Repeated-measure animal models to estimate genetic components of mature weight, hip height, and body condition score.

Information on mature weight, hip height, and body condition score from Angus cows was analyzed to estimate variance components and compare prediction models. Observations from repeated measures were analyzed with animal models with or without condition score as a covariate and with or without an effect for permanent environment. Heritability (repeatability) estimates for mature weight, hip height, and condition score from Method R procedures were 0.40 (0.77), 0.62 (0.81), and 0.11 (0.38), respectively, from animal models containing a permanent environmental effect but without a covariate for condition score. Heritability estimates from animal models without a permanent environmental effect were similar to repeatability estimates from animal models with it, suggesting inflated estimates of genetic variance from models not containing a permanent environmental effect. Regressing mature weight on condition score reduced both additive genetic variance and permanent environmental variance, increasing the heritability estimate of mature weight to 0.54 and altering the biological interpretation of the trait. The covariate for condition score had little effect on hip height. Regressions of mature weight and hip height on condition score were 25.9 kg/unit of body condition score and 0.4 cm/unit, respectively. Least-squares means for mature weight and hip height tended to increase until 7 and 5 yr of age, respectively. Condition score tended to increase until 6 yr of age and decrease after 8 yr of age. Correlations between breeding value solutions for the same trait were high whether or not prediction models included a permanent environmental effect or a covariate for condition score, and whether or not the variance components used were derived from models containing a covariate for condition score. Results suggest the importance of including a permanent environmental effect in genetic prediction models for these traits. Whether mature weight should be adjusted for body condition is arguable, depending on availability of condition score predictions and tools for analyzing mature weight and condition score predictions in an environment-specific context.

Additive genetic parameter estimates for heifer pregnancy and subsequent reproduction in Angus females.

A primary objective of this study was to determine whether the binary traits heifer pregnancy (HP) and subsequent rebreeding (SR) were heritable in an experimental population of Angus cattle. A second objective was to determine the nature of the additive genetic relationships among HP, SR, and stayability (S(5/1)) in the same population. Heifer pregnancy was defined as the observation of a heifer conceiving and remaining pregnant to palpation at 120 d, given exposure during the breeding season. Subsequent rebreeding was defined as the observation of a 2-yr-old conceiving and remaining pregnant to palpation at 105 d, given pregnancy as a yearling and exposure during the breeding season. Stayability was defined as the probability of a female having at least five calves, given she becomes a dam as a 2 yr old. Data were analyzed using a maximum a posteriori probit threshold model to predict breeding values on the liability scale and Method R procedures to estimate variance components in the determination of heritability (h2). Additive genetic groups were used in determining the additive genetic relationships among these fertility traits. Additive genetic groups were formed on one trait's breeding values and used in the prediction of another trait's breeding values. Analyses yielded h2 estimates that were out of the parameter space 8.5 and 46.3% for HP and SR, respectively, and 5.9% for the reestimation of S(5/1). The majority of point estimates outside the parameter space for SR converged toward 0, whereas those for HP and S(5/1) primarily converged toward 1. From the subsamples producing h2 estimates within the parameter space, average h2 for HP, SR, and S(5/1) were .21, .19, and .15, with standard deviations of .12, .14, and .08, respectively. The estimates of h2 indicate that HP and S(5/1) were heritable and should respond favorably to selection; however, SR did not appear heritable due to the large number of subsamples producing h2 estimates out of the parameter space. Fixed effect estimates for age of dam were significant for HP. From the analyses using additive genetic groups, the relationship among HP and S(5/1) appeared to be nonlinear. This potential nonlinear relationship seen between HP and S(5/1) indicates that selection for improved female fertility would be most effective by having predictions on both traits.

Method R variance components procedure: application on the simple breeding value model.

An algorithm for estimating variance components (Method R) based on the linear regression coefficient (R) of recent (more accurate) on previous (less accurate) individual genetic predictions is presented. The previous prediction is obtained by analyzing a subsample of the whole data set. First raw moment of R equals 1 regardless of the distribution of observations and predictions. A condition such as the use of inappropriate variance components ratio (VC) can cause this regression to deviate from its expectation. If the computed R (Rc) is greater than 1, then VC ratio has been underestimated, and if Rc is less than 1, then VC ratio has been overestimated. Several iterations are performed, changing the VC ratio at each iteration, until Rc approximately equal to 1. When an Rc is obtained that is acceptably close to 1 (precision is reached), then the appropriate VC has been used. Method R does not require computation of the inverse of the coefficient matrix and has desirable properties of convergence, precision, and computing feasibility. Additional sampling variance in the estimate of VC is expected due to the requirement of taking a subsample of the entire data set to obtain the lower accuracy predictions. This sampling variance is shown to be small for simulated datasets of size n = 10,000 with no selection.

Technical note: detection of bias in genetic predictions.

The theoretical development of a procedure to detect bias in genetic predictions is presented. The procedure is based on the expectation of three statistics. These statistics detect bias by identifying systematic, unexpected change in subsequent analyses. Expectations of the following statistics were obtained: linear correlation coefficient between subsequent predictions, linear regression of recent (more accurate) on previous (less accurate) genetic prediction, and variance of the genetic prediction difference (recent minus previous genetic prediction). Deviations from these expectations can be used to indicate bias. The covariance between subsequent BLUP of genetic value is shown to equal the variance of the early estimate, implying that the expected value of the regression of recent on previous genetic prediction equals 1 regardless of the distribution of the observations and predictions. Also, the expected value of the linear correlation coefficient between subsequent genetic predictions equals the square root of the ratio of the means of the square of accuracy values. The expected value of the variance of the genetic prediction difference was shown to be equal to the difference between prediction error variances.

Genetic effects on beef heifer puberty and subsequent reproduction.

Significant genetic variation exists within and between breeds of beef cattle for age at puberty (AP). In general, faster-gaining breed groups of larger mature size reach puberty at a later age than do slower-gaining breed groups of smaller mature size; breeds selected for milk production reach puberty at younger ages than do those breeds not selected for milk production. Heterosis, independent of heterosis effects on weight, influences most measures of puberty in females and scrotal circumference (SC) in males. Crossbred heifers reach puberty at younger ages and heavier weights than their straightbred counterparts. Scrotal circumference has been shown to be an excellent indicator of AP in yearling bulls. Furthermore, a favorable genetic relationship exists between SC in bulls and AP of female offspring. Beef cattle breeders may take a direct approach to breeding for AP and subsequent reproduction by directly selecting for measures of fertility such as SC. However, an indirect approach, involving selection for an array of traits that provide an appropriate "genetic environment" for the expression of fertility (i.e., size, milk production, calving ease) may be preferred. Although seedstock producers are limited to making change through within-breed selection, commercial producers can take advantage of both within- and between-breed selection as well as crossbreeding to achieve the same goal.

Effects of growth curve parameters on cow efficiency.

Weight-age data from 50 Retinta beef cows from 8 to 97 mo of age located in southwestern Spain were fitted to von Bertalanffy, Brody, and Richards functions to determine the relationship between growth curve parameters and cow efficiency. Only cows having at least 31 weights were included in the analysis. Von Bertalanffy, Brody, and Richards functions were fitted to weights of each cow. Relevant parameters of the three functions are A and K, associated with the asymptotic mature weight and rate of maturing, respectively. Criteria for comparisons among the three functions were computing difficulty, goodness of fit, and lack of bias of A. Productivity indicators were number of calves weaned during the first five calving seasons (NC), average birth weight (BWT), average weaning weight (WW), and average weaning weight per cow per year (WWY). The von Bertalanffy function was selected as the most appropriate. Least squares means for A and K were 650 +/- 8.17 kg and .038 +/- .001 mo-1, respectively. The values of NC, BWT, WW, and WWY were 4.0 +/- .11 calves, 38.2 +/- .4 kg, 218 +/- 5 kg, and 172 +/- 5 kg, respectively. Regression analysis for A indicated a decrease in NC when mature weight increased (P less than .05). There was a nonsignificant trend for heavier cows (higher A) to have calves with heavier BWT or WW. The value of WWY increased (P less than .05) with increased maturing rate (K) of cows. No significant associations were found between K and BWT or WW.(ABSTRACT TRUNCATED AT 250 WORDS)

A performance programmed method for computing inbreeding coefficients from large data sets for use in mixed-model analyses.

Coefficients of inbreeding are commonly used in mixed-model methods for forming inverses of Wright's numerator relationship matrix and transformation matrices used in variance component estimation and national cattle evaluation. Computation of exact coefficients of inbreeding from very large data sets has been believed to be too expensive or too difficult a task to perform. Approximate methods have been used instead. The effects of using approximation methods for inbred data that appear in national cattle data sets are demonstrated. An algorithm is given for the computation of inbreeding coefficients for large data sets. The algorithm feasibly computes inbreeding coefficients for large data sets even on small computing architectures.

Some alternatives to calving date and interval as measures of fertility in beef cattle.

Records of 594 calving dates and 493 calving intervals collected from a herd of Retinta beef cows in southwest Spain were studied. Their efficacy as reproductive measures were compared when a long breeding season was utilized. Variables used were date of present calving (DOC), date of subsequent calving (DOSC), time from start of breeding season to calving (TBSC), interval to next calving (CI), two adjustments of calving interval by subtracting the time that bulls were not available to the cow from actual CI (ACI1 and ACI2), and three scores. Period score (SCOR) measured the 20-d increment of the 220-d calving season in which the cow calved. Pair score (PAIR) was computed by subtracting the deviation of calving interval from 365 d from the average SCOR of the two calvings involved. Adjusted pair score (APAIR) was calculated in the same way as PAIR, but using ACI1 instead of CI. Heritability estimates for DOC, SCOR, and DOSC and CI were .16, .14, .13 and 0, respectively. Heritabilities of all other measures ranged from .01 to .06. Repeatability estimates for DOC, SCOR, DOSC and CI were .29, .28, .34 and .14, respectively. Repeatability values were .28, .18, .18, .23 and .32 for TBSC, ACI1, ACI2, PAIR and APAIR, respectively. Genetic and phenotypic correlations among CI and its alternative measures were very high and favorable.(ABSTRACT TRUNCATED AT 250 WORDS)

Genetic analysis of absolute growth measurements, relative growth rate and restricted selection indices in red Angus cattle.

Performance records on 41,184 Red Angus cattle were analyzed and estimates of parameters calculated for absolute growth rate, relative growth rate and restricted selection indices. Heritability estimates for birth weight, 205-d weight, 365-d weight and postweaning gain were .46 +/- .02, .39 +/- .02, .40 +/- .02 and .36 +/- .02, respectively. Heritability estimates for preweaning, postweaning and postnatal relative growth rates were identical (.33 +/- .02). Heritability estimates for restricted selection indices were .31 +/- .02, .33 +/- .02 and .31 +/- .02 for weaning index, yearling index and postweaning index, respectively. The genetic correlation between preweaning and postweaning absolute growth rate was .15. The genetic correlation between consecutive measurements of relative growth rate (RGR) was -.33. Genetic correlations of birth weight with preweaning RGR and postnatal RGR were -.68 and -.71, respectively. Correlations among measures of relative growth rate using simulated data were similar to correlations of actual data, indicating that these relationships are the result of numerator/denominator relationships and not biological causes. The genetic correlation between weaning and postweaning indices was near zero. Small genetic coefficients of variation for preweaning and postnatal relative growth rates indicate further problems with the expression of growth in this manner. Restricted selection indices exhibited much larger genetic coefficients of variation than measurements of RGR. Genetic standard deviations were 7.8%, 7.2% and 13.7% of the means for weaning, yearling and postweaning indices, respectively.

Relationships of sire scrotal circumference to offspring reproduction and growth.

Reproductive and growth data were obtained on 779 and 564 yearling beef heifers and bulls, respectively, that had sires with yearling scrotal circumference data at the San Juan Basin Research Center, Hesperus, CO. Partial regression coefficients of reproductive and growth traits on inbreeding (FXC) and age of the individual and adjusted scrotal circumference of sire (SCSI) were obtained. Growth and reproductive traits of heifers and growth and breeding soundness traits of bulls were analyzed. Separate analyses for each sex were performed, but least squares models were similar. Models included fixed effects of breed, birth year (BY), age of dam (AOD) and the covariates FXC, age (day of birth in heifer analyses) and SCSI. Scrotal circumference of sire was adjusted for age, FXC, AOD and BY using values obtained in a separate analysis. Seminal traits improved as age increased, and there was a seasonal effect present for age of puberty. Inbreeding had a detrimental effect on reproductive traits. Partial regression coefficients for the reproductive traits on SCSI were: age of puberty, -.796 d/cm; age of first calving, -.826 d/cm; julian day of first calving, -.667 d/cm; julian day of second calving, .597 d/cm; most probable producing ability, .132 %/cm; percent sperm motility, -.74 %/cm; percent primary sperm abnormalities, .08 %/cm; percent secondary sperm abnormalities, .92 %/cm; percent normal sperm, -1.28 %/cm; total breeding soundness examination score, .28 units/cm and scrotal circumference, .306 cm/cm. A heritability of .39 was obtained for scrotal circumference.

Estimation of genetic parameters among reproductive and growth traits in yearling heifers.

Growth and reproductive data were obtained on 779 beef heifers at the San Juan Basin Research Center, Hesperus, Co. Genetic parameters were estimated for age of puberty (AOP), age of first calving (AOC), julian day of first calving (DOC), julian day of second calving (DOSC), birth weight, weaning weight, yearling weight, and average daily gain from weaning to yearling and to cycling weights. The least squares model included birth year, age of dam and breed as fixed effects, sire/breed as a random variable, and day of birth and percent inbreeding as covariates. Day of birth was not included in the analyses of AOC, DOC or DOSC. Paternal half-sib estimates of heritability were: AOP, .10 +/- .17; AOC, .01 +/- .12; DOC, .09 +/- .13 and DOSC, .36 +/- .18. Genetic and phenotypic correlations were generally favorable, but genetic correlations were variable with large standard errors. Inbreeding had a detrimental effect on reproductive traits, and a seasonal effect was present for AOP.

Estimation of genetic parameters among breeding soundness examination components and growth traits in yearling bulls.

Data on breeding soundness examinations (BSE) and performance traits were obtained on 549 yearling beef bulls at the San Juan Basin Research Center, Hesperus, Co from 1976 to 1984. Genetic parameters estimated for components of BSE included percent motility (PMOT), percent primary abnormalities (PPRIM), percent secondary abnormalities (PSEC), percent normal sperm (PNOR), scrotal circumference (SC) and BSE score (BSESC). Performance traits included birth weight, weaning weight, yearling weight and average daily gain. The least squares model included birth year, age of dam and breed as fixed effects, sire/breed as a random variable, and age and percent inbreeding as covariates. Paternal half-sib estimates of heritability were PMOT, .08 +/- .07; PPRIM, .31 +/- .09; PSEC, .02 +/- .05; PNOR, .07 +/- .06; BSESC, .10 +/- .06 and SC, .40 +/- .09. Phenotypic correlations among BSE components and growth traits were generally favorable. Genetic correlations involving percent secondary abnormalities were highly variable with large standard errors. Seminal traits improved as age increased and became poorer as inbreeding increased.

Inbreeding and immunoglobulin G1 concentrations in cattle.

Immunoglobulin G1 concentration (IgG1) was measured in presuckle colostrum and calf serum obtained at 36 h and at weaning from inbred and straightbred Angus, Brangus, Hereford, Red Angus and Simmental cattle. Sources of variation considered as dam traits examined for IgG1 in colostrum and 36-h calf serum included line of sire, sire within line, age, and linear regression of IgG1 on inbreeding of dam. Only line of sire and inbreeding of dam were significant in the analysis of 36-h calf serum. Sources of variation considered as calf traits examined for IgG1 in calf serum at 36 h and at weaning included line of sire, sire within line, sex of calf, age of dam, and regressions of calf serum IgG1 on inbreeding of the calf and on dam's colostral IgG1. Only sire within line and the regression on dam's colostral IgG1 were significant for calf serum IgG1 at 36 h. Large differences existed in 36-h calf serum IgG1 between sires both within lines and when lines were ignored. Calves with 36-h serum IgG1 of less than 10 mg/ml were two to four times more likely to die before weaning than calves with higher IgG1 levels. The heritability estimates of IgG1 by paternal half-sib analysis were .41 +/- .30 for colostrum measured as a trait of the dam and .56 +/- .25 for 36-h. calf serum and .05 +/- .17 for calf serum at weaning considered as a trait of the calf. These estimates indicate that IgG1 in colostrum and 36-h calf serum could be increased by selection.(ABSTRACT TRUNCATED AT 250 WORDS)

Simulated efficiency of range beef production. I. Growth and milk production.

A revised version of the Texas A&M University Beef Cattle Production Model was used to simulate the effects of growth, milk production and management system on biological and economic efficiency of beef production in a northern plains, range environment. Animals varying in genetic potential for birth weight (BWA), yearling weight (YW), mature weight (WMA) and milk production (PMA) were simulated under both a weanling system of management (weaned calves custom-fed in the feedlot) and a yearling system (calves wintered on the ranch, then custom-fed after their second summer). The yearling system of management was biologically less efficient, but economically more efficient than the weanling system due primarily to heavier slaughter weights of fed animals. The advantage of the yearling system was most apparent for smaller genotypes. Herd efficiency improved with decreased BWA and increased YW, but changed little when WMA was varied while other growth traits were held constant. Increased PMA was favored for production of live weight at weaning and for production of slaughter product when feedlot costs were high. Increased PMA was not favored when feed costs for the cow herd were high. Economic weights generated from the simulation indicated the importance of selection for rapid early growth followed by selection for lighter birth weight. While larger genotypes were generally favored in this study, optimal cow size depended on economic conditions. Larger types were more biologically efficient and more economically efficient using standard costs, but medium- and small-size cattle were more efficient when feedlot costs were high. Small cattle were least efficient when feed costs for the cow herd were high.

Simulated efficiency of range beef production. II. Fertility traits.

A modified version of the Texas A&M University Beef Cattle Production Model was used to simulate the effects of changes in potential for age at puberty (AAP), potential for probability of conception (PCA) and winter feed levels on biological and economic efficiency of beed production in a northern plains, range environment. Two management systems were simulated: a weanling system in which all calves except replacement heifers were custom fed in a feedlot immediately post-weaning; and a yearling system in which calves were kept on the ranch through their second summer, then custom-fed. Biological efficiency was defined as the ratio of TDN input to product output, and economic efficiency was defined as the ratio of total dollar cost to 100 kg product output. A simulated increase in AAP from 365 to 425 d resulted in slightly decreased economic efficiency under a yearling system of management. An increase in PCA from .75 to .85 caused decreased biological efficiency under both weanling and yearling management systems, suggesting biological inefficiencies associated with maintaining mature cows. Simulation results indicate that optimal supplementation levels and corresponding levels of observed fertility depend on the value of product derived from cull cows relative to the value of product derived from fed animals and on the costs of developing replacement heifers relative to the costs of maintaining mature cows. Decreased fertility causes change in the sources of products, not product loss per se. For this reason, survivability may be a more important aspect of reproduction than fertility.

Simulated efficiency of range beef production. III. Culling strategies and nontraditional management systems.

A modified version of the Texas A&M Beef Cattle Production Model was used to simulate life-cycle biological and economic efficiency of various culling strategies and non-traditional management systems in a northern plains, range environment. Biological efficiency was defined as the ratio of TDN input (kg) to product output (kg), and economic efficiency was defined as the ratio of cost ($) to product output (100 kg), where products were live weight at weaning (LWW), empty body weight at slaughter (EBW) and fat-free weight at slaughter (FFW). Several economic scenarios were simulated. Culling cows at younger ages increased biological efficiency, but not necessarily economic efficiency. The simulated optimal age at culling was 8 yr, the same age at which simulated feed intake and milk production began to decline. Finishing young cows in the feedlot had little effect on biological efficiency and generally increased economic efficiency, although specific results depended on feed prices and relative values of cull cows vs fed animals. A simulated sex-controlled system in which only heifer calves were produced, while extremely biologically efficient for production of lean, resulted in relatively little output and was not economically efficient in most cases. Sex control combined with feeding of 2-yr-old cows was economically efficient, but not markedly more efficient than a conventional system. Results suggest that sex-controlled systems may be more appropriate where emphasis is on lean product and heifers can be bred at very early ages. General results indicate that producers should pay attention to relative values of cull cows and fed animals in choosing culling strategies and management systems.

Selection in Hereford cattle. I. Selection intensity, generation interval and indexes in retrospect.

Selection intensity and generation interval were evaluated in a Hereford cattle herd made up of 14 inbred lines and 14 linecross groups corresponding to the lines of inbred sires at the Suan Juan Basin Research Center, Hesperus, Colorado. Selection indexes practiced were calculated in retrospect. Analyses of the records collected from 1946 through 1973 involved weaning weight (WW) and postweaning traits in males and females. Analyses by line were performed for the inbreds, while pooled analyses were done on the inbred and linecross populations. From records of 1,239 calves weaned, age of sire averaged 3.75 yr compared with 4.52 yr for age of dam, showing faster generation turnover for sires than for dams. Generation interval determined as actual age of midparent was 4.13 yr. Selection applied for WW, evaluated as annual selection differentials within inbred lines and then pooled over all lines, averaged .55 standard deviations (sigma)/generation for sires. For females, selection was much less intense. Midparent selection differential amounted to .33 sigma/generation. For sires, pooled standardized selection differentials per generation over all lines during the postweaning gain period were .49 sigma, .46 sigma, .40 sigma, -.20 sigma, -.10 sigma and .69 sigma, respectively, for initial weight, final weight, feed consumed, feed efficiency (FE, unadjusted and adjusted) and average daily gain (ADG). Selection of females for postweaning traits was not intense. Selection index actually practiced in retrospect for sires was: IS = .4461 (WW) - .0092 (FE) + .6126 (ADG). The indexes for dams included WW, 12-mo weight (12W), 18-mo weight (18W), mature spring weight (SPW) and mature fall weight (FAW) and were: for inbred dams, ID = .1824 (WW) - .0284 (12W) + .0736 (18W) - .1097 (SPW) - .1097 (FAW); for linecross dams, ID = .2693 (WW) - .2960 (12W) + .0147 (18W) + .1185 (SPW) - .0354 (FAW). The corresponding index selection differentials were .818, .203 and .209. Sire index selection differentials represent about 79% of the total selection differentials.

Selection in Hereford cattle. II. Expected and realized response.

Data from 14 inbred lines and 14 linecross groups of Hereford cattle at the San Juan Basin Research Center, Hesperus, were used to evaluate expected and realized response in birth and weaning traits and postweaning traits in males and females over a 28-yr period. There were large differences in the means and variances of the performance traits among the inbreds and linecrosses, with the inbreds showing inbreeding depression and greater variability among lines, while the linecrosses manifested within-breed heterosis. Except for gain from weaning to 12 mo, in females, genetic progress was expected in all traits studied, mainly due to sire selection. Regressions of annual trait means on years indicated positive phenotypic trends in the inbreds for heart girth circumference at birth, adjusted weaning weight (adjusted for inbreeding), weaning score, final weight, feed consumption and the yearling weights and gains in females. Changes were negative for other traits. In the linecross group phenotypic trends were positive in all traits except heart girth circumference, weaning age, initial test weight and feed efficiency. Estimated genetic progress per generation due to within-line selection was negative in most of the traits in the inbreds but was considerably positive for the linecrosses for most of the traits. As expected, between-line selection yielded greater genetic improvement in the inbred than in the linecross population. The different patterns of response in the two populations are attributed to high rates and levels of inbreeding. Although variable, the actual progress was below prediction in most of the traits studied.

Scrotal circumference in yearling Hereford bulls: adjustment factors, heritabilities and genetic, environmental and phenotypic relationships with growth traits.

Field data on 4,233 yearling Hereford bulls were analyzed using fixed and mixed model least-squares procedures to examine factors affecting scrotal circumference; determine appropriate adjustment factors; and study genetic, environmental and phenotypic relationships among scrotal circumference and growth traits. Scrotal circumference was affected by postweaning feed level; contemporary group/feed level; age of dam; and covariates age, weight and height. Of the three covariates, weight had the greatest effect, and any factor which caused an increase in weight tended to increase scrotal circumference. Quadratic effects of age, weight, height and age X age of dam interaction effects were significant or approached significance, but were of minor importance. Large contemporary group effects suggested the need for expressing scrotal circumferences as trait ratios or as deviations from contemporary group means. Scrotal circumference adjustment factors recommended for yearling Hereford bulls were .026 cm X d-1 of age and .8, .2 and .1 for sons of 2-, 3- and 4-yr old dams, respectively. Heritability of weight-adjusted scrotal circumference was .46 +/- .06 compared with .49 +/- .06 for age-adjusted scrotal circumference, indicating considerable additive genetic variation for relative scrotal size. Correlations between scrotal circumference and growth traits were moderate to high. The genetic correlation between scrotal circumference and yearling weight was the highest of these at .44 +/- .16. Potential implications of this relationship are discussed.

Genetic and environmental aspects of the growth curve parameters in beef cows.

Brody's growth curve, a three-parameter function, and Richards' function, a four-parameter function, were fit to data from 233 inbred and linecross cows to study the genetic and environmental aspects of the growth curve parameters and to compare the two functions. Fitting Brody's curve was faster and less costly to compute than Richards' function, but Richards' function had smaller sums of squares and a better fit to actual data points. Year of birth had an effect on the A (P less than .05), b (P less than .01) and k (P less than .01) parameters of Brody's curve. Parameter estimates from data of the youngest cows were at the extremes. The b parameter was the largest when estimated from data with no recorded birth weights. Year of birth was also an important effect for the b (P less than .01), k (P less than .05) and m (P less than .01) parameters of Richards' function, but year effects were less interpretable. Mating system affected (P less than .01) the A parameter of both functions; inbreds were lighter than linecrosses at maturity. Line of sire was an important source of variation (P less than .01) for the A parameter of both functions. The heritability estimate of the A parameter from both functions was .44 +/- .27; apparently the same trait in both curves. The estimate for the b parameter from Brody's curve was .39 +/- .27, comparable with literature estimates of birth weight. The heritability estimate for k from Brody's curve was .20 +/- .26. The heritability estimates for b, k and m parameters from Richards' function were .24 +/- .26, .32 +/- .27 and .21 +/- .26, respectively. The genetic correlations between the A and k parameters in both curves indicated that cows with lighter mature weights reached that weight at younger ages.