.0 0m00.0 0000.0 0m00.0 «mmmoo ~NN~.0 0m00.0 0m00.o 0000.0 0000.0 300.0 0m00.0 0000.0 0m00.0 0000.0 N“ a 0:» 09:0 uncapmsve 0000.0 080.0 0000.0 0000.0 0000.0 HG H3 000m.0 0000.0 0000.0 0000.0 0000.0 mm+~s 000m.0 00sm.0 0000.0 000m.0 000m.0 N e on» no noapnuoene new enopoem m +Vfl 0000.0 000m.0 0000.0 000m.0 0000.0 aw +qfi 300 0m canes 80 m0. m0m0 00.0000 00.0000 00.0000 00.0000 mm. m8 00.0000 00.0000 00.0000 .0540 «Jam.m 0000. 0 00m0.0 0000.0 0000.0 0400.0 0000.0 0 madm.m 0 0000.0 momH.H md00.0 000N.H ~0mw.0 00m0.0 00 0 0 0000. m 0000.0 m000.0 0000.0 0000.0 00m0.0 0000.0 00 N0m0.m ma0m.d 000M.H mmda.0 w0wm.Ha 0000.0- 0000.m 00H0.H 0000.0 m w 00m0.0 0000.0 m000.0 0000.0- .0000.0 0000.0- 0 00000 0000.0 0000.0 0000.0 0000.0 0000.0- 0000.0- 0000.0 0 0 wmmH.m .00 00000000 0. H: 000N.H 000N.H 0000.0 0000.0. 0000.m 0 0 mm +040 0000.0 0000.0 0000.0 0000.0 0000. 0 0 0 0000.0 0 0000.0 0000.0 0000.0 0000. 0 000m.0 030. 0 0 0 0.00mi o 0003.0020000000 cmesvom 0m 00000 81 other levels of a1, and similarly for £0 and the inbreeding constants. Fixing these bases requires deletion of the a and f0 equations and 3 elements in other equations, both rows and columns. The solution to the equations in Table 37 then is: (a + g1) - L13.2, (14" 82) ' 105-2: (fih 83) ”1897.0, a1 - 38.2, a2 - 60$, a3 .- 0, f0 - 0, fl; " ~23.9 and f8 ' ~52.8. These are all in pounds of fat. Logically the inbreeding constants should be measured from the zero class, but perhaps the estimates for years should be in terms of deviations from the mean of all years. This is done by subtracting the mean of the years, 32.9, from each year. Then the year constants become: a1 " 5.3, 82 - 27.5, and a3 - 032.9. The con-starts far the (14+ gk)'s are estimates of the average producing abilities of the cows belonging to each group under the average environment of the three years and also if they were inbred the average of the population. This maximum likelihood method was used to estimate the effects of inbreeding on milk and fat yield With 586 records of 211 cows producing in the Michigan State University inbred Jersey herd from 19148 to 1961;. Records prior to 1951 were made in Califomia. Constants were fitted for 17 years. The cows were classed in intervals of 3 per cent of inbreeding except that those With no inbreeding were left at Zero and all those over 1:2 per cent were placed in one class. This made a total of 16 classes of inbreeding. The 17 groups of cows were trade according to When the cows were born. Group one was those cows born in 19145 and groups were numbered consecutively for each year up to 1962. Estimates 31.: repeatability. Intracow correlations from the data were near .14 and .5, repeatabilities used in the maximum likelihood 82 equations. Henderson et a1. (1959) indicated the repeatability used depends on the choice of grouping; hence, the data were divided into groups by year of birth, and the results are shown in Table 38. Stan- dard errors of the intraclass correlations were approximated by the method of Osborne and Patterson (1952). Maximum likelihood estimates. Tables 39 to bl show the solution of the maximum likelihood equations. Table 39 gives the estimates of the producing ability of the herd where the cows were inbred as much as they actually were and produced under an environment Which was charac- teristic of an average for all years. In Table ho estimates of the average yearly environmental effects are recorded, and Table ’41 gives the coefficients for the effect of in- breeding for each of the 16 classes. These inbreeding constants are measured from the zero class, and the environmental constants are mea- sured from the mean deviation of all years. 83 H 0000.~ + N 00004060090 + m .w.r..m 00.000. 000000. 000000. 88%. 000mg. 000 0000 sum 2000903960 000.53 you 0.0. I a. 9.6.0330. .0000 000.0 .. 00.3090 .00 .0305: 00825 I a 00.0.00. .NNO 0000 00000 00000 an.“ 05 00.80000 0030 00.000. 0000000 0000000 0000000 0.0.00 mm0 000.0: a: a 00-5 0. 000-00 00000-5. 00 0 .. 00m 0 .. 3000030902 ... .0 0060 c0958. send-0.0.0» .00 30089000 I 0 00m «00 00 30.0 0000003808 .30 850.0% .00 3.0084 3.0000 306.00 \830 0002500 2008.00 noosaom 80040.3» as 8.0050 8.3% 8h Table 39 Maxim likelihood estimtes of group constants using repeatabilitiea of .50 and .110 birth) cows m cords 9_._§_9_ 9:112 9352 9&9 191:5 2 l6 7729 7887 377 383 1:6 1 9 83514 8510 367 373 h? 1 8 5571; S737 273 282 148 3 18 6580 6702 355 359 h? 6 36 7198 7331: 3&2 3h? 1950 11 6o 7&28 7637 381 388 51 5 8 7125 7331 1:03 I412 52 9 23 6337 6921; 3241 352 S3 21 53 73 20 71131 386 391 Sh 1b 141 7276 7387 373 378 SS 17 38 67911 6880 363 366 S6 26 83 7761. 78143 1.15 1:17 57 25 116 6813 6880 358 360 58 22 52 61:91 6538 356 355 59 1h 39 6755 6812 372 373 1960 11. 32 61.22 61:59 356 356 61 20 an 6099 6132 359 360 85 ‘Ifable ho Iearly environmental deviations from maximum likelihood with repeatabilitiea of .5 and J4 Year of Number of Milk 1b Fat 1b calving records 9:52 9:32 9:19. 9:33 1918 3 1311s 1278 no 108 h? 3 79 113 62 59 So 6 -715 Jib? -9 -10 51 12 -717 ~7h8 ~31 ~32 52 18 598 553 30 28 53 28 31:6 300 20 19 Sh 31 8 13 -S «7 55 M -810 .8h2 -hh -h6 56 h? ~61: -80 -15 -15 57 18 -9 -22 .11 ..u 58 Sh -60 -56 -9 -9 59 53 -222 .187 .21. -22 1960 57 239 288 5 7 61 m; -1; .20 .15 4.3 62 51 -3 28 -280 411 4.1 63 36 188 2147 .11; .11 ea 16 157 231 -9 -6 86 Table 141 Maximum likelihood estimates of inbreeding constants using repeatability values of .50 and .140 Ezra? 141.225.3386: 9&2 11111: “211.19 922 Fat lb 52:129. 0 131 o o o o 1-3 36 113 13.1 2.6 2.5 h—6 31 .82 .79 -2.1 -2.o 7-9 1h -36 -31; .1.? 4.5 10.12 113 .13 —16 .1.? -1.6 13.15 21 .12 .11 -6.8 ~?.3 16.18 13 38 38 3.0 3.8 19-21 23 Sh 53 2.9 2.9 22—211 36 58 S? 3.2 3.0 25-27 53 33 3o 2.h 2.5 28-30 65 -22 -20 —11.0 .10.1 31-33 35 .19 .18 4.9 -1.9 3h-36 38 .23 -20 ~2.7 -2.7 37-39 2h .11; .15 -.S -.5 Ito-1:2 17 -65 -65 -1.8 -1.8 to 6 .132 .130 -6.3 4.0 DISCUSSION E5452. and variation. As the mean increases the variance tends to increase; therefore, a fraction often relates the standard deviation to the mean of the sample as a fraction of the sample mean, the resulting statistic being the relative standard deviation or coefficient of variation. Results from the several characteristics can be compared more meaningful by the relative variation since may of the measurements did increase with the age of the animal and since they so diverse in mean and variance. Table 112 lists the means, standard deviations, and coefficients of variation in per cent for each character from three months through fourth parity. Since the coefficient of variation is a ratio of two averages having the same unit of measurement, it is itself independent of the unit euployed. Thus, it is in standard measure Whether inches, feet, or centimeters are used for the original measurement. Figures 1 through 7 show graphs of the means, standard deviations, and coefficients of variation listed in Table hz. The coefficient is informtive and useful in the presence of the mean and standard deviation because an increase in the coefficient can be due to a rising standard deviation or a falling mean. Likewise a saw-tooth appearance of the coef- ficient curve may result from irregularities in either the mean or stan- dard deviation or both. he mean weight and wither height are compared to the Ragsdale standards for Jersey cattle, (Petersen 1950). The animals used in this study were slightly lighter at birth, at twelve months of age, and at first and second parity than the average Jerseys reported by Ragsdale. However, the average weight at three, six, 87 88 0mm some pa owpmwugommfio nose new dogmas?» Mo 3:33.303 nae «emowpmfirme Ravage .3on N: adobe 89 m.m ~.H m: m.~ H.: an «.4 H.: mm ~.m m. m 2. ~.m p.~ mp m.H m.~ ofi m.» :3 he; o.m a.a m: .2 mid dcm m.: cm H.m N.w Hu .3 H.m He m.~ ~.m Fwd a. m.“ a. zed «mod .aonm enemas up agenda om usages a: menace om newscasmwee pm owe spa 132$ FINN-=1 .wefisamo some geeks usages m swamp engagememees one mpnmflezta e3 o.~ .3 9m o.m RH mo: 0.: am ~.m o.m mo ~.m w.~ mo m.~ H.m mun m.od m.NOH Ham sham 325 m.: in 4.m H.a ~.m me ~.~ m.m NS“ ~.m o.: w.H an m.m 0.: mad o.m Hood w.«c. «do ma Hem p.d an o.m m.m woe o. m 3 a ”.4 3 em as we mm an 3 e3 «.fl mag 13 NH A2335 3m mA cm Now new we :6 w.m 00 dm a. N 2 3 as a; a... 0.: am man a. mm as o o omd .13 ea mm a; ed He no a. m .2 9m o.~ mm 9m 0. N mm m.m o.m me e. «H m.oa «Ma m 0.900 .96 A33 999 an op gem .>.o .Q.m 680v mean N on mumspwz .>.o .n.m aaov mafia M 3 anemia .>.o .n.m A23 space M pmoso .>.o 0Q.” Afiv N ohao guano .>.o onemw AEOV N as mmnpfis c>.o .96 moms H. a: an: caveanopoehmso soapmpoma seesaw op spawn Seam nowpmwnm> mo pseaowmmeoo new :oapww>ov camcnmpm epzmfloa mmmpmbe Mo sumac .H maswam Mean Weight in Pounds Homo HOOO omo woo mmo moo Qmo Q00 mmo moo mmo moo emo $00 umo mmo woo Hmo H00 m0 0"--.C gull-0.9.36 wmmmmmwe mamsmmuam Sons Smpmvd mamsnmua bodnmdpo: ooomwuoueSd ow e mo nacho .m cheese Mean Chest Circumference (in) gems owned npuosaweueboo 4». mumsnmun bedpmwpos qo ..-}--.Oaicsfi ooomwuopenn 0H.