Towards robust evolutionary inference with integral projection models.

Integral projection models (IPMs) are extremely flexible tools for ecological and evolutionary inference. IPMs track the distribution of phenotype in populations through time, using functions describing phenotype-dependent development, inheritance, survival and fecundity. For evolutionary inference, two important features of any model are the ability to (i) characterize relationships among traits (including values of the same traits across ages) within individuals, and (ii) characterize similarity between individuals and their descendants. In IPM analyses, the former depends on regressions of observed trait values at each age on values at the previous age (development functions), and the latter on regressions of offspring values at birth on parent values as adults (inheritance functions). We show analytically that development functions, characterized this way, will typically underestimate covariances of trait values across ages, due to compounding of regression to the mean across projection steps. Similarly, we show that inheritance, characterized this way, is inconsistent with a modern understanding of inheritance, and underestimates the degree to which relatives are phenotypically similar. Additionally, we show that the use of a constant biometric inheritance function, particularly with a constant intercept, is incompatible with evolution. Consequently, current implementations of IPMs will predict little or no phenotypic evolution, purely as artefacts of their construction. We present alternative approaches to constructing development and inheritance functions, based on a quantitative genetic approach, and show analytically and through an empirical example on a population of bighorn sheep how they can potentially recover patterns that are critical to evolutionary inference.

Demographic drivers of age-dependent sexual selection.

Sexual selection has a critical role in evolution, and it is fundamental to identify what ecological factors drive its variation. Disentangling the ecological correlates of sexual selection over the long term, however, is challenging and has rarely been done in nature. We sought to assess how demographic changes influenced the intensity, direction and form of sexual selection and whether selective pressures varied with age. We tested whether breeder sex ratio, number of competitors and age structure influenced selection differentials on horn length of wild bighorn rams (Ovis canadensis) of different age classes on Ram Mountain, Alberta. We used 21 years of data including a detailed pedigree, demographic parameters and repeated morphological measurements. Sexual selection on horn length of males of all ages was directional and positive. Selection intensity increased with the number of competitors, reflecting male-male encounter rate during the rut, but was independent of breeder sex ratio or age structure. This result can also be linked to changes in population size because the number of competitors was highly correlated to total number of sheep. This demographic effect likely arises from age-dependent mating tactics. Males aged 2-4 years are weakly competitive and experienced stronger sexual selection as they accounted for a greater proportion of all males. Selection experienced by mature males appeared independent of demography. Our study provides a rare description of the demographic determinants of sexual selection in nature.

Polygamy and an absence of fine-scale structure in Dendroctonus ponderosae (Hopk.) (Coleoptera: Curcilionidae) confirmed using molecular markers.

An understanding of mating systems and fine-scale spatial genetic structure is required to effectively manage forest pest species such as Dendroctonus ponderosae (mountain pine beetle). Here we used genome-wide single-nucleotide polymorphisms to assess the fine-scale genetic structure and mating system of D. ponderosae collected from a single stand in Alberta, Canada. Fine-scale spatial genetic structure was absent within the stand and the majority of genetic variation was best explained at the individual level. Relatedness estimates support previous reports of pre-emergence mating. Parentage assignment tests indicate that a polygamous mating system better explains the relationships among individuals within a gallery than the previously reported female monogamous/male polygynous system. Furthermore, there is some evidence to suggest that females may exploit the galleries of other females, at least under epidemic conditions. Our results suggest that current management models are likely to be effective across large geographic areas based on the absence of fine-scale genetic structure.

Sex-based differences in the adaptive value of social behavior contrasted against morphology and environment.

The adaptive nature of sociality has long been a central question in ecology and evolution. However, the relative importance of social behavior for fitness, compared to morphology and environment, remains largely unknown. We assessed the importance of sociality for fitness (lamb production and survival) in a population of mark6d bighorn sheep (Ovis canadensis) over 16 years (n = 1022 sheep-years). We constructed social networks from observations (n = 38,350) of group membership (n = 3150 groups). We then tested whether consistent individual differences in social behavior (centrality) exist and evaluated their relative importance compared to factors known to affect fitness: mass, age, parental effects, and population density. Sheep exhibited consistent individual differences in social centrality. Controlling for maternal carryover effects and age, the positive effect of centrality in a social network on adult female lamb production and survival was equal or greater than the effect of body mass or population density. Social centrality had less effect on male survival and no effect on adult male lamb production or lamb survival. Through its effect on lamb production and survival, sociality in fission-fusion animal societies may ultimately influence population dynamics equally or more than morphological or environmental effects.

Comparing measures of breeding inequality and opportunity for selection with sexual selection on a quantitative character in bighorn rams.

The reliability and consistency of the many measures proposed to quantify sexual selection have been questioned for decades. Realized selection on quantitative characters measured by the selection differential i was approximated by metrics based on variance in breeding success, using either the opportunity for sexual selection Is or indices of inequality. There is no consensus about which metric best approximates realized selection on sexual characters. Recently, the opportunity for selection on character mean OSM was proposed to quantify the maximum potential selection on characters. Using 21 years of data on bighorn sheep (Ovis canadensis), we investigated the correlations between seven indices of inequality, Is , OSM and i on horn length of males. Bighorn sheep are ideal for this comparison because they are highly polygynous and sexually dimorphic, ram horn length is under strong sexual selection, and we have detailed knowledge of individual breeding success. Different metrics provided conflicting information, potentially leading to spurious conclusions about selection patterns. Iδ, an index of breeding inequality, and, to a lesser extent, Is showed the highest correlation with i on horn length, suggesting that these indices document breeding inequality in a selection context. OSM on horn length was strongly correlated with i, Is and indices of inequality. By integrating information on both realized sexual selection and breeding inequality, OSM appeared to be the best proxy of sexual selection and may be best suited to explore its ecological bases.

Post-weaning parental care increases fitness but is not heritable in North American red squirrels.

Most empirical attempts to explain the evolution of parental care have focused on its costs and benefits (i.e. fitness consequences). In contrast, few investigations have been made of the other necessary prerequisite for evolutionary change, inheritance. Here, we examine the fitness consequences and heritability (h(2)) of a post-weaning parental care behaviour (territory bequeathal) in a wild population of North American red squirrels. Each year, a subset (average across all years = 19%) of reproductive females bequeathed their territory to a dependent offspring. Bequeathing females experienced higher annual reproductive success and did not suffer a survival cost to themselves relative to those females retaining their territory. Bequeathing females thus realized higher relative annual fitness [ω = 1.18 ± 0.03 (SE)] than nonbequeathing females [ω = 0.96 ± 0.02 (SE)]. Additive genetic influences on bequeathal behaviour, however, were not significantly different from 0 (h(2) = 1.9 × 10(-3); 95% highest posterior density interval = 3.04 × 10(-8) to 0.37) and, in fact, bequeathal behaviour was not significantly repeatable (R = 2.0 × 10(-3); 95% HPD interval = 0-0.27). In contrast, directional environmental influences were apparent. Females were more likely to bequeath in years following low food abundance and when food availability in the upcoming autumn was high. Despite an evident fitness benefit, a lack of heritable genetic variance will constrain evolution of this trait.

Estimating genome-wide heterozygosity: effects of demographic history and marker type.

Heterozygosity-fitness correlations (HFCs) are often used to link individual genetic variation to differences in fitness. However, most studies examining HFCs find weak or no correlations. Here, we derive broad theoretical predictions about how many loci are needed to adequately measure genomic heterozygosity assuming different levels of identity disequilibrium (ID), a proxy for inbreeding. We then evaluate the expected ability to detect HFCs using an empirical data set of 200 microsatellites and 412 single nucleotide polymorphisms (SNPs) genotyped in two populations of bighorn sheep (Ovis canadensis), with different demographic histories. In both populations, heterozygosity was significantly correlated across marker types, although the strength of the correlation was weaker in a native population compared with one founded via translocation and later supplemented with additional individuals. Despite being bi-allelic, SNPs had similar correlations to genome-wide heterozygosity as microsatellites in both populations. For both marker types, this association became stronger and less variable as more markers were considered. Both populations had significant levels of ID; however, estimates were an order of magnitude lower in the native population. As with heterozygosity, SNPs performed similarly to microsatellites, and precision and accuracy of the estimates of ID increased as more loci were considered. Although dependent on the demographic history of the population considered, these results illustrate that genome-wide heterozygosity, and therefore HFCs, are best measured by a large number of markers, a feat now more realistically accomplished with SNPs than microsatellites.

Genomic consequences of genetic rescue in an insular population of bighorn sheep (Ovis canadensis).

Genetic rescue is a management intervention whereby a small population is supplemented with individuals from other populations in an attempt to reverse the effects of inbreeding and increased genetic load. One such rescue was recently documented in the population of bighorn sheep (Ovis canadensis) within the National Bison Range wildlife refuge (Montana, USA). Here, we examine the locus-specific effects of rescue in this population using a newly developed genome-wide set of 195 microsatellite loci and first-generation linkage map. We found that the rate of introgression varied among loci and that 111 loci, 57% of those examined, deviated from patterns of neutral inheritance. The most common deviation was an excess of homozygous genotypes relative to neutral expectations, indicative of directional selection. As in previous study of this rescue, individuals with more introduced alleles had higher reproductive success and longevity. In addition, we found 30 loci, distributed throughout the genome, which seem to have individual effects on these life history traits. Although the potential for outbreeding depression is a major concern when translocating individuals between populations, we found no evidence of such effects in this population.

Low heritabilities, but genetic and maternal correlations between red squirrel behaviours.

Consistent individual differences in behaviour, and behavioural correlations within and across contexts, are referred to as animal personalities. These patterns of variation have been identified in many animal taxa and are likely to have important ecological and evolutionary consequences. Despite their importance, genetic and environmental sources of variation in personalities have rarely been characterized in wild populations. We used a Bayesian animal model approach to estimate genetic parameters for aggression, activity and docility in North American red squirrels (Tamiasciurus hudsonicus). We found support for low heritabilities (0.08-0.12), and cohort effects (0.07-0.09), as well as low to moderate maternal effects (0.07-0.15) and permanent environmental effects (0.08-0.16). Finally, we found evidence of a substantial positive genetic correlation (0.68) and maternal effects correlation (0.58) between activity and aggression providing evidence of genetically based behavioural correlations in red squirrels. These results provide evidence for the presence of heritable variation in red squirrel behaviour, but also emphasize the role of other sources of variation, including maternal effects, in shaping patterns of variation and covariation in behavioural traits.

QTL mapping for sexually dimorphic fitness-related traits in wild bighorn sheep.

Dissecting the genetic architecture of fitness-related traits in wild populations is key to understanding evolution and the mechanisms maintaining adaptive genetic variation. We took advantage of a recently developed genetic linkage map and phenotypic information from wild pedigreed individuals from Ram Mountain, Alberta, Canada, to study the genetic architecture of ecologically important traits (horn volume, length, base circumference and body mass) in bighorn sheep. In addition to estimating sex-specific and cross-sex quantitative genetic parameters, we tested for the presence of quantitative trait loci (QTLs), colocalization of QTLs between bighorn sheep and domestic sheep, and sex × QTL interactions. All traits showed significant additive genetic variance and genetic correlations tended to be positive. Linkage analysis based on 241 microsatellite loci typed in 310 pedigreed animals resulted in no significant and five suggestive QTLs (four for horn dimension on chromosomes 1, 18 and 23, and one for body mass on chromosome 26) using genome-wide significance thresholds (Logarithm of odds (LOD) >3.31 and >1.88, respectively). We also confirmed the presence of a horn dimension QTL in bighorn sheep at the only position known to contain a similar QTL in domestic sheep (on chromosome 10 near the horns locus; nominal P<0.01) and highlighted a number of regions potentially containing weight-related QTLs in both species. As expected for sexually dimorphic traits involved in male-male combat, loci with sex-specific effects were detected. This study lays the foundation for future work on adaptive genetic variation and the evolutionary dynamics of sexually dimorphic traits in bighorn sheep.

Sex-differential effects of inbreeding on overwinter survival, birth date and mass of bighorn lambs.

Although it is generally expected that inbreeding would lower fitness, few studies have directly quantified the effects of inbreeding in wild mammals. We investigated the effects of inbreeding using long-term data from bighorn sheep on Ram Mountain, Alberta, Canada, over 20 years. This population underwent a drastic decline from 1992 to 2002 and has since failed to recover. We used a pedigree to calculate inbreeding coefficients and examined their impact on lamb growth, birth date and survival. Inbreeding had a substantial effect on female survival: for a given mass in September, the probability of overwinter survival for inbred female lambs was about 40% lower than that of noninbred ones. Contrary to our expectations, inbred female lambs were born earlier than noninbred ones. Earlier birth led to inbred female lambs being heavier by mid-September than noninbred ones. There was a nonsignificant trend for inbred female yearlings to weigh more than noninbred ones. A stronger mass-dependent viability selection for inbred compared to noninbred female lambs may explain why surviving inbred females were heavier than noninbred ones. Survival of male lambs was not affected by inbreeding. Sex-differential effects of inbreeding may be a general pattern in sexually dimorphic mammals, because of sex-biased maternal care or sexual differences in early development strategies.

A quantitative genetic analysis of hibernation emergence date in a wild population of Columbian ground squirrels.

The life history schedules of wild organisms have long attracted scientific interest, and, in light of ongoing climate change, an understanding of their genetic and environmental underpinnings is increasingly becoming of applied concern. We used a multi-generation pedigree and detailed phenotypic records, spanning 18 years, to estimate the quantitative genetic influences on the timing of hibernation emergence in a wild population of Columbian ground squirrels (Urocitellus columbianus). Emergence date was significantly heritable [h(2) = 0.22 ± 0.05 (in females) and 0.34 ± 0.14 (in males)], and there was a positive genetic correlation (r(G) = 0.76 ± 0.22) between male and female emergence dates. In adult females, the heritabilities of body mass at emergence and oestrous date were h(2) = 0.23 ± 0.09 and h(2) = 0.18 ± 0.12, respectively. The date of hibernation emergence has been hypothesized to have evolved so as to synchronize subsequent reproduction with upcoming peaks in vegetation abundance. In support of this hypothesis, although levels of phenotypic variance in emergence date were higher than oestrous date, there was a highly significant genetic correlation between the two (r(G) = 0.98 ± 0.01). Hibernation is a prominent feature in the annual cycle of many small mammals, but our understanding of its influences lags behind that for phenological traits in many other taxa. Our results provide the first insight into its quantitative genetic influences and thus help contribute to a more general understanding of its evolutionary significance.

Evaluation of 16 loci to examine the cross-species utility of single nucleotide polymorphism arrays.

Large collections of single nucleotide polymorphisms (SNPs) have recently been identified from a number of livestock genomes. This raises the possibility that SNP arrays might be useful for analysis in related species for which few genetic markers are currently available. To address the likely success of such an approach, the aim of this study was to examine the threshold number and position of flanking mutations which act to prevent genotype calls being produced. Sequence diversity was measured across 16 loci containing SNPs known either to work successfully between species or fail between species. In pairwise comparisons between domestic and wild sheep, sequence divergence surrounding working SNP assays was significantly lower than that surrounding non-functional assays. In addition, the location of flanking mismatches tended to be closer to the target SNP in loci that failed to generate genotype calls across species. The magnitude of sequence divergence observed for both working and non-functional assays was compared with the divergence separating domestic sheep from European Mouflon, African Barbary, goat and cattle. The results suggest that the utility of SNP arrays for analysis of shared polymorphism will be restricted to closely related pairs of species. Analysis across more divergent species will, however, be successful for other objectives, such as the identification of the ancestral state of SNPs.

A quantitative review of heterozygosity-fitness correlations in animal populations.

The ease of obtaining genotypic data from wild populations has renewed interest in the relationship between individual genetic diversity and fitness-related traits (heterozygosity-fitness correlations, or HFC). Here we present a comprehensive meta-analysis of HFC studies using powerful multivariate techniques which account for nonindependence of data. We compare these findings with those from univariate techniques, and test the influence of a range of factors hypothesized to influence the strength of HFCs. We found small but significantly positive effect sizes for life-history, morphological, and physiological traits; while theory predicts higher mean effect sizes for life-history traits, effect size did not differ consistently with trait type. Newly proposed measures of variation were no more powerful at detecting relationships than multilocus heterozygosity, and populations predicted to have elevated inbreeding variance did not exhibit higher mean effect sizes. Finally, we found evidence for publication bias, with studies reporting weak, nonsignificant effects being under-represented in the literature. In general, our review shows that HFC studies do not generally reveal patterns predicted by population genetic theory, and are of small effect (less than 1% of the variance in phenotypic characters explained). Future studies should use more genetic marker data and utilize sampling designs that shed more light on the biological mechanisms that may modulate the strength of association, for example by contrasting the strength of HFCs in mainland and island populations of the same species, investigating the role of environmental stress, or by considering how selection has shaped the traits under investigation.

The ontogeny of cross-sex genetic correlations: an analysis of patterns.

The independent evolution of males and females is typically constrained by shared genetic variance. Despite substantial research, we still know little about the evolution of cross-sex genetic covariance and its standardized measure, the cross-sex genetic correlation (r(MF)). In particular, it is unclear if r(MF) tend to vary with age. We compiled 28 traits for which ontogenetic trends in r(MF) were documented. Decreases in r(MF) with age were observed significantly more often than increases and the mean effect size for the relationship between r(MF) and age was large and negative. This suggests that sexual dimorphism (SD) may typically evolve more readily for phenotypes expressed later in ontogeny and that evolutionary inferences related to the evolution of SD should be limited to the ontogenetic stage at which r(MF) was estimated. Knowledge about ontogenetic variation in r(MF) should help improving our understanding of evolutionary patterns related to SD and the resolution of intralocus sexual conflicts.

Male personality, life-history strategies and reproductive success in a promiscuous mammal.

Recent theoretical work suggests that personality is a component of life history, but links between personality and either age-dependent reproductive success or life-history strategy are yet to be established. Using quantitative genetic analyses on a long-term pedigree we estimated indices of boldness and docility for 105 bighorn sheep rams (Ovis canadensis), born between 1983 and 1999, and compared these indices to their reproductive history from 2 years of age until death. Docility and boldness were highly heritable and negatively genetically correlated. Docile and bold rams survived longer than indocile and shy rams. Docility and boldness had a weak negative effect on reproductive success early in life, but a strong positive effect on older rams. Our findings highlight an important role of personality on reproductive success and suggest that personality could be an important component of life-history strategy.

Environmental coupling of selection and heritability limits evolution.

There has recently been great interest in applying theoretical quantitative genetic models to empirical studies of evolution in wild populations. However, while classical models assume environmental constancy, most natural populations exist in variable environments. Here, we applied a novel analytical technique to a long-term study of birthweight in wild sheep and examined, for the first time, how variation in environmental quality simultaneously influences the strength of natural selection and the genetic basis of trait variability. In addition to demonstrating that selection and genetic variance vary dramatically across environments, our results show that environmental heterogeneity induces a negative correlation between these two parameters. Harsh environmental conditions were associated with strong selection for increased birthweight but low genetic variance, and vice versa. Consequently, the potential for microevolution in this population is constrained by either a lack of heritable variation (in poor environments) or by a reduced strength of selection (in good environments). More generally, environmental dependence of this nature may act to limit rates of evolution, maintain genetic variance, and favour phenotypic stasis in many natural systems. Assumptions of environmental constancy are likely to be violated in natural systems, and failure to acknowledge this may generate highly misleading expectations for phenotypic microevolution.

Male mate choice influences female promiscuity in Soay sheep.

In most animal species, males are predicted to compete for reproductive opportunities, while females are expected to choose between potential mates. However, when males' rate of reproduction is constrained, or females vary widely in 'quality', male mate choice is also predicted to occur. Such conditions exist in the promiscuous mating system of feral Soay sheep on St Kilda, Scotland, where a highly synchronized mating season, intense sperm competition and limitations on sperm production constrain males' potential reproductive rate, and females vary substantially in their ability to produce successful offspring. We show that, consistent with predictions, competitive rams focus their mating activity and siring success towards heavier females with higher inclusive fitness. To our knowledge, this is the first time that male mate choice has been identified and shown to lead to assortative patterns of parentage in a natural mammalian system, and occurs despite fierce male-male competition for mates. An additional consequence of assortative mating in this population is that lighter females experience a series of unstable consorts with less adept rams, and hence are mated by a greater number of males during their oestrus. We have thus also identified a novel male-driven mechanism that generates variation in female promiscuity, which suggests that the high levels of female promiscuity in this system are not part of an adaptive female tactic to intensify post-copulatory competition between males.

Microsatellite measures of inbreeding: a meta-analysis.

Meta-analyses of published and unpublished correlations between phenotypic variation and two measures of genetic variation at microsatellite loci, multilocus heterozygosity (MLH) and mean d2, revealed that the strength of these associations are generally weak (mean r < 0.10). Effects on life-history trait variation were significantly greater than zero for both measures over all reported effect sizes (r = 0.0856 and 0.0479 for MLH and mean d2, respectively), whereas effects on morphometric traits were not (r = 0.0052 and r = 0.0038), which is consistent with the prediction that life-history traits exhibit greater inbreeding depression than morphometric traits. Effect sizes reported using mean d2 were smaller and more variable than those reported using MLH, suggesting that MLH may be a better metric for capturing inbreeding depression most of the time. However, analyses of paired effect sizes reported using both measures from the same data did not differ significantly. Several lines of evidence suggest that published effects sizes are upwardly biased. First, effect sizes from published studies were significantly higher than those reported in unpublished studies. Second, fail-safe numbers for reported effect sizes were generally quite low, with the exception of correlations between MLH and life-history traits. Finally, the slope of the regression of effect size on sample size was negative for most sets of traits. Taken together, these results suggest that studies designed to detect inbreeding depression on a life-history trait using microsatellites will need to sample in excess of 600 individuals to detect an average effect size (r = 0.10) with reasonable statistical power (0.80). Very few published studies have used samples sizes approaching this value.