AN ANALYSIS OF VARIABILITY IN NUMBER OF DIGITS IN AN INBRED STRAIN OF GUINEA PIGS

Genetic parameters for pathogen-specific mastitis resistance in Danish Holstein Cattle

The objective of this study was to estimate heritabilities for and genetic correlations among different pathogen-specific mastitis traits. The traits were unspecific mastitis, which is all mastitis treatments regardless of the causative pathogen as well as mastitis caused by Streptococcus dysgalactiae, Escherichia coli, coagulase-negative staphylococci (CNS), Staphylococcus aureus and Streptococcus uberis. Also groups of pathogens were investigated, Gram-negative v. Gram-positive and contagious v. environmental pathogens. Data from 168 158 Danish Holstein cows calving first time between 1998 and 2006 were used in the analyses. Variances and covariances were estimated using uni- and bivariate threshold models via Gibbs sampling. Posterior means of heritabilities of pathogen-specific mastitis were lower than the heritability of unspecific mastitis, ranging from 0.035 to 0.076 for S. aureus and S. uberis, respectively. The heritabilities of groups of pathogen ranged from 0.053 to 0.087. Genetic correlations among the pathogen-specific mastitis traits ranged from 0.45 to 0.77. These estimates tended to be lowest for bacteria eliciting very different immune responses, which can be considered as the overall pleiotropic effect of genes affecting resistance to a specific pathogen, and highest for bacteria sharing characteristics regarding immune response. The genetic correlations between the groups of pathogens were high, 0.73 and 0.83. Results showed that the pathogen-specific traits used in this study should be considered as different traits. Genetic evaluation for pathogen-specific mastitis resistance may be beneficial despite lower heritabilities than unspecific mastitis because a pathogen-specific mastitis trait is a direct measure of an udder infection, and because the cost of a mastitis case caused by different pathogens has been shown to differ greatly. Sampling bias may be present because there were not pathogen information on all mastitis treatments and because some farms do not record pathogen information. Therefore, improved recording of pathogen information and mastitis treatments in general is critical for a successful genetic evaluation of udder health. Also, economic values have to be specified for each pathogen-specific trait separately.

Evaluation of a bayesian model integration-based method for censored data

OBJECTIVE

Non-random missing data can adversely affect family-based linkage detection through loss of power and possible introduction of bias depending on how censoring is modeled. We examined the statistical properties of a previously proposed quantitative trait threshold (QTT) model developed for when censored data can be reasonably inferred to be beyond an unknown threshold.

METHODS

The QTT model is a Bayesian model integration approach implemented in the PPL framework that requires neither specification of the threshold nor imputation of the missing data. This model was evaluated under a range of simulated data sets and compared to other methods with missing data imputed.

RESULTS

Across the simulated conditions, the addition of a threshold parameter did not change the PPL's properties relative to quantitative trait analysis on non-censored data except for a slight reduction in the average PPL as a reflection of the lowered information content due to censoring. This remained the case for non-normally distributed data and extreme sampling of pedigrees.

CONCLUSIONS

Overall, the QTT model showed the smallest loss of linkage information relative to alternative approaches and therefore provides a unique analysis tool that obviates the need for ad hoc imputation of censored data in gene mapping studies.

Genetic variation underlying the expression of a polyphenism

Polyphenic traits are widespread and represent a conditional strategy sensitive to environmental cues. The environmentally cued threshold (ET) model considers the switchpoint between alternative phenotypes as a polygenic quantitative trait with normally distributed variation. However, the genetic variation for switchpoints has rarely been explored empirically. Here, we used inbred lines to investigate the genetic variation for the switchpoint in the mite Rhizoglyphus echinopus, in which males are either fighters or scramblers. The conditionality of male dimorphism varied among inbred lines, indicating that there was genetic variation for switchpoints in the base population, as predicted by the ET model. Our results also suggest a mixture between canalized and conditional strategists in R. echinopus. We propose that major genes that canalize morph expression and affect the extent to which a trait can be conditionally expressed could be a feature of the genetic architecture of threshold traits in other taxa.

A comparative method for both discrete and continuous characters using the threshold model

The threshold model developed by Sewall Wright in 1934 can be used to model the evolution of two-state discrete characters along a phylogeny. The model assumes that there is a quantitative character, called liability, that is unobserved and that determines the discrete character according to whether the liability exceeds a threshold value. A Markov chain Monte Carlo algorithm is used to infer the evolutionary covariances of the liabilities for discrete characters, sampling liability values consistent with the phylogeny and with the observed data. The same approach can also be used for continuous characters by assuming that the tip species have values that have been observed. In this way, one can make a comparative-methods analysis that combines both discrete and continuous characters. Simulations are presented showing that the covariances of the liabilities are successfully estimated, although precision can be achieved only by using a large number of species, and we must always worry whether the covariances and the model apply throughout the group. An advantage of the threshold model is that the model can be straightforwardly extended to accommodate within-species phenotypic variation and allows an interface with quantitative-genetics models.

Phenotypic differentiation is associated with gender plasticity and its responsive delay to environmental changes in Alternanthera philoxeroides--phenotypic differentiation in alligator weed

Phenotypic plasticity is common in many taxa, and it may increase an organism's fitness in heterogeneous environments. However, in some cases, the frequency of environmental changes can be faster than the ability of the individual to produce new adaptive phenotypes. The importance of such a time delay in terms of individual fitness and species adaptability has not been well studied. Here, we studied gender plasticity of Alternanthera philoxeroides to address this issue through a reciprocal transplant experiment. We observed that the genders of A. philoxeroides were plastic and reversible between monoclinous and pistillody depending on habitats, the offspring maintained the maternal genders in the first year but changed from year 2 to 5, and there was a cubic relationship between the rate of population gender changes and environmental variations. This relationship indicates that the species must overcome a threshold of environmental variations to switch its developmental path ways between the two genders. This threshold and the maternal gender stability cause a significant delay of gender changes in new environments. At the same time, they result in and maintain the two distinct habitat dependent gender phenotypes. We also observed that there was a significant and adaptive life-history differentiation between monoclinous and pistillody individuals and the gender phenotypes were developmentally linked with the life-history traits. Therefore, the gender phenotypes are adaptive. Low seed production, seed germination failure and matching phenotypes to habitats by gender plasticity indicate that the adaptive phenotypic diversity in A. philoxeroides may not be the result of ecological selection, but of gender plasticity. The delay of the adaptive gender phenotype realization in changing environments can maintain the differentiation between gender systems and their associated life-history traits, which may be an important component in evolution of novel traits and taxonomic diversity.

Inheritance of kernel row number, a multicategorical threshold trait of maize ears

Information about the inheritance of threshold traits is scarce, especially in plants. We examined the genetic control of kernel row number in maize (Zea mays). Knowledge of this inheritance is especially important because it is a primary component of grain yield. This trait has a discontinuous distribution. Characters like these are conceptualized as threshold traits. Crosses were made between the inbred line Geneze 3 (G3) with many kernel rows and the inbreds Argentino IV (A4) and Dente de Cravo (DC), with fewer kernel rows. The F(1) and F(2) generations and the backcrosses BC(11) and BC(21) were obtained for the combinations G3 x A4 and G3 x DC. These populations were evaluated under field conditions, and the kernel row number was determined by direct counting of approximately 14, 140 and 75 ears for the F(1), F(2) and backcrosses, respectively. Genetic control was determined through estimates of generation means and variance analysis and was also performed by Wright's method for threshold traits. It was found that genetic control is predominantly due to additive alleles. The component a, was greater than zero, additive variance was positive and the variance of dominance did not differ from zero. In the F(2) generation, the range of the kernel row number was 10 to 28 in G3 x A4, while in G3 x DC it was 12 to 26. Inheritance of the number of kernel rows, estimated by the two methods, gave similar results. This correspondence is due to adjusting of the data to the normal distribution.

Using the product threshold model for estimating separately the effect of temperature on male and female fertility

Animals under environmental thermal stress conditions have reduced fertility due to impairment of some mechanisms involved in their reproductive performance that are different in males and females. As a consequence, the most sensitive periods of time and the magnitude of effect of temperature on fertility can differ between sexes. The objective of this study was to estimate separately the effect of temperature in different periods around the insemination time on male and on female fertility by using the product threshold model. This model assumes that an observed reproduction outcome is the result of the product of 2 unobserved variables corresponding to the unobserved fertilities of the 2 individuals involved in the mating. A total of 7,625 AI records from rabbits belonging to a line selected for growth rate and indoor daily temperature records were used. The average maximum daily temperature and the proportion of days in which the maximum temperature was greater than 25°C were used as temperature descriptors. These descriptors were calculated for several periods around the day of AI. In the case of males, 4 periods of time covered different stages of the spermatogenesis, the transit through the epididymus of the sperm, and the day of AI. For females, 5 periods of time covered the phases of preovulatory follicular maturation including day of AI and ovulation, fertilization and peri-implantational stage of the embryos, embryonic and early fetal periods of gestation, and finally, late gestation until birth. The effect of the different temperature descriptors was estimated in the corresponding male and female liabilities in a set of threshold product models. The temperature of the day of AI seems to be the most relevant temperature descriptor affecting male fertility because greater temperature records on the day of AI caused a decrease in male fertility (-6% in male fertility rate with respect to thermoneutrality). Departures from the thermal zone in temperature descriptors covering several periods before AI until early gestation had a negative effect on female fertility, with the pre- and peri-implantational period of the embryos being especially sensitive (from -5 to -6% in female fertility rate with respect to thermoneutrality). The latest period of gestation was unaffected by the temperature. Overall, magnitude and persistency of the temperatures reached in the conditions of this study do not seem to be great enough to have a large effect on male and female rabbit fertility.

Accuracy of genome-wide evaluation for disease resistance in aquaculture breeding programs

Current aquaculture breeding programs aimed at improving resistance to diseases are based on challenge tests, where performance is recorded on sibs of candidates to selection, and on selection between families. Genome-wide evaluation (GWE) of breeding values offers new opportunities for using variation within families when dealing with such traits. However, up-to-date studies on GWE in aquaculture programs have only considered continuous traits. The objectives of this study were to extend GWE methodology, in particular the Bayes B method, to analyze dichotomous traits such as resistance to disease, and to quantify, through computer simulation, the accuracy of GWE for disease resistance in aquaculture sib-based programs, using the methodology developed. Two heritabilities (0.1 and 0.3) and 2 disease prevalences (0.1 and 0.5) were assumed in the simulations. We followed the threshold liability model, which assumes that there is an underlying variable (liability) with a continuous distribution and assumed a BayesB model for the liabilities. It was shown that the threshold liability model used fits very well with the BayesB model of GWE. The advantage of using the threshold model was clear when dealing with disease resistance dichotomous phenotypes, particularly under the conditions where linear models are less appropriate (low heritability and disease prevalence). In the testing set (where individuals are genotyped but not measured), the increase in accuracy for the simulated schemes when using the threshold model ranged from 4 (for heritability equal to 0.3 and prevalence equal to 0.5) to 16% (for heritability and prevalence equal to 0.1) when compared with the linear model.

Genome-wide prediction of discrete traits using Bayesian regressions and machine learning

BACKGROUND

Genomic selection has gained much attention and the main goal is to increase the predictive accuracy and the genetic gain in livestock using dense marker information. Most methods dealing with the large p (number of covariates) small n (number of observations) problem have dealt only with continuous traits, but there are many important traits in livestock that are recorded in a discrete fashion (e.g. pregnancy outcome, disease resistance). It is necessary to evaluate alternatives to analyze discrete traits in a genome-wide prediction context.

METHODS

This study shows two threshold versions of Bayesian regressions (Bayes A and Bayesian LASSO) and two machine learning algorithms (boosting and random forest) to analyze discrete traits in a genome-wide prediction context. These methods were evaluated using simulated and field data to predict yet-to-be observed records. Performances were compared based on the models' predictive ability.

RESULTS

The simulation showed that machine learning had some advantages over Bayesian regressions when a small number of QTL regulated the trait under pure additivity. However, differences were small and disappeared with a large number of QTL. Bayesian threshold LASSO and boosting achieved the highest accuracies, whereas Random Forest presented the highest classification performance. Random Forest was the most consistent method in detecting resistant and susceptible animals, phi correlation was up to 81% greater than Bayesian regressions. Random Forest outperformed other methods in correctly classifying resistant and susceptible animals in the two pure swine lines evaluated. Boosting and Bayes A were more accurate with crossbred data.

CONCLUSIONS

The results of this study suggest that the best method for genome-wide prediction may depend on the genetic basis of the population analyzed. All methods were less accurate at correctly classifying intermediate animals than extreme animals. Among the different alternatives proposed to analyze discrete traits, machine-learning showed some advantages over Bayesian regressions. Boosting with a pseudo Huber loss function showed high accuracy, whereas Random Forest produced more consistent results and an interesting predictive ability. Nonetheless, the best method may be case-dependent and a initial evaluation of different methods is recommended to deal with a particular problem.

Evidence of major genes affecting resistance to bacterial cold water disease in rainbow trout using Bayesian methods of segregation analysis

Bacterial cold water disease (BCWD) causes significant economic loss in salmonid aquaculture. We previously detected genetic variation for BCWD resistance in our rainbow trout population, and a family-based selection program to improve resistance was initiated at the National Center for Cool and Cold Water Aquaculture (NCCCWA). This study investigated evidence of major trait loci affecting BCWD resistance using only phenotypic data (without using genetic markers) and Bayesian methods of segregation analysis (BMSA). A total of 10,603 juvenile fish from 101 full-sib families corresponding to 3 generations (2005, 2007, and 2009 hatch years) of the NCCCWA population were challenged by intraperitoneal injection with Flavobacterium psychrophilum, the bacterium that causes BCWD. The results from single- and multiple-QTL models of BMSA suggest that 6 to 10 QTL explaining 83 to 89% of phenotypic variance with either codominant or dominant disease-resistant alleles plus polygenic effects may underlie the genetic architecture of BCWD resistance. This study also highlights the importance of polygenic background effects in the genetic variation of BCWD resistance. The polygenic heritability on the observed scale of survival status is slightly larger than that previously reported for rainbow trout BCWD resistance. These findings provide the basis for designing informative crosses for QTL mapping and carrying out genome scans for QTL affecting BCWD resistance in rainbow trout.

Evolutionary demography and quantitative genetics: age-specific survival as a threshold trait

Researchers must understand how mutations affect survival at various ages to understand how ageing evolves. Many models linking mutation to age-specific survival have been proposed but there is little evidence to indicate which model is most appropriate. This is a serious problem because the predicted evolutionary endpoints of ageing depend upon the details of the specific model. We apply an explicitly quantitative genetic perspective to the problem. To determine the inheritance of dichotomous traits (such as survival), quantitative genetics has long employed a threshold model. Beginning from first principles, we show how this is the most defensible mutational model for age-specific survival and how this, relative to the standard model, predicts delayed senescence and mortality deceleration at late age. These are commonly observed patterns of ageing that heretofore have required more complicated survival models. We also show how this model can be developed further to unify quantitative genetics and evolutionary demography into a more complete conceptual framework for understanding the evolution of ageing.

Algorithmic approaches to aid species' delimitation in multidimensional morphospace

Background

The species is a fundamental unit of biological pattern and process, but its delimitation has proven a ready source of argument and disagreement. Here, we discuss four key steps that utilize statistical thresholds to describe the morphological variability within a sample and hence assess whether there is evidence for one or multiple species. Once the initial set of biologically relevant traits on comparable individuals has been identified, there is no need for the investigator to hypothesise how specimens might be divided among groups, nor the traits on which groups might be separated.

Results

Principal components are obtained using robust covariance estimates and retained only if they exceed threshold amounts of explanatory power, before model-based clustering is performed on the dimension-reduced space. We apply these steps in an attempt to resolve ongoing debates among taxonomists working on the extinct Eocene planktonic foraminifera Turborotalia, providing statistical evidence for two species shortly before the lineage's extinction near the Eocene/Oligocene boundary.

Conclusion

By estimating variance robustly (samples containing incipient species are unlikely to be scaled optimally by means and standard deviations) and identifying thresholds relevant to a particular system rather than universal standards, the steps of the framework aim to optimize the chances of delineation without imposing pre-conceived patterns onto estimates of species limits.

Simulation study on the effects of excluding offspring information for genetic evaluation versus using genomic markers for selection in dog breeding

Different modes of selection in dogs were studied with a special focus on the availability of disease information. Canine hip dysplasia (CHD) in the German shepherd dog was used as an example. The study was performed using a simulation model, comparing cases when selection was based on phenotype, true or predicted breeding value, or genomic breeding value. The parameters in the simulation model were drawn from the real population data. The data on all parents and 40% of their progeny were assumed to be available for the genetic evaluation carried out by Gibbs sampling. With respect to the use of disease records on progeny, three scenarios were considered: random exclusion of disease data (no restrictions, N), general exclusion of disease data (G) and exclusion of disease data for popular sires (P). One round of selection was considered, and the response was expressed as change of mean CHD score, proportion of dogs scored as normal, proportion of dogs scored as clearly affected and true mean breeding value in progeny of popular sires in comparison with all sires. When no restrictions on data were applied, selection on breeding value was three times more efficient than when some systematic exclusion was practised. Higher selection response than in the exclusion cases was achieved by selecting on the basis of genomic breeding value and CHD score. Genomic selection would therefore be the method of choice in the future.

Relationship of cranial robusticity to cranial form, geography and climate in Homo sapiens

Variation in cranial robusticity among modern human populations is widely acknowledged but not well-understood. While the use of "robust" cranial traits in hominin systematics and phylogeny suggests that these characters are strongly heritable, this hypothesis has not been tested. Alternatively, cranial robusticity may be a response to differences in diet/mastication or it may be an adaptation to cold, harsh environments. This study quantifies the distribution of cranial robusticity in 14 geographically widespread human populations, and correlates this variation with climatic variables, neutral genetic distances, cranial size, and cranial shape. With the exception of the occipital torus region, all traits were positively correlated with each other, suggesting that they should not be treated as individual characters. While males are more robust than females within each of the populations, among the independent variables (cranial shape, size, climate, and neutral genetic distances), only shape is significantly correlated with inter-population differences in robusticity. Two-block partial least-squares analysis was used to explore the relationship between cranial shape (captured by three-dimensional landmark data) and robusticity across individuals. Weak support was found for the hypothesis that robusticity was related to mastication as the shape associated with greater robusticity was similar to that described for groups that ate harder-to-process diets. Specifically, crania with more prognathic faces, expanded glabellar and occipital regions, and (slightly) longer skulls were more robust than those with rounder vaults and more orthognathic faces. However, groups with more mechanically demanding diets (hunter-gatherers) were not always more robust than groups practicing some form of agriculture.

General quantitative genetic methods for comparative biology: phylogenies, taxonomies and multi-trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well-tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta-analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non-Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi-trait models in which traits can follow different distributions. Meta-analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.

Accounting for additive genetic mutations on litter size in Ripollesa sheep

Little is known about mutational variability in livestock, among which only a few mutations with relatively large effects have been reported. In this manuscript, mutational variability was analyzed in 1,765 litter size records from 404 Ripollesa ewes to characterize the magnitude of this genetic source of variation and check the suitability of including mutational effects in genetic evaluations of this breed. Threshold animal models accounting for additive genetic mutations were preferred to models without mutational contributions, with an average difference in the deviance information criterion of more than 5 units. Moreover, the statistical relevance of the additive genetic mutation term was checked through a Bayes factor approach, which showed that the models with mutational variability were 8.5 to 22.7 times more probable than the others. The mutational heritability (percentage of the phenotypic variance accounted for by mutational variance) was 0.6 or 0.9%, depending on whether genetic dominance effects were accounted for by the analytical model. The inclusion of mutational effects in the genetic model for evaluating litter size in Ripollesa ewes called for some minor modifications in the genetic merit order of the individuals evaluated, which suggested that the continuous uploading of new additive mutations could be taken into account to optimize the selection scheme. This study is the first attempt to estimate mutational variances in a livestock species and thereby contribute to better characterization of the genetic background of productive traits of interest.

Detecting single-nucleotide polymorphism by single-nucleotide polymorphism interactions in rheumatoid arthritis using a two-step approach with machine learning and a Bayesian threshold least absolute shrinkage and selection operator (LASSO) model

The objective of this study was to detect interactions between relevant single-nucleotide polymorphisms (SNPs) associated with rheumatoid arthritis (RA). Data from Problem 1 of the Genetic Analysis Workshop 16 were used. These data consisted of 868 cases and 1,194 controls genotyped with the 500 k Illumina chip. First, machine learning methods were applied for preselecting SNPs. One hundred SNPs outside the HLA region and 1,500 SNPs in the HLA region were preselected using information-gain theory. The software weka was used to reduce colinearity and redundancy in the HLA region, resulting in a subset of 6 SNPs out of 1,500. In a second step, a parametric approach to account for interactions between SNPs in the HLA region, as well as HLA-nonHLA interactions was conducted using a Bayesian threshold least absolute shrinkage and selection operator (LASSO) model incorporating 2,560 covariates. This approach detected some main and interaction effects for SNPs in genes that have previously been associated with RA (e.g., rs2395175, rs660895, rs10484560, and rs2476601). Further, some other SNPs detected in this study may be considered in candidate gene studies.

Major QTL for carrot color are positionally associated with carotenoid biosynthetic genes and interact epistatically in a domesticated x wild carrot cross

We performed QTL analyses for pigment content on a carotenoid biosynthesis function map based on progeny of a wild white carrot (QAL) which accumulates no pigments x domesticated orange carrot (B493), one of the richest sources of carotenoid pigments-mainly provitamin A alpha- and beta- carotenes. Two major interacting loci, Y and Y(2) on linkage groups 2 and 5, respectively, control much variation for carotenoid accumulation in carrot roots. They are associated with carotenoid biosynthetic genes zeaxanthin epoxidase and carotene hydroxylase and carotenoid dioxygenase gene family members as positional candidate genes. Dominant Y allele inhibits carotenoid accumulation. When Y is homozygous recessive, carotenoids that accumulate are either only xanthophylls in Y(2)__ plants, or both carotenes and xanthophylls, in y(2) y(2) plants. These two genes played a major role in carrot domestication and account for the significant role that modern carrot plays in vitamin A nutrition.

Predictive ability of models for calving difficulty in US Holsteins

The performance of alternative threshold models for analyzing calving difficulty (CD) in Holstein cows was evaluated in terms of predictive ability. Four models were considered, with CD classified into either three or four categories and analysed either as a single trait or jointly with gestation length (GL). The data contained GL and CD records from 90 393 primiparous cows, sired by 1122 bulls and distributed over 935 herd-calving year classes. Predictive ability of each model was evaluated using four criteria: mean squared error of the difference between observed and predicted CD scores; a Kullback-Leibler divergence measure between the observed and predicted distributions of CD scores; Pearson's correlation between observed and predicted CD scores and ability to correctly classify bulls as above or below average for incidence of CD. In general, the four models had similar predictive abilities. The joint analysis of CD with GL produced little, if any, improvement in predictive ability over univariate models. In light of the small difference in predictive ability between models treating CD with three or four categories and considering that a greater number of categories can provide more information, analysis of CD classified into four categories seems warranted.

Resistance to Salmonella carrier state: selection may be efficient but response depends on animal's age

Increasing resistance to acute salmonellosis (defined as bacteraemia in animals showing symptoms) is not sufficient for food safety, because of the risk of carrier state (when animals excrete bacteria without showing any symptoms). Increased resistance to Salmonella carrier state is therefore needed. Two experiments of divergent selection on resistance at a younger and a later age lead to significant differences between lines and allowed estimating genetic parameters on 4262 animals. Heritability of resistance was estimated at 0.16 in chicks, while it varied from 0.14 to 0.23 with analysed organ in adult hens. Genetic correlations between contamination of the different organs ranged from 0.46 to 0.67, while correlations between resistance at both ages were estimated at -0.50, showing that increasing genetic resistance of hens will reduce resistance in chicks. Highest estimated absolute values of genetic correlations between resistance and production traits were, for chicken contamination level, with number of eggs laid between 41 and 60 (0.37) and, for adult contamination, with number of eggs laid between 18 and 24 (0.37) or 25 and 40 (-0.33) weeks of age.

Genetic parameters of direct and maternal effects for calving ease in Dutch Holstein-Friesian cattle

Genetic parameters of direct and maternal effects for calving ease in Dutch dairy cattle were estimated using 677,975 calving ease records from second calving. Particular emphasis was given to the presence and impact of environmental dam-offspring covariances on the estimated direct-maternal genetic correlation. Moreover, a measure of heritability for traits affected by maternal effects was developed. In contrast to previous parameters, this parameter reflects the amount of genetic variance that can be used to generate a response to selection in maternally affected traits. Estimated genetic correlations between direct and maternal effects on calving ease have often been moderately negative, particularly in beef cattle. Environmental dam-offspring covariances have been put forward as an explanation for such estimates. We investigated the impact of environmental dam-offspring covariances by fitting correlated residuals between dam and offspring records in the statistical model, and by comparing results of a sire-maternal grandsire model with those of an animal model. Results show that calving ease in Dutch dairy cattle has a direct heritability of approximately 0.08, a maternal heritability of approximately 0.04, a direct-maternal genetic correlation of approximately -0.20, and a total heritable variance equal to approximately 11% of phenotypic variance. Results of animal models and sire-maternal grandsire models were very similar. The direct-maternal environmental covariance was near zero, and consequently had very little impact on the estimated genetic parameters. Transformation of observations to a liability scale did not affect the estimated genetic parameters and yielded a nearly identical ranking of sires.

Zigzag: a genetic defect of the horizontal canals in the mouse

The name zigzag has been given to an inherited behaviour defect in the mouse in which the animals walk with a zigzag motion. It is inherited polygenically. The anatomical defect responsible for the abnormal behaviour was a reduction or absence of the horizontal canals of the inner ear, the reduction consisting of a constriction in the middle of the canal length, rather than a shortening of the canal.

Genetic background and phenotypic characterization over two farrowings of leg conformation defects in Landrace and Large White sows

A Bayesian threshold animal model was applied to evaluate the prevalence over 2 farrowings and genetic background of overall leg conformation score and the presence or absence of 6 specific leg defects (abnormal hoof growth, splay footed, plantigradism, straight pasterns, sickle-hocked legs, and the presence of swelling or injuries) in purebred Landrace and Large White sows. Data sets contained phenotypic records from 2,477 and 1,550 Landrace and Large White females, respectively, at the end of the growing period. Leg conformation data from first and second farrowings were available for 223 and 191 Landrace sows and 213 and 193 Large White sows, respectively. Overall leg conformation deteriorated with age, with statistically relevant differences between females at the end of the growing period, first farrowing (FF), and second farrowing (SF). In a similar way, the prevalence of the 6 specific leg defects increased between the end of the growing period and FF (with the exception of straight pasterns in the Landrace population). Differences between FF and second farrowing were statistically relevant for hoof growth (highest posterior density regions at 95% did not overlap), plantigradism, sickle-hocked legs, and overall leg conformation score in Landrace and for sickle-hocked leg and overall leg conformation score in Large White. The statistical relevance of the genetic background was tested through the Bayes factor (BF) between the model with the additive genetic component and the model with 0 heritability (nonheritable). Heritability (h(2)) was discarded (BF < 1) for sickle-hocked leg in both breeds, whereas decisive evidence (BF > 100) of genetic background was obtained for overall leg conformation score in Landrace and Large White sows (h(2) = 0.27 and 0.38, respectively), hoof growth in both breeds (h(2) = 0.22 and 0.26, respectively), and plantigradism (h(2) = 0.34) and the presence of swelling or injuries in Landrace (h(2) = 0.27). Note that a BF > 100 implies that the model with infinitesimal genetic effects was more than 100 times more suitable than the model without genetic effects, a conclusive estimate within the Bayesian framework. The remaining traits (splay footed and straight pasterns) registered BF values ranging from 11.6 to 35.1 and h(2) values ranging from 0.09 to 0.19. These results indicated a moderate genetic determinism for leg conformation in Landrace and Large White sows.

Genetic correlation between female fertility and milk yield in Lacaune sheep

A total of 416,670 lactations for 189,101 ewes from 3,603 sires and distributed across 1,978 herd-year groups were used to estimate genetic and environmental parameters of standardized milk yield (SMY(T)), fertility in ewe lambs (PR(1)), and fertility in adult ewes (PR(A)). Parameters were estimated with a multiple-trait sire linear model. Heritabilities for SMY(T), PR(1), and PR(A) were 0.27 (0.009), 0.04 (0.004), and 0.05 (0.004), respectively. These results were in accordance with the literature. The genetic correlation between PR(1) and PR(A) was 0.55, indicating that fertility is not the same trait in ewe lambs and adult ewes. The genetic correlation between milk yield and lamb fertility was not significantly different from zero. The genetic correlation between milk yield and fertility in adult ewe (-0.23) was in the range of antagonistic correlations reported in dairy cattle. Consequently, these results show that selection for milk yield can induce an indirect decrease in fertility. Nevertheless, no phenotypic decrease in fertility in artificial insemination matings has been observed in this population. This is the first time that correlation between milk yield and fertility is reported in sheep and further investigations are needed to confirm this result.

Exploring biological relationships between calving traits in primiparous cattle with a Bayesian recursive model

Structural equation models (SEMs) of a recursive type with heterogeneous structural coefficients were used to explore biological relationships between gestation length (GL), calving difficulty (CD), and perinatal mortality, also known as stillbirth (SB), in cattle, with the last two traits having categorical expression. An acyclic model was assumed, where recursive effects existed from the GL phenotype to the liabilities (latent variables) to CD and SB and from the liability to CD to that of SB considering four periods regarding GL. The data contained GL, CD, and SB records from 90,393 primiparous cows, sired by 1122 bulls, distributed over 935 herd-calving year classes. Low genetic correlations between GL and the other calving traits were found, whereas the liabilities to CD and SB were high and positively correlated, genetically. The model indicated that gestations of approximately 274 days of length (3 days shorter than the average) would lead to the lowest CD and SB and confirmed the existence of an intermediate optimum of GL with respect to these traits.

Developments in statistical analysis in quantitative genetics

A remarkable research impetus has taken place in statistical genetics since the last World Conference. This has been stimulated by breakthroughs in molecular genetics, automated data-recording devices and computer-intensive statistical methods. The latter were revolutionized by the bootstrap and by Markov chain Monte Carlo (McMC). In this overview a number of specific areas are chosen to illustrate the enormous flexibility that McMC has provided for fitting models and exploring features of data that were previously inaccessible. The selected areas are inferences of the trajectories over time of genetic means and variances, models for the analysis of categorical and count data, the statistical genetics of a model postulating that environmental variance is partly under genetic control, and a short discussion of models that incorporate massive genetic marker information. We provide an overview of the application of McMC to study model fit, and finally, a discussion is presented on the development of efficient McMC updating schemes for non-standard models.

Levels of selection on threshold characters

Threshold models are useful for understanding the evolution of dimorphic traits with polygenic bases. Selection for threshold characters on individuals is expected to be frequency dependent because of the peculiar way that selection views underlying genetic and environmental factors. Selection among individuals is inefficient because individual phenotypes fall into only two discrete categories that map imperfectly to the underlying genes. Incidence, however, can be continuously distributed among groups, making among-group selection relatively more efficient. Differently put, the group-mean phenotype can be a better predictor of an individual's genotype than that individual's own phenotype. Because evolution in group-structured populations is governed by the balance of selection within and between groups, we can expect threshold traits to evolve in fundamentally different ways when group mean fitness is a function of morph frequency. We extend the theory of selection on threshold traits to include group selection using contextual analysis. For the simple case of linear group-fitness functions, we show that the group-level component of selection, like the individual-level component, is frequency dependent. However, the conditions that determine which component dominates when levels of selection are in conflict (as described by Hamilton's rule) are not frequency dependent. Thus, enhanced group selection is not an inherent property of threshold characters. Nevertheless, we show that predicting the effects of multiple levels of selection on dimorphic traits requires special considerations of the threshold model.

The Hsp90 capacitor, developmental remodeling, and evolution: the robustness of gene networks and the curious evolvability of metamorphosis

Genetic capacitors moderate expression of heritable variation and provide a novel mechanism for rapid evolution. The prototypic genetic capacitor, Hsp90, interfaces stress responses, developmental networks, trait thresholds and expression of wide-ranging morphological changes in Drosophila and other organisms. The Hsp90 capacitor hypothesis, that stress-sensitive storage and release of genetic variation through Hsp90 facilitates adaptive evolution in unpredictable environments, has been challenged by the belief that Hsp90-buffered variation is unconditionally deleterious. Here we review recent results supporting the Hsp90 capacitor hypothesis, highlighting the heritability, selectability, and potential evolvability of Hsp90-buffered traits. Despite a surprising bias toward morphological novelty and typically invariable quantitative traits, Hsp90-buffered changes are remarkably modular, and can be selected to high frequency independent of the expected negative side-effects or obvious correlated changes in other, unselected traits. Recent dissection of cryptic signal transduction variation involved in one Hsp90-buffered trait reveals potentially dozens of normally silent polymorphisms embedded in cell cycle, differentiation and growth control networks. Reduced function of Hsp90 substrates during environmental stress would destabilize robust developmental processes, relieve developmental constraints and plausibly enables genetic network remodeling by abundant cryptic alleles. We speculate that morphological transitions controlled by Hsp90 may fuel the incredible evolutionary lability of metazoan life-cycles.

Contemporary model-free methods for linkage analysis

Model-free linkage methods are based on identifying regions of the genome in which patterns of allele sharing among family members correspond to patterns of phenotype correlation among family members. Two general classes of model-free linkage methods are discussed in this chapter, relative pair methods designed primarily for analysis of discrete traits and variance component methods designed primarily for analysis of quantitative traits. These methods have been used to identify numerous genes influencing complex human phenotypes and remain viable approaches to gene localization in the twenty-first century.