Estimation of genetic parameters for monthly egg production in laying hens based on random regression models

Heritability and genetic correlations of monthly egg production under random regression models were estimated. Three layer lines (A22, A88, K66) in six consecutive generations were analysed. A22 (13, 770 recorded hens) and A88 (13, 950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9, 351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. Eight models with different orders of Legendre polynomials were applied. Adequacy of the models was checked by the Akaike Information Criterion. According to the most adequate model including second order Legendre polynomials for fixed effects and third order for additive genetic and permanent environmental effects, relatively high heritabilities were estimated in the first (h²=0.3) and final (h² above 0.3) periods of production with a substantial decrease in heritability during the egg production peak. Methodology based on random regression animal models can be recommended for genetic evaluation of laying hens.     

Genetic gains from reciprocal recurrent and within-line selection for egg production in the fowl

Summary Selection for survivors percent egg production from first egg to 40 weeks of age was conducted for six generations. Within-line selection (WLS) on the basis of an index of individual records plus sire family and dam family means was compared with reciprocal recurrent selection (RRS) based on sire family selection among cross progeny. Genetically heterogeneous synthetic populations, the Cornell Control and the Purdue Pool strains were used.The responses to WLS (3.84 °) and RRS (2.57 °) were both significantly greater than zero, but were not significantly different from each other. Nevertheless, the responses were proportional to their predicted values (.363 vs. 340). The advantage of WLS was due to the mechanics of selection resulting in slightly greater selection intensity and an increased correlation between the criterion of selection and the trait being improved. On the contrary, the RRS method had a slightly larger realized heritability as would be expected in the presence of non-additive genetic variance. Four of five pure-lines selected under both methods had statistically significant declines in performance due to inbreeding depression effects. All of the results observed are comparable with known genetic theory.Some problems in comparing genetic gains from different selection methods or selection criteria are discussed.Journal Paper No. 4986 of the Purdue University Agricultural Experiment Station. Conducted in cooperation with the Regional Poultry Breeding Laboratory, Project N. C. 89. Supported in part by N. I. H. Grant No. ES00310.     

Identification of Promising Mutants Associated with Egg Production Traits Revealed by Genome-Wide Association Study

Egg number (EN), egg laying rate (LR) and age at first egg (AFE) are important production traits related to egg production in poultry industry. To better understand the knowledge of genetic architecture of dynamic EN during the whole laying cycle and provide the precise positions of associated variants for EN, LR and AFE, laying records from 21 to 72 weeks of age were collected individually for 1,534 F₂ hens produced by reciprocal crosses between White Leghorn and Dongxiang Blue-shelled chicken, and their genotypes were assayed by chicken 600 K Affymetrix high density genotyping arrays. Subsequently, pedigree and SNP-based genetic parameters were estimated and a genome-wide association study (GWAS) was conducted on EN, LR and AFE. The heritability estimates were similar between pedigree and SNP-based estimates varying from 0.17 to 0.36. In the GWA analysis, we identified nine genome-wide significant loci associated with EN of the laying periods from 21 to 26 weeks, 27 to 36 weeks and 37 to 72 weeks. Analysis of GTF2A1 and CLSPN suggested that they influenced the function of ovary and uterus, and may be considered as relevant candidates. The identified SNP rs314448799 for accumulative EN from 21 to 40 weeks on chromosome 5 created phenotypic differences of 6.86 eggs between two homozygous genotypes, which could be potentially applied to the molecular breeding for EN selection. Moreover, our finding showed that LR was a moderate polygenic trait. The suggestive significant region on chromosome 16 for AFE suggested the relationship between sex maturity and immune in the current population. The present study comprehensively evaluates the role of genetic variants in the development of egg laying. The findings will be helpful to investigation of causative genes function and future marker-assisted selection and genomic selection in chickens.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not the naked neck gene

In order to investigate the possibility of using the dwarf gene for egg production, two dwarf brown-egg laying lines were selected for 16 generations on average clutch length; one line (L1) was normally feathered and the other (L2) was homozygous for the naked neck gene NA. A control line from the same base population, dwarf and segregating for the NA gene, was maintained during the selection experiment under random mating. The average clutch length was normalized using a Box-Cox transformation. Genetic variability and selection response were estimated either with the mixed model methodology, or with the classical methods for calculating genetic gain, as the deviation from the control line, and the realized heritability, as the ratio of the selection response on cumulative selection differentials. Heritability of average clutch length was estimated to be 0.42 ± 0.02, with a multiple trait animal model, whereas the estimates of the realized heritability were lower, being 0.28 and 0.22 in lines L1 and L2, respectively. REML estimates of heritability were found to decline with generations of selection, suggesting a departure from the infinitesimal model, either because a limited number of genes was involved, or their frequencies were changed. The yearly genetic gains in average clutch length, after normalization, were estimated to be 0.37 ± 0.02 and 0.33 ± 0.04 with the classical methods, 0.46 ± 0.02 and 0.43 ± 0.01 with animal model methodology, for lines L1 and L2 respectively, which represented about 30% of the genetic standard deviation on the transformed scale. Selection response appeared to be faster in line L2, homozygous for the NA gene, but the final cumulated selection response for clutch length was not different between the L1 and L2 lines at generation 16.     

Evidence for genetic control of nematode egg-shedding rates in calves

Differences in nematode fecal egg counts from 167 purebred Angus calves born in 1986 and 133 born in 1987 that had been naturally exposed to infection on pasture were analyzed for sire effects. The calves were sired by 26 different bulls, all of which were related. Differences among fecal egg counts were attributable to sires (P less than 0.0002), to age of the calf (P less than 0.0007), to age of dam (P less than 0.05), and to collection year (P less than 0.0001). No variation in fecal egg count was attributable to calf sex (P greater than 0.23). After accounting for the effects of year, age of calf, and age of dam, heritability was estimated to be 29% (SE = 18%). It was concluded that a paternal contribution to the genome of each calf played an important role in determining average fecal egg output of the sire group. With heritability at 29%, selection against higher fecal egg counts or selection for lower fecal egg counts would be expected to produce measurable genetic change in a population.     

Genetic associations between weight at maturity and maturation rate with ages and weights at first and second calving in Canchim beef cattle

Genetic parameters for weight at maturity (WM), maturation rate (MR), age and weight at first calving (AFC and WFC) and second calving (ASC and WSC) were estimated for females of the Canchim breed. The number of records per trait ranged from 1440 to 1923. The restricted maximum likelihood method was used and the statistical model included the fixed effect of contemporary group and the additive genetic and residual as random effects. The mean heritability estimate and respective standard errors were 0.34±0.05 (WM), 0.13±0.04 (MR), 0.14±0.04 (AFC), 0.44±0.06 (WFC), 0.16±0.06 (ASC) and 0.39±0.06 (WSC). The heritability estimate for WM and MR suggested that it would be possible to achieve changes in the animals' growth curve through selection, but the genetic correlation between these two traits suggested that there would be antagonism between them. Selection for WM would result in animals with later growth and would also affect individuals' sexual precocity. This was also seen from the genetic correlations between WM and the other traits, which ranged from 0.37 to 0.98; and between MR and the other traits, which ranged from -0.83 to -0.25. Selection to modify WM would be expected to result in correlated responses in AFC, WFC and WSC and a moderate response in ASC. Although the heritability estimate for MR was low, selection aimed for its increase might cause a large decrease in AFC, ASC and WFC and a moderate change in WSC, and this could be an alternative for improving the progeny's overall performance.     

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.     

Curvilinear inbreeding effects on some performance traits in laying hens

Quadratic partial regression coefficients were estimated for the inbreeding level on five performance traits (body weight, average egg weight, age at first egg, percentage of fertilized eggs, and hatchability of set eggs) of two strains of laying hens. Data on 5631 of H77 layers and 3563 of N88 layers from nine consecutive generations were analysed. Only dams were accounted for. Partial regression coefficients were estimated by REML with a single-trait animal model, which included fixed effects (generation and hatching period) and random effects (additive genetic and error effects). The mean inbreeding level was 0.87% in strain H77 and 1.08% in strain N88. The inbreeding effects were analysed based on the quadratic partial regression equations. A slight inbreeding depression was found for all the traits analysed in N88. In strain H77, negative effects of inbreeding were only noted for body weight and average egg weight. The small inbreeding effects shown here resulted from a relatively low level of homozygosity in the populations studied. The strains were found to differ in the effects of inbreeding. It is worth pointing out that differences were noted both between the inbreeding depression estimated from the partial linear regression equation and the quadratic partial regression equation, as well as different inbreeding levels.     

Repeatability and heritability of reproductive traits in free-ranging snakes

The underlying genetic basis of life-history traits in free-ranging animals is critical to the effects of selection on such traits, but logistical constraints mean that such data are rarely available. Our long-term ecological studies on free-ranging oviparous snakes (keelbacks, Tropidonophis mairii (Gray, 1841), Colubridae) on an Australian floodplain provide the first such data for any tropical reptile. All size-corrected reproductive traits (egg mass, clutch size, clutch mass and post-partum maternal mass) were moderately repeatable between pairs of clutches produced by 69 female snakes after intervals of 49-1152 days, perhaps because maternal body condition was similar between clutches. Parent-offspring regression of reproductive traits of 59 pairs of mothers and daughters revealed high heritability for egg mass (h2= 0.73, SE=0.24), whereas heritability for the other three traits was low (< 0.37). The estimated heritability of egg mass may be inflated by maternal effects such as differential allocation of yolk steroids to different-sized eggs. High heritability of egg size may be maintained (rather than eroded by stabilizing selection) because selection acts on a trait (hatchling size) that is determined by the interaction between egg size and incubation substrate rather than by egg size alone. Variation in clutch size was mainly because of environmental factors (h2=0.04), indicating that one component of the trade-off between egg size and clutch size is under much tighter genetic control than the other. Thus, the phenotypic trade-off between egg size and egg number in keelback snakes occurs because each female snake must allocate a finite amount of energy into eggs of a genetically determined size.     

Inheritance of fertility in broiler chickens

Background

The fertility of a chicken''s egg is a trait which depends on both the hen that lays the egg and on her mate. It is also known that fertility of an individual changes over the laying period.

Methods

Longitudinal models including both random genetic and permanent environmental effects of both the female and her male mate were used to model the proportion of fertile eggs in a pedigree broiler population over the ages 29-54 weeks.

Results

Both the male and the female contribute to variation in fertility. Estimates of heritability of weekly records were typically 7% for female and 10% for male contributions to fertility. Repeatability estimates ranged from 24 to 33%, respectively. The estimated genetic variance remained almost constant for both sexes over the laying period and the genetic correlations between different ages were close to 1.0. The permanent environment components increased substantially towards the end of the analyzed period, and correlations between permanent environment effects at different ages declined with increasing age difference The heritability of mean fertility over the whole laying period was estimated at 13% for females and 17% for males. A small positive correlation between genetic effects for male and female fertility was found.

Conclusion

Opportunities to improve fertility in broiler stocks by selection on both sexes exist and should have an impact throughout the laying period.     

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.     

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.     

Nematospiroides dubius: direct and correlated responses to selection for high and low immune responsiveness in mice

High and low immune responder lines of mice were bred selectively from an allogeneic stock over 10 generations, based on their fecal parasite egg count assayed 3 weeks after reinfection with 100 Nematospiroides dubius larvae. By generation 10, (F10), the low immune response mice voided about 10 times as many fecal N. dubius eggs as the high immune response mice. Realized heritability for the selected trait, fecal egg count after secondary infection (= protective immunity), was 0.35 at F7. F7 was considered the selection limit. Selection for change in fecal egg count did not significantly influence the conformational nor reproductive characteristics of these mice. Significant phenotypic and genetic correlations were evident between the selected character and innate immunity to N. dubius, humoral antibody response to N. dubius infection, and establishment, growth, and reproduction of N. dubius in the selected mice.     

DNA polymorphism in various goose lines by RAPD-PCR

RAPD markers often primers were used to assess the polymorphism among pooled DNA of eight goose lines. The number of bands amplified by each primer ranged from 1 to 8, within a mean of 2.86. Some bands appeared specific for the line or genetic background. RAPD technique is an effective method for generating the polymorphic DNA marker in the goose. RAPD patterns from mixed DNA samples can reflect the genetic information of populations. The present study indicated that 10 generations selected for egg production and body weight under various pressure, resulted in genetic variation among goose lines as detected by RAPD. Selection for meat traits caused greater genetic diversity than selection for egg production.     

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.     

Estimates of genetic parameters for Holstein cows for test-day yield traits with a random regression cubic spline model

Genetic parameters were estimated with restricted maximum likelihood for individual test-day milk, fat, and protein yields and somatic cell scores with a random regression cubic spline model. Test-day records of Holstein cows that calved from 1994 through early 1999 were obtained from Dairy Records Management Systems in Raleigh, North Carolina, for the analysis. Estimates of heritability for individual test-days and estimates of genetic and phenotypic correlations between test-days were obtained from estimates of variances and covariances from the cubic spline analysis. Estimates were calculated of genetic parameters for the averages of the test days within each of the ten 30-day test intervals. The model included herd test-day, age at first calving, and bovine somatropin treatment as fixed factors. Cubic splines were fitted for the overall lactation curve and for random additive genetic and permanent environmental effects, with five predetermined knots or four intervals between days 0, 50, 135, 220, and 305. Estimates of heritability for lactation one ranged from 0.10 to 0.15, 0.06 to 0.10, 0.09 to 0.15, and 0.02 to 0.06 for test-day one to test-day 10 for milk, fat, and protein yields and somatic cell scores, respectively. Estimates of heritability were greater in lactations two and three. Estimates of heritability increased over the course of the lactation. Estimates of genetic and phenotypic correlations were smaller for test-days further apart.     

Analysis of response to 20 generations of selection for body composition in mice: fit to infinitesimal model assumptions

Data were analysed from a divergent selection experiment for an indicator of body composition in the mouse, the ratio of gonadal fat pad to body weight (GFPR). Lines were selected for 20 generations for fat (F), lean (L) or were unselected (C), with three replicates of each. Selection was within full-sib families, 16 families per replicate for the first seven generations, eight subsequently. At generation 20, GFPR in the F lines was twice and in the L lines half that of C. A log transformation removed both asymmetry of response and heterogeneity of variance among lines, and so was used throughout. Estimates of genetic variance and heritability (approximately 50%) obtained using REML with an animal model were very similar, whether estimated from the first few generations of selection, or from all 20 generations, or from late generations having fitted pedigree. The estimates were also similar when estimated from selected or control lines. Estimates from REML also agreed with estimates of realised heritability. The results all accord with expectations under the infinitesimal model, despite the four-fold changes in mean. Relaxed selection lines, derived from generation 20, showed little regression in fatness after 40 generations without selection.     

Genetic correlations between production and disease traits during first lactation in Holstein cows

The aim of this study was to estimate genetic correlations between milk yield, somatic cell score (SCS), mastitis, and claw and leg disorders (CLDs) during first lactation in Holstein cows by using a threshold–linear random regression test-day model. We used daily records of milk, fat and protein yields; somatic cell count (SCC); and mastitis and CLD incidences from 46 771 first-lactation Holstein cows in Hokkaido, Japan, that calved between 2000 and 2009. A threshold animal model for binary records (mastitis and CLDs) and linear animal model for yield traits were applied in our multiple trait analysis. For both liabilities and yield traits, additive genetic effects were used as random regression on cubic Legendre polynomials of days on milk. The highest positive genetic correlations between yields and disease incidences (0.36 for milk and mastitis, 0.56 for fat and mastitis, 0.24 for protein and mastitis, 0.32 for milk and CLD, 0.44 for fat and CLD and 0.31 for protein and CLD) were estimated at about the time of peak milk yield (36 to 65 days in milk). Selection focused on early lactation yield may therefore increase the risk of mastitis and CLDs. The positive genetic correlations of SCS with mastitis or CLD incidence imply that selection to reduce SCS in the early stages of lactation would decrease the incidence of both mastitis and CLD.     

A Bayesian generalized random regression model for estimating heritability using overdispersed count data

Background

Faecal egg counts are a common indicator of nematode infection and since it is a heritable trait, it provides a marker for selective breeding. However, since resistance to disease changes as the adaptive immune system develops, quantifying temporal changes in heritability could help improve selective breeding programs. Faecal egg counts can be extremely skewed and difficult to handle statistically. Therefore, previous heritability analyses have log transformed faecal egg counts to estimate heritability on a latent scale. However, such transformations may not always be appropriate. In addition, analyses of faecal egg counts have typically used univariate rather than multivariate analyses such as random regression that are appropriate when traits are correlated. We present a method for estimating the heritability of untransformed faecal egg counts over the grazing season using random regression.

Results

Replicating standard univariate analyses, we showed the dependence of heritability estimates on choice of transformation. Then, using a multitrait model, we exposed temporal correlations, highlighting the need for a random regression approach. Since random regression can sometimes involve the estimation of more parameters than observations or result in computationally intractable problems, we chose to investigate reduced rank random regression. Using standard software (WOMBAT), we discuss the estimation of variance components for log transformed data using both full and reduced rank analyses. Then, we modelled the untransformed data assuming it to be negative binomially distributed and used Metropolis Hastings to fit a generalized reduced rank random regression model with an additive genetic, permanent environmental and maternal effect. These three variance components explained more than 80 % of the total phenotypic variation, whereas the variance components for the log transformed data accounted for considerably less. The heritability, on a link scale, increased from around 0.25 at the beginning of the grazing season to around 0.4 at the end.

Conclusions

Random regressions are a useful tool for quantifying sources of variation across time. Our MCMC (Markov chain Monte Carlo) algorithm provides a flexible approach to fitting random regression models to non-normal data. Here we applied the algorithm to negative binomially distributed faecal egg count data, but this method is readily applicable to other types of overdispersed data.