Jarrod D. Hadfield

General quantitative genetic methods for comparative biology: phylogenies, taxonomies and multi‐trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well‐tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta‐analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non‐Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi‐trait models in which traits can follow different distributions. Meta‐analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.

How to separate genetic and environmental causes of similarity between relatives

Related individuals often have similar phenotypes, but this similarity may be due to the effects of shared environments as much as to the effects of shared genes. We consider here alternative approaches to separating the relative contributions of these two sources to phenotypic covariances, comparing experimental approaches such as cross‐fostering, traditional statistical techniques and more complex statistical models, specifically the ‘animal model’. Using both simulation studies and empirical data from wild populations, we demonstrate the ability of the animal model to reduce bias due to shared environment effects such as maternal or brood effects, especially where pedigrees contain multiple generations and immigration rates are low. However, where common environment effects are strong, a combination of both cross‐fostering and an animal model provides the best way to avoid bias. We illustrate ways of partitioning phenotypic variance into components of additive genetic, maternal genetic, maternal environment, common environment, permanent environment and temporal effects, but also show how substantial confounding between these different effects may occur. Whilst the flexibility of the mixed model approach is extremely useful for incorporating the spatial, temporal and social heterogeneity typical of natural populations, the advantages will inevitably be restricted by the quality of pedigree information and care needs to be taken in specifying models that are appropriate to the data.

Towards unbiased parentage assignment: combining genetic, behavioural and spatial data in a Bayesian framework.

Inferring the parentage of a sample of individuals is often a prerequisite for many types of analysis in molecular ecology, evolutionary biology and quantitative genetics. In all but a few cases, the method of parentage assignment is divorced from the methods used to estimate the parameters of primary interest, such as mate choice or heritability. Here we present a Bayesian approach that simultaneously estimates the parentage of a sample of individuals and a wide range of population‐level parameters in which we are interested. We show that joint estimation of parentage and population‐level parameters increases the power of parentage assignment, reduces bias in parameter estimation, and accurately evaluates uncertainty in both. We illustrate the method by analysing a number of simulated test data sets, and through a re‐analysis of parentage in the Seychelles warbler, Acrocephalus sechellensis. A combination of behavioural, spatial and genetic data are used in the analyses and, importantly, the method does not require strong prior information about the relationship between nongenetic data and parentage.

The misuse of BLUP in ecology and evolution.

Best linear unbiased prediction (BLUP) is a method for obtaining point estimates of a random effect in a mixed effect model. Over the past decade it has been used extensively in ecology and evolutionary biology to predict individual breeding values and reaction norms. These predictions have been used to infer natural selection, evolutionary change, spatial‐genetic patterns, individual reaction norms, and frailties. In this article we show analytically and through simulation and example why BLUP often gives anticonservative and biased estimates of evolutionary and ecological parameters. Although some concerns with BLUP methodology have been voiced before, the scale and breadth of the problems have probably not been widely appreciated. Bias arises because BLUPs are often used to estimate effects that are not explicitly accounted for in the model used to make the predictions. In these cases, predicted breeding values will often say more about phenotypic patterns than the genetic patterns of interest. An additional problem is that BLUPs are point estimates of quantities that are usually known with little certainty. Failure to account for this uncertainty in subsequent tests can lead to both bias and extreme anticonservatism. We demonstrate that restricted maximum likelihood and Bayesian solutions exist for these problems and show how unbiased and powerful tests can be derived that adequately quantify uncertainty. Of particular utility is a new test for detecting evolutionary change that not only accounts for prediction error in breeding values but also accounts for drift. To illustrate the problem, we apply these tests to long‐term data on the Soay sheep (Ovis aries) and the great tit (Parus major) and show that previously reported temporal trends in breeding values are not supported.

Estimating evolutionary parameters when viability selection is operating

Some individuals die before a trait is measured or expressed (the invisible fraction), and some relevant traits are not measured in any individual (missing traits). This paper discusses how these concepts can be cast in terms of missing data problems from statistics. Using missing data theory, I show formally the conditions under which a valid evolutionary inference is possible when the invisible fraction and/or missing traits are ignored. These conditions are restrictive and unlikely to be met in even the most comprehensive long-term studies. When these conditions are not met, many selection and quantitative genetic parameters cannot be estimated accurately unless the missing data process is explicitly modelled. Surprisingly, this does not seem to have been attempted in evolutionary biology. In the case of the invisible fraction, viability selection and the missing data process are often intimately linked. In such cases, models used in survival analysis can be extended to provide a flexible and justified model of the missing data mechanism. Although missing traits pose a more difficult problem, important biological parameters can still be estimated without bias when appropriate techniques are used. This is in contrast to current methods which have large biases and poor precision. Generally, the quantitative genetic approach is shown to be superior to phenotypic studies of selection when invisible fractions or missing traits exist because part of the missing information can be recovered from relatives.

DIRECTIONAL SELECTION IN TEMPORALLY REPLICATED STUDIES IS REMARKABLY CONSISTENT

Temporal variation in selection is a fundamental determinant of evolutionary outcomes. A recent paper presented a synthetic analysis of temporal variation in selection in natural populations. The authors concluded that there is substantial variation in the strength and direction of selection over time, but acknowledged that sampling error would result in estimates of selection that were more variable than the true values. We reanalyze their dataset using techniques that account for the necessary effect of sampling error to inflate apparent levels of variation and show that directional selection is remarkably constant over time, both in magnitude and direction. Thus we cannot claim that the available data support the existence of substantial temporal heterogeneity in selection. Nonetheless, we conject that temporal variation in selection could be important, but that there are good reasons why it may not appear in the available data. These new analyses highlight the importance of applying techniques that estimate parameters of the distribution of selection, rather than parameters of the distribution of estimated selection (which will reflect both sampling error and “real” variation in selection); indeed, despite availability of methods for the former, focus on the latter has been common in synthetic reviews of the aspects of selection in nature, and can lead to serious misinterpretations.

Redefine Statistical Significance

We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.

Differences in spawning date between populations of common frog reveal local adaptation

Phenotypic differences between populations often correlate with climate variables, resulting from a combination of environment-induced plasticity and local adaptation. Species comprising populations that are genetically adapted to local climatic conditions should be more vulnerable to climate change than those comprising phenotypically plastic populations. Assessment of local adaptation generally requires logistically challenging experiments. Here, using a unique approach and a large dataset (>50,000 observations from across Britain), we compare the covariation in temperature and first spawning dates of the common frog (Rana temporaria) across space with that across time. We show that although all populations exhibit a plastic response to temperature, spawning earlier in warmer years, between-population differences in first spawning dates are dominated by local adaptation. Given climate change projections for Britain in 2050–2070, we project that for populations to remain as locally adapted as contemporary populations will require first spawning date to advance by ∼21–39 days but that plasticity alone will only enable an advance of ∼5–9 days. Populations may thus face a microevolutionary and gene flow challenge to advance first spawning date by a further ∼16–30 days over the next 50 years.

Testing the phenotypic gambit: Phenotypic, genetic and environmental correlations of colour

Evolutionary theory is primarily concerned with genetic processes, yet empirical testing of this theory often involves data collected on phenotypes. To make this tenable, the implicit assumption is often made that phenotypic patterns are good predictors of genetic patterns; an assumption that coined the phenotypic gambit. Although this assumption has been validated for traits with high heritability, such as morphology, its generality for traits with low heritabilities, such as life‐history and behavioural traits, remains controversial. Using a large‐scale cross‐fostering experiment, we were able to measure genetic, common environmental and phenotypic correlations between four colour traits and two skeletal traits in a wild population of passerine birds, the blue tit (Parus caeruleus). Colour traits had little heritable variation but common environment effects were found to be important; skeletal traits showed the opposite pattern. Positive correlations because of a shared natal environment were found between all traits, obscuring negative genetic correlations between some colour and skeletal traits. Consequently, phenotypic patterns were poor surrogates for genetic patterns and we suggest that this may be common if trade‐offs or substantial parental effects exist. For this group of traits, the phenotypic gambit cannot be made and we suggest caution when inferring genetic patterns from phenotypic data, especially for behavioural and life‐history traits.

Comparing parentage inference software: reanalysis of a red deer pedigree.

Knowledge of the parentage of individuals is required to address a variety of questions concerning the evolutionary dynamics of wild populations. A major advance in parentage inference in natural populations has been the use of molecular markers and the development of statistical methods to analyse these data. Cervus, one of the most widely used parentage inference programs, uses molecular data to determine parent–offspring relationships. However, Cervus does not make use of all available information: additional phenotypic information may exist predicting parent–offspring relationships, and additional genetic information may be exploited by simultaneously considering multiple types of relationships rather than just pairwise or just parent–offspring relationships. Here we reanalyse data from a wild red deer population using two programs capable of using this additional information, MasterBayes and COLONY2, and quantify the impact of these alternative approaches by comparison with a ‘known pedigree’ estimated using a larger suite of microsatellite makers for a subset of the population. The use of phenotypic information and multiple relationships increased the number of correct assignments. We highlight the differences between programs, particularly the use of population‐ rather than individual‐level statistical confidence in Cervus. We conclude that the use of additional information allows MasterBayes and COLONY2 to assign more correct paternities, whereas their use of individual‐ rather than population‐level confidence generates fewer erroneous assignments. We suggest that maximal information may be gained by combining outputs from different programs. Higher accuracy and completeness of pedigree information will improve parameters estimated from pedigree information in studies of natural populations.