Heritable Environmental Variance Causes Nonlinear Relationships Between Traits: Application to Birth Weight and Stillbirth of Pigs

Abstract

There is recent evidence from laboratory experiments and analysis of livestock populations that not only the phenotype itself, but also its environmental variance, is under genetic control. Little is known about the relationships between the environmental variance of one trait and mean levels of other traits, however. A genetic covariance between these is expected to lead to nonlinearity between them, for example between birth weight and survival of piglets, where animals of extreme weights have lower survival. The objectives were to derive this nonlinear relationship analytically using multiple regression and apply it to data on piglet birth weight and survival. This study provides a framework to study such nonlinear relationships caused by genetic covariance of environmental variance of one trait and the mean of the other. It is shown that positions of phenotypic and genetic optima may differ and that genetic relationships are likely to be more curvilinear than phenotypic relationships, dependent mainly on the environmental correlation between these traits. Genetic correlations may change if the population means change relative to the optimal phenotypes. Data of piglet birth weight and survival show that the presence of nonlinearity can be partly explained by the genetic covariance between environmental variance of birth weight and survival. The framework developed can be used to assess effects of artificial and natural selection on means and variances of traits and the statistical method presented can be used to estimate trade-offs between environmental variance of one trait and mean levels of others.KEYWORDS genetics of environmental variance; optimum trait; fitness; complex traits; mass selection I N the classic model of quantitative genetics, the phenotype is assumed to be the sum of an effectively infinite number of genes and environmental effects; i.e., P ¼ G þ E (Falconer and Mackay 1996; Lynch and Walsh 1998). The phenotypic variance is the sum of the genetic (V G ) and environmental (V E ) variance. It is assumed that the environmental variance is homogeneous across genotypes, but recently there is evidence from laboratory experiments and analysis of livestock populations that not only the phenotype itself, but also its V E ; is under genetic control (Hill and Mulder 2010). This might be expressed as genetic heterogeneity in the withinindividual variance of a trait with repeat measurements, such as weight of individual piglets in a litter or total litter weight across parities, or as a difference in within-family variance for traits such as juvenile body weight expressed once.The median genetic coefficient of variation for V E (GCV VE ¼ s Av =V E ; where s Av is additive genetic variance in V E ) is 0.3 based on a review of 14 studies with estimates of genetic variance in V E primarily on livestock populations (Hill and Mulder 2010). This indicates that V E could be increased or decreased by 30% if changed by one genetic standard deviation. These analyses were mainly based on genetic analysis...

Genetic variation in variability: Phenotypic variability of fledging weight and its evolution in a songbird population

“…Stabilizing selection on the mean is expected to reduce V E as demonstrated by Mulder et al. (), whereas intense directional selection is expected to increase V E (Hill and Zhang ; Mulder et al. ).…”

“…As pointed out above, variation in V E can lead to variation in individual fitness and V E could hence be under selection. Stabilizing selection on the mean is expected to reduce V E as demonstrated by Mulder et al (2015), whereas intense directional selection is expected to increase V E (Hill and Zhang 2004;Mulder et al 2007). Under stabilizing selection, Zhang and Hill (2005) showed that small homogeneity costs or large temporal variation in optimal phenotype and strength of stabilizing selection can maintain V E .…”

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

“…To date, the few published estimates of additive genetic variance of predictability are restricted to a captive animal breeding environment (Hill & Mulder, ; Mulder et al ., ; Sae‐Lim et al ., ), except for one study (Mulder et al ., ). Mulder et al .…”

“…In a bivariate scenario, Mulder et al . () showed that additive genetic variance in predictability of a linearly selected trait could lead to nonlinear responses for correlated traits. The recent development of a theoretical framework (Hill & Mulder, ; Westneat et al ., ) and of suitable statistical methods (Lee & Nelder, ; Cleasby et al ., ; Mulder et al ., ) offer a way to advance our understanding of these issues.…”

“…Studies in animal breeding have estimated the additive genetic basis of within-genotype variance for multiple productivity-related traits such as litter size (Hill & Mulder, 2010) or body weight (Sae-Lim et al, 2015). However, the degree to which genetic variation for the predictability of a trait might respond to selection and influence evolution of other traits remains unclear (but see Mulder et al, 2015). In a bivariate scenario, Mulder et al (2015) showed that additive genetic variance in predictability of a linearly selected trait could lead to nonlinear responses for correlated traits.…”