Erik Postma

An ecologist's guide to the animal model.

1. Efforts to understand the links between evolutionary and ecological dynamics hinge on our ability to measure and understand how genes influence phenotypes, fitness and population dynamics. Quantitative genetics provides a range of theoretical and empirical tools with which to achieve this when the relatedness between individuals within a population is known. 2. A number of recent studies have used a type of mixed-effects model, known as the animal model, to estimate the genetic component of phenotypic variation using data collected in the field. Here, we provide a practical guide for ecologists interested in exploring the potential to apply this quantitative genetic method in their research. 3. We begin by outlining, in simple terms, key concepts in quantitative genetics and how an animal model estimates relevant quantitative genetic parameters, such as heritabilities or genetic correlations. 4. We then provide three detailed example tutorials, for implementation in a variety of software packages, for some basic applications of the animal model. We discuss several important statistical issues relating to best practice when fitting different kinds of mixed models. 5. We conclude by briefly summarizing more complex applications of the animal model, and by highlighting key pitfalls and dangers for the researcher wanting to begin using quantitative genetic tools to address ecological and evolutionary questions.

Comment on "Additive genetic breeding values correlate with the load of partially deleterious mutations".

Tomkins et al. (Reports, 14 May 2010, p. 892) reported a strong negative correlation between breeding values and mutational load in cow-pea weevils. Here, I show that this result can be attributed to a statistical artifact. By testing the observed correlation against an incorrect null hypothesis, they find a negative correlation where one does not exist.

Gene flow maintains a large genetic difference in clutch size at a small spatial scale

Understanding the capacity of natural populations to adapt to their local environment is a central topic in evolutionary biology. Phenotypic differences between populations may have a genetic basis, but showing that they reflect different adaptive optima requires the quantification of both gene flow and selection. Good empirical data are rare. Using data on a spatially structured island population of great tits (Parus major), we show here that a persistent difference in mean clutch size between two subpopulations only a few kilometres apart has a major genetic component. We also show that immigrants from outside the island carry genes for large clutches. But gene flow into one subpopulation is low, as a result of a low immigration rate together with strong selection against immigrant genes. This has allowed for adaptation to the island environment and the maintenance of small clutches. In the other area, however, higher gene flow prevents local adaptation and maintains larger clutches. We show that the observed small-scale genetic difference in clutch size is not due to divergent selection on the island, but to different levels of gene flow from outside the island. Our findings illustrate the large effect of immigration on the evolution of local adaptations and on genetic population structure.

Short- and long-term consequences of early developmental conditions: a case study on wild and domesticated zebra finches

Divergent selection pressures among populations can result not only in significant differentiation in morphology, physiology and behaviour, but also in how these traits are related to each other, thereby driving the processes of local adaptation and speciation. In the Australian zebra finch, we investigated whether domesticated stock, bred in captivity over tens of generations, differ in their response to a life‐history manipulation, compared to birds taken directly from the wild. In a ‘common aviary’ experiment, we thereto experimentally manipulated the environmental conditions experienced by nestlings early in life by means of a brood size manipulation, and subsequently assessed its short‐ and long‐term consequences on growth, ornamentation, immune function and reproduction. As expected, we found that early environmental conditions had a marked effect on both short‐ and long‐term morphological and life‐history traits in all birds. However, although there were pronounced differences between wild and domesticated birds with respect to the absolute expression of many of these traits, which are indicative of the different selection pressures wild and domesticated birds were exposed to in the recent past, manipulated rearing conditions affected morphology and ornamentation of wild and domesticated finches in a very similar way. This suggests that despite significant differentiation between wild and domesticated birds, selection has not altered the relationships among traits. Thus, life‐history strategies and investment trade‐offs may be relatively stable and not easily altered by selection. This is a reassuring finding in the light of the widespread use of domesticated birds in studies of life‐history evolution and sexual selection, and suggests that adaptive explanations may be legitimate when referring to captive bird studies.

Implications of the difference between true and predicted breeding values for the study of natural selection and micro-evolution.

The ability to predict individual breeding values in natural populations with known pedigrees has provided a powerful tool to separate phenotypic values into their genetic and environmental components in a nonexperimental setting. This has allowed sophisticated analyses of selection, as well as powerful tests of evolutionary change and differentiation. To date, there has, however, been no evaluation of the reliability or potential limitations of the approach. In this article, I address these gaps. In particular, I emphasize the differences between true and predicted breeding values (PBVs), which as yet have largely been ignored. These differences do, however, have important implications for the interpretation of, firstly, the relationship between PBVs and fitness, and secondly, patterns in PBVs over time. I subsequently present guidelines I believe to be essential in the formulation of the questions addressed in studies using PBVs, and I discuss possibilities for future research.

WHY BREEDING TIME HAS NOT RESPONDED TO SELECTION FOR EARLIER BREEDING IN A SONGBIRD POPULATION

Abstract A crucial assumption underlying the breeders equation is that selection acts directly on the trait of interest, and not on an unmeasured environmental factor which affects both fitness and the trait. Such an environmentally induced covariance between a trait and fitness has been repeatedly proposed as an explanation for the lack of response to selection on avian breeding time. We tested this hypothesis using a long‐term dataset from a Dutch great tit (Parus major) population. Although there was strong selection for earlier breeding in this population, egg‐laying dates have changed only marginally over the last decades. Using a so‐called animal model, we quantified the additive genetic variance in breeding time and predicted breeding values for females. Subsequently, we compared selection at the phenotypic and genetic levels for two fitness components, fecundity and adult survival. We found no evidence for an environmentally caused covariance between breeding time and fitness or counteracting selection on the different fitness components. Consequently, breeding time should respond to selection but the expected response to selection was too small to be detected.

What ‘animal models’ can and cannot tell ornithologists about the genetics of wild populations

Good estimates of the genetic parameters of natural populations, such as heritability, are essential for both understanding how genetic variation is maintained and estimating a population’s evolutionary potential. Long-term studies on birds are especially amenable for calculating such estimates because of the ease with which pedigrees can be inferred. Recent ‘animal model’ methodology, originally developed by animal breeders to identify animals of high genetic merit, has been applied to natural bird populations of known pedigree. Animal models are more powerful than traditional analyses such as parent–offspring regression because they use all of the available pedigree information simultaneously. In doing so, they can accommodate common phenomena like selection and inbreeding and are especially suitable for the complex and incomplete pedigrees typical of natural populations. Animal models not only provide a better way of estimating genetic and environmental variance components, they also allow individual phenotypes to be separated into their genetic and environmental components. Here we aim to provide the interested ornithologist with an accessible entry into the vast and sometimes daunting quantitative genetics literature and, in particular, into the literature on the animal model. We outline not only the possibilities offered by the animal model for the accurate estimation of genetic parameters in the wild but also associated potential pitfalls and limitations. On the whole, we aim to provide an accessible and up-to-date overview of the rapidly developing and exciting field of evolutionary genetics applied to long-term studies of wild bird populations.

Disentangling the effect of genes, the environment and chance on sex ratio variation in a wild bird population

Sex ratio theory proposes that the equal sex ratio typically observed in birds and mammals is the result of natural selection. However, in species with chromosomal sex determination, the same 1 : 1 sex ratio is expected under random Mendelian segregation. Here, we present an analysis of 14 years of sex ratio data for a population of song sparrows (Melospiza melodia) on Mandarte Island, at the nestling stage and at independence from parental care. We test for the presence of variance in sex ratio over and above the binomial variance expected under Mendelian segregation, and thereby quantify the potential for selection to shape sex ratio. Furthermore, if sex ratio variation is to be shaped by selection, we expect some of this extra-binomial variation to have a genetic basis. Despite ample statistical power, we find no evidence for the existence of either genetic or environmentally induced variation in sex ratio, in the nest or at independence. Instead, the sex ratio variation observed matches that expected under random Mendelian segregation. Using one of the best datasets of its kind, we conclude that female song sparrows do not, and perhaps cannot, adjust the sex of their offspring. We discuss the implications of this finding and make suggestions for future research.

When mothers make sons sexy: maternal effects contribute to the increased sexual attractiveness of extra-pair offspring.

Quality differences between offspring sired by the social and by an extra-pair partner are usually assumed to have a genetic basis, reflecting genetic benefits of female extra-pair mate choice. In the zebra finch (Taeniopygia guttata), we identified a colour ornament that is under sexual selection and appears to have a heritable basis. Hence, by engaging in extra-pair copulations with highly ornamented males, females could, in theory, obtain genes for increased offspring attractiveness. Indeed, sons sired by extra-pair partners had larger ornaments, seemingly supporting the genetic benefit hypothesis. Yet, when comparing ornament size of the social and extra-pair partners, there was no difference. Hence, the observed differences most likely had an environmental basis, mediated, for example, via differential maternal investment of resources into the eggs fertilized by extra-pair and social partners. Such maternal effects may (at least partly) be mediated by egg size, which we found to be associated with mean ornament expression in sons. Our results are consistent with the idea that maternal effects can shape sexual selection by altering the genotype–phenotype relationship for ornamentation. They also caution against automatically attributing greater offspring attractiveness or viability to an extra-pair mates superior genetic quality, as without controlling for differential maternal investment we may significantly overestimate the role of genetic benefits in the evolution of extra-pair mating behaviour.

Genetic variation for clutch size in natural populations of birds from a reaction norm perspective

Genetic variation for ecologically important traits determines the potential for evolutionary changes and should be measured directly. Such measurements of genetic variation based on quantitative genetic theory rely on assumptions of environmental constancy. These assumptions are not likely to hold in nature. Instead, natural environments are structured, and systematic variation in environmental conditions is an important determinant of phenotypic variation. Here we provide an introduction to quantitative genetics using a reaction norms approach, because we believe that this provides us with a good framework for combining ecology and genetics. We subsequently review the literature on genetic variation for clutch size of birds, and we show that, in spite of the inherent limitations of the methods employed, there is strong evidence that clutch size has a heritable component in natural populations of several species. However, the number of studies on the amount of genetic variation for clutch size in different species and across a range of environmental conditions is still far too small to study patterns in the relationship between heritable variation and properties of species and/or their environments. Furthermore, the role of both correlations and interactions with the environment in these estimates requires much more attention. Above all else, however, we need more information on the structure and magnitude of the environmental variation present in these studies. Future work should focus on how to obtain such data, and how to subsequently incorporate them into the proposed reaction norm framework. This requires the search for, and measurement of, relevant ecological variables. Also a more detailed investigation of the within-individual variation and the use of animal model methodology may prove to be valuable. Such additional data are essential for interpreting the amounts of genetic variation present for clutch size as a model system in the general problem of better understanding the maintenance of genetic variation in heterogeneous environments and the estimation of evolutionary potential.