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.     

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.     

QUANTITATIVE GENETICS OF SURVIVAL AND GROWTH IN IMPATIENS CAPENSIS

When variation in life-history characters is caused by many genes of small effect, then quantitative-genetic parameters may quantify constraints on rate and direction of microevolutionary change. I estimated heritabilities and genetic correlations for 16 life-history and morphological characters in two populations of Impatiens capensis, a partially self-pollinating herbaceous annual. The Madison population had little or no additive genetic variance for any of these characters, while the Milwaukee population had significant narrowsense heritabilities and genetic correlations for several traits, including adult size, which is highly correlated with fitness. All genetic correlations among fitness components were positive, hence there is no evidence for antagonistic pleiotropy among these traits. Dissimilarity of heritabilities in the two populations supports theoretical predictions that long-term changes in genetic variance-covariance patterns may occur when population sizes are small and selection is strong, as may occur in many plant species.     

EVOLUTIONARY PREDICTABILITY IN NATURAL POPULATIONS: DO MATING SYSTEM AND NONADDITIVE GENETIC VARIANCE INTERACT TO AFFECT HERITABILITIES IN PLANTAGO LANCEOLATA?

Quantitative genetics has been an immensely powerful tool in manipulating the phenotypes of domesticated plants and animals. Much of the predictive power of quantitative genetics depends on the breeder's control over the context in which phenotype and mating are being expressed. In the natural world, these contexts are often difficult to describe, let alone control. We are left, therefore, with a poor understanding of the limits of quantitative genetics in natural populations. One of the crucial contextual elements for assessing breeding value is the genetic background in which an individual's genes are being assessed. When interacting genes are polymorphic within a population, the degree of mating among relatives can influence the correlations among mates and the predictions of a response to selection. Population structure can strongly influence the degree to which dominance and epistasis influences additive genetic variance and heritability. The extent of inbreeding can also influence heritabilities through its effect on the environmental component of phenotypic variance. The applicability of standard quantitative genetic breeding designs to the measurement of heritabilities in natural populations therefore depends in part on: (1) the mating system of the population; and (2) the importance of gene interactions in determining phenotypic variation. We tested for an effect of mating structure on the partitioning of phenotypic variance and heritability by comparing two breeding designs in a common environment. Both breeding designs used 139 pollen parents taken from mapped locations in a population of Plantago lanceolata L., and crossed to 280 seed parents from the same population. One design was random-mating, the second was biased toward near-neighbor matings to an extent determined by field measure of pollen-mediated gene flow distances. The offspring were grown randomly mixed in a common garden. Nine traits were measured: central corm diameter, number of leaves, area of the most recently fully expanded leaf, density of hairs (cm^-2) on the leaves, dry weight per unit leaf area, photosynthetic capacity, transpiration rates, water use efficiency, and reproductive dry weight. Heritabilities and variance components from the two designs were compared using randomization tests. None of the variance components or the heritabilities differed significantly between breeding designs at the 0.05 level. The test could distinguish differences between the heritabilities measured in the two breeding designs as small as 0.11, on average. Thus, for the degree of inbreeding normally exhibited in P. lanceolata there is insufficient gene interaction present within populations to influence the partitioning of variance between additive and nonadditive components or to influence heritability estimates to a meaningful extent. We suggest that for Plantago other sources of variation in heritability estimates, such as maternal effects and genotype × environment interactions, are more important influences than the interaction between inbreeding and gene interactions, and standard heritability estimate based on random breeding is as accurate as one taking the natural mating structure into account.     

On the use of large marker panels to estimate inbreeding and relatedness: empirical and simulation studies of a pedigreed zebra finch population typed at 771 SNPs

In recent years there has been a dramatic increase in the availability of high density genetic marker data for both model and non‐model organisms. A potential application of these data is to infer relatedness in the absence of a complete pedigree. Using a marker panel of 771 SNPs genotyped in three generations of an extensive zebra finch pedigree, correlations between pedigree relatedness and seven marker‐based estimates of relatedness were examined, as was the relationship between heterozygosity and inbreeding. Although marker‐based and pedigree relatedness were highly correlated, the variance in estimated relatedness was high. Further, the correlation between heterozygosity and inbreeding was weak, even though mean inbreeding coefficient is typical of that seen in wild vertebrate pedigrees; the weak relationship was in part due to the small variance in inbreeding in the pedigree. Our data suggest that using marker information to reconstruct the pedigree, and then calculating relatedness from the pedigree, is likely to give more accurate relatedness estimates than using marker‐based estimators directly.     

Estimates of genetic parameters of certain characters in Hevea brasiliensis

Summary Heritability estimates of five quantitative characters, namely, yield, girth, girth increment, virgin bark and renewed bark thickness, of the breeding Phase III Hevea families have been obtained by variance component analyses. In general, the combined heritability estimates for various characters were low to moderate. The heritabilities of these characters based on female variance components, however, were high, suggesting that considerable improvement of each of the characters could be achieved in properly designed experiments.Estimates of heritability for average yields (Range: 0.11–0.34) over different years showed that the first three years' yield was adequate for predicting estimates of genetic variance for the average of five years' yield.Correlation studies on yield with other characters indicated considerable influence of environment, with genetic correlations accounting for about 0.07 to 0.36 in the characters studied.Expected direct response to selection in yield and correlated response in yield to selection for girth at opening and virgin bark thickness have been calculated using three arbitrary values of selection intensity. The efficiency of the correlated response was found to be approximately half that of the direct response. However, the indirect selection for yield using virgin bark thickness appeared to be more favourable than that using the girth at opening favoured by earlier workers.     

Comparison of genetic parameters from marker-based relationship, sibship, and combined models in Scots pine multi-site open-pollinated tests

Nine microsatellite DNA markers (simple sequence repeats, SSRs) were used to estimate pairwise relationships among 597 Scots pine (Pinus sylvestris) trees as well as to generate a sibship structure for quantitative genetic parameters’ estimation comparison. The studied trees were part of an open-pollinated progeny test of 102 first-generation parents. Three methods were used to estimate variance components and heritabilities, namely, structured pedigree (half- and full-sib), marker-based pairwise relationships (four pairwise estimators), and a combined pedigree and marker-based relationship. In each of the three methods, the same animal model was used to compute variances except when marker-based relationship was used wherein we substituted the average numerator relationship matrix (i.e., pedigree-based matrix) with that computed based on markers’ pairwise relationships. Our results showed a high correlation in estimated breeding values between the pedigree (full-sib) and the combined marker-pedigree estimates. The marker-based relationship method produced high correlations when individual site data were analyzed. In contrast, the marker-based relationship method resulted in a significant decrease in both variance estimation and their standard errors which were in concordance with earlier published results; however, no estimates were produced when across-site analyses were attempted. We concluded that the combined pedigree method is the best approach as it represents the historical (pairwise) and contemporary (pedigree) relationships among the tested individuals, a situation that cannot be attained by any of the used methods individually. This method is dependent on the number and informativeness of the markers used.     

Relatedness measured by oligonucleotide probe DNA fingerprints and an estimate of the mating system of Sea Lavender (Limonium carolinianum)

Using DNA fingerprint markers within species and populations of wild plants requires information on the relationship between fingerprint similarity and relatedness. We identified a hypervariable marker based on oliog(GATA)₄-hybridization of DpnII-cut genomic DNA from Sea Lavender (Limonium carolinianum). Banding patterns were somatically stable and highly variable among unrelated individuals. Band molecular-weight sizing errors (as a percent of band molecular weight) were estimated at 0.44%±0.003 within gels and 0.76%±0.964 between gels. Band sizing errors defined a 99% confidence bin of ±0.95% (1.90% total) of molecular weight. Band-sharing estimates were based on this bin size and on variance estimates that compensate for non-independent comparisons. Band-sharing among nine unrelated individuals () was 0.198±0.O11. Experimental pollinations designed to produce selfed, fulland half-sib progeny groups led to five selfed progeny groups and no outcrossed progeny (mean band-sharing, ovS=0.468±0.074). A linear regression between band-sharing (S) and relatedness (r) assuming 17% inbreeding was r=0.006+0.914*S (R²=0.973) and established the maximum amount of inbreeding. ovS(0.392±0.022) estimated from wild pollinated seeds from four maternal families was intermediate to unrelated individuals and experimental selfed progeny, giving evidence for mixed mating in wild plants. More extensive plant pedigrees with known levels of inbreeding will be needed to measure variation in the relationship between S and r among populations and families.     

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.     

Potential for selection on plants for water-use efficiency as estimated by carbon isotope discrimination

Water-use efficiency is thought to be related to plant performance and natural selection for plants in arid habitats, based on a general expectation that increased water-use efficiency is associated with decreased carbon gain and biomass accumulation. Using leaf carbon isotope discrimination Δ to determine integrated water-use efficiency, we estimated genetic variance for, and examined the relationships among Δ, biomass, and gas exchange characters for full-sibling families of the woody shrub, Chrysothamnus nauseosus, grown from seed collected at Tintic, Utah. In both well-watered greenhouse and common garden experiments, and water-limited common garden experiments, there were significant family differences for Δ, biomass, and morphological characters, indicating a potential for genetic change in response to selection. However, estimates of broad-sense heritabilities for Δ were low, indicating that the rate of change in response to selection would be relatively slow. This was consistent with the large amount of phenotypic plasticity observed for Δ as it differed with water treatment and year in the garden experiment. Phenotypically, aboveground biomass and Δ were negatively correlated within the well-watered treatments (i.e., more water-use efficient plants were larger), not correlated within the water-limited treatment, and positively correlated for combined well-watered and water-limited garden treatments, suggesting that variation in both photosynthetic capacity and stomatal limitation contribute to the variation in Δ. In contrast to the phenotypic correlations, genetic correlations for biomass and Δ were consistently negative within each treatment, and selection for higher water-use efficiency through low Δ for C. nauseosus plants in this population would tend to shift populations toward larger plants. For C. nauseosus, increased water-use efficiency is not necessarily associated with decreased carbon gain.     

Estimating relatedness and inbreeding using molecular markers and pedigrees: the effect of demographic history

Estimates of inbreeding and relatedness are commonly calculated using molecular markers, although the accuracy of such estimates has been questioned. As a further complication, in many situations, such estimates are required in populations with reduced genetic diversity, which is likely to affect their accuracy. We investigated the correlation between microsatellite‐ and pedigree‐based coefficients of inbreeding and relatedness in laboratory populations of Drosophila melanogaster that had passed through bottlenecks to manipulate their genetic diversity. We also used simulations to predict expected correlations between marker‐ and pedigree‐based estimates and to investigate the influence of linkage between loci and null alleles. Our empirical data showed lower correlations between marker‐ and pedigree‐based estimates in our control (nonbottleneck) population than were predicted by our simulations or those found in similar studies. Correlations were weaker in bottleneck populations, confirming that extreme reductions in diversity can compromise the ability of molecular estimates to detect recent inbreeding events. However, this result was highly dependent on the strength of the bottleneck and we did not observe or predict any reduction in correlations in our population that went through a relatively severe bottleneck of N = 10 for one generation. Our results are therefore encouraging, as molecular estimates appeared robust to quite severe reductions in genetic diversity. It should also be remembered that pedigree‐based estimates may not capture realized identity‐by‐decent and that marker‐based estimates may actually be more useful in certain situations.     

Estimating heritabilities and genetic correlations with marker-based methods: an experimental test in Mimulus guttatus

The calculation of heritabilities and genetic correlations, which are necessary for predicting evolutionary responses, requires knowledge about the relatedness between individuals. This information is often not directly available, especially not for natural populations, but can be inferred by using molecular markers such as allozymes. Several methods based on inferred relatedness from marker data have been developed to estimate heritabilities and genetic correlations in natural populations. Most methods use maximum-likelihood procedures to assign pairs or groups of individuals to predefined discrete relatedness classes (e.g., half sibs and unrelated individuals). The Ritland method, on the other hand, uses method of moments estimators to estimate pairwise relatedness among individuals as continuous values. We tested both the Ritland method and a maximum-likelihood method by applying them to a greenhouse population consisting of seed families of the herb Mimulus guttatus and comparing the results to the ones from a frequently used standard method based on half-sib families. Estimates of genetic correlations were far from accurate, especially when we used the Ritland method. However, this study shows that even with a few variable allozyme loci, it is possible to get qualitatively good indications about the presence of heritable genetic variation from marker-based methods, even though both methods underestimated it.     

Age trends in genetic parameters for growth and wood density in <Emphasis Type="Italic">Eucalyptus globulus</Emphasis>

Genetic parameters for stem diameter and wood density were compared at selection (4–5 years) and harvest (16–17 years) age in an open-pollinated progeny trial of Eucalyptus globulus in Tasmania (Australia). The study examined 514 families collected from 17 subraces of E. globulus. Wood density was assessed on a subsample of trees indirectly using pilodyn penetration at both ages and directly by core basic density at harvest age. Significant additive genetic variance and narrow-sense heritabilities ( h_\textop² h_{\text{op}}^2 ) were detected for all traits. Univariate and multivariate estimates of heritabilities were similar for each trait except harvest-age diameter. Comparable univariate estimates of selection- and harvest-age heritabilities for diameter masked changes in genetic architecture that occurred with stand development, whereby the loss of additive genetic variance through size-dependent mortality was countered by the accentuation of additive genetic differences among survivors with age. Regardless, the additive genetic (r _a) and subrace (r _s) correlations across ages were generally high for diameter (0.95 and 0.61, respectively) and pilodyn penetration (0.77 and 0.96), as were the correlations of harvest-age core basic density with selection- and harvest-age pilodyn (r _a −0.83, −0.88; r _s −0.96, −0.83). While r _s between diameter and pilodyn were close to zero at both ages, there was a significant change in r _a from adverse at selection age (0.25) to close to zero (−0.07) at harvest age. We argue that this change in the genetic correlation reflects a decoupling of the genetic association of growth and wood density with age. This result highlights the need to validate the use of selection-age genetic parameters for predicting harvest-age breeding values.     

Molecular and pedigree measures of relatedness provide similar estimates of inbreeding depression in a bottlenecked population

Individual‐based estimates of the degree of inbreeding or parental relatedness from pedigrees provide a critical starting point for studies of inbreeding depression, but in practice wild pedigrees are difficult to obtain. Because inbreeding increases the proportion of genomewide loci that are identical by descent, inbreeding variation within populations has the potential to generate observable correlations between heterozygosity measured using molecular markers and a variety of fitness related traits. Termed heterozygosity‐fitness correlations (HFCs), these correlations have been observed in a wide variety of taxa. The difficulty of obtaining wild pedigree data, however, means that empirical investigations of how pedigree inbreeding influences HFCs are rare. Here, we assess evidence for inbreeding depression in three life‐history traits (hatching and fledging success and juvenile survival) in an isolated population of Stewart Island robins using both pedigree‐ and molecular‐derived measures of relatedness. We found results from the two measures were highly correlated and supported evidence for significant but weak inbreeding depression. However, standardized effect sizes for inbreeding depression based on the pedigree‐based kin coefficients (k) were greater and had smaller standard errors than those based on molecular genetic measures of relatedness (RI), particularly for hatching and fledging success. Nevertheless, the results presented here support the use of molecular‐based measures of relatedness in bottlenecked populations when information regarding inbreeding depression is desired but pedigree data on relatedness are unavailable.     

Correlated pedigree and molecular estimates of inbreeding and their ability to detect inbreeding depression in the Icelandic sheepdog, a recently bottlenecked population of domestic dogs

We examine the relationship of the inbreeding coefficient (f) and molecular estimates of inbreeding (IR, sMLH) in the Icelandic sheepdog. The breed experienced a severe genetic bottleneck and near extinction in the last century. Molecular estimates and the inbreeding coefficient are significantly correlated despite the moderate number of markers and individuals used in this study. This is most likely an effect of the extreme relatedness and relatively high variance in individual inbreeding coefficients in the population. There is a significant relationship between inbreeding (f) and the occurrence of hip dysplasia. However, the molecular measures did not detect hip dysplasia as an inbreeding effect.     

Estimates of relatedness and inbreeding in goose strains from DNA fingerprints

The purpose of this study was to determine if DNA fingerprints (DFPs) could be used to estimate relatedness and inbreeding of strains of geese and to compare three methods of calculating relatedness indices. Strains included a control and selected strain from each of the Chinese and Synthetic (Chinese, Hungarian and Pilgrim) breeds. DFP patterns for each strain were based on individual DNA samples from six females, or on pooled DNA from 15 females different from those used for individual samples. Three relatedness indices were used, namely, genetic distance, modified Rogers distance and band sharing. All relatedness indices showed a closer relationship of strains within than between breeds. Correlation coefficients among relatedness indices were higher based on pooled DNA (r ≥|0·97|) than those based on individual DNA (r ≥|0·741). Inbreeding estimates were higher for selected compared with control strains. It appears that the use of DFPs to estimate relatedness, regardless of index used, and inbreeding can be valuable for studying geese where there is a limited breeding history.     

Cross prediction studies on spring barley

Summary Additive genetic, dominance genetic and environmental correlations between pairs of agronomically important characters in five spring barley crosses were calculated from estimates of the components of variance and covariance, obtained by Triple Test Cross analysis. Phenotypic correlations were calculated from the Triple Test Cross family means and compared to the additive genetic correlations. Phenotypic correlations were generally lower than the additive genetic correlations and, occasionally, of different sign. The highest phenotypic correlations between single plant yield and its components were found with number of tillers whereas these were the lowest additive genetic correlations, thousand grain weight giving the highest. High dominance genetic correlations were found between single plant yield and both grain number and thousand grain weight thus indirect early generation selection for single plant yield using these two characters would be ineffective. Additive and dominance genetic correlations confirm association of the erectoides dwarfing gene with low thousand grain weight and plant yield.     

Inheritance of size and shape in a natural population of collared flycatchers,Ficedula albicollis

Four external skeletal and three feather dimensions were measured on adult collared flycatchers (Ficedula albicollis) and their adult offspring. By using mid-offspring-midparent regressions, all traits were found to be heritable with an arithmetic mean heritability of 0.46. Heritability estimates from full-sib analyses were about 1.5 times higher (mean 0.67), indicating that variation in traits was affected by shared nest environment among full-sibs. The overall body size as measured by principal component one (PC1) was found to be heritable (h² = 0.40). However, this multivariate measure of heritability was not significant in offspring-father comparison, while highly so in offspring-mother comparison (h² = 0.60). Low offspring-father resemblance was evident also in univariate estimates of heritability. Possible causes of this (extra-pair copulations, maternal effects, sex-linked variance) are discussed. Genetic correlations among seven traits were estimated to be low (mean 0.22), and of similar magnitude or higher than phenotypic correlations (mean 0.18). All genetic correlations were positive. Genetic and phenotypic correlations as well as covariances were fairly similar to each other (r = 0.85 and r = 0.87, respectively). Environmental correlations did not follow the pattern of genetic correlations (r = 0.11), but were more similar to phenotypic correlations (r = 0.60). Given the low genetic correlations and moderate heritabilities, the overall conclusion is that the external morphology of collared flycatchers is largely under additive genetic control and that there is a strong potential for evolutionary change in morphology even under complex multivariate selection.     

Multivariate selection under adverse genetic correlations: impacts of population sizes and selection strategies on gains and coancestry in forest tree breeding

We examined gene models for two traits with and without antagonistic pleiotropy using a locus-based simulation model to investigate the effects of different population sizes, heritabilities and economic weights, using index selection, and index selection with optimum selection (OS), over 10 generations. Gene models included additive and dominance gene action, with equal and varying initial allele frequencies with and without pleiotropy for a fixed level of resources (i.e. founder sizes each generation of 40, 80 and 160 with progeny arrays that totaled 800 per generation). Pleiotropy (with an initial r _g of −0.5), reduced gain by ~8–10% when heritabilities for both traits were the same (0.2), relative to non-pleiotropic cases. When traits had different heritabilities (i.e. 0.2 and 0.4), gains in the lower heritability trait were substantially lower, especially with pleiotropy present. In general, OS with slightly larger population sizes could offset losses in gain, but rarely overrode the large effects of different heritabilities or economic weights. Pleiotropy increased response variance among traits, which was magnified when heritabilities were different. Identifying an appropriate weight on relatedness in the OS process is important to manage coancestry expectations around the loss of alleles (or fixation of recessive alleles) and to minimise response variance. The dynamics of selection intensity, drift, rate of coancestry build-up, response variance, etc. are complex for multi-trait selection; however, a few economically viable strategies could reduce the adverse effects of selecting against genetic correlations without drastically impairing gain.