Quantitative genetic modeling and inference in the presence of nonignorable missing data

The missing fraction problem as an episodes of selection problem

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

The genetic basis of dispersal in a vertebrate metapopulation

Dispersal affects evolutionary processes by changing population size and genetic composition, influencing the viability and persistence of populations. Investigating which mechanisms underlie variation in dispersal phenotypes and whether populations harbour adaptive potential for dispersal is crucial to understanding the eco-evolutionary dynamics of this important trait. Here, we investigate the genetic architecture of dispersal among successfully recruited individuals in an insular metapopulation of house sparrows. We use an extensive long-term individual-based ecological data set and high-density single-nucleotide polymorphism (SNP) genotypes for over 2500 individuals. We conducted a genome-wide association study (GWAS), and found a relationship between dispersal probability and a SNP located near genes known to regulate circadian rhythm, glycogenesis and exercise performance, among other functions. However, this SNP only explained 3.8% of variance, suggesting that dispersal is a polygenic trait. We then used an animal model to estimate heritable genetic variation (σA 2 ), which composes 10% of the total variation in dispersal probability. Finally, we investigated differences in σA 2 across populations occupying ecologically relevant habitat types (farm vs. non-farm) using a genetic groups animal model. We found different adaptive potentials across habitats, with higher mean breeding value, σA 2 , and heritability for the habitat presenting lower dispersal rates, suggesting also different roles of environmental variation. Our results suggest a complex genetic architecture of dispersal and demonstrate that adaptive potential may be environment dependent in key eco-evolutionary traits. The eco-evolutionary implications of such environment dependence and consequent spatial variation are likely to become ever more important with the increased fragmentation and loss of suitable habitats for many natural populations.

Resurrected seeds from herbarium specimens reveal rapid evolution of drought resistance in a selfing annual

PREMISE

Increased aridity and drought associated with climate change are exerting unprecedented selection pressures on plant populations. Whether populations can rapidly adapt, and which life history traits might confer increased fitness under drought, remain outstanding questions.

METHODS

We utilized a resurrection ecology approach, leveraging dormant seeds from herbarium collections to assess whether populations of Plantago patagonica from the semi-arid Colorado Plateau have rapidly evolved in response to approximately ten years of intense drought in the region. We quantified multiple traits associated with drought escape and drought resistance and assessed the survival of ancestors and descendants under simulated drought.

RESULTS

Descendant populations displayed a significant shift in resource allocation, in which they invested less in reproductive tissues and relatively more in both above- and below-ground vegetative tissues. Plants with greater leaf biomass survived longer under terminal drought; moreover, even after accounting for the effect of increased leaf biomass, descendant seedlings survived drought longer than their ancestors.

CONCLUSIONS

Our results document rapid adaptive evolution in response to climate change in a selfing annual and suggest that shifts in tissue allocation strategies may underlie adaptive responses to drought in arid or semi-arid environments. This work also illustrates a novel approach, documenting that under specific circumstances, seeds from herbarium specimens may provide an untapped source of dormant propagules for future resurrection experiments.

Longitudinal telomere dynamics within natural lifespans of a wild bird

Telomeres, the nucleotide sequences that protect the ends of eukaryotic chromosomes, shorten with each cell division and telomere loss may be influenced by environmental factors. Telomere length (TL) decreases with age in several species, but little is known about the sources of genetic and environmental variation in the change in TL (∆TL) in wild animals. In this study, we tracked changes in TL throughout the natural lifespan (from a few months to almost 9 years) of free-living house sparrows (Passer domesticus) in two different island populations. TL was measured in nestlings and subsequently up to four times during their lifetime. TL generally decreased with age (senescence), but we also observed instances of telomere lengthening within individuals. We found some evidence for selective disappearance of individuals with shorter telomeres through life. Early-life TL positively predicted later-life TL, but the within-individual repeatability in TL was low (9.2%). Using genetic pedigrees, we found a moderate heritability of ∆TL (h² = 0.21), which was higher than the heritabilities of early-life TL (h² = 0.14) and later-life TL measurements (h² = 0.15). Cohort effects explained considerable proportions of variation in early-life TL (60%), later-life TL (53%), and ∆TL (37%), which suggests persistent impacts of the early-life environment on lifelong telomere dynamics. Individual changes in TL were independent of early-life TL. Finally, there was weak evidence for population differences in ∆TL that may be linked to ecological differences in habitat types. Combined, our results show that individual telomere biology is highly dynamic and influenced by both genetic and environmental variation in natural conditions.

Spatial modelling improves genetic evaluation in smallholder breeding programs

BACKGROUND

Breeders and geneticists use statistical models to separate genetic and environmental effects on phenotype. A common way to separate these effects is to model a descriptor of an environment, a contemporary group or herd, and account for genetic relationship between animals across environments. However, separating the genetic and environmental effects in smallholder systems is challenging due to small herd sizes and weak genetic connectedness across herds. We hypothesised that accounting for spatial relationships between nearby herds can improve genetic evaluation in smallholder systems. Furthermore, geographically referenced environmental covariates are increasingly available and could model underlying sources of spatial relationships. The objective of this study was therefore, to evaluate the potential of spatial modelling to improve genetic evaluation in dairy cattle smallholder systems.

METHODS

We performed simulations and real dairy cattle data analysis to test our hypothesis. We modelled environmental variation by estimating herd and spatial effects. Herd effects were considered independent, whereas spatial effects had distance-based covariance between herds. We compared these models using pedigree or genomic data.

RESULTS

The results show that in smallholder systems (i) standard models do not separate genetic and environmental effects accurately, (ii) spatial modelling increases the accuracy of genetic evaluation for phenotyped and non-phenotyped animals, (iii) environmental covariates do not substantially improve the accuracy of genetic evaluation beyond simple distance-based relationships between herds, (iv) the benefit of spatial modelling was largest when separating the genetic and environmental effects was challenging, and (v) spatial modelling was beneficial when using either pedigree or genomic data.

CONCLUSIONS

We have demonstrated the potential of spatial modelling to improve genetic evaluation in smallholder systems. This improvement is driven by establishing environmental connectedness between herds, which enhances separation of genetic and environmental effects. We suggest routine spatial modelling in genetic evaluations, particularly for smallholder systems. Spatial modelling could also have a major impact in studies of human and wild populations.

Animal models with group-specific additive genetic variances: extending genetic group models

BACKGROUND

The animal model is a key tool in quantitative genetics and has been used extensively to estimate fundamental parameters, such as additive genetic variance or heritability. An implicit assumption of animal models is that all founder individuals derive from a single population. This assumption is commonly violated, for instance in crossbred livestock or when a meta-population is split into genetically differentiated subpopulations. Ignoring that base populations are genetically heterogeneous and thus split into different 'genetic groups' may lead to biased parameter estimates, especially for additive genetic variance. To avoid such biases, genetic group animal models, which account for the presence of more than one genetic group, have been proposed. Unfortunately, the method to date is only computationally feasible when the breeding values of the groups are allowed to differ in their means, but not in their variances.

RESULTS

We present an extension of the animal model that permits estimation of group-specific additive genetic variances. This is achieved by employing group-specific relatedness matrices for the breeding value components to different genetic groups. We derive these matrices by decomposing the full relatedness matrix via the generalized Cholesky decomposition, and by scaling the respective matrix components for each group. We propose a computationally convenient approximation for the matrix component that encodes for the Mendelian sampling variance, and show that this approximation is not critical. In addition, we explain why segregation variances are often negligible when analyzing the complex polygenic traits that are frequently the focus of evolutionary ecologists and animal breeders. Simulations and an example from an insular meta-population of house sparrows in Norway with three distinct genetic groups illustrate that the method is successful in estimating group-specific additive genetic variances, and that segregation variances are indeed negligible in the empirical example.

CONCLUSIONS

Quantifying differences in additive genetic variance within and among populations is of major biological interest in ecology, evolution, and animal and plant breeding. The proposed method allows to estimate such differences for subpopulations that form a connected set of populations, and may thus also be useful to study temporal or spatial variation of additive genetic variances.

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature.

Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.

Detecting the "invisible fraction" bias in resurrection experiments

The resurrection approach is a powerful tool for estimating phenotypic evolution in response to global change. Ancestral generations, revived from dormant propagules, are grown side by side with descendent generations in the same environment. Phenotypic differences between the generations can be attributed to genetic change over time. Project Baseline was established to capitalize on this potential in flowering plants. Project participants collected, froze, and stored seed from 10 or more natural populations of 61 North American plant species. These will be made available in the future for resurrection experiments. One problem with this approach can arise if nonrandom mortality during storage biases the estimate of ancestral mean phenotype, which in turn would bias the estimate of evolutionary change. This bias—known as the “invisible fraction” problem—can arise if seed traits that affect survival during storage and revival are genetically correlated to postemergence traits of interest. The bias is trivial if seed survival is high. Here, I show that with low seed survival, bias can be either trivial or catastrophic. Serious bias arises when (i) most seeds deaths are selective with regard to the seed traits, and (ii) the genetic correlations between the seed and postemergence traits are strong. An invisible fraction bias can be diagnosed in seed collections that are family structured. A correlation between the family mean survival rate and the family mean of a focal postemergence trait indicates that seed mortality was not random with respect to genes affecting the focal trait, biasing the sample mean. Fortunately, family structure was incorporated into the sampling scheme for the Project Baseline collection, which will allow bias detection. New and developing statistical procedures that can incorporate genealogical information into the analysis of resurrection experiments may enable bias correction.

Bigger Is Fitter? Quantitative Genetic Decomposition of Selection Reveals an Adaptive Evolutionary Decline of Body Mass in a Wild Rodent Population

In natural populations, quantitative trait dynamics often do not appear to follow evolutionary predictions. Despite abundant examples of natural selection acting on heritable traits, conclusive evidence for contemporary adaptive evolution remains rare for wild vertebrate populations, and phenotypic stasis seems to be the norm. This so-called “stasis paradox” highlights our inability to predict evolutionary change, which is especially concerning within the context of rapid anthropogenic environmental change. While the causes underlying the stasis paradox are hotly debated, comprehensive attempts aiming at a resolution are lacking. Here, we apply a quantitative genetic framework to individual-based long-term data for a wild rodent population and show that despite a positive association between body mass and fitness, there has been a genetic change towards lower body mass. The latter represents an adaptive response to viability selection favouring juveniles growing up to become relatively small adults, i.e., with a low potential adult mass, which presumably complete their development earlier. This selection is particularly strong towards the end of the snow-free season, and it has intensified in recent years, coinciding which a change in snowfall patterns. Importantly, neither the negative evolutionary change, nor the selective pressures that drive it, are apparent on the phenotypic level, where they are masked by phenotypic plasticity and a non causal (i.e., non genetic) positive association between body mass and fitness, respectively. Estimating selection at the genetic level enabled us to uncover adaptive evolution in action and to identify the corresponding phenotypic selective pressure. We thereby demonstrate that natural populations can show a rapid and adaptive evolutionary response to a novel selective pressure, and that explicitly (quantitative) genetic models are able to provide us with an understanding of the causes and consequences of selection that is superior to purely phenotypic estimates of selection and evolutionary change.

A population of snow voles provides a rare example of contemporary adaptive evolution in the wild, but without a quantitative genetic perspective this genetic change, and the selective pressure that underlies it, would have gone undetected.

Biologists struggle to demonstrate adaptive evolution in wild populations: while they routinely observe natural selection on heritable traits, in only a handful of cases could they demonstrate an evolutionary response. Although various explanations for this paradox have been proposed, comprehensive empirical tests are lacking. Over the past years, we have therefore studied an alpine population of snow voles. Following all individuals throughout their lives, we found that body mass is heritable and that heavy voles have a higher fitness. Nevertheless, mean body mass did not increase. To resolve this, we disentangled the role of genes and the environment in shaping body mass. This revealed that the population did evolve, but that this was masked by environmental variation. Furthermore, although the genetic change was adaptive, it was opposite to our initial expectation: the population evolved to become lighter, not heavier. This was because although heavy voles have the highest fitness, their mass does not cause high fitness. Instead, it is the voles with the genes for being light that do best, especially when the first winter snow arrives early. This shows that populations can evolve rapidly, but that without a genetic perspective, this, and its underlying mechanism, may go undetected.

Is my study system good enough? A case study for identifying maternal effects

In this paper, we demonstrate how simulation studies can be used to answer questions about identifiability and consequences of omitting effects from a model. The methodology is presented through a case study where identifiability of genetic and/or individual (environmental) maternal effects is explored. Our study system is a wild house sparrow (Passer domesticus) population with known pedigree. We fit pedigree‐based (generalized) linear mixed models (animal models), with and without additive genetic and individual maternal effects, and use deviance information criterion (DIC) for choosing between these models. Pedigree and R‐code for simulations are available. For this study system, the simulation studies show that only large maternal effects can be identified. The genetic maternal effect (and similar for individual maternal effect) has to be at least half of the total genetic variance to be identified. The consequences of omitting a maternal effect when it is present are explored. Our results indicate that the total (genetic and individual) variance are accounted for. When an individual (environmental) maternal effect is omitted from the model, this only influences the estimated (direct) individual (environmental) variance. When a genetic maternal effect is omitted from the model, both (direct) genetic and (direct) individual variance estimates are overestimated.

The genetic covariance between life cycle stages separated by metamorphosis

Metamorphosis is common in animals, yet the genetic associations between life cycle stages are poorly understood. Given the radical changes that occur at metamorphosis, selection may differ before and after metamorphosis, and the extent that genetic associations between pre- and post-metamorphic traits constrain evolutionary change is a subject of considerable interest. In some instances, metamorphosis may allow the genetic decoupling of life cycle stages, whereas in others, metamorphosis could allow complementary responses to selection across the life cycle. Using a diallel breeding design, we measured viability at four ontogenetic stages (embryo, larval, juvenile and adult viability), in the ascidian Ciona intestinalis and examined the orientation of additive genetic variation with respect to the metamorphic boundary. We found support for one eigenvector of G: (gobsmax ), which contrasted larval viability against embryo viability and juvenile viability. Target matrix rotation confirmed that while gobsmax shows genetic associations can extend beyond metamorphosis, there is still considerable scope for decoupled phenotypic evolution. Therefore, although genetic associations across metamorphosis could limit that range of phenotypes that are attainable, traits on either side of the metamorphic boundary are capable of some independent evolutionary change in response to the divergent conditions encountered during each life cycle stage.

Sleep and vigilance linked to melanism in wild barn owls

Understanding the function of variation in sleep requires studies in the natural ecological conditions in which sleep evolved. Sleep has an impact on individual performance and hence may integrate the costs and benefits of investing in processes that are sensitive to sleep, such as immunity or coping with stress. Because dark and pale melanic animals differentially regulate energy homeostasis, immunity and stress hormone levels, the amount and/or organization of sleep may covary with melanin-based colour. We show here that wild, cross-fostered nestling barn owls (Tyto alba) born from mothers displaying more black spots had shorter non-REM (rapid eye movement) sleep bouts, a shorter latency until the occurrence of REM sleep after a bout of wakefulness and more wakefulness bouts. In male nestlings, the same sleep traits also correlated with their own level of spotting. Because heavily spotted male nestlings and the offspring of heavily spotted biological mothers switched sleep-wakefulness states more frequently, we propose the hypothesis that they could be also behaviourally more vigilant. Accordingly, nestlings from mothers displaying many black spots looked more often towards the nest entrance where their parents bring food and towards their sibling against whom they compete. Owlets from heavily spotted mothers might invest more in vigilance, thereby possibly increasing associated costs due to sleep fragmentation. We conclude that different strategies of the regulation of brain activity have evolved and are correlated with melanin-based coloration.

On estimation and identifiability issues of sex-linked inheritance with a case study of pigmentation in Swiss barn owl (Tyto alba)

Genetic evaluation using animal models or pedigree-based models generally assume only autosomal inheritance. Bayesian animal models provide a flexible framework for genetic evaluation, and we show how the model readily can accommodate situations where the trait of interest is influenced by both autosomal and sex-linked inheritance. This allows for simultaneous calculation of autosomal and sex-chromosomal additive genetic effects. Inferences were performed using integrated nested Laplace approximations (INLA), a nonsampling-based Bayesian inference methodology. We provide a detailed description of how to calculate the inverse of the X- or Z-chromosomal additive genetic relationship matrix, needed for inference. The case study of eumelanic spot diameter in a Swiss barn owl (Tyto alba) population shows that this trait is substantially influenced by variation in genes on the Z-chromosome ( and ). Further, a simulation study for this study system shows that the animal model accounting for both autosomal and sex-chromosome-linked inheritance is identifiable, that is, the two effects can be distinguished, and provides accurate inference on the variance components.