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.

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.

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.

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.

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.

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.

Quantifying the causal pathways contributing to natural selection.

The consequences of natural selection can be understood from a purely statistical perspective. In contrast, an explicitly causal approach is required to understand why trait values covary with fitness. In particular, key evolutionary constructs, such as sexual selection, fecundity selection, and so on, are best understood as selection via particular fitness components. To formalize and operationalize these concepts, we must disentangle the various causal pathways contributing to selection. Such decompositions are currently only known for linear models, where they are sometimes referred to as "Wright's rules." Here, we provide a general framework, based on path analysis, for partitioning selection among its contributing causal pathways. We show how the extended selection gradient-which represents selection arising from a trait's causal effects on fitness-can be decomposed into path-specific selection gradients, which correspond to distinct causal mechanisms of selection. This framework allows for nonlinear effects and nonadditive interactions among variables, which may be estimated using standard statistical methods (e.g., generalized linear [mixed] models or generalized additive models). We thus provide a generalization of Wright's path rules that accommodates the nonlinear and nonadditive mechanisms by which natural selection commonly arises.

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.

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.

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.

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.

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.

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.

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.