Accounting for genetic differences among unknown parents in microevolutionary studies: how to include genetic groups in quantitative genetic animal models

Abstract

Quantifying and predicting microevolutionary responses to environmental change requires unbiased estimation of quantitative genetic parameters in wild populations. 'Animal models', which utilize pedigree data to separate genetic and environmental effects on phenotypes, provide powerful means to estimate key parameters and have revolutionized quantitative genetic analyses of wild populations. However, pedigrees collected in wild populations commonly contain many individuals with unknown parents. When unknown parents are non-randomly associated with genetic values for focal traits, animal model parameter estimates can be severely biased. Yet, such bias has not previously been highlighted and statistical methods designed to minimize such biases have not been implemented in evolutionary ecology. We first illustrate how the occurrence of non-random unknown parents in population pedigrees can substantially bias animal model predictions of breeding values and estimates of additive genetic variance, and create spurious temporal trends in predicted breeding values in the absence of local selection. We then introduce 'genetic group' methods, which were developed in agricultural science, and explain how these methods can minimize bias in quantitative genetic parameter estimates stemming from genetic heterogeneity among individuals with unknown parents. We summarize the conceptual foundations of genetic group animal models and provide extensive, step-by-step tutorials that demonstrate how to fit such models in a variety of software programs. Furthermore, we provide new functions in r that extend current software capabilities and provide a standardized approach across software programs to implement genetic group methods. Beyond simply alleviating bias, genetic group animal models can directly estimate new parameters pertaining to key biological processes. We discuss one such example, where genetic group methods potentially allow the microevolutionary consequences of local selection to be distinguished from effects of immigration and resulting gene flow. We highlight some remaining limitations of genetic group models and discuss opportunities for further development and application in evolutionary ecology. We suggest that genetic group methods should no longer be overlooked by evolutionary ecologists, but should become standard components of the toolkit for animal model analyses of wild population data sets.

Keywords: WOMBAT; ASReml; MCMCglmm; base population; dispersal; heritability; nadiv; numerator relationship matrix; phantom parents; total additive genetic effects.

Figure 1

Percentages of pedigreed individuals that have unknown dams (black bars) or sires (grey bars) in wild population pedigrees. Further details are in Appendix S2.

Figure 2

Simulated (a) phenotypes and (b) breeding values across 15 generations, and (c) predicted breeding values from a basic animal model using a pedigree where immigrants have unknown parents. Alternating dark and light grey points distinguish consecutive generations of founders and their descendants. In (a), immigrant phenotypes are plotted in the generation they arrive (black points). In (b) and (c), immigrant simulated and predicted breeding values are plotted to the left of generation one to illustrate that their phantom parents are assigned to the animal model base population. Black brackets demarcate the range and hence variance in breeding values in the (b) founder population and (c) the offspring of the default animal model base population.

Figure 3

Simple example pedigrees and matrices illustrating (a) a pedigree containing individuals with unknown parents (NA), (b) phantom parents assigned to two genetic groups (g1 and g2), (c) the proportional contributions of each genetic group to each individual's genome, as is used to explicitly model genetic groups as fixed covariate regressions, (d) the inverse relatedness matrix (A ⁻¹) for the pedigree in (a), and (e) the augmented inverse relatedness matrix (A*), used to model genetic group effects implicitly within the random effects.

Figure 4

(a) Simulated total additive genetic effects and predicted (b) total additive genetic effects and (c) breeding values from an animal model fitting genetic group effects. Alternating dark and light grey points distinguish consecutive generations of founders and their descendants. Simulated data correspond to the phenotypes in Fig. 2a. Immigrant values (black points) are plotted to the left of generation one to illustrate that their phantom parents are assigned to the animal model base population.