Heritable environmental variance causes nonlinear relationships between traits: application to birth weight and stillbirth of pigs

Invited review: Recursive models in animal breeding: Interpretation, limitations, and extensions

Structural equation models allow causal effects between 2 or more variables to be considered and can postulate unidirectional (recursive models; RM) or bidirectional (simultaneous models) causality between variables. This review evaluated the properties of RM in animal breeding and how to interpret the genetic parameters and the corresponding estimated breeding values. In many cases, RM and mixed multitrait models (MTM) are statistically equivalent, although subject to the assumption of variance-covariance matrices and restrictions imposed for achieving model identification. Inference under RM requires imposing some restrictions on the (co)variance matrix or on the location parameters. The estimates of the variance components and the breeding values can be transformed from RM to MTM, although the biological interpretation differs. In the MTM, the breeding values predict the full influence of the additive genetic effects on the traits and should be used for breeding purposes. In contrast, the RM breeding values express the additive genetic effect while holding the causal traits constant. The differences between the additive genetic effect in RM and MTM can be used to identify the genomic regions that affect the additive genetic variation of traits directly or causally mediated for another trait or traits. Furthermore, we presented some extensions of the RM that are useful for modeling quantitative traits with alternative assumptions. The equivalence of RM and MTM can be used to infer causal effects on sequentially expressed traits by manipulating the residual (co)variance matrix under the MTM. Further, RM can be implemented to analyze causality between traits that might differ among subgroups or within the parametric space of the independent traits. In addition, RM can be expanded to create models that introduce some degree of regularization in the recursive structure that aims to estimate a large number of recursive parameters. Finally, RM can be used in some cases for operational reasons, although there is no causality between traits.

A cross-specific multiplicative binomial recursive model for the analysis of perinatal mortality in a diallel cross among three varieties of Iberian pig

Perinatal piglet mortality is an important factor in pig production from economic and animal welfare perspectives; however, the statistical analysis of mortality is difficult because of its categorical nature. Recent studies have suggested that a binomial model for the survival of each specific piglet with a logit approach is appropriate and that recursive relationships between traits are useful for taking into account non-genetic relationships with other traits. In this study, the recursive binomial model is expanded in two directions: (1) the recursive phenotypic dependence among traits is allowed to vary among groups of individuals or crosses, and (2) the binomial distribution is replaced by the multiplicative binomial distribution to account for over or underdispersion. In this study, five recursive multiplicative binomial models were used to obtain estimates of the Dickerson crossbreeding parameters in a diallel cross among three varieties of Iberian pigs [Entrepelado (EE), Torbiscal (TT), and Retinto (RR)]. Records (10,255) from 2110 sows were distributed as follows: EE (433 records, 100 sows), ER (2336, 527), ET (942, 177), RE (806, 196), RR (870, 175), RT (2450, 488), TE (193, 36), TR (1993, 359), and TT (232, 68). Average litter size [Total Number Born (TNB)] and number of stillborns (SB) were 8.46 ± 2.27 and 0.25 ± 0.72, respectively. The overdispersion was evident with all models. The model with the best fit included a linear recursive relationship between TNB and the logit of [Formula: see text] of the multiplicative binomial distribution, and it implies that piglet mortality increases with litter size. Estimates of direct effects showed small differences among populations. The analysis of maternal effects indicated that the dams whose mothers were EE had a larger SB, while dams with RR mothers reduced the probability of born dead. The posterior estimates of heterosis suggested a reduction in SB when the sow is crosbred. The multiplicative binomial distribution provides a useful alternative to the binomial distribution when there is overdispersion in the data. Recursive models can be used for modeling non-genetic relationships between traits, even if the phenotypic dependency between traits varies among environments or groups of individuals. Piglet perinatal mortality increased with TNB and is reduced by maternal heterosis.

Patterns of environmental variance across environments and traits in domestic cattle

The variance in phenotypic trait values is a product of environmental and genetic variation. The sensitivity of traits to environmental variation has a genetic component and is likely to be under selection. However, there are few studies investigating the evolution of this sensitivity, in part due to the challenges of estimating the environmental variance. The livestock literature provides a wealth of studies that accurately partition components of phenotypic variance, including the environmental variance, in well-defined environments. These studies involve breeds that have been under strong selection on mean phenotype in optimal environments for many generations, and therefore represent an opportunity to study the potential evolution of trait sensitivity to environmental conditions. Here, we use literature on domestic cattle to examine the evolution of micro-environmental variance (CVR-the coefficient of residual variance) by testing for differences in expression of CVR in animals from the same breed reared in different environments. Traits that have been under strong selection did not follow a null expectation of an increase in CVR in heterogenous environments (e.g., grazing), a pattern that may reflect evolution of increased uniformity in heterogeneous environments. When comparing CVR across environments of different levels of optimality, here measured by trait mean, we found a reduction in CVR in the more optimal environments for both life history and growth traits. Selection aimed at increasing trait means in livestock breeds typically occurs in the more optimal environments, and we therefore suspect that the decreased CVR is a consequence of evolution of the expression of micro-environmental variance in this environment. Our results highlight the heterogeneity in micro-environmental variance across environments and point to possible connections to the intensity of selection on trait means.

The Evolution of Variance Control

Genetically identical individuals can be phenotypically variable, even in constant environmental conditions. The ubiquity of this phenomenon, known as 'intra-genotypic variability', is increasingly evident and the relevant mechanistic underpinnings are beginning to be understood. In parallel, theory has delineated a number of formal expectations for contexts in which such a feature would be adaptive. Here, we review empirical evidence across biological systems and theoretical expectations, including nonlinear averaging and bet hedging. We synthesize existing results to illustrate the dependence of selection outcomes both on trait characteristics, features of environmental variability, and species' demographic context. We conclude by discussing ways to bridge the gap between empirical evidence of intra-genotypic variability, studies demonstrating its genetic component, and evidence that it is adaptive.

Genetics and genomics of uniformity and resilience in livestock and aquaculture species: A review

Genetic control of residual variance offers opportunities to increase uniformity and resilience of livestock and aquaculture species. Improving uniformity and resilience of animals will improve health and welfare of animals and lead to more homogenous products. Our aims in this review were to summarize the current models and methods to study genetic control of residual variance, genetic parameters and genomic results for residual variance and discuss future research directions. Typically, the genetic coefficient of variation is high (median = 0.27; range 0-0.86) and the heritability of residual variance is low (median = 0.01; range 0-0.10). Higher heritabilities can be achieved when increasing the number of records per animal. Divergent selection experiments have supported the feasibility of selecting for high or low residual variance. Genomic studies have revealed associations in regions related to stress, including those from the heat shock protein family. Although the number of studies is growing, genetic control of residual variance is still poorly understood, but big data and genomics offer great opportunities.

Invited review: Piglet survival: benefits of the immunocompetence

Piglet mortality has a negative impact on animal welfare and public acceptance. Moreover, the number of weaned piglets per sow mainly determines the profitability of piglet production. Increased litter sizes are associated with lower birth weights and piglet survival. Decreased survival rates and performance of piglets make the control of diseases and infections within pig production even more crucial. Consequently, selection for immunocompetence becomes an important key aspect within modern breeding programmes. However, the phenotypic recording of immune traits is difficult and expensive to realize within farm routines. Even though immune traits show genetic variability, only few examples exist on their respective suitability within a breeding programme and their relationships to economically important production traits. The analysis of immune traits for an evaluation of immunocompetence to gain a generally improved immune response is promising. Generally, in-depth knowledge of the genetic background of the immune system is needed to gain helpful insights about its possible incorporation into breeding programmes. Possible physiological drawbacks for enhanced immunocompetence must be considered with regards to the allocation theory and possible trade-offs between the immune system and performance. This review aims to discuss the relationships between the immunocompetence of the pig, piglet survival as well as the potential of these traits to be included into a breeding strategy for improved robustness.

Opportunities to Improve Resilience in Animal Breeding Programs

Resilience is the capacity of an animal to be minimally affected by disturbances or to rapidly return to the state pertained before exposure to a disturbance. However, indicators for general resilience to environmental disturbances have not yet been defined, and perhaps therefore resilience is not yet included in breeding goals. The current developments on big data collection give opportunities to determine new resilience indicators based on longitudinal data, which can aid to incorporate resilience in animal breeding goals. The objectives of this paper were: (1) to define resilience indicator traits based on big data, (2) to define economic values for resilience, and (3) to show the potential to improve resilience of livestock through inclusion of resilience in breeding goals. Resilience might be measured based on deviations from expected production levels over a period of time. Suitable resilience indicators could be the variance of deviations, the autocorrelation of deviations, the skewness of deviations, and the slope of a reaction norm. These (new) resilience indicators provide opportunity to include resilience in breeding programs. Economic values of resilience indicators in the selection index can be calculated based on reduced costs due to labor and treatments. For example, when labor time is restricted, the economic value of resilience increases with an increasing number of animals per farm, and can become as large as the economic value of production. This shows the importance of including resilience in breeding goals. Two scenarios were described to show the additional benefit of including resilience in breeding programs. These examples showed that it is hard to improve resilience with only production traits in the selection index, but that it is possible to greatly improve resilience by including resilience indicators in the selection index. However, when health-related traits are already present in the selection index, the effect is smaller. Nevertheless, inclusion of resilience indicators in the selection index increases the response in the breeding goal and resilience, which results in less labor-demanding, and thus easier-to-manage livestock. Current developments on massive collection of data, and new phenotypes based on these data, offer exciting opportunities to breed for improved resilience of livestock.

QTL Mapping on a Background of Variance Heterogeneity

Standard QTL mapping procedures seek to identify genetic loci affecting the phenotypic mean while assuming that all individuals have the same residual variance. But when the residual variance differs systematically between groups, perhaps due to a genetic or environmental factor, such standard procedures can falter: in testing for QTL associations, they attribute too much weight to observations that are noisy and too little to those that are precise, resulting in reduced power and and increased susceptibility to false positives. The negative effects of such "background variance heterogeneity" (BVH) on standard QTL mapping have received little attention until now, although the subject is closely related to work on the detection of variance-controlling genes. Here we use simulation to examine how BVH affects power and false positive rate for detecting QTL affecting the mean (mQTL), the variance (vQTL), or both (mvQTL). We compare linear regression for mQTL and Levene's test for vQTL, with tests more recently developed, including tests based on the double generalized linear model (DGLM), which can model BVH explicitly. We show that, when used in conjunction with a suitable permutation procedure, the DGLM-based tests accurately control false positive rate and are more powerful than the other tests. We also find that some adverse effects of BVH can be mitigated by applying a rank inverse normal transform. We apply our novel approach, which we term "mean-variance QTL mapping", to publicly available data on a mouse backcross and, after accommodating BVH driven by sire, detect a new mQTL for bodyweight.

Heritable Micro-environmental Variance Covaries with Fitness in an Outbred Population of Drosophila serrata

The genetic basis of stochastic variation within a defined environment, and the consequences of such micro-environmental variance for fitness are poorly understood . Using a multigenerational breeding design in Drosophila serrata, we demonstrated that the micro-environmental variance in a set of morphological wing traits in a randomly mating population had significant additive genetic variance in most single wing traits. Although heritability was generally low (<1%), coefficients of additive genetic variance were of a magnitude typical of other morphological traits, indicating that the micro-environmental variance is an evolvable trait. Multivariate analyses demonstrated that the micro-environmental variance in wings was genetically correlated among single traits, indicating that common mechanisms of environmental buffering exist for this functionally related set of traits. In addition, through the dominance genetic covariance between the major axes of micro-environmental variance and fitness, we demonstrated that micro-environmental variance shares a genetic basis with fitness, and that the pattern of selection is suggestive of variance-reducing selection acting on micro-environmental variance.

Selection for environmental variance of litter size in rabbits

Background

In recent years, there has been an increasing interest in the genetic determination of environmental variance. In the case of litter size, environmental variance can be related to the capacity of animals to adapt to new environmental conditions, which can improve animal welfare.

Results

We developed a ten-generation divergent selection experiment on environmental variance. We selected one line of rabbits for litter size homogeneity and one line for litter size heterogeneity by measuring intra-doe phenotypic variance. We proved that environmental variance of litter size is genetically determined and can be modified by selection. Response to selection was 4.5% of the original environmental variance per generation. Litter size was consistently higher in the Low line than in the High line during the entire experiment.

Conclusions

We conclude that environmental variance of litter size is genetically determined based on the results of our divergent selection experiment. This has implications for animal welfare, since animals that cope better with their environment have better welfare than more sensitive animals. We also conclude that selection for reduced environmental variance of litter size does not depress litter size.

Genetic basis of between-individual and within-individual variance of docility

Between-individual variation in phenotypes within a population is the basis of evolution. However, evolutionary and behavioural ecologists have mainly focused on estimating between-individual variance in mean trait and neglected variation in within-individual variance, or predictability of a trait. In fact, an important assumption of mixed-effects models used to estimate between-individual variance in mean traits is that within-individual residual variance (predictability) is identical across individuals. Individual heterogeneity in the predictability of behaviours is a potentially important effect but rarely estimated and accounted for. We used 11 389 measures of docility behaviour from 1576 yellow-bellied marmots (Marmota flaviventris) to estimate between-individual variation in both mean docility and its predictability. We then implemented a double hierarchical animal model to decompose the variances of both mean trait and predictability into their environmental and genetic components. We found that individuals differed both in their docility and in their predictability of docility with a negative phenotypic covariance. We also found significant genetic variance for both mean docility and its predictability but no genetic covariance between the two. This analysis is one of the first to estimate the genetic basis of both mean trait and within-individual variance in a wild population. Our results indicate that equal within-individual variance should not be assumed. We demonstrate the evolutionary importance of the variation in the predictability of docility and illustrate potential bias in models ignoring variation in predictability. We conclude that the variability in the predictability of a trait should not be ignored, and present a coherent approach for its quantification.

Genetic parameters for uniformity of harvest weight and body size traits in the GIFT strain of Nile tilapia

Background

Animal breeding programs have been very successful in improving the mean levels of traits through selection. However, in recent decades, reducing the variability of trait levels between individuals has become a highly desirable objective. Reaching this objective through genetic selection requires that there is genetic variation in the variability of trait levels, a phenomenon known as genetic heterogeneity of environmental (residual) variance. The aim of our study was to investigate the potential for genetic improvement of uniformity of harvest weight and body size traits (length, depth, and width) in the genetically improved farmed tilapia (GIFT) strain. In order to quantify the genetic variation in uniformity of traits and estimate the genetic correlations between level and variance of the traits, double hierarchical generalized linear models were applied to individual trait values.

Results

Our results showed substantial genetic variation in uniformity of all analyzed traits, with genetic coefficients of variation for residual variance ranging from 39 to 58 %. Genetic correlation between trait level and variance was strongly positive for harvest weight (0.60 ± 0.09), moderate and positive for body depth (0.37 ± 0.13), but not significantly different from 0 for body length and width.

Conclusions

Our results on the genetic variation in uniformity of harvest weight and body size traits show good prospects for the genetic improvement of uniformity in the GIFT strain. A high and positive genetic correlation was estimated between level and variance of harvest weight, which suggests that selection for heavier fish will also result in more variation in harvest weight. Simultaneous improvement of harvest weight and its uniformity will thus require index selection.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-016-0218-9) contains supplementary material, which is available to authorized users.