Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Genetic parameters and response to selection for growth in tambaqui

Although the tambaqui (Colossoma macropomum) is the most cultivated native fish species in Brazil, estimated breeding values for growth traits are rarely used for selection of superior individuals in commercial fingerling production. This study aimed to estimate the (co)variance components of growth traits. Body weight, length and width of 2500 tambaqui were determined at tagging and at 6 and 12 months after tagging in a commercial breeding programme in Brazil. Heritability estimates were low for traits measured at tagging (0.10 to 0.19) and moderate to high for traits measured at 6 and 12 months (0.23 to 0.81). Common full-sib effects were high at tagging (>73%), low at 6 months and negligible at 12 months. Positive genetic correlations were found among growth traits at 12 months (0.84 to 0.99) and between growth traits at 6 and 12 months (0.80 to 0.92). These results show that animal selection can be performed at 6 months after tagging. Expected genetic gains for growth traits ranged from 8% to 31%. A simulation of the sex ratio was performed, as individuals did not reach sexual maturity during the experimental period. Because of the sexual dimorphism, more accurate heritability estimates were obtained when considering the female proportion to be 90% in the high-weight group. The findings indicate that it is possible to obtain considerable genetic gains in growth by selecting for growth traits. The development of a tool to determine the sex of animals at early stages can improve the response to selection in tambaqui.     

Testing for biases in selection on avian reproductive traits and partitioning direct and indirect selection using quantitative genetic models

Key life history traits such as breeding time and clutch size are frequently both heritable and under directional selection, yet many studies fail to document microevolutionary responses. One general explanation is that selection estimates are biased by the omission of correlated traits that have causal effects on fitness, but few valid tests of this exist. Here, we show, using a quantitative genetic framework and six decades of life‐history data on two free‐living populations of great tits Parus major, that selection estimates for egg‐laying date and clutch size are relatively unbiased. Predicted responses to selection based on the Robertson–Price Identity were similar to those based on the multivariate breeder's equation (MVBE), indicating that unmeasured covarying traits were not missing from the analysis. Changing patterns of phenotypic selection on these traits (for laying date, linked to climate change) therefore reflect changing selection on breeding values, and genetic constraints appear not to limit their independent evolution. Quantitative genetic analysis of correlational data from pedigreed populations can be a valuable complement to experimental approaches to help identify whether apparent associations between traits and fitness are biased by missing traits, and to parse the roles of direct versus indirect selection across a range of environments.     

Genetic parameters for test day milk yields of first lactation Holstein cows by random regression models

Covariance components for test day milk yield using 263 390 first lactation records of 32 448 Holstein cows were estimated using random regression animal models by restricted maximum likelihood. Three functions were used to adjust the lactation curve: the five-parameter logarithmic Ali and Schaeffer function (AS), the three-parameter exponential Wilmink function in its standard form (W) and in a modified form (W*), by reducing the range of covariate, and the combination of Legendre polynomial and W (LEG+W). Heterogeneous residual variance (RV) for different classes (4 and 29) of days in milk was considered in adjusting the functions. Estimates of RV were quite similar, rating from 4.15 to 5.29 kg². Heritability estimates for AS (0.29 to 0.42), LEG+W (0.28 to 0.42) and W* (0.33 to 0.40) were similar, but heritability estimates used W (0.25 to 0.65) were highest than those estimated by the other functions, particularly at the end of lactation. Genetic correlations between milk yield on consecutive test days were close to unity, but decreased as the interval between test days increased. The AS function with homogeneous RV model had the best fit among those evaluated.     

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.     

Genetic covariances within and between species: indirect selection for hybrid inviability

Genotype-environment interactions and natural selection can result in local specialization when different genotypes are favored in different environments. Restricted gene flow or genetic subdivision enhances local genetic diversification across a species when natural selection acts on such variation. The indirect evolution of reproductive isolation and the restriction of gene flow between species in statu nascendi may provide a central role for genotype-environment interactions in speciation genetics. We derive the expected genetic covariance between heterospecific and conspecific viability fitness under several different models of selection, dominance, and breeding structure. Standard quantitative genetic methods can be used to estimate these covariances in experimental studies. These genetic covariances permit us to evaluate in a formal way the indirect effects of selection within a species on the evolution of hybrid inviability between species. We find that, for autosomal loci and random mating, the genetic covariance across species is equal to the product of three quantities: (1) the viability of the best hybrid genotype; (2) the viability effect of an allele in hybrids; and, (3) the change in allele frequency due to selection in the conspecific population. Inbreeding within the conspecific population, expressed as Wright's coefficient, F, increases the genetic covariance by a factor (1 + F). In all cases, a negative genetic covariance across species is evidence for hybrid inviability evolving as an indirect effect of selection within species for adaptive (as opposed to neutral) genetic change. “It is an irony of evolutionary genetics, that although it is a fusion of Mendelism and Darwinism, it has made no direct contribution to what Darwin obviously saw as the fundamental problem: the origin of species…. While it is a question of elementary population genetics to state how many generations will be required for the frequency of an allele to change from q₁ to q₂, we do not know how to incorporate such a statement into speciation theory, in large part because we know virtually nothing about the genetic changes that occur in species formation.” (Lewontin 1974, p. 159)     

Random regression models for genetic evaluation of clinical mastitis in dairy cattle

A genetic analysis of longitudinal binary clinical mastitis (CM) data recorded on about 90 000 first-lactation Swedish Holstein cows was carried out using linear random regression models (RRM). This method for genetic evaluation of CM has theoretical advantages compared to the method of linear cross-sectional models (CSM), which is currently being used. The aim of this study was to investigate the feasibility and suitability of estimating genetic parameters and predicting breeding values for CM with a linear sire RRM. For validation purposes, the estimates and predictions from the RRM were compared to those from linear sire longitudinal multivariate models (LMVM) and CSM. For each cow, the period from 10 days before to 241 days after calving was divided into four 1-week intervals followed by eight 4-week intervals. Within each interval, presence or absence of CM was scored as '1' or '0'. The linear RRM used to explain the trajectory of CM over time included a set of explanatory variables plus a third-order Legendre polynomial function of time for the sire effect. The time-dependent heritabilities and genetic correlations from the chosen RRM corresponded fairly well with estimates obtained from the linear LMVM for the separate intervals. Some discrepancy between the two methods was observed, with the more unstable results being obtained from the linear LMVM. Both methods indicated clearly that CM was not genetically the same trait throughout lactation. The correlations between predicted sire breeding values from the RRM, summarized over different time periods, and from linear CSM were rather high. They were, however, less than unity (0.74 to 0.96), which indicated some re-ranking of sires. Sire curves based on the time-specific breeding values from the RRM illustrated differences in intercept and slope among the best and the worst sires. To conclude, a linear sire RRM seemed to work well for genetic evaluation purposes, but was sensitive for estimation of genetic parameters.     

Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning

Records for birth and subsequent, monthly weights until weaning on beef calves of two breeds in a selection experiment were analysed fitting random regression models. Independent variables were orthogonal (Legendre) polynomials of age at weighing in days. Orders of polynomial fit up to 6 were considered. Analyses were carried out fitting sets of random regression coefficients due to animals'' direct and maternal, additive genetic and permanent environmental effects, with changes in variances due to temporary environmental effects modelled through a variance function, estimating up to 67 parameters. Results identified similar patterns of variation for both breeds, with maternal effects considerably more important in purebred Polled Herefords than a four-breed synthetic, the so-called Wokalups. Conversely, repeatabilities were higher for the latter. For both breeds, heritabilities decreased after birth, being lowest when maternal effects were most important around 100 days of age. Estimates at birth and weaning were consistent with previous, univariate results.     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

Genetic variation for growth and selection in adult plants of Eucalyptus badjensis

The aim of this study was to evaluate Eucalyptus badjensis concerning the genetic variation for growth traits and the potential of the species in supporting a breeding programme. The field trial was a provenance/progeny test established in Campina da Alegria, Santa Catarina, Brazil (latitude 26°52′05.1″ S, longitude 51°48′47.5″ W, altitude 1,015 m) in a soil classified as Latossolic Alumino-Ferric Brown Nitosol. The experiment comprised 60 open-pollinated progenies from the provenances Glenbog and Badja State Forest, New South Wales, Australia. Ten replicates and plots with six plants in row were used. At the age of 17 years, 279 trees were assessed for diameter of the bole at breast height (DBH), total tree height (H) and volume of wood with bark (Vol). After submitting the data to statistical genetic analysis, the overall means for DBH, H and Vol were 45.17 cm, 33.30 m and 2.84 m³, and the estimates of additive coefficient of variation [CV^a(%)] were 12.59%, 5.91% and 26.51%, respectively. Heritability coefficients of additive effects (h^a2) were also estimated and the following values were found: 0.443, 0.312 and 0.358. Thirty-nine trees from 25 different progenies were selected. The expected means of the provenances after improvement were 50.02 cm, 34.35 m and 3.47 m³ for DBH, H and Vol, respectively.     

Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models

Variance components for five consecutive measurements of body weight in Polish sheep were estimated using random regression and multi-trait animal models. The data included between 7856 and 31694 body weight records at 5 age classes from birth to 150 days of age. The random additive genetic, maternal environmental and individual permanent environmental effects were fitted. All variance components were increasing over time (not at equal rates), which reflects increasing phenotypic mean and variance with age. Direct heritability tended to increase with age, whereas the effect of dam was reduced for older ages, and the proportion of permanent environmental component was relatively stable. Generally, similar tendencies were registered for estimates obtained via multi-trait animal model. The results confirm that there is a scope for genetic improvement in growth pattern in Polish sheep.     

Semiparametric models for missing covariate and response data in regression models

We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.     

Genetic (co)variation in skin pigmentation patterns and growth in rainbow trout

From a physiological-behavioral perspective, it has been shown that fish with a higher density of black eumelanin spots are more dominant, less sensitive to stress, have higher feed intake, better feed efficiency and therefore are larger in size. Thus, we hypothesized that genetic (co)variation between skin pigmentation patterns and growth exists and it is advantageous in rainbow trout. The objective of this study was to determine the genetic relationships between skin pigmentation patterns and BW in a breeding population of rainbow trout. We performed a genetic analysis of pigmentation traits including dorsal color (DC), lateral band (LB) intensity, amount of spotting above (SA) and below (SB) the lateral line, and BW at harvest (HW). Variance components were estimated using a multi-trait linear animal model fitted by restricted maximum likelihood. Estimated heritabilities were 0.08±0.02, 0.17±0.03, 0.44±0.04, 0.17±0.04 and 0.23±0.04 for DC, LB, SA, SB and HW, respectively. Genetic correlations between HW and skin color traits were 0.42±0.13, 0.32±0.14 and 0.25±0.11 for LB, SA and SB, respectively. These results indicate positive, but low to moderate genetic relationships between the amount of spotting and BW in rainbow trout. Thus, higher levels of spotting are genetically associated with better growth performance in this population.     

Non-linear recursive models for growth traits in the Pirenaica beef cattle breed

One of the main goals of selection schemes in beef cattle populations is to increase carcass weight at slaughter. Live weights at different growth stages are frequently used as selection criteria under the hypothesis that they usually have a high and positive genetic correlation with weight at slaughter. However, the presence of compensatory growth may bias the prediction ability of early weights for selection purposes. Recursive models may represent an interesting alternative for understanding the genetic and phenotypic relationship between weight traits during growth. For the purposes of this study, the analysis was performed for three different set of data from the Pirenaica beef cattle breed: weight at 120 days (W120) and at 210 days (W210); W120 and carcass weight at slaughter at 365 days (CW365); W210 and CW365. The number of records for each analysis was 8592, 4648 and 3234, respectively. A pedigree composed of 56323 individuals was also included. The statistical model comprised sex, year-season of birth, herd and slaughterhouse, plus a non-linear recursive dependency between traits. The dependency was modeled as a polynomial up to the 4th degree and models were compared using a Logarithm of Conditional Predictive Ordinates. The results of model comparison suggest that the best models were the 3rd degree polynomial for W120-W210 and W120-CW365 and the 2nd degree polynomial for W210-CW365. The posterior mean estimates for heritabilities ranged between 0.29 and 0.44 and the posterior mean estimates of the genetic correlations were null or very low, indicating that the relationship between traits is fully captured by the recursive dependency. The results imply that the predictive ability of the performance of future growth is low if it is only based on records of early weights. The usefulness of slaughterhouse records in beef cattle breeding evaluation is confirmed.     

Genetic gain from selection for rooting ability and early growth in vegetatively propagated clones of loblolly pine

A successful clonal forestry program for loblolly pine based on rooted cutting technology needs to consider selection for both rooting ability and subsequent field growth. Rooting ability and second-year height were assessed in more than 2,000 clones from 70 full-sib families of loblolly pine. The bivariate analysis of rooting ability from five rooting trials and field growth from six field trials allowed for estimation of the genetic covariance between rooting ability and second-year height for parental effects, full-sib family effects, and the total genetic value of clones within full-sib family. There was a positive genetic relationship between rooting ability and second-year height at all three genetic levels. The genetic correlation at the parental level between rooting ability and second-year height was 0.32. At the full-sib family level, the genetic correlation between traits was 0.39. The correlation of total genetic values of clones for rooting ability and second-year height was 0.29. The genetic gain in rooting ability and second-year height was estimated for a number of deployment options based on various selection scenarios using the best linear unbiased prediction (BLUP) values from the bivariate analysis. The deployment strategies compared were (1) half-sib family deployment, (2) full-sib family deployment, and (3) clonal deployment. Moderate to high family and clonal mean heritabilities, moderate to high type B genetic correlations, and substantial among-family and among-clone genetic variation indicate the potential for increasing rooting efficiency and improving growth.     

Genetic parameters and selection efficiency using part-records for production traits in strawberries

Summary The efficiency of selection for yield and fruit size using parts of the complete-season record was evaluated using data collected for individual strawberry seedlings (Fragaria x annanasa) in four genetic tests. Part-records were generated for each trait using cumulative weekly sums, and these were compared with complete records to assess the value of extended data collection. In addition, part-records were generated using data from alternate weeks of harvest. Scoring separate sets of seedlings in alternate weeks was assumed to allow a doubling of the unselected population size, halving the selection proportion and increasing selection intensity. Heritabilities estimated for part-records were often larger for mid-season cumulative part-records than for the complete-season records. Seasonal patterns for broad-sense and narrow-sense heritabilities differed, suggesting temporal expression of genes that condition yield and fruit size. Predicted genetic gains were largest using cumulative part-records between 4 and 12 weeks of the 15-week season, depending on trait and breeding objective (breeding value versus clonal value), with 8–9 weeks as a reasonable compromise. Selection using alternate-weeks records was identified as an efficient alternative to selection using total complete-season records. Superiority of the alternate-weeks option depends on the balance between increased selection intensity and decreased individual genetic information, and will differ for specific traits and program designs.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Genetic parameters for growth, reproductive and maternal traits in a multibreed meat sheep population

The genetic parameters for growth, reproductive and maternal traits in a multibreed meat sheep population were estimated by applying the Average Information Restricted Maximum Likelihood method to an animal model. Data from a flock supported by the Programa de Melhoramento Genético de Caprinos e Ovinos de Corte (GENECOC) were used. The traits studied included birth weight (BW), weaning weight (WW), slaughter weight (SW), yearling weight (YW), weight gain from birth to weaning (GBW), weight gain from weaning to slaughter (GWS), weight gain from weaning to yearling (GWY), age at first lambing (AFL), lambing interval (LI), gestation length (GL), lambing date (LD - number of days between the start of breeding season and lambing), litter weight at birth (LWB) and litter weight at weaning (LWW). The direct heritabilities were 0.35, 0.81, 0.65, 0.49, 0.20, 0.15 and 0.39 for BW, WW, SW, YW, GBW, GWS and GWY, respectively, and 0.04, 0.06, 0.10, 0.05, 0.15 and 0.11 for AFL, LI, GL, LD, LWB and LWW, respectively. Positive genetic correlations were observed among body weights. In contrast, there was a negative genetic correlation between GBW and GWS (-0.49) and GBW and GWY (-0.56). Positive genetic correlations were observed between AFL and LI, LI and GL, and LWB and LWW. These results indicate a strong maternal influence in this herd and the presence of sufficient genetic variation to allow mass selection for growth traits. Additive effects were of little importance for reproductive traits, and other strategies are necessary to improve the performance of these animals.     

The constancy of the G matrix through species divergence and the effects of quantitative genetic constraints on phenotypic evolution: a case study in crickets

Long-term phenotypic evolution can be modeled using the response-to-selection equation of quantitative genetics, which incorporates information about genetic constraints (the G matrix). However, little is known about the evolution of G and about its long-term importance in constraining phenotypic evolution. We first investigated the degree of conservation of the G matrix across three species of crickets and qualitatively compared the pattern of variation of G to the phylogeny of the group. Second, we investigated the effect of G on phenotypic evolution by comparing the direction of greatest quantitative genetic variation within species (g(max)) to the direction of phenotypic divergence between species (Delta(z)). Each species, Gryllus veletis, G. firmus, and G. pennsylvanicus, was reared in the laboratory using a full-sib breeding design to extract quantitative genetic information. Five morphological traits related to size were measured. G matrices were compared using three statistical approaches: the T method, the Flury hierarchy, and the MANOVA method. Results revealed that the differences between matrices were small and mostly caused by differences in the magnitude of the genetic variation, not by differences in principal component structure. This suggested that the G matrix structure of this group of species was preserved, despite significant phenotypic divergence across species. The small observed differences in G matrices across species were qualitatively consistent with genetic distances, whereas ecological information did not provide a good prediction of G matrix variation. The comparison of g(max) and Delta(z) revealed that the angle between these two vectors was small in two of three species comparisons, whereas the larger angle corresponding to the third species comparison was caused in large part by one of the five traits. This suggests that multivariate phenotypic divergence occurred mostly in a direction predicted by the direction of greatest genetic variation, although it was not possible to demonstrate the causal relationship from G to Delta(z). Overall, this study provided some support for the validity of the predictive power of quantitative genetics over evolutionary time scales.     

Longitudinal analysis of residual feed intake and BW in mink using random regression with heterogeneous residual variance

The aim of this study was to determine the genetic background of longitudinal residual feed intake (RFI) and BW gain in farmed mink using random regression methods considering heterogeneous residual variances. The individual BW was measured every 3 weeks from 63 to 210 days of age for 2139 male+female pairs of juvenile mink during the growing-furring period. Cumulative feed intake was calculated six times with 3-week intervals based on daily feed consumption between weighing’s from 105 to 210 days of age. Genetic parameters for RFI and BW gain in males and females were obtained using univariate random regression with Legendre polynomials containing an animal genetic effect and permanent environmental effect of litter along with heterogeneous residual variances. Heritability estimates for RFI increased with age from 0.18 (0.03, posterior standard deviation (PSD)) at 105 days of age to 0.49 (0.03, PSD) and 0.46 (0.03, PSD) at 210 days of age in male and female mink, respectively. The heritability estimates for BW gain increased with age and had moderate to high range for males (0.33 (0.02, PSD) to 0.84 (0.02, PSD)) and females (0.35 (0.03, PSD) to 0.85 (0.02, PSD)). RFI estimates during the growing period (105 to 126 days of age) showed high positive genetic correlations with the pelting RFI (210 days of age) in male (0.86 to 0.97) and female (0.92 to 0.98). However, phenotypic correlations were lower from 0.47 to 0.76 in males and 0.61 to 0.75 in females. Furthermore, BW records in the growing period (63 to 126 days of age) had moderate (male: 0.39, female: 0.53) to high (male: 0.87, female: 0.94) genetic correlations with pelting BW (210 days of age). The result of current study showed that RFI and BW in mink are highly heritable, especially at the late furring period, suggesting potential for large genetic gains for these traits. The genetic correlations suggested that substantial genetic gain can be obtained by only considering the RFI estimate and BW at pelting, however, lower genetic correlations than unity indicate that extra genetic gain can be obtained by including estimates of these traits during the growing period. This study suggests random regression methods are suitable for analysing feed efficiency and BW gain; and genetic selection for RFI in mink is promising.