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.     

Marker-inferred relatedness as a tool for detecting heritability in nature

This paper presents a perspective of how inferred relatedness, based on genetic marker data such as microsatellites or amplified fragment length polymorphisms (AFLPs), can be used to demonstrate quantitative genetic variation in natural populations. Variation at two levels is considered: among pairs of individuals within populations, and among pairs of subpopulations within a population. In the former, inferred pairwise relatedness, combined with trait measures, allow estimates of heritability 'in the wild'. In the latter, estimates of QST are obtained, in the absence of known heritabilities, via estimates of pairwise FST. Estimators of relatedness based on the 'Kronecker operator' are given. Both methods require actual variation of relationship, a rarely studied aspect of population structure, and not necessarily present. Some conditions for appropriate population structures in the wild are identified, in part through a review of recent studies.     

Consistency between marker- and genealogy-based heritability estimates in an experimental stand of Prosopis alba (Leguminosae)

Prosopis represents a valuable forest resource in arid and semiarid regions. Management of promising species requires information about genetic parameters, mainly the heritability (h(2)) of quantitative profitable traits. This parameter is traditionally estimated from progeny tests or half-sib analysis conducted in experimental stands. Such an approach estimates h(2) from the ratio of between-family/total phenotypic variance. These analyses are difficult to apply to natural populations of species with a long life cycle, overlapping generations, and a mixed mating system, without genealogical information. A promising alternative is the use of molecular marker information to infer relatedness between individuals and to estimate h(2) from the regression of phenotypic similarity on inferred relatedness. In the current study we compared h(2) of 13 quantitative traits estimated by these two methods in an experimental stand of P. alba, where genealogical information was available. We inferred pairwise relatedness by Ritland's method using six microsatellite loci. Relatedness and heritability estimates from molecular information were highly correlated to the values obtained from genealogical data. Although Ritland's method yields lower h(2) estimates and tends to overestimate genetic correlations between traits, this approach is useful to predict the expected relative gain of different quantitative traits under selection without genealogical information.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

INFERENCES ABOUT QUANTITATIVE INHERITANCE BASED ON NATURAL POPULATION STRUCTURE IN THE YELLOW MONKEYFLOWER,MIMULUS GUTTATUS

We used a nonmanipulative, marker-based method to study quantitative genetic inheritance in two habitats of a common monkeyflower population. The method involved regressing quantitative trait similarity on marker-estimated relatedness between individuals sampled in the field. We sampled 300 adult plants from each of two transects, one along a stream habitat and another through a meadow habitat. For each plant we measured 10 quantitative characters and assayed 10 polymorphic isozyme loci. In the meadow habitat, relatedness of plants within 1 m was moderate (r = 0.125, corresponding to half-sibs) as was actual variance of relatedness (V_r = 0.044). Significant heritabilities of 50–70% were found for corolla width and the fitness characters of flower number and plant weight. Genetic correlations were strongly positive, but sharing of environmental effects within 1 m was weak. In the stream habitat, levels of relatedness were lower and similar heritabilities were indicated. To detect dominance variance and the correlation of phenotypes due to shared inbreeding, we also estimated higher-order coefficients of relationship and inbreeding, but these did not significantly differ from zero. Laboratory-based estimates of heritability in the field were lower than the marker-based estimates, indicating that natural heritabilities and genetic correlations may be stronger than indicated by controlled studies.     

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.     

Realized Sampling Variances of Estimates of Genetic Parameters and the Difference between Genetic and Phenotypic Correlations

A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.     

Estimating genetic correlations in natural populations

Information on the genetic correlation between traits provides fundamental insight into the constraints on the evolutionary process. Estimates of such correlations are conventionally obtained by raising individuals of known relatedness in artificial environments. However, many species are not readily amenable to controlled breeding programmes, and considerable uncertainty exists over the extent to which estimates derived under benign laboratory conditions reflect the properties of populations in natural settings. Here, non-invasive methods that allow the estimation of genetic correlations from phenotypic measurements derived from individuals of unknown relatedness are introduced. Like the conventional approach, these methods demand large sample sizes in order to yield reasonably precise estimates, and special precautions need to be taken to eliminate bias from shared environmental effects. Provided the sample consists of at least 20% or so relatives, informative estimates of the genetic correlation are obtainable with sample sizes of several hundred individuals, particularly if supplemental information on relatedness is available from polymorphic molecular markers.     

Estimating genetic correlations based on phenotypic data: a simulation-based method

Knowledge of genetic correlations is essential to understand the joint evolution of traits through correlated responses to selection, a difficult and seldom, very precise task even with easy-to-breed species. Here, a simulation-based method to estimate genetic correlations and genetic covariances that relies only on phenotypic measurements is proposed. The method does not require any degree of relatedness in the sampled individuals. Extensive numerical results suggest that the propose method may provide relatively efficient estimates regardless of sample sizes and contributions from common environmental effects.     

Heritability of hemostasis phenotypes and their correlation with type 2 diabetes status in Mexican Americans

Hypercoagulation often occurs in type 2 diabetes, suggesting pleiotropy of the genes that influence disease liability and hemostasis-related phenotypes. To better understand the relationship between hemostasis and diabetes, we first used maximum-likelihood methods to estimate the relative contribution of additive genetic, measured environmental, and shared household effects to the normal variance of 16 hemostasis-related traits in 813 individuals participating in the San Antonio Family Heart Study. We estimated moderate to high heritabilities (0.20-0.60) for each phenotype. Von Willebrand factor (VWF), thrombin activatable fibrinolysis inhibitor, activated protein C (APC) ratio, factor V, and prothrombin time had heritabilities greater than 0.50. The correlation between type 2 diabetes status and the hemostasis-related traits was then partitioned into genetic and environmental components using bivariate variance-components methods. Significant (p < or = 0.05) positive genetic correlations (0.37-0.51) occurred with factors II and VIII, VWF, total protein S (tPS), and tissue factor pathway inhibitor. Significant negative genetic correlations were estimated for activated partial thromboplastin time (-0.49) and APC ratio (-0.38). By contrast, significant environmental correlations occurred only with factor II (-0.40) and tPS (-0.31). Our results suggest that genes are important contributors to the normal variation in hemostasis-related traits and that genes influencing hemostasis-related traits pleiotropically influence diabetes risk.     

Genetic and phenotypic correlations in a natural population of song sparrows

We estimated heritabilities, and genetic and phenotypic correlations between beak and body traits in the song sparrow ( Melospiza melodia ). We compared these estimates to values for the same traits in the Galápagos finches, Geospiza (Boag, 1983; Grant, 1983). Morphological variance is low in the song sparrow, and our results show that genetic and phenotypic correlations are considerably lower than correlations in the morphologically more variable Geospiza. Comparison using a larger sample of Galapagos populations confirms the existence of an association between variance and correlation for phenotypic values. We suggest two possible explanations for this association. First, most traits studied are functionally related, and the joint evolution of variance and correlation may have resulted from stabilizing selection about a line of optimal allometry between traits. Alternatively, introgression between populations and species could have caused correlation and variance to evolve jointly. Both selection and introgression were probably influential in producing the observed pattern, but it is not possible to estimate their relative importance with current data. Genetic and phenotypic correlations were correlated in the song sparrow, but heritabilities of traits varied greatly. As a result, the genetic variance-covariance matrix for traits is not simply a constant multiple of the phenotypic matrix. Evolutionary response to natural selection cannot, therefore, be predicted from the measurement of phenotypic characteristics alone.     

Delayed genetic effects of habitat fragmentation on the ecologically specialized Florida sand skink (Plestiodon reynoldsi)

Populations rarely show immediate genetic responses to habitat fragmentation, even in taxa that possess suites of traits known to increase their vulnerability to extinction. Thus conservation geneticists must consider the time scale over which contemporary evolutionary processes operate to accurately portray the effects of habitat isolation. Here, we examine the genetic impacts of fragmentation on the Florida sand skink Plestiodon reynoldsi, a sand swimming lizard that is highly adapted to the upland scrub habitat of central Florida. We studied fragments located on the southern Lake Wales Ridge, where human activity in the latter half of the 20th century has modified the natural patchiness of the landscape. Based on a relaxed molecular clock method, we estimate that sand skinks have persisted in this region for approximately 1.5 million years and that the time frame of human disturbance is equivalent to fewer than 30 skink generations. Using genotypes from eight microsatellite loci, we screened for molecular signatures of this disturbance by assessing congruence between population structure, as inferred from spatially-informed Bayesian assignment tests, and the current geography of scrub fragments. We also tested for potential intrapopulation genetic effects of inbreeding in isolated populations by comparing the average pairwise relatedness of individuals within fragments of different areas and isolation. Our results indicate that although some patches show a higher degree of relatedness than expected under random mating, the genetic effects of recent isolation are not evident in this part of the species’ range. We argue that this result is an artefact of a time-lag in the response to disturbance, and that species-typical demographic features may explain the genetic inertia observed in these populations.     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

STR markers for kinship analysis

The analysis of short tandem repeats is a widely used method to estimate relatedness between closely related populations or individuals. The AmpFlSTR PCR Amplification Kit has 15 highly variable autosomal markers of tetranucleotide repeats and is principally made to identify individuals and first- or second-degree relatives. However, in many studies one is searching for individuals who are related through more than one generation. We wanted to test whether the amplification kit can also be used to identify more distantly related individuals. Therefore we compared 16 different methods that calculate genetic distance with regard to each method's ability to cluster more distantly related individuals from two test families. Among all the tested methods Nei et al.'s (1983) DA distance performed well in clustering family members within a group of unrelated individuals for a broad range of scenarios. However, second-degree relatives were difficult to cluster with any of the examined methods when other family members were absent. With a simulation we further estimated how many markers would actually be needed to detect a certain degree of relatedness. According to this simulation, one would need at least 123 independent microsatellite markers to detect third-degree relatives with 90% probability. In conclusion, the 15 STR markers in the amplification kit are suitable for detecting only very closely related individuals or entire families.     

SSRs,SNPs and DArTs comparison on estimation of relatedness and genetic parameters’ precision from a small half-sib sample population of <Emphasis Type="Italic">Eucalyptus grandis</Emphasis>

Simple sequence repeats (SSR) are the most widely used molecular markers for relatedness inference due to their multi-allelic nature and high informativeness. However, there is a growing trend toward using high-throughput and inter-specific transferable single-nucleotide polymorphisms (SNP) and Diversity Arrays Technology (DArT) in forest genetics owing to their wide genome coverage. We compared the efficiency of 15 SSRs, 181 SNPs and 2816 DArTs to estimate the relatedness coefficients, and their effects on genetic parameters’ precision, in a relatively small data set of an open-pollinated progeny trial of Eucalyptus grandis (Hill ex Maiden) with limited relationship from the pedigree. Both simulations and real data of Eucalyptus grandis were used to study the statistical performance of three relatedness estimators based on co-dominant markers. Relatedness estimates in pairs of individuals belonging to the same family (related) were higher for DArTs than for SNPs and SSRs. DArTs performed better compared to SSRs and SNPs in estimated relatedness coefficients in pairs of individuals belonging to different families (unrelated) and showed higher ability to discriminate unrelated from related individuals. The likelihood-based estimator exhibited the lowest root mean squared error (RMSE); however, the differences in RMSE among the three estimators studied were small. For the growth traits, heritability estimates based on SNPs yielded, on average, smaller standard errors compared to those based on SSRs and DArTs. Estimated relatedness in the realized relationship matrix and heritabilities can be accurately inferred from co-dominant or sufficiently dense dominant markers in a relatively small E. grandis data set with shallow pedigree.     

Genetic architecture of knee radiographic joint space in healthy young adults

Evidence of a significant genetic component to the age-related degenerative joint disease osteoarthritis has been established, but the nature of genetic influences on normal joint morphology in healthy individuals remains unclear. Following up on our previous findings on the influence of body habitus on phenotypic variation in knee joint space [Duren et al., Human Biology 78:353-364 (2006)], the objective of the current study was to estimate the heritability of radiographic joint space in the knees of healthy young adults from a community-based sample of families. A sample of 253 subjects (mean age = 18.02 years) from 87 randomly ascertained nuclear and extended families was examined. Joint width (JW) and minimum joint space in the medial (MJS) and lateral (LJS) knee compartments were measured. A maximum-likelihood variance components method was used to estimate the heritability of MJS, LJS, and JW. Covariate effects of age, sex, age-by-sex interactions, stature, weight, and BMI were simultaneously estimated. Genetic correlation analyses were then conducted to examine relationships between trait pairs. MJS, LJS, and JW were each significantly heritable (p < 0.001), with heritabilities of 0.52, 0.53, and 0.63, respectively. The genetic correlation between MJS and LJS was not significantly different from 1. Genetic correlations between each joint space measure and JW were not significantly different from 0. This study demonstrates a significant genetic component to radiographic knee joint space during young adulthood in healthy subjects. This suggests that there are specific but as yet unidentified genes that influence the morphology of healthy articular cartilage, the target tissue of osteoarthritis. Genetic correlation analyses indicate complete pleiotropy between MJS and LJS but genetic independence of joint space and JW.     

Laboratory Estimates of Heritabilities and Genetic Correlations in Nature

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.     

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.     

Estimating genetic correlations in natural populations in the absence of pedigree information: accuracy and precision of the Lynch method

Usually, genetic correlations are estimated from breeding designs in the laboratory or greenhouse. However, estimates of the genetic correlation for natural populations are lacking, mostly because pedigrees of wild individuals are rarely known. Recently Lynch (1999) proposed a formula to estimate the genetic correlation in the absence of data on pedigree. This method has been shown to be particularly accurate provided a large sample size and a minimum (20%) proportion of relatives. Lynch (1999) proposed the use of the bootstrap to estimate standard errors associated with genetic correlations, but did not test the reliability of such a method. We tested the bootstrap and showed the jackknife can provide valid estimates of the genetic correlation calculated with the Lynch formula. The occurrence of undefined estimates, combined with the high number of replicates involved in the bootstrap, means there is a high probability of obtaining a biased upward, incomplete bootstrap, even when there is a high fraction of related pairs in a sample. It is easier to obtain complete jackknife estimates for which all the pseudovalues have been defined. We therefore recommend the use of the jackknife to estimate the genetic correlation with the Lynch formula. Provided data can be collected for more than two individuals at each location, we propose a group sampling method that produces low standard errors associated with the jackknife, even when there is a low fraction of relatives in a sample.     

Indirect genetic estimates of breeding population size in the polyploid green sturgeon (Acipenser medirostris)

The utility of genetic measures for kinship reconstruction in polysomic species is not well evaluated. We developed a framework to test hypotheses about estimating breeding population size indirectly from collections of outmigrating green sturgeon juveniles. We evaluated a polysomic dataset, in allelic frequency and phenotypic formats, from green sturgeon to describe the relationship among known progeny from experimental families. The distributions of relatedness values for kin classes were used for reconstructing green sturgeon pedigrees from juveniles of unknown relationship. We compared three rarefaction functions that described the relationship between the number of kin groups and number of samples in a pedigree to estimate the annual abundance of spawners contributing to the threatened green sturgeon Southern Distinct Population Segment in the upper Sacramento River. Results suggested the estimated abundance of breeding green sturgeon remained roughly constant in the upper Sacramento River over a 5‐year period, ranging from 10 to 28 individuals depending on the year and rarefaction method. These results demonstrate an empirical understanding for the distribution of relatedness values among individuals is a benefit for assessing pedigree reconstruction methods and identifying misclassification rates. Monitoring of rare species using these indirect methods is feasible and can provide insight into breeding and ontogenetic behaviour. While this framework was developed for specific application to studying fish populations in a riverscape, the framework could be advanced to improve genetic estimation of breeding population size and to identify important breeding habitats of rare species when combined with finer‐scaled sampling of offspring.