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

The phylogeny of Heliconia (Heliconiaceae) and the evolution of floral presentation

Heliconia (Heliconiaceae, order Zingiberales) is among the showiest plants of the Neotropical rainforest and represent a spectacular co-evolutionary radiation with hummingbirds. Despite the attractiveness and ecological importance of many Heliconia, the genus has been the subject of limited molecular phylogenetic studies. We sample seven markers from the plastid and nuclear genomes for 202 samples of Heliconia. This represents ca. 75% of accepted species and includes coverage of all taxonomic subgenera and sections. We date this phylogeny using fossils associated with other families in the Zingiberales; in particular we review and evaluate the Eocene fossil Ensete oregonense. We use this dated phylogenetic framework to evaluate the evolution of two components of flower orientation that are hypothesized to be important for modulating pollinator discrimination and pollen placement: resupination and erect versus pendant inflorescence habit. Our phylogenetic results suggest that the monophyletic Melanesian subgenus Heliconiopsis and a small clade of Ecuadorian species are together the sister group to the rest of Heliconia. Extant diversity of Heliconia originated in the Late Eocene (39Ma) with rapid diversification through the Early Miocene, making it the oldest known clade of hummingbird-pollinated plants. Most described subgenera and sections are not monophyletic, though closely related groups of species, often defined by shared geography, mirror earlier morphological cladistic analyses. Evaluation of changes in resupination and inflorescence habit suggests that these characters are more homoplasious than expected, and this largely explains the non-monophyly of previously circumscribed subgenera, which were based on these characters. We also find strong evidence for the correlated evolution of resupination and inflorescence habit. The correlated model suggests that the most recent common ancestor of all extant Heliconia had resupinate flowers and erect inflorescences. Finally, we note our nearly complete species sampling and dated phylogeny allow for an assessment of taxonomic history in terms of phylogenetic diversity. We find approximately half of the currently recognized species, corresponding to half of the phylogenetic diversity, have been described since 1975, highlighting the continued importance of basic taxonomic research and conservation initiatives to preserve both described and undiscovered species of Heliconia.

Loss of maternal ANNEXIN A10 via a 34-kb deleted-type copy number variation is associated with embryonic mortality in Japanese Black cattle

Background

Conception is a fundamental trait for successful cattle reproduction. However, conception rates in Japanese Black cattle have been gradually declining over the last two decades. Although conception failures are mainly caused by embryonic mortality, the role of maternal genetic factors in the process remains unknown. Copy number variation (CNV), defined as large-scale genomic structural variants, contributes to several genetic disorders. To identify CNV associated with embryonic mortality in Japanese Black cattle, we evaluated embryonic mortality as a categorical trait with a threshold model and conducted a genome-wide CNV association study for embryonic mortality using 791 animals.

Results

We identified a deleted-type CNV ranging from 378,127 to 412,061 bp on bovine chromosome 8, which was associated with embryonic mortality at 30–60 days after artificial insemination (AI). The CNV harbors exon 2 to 6 of ANNEXIN A10 (ANXA10). Analysis of sequence traces from the CNV identified that 63 bp reads bridging the breakpoint were present on both sides of the CNV, indicating that the CNV was generated by non-allelic homologous recombination using the 63 bp homologous sequences. Western blot analysis showed that the CNV results in a null allele of ANXA10. This association was replicated using a sample population size of 2552 animals. To elucidate the function of ANXA10 in vivo, we generated Anxa10 null mice using the CRISPR/Cas9 system. Crossbreeding experiments showed that litter size from crosses of both Anxa10^-/- and Anxa10^+/- females had fewer pups than did Anxa10^+/+ females, and embryos of Anxa10^-/- females died between implantation stages E4.5 and E12.5. These results indicate that loss of maternal Anxa10 causes embryonic mortality.

Conclusions

This study identified a deleted-type CNV encompassing ANXA10 in cows that was associated with embryonic mortality at 30–60 days after AI. Using a mouse model, we confirmed that litter sizes were smaller in crosses of both Anxa10^-/- and Anxa10^+/- females relative to those of wild females. These results indicate that ANXA10 is a maternal factor that is critical for embryo development.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-016-3312-z) contains supplementary material, which is available to authorized users.

Range size heritability and diversification patterns in the liverwort genus Radula

Why some species exhibit larger geographical ranges than others, and to what extent does variation in range size affect diversification rates, remains a fundamental, but largely unanswered question in ecology and evolution. Here, we implement phylogenetic comparative analyses and ancestral area estimations in Radula, a liverwort genus of Cretaceous origin, to investigate the mechanisms that explain differences in geographical range size and diversification rates among lineages. Range size was phylogenetically constrained in the two sub-genera characterized by their almost complete Australasian and Neotropical endemicity, respectively. The congruence between the divergence time of these lineages and continental split suggests that plate tectonics could have played a major role in their present distribution, suggesting that a strong imprint of vicariance can still be found in extant distribution patterns in these highly mobile organisms. Amentuloradula, Volutoradula and Metaradula species did not appear to exhibit losses of dispersal capacities in terms of dispersal life-history traits, but evidence for significant phylogenetic signal in macroecological niche traits suggests that niche conservatism accounts for their restricted geographic ranges. Despite their greatly restricted distribution to Australasia and Neotropics respectively, Amentuloradula and Volutoradula did not exhibit significantly lower diversification rates than more widespread lineages, in contrast with the hypothesis that the probability of speciation increases with range size by promoting geographic isolation and increasing the rate at which novel habitats are encountered. We suggest that stochastic long-distance dispersal events may balance allele frequencies across large spatial scales, leading to low genetic structure among geographically distant areas or even continents, ultimately decreasing the diversification rates in highly mobile, widespread lineages.

General Methods for Evolutionary Quantitative Genetic Inference from Generalized Mixed Models

Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of the response to selection, are best developed for traits with normal distributions. Many traits of evolutionary interest, including many life history and behavioral traits, have inherently nonnormal distributions. The generalized linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for nonnormal traits. However, whereas GLMMs provide inference on a statistically convenient latent scale, it is often desirable to express quantitative genetic parameters on the scale upon which traits are measured. The parameters of fitted GLMMs, despite being on a latent scale, fully determine all quantities of potential interest on the scale on which traits are expressed. We provide expressions for deriving each of such quantities, including population means, phenotypic (co)variances, variance components including additive genetic (co)variances, and parameters such as heritability. We demonstrate that fixed effects have a strong impact on those parameters and show how to deal with this by averaging or integrating over fixed effects. The expressions require integration of quantities determined by the link function, over distributions of latent values. In general cases, the required integrals must be solved numerically, but efficient methods are available and we provide an implementation in an R package, QGglmm. We show that known formulas for quantities such as heritability of traits with binomial and Poisson distributions are special cases of our expressions. Additionally, we show how fitted GLMM can be incorporated into existing methods for predicting evolutionary trajectories. We demonstrate the accuracy of the resulting method for evolutionary prediction by simulation and apply our approach to data from a wild pedigreed vertebrate population.

Genetic analyses of lamb survival in Rambouillet and Finnsheep flocks by linear and threshold models

Data on lamb survival from birth to weaning of Rambouillet and Finnsheep were analysed with sire-maternal grandsire linear (LM) and threshold (TM) models. Models for the Rambouillet included the effects of year, type of birth, age of dam and sex as fixed effects and sire, maternal grandsire and residual as random effects. For the Finnsheep, fixed effects were year-age of dam combination, type of birth-rearing and sex, and random effects were sire, maternal grandsire and residual. Restricted maximum likelihood (REML) and marginal maximum likelihood (MML) estimates of variance and covariance components were obtained under LM and TM, respectively. The performance of LM and TM was assessed in terms of goodness of fit and predictive ability. Within the Rambouillet breed, heritabilities of additive direct (0·06), additive maternal (0·04) and total effects (0·13) obtained with TM were 2, 1·3 and 1·9 times greater than those obtained with LM, respectively. For the Finnsheep data, estimated heritabilities of direct (0·17), maternal (0·26) and total (0·34) effects using TM were 1·9, 1·4 and 1·6 times greater than the estimates using LM, respectively. Estimated genetic correlation between direct and maternal effects was 0·14 for the Finnsheep with both the LM and TM. Higher genetic correlations between direct and maternal effects (0·44 and 0·62 with LM and TM, respectively) were obtained for the Rambouillet data. Goodness of fit and predictive ability of the models used with the Finnsheep data were better than for the models used with the Rambouillet data, but within breed, no sizable or significant differences were detected between LM and TM. Results indicate that maternal effects were important in lamb survival to weaning; especially in the more prolific Finnsheep breed.

Genetic parameters for clinical mastitis in Holstein-Friesians in the United Kingdom: a Bayesian analysis

A Bayesian threshold-liability model with Markov chain Monte Carlo techniques was used to infer genetic parameters for clinical mastitis records collected on Holstein-Friesian cows by one of the United Kingdom’s national recording schemes. Four data sets were created to investigate the effect of data sampling methods on genetic parameter estimates for first and multi-lactation cows, separately. The data sets were: (1) cows with complete first lactations only (8671 cows); (2) all cows, with first lactations whether complete or incomplete (10 967 cows); (3) cows with complete multi-lactations (32 948 records); and (4) all cows with multiple lactations whether complete or incomplete (44 268 records). A Gaussian mixed linear model with sire effects was adopted for liability. Explanatory variables included in the model varied for each data set. Analyses were conducted using Gibbs sampling and estimates were on the liability scale. Posterior means of heritability for clinical mastitis were higher for first lactations (0·11 and 0·10 for data sets 1 and 2, respectively) than for multiple lactations (0·09 and 0·07, for data sets 3 and 4, respectively). For multiple lactations, estimates of permanent environmental variance were higher for complete than incomplete lactations. Repeatability was 0·21 and 0·17 for data sets 3 and 4, respectively. This suggests the existence of effects, other than additive genetic effects, on susceptibility to mastitis that are common to all lactations. In first or multi-lactation data sets, heritability was proportionately 0·10 to 0·19 lower for data sets with all records (in which case the models had days in milk as a covariate) than for data with only complete lactation records (models without days in milk as a covariate). This suggests an effect of data sampling on genetic parameter estimates. The regression of liability on days in milk differed from zero, indicating that the probability of mastitis is higher for longer lactations, as expected. Results also indicated that a regression on days in milk should be included in a model for genetic evaluation of sires for mastitis resistance based on records in progress.

Reflections on the Field of Human Genetics: A Call for Increased Disease Genetics Theory

Development of human genetics theoretical models and the integration of those models with experiment and statistical evaluation are critical for scientific progress. This perspective argues that increased effort in disease genetics theory, complementing experimental, and statistical efforts, will escalate the unraveling of molecular etiologies of complex diseases. In particular, the development of new, realistic disease genetics models will help elucidate complex disease pathogenesis, and the predicted patterns in genetic data made by these models will enable the concurrent, more comprehensive statistical testing of multiple aspects of disease genetics predictions, thereby better identifying disease loci. By theoretical human genetics, I intend to encompass all investigations devoted to modeling the heritable architecture underlying disease traits and studies of the resulting principles and dynamics of such models. Hence, the scope of theoretical disease genetics work includes construction and analysis of models describing how disease-predisposing alleles (1) arise, (2) are transmitted across families and populations, and (3) interact with other risk and protective alleles across both the genome and environmental factors to produce disease states. Theoretical work improves insight into viable genetic models of diseases consistent with empirical results from linkage, transmission, and association studies as well as population genetics. Furthermore, understanding the patterns of genetic data expected under realistic disease models will enable more powerful approaches to discover disease-predisposing alleles and additional heritable factors important in common diseases. In spite of the pivotal role of disease genetics theory, such investigation is not particularly vibrant.

Efficient Recycled Algorithms for Quantitative Trait Models on Phylogenies

We present an efficient and flexible method for computing likelihoods for phenotypic traits on a phylogeny. The method does not resort to Monte Carlo computation but instead blends Felsenstein’s discrete character pruning algorithm with methods for numerical quadrature. It is not limited to Gaussian models and adapts readily to model uncertainty in the observed trait values. We demonstrate the framework by developing efficient algorithms for likelihood calculation and ancestral state reconstruction under Wright’s threshold model, applying our methods to a data set of trait data for extrafloral nectaries across a phylogeny of 839 Fabales species.

Species selection and random drift in macroevolution

Species selection resulting from trait-dependent speciation and extinction is increasingly recognized as an important mechanism of phenotypic macroevolution. However, the recent bloom in statistical methods quantifying this process faces a scarcity of dynamical theory for their interpretation, notably regarding the relative contributions of deterministic versus stochastic evolutionary forces. I use simple diffusion approximations of birth-death processes to investigate how the expected and random components of macroevolutionary change depend on phenotype-dependent speciation and extinction rates, as can be estimated empirically. I show that the species selection coefficient for a binary trait, and selection differential for a quantitative trait, depend not only on differences in net diversification rates (speciation minus extinction), but also on differences in species turnover rates (speciation plus extinction), especially in small clades. The randomness in speciation and extinction events also produces a species-level equivalent to random genetic drift, which is stronger for higher turnover rates. I then show how microevolutionary processes including mutation, organismic selection, and random genetic drift cause state transitions at the species level, allowing comparison of evolutionary forces across levels. A key parameter that would be needed to apply this theory is the distribution and rate of origination of new optimum phenotypes along a phylogeny.

Genetic parameters of objectionable fibers and of their associations with fleece traits in Corriedale sheep

The aim of this research was to assess the variability and genetic relationships among binary traits denoting the presence or absence of objectionable fibers, namely pigmented (BINPPF), medullated (BINPMED), and kemp fibers (BINPK), and of fleece traits (fiber diameter [FD] and clean fleece weight [CFW]) in Corriedale sheep. Additionally, the total response to selection against objectionable fibers and indirect responses when selecting for fleece traits were evaluated. Fiber records from 679 animals and fleece records from 795 animals obtained from 2 experimental flocks (from 2005 to 2007) were used; the pedigree file included a total of 3,792 animals. Heritability and genetic correlations among the traits were estimated with a multivariate animal model under a Bayesian setting. Heritability estimates (posterior SD) for BINPPF, BINPMED, and BINPK were 0.35 (0.08), 0.37 (0.10), and 0.63 (0.09), respectively; for CFW and FD, estimates were 0.42 (0.09) and 0.43 (0.08), respectively. The genetic correlations between CFW and the 3 types of objectionable fibers were very low (i.e., <0.2). Thus selection for CFW is not expected to affect the number of such fibers in any direction. The same occurred for the genetic correlation between BINPK and FD. Genetic correlations between FD and BINPMED and FD and BINPPF were positive and favorable (0.50 and 0.56, respectively). Selecting for lower FD would decrease the numbers of objectionable fibers. The expected correlated responses in BINPPF, BINPMED, and BINPK when selecting for CFW were -0.03 (0.11), 0.03 (0.11), and -0.05 (0.18), respectively; when selecting for FD, the correlated responses were -0.26 (0.11), -0.26 (0.11), and -0.14 (0.16). Overall, this study reports novel information on genetic parameters for the presence of objectionable fibers and their associations with fleece traits in sheep. Our findings suggest that it could be possible to improve FD while at the same time reducing the content of BINPMED and BINPPF in wool; however, improvements in CFW are likely to have no effect on the numbers of objectionable fibers.

Investigating the genetic architecture of conditional strategies using the environmental threshold model

The threshold expression of dichotomous phenotypes that are environmentally cued or induced comprise the vast majority of phenotypic dimorphisms in colour, morphology, behaviour and life history. Modelled as conditional strategies under the framework of evolutionary game theory, the quantitative genetic basis of these traits is a challenge to estimate. The challenge exists firstly because the phenotypic expression of the trait is dichotomous and secondly because the apparent environmental cue is separate from the biological signal pathway that induces the switch between phenotypes. It is the cryptic variation underlying the translation of cue to phenotype that we address here. With a 'half-sib common environment' and a 'family-level split environment' experiment, we examine the environmental and genetic influences that underlie male dimorphism in the earwig Forficula auricularia. From the conceptual framework of the latent environmental threshold (LET) model, we use pedigree information to dissect the genetic architecture of the threshold expression of forceps length. We investigate for the first time the strength of the correlation between observable and cryptic 'proximate' cues. Furthermore, in support of the environmental threshold model, we found no evidence for a genetic correlation between cue and the threshold between phenotypes. Our results show strong correlations between observable and proximate cues and less genetic variation for thresholds than previous studies have suggested. We discuss the importance of generating better estimates of the genetic variation for thresholds when investigating the genetic architecture and heritability of threshold traits. By investigating genetic architecture by means of the LET model, our study supports several key evolutionary ideas related to conditional strategies and improves our understanding of environmentally cued decisions.

Shifting Thresholds: Rapid Evolution of Migratory Life Histories in Steelhead/Rainbow Trout, Oncorhynchus mykiss

Expression of phenotypic plasticity depends on reaction norms adapted to historic selective regimes; anthropogenic changes in these selection regimes necessitate contemporary evolution or declines in productivity and possibly extinction. Adaptation of conditional strategies following a change in the selection regime requires evolution of either the environmentally influenced cue (e.g., size-at-age) or the state (e.g., size threshold) at which an individual switches between alternative tactics. Using a population of steelhead (Oncorhynchus mykiss) introduced above a barrier waterfall in 1910, we evaluate how the conditional strategy to migrate evolves in response to selection against migration. We created 9 families and 917 offspring from 14 parents collected from the above- and below-barrier populations. After 1 year of common garden-rearing above-barrier offspring were 11% smaller and 32% lighter than below-barrier offspring. Using a novel analytical approach, we estimate that the mean size at which above-barrier fish switch between the resident and migrant tactic is 43% larger than below-barrier fish. As a result, above-barrier fish were 26% less likely to express the migratory tactic. Our results demonstrate how rapid and opposing changes in size-at-age and threshold size contribute to the contemporary evolution of a conditional strategy and indicate that migratory barriers may elicit rapid evolution toward the resident life history on timescales relevant for conservation and management of conditionally migratory species.

Quantitative genetics of disease traits

John James authored two key papers on the theory of risk to relatives for binary disease traits and the relationship between parameters on the observed binary scale and an unobserved scale of liability (James Annals of Human Genetics, 1971; 35: 47; Reich, James and Morris Annals of Human Genetics, 1972; 36: 163). These two papers are John James' most cited papers (198 and 328 citations, November 2014). They have been influential in human genetics and have recently gained renewed popularity because of their relevance to the estimation of quantitative genetics parameters for disease traits using SNP data. In this review, we summarize the two early papers and put them into context. We show recent extensions of the theory for ascertained case-control data and review recent applications in human genetics.

ASSESSING PHENOTYPIC CORRELATION THROUGH THE MULTIVARIATE PHYLOGENETIC LATENT LIABILITY MODEL

Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the correlation between multiple types of data, while simultaneously controlling for their unknown shared evolutionary history informed through molecular sequences. The latent formulation enables us to consider in a single model combinations of continuous traits, discrete binary traits, and discrete traits with multiple ordered and unordered states. Previous approaches have entertained a single data type generally along a fixed history, precluding estimation of correlation between traits and ignoring uncertainty in the history. We implement our model in a Bayesian phylogenetic framework, and discuss inference techniques for hypothesis testing. Finally, we showcase the method through applications to columbine flower morphology, antibiotic resistance in Salmonella, and epitope evolution in influenza.

Ecological constraint and the evolution of sexual dichromatism in darters

It is not known how environmental pressures and sexual selection interact to influence the evolution of extravagant male traits. Sexual and natural selection are often viewed as antagonistic forces shaping the evolution of visual signals, where conspicuousness is favored by sexual selection and crypsis is favored by natural selection. Although typically investigated independently, the interaction between natural and sexual selection remains poorly understood. Here, we investigate whether sexual dichromatism evolves stochastically, independent from, or in concert with habitat use in darters, a species-rich lineage of North American freshwater fish. We find the evolution of sexual dichromatism is coupled to habitat use in darter species. Comparative analyses reveal that mid-water darter lineages exhibit a narrow distribution of dichromatism trait space surrounding a low optimum, suggesting a constraint imposed on the evolution of dichromatism, potentially through predator-mediated selection. Alternatively, the transition to benthic habitats coincides with greater variability in the levels of dichromatism that surround a higher optimum, likely due to relaxation of the predator-mediated selection and heterogeneous microhabitat dependent selection regimes. These results suggest a complex interaction of sexual selection with potentially two mechanisms of natural selection, predation and sensory drive, that influence the evolution of diverse male nuptial coloration in darters.

One hundred years of statistical developments in animal breeding

Statistical methodology has played a key role in scientific animal breeding. Approximately one hundred years of statistical developments in animal breeding are reviewed. Some of the scientific foundations of the field are discussed, and many milestones are examined from historical and critical perspectives. The review concludes with a discussion of some future challenges and opportunities arising from the massive amount of data generated by livestock, plant, and human genome projects.

Kernel-based whole-genome prediction of complex traits: a review

Prediction of genetic values has been a focus of applied quantitative genetics since the beginning of the 20th century, with renewed interest following the advent of the era of whole genome-enabled prediction. Opportunities offered by the emergence of high-dimensional genomic data fueled by post-Sanger sequencing technologies, especially molecular markers, have driven researchers to extend Ronald Fisher and Sewall Wright's models to confront new challenges. In particular, kernel methods are gaining consideration as a regression method of choice for genome-enabled prediction. Complex traits are presumably influenced by many genomic regions working in concert with others (clearly so when considering pathways), thus generating interactions. Motivated by this view, a growing number of statistical approaches based on kernels attempt to capture non-additive effects, either parametrically or non-parametrically. This review centers on whole-genome regression using kernel methods applied to a wide range of quantitative traits of agricultural importance in animals and plants. We discuss various kernel-based approaches tailored to capturing total genetic variation, with the aim of arriving at an enhanced predictive performance in the light of available genome annotation information. Connections between prediction machines born in animal breeding, statistics, and machine learning are revisited, and their empirical prediction performance is discussed. Overall, while some encouraging results have been obtained with non-parametric kernels, recovering non-additive genetic variation in a validation dataset remains a challenge in quantitative genetics.

Estimating the inbreeding depression on cognitive behavior: a population based study of child cohort

BACKGROUND

Cognitive ability tests are widely assumed to measure maximal intellectual performance and predictive associations between intelligence quotient (IQ) scores and later mental health problems. Very few epidemiologic studies have been done to demonstrate the relationship between familial inbreeding and modest cognitive impairments in children.

OBJECTIVE

We aimed to estimate the effect of inbreeding on children's cognitive behavior in comparison with non-inbred children.

METHODOLOGY

A cohort of 408 children (6 to 15 years of age) was selected from inbred and non-inbred families of five Muslim populations of Jammu region. The Wechsler Intelligence Scales for Children (WISC) was used to measure the verbal IQ (VIQ), performance IQ (PIQ) and full scale IQ (FSIQ). Family pedigrees were drawn to access the family history and children's inbred status in terms of coefficient of inbreeding (F).

RESULTS

We found significant decline in child cognitive abilities due to inbreeding and high frequency of mental retardation among offspring from inbred families. The mean differences (95% C.I.) were reported for the VIQ, being -22.00 (-24.82, -19.17), PIQ -26.92 (-29.96, -23.87) and FSIQ -24.47 (-27.35,-21.59) for inbred as compared to non-inbred children (p<0.001) [corrected].The higher risk of being mentally retarded was found to be more obvious among inbred categories corresponding to the degree of inbreeding and the same accounts least for non-inbred children (p<0.0001). We observed an increase in the difference in mean values for VIQ, PIQ and FSIQ with the increase of inbreeding coefficient and these were found to be statistically significant (p<0.05). The regression analysis showed a fitness decline (depression) for VIQ (R2 = 0.436), PIQ (R2 = 0.468) and FSIQ (R2 = 0.464) with increasing inbreeding coefficients (p<0.01).

CONCLUSIONS

Our comprehensive assessment provides the evidence for inbreeding depression on cognitive abilities among children.

Whole-genome analyses of lung function, height and smoking

A joint analysis of FEV1 (forced expiratory volume after one second) and height is reported using novel methodology, as well as a single-trait analysis of smoking status. A first goal of the study was to incorporate dense genetic marker information in a random regression (Bayesian) model to quantify the relative contributions of genomic and environmental factors to the relationship between FEV1 and height. Smoking status was analysed using a probit random regression model and a second goal of the study was to estimate the genomic heritability of smoking status. Estimates of genomic heritabilities for height and FEV1 are equal to 0.47 and to 0.30, respectively. The estimates of the genomic and environmental correlations between height and FEV1 are 0.78 and 0.34, respectively. The posterior mean of the genomic heritability of smoking status is equal to 0.14 and provides evidence for the presence of genetic factors associated with the trait. Under the data augmentation strategy introduced, the joint posterior distribution of FEV1 and height factorises into two independent posterior distributions. This simplifies programming and results in excellent numerical behaviour. The approach can be readily extended for the joint analysis of an arbitrary number of traits. Details are shown in an Appendix.

Genetic parameters of postnatal mortality and birth weight in Japanese Black calves

Postnatal mortality (PM) of calves is an economically important trait, because a high mortality rate of calves decreases farm income and significantly increases production costs. In spite of the economic importance of PM, genetic studies on PM have been scarce for Japanese Black cattle. The objectives of this study were to estimate the direct and maternal heritability for PM using a Bayesian threshold model with Gibbs sampling in Japanese Black cattle. The original data consisted of 43 723 records of animals born from January 2005 to June 2006. Four binary traits of mortality were considered: D1-14, D15-60, D61-180 and D1-180 with numbers indicating the period of risk in days after birth. Direct heritabilities for PM ranged from 0.12 to 0.31 and maternal heritabilities for PM were lower than the direct heritabilities and ranged from 0.02 to 0.16. Direct genetic correlations between D1-14 and D15-60, between D15-60 and D61-180, and between D1-14 and D61-180 were 0.501, 0.689 and 0.062, respectively. Direct genetic correlations of birth weight with D1-14, D15-60, D61-180 and D1-180 were 0.089, 0.482, 0.434 and 0.394, respectively. These results indicated that different genes were responsible for early and late PM and early PM (D1-14) can be genetically reduced without influencing birth weight.

Reduction in accuracy of genomic prediction for ordered categorical data compared to continuous observations

BACKGROUND

Accuracy of genomic prediction depends on number of records in the training population, heritability, effective population size, genetic architecture, and relatedness of training and validation populations. Many traits have ordered categories including reproductive performance and susceptibility or resistance to disease. Categorical scores are often recorded because they are easier to obtain than continuous observations. Bayesian linear regression has been extended to the threshold model for genomic prediction. The objective of this study was to quantify reductions in accuracy for ordinal categorical traits relative to continuous traits.

METHODS

Efficiency of genomic prediction was evaluated for heritabilities of 0.10, 0.25 or 0.50. Phenotypes were simulated for 2250 purebred animals using 50 QTL selected from actual 50k SNP (single nucleotide polymorphism) genotypes giving a proportion of causal to total loci of.0001. A Bayes C π threshold model simultaneously fitted all 50k markers except those that represented QTL. Estimated SNP effects were utilized to predict genomic breeding values in purebred (n = 239) or multibreed (n = 924) validation populations. Correlations between true and predicted genomic merit in validation populations were used to assess predictive ability.

RESULTS

Accuracies of genomic estimated breeding values ranged from 0.12 to 0.66 for purebred and from 0.04 to 0.53 for multibreed validation populations based on Bayes C π linear model analysis of the simulated underlying variable. Accuracies for ordinal categorical scores analyzed by the Bayes C π threshold model were 20% to 50% lower and ranged from 0.04 to 0.55 for purebred and from 0.01 to 0.44 for multibreed validation populations. Analysis of ordinal categorical scores using a linear model resulted in further reductions in accuracy.

CONCLUSIONS

Threshold traits result in markedly lower accuracy than a linear model on the underlying variable. To achieve an accuracy equal or greater than for continuous phenotypes with a training population of 1000 animals, a 2.25 fold increase in training population size was required for categorical scores fitted with the threshold model. The threshold model resulted in higher accuracies than the linear model and its advantage was greatest when training populations were smallest.

Reduction in accuracy of genomic prediction for ordered categorical data compared to continuous observations

Background

Accuracy of genomic prediction depends on number of records in the training population, heritability, effective population size, genetic architecture, and relatedness of training and validation populations. Many traits have ordered categories including reproductive performance and susceptibility or resistance to disease. Categorical scores are often recorded because they are easier to obtain than continuous observations. Bayesian linear regression has been extended to the threshold model for genomic prediction. The objective of this study was to quantify reductions in accuracy for ordinal categorical traits relative to continuous traits.

Methods

Efficiency of genomic prediction was evaluated for heritabilities of 0.10, 0.25 or 0.50. Phenotypes were simulated for 2250 purebred animals using 50 QTL selected from actual 50k SNP (single nucleotide polymorphism) genotypes giving a proportion of causal to total loci of.0001. A Bayes C π threshold model simultaneously fitted all 50k markers except those that represented QTL. Estimated SNP effects were utilized to predict genomic breeding values in purebred (n = 239) or multibreed (n = 924) validation populations. Correlations between true and predicted genomic merit in validation populations were used to assess predictive ability.

Results

Accuracies of genomic estimated breeding values ranged from 0.12 to 0.66 for purebred and from 0.04 to 0.53 for multibreed validation populations based on Bayes C π linear model analysis of the simulated underlying variable. Accuracies for ordinal categorical scores analyzed by the Bayes C π threshold model were 20% to 50% lower and ranged from 0.04 to 0.55 for purebred and from 0.01 to 0.44 for multibreed validation populations. Analysis of ordinal categorical scores using a linear model resulted in further reductions in accuracy.

Conclusions

Threshold traits result in markedly lower accuracy than a linear model on the underlying variable. To achieve an accuracy equal or greater than for continuous phenotypes with a training population of 1000 animals, a 2.25 fold increase in training population size was required for categorical scores fitted with the threshold model. The threshold model resulted in higher accuracies than the linear model and its advantage was greatest when training populations were smallest.

Breed predisposition and heritability of atrial fibrillation in the Standardbred horse: a retrospective case-control study

OBJECTIVES

To assess evidence for genetic contributions to atrial fibrillation (AF) in the Standardbred horse.

ANIMALS

Equine referrals to the Ontario Veterinary College Health Sciences Centre (OVCHSC) for 1985-2009, and age and gait matched breed registry controls.

METHODS

Breeds presenting ≥ 5 times annually were tabulated (admission year and diagnosis; total 40,039; AF 396; no AF 39,643), and breed and year effects examined. Heritability and inbreeding coefficients were determined for Standardbred AF cases and racing contemporaries, and odds ratios for AF were calculated for frequently occurring sires.

RESULTS

Year and breed effects on diagnosis were highly significant (Chi-Square 212.85, p < 0.0001, and 304.25, p < 0.0001, respectively). Year effect on diagnosis by breed was significant from 1997, and due to Standardbred admissions each year. Quarterhorses were significantly less likely to present with AF (OR 0.0578-0.6048), Standardbreds were more likely (OR 4.3874-10.9006). Heritability of AF on the underlying scale (h²(u)) was estimated at 29.6 ± 3.9% and on the observed binomial scale (h²(o)), at 9.6%. For horses born in 1994 or later, h²(u) was 31.1 ± 4.3% and h²(o), 10.1%. Of 22 first generation sires appearing ≥ 10 times in the case/control file, seven pacing and one trotting sire produced affected horses more frequently than expected (OR 2.66-66.32). Inbreeding was not a factor.

CONCLUSIONS

There is genetic liability to AF in Standardbred horses, likely due to more than single genes with simple Mendelian inheritance. Genomic studies are required.

Heritability estimation of osteoarthritis in the pig-tailed macaque (Macaca nemestrina) with a look toward future data collection

We examine heritability estimation of an ordinal trait for osteoarthritis, using a population of pig-tailed macaques from the Washington National Primate Research Center (WaNPRC). This estimation is non-trivial, as the data consist of ordinal measurements on 16 intervertebral spaces throughout each macaque's spinal cord, with many missing values. We examine the resulting heritability estimates from different model choices, and also perform a simulation study to compare the performance of heritability estimation with these different models under specific known parameter values. Under both the real data analysis and the simulation study, we find that heritability estimates from an assumption of normality of the trait differ greatly from those of ordered probit regression, which considers the ordinality of the trait. This finding indicates that some caution should be observed regarding model selection when estimating heritability of an ordinal quantity. Furthermore, we find evidence that our real data have little information for valid heritability estimation under ordered probit regression. We thus conclude with an exploration of sample size requirements for heritability estimation under this model. For an ordinal trait, an incorrect assumption of normality can lead to severely biased heritability estimation. Sample size requirements for heritability estimation of an ordinal trait under the threshold model depends on the pedigree structure, trait distribution and the degree of relatedness between each phenotyped individual. Our sample of 173 monkeys did not have enough information from which to estimate heritability, but estimable heritability can be obtained with as few as 180 related individuals under certain scenarios examined here.

Age-related macular degeneration: genetics and biology coming together

Genetic and genomic studies have enhanced our understanding of complex neurodegenerative diseases that exert a devastating impact on individuals and society. One such disease, age-related macular degeneration (AMD), is a major cause of progressive and debilitating visual impairment. Since the pioneering discovery in 2005 of complement factor H (CFH) as a major AMD susceptibility gene, extensive investigations have confirmed 19 additional genetic risk loci, and more are anticipated. In addition to common variants identified by now-conventional genome-wide association studies, targeted genomic sequencing and exome-chip analyses are uncovering rare variant alleles of high impact. Here, we provide a critical review of the ongoing genetic studies and of common and rare risk variants at a total of 20 susceptibility loci, which together explain 40-60% of the disease heritability but provide limited power for diagnostic testing of disease risk. Identification of these susceptibility loci has begun to untangle the complex biological pathways underlying AMD pathophysiology, pointing to new testable paradigms for treatment.

Applications of population genetics to animal breeding, from wright, fisher and lush to genomic prediction

Although animal breeding was practiced long before the science of genetics and the relevant disciplines of population and quantitative genetics were known, breeding programs have mainly relied on simply selecting and mating the best individuals on their own or relatives' performance. This is based on sound quantitative genetic principles, developed and expounded by Lush, who attributed much of his understanding to Wright, and formalized in Fisher's infinitesimal model. Analysis at the level of individual loci and gene frequency distributions has had relatively little impact. Now with access to genomic data, a revolution in which molecular information is being used to enhance response with "genomic selection" is occurring. The predictions of breeding value still utilize multiple loci throughout the genome and, indeed, are largely compatible with additive and specifically infinitesimal model assumptions. I discuss some of the history and genetic issues as applied to the science of livestock improvement, which has had and continues to have major spin-offs into ideas and applications in other areas.

Ancestral character estimation under the threshold model from quantitative genetics

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for discretely valued traits. This approach is based on the threshold model from evolutionary quantitative genetics. Under the threshold model, the value exhibited by an individual or species for a discrete character is determined by an underlying, unobserved continuous trait called "liability." In this new method for ancestral state reconstruction, I use Bayesian Markov chain Monte Carlo (MCMC) to sample the liabilities of ancestral and tip species, and the relative positions of two or more thresholds, from their joint posterior probability distribution. Using data simulated under the model, I find that the method has very good performance in ancestral character estimation. Use of the threshold model for ancestral state reconstruction relies on a priori specification of the order of the discrete character states along the liability axis. I test the use of a Bayesian MCMC information theoretic criterion based approach to choose among different hypothesized orderings for the discrete character. Finally, I apply the method to the evolution of feeding mode in centrarchid fishes.

Evolution of discrete phenotypes from continuous norms of reaction

Discrete phenotypic variation often involves threshold expression of a trait with polygenic inheritance. How such discrete polyphenisms evolve starting from continuously varying phenotypes has received little theoretical attention. We model the evolution of sigmoid norms of reaction in response to variation in an underlying trait or in a continuous environment to identify conditions for the evolution of discontinuity. For traits with expression depending on a randomly varying underlying factor, such as developmental noise, polyphenism is unstable under constant phenotypic selection for two selective peaks, and reaction norm evolution results in a phenotypic distribution concentrated at only one peak. But with frequency-dependent selection between two adaptive peaks, a steep threshold maintaining polyphenism can evolve. For inducible plastic traits with expression conditioned on an environmental variable that also affects phenotypic selection, the steepness of the evolved reaction norm depends both on the differentiation of the environment in time or space and on its predictability between development and selection. Together with recent measurements of genetic variance of threshold steepness, these predictions suggest that quasi-discrete phenotypic variation may often evolve from continuous norms of reactions rather than being an intrinsic property of development.

Annals of morphology. Atavisms: phylogenetic Lazarus?

Dedication: with highest respect and affection to Prof. Giovanni Neri on the eve of his official administrative retirement as Chair of the Institute of Medical Genetics of the Università Cattolica of Rome for leadership in medical genetics and medical science and friendship for decades. The concept "atavism," reversion, throwback, Rückschlag remains an epistemological challenge in biology; unwise or implausible over-interpretation of a given structure as such has led some to almost total skepticism as to its existence. Originating in botany in the 18th century it became applied to zoology (and humans) with increasing frequency over the last two centuries such that the very concept became widely discredited. Presently, atavisms have acquired a new life and reconsideration given certain reasonable criteria, including: Homology of structure of the postulated atavism to that of ancestral fossils or collateral species with plausible soft tissue reconstructions taking into account relationships of parts, obvious sites of origin and insertion of muscles, vascular channels, etc. Most parsimonious, plausible phylogenetic assumptions. Evident rudimentary or vestigial anatomical state in prior generations or in morphogenesis of a given organism. Developmental instability in prior generations, that is, some closely related species facultatively with or without the trait. Genetic identity or phylogenomic similarity inferred in ancestors and corroborated in more or less closely related species. Fluctuating asymmetry may be the basis for the striking evolutionary diversification and common atavisms in limbs; however, strong selection and developmental constraints would make atavisms in, for example, cardiac or CNS development less likely. Thus, purported atavisms must be examined critically in light of the above criteria.

An evaluation of a novel estimator of linkage disequilibrium

The analysis of systems involving many loci is important in population and quantitative genetics. An important problem is the study of linkage disequilibrium (LD), a concept relevant in genome-enabled prediction of quantitative traits and in exploration of marker-phenotype associations. This article introduces a new estimator of a LD parameter (ρ(2)) that is much easier to compute than a maximum likelihood (or Bayesian) estimate of a tetra-choric correlation. We examined the conjecture that the sampling distribution of the estimator of ρ(2) could be less frequency dependent than that of the estimator of r(2), a widely used metric for assessing LD. This was done via an empirical evaluation of LD in 806 Holstein-Friesian cattle using 771 single-nucleotide polymorphism (SNP) markers and of HapMap III data on 21,991 SNPs (chromosome 3) observed in 88 unrelated individuals from Tuscany. Also, 1600 haplotypes over a region of 1 Mb simulated under the coalescent were used to estimate LD using the two measures. Subsequently, a simulation study compared the new estimator with that of r(2) using several scenarios of LD and allelic frequencies. From these studies, it is concluded that ρ(2) provides a useful metric for the study of LD as the distribution of its estimator is less frequency dependent than that of the standard estimator of r(2).

Identifying hidden rate changes in the evolution of a binary morphological character: the evolution of plant habit in campanulid angiosperms

The growth of phylogenetic trees in scope and in size is promising from the standpoint of understanding a wide variety of evolutionary patterns and processes. With trees comprised of larger, older, and globally distributed clades, it is likely that the lability of a binary character will differ significantly among lineages, which could lead to errors in estimating transition rates and the associated inference of ancestral states. Here we develop and implement a new method for identifying different rates of evolution in a binary character along different branches of a phylogeny. We illustrate this approach by exploring the evolution of growth habit in Campanulidae, a flowering plant clade containing some 35,000 species. The distribution of woody versus herbaceous species calls into question the use of traditional models of binary character evolution. The recognition and accommodation of changes in the rate of growth form evolution in different lineages demonstrates, for the first time, a robust picture of growth form evolution across a very large, very old, and very widespread flowering plant clade.

Evolution of viviparity: a phylogenetic test of the cold-climate hypothesis in phrynosomatid lizards

The evolution of viviparity is a key life-history transition in vertebrates, but the selective forces favoring its evolution are not fully understood. With >100 origins of viviparity, squamate reptiles (lizards and snakes) are ideal for addressing this issue. Some evidence from field and laboratory studies supports the "cold-climate" hypothesis, wherein viviparity provides an advantage in cold environments by allowing mothers to maintain higher temperatures for developing embryos. Surprisingly, the cold-climate hypothesis has not been tested using both climatic data and phylogenetic comparative methods. Here, we investigate the evolution of viviparity in the lizard family Phrynosomatidae using GIS-based environmental data, an extensive phylogeny (117 species), and recently developed comparative methods. We find significant relationships between viviparity and lower temperatures during the warmest (egg-laying) season, strongly supporting the cold-climate hypothesis. Remarkably, we also find that viviparity tends to evolve more frequently at tropical latitudes, despite its association with cooler climates. Our results help explain this and two related patterns that seemingly contradict the cold-climate hypothesis: the presence of viviparous species restricted to low-elevation tropical regions and the paucity of viviparous species at high latitudes. Finally, we examine whether viviparous taxa may be at higher risk of extinction from anthropogenic climate change.

Genome-wide association study of infectious bovine keratoconjunctivitis in Angus cattle

BACKGROUND

Infectious Bovine Keratoconjunctivitis (IBK) in beef cattle, commonly known as pinkeye, is a bacterial disease caused by Moraxellabovis. IBK is characterized by excessive tearing and ulceration of the cornea. Perforation of the cornea may also occur in severe cases. IBK is considered the most important ocular disease in cattle production, due to the decreased growth performance of infected individuals and its subsequent economic effects. IBK is an economically important, lowly heritable categorical disease trait. Mass selection of unaffected animals has not been successful at reducing disease incidence. Genome-wide studies can determine chromosomal regions associated with IBK susceptibility. The objective of the study was to detect single-nucleotide polymorphism (SNP) markers in linkage disequilibrium (LD) with genetic variants associated with IBK in American Angus cattle.

RESULTS

The proportion of phenotypic variance explained by markers was 0.06 in the whole genome analysis of IBK incidence classified as two, three or nine categories. Whole-genome analysis using any categorisation of (two, three or nine) IBK scores showed that locations on chromosomes 2, 12, 13 and 21 were associated with IBK disease. The genomic locations on chromosomes 13 and 21 overlap with QTLs associated with Bovine spongiform encephalopathy, clinical mastitis or somatic cell count.

CONCLUSIONS

Results of these genome-wide analyses indicated that if the underlying genetic factors confer not only IBK susceptibility but also IBK severity, treating IBK phenotypes as a two-categorical trait can cause information loss in the genome-wide analysis. These results help our overall understanding of the genetics of IBK and have the potential to provide information for future use in breeding schemes.

Bayesian methods for estimating GEBVs of threshold traits

Estimation of genomic breeding values is the key step in genomic selection (GS). Many methods have been proposed for continuous traits, but methods for threshold traits are still scarce. Here we introduced threshold model to the framework of GS, and specifically, we extended the three Bayesian methods BayesA, BayesB and BayesCπ on the basis of threshold model for estimating genomic breeding values of threshold traits, and the extended methods are correspondingly termed BayesTA, BayesTB and BayesTCπ. Computing procedures of the three BayesT methods using Markov Chain Monte Carlo algorithm were derived. A simulation study was performed to investigate the benefit of the presented methods in accuracy with the genomic estimated breeding values (GEBVs) for threshold traits. Factors affecting the performance of the three BayesT methods were addressed. As expected, the three BayesT methods generally performed better than the corresponding normal Bayesian methods, in particular when the number of phenotypic categories was small. In the standard scenario (number of categories=2, incidence=30%, number of quantitative trait loci=50, h² = 0.3), the accuracies were improved by 30.4%, 2.4%, and 5.7% points, respectively. In most scenarios, BayesTB and BayesTCπ generated similar accuracies and both performed better than BayesTA. In conclusion, our work proved that threshold model fits well for predicting GEBVs of threshold traits, and BayesTCπ is supposed to be the method of choice for GS of threshold traits.

Lost in the map

Organismal development and evolution are complex, multifaceted processes that depend intimately on context. They are subject to environmental influences, chance appearance and fixation of mutations, and numerous other idiosyncrasies. Genomics is detailing the molecular signature of effects of these mechanisms on phenotypes, but because numerous distinct evolutionary explanations can produce a given genomic pattern, the molecular details, rather than elucidating process, typically distract from explanatory insight and contribute little to predictive capability. While genomic research has burgeoned, direct study of evolutionary and developmental processes has lagged. We advocate for reinvigoration of direct study of process, along with refocusing of attention on questions of broad biological import, as more productive of urgently needed insights, which genomic approaches are not providing.