The missing fraction problem as an episodes of selection problem

In evolutionary quantitative genetics, the missing fraction problem refers to a specific kind of bias in parameters estimated later in life that occurs when nonrandom subsets of phenotypes are missing from the population due to prior viability selection on correlated traits. The missing fraction problem thus arises when the following hold: (a) viability selection and (b) correlation between later-life traits and traits important for early-life survival. Although it is plausible that these conditions are widespread in wild populations, this problem has received little empirical attention. This may be natural: the problem could appear intractable, given that it is impossible to measure phenotypes of individuals that have previously died. However, it is not impossible to correctly measure lifetime selection, or correctly predict evolutionary trajectories, of later-life traits in the presence of the missing fraction. Two basic strategies are available. First, given phenotypic data on selected early life traits, well established but underused episodes of selection theory can yield correct values of evolutionary parameters throughout life. Second, when traits subjected to early-life viability selection are not known and/or measured, it is possible to use the genetic association of later-life traits with early-life viability to correctly infer important information about the consequences of prior viability selection for later-life traits. By carefully reviewing the basic nature of the missing fraction problem, and describing the tractable solutions to the problem, we hope that future studies will be able to be better designed to cope with the (likely pervasive) consequences of early-life viability selection.

Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions

Log-linear models are widely used for assessing determinants of fitness in empirical studies, for example, in determining how reproductive output depends on trait values or environmental conditions. Similarly, theoretical works of fitness and natural selection employ log-linear models, often with a negative quadratic term, generating Gaussian fitness functions. However, in the specific application of regression-based analysis of natural selection, such models are rarely employed. Rather, OLS regression is the predominant means of assessing the form of natural selection. OLS regressions allow specific evolutionary quantitative parameters, selection gradients, to be estimated, and benefit from the fact that the associated statistical models are easily applied. We examine whether selection gradients can be directly expressed in terms of the coefficients of models using exponential fitness functions with linear or quadratic arguments. Such models can be easily fitted with generalized linear models (GLMs). The expressions we obtain coincide with those for Gaussian functions, but relax the major constraint that the (log) fitness function is concave (downwardly curved). Additionally these results lead to univariate and multivariate analyses of both linear and quadratic selection that potentially incorporate pragmatic and interpretable models of fitness functions, where the parameters can be related analytically to selection gradients, and that can be operationalized using widely available statistical tools.

Genetic variance in fitness indicates rapid contemporary adaptive evolution in wild animals

The rate of adaptive evolution, the contribution of selection to genetic changes that increase mean fitness, is determined by the additive genetic variance in individual relative fitness. To date, there are few robust estimates of this parameter for natural populations, and it is therefore unclear whether adaptive evolution can play a meaningful role in short-term population dynamics. We developed and applied quantitative genetic methods to long-term datasets from 19 wild bird and mammal populations and found that, while estimates vary between populations, additive genetic variance in relative fitness is often substantial and, on average, twice that of previous estimates. We show that these rates of contemporary adaptive evolution can affect population dynamics and hence that natural selection has the potential to partly mitigate effects of current environmental change.

A synthesis of senescence predictions for indeterminate growth, and support from multiple tests in wild lake trout

Senescence-the deterioration of functionality with age-varies widely across taxa in pattern and rate. Insights into why and how this variation occurs are hindered by the predominance of laboratory-focused research on short-lived model species with determinate growth. We synthesize evolutionary theories of senescence, highlight key information gaps and clarify predictions for species with low mortality and variable degrees of indeterminate growth. Lake trout are an ideal species to evaluate predictions in the wild. We monitored individual males from two populations (1976-2017) longitudinally for changes in adult mortality (actuarial senescence) and body condition (proxy for energy balance). A cross-sectional approach (2017) compared young (ages 4-10 years) and old (18-37 years) adults for (i) phenotypic performance in body condition, and semen quality-which is related to fertility under sperm competition (reproductive senescence)-and (ii) relative telomere length (potential proxy for cellular senescence). Adult growth in these particular populations is constrained by a simplified foodweb, and our data support predictions of negligible senescence when maximum size is only slightly larger than maturation size. Negative senescence (aka reverse senescence) may occur in other lake trout populations where diet shifts allow maximum sizes to greatly exceed maturation size.

Causation, not collinearity: Identifying sources of bias when modelling the evolution of brain size and other allometric traits

Many biological traits covary with body size, resulting in an allometric relationship. Identifying the evolutionary drivers of these traits is complicated by possible relationships between a candidate selective agent and body size itself, motivating the widespread use of multiple regression analysis. However, the possibility that multiple regression may generate misleading estimates when predictor variables are correlated has recently received much attention. Here, we argue that a primary source of such bias is the failure to account for the complex causal structures underlying brains, bodies, and agents. When brains and bodies are expected to evolve in a correlated manner over and above the effects of specific agents of selection, neither simple nor multiple regression will identify the true causal effect of an agent on brain size. This problem results from the inclusion of a predictor variable in a regression analysis that is (in part) a consequence of the response variable. We demonstrate these biases with examples and derive estimators to identify causal relationships when traits evolve as a function of an existing allometry. Model mis‐specification relative to plausible causal structures, not collinearity, requires further consideration as an important source of bias in comparative analyses.

Multivariate analysis of morphology, behaviour, growth and developmental timing in hybrids brings new insights into the divergence of sympatric Arctic charr morphs

BACKGROUND

Studying the development of fitness related traits in hybrids from populations diverging in sympatry is a fundamental approach to understand the processes of speciation. However, such traits are often affected by covariance structures that complicate the comprehension of these processes, especially because the interactive relationships between traits of different nature (e.g. morphology, behaviour, life-history) remain largely unknown in this context. In a common garden setup, we conducted an extensive examination of a large suit of traits putatively involved in the divergence of two morphs of Arctic charr (Salvelinus alpinus), and investigated the consequences of potential patterns of trait covariance on the phenotype of their hybrids. These traits were measured along ontogeny and involved growth, yolk sac resorption, developmental timing (hatching and the onset of exogeneous feeding), head morphology and feeding behaviour.

RESULTS

Growth trajectories provided the strongest signal of phenotypic divergence between the two charr. Strikingly, the first-generation hybrids did not show intermediate nor delayed growth but were similar to the smallest morph, suggesting parental biases in the inheritance of growth patterns. However, we did not observe extensive multivariate trait differences between the two morphs and their hybrids. Growth was linked to head morphology (suggesting that morphological variations in early juveniles relate to simple allometric effects) but this was the only strong signal of covariance observed between all the measured traits. Furthermore, we did not report evidence for differences in overall phenotypic variance between morphs, nor for enhanced phenotypic variability in their hybrids.

CONCLUSION

Our study shed light on the multivariate aspect of development in a context of adaptive divergence. The lack of evidence for the integration of most traits into a single covariance structure suggested that phenotypic constraints may not always favour nor impede divergence toward ecological niches differing in numerous physical and ecological variables, as observed in the respective habitats of the two charr. Likewise, the role of hybridization as a disruptive agent of trait covariance may not necessarily be significant in the evolution of populations undergoing resource polymorphism.

Re-identification of individuals from images using spot constellations: a case study in Arctic charr (Salvelinus alpinus)

The ability to re-identify individuals is fundamental to the individual-based studies that are required to estimate many important ecological and evolutionary parameters in wild populations. Traditional methods of marking individuals and tracking them through time can be invasive and imperfect, which can affect these estimates and create uncertainties for population management. Here we present a photographic re-identification method that uses spot constellations in images to match specimens through time. Photographs of Arctic charr (Salvelinus alpinus) were used as a case study. Classical computer vision techniques were compared with new deep-learning techniques for masks and spot extraction. We found that a U-Net approach trained on a small set of human-annotated photographs performed substantially better than a baseline feature engineering approach. For matching the spot constellations, two algorithms were adapted, and, depending on whether a fully or semi-automated set-up is preferred, we show how either one or a combination of these algorithms can be implemented. Within our case study, our pipeline both successfully identified unmarked individuals from photographs alone and re-identified individuals that had lost tags, resulting in an approximately 4% increase in our estimate of survival rate. Overall, our multi-step pipeline involves little human supervision and could be applied to many organisms.

Horn growth appears to decline under intense trophy hunting, but biases in hunt data challenge the interpretation of the evolutionary basis of trends

A recent article in Evolutionary Applications by LaSharr et al. reports on trends in the size of horns of bighorn sheep (Ovis canadensis) throughout much of the species' range. The article concludes that there are "... stable or increasing trends in horn growth over nearly 3 decades in the majority of hunt areas throughout the western U.S. and Canada." However, the article equates nonsignificance of predominantly negative trends in the areas with the most selective harvest as evidence for the null hypothesis of no trends and also fails to consider well-known and serious biases in the use of data collected in size-regulated hunts. By applying meta-analysis to the estimates reported by LaSharr et al., we show that there has been a pervasive overall trend of declining horn sizes in Alberta, where the combination of horn size-based legality, combined with unrestricted hunter numbers are understood to generate the greatest selective pressures. Given the nature of the biases in the underlying data, the magnitudes of the trends resulting from our re-analysis of LaSharr et al.'s (Evolutionary Applications, 2019, 12, 1823) trend estimates are probably underestimated.

Fluctuating optimum and temporally variable selection on breeding date in birds and mammals

Temporal variation in natural selection is predicted to strongly impact the evolution and demography of natural populations, with consequences for the rate of adaptation, evolution of plasticity, and extinction risk. Most of the theory underlying these predictions assumes a moving optimum phenotype, with predictions expressed in terms of the temporal variance and autocorrelation of this optimum. However, empirical studies seldom estimate patterns of fluctuations of an optimum phenotype, precluding further progress in connecting theory with observations. To bridge this gap, we assess the evidence for temporal variation in selection on breeding date by modeling a fitness function with a fluctuating optimum, across 39 populations of 21 wild animals, one of the largest compilations of long-term datasets with individual measurements of trait and fitness components. We find compelling evidence for fluctuations in the fitness function, causing temporal variation in the magnitude, but not the direction of selection. However, fluctuations of the optimum phenotype need not directly translate into variation in selection gradients, because their impact can be buffered by partial tracking of the optimum by the mean phenotype. Analyzing individuals that reproduce in consecutive years, we find that plastic changes track movements of the optimum phenotype across years, especially in bird species, reducing temporal variation in directional selection. This suggests that phenological plasticity has evolved to cope with fluctuations in the optimum, despite their currently modest contribution to variation in selection.

Analogues of the fundamental and secondary theorems of selection, assuming a log-normal distribution of expected fitness

It is increasingly common for studies of evolution in natural populations to infer the quantitative genetic basis of fitness (e.g., the additive genetic variance for relative fitness), and of relationships between traits and fitness (e.g., the additive genetic covariance of traits with relative fitness). There is a certain amount of tension between the theory that justifies estimating these quantities, and methodological considerations relevant to their empirical estimation. In particular, the additive genetic variances and covariances involving relative fitness are justified by the fundamental and secondary theorems of selection, which pertain to relative fitness on the scale that it is expressed. However, naturally-occurring fitness distributions lend themselves to analysis with generalized linear mixed models (GLMMs), which conduct analysis on a different scale, typically on the scale of the logarithm of expected values, from which fitness is expressed. This note presents relations between evolutionary change in traits, and the rate of adaptation in fitness, and log quantitative genetic parameters of fitness, potentially reducing the discord between theoretical and methodological considerations to the operationalization of the secondary and fundamental theorems of selection.

Pedigree-Based Estimation of Reproductive Value

How successful an individual or cohort is, in terms of their genetic contribution to the future population, is encapsulated in the concept of reproductive value, and is crucial for understanding selection and evolution. Long-term studies of pedigreed populations offer the opportunity to estimate reproductive values directly. However, the degree to which genetic contributions, as defined by a pedigree, may converge on their long-run values within the time frames of available data sets, such that they may be interpreted as estimates of reproductive value, is unclear. We develop a system for pedigree-based calculation of the expected genetic representation that both individuals and cohorts make to the population in the years following their birth. We apply this system to inference of individual and cohort reproductive values in Soay sheep (Ovis aries) from St Kilda, Outer Hebrides. We observe that these genetic contributions appear to become relatively stable within modest time frames. As such, it may be reasonable to consider pedigree-based calculations of genetic contributions to future generations as estimates of reproductive value. This approach and the knowledge that the estimates can stabilize within decades should offer new opportunities to analyze data from pedigreed wild populations, which will be of value to many fields within evolutionary biology and demography.

Herbivore-mediated negative frequency-dependent selection underlies a trichome dimorphism in nature

Negative frequency-dependent selection (NFDS) has been shown to maintain polymorphism in a diverse array of traits. The action of NFDS has been confirmed through modeling, experimental approaches, and genetic analyses. In this study, we investigated NFDS in the wild using morph-frequency changes spanning a 20-year period from over 30 dimorphic populations of Datura wrightii. In these populations, plants either possess glandular (sticky) or non-glandular (velvety) trichomes, and the ratio of these morphs varies substantially among populations. Our method provided evidence that NFDS, rather than drift or migration, is the primary force maintaining this dimorphism. Most populations that were initially dimorphic remained dimorphic, and the overall mean and variance in morph frequency did not change over time. Furthermore, morph-frequency differences were not related to geographic distances. Together, these results indicate that neither directional selection, drift, or migration played a substantial role in determining morph frequencies. However, as predicted by negative frequency-dependent selection, we found that the rare morph tended to increase in frequency, leading to a negative relationship between the change in the frequency of the sticky morph and its initial frequency. In addition, we found that morph-frequency change over time was significantly correlated with the damage inflicted by two herbivores: Lema daturaphila and Tupiochoris notatus. The latter is a specialist on the sticky morph and damage by this herbivore was greatest when the sticky morph was common. The reverse was true for L. daturaphila, such that damage increased with the frequency of the velvety morph. These findings suggest that these herbivores contribute to balancing selection on the observed trichome dimorphism.

The role of selection and evolution in changing parturition date in a red deer population

Changing environmental conditions cause changes in the distributions of phenotypic traits in natural populations. However, determining the mechanisms responsible for these changes—and, in particular, the relative contributions of phenotypic plasticity versus evolutionary responses—is difficult. To our knowledge, no study has yet reported evidence that evolutionary change underlies the most widely reported phenotypic response to climate change: the advancement of breeding times. In a wild population of red deer, average parturition date has advanced by nearly 2 weeks in 4 decades. Here, we quantify the contribution of plastic, demographic, and genetic components to this change. In particular, we quantify the role of direct phenotypic plasticity in response to increasing temperatures and the role of changes in the population structure. Importantly, we show that adaptive evolution likely played a role in the shift towards earlier parturition dates. The observed rate of evolution was consistent with a response to selection and was less likely to be due to genetic drift. Our study provides a rare example of observed rates of genetic change being consistent with theoretical predictions, although the consistency would not have been detected with a solely phenotypic analysis. It also provides, to our knowledge, the first evidence of both evolution and phenotypic plasticity contributing to advances in phenology in a changing climate.

Adaptive genetic evolution and phenotypic plasticity both contribute to a two-week advancement of birth dates earlier in spring in a deer population subject to temperature warming over four decades.

A note on simulating null distributions for G matrix comparisons

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G. We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti-conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.

Quantification and decomposition of environment-selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait-absolute fitness relationship remains constant. We apply and extend a regression-based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment-selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait-fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.

No evidence that warmer temperatures are associated with selection for smaller body sizes

Reductions in animal body size over recent decades are often interpreted as an adaptive evolutionary response to climate warming. However, for reductions in size to reflect adaptive evolution, directional selection on body size within populations must have become negative, or where already negative, to have become more so, as temperatures increased. To test this hypothesis, we performed traditional and phylogenetic meta-analyses of the association between annual estimates of directional selection on body size from wild populations and annual mean temperatures from 39 longitudinal studies. We found no evidence that warmer environments were associated with selection for smaller size. Instead, selection consistently favoured larger individuals, and was invariant to temperature. These patterns were similar in ectotherms and endotherms. An analysis using year rather than temperature revealed similar patterns, suggesting no evidence that selection has changed over time, and also indicating that the lack of association with annual temperature was not an artefact of choosing an erroneous time window for aggregating the temperature data. Although phenotypic trends in size will be driven by a combination of genetic and environmental factors, our results suggest little evidence for a necessary ingredient-negative directional selection-for declines in body size to be considered an adaptive evolutionary response to changing selection pressures.

Estimation of Genetic Variance in Fitness, and Inference of Adaptation, When Fitness Follows a Log-Normal Distribution

Additive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))−1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

Natural selection for body shape in resource polymorphic Icelandic Arctic charr

Resource polymorphisms exhibit remarkable intraspecific diversity and in many cases are expected to be maintained by diversifying selection. Phenotypic trade-offs can constrain morphologically intermediate individuals from effectively exploiting both alternate resources, resulting in ecological barriers to gene flow. Determining if and how phenotypic trade-offs cause fitness variation in the wild is challenging because of phenotypic and environmental correlations associated with alternative resource strategies. We investigated multiple pathways through which morphology could affect organismal performance, as measured by growth rate, and whether these effects generate diversifying selection in polymorphic Icelandic Arctic charr (Salvelinus alpinus) populations. We considered direct effects of morphology on growth and indirect effects via trophic resource use, estimated by stable isotopic signatures, and via parasitism associated with trophic resources. We sampled over 3 years in (lakes) Thingvallavatn and Vatnshlíðarvatn using the extended selection gradient path analytical approach and estimating size-dependent mortality. We found evidence for diversifying selection only in Thingvallavatn: more streamlined and terminally mouthed planktivore charr experienced greater growth, with the opposite pattern in small benthic charr. However, this effect was mediated by parasitism and nontrophic pathways, rather than trophic performance as often expected. Detection of between-morph differences in the presence (Vatnshlíðarvatn) and direction (Thingvallavatn) of size-dependent mortality, together with nontrophic effects of shape, suggests that a morphological trophic performance explanation for polymorphism is insufficient. This rare insight into selection during early diversification suggests that a complex of interacting local factors must be considered to understand how phenotype influences fitness, despite morphological variation reflecting intuitive trade-off explanations.

Into the wild-WAMBAM goes to Canada

The sixth Wild Animal Models Bi-Annual Meeting was held in July 2017 in Québec, with 42 participants. This report documents the evolution of questions asked and approaches used in evolutionary quantitative genetic studies of wild populations in recent decades, and how these questions and approaches were represented at the recent meeting. We explore how ideas from previous meetings in this series have developed to their present states, and consider how the format of the meetings may be particularly useful at fostering the rapid development and proliferation of ideas and approaches.

Meta-analysis of magnitudes, differences and variation in evolutionary parameters

Meta-analysis is increasingly used to synthesize major patterns in the large literatures within ecology and evolution. Meta-analytic methods that do not account for the process of observing data, which we may refer to as 'informal meta-analyses', may have undesirable properties. In some cases, informal meta-analyses may produce results that are unbiased, but do not necessarily make the best possible use of available data. In other cases, unbiased statistical noise in individual reports in the literature can potentially be converted into severe systematic biases in informal meta-analyses. I first present a general description of how failure to account for noise in individual inferences should be expected to lead to biases in some kinds of meta-analysis. In particular, informal meta-analyses of quantities that reflect the dispersion of parameters in nature, for example, the mean absolute value of a quantity, are likely to be generally highly misleading. I then re-analyse three previously published informal meta-analyses, where key inferences were of aspects of the dispersion of values in nature, for example, the mean absolute value of selection gradients. Major biological conclusions in each original informal meta-analysis closely match those that could arise as artefacts due to statistical noise. I present alternative mixed-model-based analyses that are specifically tailored to each situation, but where all analyses may be implemented with widely available open-source software. In each example meta-re-analysis, major conclusions change substantially.

Precipitation drives global variation in natural selection

Climate change has the potential to affect the ecology and evolution of every species on Earth. Although the ecological consequences of climate change are increasingly well documented, the effects of climate on the key evolutionary process driving adaptation-natural selection-are largely unknown. We report that aspects of precipitation and potential evapotranspiration, along with the North Atlantic Oscillation, predicted variation in selection across plant and animal populations throughout many terrestrial biomes, whereas temperature explained little variation. By showing that selection was influenced by climate variation, our results indicate that climate change may cause widespread alterations in selection regimes, potentially shifting evolutionary trajectories at a global scale.

Identifying consistent allele frequency differences in studies of stratified populations

With increasing application of pooled‐sequencing approaches to population genomics robust methods are needed to accurately quantify allele frequency differences between populations. Identifying consistent differences across stratified populations can allow us to detect genomic regions under selection and that differ between populations with different histories or attributes. Current popular statistical tests are easily implemented in widely available software tools which make them simple for researchers to apply. However, there are potential problems with the way such tests are used, which means that underlying assumptions about the data are frequently violated.

These problems are highlighted by simulation of simple but realistic population genetic models of neutral evolution and the performance of different tests are assessed. We present alternative tests (including Generalised Linear Models [GLMs] with quasibinomial error structure) with attractive properties for the analysis of allele frequency differences and re‐analyse a published dataset.

The simulations show that common statistical tests for consistent allele frequency differences perform poorly, with high false positive rates. Applying tests that do not confound heterogeneity and main effects significantly improves inference. Variation in sequencing coverage likely produces many false positives and re‐scaling allele frequencies to counts out of a common value or an effective sample size reduces this effect.

Many researchers are interested in identifying allele frequencies that vary consistently across replicates to identify loci underlying phenotypic responses to selection or natural variation in phenotypes. Popular methods that have been suggested for this task perform poorly in simulations. Overall, quasibinomial GLMs perform better and also have the attractive feature of allowing correction for multiple testing by standard procedures and are easily extended to other designs.

Multivariate selection and intersexual genetic constraints in a wild bird population

When selection differs between the sexes for traits that are genetically correlated between the sexes, there is potential for the effect of selection in one sex to be altered by indirect selection in the other sex, a situation commonly referred to as intralocus sexual conflict (ISC). While potentially common, ISC has rarely been studied in wild populations. Here, we studied ISC over a set of morphological traits (wing length, tarsus length, bill depth and bill length) in a wild population of great tits (Parus major) from Wytham Woods, UK. Specifically, we quantified the microevolutionary impacts of ISC by combining intra- and intersex additive genetic (co)variances and sex-specific selection estimates in a multivariate framework. Large genetic correlations between homologous male and female traits combined with evidence for sex-specific multivariate survival selection suggested that ISC could play an appreciable role in the evolution of this population. Together, multivariate sex-specific selection and additive genetic (co)variance for the traits considered accounted for additive genetic variance in fitness that was uncorrelated between the sexes (cross-sex genetic correlation = -0.003, 95% CI = -0.83, 0.83). Gender load, defined as the reduction in a population's rate of adaptation due to sex-specific effects, was estimated at 50% (95% CI = 13%, 86%). This study provides novel insights into the evolution of sexual dimorphism in wild populations and illustrates how quantitative genetics and selection analyses can be combined in a multivariate framework to quantify the microevolutionary impacts of ISC.

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.

Calibrating animal-borne proximity loggers

Growing interest in the structure and dynamics of animal social networks has stimulated efforts to develop automated tracking technologies that can reliably record encounters in free-ranging subjects. A particularly promising approach is the use of animal-attached 'proximity loggers', which collect data on the incidence, duration and proximity of spatial associations through inter-logger radio communication. While proximity logging is based on a straightforward physical principle - the attenuation of propagating radio waves with distance - calibrating systems for field deployment is challenging, since most study species roam across complex, heterogeneous environments.In this study, we calibrated a recently developed digital proximity-logging system ('Encounternet') for deployment on a wild population of New Caledonian crows Corvus moneduloides. Our principal objective was to establish a quantitative model that enables robust post hoc estimation of logger-to-logger (and, hence, crow-to-crow) distances from logger-recorded signal-strength values. To achieve an accurate description of the radio communication between crow-borne loggers, we conducted a calibration exercise that combines theoretical analyses, field experiments, statistical modelling, behavioural observations, and computer simulations.We show that, using signal-strength information only, it is possible to assign crow encounters reliably to predefined distance classes, enabling powerful analyses of social dynamics. For example, raw data sets from field-deployed loggers can be filtered at the analysis stage to include predominantly encounters where crows would have come to within a few metres of each other, and could therefore have socially learned new behaviours through direct observation. One of the main challenges for improving data classification further is the fact that crows - like most other study species - associate across a wide variety of habitats and behavioural contexts, with different signal-attenuation properties.Our study demonstrates that well-calibrated proximity-logging systems can be used to chart social associations of free-ranging animals over a range of biologically meaningful distances. At the same time, however, it highlights that considerable efforts are required to conduct study-specific system calibrations that adequately account for the biological and technological complexities of field deployments. Although we report results from a particular case study, the basic rationale of our multi-step calibration exercise applies to many other tracking systems and study species.

Selection and evolution of causally covarying traits

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait-fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining "extended" selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.

The prediction of adaptive evolution: empirical application of the secondary theorem of selection and comparison to the breeder's equation

Adaptive evolution occurs when fitness covaries with genetic merit for a trait (or traits). The breeder's equation (BE), in both its univariate and multivariate forms, allows us to predict this process by combining estimates of selection on phenotype with estimates of genetic (co)variation. However, predictions are only valid if all factors causal for trait-fitness covariance are measured. Although this requirement will rarely (if ever) be met in practice, it can be avoided by applying Robertson's secondary theorem of selection (STS). The STS predicts evolution by directly estimating the genetic basis of trait-fitness covariation without any explicit model of selection. Here we apply the BE and STS to four morphological traits measured in Soay sheep (Ovis aries) from St. Kilda. Despite apparently positive selection on heritable size traits, sheep are not getting larger. However, although the BE predicts increasing size, the STS does not, which is a discrepancy that suggests unmeasured factors are upwardly biasing our estimates of selection on phenotype. We suggest this is likely to be a general issue, and that wider application of the STS could offer at least a partial resolution to the common discrepancy between naive expectations and observed trait dynamics in natural populations.

Genetic analysis of life-history constraint and evolution in a wild ungulate population

Trade-offs among life-history traits are central to evolutionary theory. In quantitative genetic terms, trade-offs may be manifested as negative genetic covariances relative to the direction of selection on phenotypic traits. Although the expression and selection of ecologically important phenotypic variation are fundamentally multivariate phenomena, the in situ quantification of genetic covariances is challenging. Even for life-history traits, where well-developed theory exists with which to relate phenotypic variation to fitness variation, little evidence exists from in situ studies that negative genetic covariances are an important aspect of the genetic architecture of life-history traits. In fact, the majority of reported estimates of genetic covariances among life-history traits are positive. Here we apply theory of the genetics and selection of life histories in organisms with complex life cycles to provide a framework for quantifying the contribution of multivariate genetically based relationships among traits to evolutionary constraint. We use a Bayesian framework to link pedigree-based inference of the genetic basis of variation in life-history traits to evolutionary demography theory regarding how life histories are selected. Our results suggest that genetic covariances may be acting to constrain the evolution of female life-history traits in a wild population of red deer Cervus elaphus: genetic covariances are estimated to reduce the rate of adaptation by about 40%, relative to predicted evolutionary change in the absence of genetic covariances. Furthermore, multivariate phenotypic (rather than genetic) relationships among female life-history traits do not reveal this constraint.

Indirect genetics effects and evolutionary constraint: an analysis of social dominance in red deer, Cervus elaphus

By determining access to limited resources, social dominance is often an important determinant of fitness. Thus, if heritable, standard theory predicts mean dominance should evolve. However, dominance is usually inferred from the tendency to win contests, and given one winner and one loser in any dyadic contest, the mean proportion won will always equal 0.5. Here, we argue that the apparent conflict between quantitative genetic theory and common sense is resolved by recognition of indirect genetic effects (IGEs). We estimate selection on, and genetic (co)variance structures for, social dominance, in a wild population of red deer Cervus elaphus, on the Scottish island of Rum. While dominance is heritable and positively correlated with lifetime fitness, contest outcomes depend as much on the genes carried by an opponent as on the genotype of a focal individual. We show how this dependency imposes an absolute evolutionary constraint on the phenotypic mean, thus reconciling theoretical predictions with common sense. More generally, we argue that IGEs likely provide a widespread but poorly recognized source of evolutionary constraint for traits influenced by competition.

Evolution of adaptive diversity and genetic connectivity in Arctic charr (Salvelinus alpinus) in Iceland

The ecological theory of adaptive radiation predicts that the evolution of phenotypic diversity within species is generated by divergent natural selection arising from different environments and competition between species. Genetic connectivity among populations is likely also to have an important role in both the origin and maintenance of adaptive genetic diversity. Our goal was to evaluate the potential roles of genetic connectivity and natural selection in the maintenance of adaptive phenotypic differences among morphs of Arctic charr, Salvelinus alpinus, in Iceland. At a large spatial scale, we tested the predictive power of geographic structure and phenotypic variation for patterns of neutral genetic variation among populations throughout Iceland. At a smaller scale, we evaluated the genetic differentiation between two morphs in Lake Thingvallavatn relative to historically explicit, coalescent-based null models of the evolutionary history of these lineages. At the large spatial scale, populations are highly differentiated, but weakly structured, both geographically and with respect to patterns of phenotypic variation. At the intralacustrine scale, we observe modest genetic differentiation between two morphs, but this level of differentiation is nonetheless consistent with strong reproductive isolation throughout the Holocene. Rather than a result of the homogenizing effect of gene flow in a system at migration-drift equilibrium, the modest level of genetic differentiation could equally be a result of slow neutral divergence by drift in large populations. We conclude that contemporary and recent patterns of restricted gene flow have been highly conducive to the evolution and maintenance of adaptive genetic variation in Icelandic Arctic charr.

pedantics: an r package for pedigree-based genetic simulation and pedigree manipulation, characterization and viewing

Analyses of pedigrees and pedigree-derived parameters (e.g. relatedness and fitness) provide some of the most informative types of studies in evolutionary biology. The r package pedantics implements tools to facilitate power and sensitivity analyses of pedigree-related studies of natural populations. Functions are available to permute pedigree data in various ways with the goal of mimicking patterns of pedigree errors and missingness that occur in studies of natural populations. Another set of functions simulates genetic and phenotypic data based on arbitrary pedigrees. Finally, functions are also available with which visual and numerical representations of pedigree structure can be generated.

Marker-assisted determination of the relationship between body size and reproductive success and consequences for evaluation of adaptive life histories

We tested for differences in the predicted optimal ages at first maturity in brook charr (Salvelinus fontinalis) in Freshwater River, Newfoundland, when life-history data were collated based on the marker-assisted estimation of the relationship between body size and reproductive success rather than using fecundity as a surrogate for reproductive success. Jointly with capture-recapture data to estimate the growth and survival costs of reproduction, we found that weak relationships between body size and reproductive success generate selection against delayed maturation. This finding would not have held for females if the relationship between body size and fecundity had been used as a surrogate for the relationship between body size and reproductive success. This shows that predictions of optimal life histories can be qualitatively changed when using molecular markers to directly evaluate age- and/or size-specific effects of body size on reproductive success.

A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in Soay sheep (Ovis aries)

Studies of the quantitative genetics of natural populations have contributed greatly to evolutionary biology in recent years. However, while pedigree data required are often uncertain (i.e. incomplete and partly erroneous) and limited, means to evaluate the effects of such uncertainties have not been developed. We have therefore developed a general framework for power and sensitivity analyses of such studies. We propose that researchers first generate a set of pedigree data that they wish to use in a quantitative genetic study, as well as data regarding errors that occur in that pedigree. This pedigree is then permuted using the data regarding errors to generate hypothetical 'true' and 'assumed' pedigrees that differ so as to mimic pedigree errors that might occur in the study system under consideration. Phenotypic data are then simulated across the true pedigree (according to user-defined genetic and environmental covariance structures), before being analysed with standard quantitative genetic techniques in conjunction with the 'assumed' pedigree data. To illustrate this approach, we conducted power and sensitivity analyses in a well-known study of Soay sheep (Ovis aries). We found that, although the estimation of simple genetic (co)variance structures is fairly robust to pedigree errors, some potentially serious biases were detected under more complex scenarios involving maternal effects. Power analyses also showed that this study system provides high power to detect heritabilities as low as about 0.09. Given this range of results, we suggest that such power and sensitivity analyses could greatly complement empirical studies, and we provide the computer program PEDANTICS to aid in their application.

The potential costs of accounting for genotypic errors in molecular parentage analyses

Genotypic errors, whether due to mutation or laboratory error, can cause the genotypes of parents and their offspring to appear inconsistent with Mendelian inheritance. As a result, molecular parentage analyses are expected to benefit when allowances are made for the presence of genotypic errors. However, a cost of allowing for genotypic errors might also be expected under some analytical conditions, primarily because parentage analyses that assume nonzero genotypic error rates can neither assign nor exclude parentage with certainty. The goal of this work was therefore to determine whether or not such costs might be important under conditions relevant to parentage analyses, particularly in natural populations. Simulation results indicate that the costs may often outweigh the benefits of accounting for nonzero error rates, except in situations where data are available for many marker loci. Consequently, the most powerful approach to handling genotypic errors in parentage analyses might be to apply likelihood equations with error rates set to values substantially lower than the rates at which genotypic errors occur. When applying molecular parentage analyses to natural populations, we advocate an increased consideration of optimal strategies for handling genotypic errors. Currently available software packages contain procedures that can be used for this purpose.