SOME FACTORS AFFECTING PRODUCTION TRAITS IN BRAHMAN CATTLE IN MEXICO ThBSIsfortheOegreeofM.S. MICHIGAN STATE UNIVERSITY MANUEL VILLAIIREAL 1975 ABSTRACT SOME FACTORS AFFECTING PRODUCTION TRAITS IN BRAHMAN CATTLE IN MEXICO by Manuel Villarreal“ The purpose of this study was to determine the relative importance of some environmental factors influ- encing production traits and to estimate heritabilities for the traits after adjusting for the effects of these environmental factors in a Brahman herd in northeastern Mexico. The data included records on 1130 Brahman calves born over a 13-year period 1961 to 1973 inclusive, at a ranch on the gulf coast of Mexico (Huasteca Potosina). The animals were kept under range conditions to two years of age. .Traits studied were birth, weaning, yearling and two-year weight as well as average daily gain to weaning, weaning to yearling and yearling to two-year old. The influence of age and sex of calf (bulls or heifers), age of dam and year and month of birth on the traits studied 1 Manuel Villarreal was analyzed by the method "Least Square analysis of data with unequal subclass numbers" (Harvey, 1960). All the factors were shown to have highly significant influences (P < .01) on the traits except age of dam did not have a significant influence on postweaning growth and two—year weight and month of birth did not have a significant effect on birth weight. Least square estimates of the mean performance for each of the factor-trait combinations was calculated. The mean values found for age of dam effect on influenced traits increased with age of dam from 3 to 8 years of age and slightly declined after 10 years of age. An unusually high value was found for effect of the 2-years-old age of dam class. The later onset of puberty in Brahman cattle is the apparent reason for this unusual effect. The least square means for sex showed that bulls were heavier than heifers by 1.2, 15.6, 30.8, 59 kg for birth, weaning, yearling and two-year weight, respectively. Month of birth values indicated that calves born before summer (when the grazing conditions are best) had the highest weights and gains. Calves born during the rainy season (May through August), had the lowest growth Manuel Villarreal rate. There was not a defined trend over the rest of the year. Linear regression coefficients of .337, .295, and .323 kg per day were calculated for age at weaning, year- ling and two-years-old weights, respectively. Paternal half-sib heritability estimates were: birth weight, .27; weaning weight, .48; yearling weight, .44- two-year weight, .29; average daily gain to weaning, .l9; and ADG to two years .09. .40; ADG to yearling, SOME FACTORS AFFECTING PRODUCTION TRAITS IN BRAHMAN CATTLE IN MEXICO, BY Manuel Villarreal A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Animal Husbandry 1975 TABLE OF LIST OF TABLES. . . . . . . . INTRODUCTION. . . . . . . . . REVIEW OF LITERATURE. . . . . Birth weight 0 O O O O 0 CONTENTS Page 0 O O O O O O O I I O O 3 Average Daily Gain to Weaning . . . . . . . . . 6 Weaning weight. . . . . Average Daily Gain from Yearling Weight . . . . Two-Year Weight . . . . Interactions of Certain Calf Performance. . . Heritability Estimates. DATA AND ANALYSIS METHODS . . Data. . . . . . . . . . Method of Analysis. . . Heritability Estimates. 0 O O O O O O O O O O O 9 Weaning to Yearling . . 13 ii TABLE OF CONTENTS (cont'd.) Page RESULTS AND DISCUSSION. . . . . . . . . . . . . . . . 35 Factors Affecting Production”Traits . . . . . . 35 Heritability Estimates. . . . . . . . . . . . . 43 SUMMARY 0 O O O .1 O O O I O O O O O O O O O O O O O 0 4 5 BIBLIOGMPHY O O O I O O O O I O O O O O O O I O O O O 4 7 iii Table 10. LIST OF TABLES ISUMMARY OF BIRTH WEIGHTS OF BEEF CATTLE BY BEED AND SEX. O O O O O O O O O O O O O O O ESTIMATES OF AGE OF DAMQEFFECT ON PREWEANING G ROWT H O O O O O O O O O O O O O O O O O O 0 SUMMARY OF HERITABILITY ESTIMATES FOR BEEF CATTLE CHARACTERISTICS . . . . . . . . . . . SUMMARY OF HERITABILITY ESTIMATES REPORTED FOR BMHMAN CATTLE O O O O O O O O O O O O O DISTRIBUTION OF BIRTHS By AGE OF DAM . . . . . ANALYSIS OF VARIANCE FOR FACTORS INFLUENCING VARIOUS BEEF PRODUCTION TRAITS . . . . . . . LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR SEX. O D O O O O O O O O I 0 O O O O C . LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR AGE OF DAM . . . . . . . . . . . . . . . LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR MONTH OF B IRTH O O O O O O C O O C I O I PATERNAL HALF-SIB HERITABILITY ESTIMATES AND STANDARD DEVIATIONS. . . . . . . . . . . . . iv Page 19 21 26 36 37 38 41 43 INTRODUCTION It is well documented that sources of variation such as age, sex, year, and month of birth of calves and age of dam have important influences on growth rate of beef cattle. The accuracy of any evaluation of genetic differences among animals is increased by adjusting the data for these environmental effects. The greatest in- crease in accuracy is obtained when the adjustment fac- tors used have been develoPed from animals raised under the same conditions as those existing in the population being studied. Estimates of the relative magnitude of these en- vironmental sources of variation on Brahman cattle in Mexico are scarce. The pOpulation in this study is dif- ferent enough in climate and management to assume differ- ences in performance from populations previously studied.- We were interested in evaluating environmental sources of variation in this cattle pOpulation and eval- iuating genetic differences among animals after the effect of these environmental factors had been removed from sire l effects. To do this a mathematical model was used which fit all of the above environmental effects and sire effects simultaneously. The specific objectives of this study include the following: 1. Estimate the influence of the following factors: a. Age of dam b. Sex c. Age of offspring d. Month and year of birth On the following production traits of Brahman cattle: a. Birth weight b. Weaning weight c. Yearling weight d. Two-year weight e. Average daily gain to weaning f. Average daily gain to yearling g. Average daily gain to two years 2. Obtain heritability estimates for the same productive traits. REVIEW OF LITERATURE Very few studies have been conducted on Brahman cattle to evaluate the influence on performance of sev- eral factors such as age, sex, month and year of birth of calves and age of dam. These sources of variation are widely known as having an important effect on the performance of cattle. For this review we have concentrated our efforts on studies dealing with beef breeds. The similarity in management and production goals among these breeds make the findings of the studies relevant to the present study. In order to present this review in a logical man- ner we have chosen to study each of the sources of varia- tion as affecting the traits of interest. Birth Weight Sex of Calf It has long been noted that bull calves are sig- nificantly heavier at birth than heifers. Among the beef 3 breeds the sex difference ranged from 1 to 3 kg. Among others, Burris and Blunn (1952); Dawson et al. (1947); Gregory et al. (1950); Koch and Clark (1955); Koch et al. (1959); and Brink et al. (1961) have contributed to es- tablish this. Burris and Blunn (1952) found the weight differ- ence among sexes to be associated with the longer gesta- tion length of bull calves. They also reported a net .5 difference even when the weights are adjusted for gesta- tion length. Birth weights by breed and sex are reported by several authors as shown in Table 1. TABLE 1 SUMMARY OF BIRTH-WEIGHTS OF BEEF CATTLE BY BREED AND SEX3 Breed Male Female Source Hereford 31.8 29.7 Burris & Blunn (1952) Hereford 32.0 31.2 Dawson et al. (1947) Hereford 35.5 33.7 Brinks et al. (1961) Angus 30.5 28.1 Burris & Blunn (1952) Angus 28.3 26.3 Alexander & Bogart (1961) Shorthorn 30.3 28.1 Burris & Blunn (1952) Indobrazil ' 27.7 25.2 Mattoso (1959) Nellore 26.2 23.3 " Guzerat 28.3 26.7 " Git 21.7 20.2 " akg. Age of Dam The research studying the influence of age of dam on birth weight in beef cattle conclude in general that the birth weights of calves increased with age of dam un- til 6 to 7 years of age, the greatest change being be- tween the ages of 3, 4,'and 10 years or older (Burris and Blunn (1952), and Koch and Clark (1955). It has been re- ported by Dawson et_al..(l947) in a regression study of birth weight on age of dam a linear increase of .100 kg for each increase of one month in the age of dam to six years of age. The regressions done separately for males and females did not deviate significantly from linearity. Month of Birth Koch and Clark (1955) found that calves born later in the calving season were slightly heavier at birth. This slight difference could be due to better pasture conditions or possibly to the weight difference caused by variation in gestation length of cows. The regression of birth weight on weaning age reported was -.04 kg.per day. Everett and Magee (1965) reported significant effects of years and seasons on birth weight in Holstein calves. Brown and Galvez (1969) found differences due to season of birth on birth weight. Beltran 25411. (1975) reported a significant year and month of birth effect on birth weight of Brahman cattle. In general these authors agree with Koch and Clark (1955) indicat- ing heavier weights at birth for calves born later in the calving season. In these studies the calving sea- sons were about 90 days in‘the spring. Average Daily Gain to Weaning Sex of Calf Several authors have reported that sex has a highly significant influence in preweaning growth. Mar- lowe §£_31. (1965) and Marlowe and Gaines (1958) found that steer calves grew approximately 6% faster than heifer calves and bull calves grew approximately 6.6% faster than steer calves. This represents in a 210 ad- justed weaning weight that males outweigh heifers in 12.23 kg and 22.70 kg respectively. These differences were somewhat larger when all calves were creep fed. Brinks e£;313 (1961) reported a difference of 0.04 kgs in ADG in favor of steers over heifers. Koch gt_gl. (1959) found that bull calves gained 0.050 kg faster per day or 1.075 times greater than heifers from birth to weaning. Rollins and Guilbert (1954) found that when growth was at a high level throughout the season, bulls gained .06 kg per day faster than heifers during the first 120 days. Cunningham and Henderson (1965) in a similar study found a difference of 0.05 kg in ADG be- tween bulls and steers and a difference of .06 kg be- tween steers and heifers. Age of Dam Brown (1960), Cunningham and Henderson (1965), Marlowe et_al. (1965) and Francoice et_al. (1973) con- cluded that calves‘ gains increased with age of dam from 2 to 7 years. There was no significant difference in gains of calves from 7 through 11 year old cows. Calf gains decreased slightly as cow age increased beyond 11 years. The values reported by Cunningham and Henderson (1965) are presented in Table 2. TABLE 2 ESTIMATE OF AGE OF DAM EFFECT ON PREWEANING GROWTH (Cunningham and Henderson (1965)) Age of Dam (years) ADGa -.118 -.O72 -.031 -.016 6 -.011 7-10 .00 >10 -.013 Ulnwa kg. Month of Birth Marlowe et_al. (1965) pointed out the influence of month of birth in the preweaning growth. Calves drOpped during March and April made fastest gains when other environmental factors were held constant. Calves born during August and September made the slowest gain. This difference was approximately 0.11 kg per day for non-creep calves. Creep feeding tended to decrease the magnitude of these differences. Rollins and Guilbert (1954) reported that calves born during August through November 15 gained .12 kg per day less from birth to 4 months of age than calves born ' during March through May. Calves born from November 15 through February were intermediate in growth rate. Simi- lar findings were reported‘by Lehmann, et_§1. (1961). Koch and Clark (1955) reported a non-significant influence of time of birth on preweaning growth. Nelms and Bogart (1956) and Swiger et_al. (1962) reported that early calves gained at a considerably higher rate than did calves born late in the calving season. Year of Birth The effect of year has been found highly signifi- cant by Cunningham and Henderson (1965) and Marlowe gt El° (1965). The last study also reported a breed by year interaction for ADG to weaning. WeaningyWeight Age at Weaning The comparison of animals for genetic differences requires that the calves are compared at a constant age. Some correction factors are needed to put the calves on an equal basis. According to Marlowe et al. (1965) as '10 calves increased in age their gains decreased. In the same study it was shown that growth is essentially linear for non-creep—fed calves from 120 days to weaning. A previous study by Swiger et_al. (1962) reported a linear regression on age“from birth to 130 days, but a significant curvilinear effect from 120 to 200 days; how- ever, their age and seasonal effects were confounded. Johnson and Dunkel (1951) reported a linear correction factor of .460 kg per day based on 182 days weaning weight. Kroger and Knox (1945) found the regression of weight on age to be .602 kg per day. Botkin and Whatley (1953) reported a value of .66 kg per day for Hereford calves. Burgess et_al. (1954) found a value of .75 kg increase in weight for each day increase in age of calf. Sex of Calf As a consequence of the higher growth rate of males they tend to haVe higher weights at weaning. In general reports in the literature indicate an average sex difference range from 12-30 kg. Studies that in- cluded all three sex classes indicate an average differ- ence of 15-30 kg between steers and bulls and of 12-20 between steers and heifers. It is also suggested that 11 the bull-steer difference can be affected by the selec- tion involved in retaining the better male calves as bulls; Koch and Clark (1955); Botkin and Whatley (1953), Burgess et_al. (1954); Brinks et_al. (1961); Cunningham and Henderson (1965); and Marlowe et_al. (1965) have discussed the effect of sex of calf on weaning weight. Age of Dam Weaning weight and preweaning growth are an ex- pression of the genes trasmitted to the calves and the‘ maternal environment they are provided. Physiological change in function such as increased milk production which may accompany the aging process might be expected to influence the offspring's environment. Research has shown that age of dam affects the weaning weight of calves presumably through changes in udder development, milking ability and cow's ability to withstand the rigors of range conditions (Koch, 1951). In general the researchers agree that the wean- ing weight increased steadily from two to six years of.' age for the dam and then declined after 10 years. Bot— kin and Whatley (1953), and Koch and Clark (1955), Bur- gess et a1. (1954), Rollins and Guilbert (1954), Rollins 12 and Wagnon (1956), Kroger and Knox (1945b), Lehmann gt El: (1961), Francoise et al.(l973) and Cundiff et al. (1966) have contributed to the study of this matter and presented different sets of c0nstants. Month of Birth Reports in the literature are in close agreement about the effect of month of birth. Brown (1958 and 1960), Marlowe and Gaines (1958),'Marlowe (1962), Mar- lowe g£_al. (1965) and Cundiff eg_al. (1966) have con- cluded that calves born in February, March and Aprilhad an advantage in adjusted 205-day weaning weights over those born in any other season. Calves born in August, September and October were at the greatest disadvantage. There was a steady increase in weights of calves born from November through March. Year of Birth The effect of year on weaning weight has been re- ported to have a highly significant effect by Brown (1960), Swiger (1961) and Cardellino and Frahm (1971). 13 Average Dailngain from Weaning to Yearling Few reports are found in the literature in which studies of post-weaning gain had been conducted. Most of the research has been oriented to a lifetime growth rate (birth to final weight) hence the factors affecting pre- weaning growth would be of similar importance. We will present a review of literature in both cases. Sex of Calf Guilbert and Gregory (1952), Dahmen and Bogart (1952) and Swiger (1961) have reported a gain difference between heifers and bulls of up to .25 kg. The study of Swiger included comparison in various post-weaning periods of the sex differences. He found an increasing trend in gain difference between sexes. In these studies all ani- mals were fed the same ration. Age of Dam Some studies have reported significant age of dam effects on the lifetime growth rate of yearling cattle (Koch and Clark, 1955; Shaller and Marlowe, 1967; and Tay- lor, 1967). In a study by Waugh and Marlowe (1970) it 14 was shown that the size of coefficients reported were only one half to three-fourths the_size of the constants estimates reported by Marlowe e£_gl, (1965) for weaning calves, the decrease in the size of the constants appears to be simply a result of spreading the differences at weaning over an additional period of the animal's life. This is in agreement with the findings of Swiger EEEE£° (1963) who reported no significant effect of age of dam on gains during the post-weaning period. A nonsignifi— cant effect of age of dam on ADG to yearling was also re— ported by Brinks et al. (1962). -Month of Birth According to Waugh and Marlowe (1970) mOnth of birth appeared to have no significant influence on the continuous growth of yearling cattle. YearlinggWeight Age of Yearling Brinks et al. (1962) reported age of animal to ”'have a significant effect on final weight. The regression 15 of yearling weight found was .754 kg per day based on a 376-day yearling age. Sex of Calf Brown e£_gl. (1956a and 1956b) reported an aver- age yearling weight difference of 60 kg between bulls and heifers at yearling. The studies on ADG to yearling mentioned earlier support this difference given the high- er lifetime bull's gain. Age of Dam Koch and Clark (1955) reported that the yearling weight increased progressively with the age of dam until the cow reached six years old. However, other studies suggest that this may be due to the effect of age on pre- weaning growth (mentioned when reviewing post-weaning gain.) Month of Birth Waugh and Marlowe (1970) in a study on supple- mented yearling cattle reported a nonsignificant influ- ence of month of birth on continuous growth. 16 Year of Birth Waugh and Marlowe (1970) reported a highly sig- nificant year effect on yearling weight. Two—Year Weight No reports are found in the literature about in— fluences on cattle performance to twoyears of age. The characteristics of rapid growth of the British origin breeds studied, the intensive post-weaning management in contrast with the lower growth on range conditions of Brahman cattle, limit its importance. We believe that the sources of variation with effect on post—weaning growth will tend to have a simi- lar effect on growth and weight to two years old. Interactions of Certain Factors of Calf Performance Several authors have conducted studies to deter— mine the importance of interactions in beef cattle data, since the assumption of zero interactions may lead to l7 biased estimates of the effects studied. Landblom (1954) reported a significant interaction of sex and age of dam using an approximate method for testing the significance of the two-factor interaction and the three-factor inter- action involving sex, age of dam, and year. Swiger (1961) tested the significance of all two-factor interactions in- volving age of calf, year, sex and age of dam, and found only the interactions age of calf by sex and age of dam sby year to be significant. Panish etggl.’(l96l) reported a significant sex by year interaction, but no evidence of a sex by sire interaction within ranches and years. Ver- non g£_gl. (1964) reported the interaction between age of dam by years. The effects of age of dam were larger in poor years. Harwin et_gl. (1966) in a study on all the two-factor interactions involving year, sex, mating sys- tem, age of dam found the interactions effects of year x age of dam, sex x age of dam, sex x mating system, and year x age of calf significant. Schaeffer and Wilton (1974) also reported a significant age of dam x sex in- teraction and age of dam by level of herd performance. Other studies have reported a nonsignificant age of dam by sex, age of dam by creep feeding and sex of calf by creep feeding interactions. See Cunningham and Henderson 18 (1965) , Cundiff e_t_a_l_._. ((1966) , Cardellino and Frahm (1971), Marlowe and Gaines (1958). A study on all three-way interactions involving age of dam, sex, and environmental factors was reported by Schaeffer and Wilton (1974). There was no evidence that three-way interactions were significant except for age of dam by sex by feeding system for Herefords. The practical importance of these interactions is limited to the extent of the degree of improvement by using them on the beef cattle selection programs. None of the interactions appear to be large enough to justify including them in correction factors used to adjust for environmental effects. Such corrections are not yet recommended by the Beef Improvement Federation (1974). Heritability_Estimates The literature contains numerous studies of her- itability estimates for economic traits in beef cattle. Warwick (1958) summarized those which were known up un- til that time. Using the Warwick's summary as a base 19 Dunn (1968) reviewed the literature. His attempt to summarize heritability studies since Warwick completed his summary are shown in Table 3. TABLE 3 SUMMARY OF HERITABILITY ESTIMATES FOR BEEF CATTLE CHARACTERISTICS Character No. of Av. of Range of Estimates Estimates Estimates Birth Weight 17 44 11 - 100% Weaning Weight 40 35 -12 - 100 Final Feed Lot Weight 17 55 2 - 100 Long Yearling 10 40 10 _ 71 Pasture Weight The estimate is a simple arithmetic average of the values reported by the research workers.. No attempt was made to adjust values to number of head of cattle included and variance of the estimates. When more than one value was reported (different sexes, different breeds, different planes of nutrition, etc.) one com- bined average value was obtained. 20 Gregory (1961), and Clark et_gl. (1963) presen- ted summaries similar to that of Warwick. Petty and Cartwright (1966) prepared a summary of genetic and environmental statistics for growth and conformation traits of young beef cattle. They presented unweighted and weighted averages of paternal half-sib estimates. The weighted average estimates were obtained by weighting them with either the number of sires in— cluded in each estimate or the estimated number of sires based on the average number of offspring per sire in the other estimates of that trait. These estimates are essentially the same as those reported by Dunn (1968). The authors tried to select the most independent and pertinent information available dating back to the first studies (1946). Very few reports are found in the literature on heritability estimates of productive traits in Brahman cattle. Authors and estimates are presented in Table 4. All these estimates were obtained by paternal half-sib method. 21 TABLE 4 SUMMARY OF HERITABILITY ESTIMATES. REPORTED FOR BRAHMAN CATTLE 1* T R A I T AUTHOR Birth Weaning ADG Feed Lot Weight Weight (weaning) Gain Berruecos and Robison (1968) '41i-16 .47i.18 .43:.17 f, __ Miquel and Cartwright .16 .44 —_ -_ (1963) Beltran et al. DATA AND ANALYSIS METHODS Data The performance records of 1,130 Brahman calves raised at a privately owned ranch located on the Gulf Coast of Mexico (Huasteca Potosina) during the period of 1961 through 1973 were used in this study. The climate of the area of study is classified as Aw according to depen's climatic classification. This tropical climate is characterized by a dry and rainy season with 75% of the average annual rainfall, ’1200 mm., occurring from May to November. The ranch is a purebred Operation under resident management.‘ The animals graze on improved pasture of tropical grasses including Pangola (Digitaria decumbes) and Guinea (Panicum maximun) with limited supplementa- tion during adverse weather conditions.‘ The calves were weaned in approximately the seventh month after the month of birth. 22 23 Data were collected by the ranch personnel super- vised by the staff of the Mexican Livestock Research In— Stitute, Mexican Department of Agriculture (Instituto Nacional de Investigaciones Pecuarias, Palo Alto D.F.). The information available for each animal was the follow- ing: identification number, sire, dam, age of dam, birth date, birth weight (BW), weaning weight (WW), yearling weight (YW), two-year weight (TYW) and days of age for each of the weights. The average daily gains were calculated in the following manner: To weaning: ADW = (WW - BW) / weaning age From weaning to yearling: ADY = (YW - WW) / (Yearling age—weaning age) From yearling to two years old: ADT = (TYW - YW) / (2 years age-yearling age) 24 Method of Analysis @2921 A mathematical model that would describe the sources of variation was selected for each of the traits of interest. The objectives of the study and the data available determine, in part, the elements of the model. For traits weaning weight, yearling weight and two-year-old weight the model was Model I. Model I ' ,_ = + Bi + d + + + An + blx ,. yijkmnp U j Yk pm ijkmnp+ eijkmnp Where: Y.. . . . . . ijkmnp = an observation on weaning weight, yearling weight or two years weight n = constant to all observations . .th . B1 = a random effect common to progeny of the i Sire i = l...27 Bi assumed to be normally2 independent, distributed with mean zero and variance 0: which is symbolized as NH>(0,cfi ) fixed effect due to jth age of dam Q II j = 2...10, >10 fixed effect due to kth sex .< ll k = 1, 2; l = bulls, 2 = heifers 25 th fixed effect due to m year pm = m: 1.0013 . ' th 1n = fixed effect due to n month n = 1...12 b1 = regression coefficient of yij p on age .. th . X,, = age of the ijkmnp observation ijkmnp . . .. th . e,, = random error assoc1ated With ijkmnp observation ijkmnp assumed to be: e ~ NID (O, 0:) For traits birth weight, average daily gains to weaning, yearling and two years 61d, Model II was used. Model II was the same as Model I except the co—variant for age was deleted. Interactions were not included in the model be- cause work by other authors has shown that the interac- tions of these factors were not of enough biological im- portance to include them in any correction of data for performance record programs. It was decided to use the age as a co-variant rather than adjust the weights to a constant age by using the average daily gain for each animal for some fixed number of days. 26 The ages of dam were from 2 to 10 years and cows over 10 years of age. The calving was spread through the year with less number of births during September, August and October. The distribution of births by age of dam is shdwn in Table 5. TABLE 5 DISTRIBUTION OF BIRTHS BY AGE OF DAM Age of Dam No. Births 2 16 3 136 4 106 5 87 6 99 7 102 8 103 9 87 10 73 >10 321 27 The method of analyzing used was the one described by Harvey, “Least Square Analysis of Data with Unequal Sub- class Numbers“ (1960). The method of Least Squares is based upon a philos— ophy of deriving estimates which minimize the probability of error, which can be expressed in the following way: n X Y - E (Y.) _ .1. The idea is to minimize predictor error by minimizing the squared error. The process is described as follows in matrix notation, Our basic model is of the form:1 x = Xb + 2 Where ylis an n x 1 vector of observations; b_is a p'x 1 vector of parameters (levels of factors); and e_is a vec- tor of random error terms. The matrix §_is n x p of 0's and 1's. It is called the designed matrix or the inci- dence matrix, because the location of 0‘s and 1‘s through- out its element represents the incidence of terms of the model among the observations and hence of the classifica- tion in which the observation lie. In Model I where age 1Underlined small case letter = vector; underlined large case letter = matrix. 28 is used as a relationship variable, the value of the ob- servation is used instead of the l or o of the classifi- cation variables. Using the calculus procedures to obtain the mini- mum value for Le2 we can derive a set of normal equations used to solve for b. In matrix notation the normal equa- tions were: B d. H i j Yk pm gn b l r— — r- -v — ‘— n..... n..... n..... no. 0. n... 0 no... x00... g Y..... i J k m n n..... n..... n....o n.. o. n.09 o n.090 X.oooo g. Y..... i i l]. J.k i In 1 n i i i n. 0.. n 0.. n. .0. n. 00 no.0 I n. O. X. .0. g Y. 0.. J 13 3 3k J m J n J J J n.. O. n O 0. no 0. O. .9 no. 0 n.. 0 x0. .0 Y.. O. k 1 k 3k n k km k n k Yk k n... o n... o no... 0 n.. 0 nos. 0 n... X... o 5 Y... o m i m j m km m mn m m m n....n n.... n. .. n.. . n... n.... X.... A Y....n i n j n k n mn. n n n XOOOOO x..... x..... x.. O. x... 0 x0... b 1 J k m n. J L1H I... _ zzzzzzxii ijkmn’ p 3 p ZZZZZZX, ‘I’ Y. . ijkmnp ijkmnp ijklmn 29 The normal equations for Model II were the same except that the column and row correspondent to 81 was deleted. The §f§_matrix is not of full rank because the sum of the equations for each set is equal to the sum of each other set and to the N equation. i Thus the inverse does not exist and the equations can not be solved. In order to obtain a set of solutions some restrictions must be imposed. One method used to ob- tain a full-rank matrix is to impose the restrictions that sum of effects for each set is equal to zero. For Model I the restrictions are: When restrictions are imposed the coefficients of one equation in each of the sets must be subtracted from other coefficients in the set by columns and then by rows. This gives a restricted §f§ matrix and correSponding Right Hand Side (R.H.S.). In our study the restrictions required to develop the restricted §f§_matrix and R.H.S. were imposed as the individual data were read into the computer. To do this we generated variables by setting a Specific dummy variable 30 equal to l for each of the d-l parameters within a set or setting all the dummy variables associated with the set equal to -l for the dth_parameter(where d is the number of parameter in any set). This was done on a CDC 6500 com— puter using a subroutine trans. The rest of the analysis was executed using the computer programs "ICMATRIX" and "LS" of the M.S.U. Stat System. The reduced least square equations were inverted and solved using ordinary procedures to obtain a set of solutions of the constants B, B1 dj §k 5m in and B1 when they apply. The reduced constant of any set is equal to the sum of the estimated effects in the set, with the sign changed, e.g.. 5:”: B i=1 The subclass mean (mean effects)were computed in the following manner for Model I. 11> ll :2 + Q: + U”) x: unadjusted age mean. XI II 31 For Model II, The calculations to obtain sums of square for each set of effects was done following the procedure outlined by Harvey (1960). Thus the value for each set was: -1 I Z Ive |Uz Sum of Squares = Where bf is a row vector of the estimates for a given set -1 (such as the dj); E is the inverse of the segment of the inverse of the §f§_matrix corresponding by row and column, to this set of estimates} and glis a column vector of the set of estimates. The sum of squares for a set is equal to the reduction in sum of squares due to fitting all esti— mates minus the reduction in sum of squares due to fitting all estimates except the set being considered. Heritability Estimates Heritability in the narrow sense is defined by Lush (1948) as: 32 where: ' of; = variance due to addititive gene effects 0; = variance due to all gene effects 0; = environmental variance The estimates of variance components from half—sib analyses are widely used to estimate heritability. This is based on the expected values for sire component (0:) which is approximately equal to 1/4 c; and the within sire component (0:) which contain the random environmental variance, the dominance variance, three-fourths of the additive genetic variance and most of the epistatic vari- ance o 10: also includes a small amount of the epistatic variance due to the interactions of additive effects of the genes on different loci. These are usually considered to be so small that they are not considered when heritabil- ities are estimated. 33 The mean square estimates of variance from our analysis were used according to the following partition of the variance to solve for a: and‘o: Source of Variation E[MS] Between Sires 03 + k0 02 Within Sires 0: where: k0 = Coefficient for Unequal Number of Progeny per Sire calculated as described by Snede- cor (1967) 1 ( Zni \ k = -—— n. - o s-l \\ n. where: s = number of sires total number of individuals :3 II n. = number of individuals with ith sire. The approximate value for standard error of heritability was calculated as suggested by Swiger et a1. (1964). Normality of the intraclass correlation t was assumed. 34 2(n.-l) (i-t)2 [1+(kO-l) tlz S.E. (h2) = 4 s k: (n.—s) (s-l) RESULTS AND DISCUSSION Factors Affecting Production Traits , The analysis of variance for all the factors con- sidered are shown in Table 6. All the sources of variation were significant for most traits. The influence of each independent variable on the dependent variable is presented and discussed individually.‘ Sex of Calf The effect of sex was highly significant on all the traits studied.‘ Least squares means for sex are shown in Table‘7.' This is in agreement with the findings of all the studies of this nature. The difference between sexes tended to increase during the lifetime; this has also been found in other Studies. I' The greater growth of males when compared to females can be attributed to the genetic differences with reSpect to sex chromosomes. This genetic difference directly affEcts the phySiological and biochemical functions of the animal which are related to growth. 35 36 .mx Ga mum musmflm3 Ham .ucmoHMHsmHmsoz .mmEHu omega um unmflmz How DHQmHum>oo M MD new mm3 mummm 03» was mama mso mcflsmm3 um mom .m.G oHO. V m UM HGMUHMHGOflm mm3 COHUMHHM> MO OOHSOm SUMM¥¥ Q .Uao Hmo>|o3u on seam >HHMU momuo>muao< Roseanne» on demo maflmp omnum>mnwa< «mcflcmm3 ou samm >HHMD omnum>muza< aunmflms Ham» losenzwa «usmwms maaaummwuzm aunmflmz mcflsmm3n33 “unmfloz suuflnnzm “mum muflmuu on» How maonfiam DEBS moo. vac. mao. o.mwva m.mmh m.mhv 0.5 AOBOHV Am®OHvQHOHHm l l l «to.thmmN «an.mmmm¢ «am.mvomv I AOVH amm4 taom.H «Roo.m ««v¢.m aao.hmam «sh.mamv ash.mhom «no.5N 0N mmHHm. «sac. Rama. tamo. «so.mmmm «am.mvmv «am.VNHm .m.Go.m HA SUEDE «ama. «com. *«me «so.VVNm aah.mvaH aav.avmm «av.mm NH mummw .m.cwoo. .m.cmoo. samo. .m.:o.mwv~ «am.mmmm «an.ahmm «RB.VN m Emv mo mofi «amm.m aamm.m cams. «am.mahmhh «Rh.Nvomam «av.®mmmw «am.omm H xmm Bad Mflfl BOG 3MB 3% . 33 3m .M.fl mumDOm, mmmsam zamz mBHflmB ZOHfioboomm mmmm mDOHm<> UZHUZWDQMZH mMOBO¢m mom mUZ4Hm<> m0 mHmMA¢24 M w mamde 37 TABLE 7 . a LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR SEX b TRAIT Sex BW WW YW TYW ADW ADY ADT Female 25.4 174.2 214.7 307.2 .684 .278 .324 Male 26.7 189.9 245.5 366.2 .742' .384 .425 aAll weights are in kg. bTraits symbols as in Table 6. Age of Dam The age of dam had a highly significant effect on BW, WW, YW, and ADG to weaning. Least square means for age of dam effect are shown in Table 8. The mean values of all the traits in general increased with age of dam until 7 to 8 years of age. This is in general in agree- ment with the reports in the literature. We notice a non-significant effect of age of dam 0n post-weaning growth. This is also in accordance with the reports of Swiger et_§l. (1963) and Brinks et_al. (1962). However, the age of dam effect could still be 38 TABLE 8 a LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR AGE OF DAM ~—1r i:====.=ge- TRAITb Age of Dam , BW WW YW TYW ADW ADY ADT 2 26.2 180.8 230.1 339.9 .747 .347 .389 3 p 25.1 169.3 218.8 330.6 .649 .339‘ .391 4 25.9 176.7 224.4 331.6 .680 .322 .375 5 26.6 184.3 231.8 337.0 .727 .329 .370 6 26.2 186.0 232.4 334.7 .723 .319 .361 7 26.4 187.4 235.2 337.0 .736 .329 .362 8 26.0 188.4 236.7 345.6 .743 .328 .376 9 26.0 185.5 232.8 339.8 .725 '.334 .371 ' 10 26.4 184.2 232.2 339.2 .710 .329 .377 >10 26.5 177.8 226.0 331.2 .693 .328 .374 a All weights are in kg. bTrait symbols as in Table 6. 39 noticed on yearling weight. The higher value found for the 2-years old age of dam class is unusual. There is no re— port on this condition in the literature. Warnick eg_el. (1956) and Reynolds ejhel. (1963) reported that first estrus occurred later in Brahman cattle than in British origin breeds or their crossbreds in the Gulproast area of the United States. Plasse et_§l. (1968) in a thorough study On the reproductive behavior of Brahman cattle in Florida reported an average age at puberty of 19.4 months with a range of 14 to 24 months. In this study also was reported a correlation between 205-day weaning weight and age Of puberty of -.45. This indicates that just the fastest growing heifers would be able to calve by the 2- years old age, hence they form a selected group of cows. Apparently this select group of cows has the genetic po- tential and size and development for the mothering abil- ity as two-year-olds to produce heavier calves at that age than all the cows to produce calves as three-year-olds. Month of Birth The effect of month of birth was highly significant in all but one of the traits studied. Birth weight was not affected by month of birth. This is contrary to what has 40 been indicated in the literature. Most of these reports, however, are from studies of herds with a defined calving season. It was our interest to find out the better months .for calving with the purpose of recommending a herd manage? ment change. Further study is recommended. Grouping the months in seasons would be a possible way to detect a I broader influence. I For all the other traits the influence of month of birth was in general the same. Calves drOpped during the rainy season (May through August) made the lowest gains and had the lowest weights. This indicates that those calves born before favorable summer grazing conditions had a better environment during their lifetime. Least square means for month of birth effect are presented in Table 9. Rollings and Guilbert (1954); Lehman et_el. (1961) and Marlowe et_el. (1965) in studies of preweaning growth also reported a similar month of birth effect indicating that calves born in the early spring made fastest gains. Waught and Marlowe (1970) reported a non—significant in- fluence of month of birth on postweaning growth which is not in agreement with what we found. Marlowe et_al. (1965) in a study on preweaning growth reported that creep feeding ' tended to decrease the magnitude of the differences of the 41 TABLE 9 LEAST SQUARE ESTIMATES OF THE MEAN PERFORMANCE FOR MONTH OF BIRTHa munch MONTH Bw ww YW TYW ADW ADY ADT J 26.1 184.3 227.1 339.8 .749 .304' .371 F 26.8 196.6 242.0 358.3 .792 p.338 .388 MR 25.8 186.9 227.3 341.3 .748 .274 .376 AP 26.2 185.0 220.4 331.8 .732 .244 .357 MY 26.4 181.1 219.4 327.8 .741 .270 .358 JN 26.2 176.6 219.3 334.8 .706 .287 .378‘ JY 26.5 170.6 219.8 324.4 .684 .339 .369 AU 25.6 166.8 210.6 316.9 .671 .319 .361 S 25.3 166.3 264.1 348.6 .629 .599 .459 O 26.7 197.5 249.7 353.2 .682 .361 .375 N 25.2 182.9 225.4 320.0 .697 .313 .351 D 25.8 174.5 224.6 330.1 .692 .348 .494 a . All weights are in kg. bTrait symbols as in Table 6. 42 effect of month of birth on weaning weight. The range con- ditions of the animals in this study may be the reason why the month of birth may have a higher effect on post-weaning growth. Year of Birth The influence of year of birth was highly signifi- cant on all the traits studied.) This study covers data from a 13 -year period. It is logical to suppose a greater influence of the climatic conditions on rage cattle with- out supplementation. Few studies are found in the litera— ture on the influence of year because most of them are be- ing done on a within-year basis, reducing the source of variation represented by year. The estimation of specific year constants is not of any practical use for future data analysis Since these Years will not occur again. The im— portant point is that the specific years involved in any study will probably be an important sOurce of variation. Age of Animal The age of animal used as covariate on weaning, yearling and two-year weight had highly significant effect. 43 Linear regression coefficients of .337, .295, and .323 kg per day for weaning yearling and two-year-old weight were found based on 216, 363, and 640 days respectively. These values are in general smaller than those reported for other breeds in the literature. Heritability Estimates The paternal half-sib heritability estimates com— puted in this study are shown in Table 10. - TABLE 10 PATERNAL HALF-SIB HERITABILITY ESTIMATES AND STANDARD DEVIATIONS Traita . . Estimate BW .27 i .10 'WW - _ .48 i .14. YW .44 i .13 TYW } .29 i .10 ADW .40 i .12 ADY .19 i .07 ADT .09 i .05 aSymbols as in Table 6. 44 All the values but two-year weight and average daily gain to two years old agree reasonably well with the average estimates summarized and presented in the Literature Re- ‘View. The values found for TYW and ADT are smaller than those reported for feed lot gain and final weight. A major cause of this difference isdue to maintaining the animals on pasture with minimum supplementationrw Other heritability estimates obtained on Brahman cattle are very similar to those of this study. The birth weight heritability value is 10wer than previously‘reported by Berruecos and Robison (1968) in Mexico and Beltran (1975) in Venezuela but higher than reported by Miquel and Cart— ,wright (1963) in Texas. SUMMARY The data included records on 1130 Brahman calves born over a l3-year period, 1961 to 1973 inclusive, at a ranch on the gulf coast of Mexico (Huasteca Potosina). The animals were kept under range conditions to two years of age. Traits studied were birth, weaning, yearling, and two-year weight, as well as average daily gain to weaning, weaning to yearling, and yearling to twoeyear old. The influences of age and sex of calf, age of dam and year and month of birth on the traits studied were analyzed. All the factors were shown to have highly signif- icant influences (P < .01) on the traits studied except age of dam did not have a significant influence on post- weaning growth and two-year weight and month of birth did not have a significant effect on birth weight. Least square estimates of the mean performance for each of the factor trait combinations was calculated. The mean values found for age of dam effect on influenced traits increased with age of dam from 3 to 8 years of age 45 46 and slightly declined after 10 years of age. An unusually high value was found for effect of the two-years-old age of dam class. The later onset of puberty in Brahman cattle is a major reason. The least square means for sex showed that bulls were heavier by 1.2, 15.6, 30.8, 59 kg for birth, weaning, yearling, and two—year weight respec- tively. Month of birth mean values indicated that calves born before summer grazing conditions had the highest weights and gains, calves born during the rainy season (May through August) had the lowest. There was not a de— fined trend over the rest of the year.’ Linear regression coefficients of .337, .295, and .323 kg per day were calculated for weaning, yearling and two-years-old weight based on a mean of 216, 363, and 640 days, respectively. Paternal half-sib heritability estimates were: birth weight, .27; weaning weight, .48; yearling weight, .44; two-year weight, .29; average daily gain to weaning, .40; ADG to yearling, .19, only,and ADG to two years, .09. BIBLIOGRAPHY ' BIBLIOGRAPHY Alexander, G. I. and R. Bogart. 1961. Effect of inbreed- ing and selection on performance characteristics of beef cattle. J: Anim. Sci. 20:702. Beef Improvement Federation Recommendation. 1974. Guide- lines for uniform beef improvement programs. Ex- tension Service, USDA. Wash. D.C. Beltran, J., D. E. Franke, D. Plasse and O. Verde. (1975. Influence on early Brahman calf growth. J. Anim. Sci. 33:245.(Abstr.)r Berrvecos, J. M. and O. W. Robinson, 1968. Preweaning Growth in Brahmans. J. Anim. 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