Assessing variation in life‐history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists

Mixed models are now well‐established methods in ecology and evolution because they allow accounting for and quantifying within‐ and between‐individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi‐modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life‐history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life‐history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long‐term studies of large mammals to illustrate the potential of using mixture models for assessing within‐population variation in life‐history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life‐history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.     

Selection on incremental variation of eye size in a wild population of Daphnia

Several studies of eye morphology have analysed macroevolutionary patterns in the diversity of eyes, and although these studies are often linked to environment or behaviour, they provide only indirect evidence of selection. Specific data to show the microevolutionary potential for adaptation by natural selection in eye morphology have been lacking. We document directional selection on eye size, an important determinant of visual capabilities, in a wild population of the freshwater microcrustacean Daphnia. We show that even slight changes in eye size may have major consequences for fitness. An increase in eye diameter of 19.9 μm – slightly more than one standard deviation – is associated with an increase in clutch size of one egg, or an increase of nearly 20% of the mean clutch size. Furthermore, relative eye size is genetically variable and thus could evolve in response to the observed selective pressure. We conclude that selection on incremental variation in eye size may have led to differences observed on broader taxonomic scales.     

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

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

Genetic analysis of body weights of individually fed beef bulls in South Africa using random regression models

The aim of this study was to estimate genetic parameters for body weights of individually fed beef bulls measured at centralized testing stations in South Africa using random regression models. Weekly body weights of Bonsmara bulls (N = 2919) tested between 1999 and 2003 were available for the analyses. The model included a fixed regression of the body weights on fourth-order orthogonal Legendre polynomials of the actual days on test (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, and 84) for starting age and contemporary group effects. Random regressions on fourth-order orthogonal Legendre polynomials of the actual days on test were included for additive genetic effects and additional uncorrelated random effects of the weaning-herd-year and the permanent environment of the animal. Residual effects were assumed to be independently distributed with heterogeneous variance for each test day. Variance ratios for additive genetic, permanent environment and weaning-herd-year for weekly body weights at different test days ranged from 0.26 to 0.29, 0.37 to 0.44 and 0.26 to 0.34, respectively. The weaning-herd-year was found to have a significant effect on the variation of body weights of bulls despite a 28-day adjustment period. Genetic correlations amongst body weights at different test days were high, ranging from 0.89 to 1.00. Heritability estimates were comparable to literature using multivariate models. Therefore, random regression model could be applied in the genetic evaluation of body weight of individually fed beef bulls in South Africa.     

Latitudinal patterns in European ant assemblages: variation in species richness and body size

Using published distributions of 65 species from the British Isles and northern Europe, we show that ant assemblages change with latitude in two ways. First, as commonly found for many types of organisms, the number of ant species decreased significantly with increasing latitude. For Ireland and Great Britain, species richness also increased significantly with region area. Second, although rarely demonstrated for ectotherms, the body size of ant species, as measured by worker length, increased significantly with increasing latitude. We found that this body-size pattern existed in the subfamily Formicinae and, to a lesser extent, in the Myrmicinae, which together comprised 95% of the ant species in our study area. There was a trend for formicines to increase in size with latitude faster than myrmicines. We also show that the pattern of increasing body size was due primarily to the ranges of ant species shifting to higher latitudes as their body sizes increased, with larger formicines becoming less represented at southerly latitudes and larger myrmicines becoming more represented at northerly latitudes. We conclude by discussing five potential mechanisms for generating the observed body-size patterns: the heat-conservation hypothesis, two hypotheses concerning phylogenetic history, the migration-ability hypothesis, and the starvation-resistance hypothesis.     

Mainland size variation informs predictive models of exceptional insular body size change in rodents

The tendency for island populations of mammalian taxa to diverge in body size from their mainland counterparts consistently in particular directions is both impressive for its regularity and, especially among rodents, troublesome for its exceptions. However, previous studies have largely ignored mainland body size variation, treating size differences of any magnitude as equally noteworthy. Here, we use distributions of mainland population body sizes to identify island populations as ‘extremely’ big or small, and we compare traits of extreme populations and their islands with those of island populations more typical in body size. We find that although insular rodents vary in the directions of body size change, ‘extreme’ populations tend towards gigantism. With classification tree methods, we develop a predictive model, which points to resource limitations as major drivers in the few cases of insular dwarfism. Highly successful in classifying our dataset, our model also successfully predicts change in untested cases.     

Age-related variation in immunity in a wild mammal population

Age‐related changes in immunity are well documented in humans and laboratory mammals. Using blood samples collected from wild Soay sheep, we show that pronounced differences in T‐cell subsets and inflammatory markers amongst age classes are also evident under natural conditions. These shifts parallel those observed in mammals experiencing protected environments. We found progressive declines in the proportion of naïve CD4 T cells with age, a precipitous drop in γδ T cells after the second year of life and an increase in acute phase protein levels amongst geriatric sheep. Our findings suggest immune aging patterns observed in laboratory and domestic mammals may generalize to more complex, challenging environments and could have fitness costs under natural conditions.     

Age-related reproductive variation in a wild marine mammal population

Life history theory predicts a change in reproduction success with age as energy resources are limited and must be allocated effectively to maximize reproduction and survival. In this study, we use three reproductive performance measures, maternal expenditure, offspring weaning mass, and first-year survival, to investigate the role that maternal age plays in successful reproduction. Long-term uninterrupted life history data available for Marion Island’s southern elephant seals and mass change estimates from photogrammetry data allow for assessment of age-related reproduction performance and trade-offs. Known-aged adult females were photographed for photogrammetric mass estimation (n = 29) and their pups weighed at weaning during the 2009 breeding season. Maternal age and proportional mass loss positively influenced pup weaning mass. In turn, first-year pup return rates (as a proxy for survival) were assessed through the intensive mark–recapture program. Pup survival increased with female age and weaning mass. Pups of young females aged 3–6 years have a lower first-year survival probability compared with pups of older and larger females.     

Adaptive variation in senescence: reproductive lifespan in a wild salmon population

The antagonistic pleiotropy theory of senescence postulates genes or traits that have opposite effects on early-life and late-life performances. Because selection is generally weaker late in life, genes or traits that improve early-life performance but impair late-life performance should come to predominate. Variation in the strength of age-specific selection should then generate adaptive variation in senescence. We demonstrate this mechanism by comparing early and late breeders within a population of semelparous capital-breeding sockeye salmon (Oncorhynchus nerka). We show that early breeders (but not late breeders) are under strong selection for a long reproductive lifespan (RLS), which facilitates defence of their nests against disturbance by later females. Accordingly, early females invest less energy in egg production while reserving more for nest defence. Variation along this reproductive trade-off causes delayed or slower senescence in early females (average RLS of 26 days) than in late females (reproductive lifespan of 12 days). We use microsatellites to confirm that gene flow is sufficiently limited between early and late breeders to allow adaptive divergence in response to selection. Because reproductive trade-offs should be almost universal and selection acting on them should typically vary in time and space, the mechanism described herein may explain much of the natural variation in senescence.     

Evidence for host variation in parasite tolerance in a wild fish population

Hosts can protect themselves against parasites by actively reducing parasites burden (i.e. resistance) or by limiting the damages caused by parasites (i.e. tolerance). Disentangling between tolerance and resistance is important for predicting the evolutionary outcomes of host-parasite interaction. Dace (Leuciscus leuciscus) are often parasitized by the ectoparasite Tracheliastes polycolpus which feeds on (and destroys) fins, reducing thus the host’s condition. We tested the hypothesis that genetically-based variation in ectoparasite tolerance exists in a wild dace population. We found that moderately heterozygous dace, which are less resistant than highly heterozygous or homozygous dace, tolerated better the effect imposed by T. polycolpus for a given parasite burden. However, tolerance also varied upon environmental conditions, suggesting that genetic and environmentally-based variation exists for both resistance and tolerance in this natural host-parasite system. Moreover, a negative genetic correlation may exist between tolerance and resistance, and hence several evolutionary outcomes are possible in this interacting system.     

Estimating termite population size using spatial statistics for termite tunnel patterns

Subterranean termites build underground tunnels for foraging. The obtained food is transported to the nest through these tunnels, and consumed to maintain the termite colony. In this process, termites can cause damage to wooden structures. To develop effective control strategies to reduce termite damage, it is important to know the sizes of the termite populations in the tunnels. In this study, we proposed a method for estimating the termite population size using the spatial statistic indices including fractal dimension (FD), local density (LD), and join count statistic (JCS) for the tunnel patterns. However, the method needs further improvement to be applied in field conditions. For the method, we generated 8,000 tunnel pattern images (1,000 images for each N) using an agent-based model based on experimental data. Here, N (= 3, 4, ..., 10) represents the number of termites participating in tunnel construction in the simulation. Subsequently, we calculated the FD, LD and JCS values of the tunnel pattern and trained and verified the k-nearest neighbors (KNN) algorithm, using 5,600 and 2,400 images, respectively. The population size (N) was estimated based on the FD, LD and JCS using the KNN algorithm. The estimated accuracy for all N was 60% to 97% in the range of k = 1 to 300. If the model for tunnel pattern generation includes heterogeneous environmental conditions, the proposed method could be used to effectively estimate the actual number of termite populations. Finally, we briefly discuss the challenges affecting our model, and how these could be overcome.     

Quantifying heritable variation in fitness-related traits of wild,farmed and hybrid Atlantic salmon families in a wild river environment

Farmed fish are typically genetically different from wild conspecifics. Escapees from fish farms may contribute one-way gene flow from farm to wild gene pools, which can depress population productivity, dilute local adaptations and disrupt coadapted gene complexes. Here, we reanalyse data from two experiments (McGinnity et al., 1997, 2003) where performance of Atlantic salmon (Salmo salar) progeny originating from experimental crosses between farm and wild parents (in three different cohorts) were measured in a natural stream under common garden conditions. Previous published analyses focussed on group-level differences but did not account for pedigree structure, as we do here using modern mixed-effect models. Offspring with one or two farm parents exhibited poorer survival in their first and second year of life compared with those with two wild parents and these group-level inferences were robust to excluding outlier families. Variation in performance among farm, hybrid and wild families was generally similar in magnitude. Farm offspring were generally larger at all life stages examined than wild offspring, but the differences were moderate (5–20%) and similar in magnitude in the wild versus hatchery environments. Quantitative genetic analyses conducted using a Bayesian framework revealed moderate heritability in juvenile fork length and mass and positive genetic correlations (>0.85) between these morphological traits. Our study confirms (using more rigorous statistical techniques) previous studies showing that offspring of wild fish invariably have higher fitness and contributes fresh insights into family-level variation in performance of farm, wild and hybrid Atlantic salmon families in the wild. It also adds to a small, but growing, number of studies that estimate key evolutionary parameters in wild salmonid populations. Such information is vital in modelling the impacts of introgression by escaped farm salmon.     

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.     

Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models

Variance components for five consecutive measurements of body weight in Polish sheep were estimated using random regression and multi-trait animal models. The data included between 7856 and 31694 body weight records at 5 age classes from birth to 150 days of age. The random additive genetic, maternal environmental and individual permanent environmental effects were fitted. All variance components were increasing over time (not at equal rates), which reflects increasing phenotypic mean and variance with age. Direct heritability tended to increase with age, whereas the effect of dam was reduced for older ages, and the proportion of permanent environmental component was relatively stable. Generally, similar tendencies were registered for estimates obtained via multi-trait animal model. The results confirm that there is a scope for genetic improvement in growth pattern in Polish sheep.     

Partitioning of genetic variation across the genome using multimarker methods in a wild bird population

The underlying basis of genetic variation in quantitative traits, in terms of the number of causal variants and the size of their effects, is largely unknown in natural populations. The expectation is that complex quantitative trait variation is attributable to many, possibly interacting, causal variants, whose effects may depend upon the sex, age and the environment in which they are expressed. A recently developed methodology in animal breeding derives a value of relatedness among individuals from high‐density genomic marker data, to estimate additive genetic variance within livestock populations. Here, we adapt and test the effectiveness of these methods to partition genetic variation for complex traits across genomic regions within ecological study populations where individuals have varying degrees of relatedness. We then apply this approach for the first time to a natural population and demonstrate that genetic variation in wing length in the great tit (Parus major) reflects contributions from multiple genomic regions. We show that a polygenic additive mode of gene action best describes the patterns observed, and we find no evidence of dosage compensation for the sex chromosome. Our results suggest that most of the genomic regions that influence wing length have the same effects in both sexes. We found a limited amount of genetic variance in males that is attributed to regions that have no effects in females, which could facilitate the sexual dimorphism observed for this trait. Although this exploratory work focuses on one complex trait, the methodology is generally applicable to any trait for any laboratory or wild population, paving the way for investigating sex‐, age‐ and environment‐specific genetic effects and thus the underlying genetic architecture of phenotype in biological study systems.     

Parent-offspring regression suggests heritable susceptibility to ectoparasites in a natural population of kittiwake Rissa tridactyla

Little information is available on the genetic variability of host susceptibility to parasites in natural populations despite its importance for the understanding of the evolution of host-parasite interactions. A long-term demographic and epidemiologic survey of a seabird population allowed us to investigate the potential correlation between parent and offspring ectoparasite load, while controlling for various environmental factors. In particular, parasite loads were measured for all individuals (i.e., parents and offspring) when they were nestlings and the effect of the year and breeding cliff were taken into account. The positive correlation found between parent and offspring parasite loads suggests a heritable susceptibility to ectoparasitism by ticks in this host population and that this character has the potential to respond to natural selection.     

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.     

Within-clutch variation in offspring sex determined by differences in sire body size: cryptic mate choice in the wild

Sexual selection theory predicts that paternal quality should drive female investment in progeny. We tested whether polyandrous female side-blotched lizards, Uta stansburiana, would adjust within-clutch progeny investment according to sire phenotypes. In two different years, polyandrous females selectively used sperm from larger sires to produce sons and used sperm from smaller sires to produce daughters. This cryptic sperm choice had significant effects on progeny survival to maturity that were consistent with sexually antagonistic effects associated with sire body size. Large sires produced sons with high viability and small sires produced daughters with high viability. These results are consistent with our previous findings that alleles for male body size have different fitness effects in male and female progeny. Breeding experiments in the laboratory indicate that results from the wild are more likely due to female choice than biased sperm production by males. Our results demonstrate highly refined gender-specific female choice for sperm and indicate that sire body size may signal the quality of sons or daughters that a sire will produce.