Evolutionary potential in the wild: more than meets the eye

The genus Aquilegia consists of 60–70 perennial plant species widely distributed throughout the northern hemisphere. Its flowers have a delicate and ornamental appearance that makes them a favourite of gardeners. In this genus, adaptive radiations for both floral and vegetative traits have occurred. These adaptive radiations, and the key phylogenetic placement of Aquilegia between Arabidopsis and rice, make this genus a ‘model system’ for plant evolution ( Kramer 2009 ). In this issue, Castellanos et al. (2011) use a marker‐based method to infer heritability for floral and vegetative traits in two Aquilegia species. Layered on top of this are estimates of the strength of natural selection. This novel joint estimation of heritability and selection in the wild showed that vegetative traits, compared to floral traits, have the highest evolutionarily potential. Evolutionary potential is the most important quantity to measure in wild populations. It combines inheritance and strength of selection and predicts the potential for populations to adapt to changing environments. The combination of molecular techniques with species in natural environments makes this work a model for molecular ecological investigations.     

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.     

How to use molecular marker data to measure evolutionary parameters in wild populations

Estimating the genetic basis of phenotypic traits and the selection pressures acting on them are central to our understanding of the evolution and conservation of wild populations. However, obtaining such evolutionary-related parameters is not an easy task as it requires accurate information on both relatedness among individuals and their breeding success. Polymorphic molecular markers are very useful in estimating relatedness between individuals and parentage analyses are now extensively used in most taxa. The next step in the application of molecular data to wild populations is to use them to derive estimates of evolutionary-related parameters for quantitative traits, such as quantitative genetic parameters (e.g. heritability, genetic correlations) and measures of selection (e.g. selection gradients). Despite their great appeal and potential, the optimal use of molecular tools is still debated and it remains unclear how they should best be used to obtain reliable estimates of evolutionary parameters in the wild. Here, we review the methods available for estimating quantitative genetic and selection parameters and discuss their merits and shortcomings, to provide a tool that summarizes the potential uses of molecular data to obtain such parameters in wild populations.     

The quantitative genetics of floral trait variation in Lobelia: potential constraints on adaptive evolution

Abstract Although pollinator-mediated natural selection has been measured on many floral traits and in many species, the extent to which selection is constrained from producing optimal floral phenotypes is less frequently studied. In particular, negative correlations between flower size and flower number are hypothesized to be a major constraint on the evolution of floral displays, yet few empirical studies have documented such a trade-off. To determine the potential for genetic constraints on the adaptive evolution of floral displays, I estimated the quantitative genetic basis of floral trait variation in two populations of Lobelia siphilitica . Restricted maximum likelihood (REML) analyses of greenhouse-grown half-sib families were used to estimate genetic variances and covariances for flower number and six measures of flower size. There was significant genetic variation for all seven floral traits in both populations. Flower number was negatively genetically correlated with four measures of flower size in one population and three measures in the other. When the genetic variance-covariance matrices were combined with field estimates of phenotypic selection gradients, the predicted multivariate evolutionary response was less than or opposite in sign to the selection gradient for flower number and five of six measures of flower size, suggesting genetic constraints on the evolution of these traits. More generally, my results indicate that the adaptive evolution of floral displays can be constrained by tradeoffs between flower size and number, as has been assumed by many theoretical models of floral evolution.     

Multilevel selection 1: Quantitative genetics of inheritance and response to selection

Interaction among individuals is universal, both in animals and in plants, and substantially affects evolution of natural populations and responses to artificial selection in agriculture. Although quantitative genetics has successfully been applied to many traits, it does not provide a general theory accounting for interaction among individuals and selection acting on multiple levels. Consequently, current quantitative genetic theory fails to explain why some traits do not respond to selection among individuals, but respond greatly to selection among groups. Understanding the full impacts of heritable interactions on the outcomes of selection requires a quantitative genetic framework including all levels of selection and relatedness. Here we present such a framework and provide expressions for the response to selection. Results show that interaction among individuals may create substantial heritable variation, which is hidden to classical analyses. Selection acting on higher levels of organization captures this hidden variation and therefore always yields positive response, whereas individual selection may yield response in the opposite direction. Our work provides testable predictions of response to multilevel selection and reduces to classical theory in the absence of interaction. Statistical methodology provided elsewhere enables empirical application of our work to both natural and domestic populations.     

Plasticity and environment-specific covariances: an investigation of floral-vegetative and within flower correlations

Floral traits are commonly thought to be more canalized than vegetative ones. In addition, floral and vegetative traits are hypothesized to be genetically decoupled, enabling vegetative structures to respond plastically to environmental heterogeneity, and to evolve in response to selection without disrupting the reproductive function of flowers. To test these hypotheses, we evaluate the genetic architecture of floral and vegetative traits in natural populations of Arabidopsis thaliana raised under variable light-quality environments. Plants were grown either under high or low ratios of red to far-red (R:FR) light, an aspect of light quality that varies with neighbor proximity and regulates competitive shade-avoidance responses. Across environments, we detected significant genetic variation for the average expression of all measured floral traits (petal length and width, stamen length, pistil length, stigma-anther separation, and exsertion of both the stamen and pistil beyond the corolla). Light quality significantly influenced the absolute size of several floral traits as well as the allometry (i.e., relative scaling) of all floral traits, and genotypes differed in the plasticity of floral traits to the light treatments. Exposure to low relative to high R:FR resulted in significantly greater elongation in the vegetative trait, petiole length, and genotypes again differed in the plasticity of this trait to R:FR. Consistent with prior studies, most floral traits were less plastic than the vegetative trait; herkogamy (i.e., stigma-anther separation) was the exception and expressed more variable trait values across environments than petiole length, apparently as a consequence of the independent responses of stamens and pistils. Flowers also showed strong phenotypic integration; genotypic correlations were significantly positive among floral traits within each light treatment. Although floral-vegetative correlations were not significant in the high R:FR light treatment, significant correlations were detected between petal traits, pistil length, and petiole length under low R:FR, in contrast to the widely held hypothesis that floral and vegetative traits are genetically independent. Finally, we detected selection for reduced herkogamy in the low R:FR light treatment. The observed correlation between functional trait groups suggest that vegetative plasticity may affect the expression of floral traits in some environments, and that environment-specific constraints may exist on the evolution of floral and vegetative traits.     

The role of genetic constraints on the diversification of Iberian taxa of the genus Aquilegia (Ranunculaceae)

The microevolutionary process of adaptive phenotypic differentiation of quantitative traits between populations or closely‐related taxa depends on the response of populations to the action of natural selection. However, this response can be constrained by the structure of the matrix of additive genetic variance and covariance between traits in each population ( G matrix). In the present study, we obtained additive genetic variance and narrow sense heritability for 25 floral and vegetative traits of three subspecies of Aquilegia vulgaris, and one subspecies of Aquilegia pyrenaica through a common garden crossing experiment. For two vegetative and one floral trait, we also obtained the G matrix and genetic correlations between traits in each subspecies. The amount of genetic variation available in wild populations is not responsible for the larger differentiation of vegetative than floral traits found in this group of columbines. However, the low heritability of some traits constrained their evolution because phenotypic variability among taxa was larger for traits with larger heritability. We confirmed that the process of diversification of the studied taxa involved shifts in the G matrix, mainly determined by changes in the genetic covariance between floral and vegetative traits, probably caused by linkage disequilibrium in narrow endemic taxa. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 111 , 252–261.     

Genetic constraints on phenotypic evolution in Nigella (Ranunculaceae)

The present investigation examines the role of genetic constraints in shaping evolutionary change in the Nigella arvensis species complex. Parent-offspring analyses of two populations of N. degenii demonstrated high heritabilities for a wide range of vegetative and floral characters, indicating a great potential for further adaptive change. The populations differed significantly in the heritability for leaf length and in the genetic correlation between plant height and peduncle length, suggesting that these populations would respond differently to identical selection pressures. There was a tendency for large-scale diversity to extrapolate within-population variability, at least for the floral trait associations, while genetic data from a segregating F3 hybrid population indicated stability in the correlation structure across two environments. On the basis of hybrid data, I propose that inbreeding effects and pleiotropic relationships with leaf size may have facilitated the reduction in floral morphology accompanying the evolution of autogamy in related taxa.     

Can indirect selection and genetic context contribute to trait diversification? A transition‐probability study of blossom‐colour evolution in two genera

Darwin recognized that biological diversity has accumulated as a result of both adaptive and nonadaptive processes. Very few studies, however, have addressed explicitly the contribution of nonadaptive processes to evolutionary diversification, and no general procedures have been established for distinguishing between adaptive and nonadaptive processes as sources of trait diversity. I use the diversification of flower colour as a model system for attempting to identify adaptive and nonadaptive causes of trait diversification. It is widely accepted that variation in flower colour reflects direct, adaptive response to divergent selective pressures generated by different pollinators. However, diversification of flower colour may also result from the effects of nonadaptive, pleiotropic relationships with vegetative traits. Floral pigments that have pleiotropic relationships to vegetative pigments may evolve and diversify in at least two nonadaptive ways. (1) Indirect response to selection on the pleiotropically related nonfloral traits may occur (indirect selection). (2) Divergent evolution in response to parallel selective pressures (e.g. selection by pollinators for visually obvious flowers) may occur because populations are at different genetic starting points, and each population follows its own genetic `line of least resistance.' A survey of literature suggests that pleiotropic relationships between flower colour and vegetative traits are common. Phylogenetically informed analyses of comparative data from Dalechampia (Euphorbiaceae) and Acer (Aceraceae), based on trait‐transition probabilities and maximum likelihood, indicated that floral and vegetative pigments are probably pleiotropically related in these genera, and this relationship better explains the diversification of floral colour than does direct selection by pollinators. In Dalechampia pink/purple floral bract colour may have originated by indirect response to selection on stem and leaf pigments. In Acer selection by pollinators for visually obvious flowers may to have led to the evolution of red or purple flowers in lineages synthesizing and deploying red anthocyanins in leaves, and pale‐green or yellow flowers in species not deploying red anthocyanins in vegetative structures. This study illustrates the broader potential of indirect selection and parallel selection on different genetic starting points to contribute to biological diversity, and the value of testing directly for the operation of these nonadaptive diversifying processes.     

Sources of phenotypic variation in floral traits in wild radish, Raphanus raphanistrum (Brassicaceae)

Pollinator-mediated natural selection has been shown to act on phenotypic variation in floral morphology, and this variation has often been demonstrated to be heritable, but few details are available concerning the sources of floral variation. We examined phenotypic variation in seven floral traits in wild radish (Raphanus raphanistrum) at six levels: between two populations grown in a common garden, among plants within populations, among flowers measured on different weeks, between flowers on two flowering stalks measured on the same day, between adjacent flowers on a flowering stalk, and within individual flowers. There were no significant differences between plants derived from the two source populations, which were ～800 km apart. Most of the variance was within individual plants; repeatabilities were all <0.35. There were highly significant differences between flowers measured in different weeks and also highly significant plant by week interactions, indicating that the among-plant variation was not consistent over time. There was substantial variance among adjacent flowers on the same stalk, particularly in the gynoecium. This high within-plant variance is partly responsible for the low heritability of floral traits in the field and the weak selection on floral traits found in previous studies of wild radish.     

The prediction of adaptive evolution: empirical application of the secondary theorem of selection and comparison to the breeder's equation

Adaptive evolution occurs when fitness covaries with genetic merit for a trait (or traits). The breeder's equation (BE), in both its univariate and multivariate forms, allows us to predict this process by combining estimates of selection on phenotype with estimates of genetic (co)variation. However, predictions are only valid if all factors causal for trait-fitness covariance are measured. Although this requirement will rarely (if ever) be met in practice, it can be avoided by applying Robertson's secondary theorem of selection (STS). The STS predicts evolution by directly estimating the genetic basis of trait-fitness covariation without any explicit model of selection. Here we apply the BE and STS to four morphological traits measured in Soay sheep (Ovis aries) from St. Kilda. Despite apparently positive selection on heritable size traits, sheep are not getting larger. However, although the BE predicts increasing size, the STS does not, which is a discrepancy that suggests unmeasured factors are upwardly biasing our estimates of selection on phenotype. We suggest this is likely to be a general issue, and that wider application of the STS could offer at least a partial resolution to the common discrepancy between naive expectations and observed trait dynamics in natural populations.     

Heritability and social brood effects on personality in juvenile and adult life‐history stages in a wild passerine

How has evolution led to the variation in behavioural phenotypes (personalities) in a population? Knowledge of whether personality is heritable, and to what degree it is influenced by the social environment, is crucial to understanding its evolutionary significance, yet few estimates are available from natural populations. We tracked three behavioural traits during different life‐history stages in a pedigreed population of wild house sparrows. Using a quantitative genetic approach, we demonstrated heritability in adult exploration, and in nestling activity after accounting for fixed effects, but not in adult boldness. We did not detect maternal effects on any traits, but we did detect a social brood effect on nestling activity. Boldness, exploration and nestling activity in this population did not form a behavioural syndrome, suggesting that selection could act independently on these behavioural traits in this species, although we found no consistent support for phenotypic selection on these traits. Our work shows that repeatable behaviours can vary in their heritability and that social context influences personality traits. Future efforts could separate whether personality traits differ in heritability because they have served specific functional roles in the evolution of the phenotype or because our concept of personality and the stability of behaviour needs to be revised.     

On the evolution of clonal plant life histories

Clonal plant life histories are special in at least four respects: (1) Clonal plants can also reproduce vegetatively, (2) vegetative reproduction can be realised with short or long spacers, (3) and it may allow to plastically place vegetative offspring in benign patches. (4) Moreover, ramets of clonal plants may remain physically and physiologically integrated. Because of the apparent utility of such traits and because ecological patterns of distribution of clonal and non-clonal plants differ, adaptation is a tempting explanation of observed clonal life-history variation. However, adaptive evolution requires (1) heritable genetic variation and (2) a trait effect on fitness, and (3) it may be constrained if other evolutionary forces are overriding selection or by constraints, costs and trade-offs. (1) The few studies undertaken so far reported broad-sense heritability for clonal traits. Variation in selectively neutral genetic markers appears as pronounced in populations of clonal as non-clonal plants. However, neutral markers may not reflect heritable variation of life-history traits. Moreover, clonal plants may have been sampled at larger spatial scales. Empirical information on the contribution of somatic mutations to heritable variation is lacking. (2) Clonal life-history traits were found to affect fitness. However, much of this evidence stems from artificial rather than natural environments. (3) The relative importance of gene flow, inbreeding, and genetic drift, compared with selection, in the evolution of clonal life histories is hardly explored. Benefits of clonal life-history traits were frequently studied and found. However, there is also evidence for constraints, trade-offs, and costs. In conclusion, though it is very likely, that clonal life-history traits are adaptive, it is neither clear to which degree this is the case, nor which clonal life-history traits constitute adaptations to which environmental factors. Moreover, evolutionary interactions among clonal life-history traits and between clonal and non-clonal ones, such as the mating system, are not well explored. There remains much interesting work to be done in this field – which will be particularly interesting if it is done in the field.     

QUANTITATIVE GENETIC VARIATION IN POPULATIONS OF AMSINCKIA SPECTABILIS THAT DIFFER IN RATE OF SELF-FERTILIZATION

Self-fertilization is expected to reduce genetic diversity within populations and consequently to limit adaptability to changing environments. Little is known, however, about the way the evolution of self-fertilization changes the amount or pattern of the components of genetic variation in natural populations. In this study, a reciprocal North Carolina II design and maximum-likelihood methods were implemented to investigate the genetic basis of variation for 15 floral and vegetative traits in four populations of the annual plant Amsinckia spectabilis (Boraginaceae) differing in mating system. Six variance components were estimated according to Cockerham and Weir's "bio" model c. Compared to the three partially selfing populations, we found significantly lower levels of nuclear variance for several traits in the nearly completely self-fertilizing population. Furthermore, for 11 of 15 traits we did not detect nuclear variation to be significantly greater than zero. We also found high maternal variance in one of the partially selfing populations for several traits, and little dominance variance in any population. These results are in agreement with the evolutionary dead-end hypothesis for highly self-fertilizing taxa.     

Expression of additive genetic variances and covariances for wild radish floral traits: comparison between field and greenhouse environments

Measurements of the genetic variation and covariation underlying quantitative traits are crucial to our understanding of current evolutionary change and the mechanisms causing this evolution. This fact has spurred a large number of studies estimating heritabilities and genetic correlations in a variety of organisms. Most of these studies have been done in laboratory or greenhouse settings, but it is not well known how accurately these measurements estimate genetic variance and covariance expressed in the field. We conducted a quantitative genetic half-sibling analysis on six floral traits in wild radish. Plants were grown from seed in the field and were exposed to natural environmental variation throughout their lives, including herbivory and intra- and interspecific competition. The estimates of heritabilities and the additive genetic variance-covariance matrix (G) obtained from this analysis were then compared to previous greenhouse estimates of the same floral traits from the same natural population. Heritabilities were much lower in the field for all traits, and this was due to both large increases in environmental variance and decreases in additive genetic variance. Additive genetic covariance expressed was also much lower in the field. These differences resulted in highly significant differences in the G matrix between the greenhouse and field environments using two complementary testing methods. Although the G matrices shared some principal components in common, they were not simply proportional to each other. Therefore, the greenhouse results did not accurately depict how the floral traits would respond to natural selection in the field.     

Multilevel selection 2: Estimating the genetic parameters determining inheritance and response to selection

Interactions among individuals are universal, both in animals and in plants and in natural as well as domestic populations. Understanding the consequences of these interactions for the evolution of populations by either natural or artificial selection requires knowledge of the heritable components underlying them. Here we present statistical methodology to estimate the genetic parameters determining response to multilevel selection of traits affected by interactions among individuals in general populations. We apply these methods to obtain estimates of genetic parameters for survival days in a population of layer chickens with high mortality due to pecking behavior. We find that heritable variation is threefold greater than that obtained from classical analyses, meaning that two-thirds of the full heritable variation is hidden to classical analysis due to social interactions. As a consequence, predicted responses to multilevel selection applied to this population are threefold greater than classical predictions. This work, combined with the quantitative genetic theory for response to multilevel selection presented in an accompanying article in this issue, enables the design of selection programs to effectively reduce competitive interactions in livestock and plants and the prediction of the effects of social interactions on evolution in natural populations undergoing multilevel selection.     

青藏高原及周边高山地区的植物繁殖生态学研究进展

青藏高原及周边高山地区孕育了极为丰富的植物多样性资源, 研究该地区植物如何顺利完成繁殖过程有助于我们理解植物对典型高山环境的进化和适应机制。该文综述了青藏高原地区高山植物在资源分配、繁殖方式、花部特征演化等方面的研究进展, 包括全球气候变化对植物繁殖特征的影响, 以及一些新技术和新方法在本研究领域的应用。在高山地区限制性环境中, 随海拔升高, 繁殖分配通常表现出增大的趋势, 其中投入到雄性资源的比例上升, 但具体的资源分配模式还要取决于植株的交配系统、个体大小、生活史特征、遗传特性以及环境中的资源有效性等。面对资源和传粉的双重限制, 植物在不同繁殖方式之间存在权衡, 当传粉者稀少时, 克隆繁殖和自交有利于繁殖保障; 而有性繁殖和异交能够提高种子的质量和后代的遗传多样性, 从而在复杂多变的气候条件下有利于种群的维持。因此, 不同繁殖方式的结合以及泛化的传粉互作网络可能是应对高山限制性环境的最优选择。花部特征的演化主要受到当地传粉者的选择压力, 但是外来传粉者、植食者、盗蜜者以及非生物环境(如温度、雨水和紫外辐射等)对花部性状的影响越来越受到重视。近年来, 青藏高原因其脆弱性和对气候变化的高度敏感性而在全球气候变化研究中备受关注, 以全球变暖和氮沉降增加为显著特征的全球气候变化正在直接或间接地影响着该地区高山植物的繁殖特征。气候变化影响植物和传粉者的物候并引起物种的迁移, 最终将导致植物与传粉者的时空不匹配。植物通过改变花部特征(花展示、花冠结构、花报酬的数量和质量)来响应气候变化, 这可能会改变其传粉者的类型、数量和访花行为, 从而最终影响植物的繁殖成功。3D打印和高通量测序等新技术和新方法的应用有助于促进植物繁殖生态学研究的进一步发展。3D打印的花能够精确控制其形态构造, 可以用于研究精细的花部特征变化对于传粉者行为的影响, 在此基础上与人工饲养的传粉者结合使用, 有助于进一步研究传粉者介导的花部特征演化。随着高通量测序技术的发展, 植物繁殖生态学领域, 尤其是花部特征演化的许多重要问题的潜在机制得以深入研究。该文最后提出了目前研究中需要注意的问题以及值得深入研究的发展方向。     

Adaptive differentiation of quantitative traits in the globally distributed weed, wild radish (Raphanus raphanistrum)

Weedy species with wide geographical distributions may face strong selection to adapt to new environments, which can lead to adaptive genetic differentiation among populations. However, genetic drift, particularly due to founder effects, will also commonly result in differentiation in colonizing species. To test whether selection has contributed to trait divergence, we compared differentiation at eight microsatellite loci (measured as F(ST)) to differentiation of quantitative floral and phenological traits (measured as Q(ST)) of wild radish (Raphanus raphanistrum) across populations from three continents. We sampled eight populations: seven naturalized populations and one from its native range. By comparing estimates of Q(ST) and F(ST), we found that petal size was the only floral trait that may have diverged more than expected due to drift alone, but inflorescence height, flowering time, and rosette formation have greatly diverged between the native and nonnative populations. Our results suggest the loss of a rosette and the evolution of early flowering time may have been the key adaptations enabling wild radish to become a major agricultural weed. Floral adaptation to different pollinators does not seem to have been as necessary for the success of wild radish in new environments.     

Strong artificial selection in the wild results in predicted small evolutionary change

Estimates of genetic variation and selection allow for quantitative predictions of evolutionary change, at least in controlled laboratory experiments. Natural populations are, however, different in many ways, and natural selection on heritable traits does not always result in phenotypic change. To test whether we were able to predict the evolutionary dynamics of a complex trait measured in a natural, heterogeneous environment, we performed, over an 8-year period, a two-way selection experiment on clutch size in a subdivided island population of great tits (Parus major). Despite strong artificial selection, there was no clear evidence for evolutionary change at the phenotypic level. Environmentally induced differences in clutch size among years are, however, large and can mask evolutionary changes. Indeed, genetic changes in clutch size, inferred from a statistical model, did not deviate systematically from those predicted. Although this shows that estimates of genetic variation and selection can indeed provide quantitative predictions of evolutionary change, also in the wild, it also emphasizes that demonstrating evolution in wild populations is difficult, and that the interpretation of phenotypic trends requires great care.     

Estimation of quantitative genetic parameters using marker-inferred relatedness in Japanese flounder: a case study of upward bias

Marker-based methods for estimating heritability have been proposed as an effective means to study quantitative traits in long-lived organisms and natural populations. However, practical examinations to evaluate the usefulness and robustness of a regression method are limited. Using several quantitative traits of Japanese flounder Paralichthys olivaceus, the present study examined the influence of relatedness estimator and population structure on the estimation of heritability and genetic correlation under a regression method with 7 microsatellite loci. Significant heritability and genetic correlation were detected for several quantitative traits in 2 laboratory populations but not in a natural population. In the laboratory populations, upward bias in heritability appeared depending on the relatedness estimators and the populations. Upward bias in heritability increased with decreasing the actual variance of relatedness, suggesting that the estimates of heritability under the regression method tend to be overestimated due to the underestimation of the actual variance of relatedness. Therefore, relationship structure and precise estimation of relatedness are critical for applying this method.