Genetic and phenotypic parameters for test day milk yield of Sahiwal cattle in the semi-arid tropics

A total of 19 376 test day (TD) milk yield records from the first three lactations of 1618 cows daughters of 162 sires were used to estimate genetic and phenotypic parameters and determine the relationship between daily milk yield and lactation milk yield in the Sahiwal cattle in Kenya. Variance components were estimated using animal models based on a derivative free restricted maximum likelihood procedure. Variance components were estimated using various univariate and multi-trait fixed regression test day models (TDM) that defined contemporary groups either based on the year-season of calving (YSCV) or on the year-season of TD milk sampling (YSTD). Variance components were influenced by CG which resulted in differences in heritability and repeatability estimates between TDM. Models considering YSTD resulted in higher additive genetic variances and lower residual variances compared with models in which YSCV was considered. Heritability estimates for daily yield ranged from 0.28 to 0.46, 0.38 to 0.52 and 0.33 to 0.52 in the first, second and third lactation, respectively. In the first and second lactation, the heritability estimates were highest between TD 2 and TD 4. Genetic correlations among daily milk yields ranged from 0.41 to 0.93, 0.50 to 0.83 and 0.43 to 86 in the first, second and third lactation, respectively. The phenotypic correlations were correspondingly lower. Genetic correlations were different from unit when fitting multi-trait TDM. Therefore, a multiple trait model would be more ideal in determining the genetic merit of dairy sires and bulls based on daily yield records. Genetic and phenotypic correlations between daily yield and lactation yields were high and positive. Genetic correlations ranged from 0.84 to 0.99, 0.94 to 1.00 and 0.94 to 0.97 in the first, second and third lactations, respectively. The corresponding phenotypic correlation estimates ranged from 0.50 to 0.85, 0.50 to 0.83 and 0.53 to 0.87. The high genetic correlation between daily yield and lactation yield imply that both traits are influenced by similar genes. Therefore daily yields records could be used in genetic evaluation in the Sahiwal cattle breeding programme.     

Theory for the number of genes affecting quantitative characters

Summary A general expression for gene number estimation which encompasses the conventional formula was derived. It provides a basis for gene number estimation from the data of recurrent selection experiments that are not of sufficient duration to measure total response to selection.Gene number estimates are considerably more reliable when heritability is high. The effect of heritability on sampling variance is particularly important when gene number is large.Generally the most effective ways of decreasing the variance of a gene number estimate will be 1) to increase the number of generations in a primary selection program, 2) to increase the number of generations in the two way selection program and 3) to increase population size.From a thesis submitted by the author in partial fulfillment of the requirements for the Ph.D. degree. Received March, 1975. Work supported by Public Health Service Grant GM 16074, by the Minnesota Agricultural Experiment Station and by National Institutes of Environmental Health Sciences Grant No. 5T32 ES07011-02.Former Research Assistant, Genetics and Cell Biology, University of Minnesota; Currently Post-doctoral Fellow in Environmental Health Measurement and Statistics.     

On estimating the proportion of variance in a phenotypic trait attributable to a measured locus

The measured genotype approach can be used to estimate the variance contributions of specific candidate loci to quantitative traits of interest. We show here that both the naive estimate of measured-locus heritability, obtained by invoking infinite-sample theory, and an estimate obtained from a bias-corrected variance estimate based on finite-sample theory, produce biased estimates of heritability. We identify the sources of bias, and quantify their effects. The two sources of bias are: (1) the estimation of heritability from population samples as the ratio of two variances, and (2) the existence of sampling error. We show that neither heritability estimator is less biased (in absolute value) than the other in all situations, and the choice of an ideal estimator is therefore a function of the sample size and magnitude of the locus-specific contribution to the overall phenotypic variance. In most cases the bias is small, so that the practical implications of using either estimator are expected to be minimal.     

EVOLUTIONARY POTENTIAL OF A LARGE MARINE VERTEBRATE: QUANTITATIVE GENETIC PARAMETERS IN A WILD POPULATION

Estimating quantitative genetic parameters ideally takes place in natural populations, but relatively few studies have overcome the inherent logistical difficulties. For this reason, no estimates currently exist for the genetic basis of life-history traits in natural populations of large marine vertebrates. And yet such estimates are likely to be important given the exposure of this taxon to changing selection pressures, and the relevance of life-history traits to population productivity. We report such estimates from a long-term (1995–2007) study of lemon sharks ( Negaprion brevirostris ) conducted at Bimini, Bahamas. We obtained these estimates by genetically reconstructing a population pedigree (117 dams, 487 sires, and 1351 offspring) and then using an "animal model" approach to estimate quantitative genetic parameters. We find significant additive genetic (co)variance, and hence moderate heritability, for juvenile length and mass. We also find substantial maternal effects for these traits at age-0, but not age-1, confirming that genotype–phenotype interactions between mother and offspring are strongest at birth; although these effects could not be parsed into their genetic and nongenetic components. Our results suggest that human-imposed selection pressures (e.g., size-selective harvesting) might impose noteworthy evolutionary change even in large marine vertebrates. We therefore use our findings to explain how maternal effects may sometimes promote maladaptive juvenile traits, and how lemon sharks at different nursery sites may show "constrained local adaptation." We also show how single-generation pedigrees, and even simple marker-based regression methods, can provide accurate estimates of quantitative genetic parameters in at least some natural systems.     

Polyandry and postcopulatory sexual selection in a wild population

When females mate multiply, postcopulatory sexual selection can occur via sperm competition and cryptic female choice. Although postcopulatory selection has the potential to be a major force in driving evolution, few studies have estimated its strength in natural populations. Likewise, although polyandry is widespread across taxa and is the focus of a growing body of research, estimates of natural female mating rates are still limited in number. Microsatellites can be used to estimate the number of mates represented in females' sperm stores and the number of sires contributing to their offspring, enabling comparisons both of polyandry and of two components of postcopulatory selection: the proportion of males that mate but fail to sire offspring, and the degree of paternity skew among the males that do sire offspring. Here, we estimate the number of mates and sires among wild females in the Hawaiian swordtail cricket Laupala cerasina. We compare these estimates to the actual mating rates and paternity shares we observed in a semi‐natural population. Our results show that postcopulatory sexual selection operates strongly in this species: wild females mated with an average minimum of 3.6 males but used the sperm from only 58% of them. Furthermore, among the males that did sire offspring, paternity was significantly skewed. These patterns were similar to those observed in the field enclosure, where females mated with an average of 5.7 males and used the sperm from 62% of their mates, with paternity significantly skewed among the sires.     

Genetic estimates for plasma lipids and lipoproteins in cynomolgus monkeys under assortative mating

Data obtained from cynomolgus monkeys selected for total plasma cholesterol (TPC) response to dietary cholesterol and nonselected controls were used to estimate heritability of TPC and lipoprotein concentrations. A total of 345 observations were collected on 57 progeny from 18 sires. Heritability estimates obtained by a paternal half-sib analysis and by regression of offspring on mid-parent values were 0.45 ± 0.24 and 0.69 ± 0.18 for TPC, 0.63 ± 0.30 and 0.64 ± 0.17 for LDLC, and 0.80 ± 0.36 and 0.59 ± 0.14 for HDLC, respectively. These results suggest that TPC and lipoprotein concentrations are influenced by additive genetic effects in cynomolgus monkeys, establishing their importance as an animal model for studying the genetics of lipoproteins.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Realized Sampling Variances of Estimates of Genetic Parameters and the Difference between Genetic and Phenotypic Correlations

A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.     

Genetic parameters for direct and maternal effects on body weights of Draa goats

Genetic parameters and (co)variance components were estimated for weights at birth and at 30, 90 and 180 days of age for Draa goat maintained at Ouarzazate station over a period of 18 years (1988–2005). Records of 1498 kids, the progeny of 46 sires and 404 dams were used in the study. Analyses were carried out by restricted maximum likelihood. Six different animal models including or ignoring maternal genetic or permanent environmental effects were fitted for all traits. The Model 2 with only permanent environmental maternal effects seemed most suitable. Estimates of direct heritability from this model were 0.16 for birth weight and 0.07, 0.11 and 0.11 for weights at 30, 90 and 180 days, respectively. Maternal heritability estimates varied from 0.00 to 0.24 for all traits according to the model used (Models 4–6). Bivariate analysis by Model 2 was also used to estimate genetic correlations between traits. The estimates of genetic and phenotypic correlations among weights were positive and intermediate to high in value. Despite the low estimated heritabilities of body weight traits of Draa goat, there is a small genetic variability that may be exploited to improve growth performance.     

Possible biases in heritability estimates from intraclass correlation

Summary There is an inherent bias in intraclass correlations since the expectation of a ratio does not equal the ratio of expectations. A simple accurate approximation for this bias is derived, and it is found that the inherent bias is usually negligible. Selection of sires is known to bias half-sib heritability estimates, and appropriate formulae are given and discussed.     

单元内混合家系相关法和阈性状法估计遗传力的比较研究

本文提出了一种估计遗传力的方法即单元内混合家系相关法,并用这种方法及阈性状分析法进行了猪肢蹄结实度的遗传力估计,结果表明,对于多阈性状,用单元内混合家系相关法估计的结果准确性好。     

Making decisions about the optimal selection environment using Gibbs sampling

The use of Gibbs sampling in making decisions about the optimal selection environment was demonstrated. Marginal posterior distributions of the efficiency of selection across sites were obtained using the Gibbs sampler, a Bayesian method, from which the probability that the efficiency of selection lay between specified values and the variance of the distribution were computed, providing a lot of information on which to make decisions regarding the location of genetic tests. The heritability, genetic correlations and efficiencies of selection estimated using REML and Gibbs sampling were similar. However, the latter approach showed that the point estimates of the efficiencies of selection were subject to substantial error. The decision regarding selection at maturity was consistent with that obtained using point estimates from REML, but Gibbs sampling allowed the efficiencies of selection to be interpreted with more confidence. The decision regarding early selection differed from that based on REML point estimates. Generally, the decisions to make early selections at site B for planting at both site B and A, and to make selections at maturity at each individual site, were robust to different priors in the Gibbs sampling. Received: 19 June 2000 / Accepted: 18 October 2000     

Genetic correlation between heifer pregnancy and scrotal circumference measured at 15 and 18 months of age in Nellore cattle

Data of pregnancy diagnosis from 24,945 Nellore heifers, raised under tropical conditions in Brazil and exposed to breeding at about 14 months of age, were analyzed simultaneously with 13,742 (analysis 1), 36,091 (analysis 2), 8,405 (analysis 3), and 8,405 (analysis 4) scrotal circumference (SC) records of contemporary young bulls in order to estimate heritability (h(2)) for yearling heifer pregnancy (HP) and for SC measured at around 15 (SC15) and 18 (SC18) months of age and to estimate genetic correlation between HP and SC15 (SC18). Heifer pregnancy was considered as a categorical trait, with the value 1 (success) assigned to heifers that were detected as pregnant by rectal palpation approximately 60 days after the end of a 90-day breeding season and the value 0 (failure) otherwise. In analyses 1 and 3, SC was measured at around 15 months of age and in analysis 2 and 4 it was measured at around 18 months of age. Only 8,848 animals from datasets 1 and 2 were common in both files, which means the same animals measured at different ages. Datasets used in analyses 3 and 4 included the same animals, measured at 15 and at 18 months of age, respectively. Heritability estimates for HP were similar in all analyses, with values ranging from 0.66 +/- 0.08 to 0.67 +/- 0.008. For SC15, the estimates were 0.57 +/- 0.05 in analysis 1 and 0.60 +/- 0.07 in analysis 3. For SC18, the estimates were 0.53 +/- 0.03 in analysis 2 and 0.64 +/- 0.06 in analysis 4. The estimates of genetic correlation between HP and SC15 were 0.15 +/- 0.10 in analysis 1 and 0.11 +/- 0.11 in analysis 3. For the correlation between HP and SC18, the values were 0.27 +/- 0.10 in analysis 2 and 0.16 +/- 0.11 in analysis 4. Based on standard errors and confidence intervals, the best heritability and genetic correlation estimates were obtained from analysis 2, which included more data and a better pedigree structure. Pearson correlation between HP and SC breeding values was similar to the genetic correlation estimates obtained from two-trait models, when all animals in the pedigree file were considered for its calculation. If only sires were considered for the calculation, Pearson correlation was higher but the pattern was the same as from two-trait analyses. The high heritability estimates obtained in the present study confirm that expected progeny difference (EPD) for HP can be used to select bulls for the production of precocious daughters and that the low genetic correlation between SC and HP indicates a greater efficacy of selection based on heifer pregnancy EPD than of selection based on scrotal circumference EPD. The results of the present study, although not conclusive, indicate that SC measured at around SC18 would have a higher genetic correlation with HP than would SC measured at around SC15.     

EVOLUTION OF FLORAL TRAITS IN A HERMAPHRODITIC PLANT: FIELD MEASUREMENTS OF HERITABILITIES AND GENETIC CORRELATIONS

Genetic variances, heritabilities, and genetic correlations of floral traits were measured in the monocarpic perennial Ipomopsis aggregata (Polemoniaceae). A paternal half-sib design was employed to generate seeds in each of four years, and seeds were planted back in the field near the parental site. The progeny were followed for up to eight years to estimate quantitative genetic parameters subject to natural levels of environmental variation over the entire life cycle. Narrow-sense heritabilities of 0.2–0.8 were detected for the morphometric traits of corolla length, corolla width, stigma position, and anther position. The proportion of time spent by the protandrous flowers in the pistillate phase (“proportion pistillate”) also exhibited detectable heritability of near 0.3. In contrast, heritability estimates for nectar reward traits were low and not significantly different from zero, due to high environmental variance between and within flowering years. The estimates of genetic parameters were combined with phenotypic selection gradients to predict evolutionary responses to selection mediated by the hummingbird pollinators. One trait, corolla width, showed the potential for a rapid response to ongoing selection through male function, as it experienced both direct selection, by influencing pollen export, and relatively high heritability. Predicted responses were lower for proportion pistillate and corolla length, even though these traits also experienced direct selection. Stigma position was expected to respond positively to indirect selection of proportion pistillate but negatively to selection of corolla length, with the net effect sensitive to variation in the selection estimates. Anther position also was not directly selected but could respond to indirect selection of genetically correlated traits.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

The value of cows in reference populations for genomic selection of new functional traits

Today, almost all reference populations consist of progeny tested bulls. However, older progeny tested bulls do not have reliable estimated breeding values (EBV) for new traits. Thus, to be able to select for these new traits, it is necessary to build a reference population. We used a deterministic prediction model to test the hypothesis that the value of cows in reference populations depends on the availability of phenotypic records. To test the hypothesis, we investigated different strategies of building a reference population for a new functional trait over a 10-year period. The trait was either recorded on a large scale (30 000 cows per year) or on a small scale (2000 cows per year). For large-scale recording, we compared four scenarios where the reference population consisted of 30 sires; 30 sires and 170 test bulls; 30 sires and 2000 cows; or 30 sires, 2000 cows and 170 test bulls in the first year with measurements of the new functional trait. In addition to varying the make-up of the reference population, we also varied the heritability of the trait (h2 = 0.05 v. 0.15). The results showed that a reference population of test bulls, cows and sires results in the highest accuracy of the direct genomic values (DGV) for a new functional trait, regardless of its heritability. For small-scale recording, we compared two scenarios where the reference population consisted of the 2000 cows with phenotypic records or the 30 sires of these cows in the first year with measurements of the new functional trait. The results showed that a reference population of cows results in the highest accuracy of the DGV whether the heritability is 0.05 or 0.15, because variation is lost when phenotypic data on cows are summarized in EBV of their sires. The main conclusions from this study are: (i) the fewer phenotypic records, the larger effect of including cows in the reference population; (ii) for small-scale recording, the accuracy of the DGV will continue to increase for several years, whereas the increases in the accuracy of the DGV quickly decrease with large-scale recording; (iii) it is possible to achieve accuracies of the DGV that enable selection for new functional traits recorded on a large scale within 3 years from commencement of recording; and (iv) a higher heritability benefits a reference population of cows more than a reference population of bulls.     

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background

Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model.

Methods

We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters.

Results

Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed.

Conclusion

The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.     

Impact of genomic selection of AI dairy sires on their likely utilization and methods to estimate fertility: a paradigm shift

Breeding of dairy cattle is undergoing a paradigm shift to genomic selection of potential sires and dams. This undoubtedly will affect how bulls are managed in an artificial insemination (AI) center and impact methods to estimate their ‘fertility'. Our goal is to help decision-makers understand the contents of a straw of semen, current estimates of sire fertility, and how estimates might evolve in a genomic era. Sire fertility is estimated from outcome (pregnant or not) after 300 to > 2,000 inseminations and reported in units (U) as a sire's deviation from a population (> 500 bulls) average pregnancy rate (PR). Too often users do not recognize that imprecision of an estimate encompasses a 3-U range, or more. ‘True fertility' of the sire whose semen is inseminated influences outcome far less than ‘true fertility' of each female and a myriad of microenvironment and management factors. Further, AI centers discard substandard collections and intentionally adjust number of sperm per straw so that differences in pregnancy rates achieved by different sires are minimized! For > 80% of Holstein bulls, estimated ‘sire conception rates' are within a 5.4-U range. In the future, most sires will be 15 to 40 mo old and services will accumulate at > 1,000/mo. Estimated sire conception rates still will be a deviation from the population mean, but should be based on records for the most recent 6 or 12 mo, rather than 48 or 60 mo. Repeated ‘snap shots' every 2 mo would allow AI centers to adjust number of sperm per AI straw from genomic-sires in a timely manner, to maintain high pregnancy rates, and to meet market demands with sires producing ∼40% as many sperm as mature ‘proven sires' of yesteryear.     

Genetic parameters for feed intake,litter weight,body condition and rebreeding success in primiparous Norwegian Landrace sows

The aim of this study was to estimate genetic parameters for feed intake recorded as farmers’ perception of young sows’ appetite for the first 3 weeks of lactation (APP) and feed intake recorded for one day in the 3rd week of lactation (FEED), litter weight (LW) at 3 weeks, sow body condition at weaning (BC) and the following five reproduction traits: weaning-to-service interval of 1 to 7 days (WSI7), weaning-to-service interval of 1 to 50 days (WSI50), delayed service or not (DELAYED), pregnant on first service or not (PREGNANT) and litter size in 2nd parity (NBT2). The analyses included data on 4606 Norwegian Landrace 1st-parity sows and their litters. The Gibbs sampling method was used. The traits DELAYED and PREGNANT were analysed as threshold traits and APP, FEED, LW, BC, WSI7, WSI50 and NBT2 were analysed as linear traits. The heritability estimates for APP and FEED were low (<0.1), whereas the estimates for DELAYED and PREGNANT were rather high (0.4 and 0.3). The heritability estimate for BC was 0.2. The genetic correlations confirmed the complexity of breeding for sow performance; selection for heavy 1st litters may lead to lower body condition at weaning, which in turn leads to lower reproductive performance and smaller litters in 2nd parity. Selection for higher sow feed intake would improve body condition, but the simple way of measuring feed intake tested in this study (APP and FEED) cannot be recommended because of the low heritability obtained for these traits.     

Variation in the peacock’s train shows a genetic component

Female peafowl (Pavo cristatus) show a strong mating preference for males with elaborate trains. This, however, poses something of a paradox because intense directional selection should erode genetic variation in the males’ trains, so that females will no longer benefit by discriminating among males on the basis of these traits. This situation is known as the ‘lek paradox’, and leads to the theoretical expectation of low heritability in the peacock’s train. We used two independent breeding experiments, involving a total of 42 sires and 86 of their male offspring, to estimate the narrow sense heritabilities of male ornaments and other morphometric traits. Contrary to expectation, we found significant levels of heritability in a trait known to be used by females during mate choice (train length), while no significant heritabilities were evident for other, non-fitness related morphological traits (tarsus length, body weight or spur length). This study adds to the building body of evidence that high levels of additive genetic variance can exist in secondary sexual traits under directional selection, but further emphasizes the main problem of what maintains this variation.