Quantitative Genetic Models Research Articles

The best of both worlds: Combining population genetic and quantitative genetic models

Numerous traits under migration–selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymorphism at a single major-effect locus is stable in the symmetric case, there exist no analytical predictions on how this polymorphism holds when a polygenic background also contributes to the trait. Here we propose to answer this question by introducing a new eco-evo methodology that allows us to take into account the combined contributions of a major-effect locus and of a quantitative background resulting from small-effect loci, where inheritance is encoded according to an extension to the infinitesimal model. In a regime of small variance contributed by the quantitative loci, we justify that traits are concentrated around the major alleles, according to a normal distribution, using new convex analysis arguments. This allows a reduction in the complexity of the system using a separation of time scales approach. We predict an undocumented phenomenon of loss of polymorphism at the major-effect locus despite strong selection for local adaptation, because the quantitative background slowly disrupts the rapidly established polymorphism at the major-effect locus, which is confirmed by individual-based simulations. Our study highlights how segregation of a quantitative background can greatly impact the dynamics of major-effect loci by provoking migrational meltdowns. We also provide a comprehensive toolbox designed to describe how to apply our method to more complex population genetic models.

Early-Onset Type 2 Diabetes and Mood, Anxiety, and Stress-Related Disorders: A Genetically Informative Register-Based Cohort Study.

To assess the association and familial coaggregation between early-onset type 2 diabetes (diagnosed before age 45 years) and mood, anxiety, and stress-related disorders and estimate the contribution of genetic and environmental factors to their co-occurrence. This population-based cohort study included individuals born in Sweden during 1968-1998, from whom pairs of full siblings, half-siblings, and cousins were identified. Information on diagnoses of early-onset type 2 diabetes and mood (including unipolar depression and bipolar disorder), anxiety, and stress-related disorders was obtained from the National Patient Register. Logistic and Cox regression models were used to assess the phenotypic association and familial coaggregation between type 2 diabetes and psychiatric disorders. Quantitative genetic modeling was conducted in full and maternal half-sibling pairs to estimate the relative contributions of genetic and environmental factors to the association. Among a total of 3,061,192 individuals, 7,896 (0.3%) were diagnosed with early-onset type 2 diabetes. These individuals had higher risks of any diagnosis (odds ratio [OR] 3.62 [95% CI 3.44, 3.80]) and specific diagnosis of unipolar depression (3.97 [3.75, 4.22]), bipolar disorder (4.17 [3.68, 4.73]), anxiety (3.76 [3.54, 3.99]), and stress-related disorders (3.35 [3.11, 3.61]). Relatives of individuals with early-onset type 2 diabetes also had higher overall risks of the examined psychiatric disorders (ORs 1.03-1.57). These associations are largely explained by genetic factors (51-78%), with the rest explained by nonshared environmental factors. Our findings highlight the burden of mood, anxiety, and stress-related disorders in early-onset type 2 diabetes and demonstrate that shared familial liability may contribute to their co-occurrence, suggesting that in the future research investigators should aim to identify shared risk factors and ultimately refine preventive and intervention strategies.

Genetic and Environmental Contribution to the Co-Occurrence of Endocrine-Metabolic Disorders and Depression: A Nationwide Swedish Study of Siblings.

Depression is common in individuals with endocrine-metabolic disorders and vice versa, and a better understanding of the underlying factors contributing to the comorbidity of these disorders is needed. This study investigated the familial coaggregation of depression and endocrine-metabolic disorders and estimated the contribution of genetic and environmental factors to their co-occurrence. This population-based cohort study included 2.2 million individuals born in Sweden between 1973 and 1996, with follow-up through 2013. Participants were linked to their biological parents, allowing identification of full siblings, maternal half siblings, and paternal half siblings. Diagnoses of depression and endocrine-metabolic conditions were investigated, with the latter grouped into autoimmune disorders (autoimmune hypothyroidism, Graves' disease, and type 1 diabetes) and non-autoimmune disorders (type 2 diabetes, obesity, and polycystic ovary syndrome). Logistic regression and Cox regression were used to estimate the associations between endocrine-metabolic disorders and depression within the same individual and across siblings. Quantitative genetic modeling was performed to investigate the relative contribution of genetic and environmental influences. Individuals with endocrine-metabolic disorders had a significantly higher risk of depression, with odds ratios ranging from 1.43 (95% CI=1.30, 1.57) for Graves' disease to 3.48 (95% CI=3.25, 3.72) for type 2 diabetes. Increased risks extended to full and half siblings. These correlations were mainly explained by shared genetic influences for non-autoimmune conditions, and by nonshared environmental factors for autoimmune disorders, especially for type 1 diabetes. These findings provide phenotypic and etiological insights into the co-occurrence of depression and various endocrine-metabolic conditions, which could guide future research aiming at identifying pathophysiological mechanisms and intervention targets.

Genetic architecture of dispersal and local adaptation drives accelerating range expansions

Contemporary evolution has the potential to significantly alter biotic responses to global change, including range expansion dynamics and biological invasions. Models predicting range dynamics often make highly simplifying assumptions about the genetic architecture underlying relevant traits. However, genetic architecture defines evolvability and higher-order evolutionary processes, which determine whether evolution will be able to keep up with environmental change or not. Therefore, we here study the impact of the genetic architecture of dispersal and local adaptation, two central traits of high relevance for range expansions, on the dynamics and predictability of invasion into an environmental gradient, such as temperature. In our theoretical model we assume that dispersal and local adaptation traits result from the products of two noninteracting gene-regulatory networks (GRNs). We compare our model to simpler quantitative genetics models and show that in the GRN model, range expansions are accelerating and less predictable. We further find that accelerating dynamics in the GRN model are primarily driven by an increase in the rate of local adaptation to novel habitats which results from greater sensitivity to mutation (decreased robustness) and increased gene expression. Our results highlight how processes at microscopic scales, here within genomes, can impact the predictions of large-scale, macroscopic phenomena, such as range expansions, by modulating the rate of evolution.

Effects of Plasticity on Elevational Range Size and Species Richness.

AbstractElevational ranges within many taxa are greater in the north temperate region than the tropics. Two hypotheses to explain the pattern are, first, that large elevational ranges in the temperate region arise because species have evolved broad tolerance curves in response to seasonality and, second, that a low diversification rate in the temperate region (speciation minus extinction) has led to relatively few species, each of which occupies a large elevational range in the absence of competitors (character release). We build a quantitative genetic model of selection on a phenotypic trait, whereby increased tolerance is modeled as arising from plasticity in the trait. We show that broad tolerances result in evolution of large elevational ranges because they induce shallower genotypic clines and hence reduced maladaptive gene flow. The evolution of large elevational ranges results in relatively few competing species arranged along the elevational gradient at a species carrying capacity. In such saturated communities, species have much elevational overlap. In contrast, in similar-sized communities that could accommodate many more species, the resulting character release is associated with smaller elevational overlaps. Empirical assessment of these predictions should contribute to assessing any role for ecological limits in driving the latitudinal diversity gradient in species richness.

Dynamics of lineages in adaptation to a gradual environmental change

We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by the adaptation to the varying environment. The individuals are characterized by a one-dimensional trait. The dynamics -- births and deaths -- depend on a time-changing mortality rate that shifts the optimal trait to the right at constant speed. The population size is regulated by a nonlinear non-local logistic competition term. The macroscopic behaviour can be described by a PDE that admits a unique positive stationary solution. In the stationary regime, the population can persist, but with a lag in the trait distribution due to the environmental change. For the microscopic (individual-based) stochastic process, the evolution of the lineages can be traced back using the historical process, that is, a measure-valued process on the set of continuous real functions of time. Assuming stationarity of the trait distribution, we describe the limiting distribution, in large populations, of the path of an individual drawn at random at a given time $T$. Freezing the non-linearity due to competition allows the use of a many-to-one identity together with Feynman-Kac's formula. This path, in reversed time, remains close to a simple Ornstein-Uhlenbeck process. It shows how the lagged bulk of the present population stems from ancestors once optimal in trait but still in the tail of the trait distribution in which they lived.

Does sleep duration moderate genetic and environmental contributions to cognitive performance?

While prior research has demonstrated a relationship between sleep and cognitive performance, how sleep relates to underlying genetic and environmental etiologies contributing to cognitive functioning, regardless of the level of cognitive function, is unclear. The present study assessed whether the importance of genetic and environmental contributions to cognition vary depending on an individual's aging-related sleep characteristics. The large sample consisted of twins from six studies within the Interplay of Genes and Environment across Multiple Studies (IGEMS) consortium spanning mid- to late-life (Average age [Mage] = 57.6, range = 27-91 years, N = 7052, Female = 43.70%, 1525 complete monozygotic [MZ] pairs, 2001 complete dizygotic [DZ] pairs). Quantitative genetic twin models considered sleep duration as a primary moderator of genetic and environmental contributions to cognitive performance in four cognitive abilities (Semantic Fluency, Spatial-Visual Reasoning, Processing Speed, and Episodic Memory), while accounting for age moderation. Results suggested genetic and both shared and nonshared environmental contributions for Semantic Fluency and genetic and shared environmental contributions for Episodic Memory vary by sleep duration, while no significant moderation was observed for Spatial-Visual Reasoning or Processing Speed. Results for Semantic Fluency and Episodic Memory illustrated patterns of higher genetic influences on cognitive function at shorter sleep durations (i.e. 4 hours) and higher shared environmental contributions to cognitive function at longer sleep durations (i.e. 10 hours). Overall, these findings may align with associations of upregulation of neuroinflammatory processes and ineffective beta-amyloid clearance in short sleep contexts and common reporting of mental fatigue in long sleep contexts, both associated with poorer cognitive functioning.

Influence of the Human Lipidome on Epicardial Fat Volume in Mexican American Individuals.

IntroductionCardiovascular disease (CVD) is the leading cause of mortality worldwide and is the leading cause of death in the US. Lipid dysregulation is a well-known precursor to metabolic diseases, including CVD. There is a growing body of literature that suggests MRI-derived epicardial fat volume, or epicardial adipose tissue (EAT) volume, is linked to the development of coronary artery disease. Interestingly, epicardial fat is also actively involved in lipid and energy homeostasis, with epicardial adipose tissue having a greater capacity for release and uptake of free fatty acids. However, there is a scarcity of knowledge on the influence of plasma lipids on EAT volume.AimThe focus of this study is on the identification of novel lipidomic species associated with CMRI-derived measures of epicardial fat in Mexican American individuals.MethodsWe performed lipidomic profiling on 200 Mexican American individuals. High-throughput mass spectrometry enabled rapid capture of precise lipidomic profiles, providing measures of 799 unique species from circulating plasma samples. Because of our extended pedigree design, we utilized a standard quantitative genetic linear mixed model analysis to determine whether lipids were correlated with EAT by formally testing for association between each lipid species and the CMRI epicardial fat phenotype.ResultsAfter correction for multiple testing using the FDR approach, we identified 135 lipid species showing significant association with epicardial fat. Of those, 131 lipid species were positively correlated with EAT, where increased circulating lipid levels were correlated with increased epicardial fat. Interestingly, the top 10 lipid species associated with an increased epicardial fat volume were from the deoxyceramide (Cer(m)) and triacylglycerol (TG) families. Deoxyceramides are atypical and neurotoxic sphingolipids. Triacylglycerols are an abundant lipid class and comprise the bulk of storage fat in tissues. Pathologically elevated TG and Cer(m) levels are related to CVD risk and, in our study, to EAT volume.ConclusionOur results indicate that specific lipid abnormalities such as enriched saturated triacylglycerols and the presence of toxic ceramides Cer(m) in plasma of our individuals could precede CVD with increased EAT volume.

Persistence of Anxiety/Depression Symptoms in Early Adolescence: A Prospective Study of Daily Life Stress, Rumination, and Daytime Sleepiness in a Genetically Informative Cohort.

In this prospective study of mental health, we examine the influence of three interrelated traits - perceived stress, rumination, and daytime sleepiness - and their association with symptoms of anxiety and depression in early adolescence. Given the known associations between these traits, an important objective is to determine the extent to which they may independently predict anxiety/depression symptoms. Twin pairs from the Queensland Twin Adolescent Brain (QTAB) project were assessed on two occasions (N = 211 pairs aged 9-14 years at baseline and 152 pairs aged 10-16 years at follow-up). Linear regression models and quantitative genetic modeling were used to analyze the data. Prospectively, perceived stress, rumination, and daytime sleepiness accounted for 8-11% of the variation in later anxiety/depression; familial influences contributed strongly to these associations. However, only perceived stress significantly predicted change in anxiety/depression, accounting for 3% of variance at follow-up after adjusting for anxiety/depression at baseline, although it did not do so independently of rumination and daytime sleepiness. Bidirectional effects were found between all traits over time. These findings suggest an underlying architecture that is shared, to some degree, by all traits, while the literature points to hypothalamic-pituitary-adrenal (HPA) axis and/or circadian systems as potential sources of overlapping influence and possible avenues for intervention.

A generalist–specialist trade-off between switchgrass cytotypes impacts climate adaptation and geographic range

Polyploidy results from whole-genome duplication and is a unique form of heritable variation with pronounced evolutionary implications. Different ploidy levels, or cytotypes, can exist within a single species, and such systems provide an opportunity to assess how ploidy variation alters phenotypic novelty, adaptability, and fitness, which can, in turn, drive the development of unique ecological niches that promote the coexistence of multiple cytotypes. Switchgrass, Panicum virgatum, is a widespread, perennial C4 grass in North America with multiple naturally occurring cytotypes, primarily tetraploids (4×) and octoploids (8×). Using a combination of genomic, quantitative genetic, landscape, and niche modeling approaches, we detect divergent levels of genetic admixture, evidence of niche differentiation, and differential environmental sensitivity between switchgrass cytotypes. Taken together, these findings support a generalist (8×)–specialist (4×) trade-off. Our results indicate that the 8× represent a unique combination of genetic variation that has allowed the expansion of switchgrass’ ecological niche and thus putatively represents a valuable breeding resource.

Genetic and environmental correlational structure among metabolic syndrome endophenotypes.

Metabolic syndrome (MetS) is diagnosed by the presence of high scores on three or more metabolic traits, including systolic and diastolic blood pressure (SBP, DBP), glucose and insulin levels, cholesterol and triglyceride (TG) levels, and central obesity. A diagnosis of MetS is associated with increased risk of cardiovascular disease and type 2 diabetes. The components of MetS have long been demonstrated to have substantial genetic components, but their genetic overlap is less well understood. The present paper takes a multi-prong approach to examining the extent of this genetic overlap. This includes the quantitative genetic and additive Bayesian network modeling of the large TwinsUK project and examination of the results of genome-wide association study (GWAS) of UK Biobank data through use of LD score regression and examination of the number of genes and pathways identified in the GWASes which overlap across MetS traits. Results demonstrate a modest genetic overlap, and the genetic correlations obtained from TwinsUK and UK Biobank are nearly identical. However, these correlations imply more genetic dissimilarity than similarity. Furthermore, examination of the extent of overlap in significant GWAS hits, both at the gene and pathway level, again demonstrates only modest but significant genetic overlap. This lends support to the idea that in clinical treatment of MetS, treating each of the components individually may be an important way to address MetS.

Quantifying heritability and estimating evolutionary potential in the wild when individuals that share genes also share environments.

Accurate heritability estimates for fitness-related traits are required to predict an organism's ability to respond to global change. Heritability estimates are theoretically expected to be inflated if, due to limited dispersal, individuals that share genes are also likely to share similar environments. However, if relatives occupy similar environments due, at least partly, to genetic variation for habitat selection, then accounting for environmental similarity in quantitative genetic models may result in diminished heritability estimates in wild populations. This potential issue has been pointed out in the literature, but has not been evaluated by empirical studies. Here, we investigate whether environmental similarity among individuals can be partly explained by genetic variation for habitat selection, and how this link potentially blurs estimates for heritability in fitness-related traits. Using intensive GPS monitoring, we quantified home-range habitat composition for 293 roe deer inhabiting a heterogeneous landscape to assess environmental similarity. To investigate if environmental similarity might harbour genetic variation, we combined genome-wide data in a quantitative genetic framework to evaluate genetic variation for home-range habitat composition, which is partly the result of habitat selection at settlement. Finally, we explored how environmental similarity affects heritability estimates for behaviours related to the risk avoidance-resource acquisition trade-off (i.e. being in open habitat and distance to roads) and proxies of individual performance (i.e. body mass and hind foot length). We found substantial heritability for home-range habitat composition, with estimates ranging from 0.40 (proportion of meadows) to 0.85 (proportion of refuge habitat). Accounting for similarity in habitat composition between relatives decreased the heritability estimates for both behavioural and morphological traits (reduction ranging from 55% to 100% and from 22% to 41% respectively). As a consequence, only half of these heritability estimates remained significantly different from zero. Our results show that similar genotypes occupy similar environments, which could lead to heritable variation being incorrectly attributed to environmental effects. To accurately distinguish the sources of phenotypic variation and predict the ability of organisms to respond to global change, it is necessary to develop quantitative genetic studies investigating the mechanisms underpinning environmental similarity among relatives.

A Synthesis of Game Theory and Quantitative Genetic Models of Social Evolution.

Two popular approaches for modeling social evolution, evolutionary game theory and quantitative genetics, ask complementary questions but are rarely integrated. Game theory focuses on evolutionary outcomes, with models solving for evolutionarily stable equilibria, whereas quantitative genetics provides insight into evolutionary processes, with models predicting short-term responses to selection. Here we draw parallels between evolutionary game theory and interacting phenotypes theory, which is a quantitative genetic framework for understanding social evolution. First, we show how any evolutionary game may be translated into two quantitative genetic selection gradients, nonsocial and social selection, which may be used to predict evolutionary change from a single round of the game. We show that synergistic fitness effects may alter predicted selection gradients, causing changes in magnitude and sign as the population mean evolves. Second, we show how evolutionary games involving plastic behavioral responses to partners can be modeled using indirect genetic effects, which describe how trait expression changes in response to genes in the social environment. We demonstrate that repeated social interactions in models of reciprocity generate indirect effects and conversely, that estimates of parameters from indirect genetic effect models may be used to predict the evolution of reciprocity. We argue that a pluralistic view incorporating both theoretical approaches will benefit empiricists and theorists studying social evolution. We advocate the measurement of social selection and indirect genetic effects in natural populations to test the predictions from game theory and, in turn, the use of game theory models to aid in the interpretation of quantitative genetic estimates.

Genetic variation in leaf traits and gas exchange responses to vapour pressure deficit in contrasting conifer species

Abstract Mechanistically predicting the evolutionary response of tree species to climate change requires an understanding of genetic variation in relevant traits. Here we compared the phenotypic and genetic variation in the Leaf Economics Spectrum (LES) traits and the response of gas exchange to vapour pressure deficit (VPD) in lodgepole pine (Pico) and white spruce (Pigl), an early and a late successional species dominating the boreal forests of western Canada. We measured gas exchange, foliar nitrogen and lamina mass to area ratio in 697 c. 30‐year‐old trees in two field progeny trials. We analysed the response of gas exchange rates to VPD using a novel quantitative genetic model, the function‐valued trait approach. Pico showed greater phenotypic variation in the LES traits and greater genetic variation in photosynthetic rate than Pigl, but the species showed no significant difference in their phenotypic correlations between the LES traits. Pico showed a less sensitive stomatal response to VPD than Pigl and no significant genetic variation in stomatal sensitivity. In contrast, Pigl showed a positive correlation between the genetic values of stomatal sensitivity to VPD and stomatal conductance under low VPD. Our study region is projected to see an increase in VPD with climate change; the less sensitive and genetically diverse stomatal response to VPD in Pico could make this species more vulnerable to climate‐change‐induced droughts. A free Plain Language Summary can be found within the Supporting Information of this article.

Genetic and Environmental Architecture of Five Factor Model and Super-Factors: An Italian Twin Study.

No previous research explored the genetic and environmental structure of Big Five dimensions of personality and higher-order factors in a single twin study, except, in part, for just one study. We used the twin design to estimate the effects of genes and environment on both Five Factor model and related second- and third-order factors (i.e., Alpha [stability], Beta [plasticity], and GFP [general factor of personality]). We analyzed data from 314 adult twins (157 pairs: 83 monozygotic, 74 dizygotic; mean age: 52 years) enrolled in the Italian Twin Register. Participants underwent clinical and instrumental evaluations, and completed a 25-adjective list drawn from the Short Adjectives Checklist to Measure Big Five (SACBIF). We applied quantitative genetic models to unravel the sources of variation and covariation for the Big Five and higher-order factors. We found a similar etiological architecture across the different levels of analysis, with moderate to substantial non-additive genetic and unique environmental influences on all the personality traits, and no shared environmental contribution for any of them. We also detected significant genetic correlations for the Big Five dimensions and the Alpha and Beta super-factors. With some limitations, our results suggest that the etiological architecture of personality may be invariant to the factor level of analysis.

Are Genetic and Environmental Contributions to Verbal Fluency and Episodic Memory Solely Moderated by Sleep?

Decreases in sleep duration and cognitive functioning often occur and co-occur in aging although these patterns are not universal. Underlying etiologies, i.e., genetic and environmental factors, contribute to why people differ on cognitive functioning at shorter versus longer sleep durations. The current study tested whether sleep duration alters the genetic and environmental contributions to why middle-aged and older adults vary on cognitive functioning. Using 4 twin studies from the Interplay of Genes and Environment Across Multiple Studies (IGEMS) consortium (Mage=56.5, range=35.0-91.2, N=5,210, 1,083 complete MZ pairs, 1,522 complete DZ pairs) we tested quantitative genetic twin models considering sleep, depressive symptoms, and age as moderators of verbal fluency (i.e., Animal Naming) and episodic memory (i.e., Word List). For verbal fluency, sleep duration and depressive symptoms were significant when dropped together from the model (χ2(6)=15.22, p=0.02) but not individually (χ2sleep(3)=7.17, p=0.07; χ2dep(3)=5.81, p=0.12), indicating that both moderators may affect differences in verbal fluency performance. For episodic memory, sleep duration moderation was only significant via the shared environmental factor (χ2(1)=5.26, p=0.02), indicating that sleep may affect differences in episodic memory performance via environmental influences that make siblings more similar to one another. Overall, results illustrate patterns of higher genetic influences on cognitive function at short sleep (4 hours) and higher shared environmental influences on cognitive function at long sleep (10 hours). These findings may align with associations of upregulation of neuroinflammatory processes at short sleep and common reporting of mental fatigue at long sleep, both of which are associated with poorer cognitive functioning.

Social Selection and the Evolution of Maladaptation.

Evolution by natural selection is often viewed as a process that inevitably leads to adaptation or an increase in population fitness over time. However, maladaptation, an evolved decrease in fitness, may also occur in response to natural selection under some conditions. Social selection, which arises from the effects of social partners on fitness, has been identified as a potential cause of maladaptation, but we lack a general rule identifying when social selection should lead to a decrease in population mean fitness. Here we use a quantitative genetic model to develop such a rule. We show that maladaptation is most likely to occur when social selection is strong relative to nonsocial selection and acts in an opposing direction. In this scenario, the evolution of traits that impose fitness costs on others may outweigh evolved gains in fitness for the individual, leading to a net decrease in population mean fitness. Furthermore, we find that maladaptation may also sometimes occur when phenotypes of interacting individuals negatively covary. We outline the biological situations where maladaptation in response to social selection can be expected, provide both quantitative genetic and phenotypic versions of our derived result, and suggest what empirical work would be needed to test it. We also consider the effect of social selection on inclusive fitness and support previous work showing that inclusive fitness cannot suffer an evolutionary decrease. Taken together, our results show that social selection may decrease population mean fitness when it opposes individual-level selection, even as inclusive fitness increases.

The maintenance of standing genetic variation: Gene flow vs. selective neutrality in Atlantic stickleback fish

Adaptation to derived habitats often occurs from standing genetic variation. The maintenance within ancestral populations of genetic variants favourable in derived habitats is commonly ascribed to long‐term antagonism between purifying selection and gene flow resulting from hybridization across habitats. A largely unexplored alternative idea based on quantitative genetic models of polygenic adaptation is that variants favoured in derived habitats are neutral in ancestral populations when their frequency is relatively low. To explore the latter, we first identify genetic variants important to the adaptation of threespine stickleback fish (Gasterosteus aculeatus) to a rare derived habitat—nutrient‐depleted acidic lakes—based on whole‐genome sequence data. Sequencing marine stickleback from six locations across the Atlantic Ocean then allows us to infer that the frequency of these derived variants in the ancestral habitat is unrelated to the likely opportunity for gene flow of these variants from acidic‐adapted populations. This result is consistent with the selective neutrality of derived variants within the ancestor. Our study thus supports an underappreciated explanation for the maintenance of standing genetic variation, and calls for a better understanding of the fitness consequences of adaptive variation across habitats and genomic backgrounds.

Evolution of male nuptial gift and female remating: A quantitative genetic model

In some species of separate sexes, males present a nuptial gift containing nutrition to their mate. Producing a large nuptial gift is a considerable cost to the male, but it may improve his siring success if the female reduces the likelihood to accept another male after receiving a large gift. The female may receive a direct benefit by accepting another male who provides an additional nuptial gift. Additionally, the female may receive an indirect fitness benefit via laying offspring sired by a male who is able to produce a large nuptial gift. We formalized the multivariate quantitative genetics model describing the coevolution of the size of nuptial gift produced by the male (x) and the female’s propensity to engage in remating (y). We analyzed the model focusing two cases: [1] remating females receive no indirect fitness benefit, but enjoy direct benefit of nutrition; and [2] remating females receive no direct benefit, but enjoy an indirect fitness benefit due to a positive genetic correlation of x and y, which is possible if random mutations tend to make males produce small nuptial gifts. In both cases, the stable evolutionary equilibrium with neither nuptial gift nor remating (x-=y-=0) always exists. Another stable equilibrium may exist in which male produces nuptial gifts (x->0) and female engage in multiple mating (y->0). We discussed implications to the sexual conflict.

Peak shifts and extinction under sex-specific selection

A well-known property of sexual selection combined with a cross-sex genetic correlation (rmf) is that it can facilitate a peak shift on the adaptive landscape. How do these diversifying effects of sexual selection + rmf balance with the constraints imposed by such sexual antagonism, to affect the macroevolution of sexual dimorphism? Here, I extend existing quantitative genetic models of evolution on complex adaptive landscapes. Beyond recovering classical predictions for the conditions promoting a peak shift, I show that when rmf is moderate to strong, relatively weak sexual selection is required to induce a peak shift in males only. Increasing the strength of sexual selection leads to a sexually concordant peak shift, suggesting that macroevolutionary rates of sexual dimorphism may be largely decoupled from the strength of within-population sexual selection. Accounting explicitly for demography further reveals that sex-specific peak shifts may be more likely to be successful than concordant shifts in the face of extinction, especially when natural selection is strong. An overarching conclusion is that macroevolutionary patterns of sexual dimorphism are unlikely to be readily explained by within-population estimates of selection or constraint alone.