Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

Natural selection and inheritance of breeding time and clutch size in the collared flycatcher

Many characteristics of organisms in free-living populations appear to be under directional selection, possess additive genetic variance, and yet show no evolutionary response to selection. Avian breeding time and clutch size are often-cited examples of such characters. We report analyses of inheritance of, and selection on, these traits in a long-term study of a wild population of the collared flycatcher Ficedula albicollis. We used mixed model analysis with REML estimation ("animal models") to make full use of the information in complex multigenerational pedigrees. Heritability of laying date, but not clutch size, was lower than that estimated previously using parent-offspring regressions, although for both traits there was evidence of substantial additive genetic variance (h2 = 0.19 and 0.29, respectively). Laying date and clutch size were negatively genetically correlated (rA = -0.41 +/- 0.09), implying that selection on one of the traits would cause a correlated response in the other, but there was little evidence to suggest that evolution of either trait would be constrained by correlations with other phenotypic characters. Analysis of selection on these traits in females revealed consistent strong directional fecundity selection for earlier breeding at the level of the phenotype (beta = -0.28 +/- 0.03), but little evidence for stabilising selection on breeding time. We found no evidence that clutch size was independently under selection. Analysis of fecundity selection on breeding values for laying date, estimated from an animal model, indicated that selection acts directly on additive genetic variance underlying breeding time (beta = -0.20 +/- 0.04), but not on clutch size (beta = 0.03 +/- 0.05). In contrast, selection on laying date via adult female survival fluctuated in sign between years, and was opposite in sign for selection on phenotypes (negative) and breeding values (positive). Our data thus suggest that any evolutionary response to selection on laying date is partially constrained by underlying life-history trade-offs, and illustrate the difficulties in using purely phenotypic measures and incomplete fitness estimates to assess evolution of life-history trade-offs. We discuss some of the difficulties associated with understanding the evolution of laying date and clutch size in natural populations.     

Intra-population comparison of vegetative and floral trait heritabilities estimated from molecular markers in wild Aquilegia populations

Measuring heritable genetic variation is important for understanding patterns of trait evolution in wild populations, and yet studies of quantitative genetic parameters estimated directly in the field are limited by logistic constraints, such as the difficulties of inferring relatedness among individuals in the wild. Marker-based approaches have received attention because they can potentially be applied directly to wild populations. For long-lived, self-compatible plant species where pedigrees are inadequate, the regression-based method proposed by Ritland has the appeal of estimating heritabilities from marker-based estimates of relatedness. The method has been difficult to implement in some plant populations, however, because it requires significant variance in relatedness across the population. Here, we show that the method can be readily applied to compare the ability of different traits to respond to selection, within populations. For several taxa of the perennial herb genus Aquilegia, we estimated heritabilities of floral and vegetative traits and, combined with estimates of natural selection, compared the ability to respond to selection of both types of traits under current conditions. The intra-population comparisons showed that vegetative traits have a higher potential for evolution, because although they are as heritable as floral traits, selection on them is stronger. These patterns of potential evolution are consistent with macroevolutionary trends in the European lineage of the genus.     

Using partial genotyping to estimate the genetic and maternal determinants of adaptive traits in a progeny trial of <Emphasis Type="Italic">Fagus sylvatica</Emphasis>

Understanding the determinants of phenotypic variation is critical to evaluate the ability of traits to evolve in a changing environment. In trees, the genetic component of the phenotypic variance is most often estimated based on maternal progeny tests. However, the lack of knowledge about the paternal relatedness hampers the accurate estimation of additive genetic and maternal effects. Here, we investigate how different methods accounting for paternal relatedness allow the estimation of heritability and maternal determinants of adaptive traits in a natural population of Fagus sylvatica L., presenting non-random mating. Twelve potentially adaptive functional traits were measured in 60 maternal families in a nursery. We genotyped a subset of offspring and of all the potentially reproductive adults in the population at 13 microsatellite markers to infer paternal relationships and to estimate average relatedness within and between maternal families. This relatedness information was then used in family and animal models to estimate the components of phenotypic variance. All the studied traits displayed significant genetic variance and moderate heritability. Maternal effects were detected for the diameter increment, stem volume and bud burst. Comparison of family and animal models showed that unbalanced mating system led to only slight departures from maternal family assumptions in the progeny trial. However, neglecting the significant maternal effects led to an overestimation of the heritability. Overall, we highlighted the usefulness of relatedness pattern analyses using polymorphic molecular markers to accurately analyse tree sibling designs.     

Marker-Based Estimation of Heritability in Immortal Populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.     

EVOLUTIONARY POTENTIAL OF A LARGE MARINE VERTEBRATE: QUANTITATIVE GENETIC PARAMETERS IN A WILD POPULATION

Estimating quantitative genetic parameters ideally takes place in natural populations, but relatively few studies have overcome the inherent logistical difficulties. For this reason, no estimates currently exist for the genetic basis of life-history traits in natural populations of large marine vertebrates. And yet such estimates are likely to be important given the exposure of this taxon to changing selection pressures, and the relevance of life-history traits to population productivity. We report such estimates from a long-term (1995–2007) study of lemon sharks ( Negaprion brevirostris ) conducted at Bimini, Bahamas. We obtained these estimates by genetically reconstructing a population pedigree (117 dams, 487 sires, and 1351 offspring) and then using an "animal model" approach to estimate quantitative genetic parameters. We find significant additive genetic (co)variance, and hence moderate heritability, for juvenile length and mass. We also find substantial maternal effects for these traits at age-0, but not age-1, confirming that genotype–phenotype interactions between mother and offspring are strongest at birth; although these effects could not be parsed into their genetic and nongenetic components. Our results suggest that human-imposed selection pressures (e.g., size-selective harvesting) might impose noteworthy evolutionary change even in large marine vertebrates. We therefore use our findings to explain how maternal effects may sometimes promote maladaptive juvenile traits, and how lemon sharks at different nursery sites may show "constrained local adaptation." We also show how single-generation pedigrees, and even simple marker-based regression methods, can provide accurate estimates of quantitative genetic parameters in at least some natural systems.     

Field heritability of a plant adaptation to fire in heterogeneous landscapes

The strong association observed between fire regimes and variation in plant adaptations to fire suggests a rapid response to fire as an agent of selection. It also suggests that fire‐related traits are heritable, a precondition for evolutionary change. One example is serotiny, the accumulation of seeds in unopened fruits or cones until the next fire, an important strategy for plant population persistence in fire‐prone ecosystems. Here, we evaluate the potential of this trait to respond to natural selection in its natural setting. For this, we use a SNP marker approach to estimate genetic variance and heritability of serotiny directly in the field for two Mediterranean pine species. Study populations were large and heterogeneous in climatic conditions and fire regime. We first estimated the realized relatedness among trees from genotypes, and then partitioned the phenotypic variance in serotiny using Bayesian animal models that incorporated environmental predictors. As expected, field heritability was smaller (around 0.10 for both species) than previous estimates under common garden conditions (0.20). An estimate on a subset of stands with more homogeneous environmental conditions was not different from that in the complete set of stands, suggesting that our models correctly captured the environmental variation at the spatial scale of the study. Our results highlight the importance of measuring quantitative genetic parameters in natural populations, where environmental heterogeneity is a critical aspect. The heritability of serotiny, although not high, combined with high phenotypic variance within populations, confirms the potential of this fire‐related trait for evolutionary change in the wild.     

Heritability of phenolics in Quercus laevis inferred using molecular markers.

Studies of quantitative inheritance of phenotypes do not generally encompass the range of environmental conditions to which a population may be exposed in a natural setting and are rarely conducted on long-lived species due to the time required for traditional crossing experiments. We used a marker-based method to estimate relatedness with microsatellite markers in a natural population of a long-lived oak, then used this inferred relatedness to examine quantitative genetic variation in the concentration of foliar phenolics. Estimating heritability using this method requires both significant relatedness and variance in relatedness over distance. However, this population did not show significant variance of relatedness, so only the presence of heritability, and its ranking among traits and environments, could be estimated. Seven foliar phenolics showed a significant relationship between phenotypic similarity and relatedness. The significance of this relationship varied among individual phenolic compounds, as well as by season. Genetic factors appeared to have a more measurable influence on the production of secondary compounds early in the season. After leaf expansion, covariance of relatedness and phenotypic variance appear to become less significant. Therefore heritability may vary seasonally for these traits.     

Pedigree-free animal models: the relatedness matrix reloaded

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.     

Performance of marker-based relatedness estimators in natural populations of outbred vertebrates

Knowledge of relatedness between pairs of individuals plays an important role in many research areas including evolutionary biology, quantitative genetics, and conservation. Pairwise relatedness estimation methods based on genetic data from highly variable molecular markers are now used extensively as a substitute for pedigrees. Although the sampling variance of the estimators has been intensively studied for the most common simple genetic relationships, such as unrelated, half- and full-sib, or parent-offspring, little attention has been paid to the average performance of the estimators, by which we mean the performance across all pairs of individuals in a sample. Here we apply two measures to quantify the average performance: first, misclassification rates between pairs of genetic relationships and, second, the proportion of variance explained in the pairwise relatedness estimates by the true population relatedness composition (i.e., the frequencies of different relationships in the population). Using simulated data derived from exceptionally good quality marker and pedigree data from five long-term projects of natural populations, we demonstrate that the average performance depends mainly on the population relatedness composition and may be improved by the marker data quality only within the limits of the population relatedness composition. Our five examples of vertebrate breeding systems suggest that due to the remarkably low variance in relatedness across the population, marker-based estimates may often have low power to address research questions of interest.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

Wild pedigrees: the way forward

Metrics derived from pedigrees are key to investigating several major issues in evolutionary biology, including the quantitative genetic architecture of traits, inbreeding depression, and the evolution of cooperation and inbreeding avoidance. There is merit in studying these issues in natural populations experiencing spatially and temporally variable environmental conditions, since these analyses may yield different results from laboratory studies and allow us to understand population responses to rapid environmental change. Partial pedigrees are now available for several natural populations which are the subject of long-term individual-based studies, and analyses using these pedigrees are leading to important insights. Accurate pedigree construction supported by molecular genetic data is now feasible across a wide range of taxa, and even where only imprecise pedigrees are available it is possible to estimate the consequences of imprecision for the questions of interest. In outbred diploid populations, the pedigree approach is superior to analyses based on marker-based pairwise estimators of coancestry.     

HOW TO MEASURE INDIRECT GENETIC EFFECTS: THE CONGRUENCE OF TRAIT-BASED AND VARIANCE-PARTITIONING APPROACHES

Indirect genetic effects (IGEs), which occur when phenotypic expression in one individual is influenced by genes in another conspecific individual, may have a drastic effect on evolutionary response to selection. General evolutionary models of IGEs have been developed using two distinct theoretical frameworks derived from maternal effects theory. The first framework is trait-based and focuses on how phenotypes are influenced by specific traits in a social partner, with the strength of interactions defined by the matrix Ψ. The second framework partitions total genetic variance into components representing direct effects, indirect effects, and the covariance between them, without identifying specific social traits responsible for IGEs. The latter framework has been employed more commonly by empiricists because the methods for estimating variance components are relatively straightforward. Here, we show how these two theoretical frameworks are related to each other and derive equations that can be used to translate between them. This translation leads to a generalized method that can be used to estimate Ψ via standard quantitative genetic breeding designs or pedigrees from natural populations. This method can be used in a very general set of circumstances and is widely applicable to all IGEs, including maternal effects and other interactions among relatives.     

Does natural selection promote population divergence? A comparative analysis of population structure using amplified fragment length polymorphism markers and quantitative traits

Divergent natural selection is considered an important force in plant evolution leading to phenotypic differentiation between populations exploiting different environments. Extending an earlier greenhouse study of population differentiation in the selfing annual plant Senecio vulgaris, we estimated the degree of population divergence in several quantitative traits related to growth and life history and compared these estimates with those based on presumably neutral molecular markers (amplified fragment length polymorphisms; AFLPs). This approach allowed us to disentangle the effects of divergent selection from that of other evolutionary forces (e.g. genetic drift). Five populations were examined from each of two habitat types (ruderal and agricultural habitats). We found a high proportion of total genetic variance to be among populations, both for AFLP markers (phiST = 0.49) and for quantitative traits (range of QST: 0.26-0.77). There was a strong correlation between molecular and quantitative genetic differentiation between pairs of populations (Mantel's r = 0.59). However, estimates of population differentiation in several quantitative traits exceeded the neutral expectation (estimated from AFLP data), suggesting that divergent selection contributed to phenotypic differentiation, especially between populations from ruderal and agricultural habitats. Estimates of within-population variation in AFLP markers and quantitative genetic were poorly correlated, indicating that molecular marker data may be of limited value to predict the evolutionary potential of populations of S. vulgaris.     

Predicting Quantitative Traits With Regression Models for Dense Molecular Markers and Pedigree

The availability of genomewide dense markers brings opportunities and challenges to breeding programs. An important question concerns the ways in which dense markers and pedigrees, together with phenotypic records, should be used to arrive at predictions of genetic values for complex traits. If a large number of markers are included in a regression model, marker-specific shrinkage of regression coefficients may be needed. For this reason, the Bayesian least absolute shrinkage and selection operator (LASSO) (BL) appears to be an interesting approach for fitting marker effects in a regression model. This article adapts the BL to arrive at a regression model where markers, pedigrees, and covariates other than markers are considered jointly. Connections between BL and other marker-based regression models are discussed, and the sensitivity of BL with respect to the choice of prior distributions assigned to key parameters is evaluated using simulation. The proposed model was fitted to two data sets from wheat and mouse populations, and evaluated using cross-validation methods. Results indicate that inclusion of markers in the regression further improved the predictive ability of models. An R program that implements the proposed model is freely available.     

Footprints in time: comparative quantitative trait loci mapping of the pitcher-plant mosquito,Wyeomyia smithii

Identifying regions of the genome contributing to phenotypic evolution often involves genetic mapping of quantitative traits. The focus then turns to identifying regions of ‘major’ effect, overlooking the observation that traits of ecological or evolutionary relevance usually involve many genes whose individual effects are small but whose cumulative effect is large. Herein, we use the power of fully interfertile natural populations of a single species of mosquito to develop three quantitative trait loci (QTL) maps: one between two post-glacially diverged populations and two between a more ancient and a post-glacial population. All demonstrate that photoperiodic response is genetically a highly complex trait. Furthermore, we show that marker regressions identify apparently ‘non-significant’ regions of the genome not identified by composite interval mapping, that the perception of the genetic basis of adaptive evolution is crucially dependent upon genetic background and that the genetic basis for adaptive evolution of photoperiodic response is highly variable within contemporary populations as well as between anciently diverged populations.     

Inferring relatedness and heritability using molecular markers in radiata pine

A set of eight unlinked microsatellite markers was used to estimate relatedness among 355 individuals of a Pinus radiata breeding population. The average performance of open-pollinated progeny of each individual, for wood density, was considered to represent the phenotype of all 355 individuals. Marker-based estimates of relationship were compared with the pedigree-based coefficients of relationships. The phenotypic similarity among all pairs of individuals was regressed on marker-estimated relatedness to estimate the inheritance of wood density. The marker-based estimate of heritability was compared with that obtained using classical quantitative genetic methods. Overall, a low correlation (0.13) was observed between marker-based and pedigree-based estimates of relatedness. After discarding negative estimates of relatedness, the average coefficient of relationship among known groups of maternal half-sibs, full-sibs and unrelated individuals, increased from 0.24 to 0.29 (0.25 expected), from 0.43 to 0.48 (0.50 expected) and from –0.04 to 0.15 (0 expected), respectively. Marker-based and conventional estimates of heritability of wood density were 0.79 and 0.38, respectively. However, by using only marker loci with expected Hardy–Weinberg frequencies, marker-based estimate of heritability was 0.33, which is very similar to that obtained from conventional approaches. The use of molecular markers to understand quantitative genetic variation is discussed.     

Accuracy of dominant markers for estimation of relatedness and heritability in an experimental stand of Prosopis alba (Leguminosae)

The estimation of genetic components of phenotypic variance is based on the resemblance between relatives. In natural populations of most forest tree species without genealogical information, a possible alternative approach is the use of relatedness estimates obtained indirectly from molecular marker data. Heritability (h ²) is then estimated from the covariance of estimated relatedness and phenotypic resemblance. In a stand of Prosopis alba planted in 1991 in Argentina, relatedness was estimated for all individual pairs of trees by means of the information proceeding from 128 dominant markers (57 AFLPs and 71 ISSRs) and compared with estimates obtained from six microsatellite loci previously studied. We empirically compared the accuracy of different relatedness estimators based on dominant markers proposed by Lynch and Milligan (Mol Ecol 3:91–99, 1994), Hardy (Mol Ecol 12:1577–1588, 2003), Wang (Mol Ecol 13:3169–3178, 2004), and Ritland (Mol Ecol 14:3157–3165, 2005). Heritabilities of 13 quantitative traits were then estimated from the regression of pairwise phenotypic distances on pairwise relatedness according to Ritland (Genet Res 67:175–185, 1996a). Relatedness inferred from molecular markers was in all cases significantly correlated with actual relatedness, although Ritland's estimator showed the highest bias but the lowest variance. Dominant marker-based h ² estimates were evidently downwards biased and showed poor correlation with those based on family records. In conclusion, the use of dominant molecular markers evidently produces much greater underestimates of h ² than from using co-dominant ones, attributable to the lower accuracy in the indirect estimation of relatedness coefficient. Many traits with enough genetic variability as to respond readily to selection would remain undetected; only those with very high heritability would show significant h ² estimates.     

The influence of nonrandom extra‐pair paternity on heritability estimates derived from wild pedigrees

Quantitative genetic analysis is often fundamental for understanding evolutionary processes in wild populations. Avian populations provide a model system due to the relative ease of inferring relatedness among individuals through observation. However, extra‐pair paternity (EPP) creates erroneous links within the social pedigree. Previous work has suggested this causes minor underestimation of heritability if paternal misassignment is random and hence not influenced by the trait being studied. Nevertheless, much literature suggests numerous traits are associated with EPP and the accuracy of heritability estimates for such traits remains unexplored. We show analytically how nonrandom pedigree errors can influence heritability estimates. Then, combining empirical data from a large great tit (Parus major) pedigree with simulations, we assess how heritability estimates derived from social pedigrees change depending on the mode of the relationship between EPP and the focal trait. We show that the magnitude of the underestimation is typically small (<15%). Hence, our analyses suggest that quantitative genetic inference from pedigrees derived from observations of social relationships is relatively robust; our approach also provides a widely applicable method for assessing the consequences of nonrandom EPP.     

Geonomics: Forward-Time,Spatially Explicit,and Arbitrarily Complex Landscape Genomic Simulations

Understanding the drivers of spatial patterns of genomic diversity has emerged as a major goal of evolutionary genetics. The flexibility of forward-time simulation makes it especially valuable for these efforts, allowing for the simulation of arbitrarily complex scenarios in a way that mimics how real populations evolve. Here, we present Geonomics, a Python package for performing complex, spatially explicit, landscape genomic simulations with full spatial pedigrees that dramatically reduces user workload yet remains customizable and extensible because it is embedded within a popular, general-purpose language. We show that Geonomics results are consistent with expectations for a variety of validation tests based on classic models in population genetics and then demonstrate its utility and flexibility with a trio of more complex simulation scenarios that feature polygenic selection, selection on multiple traits, simulation on complex landscapes, and nonstationary environmental change. We then discuss runtime, which is primarily sensitive to landscape raster size, memory usage, which is primarily sensitive to maximum population size and recombination rate, and other caveats related to the model’s methods for approximating recombination and movement. Taken together, our tests and demonstrations show that Geonomics provides an efficient and robust platform for population genomic simulations that capture complex spatial and evolutionary dynamics.