Comparison of genetic (co)variance matrices within and between Scabiosa canescens and S. columbaria

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G ‐matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G ‐matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G ‐matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two ‘species matrices’ were found to be unrelated, both for raw data and data standardized over populations, and there was significant between‐population variation in the G ‐matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G ‐matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G ‐matrices, at least in S. columbaria and at the between‐species level.     

An analysis of G matrix variation in two closely related cricket species,Gryllus firmus and G. pennsylvanicus

An important issue in evolutionary biology is understanding the pattern of G matrix variation in natural populations. We estimated four G matrices based on the morphological traits of two cricket species, Gryllus firmus and G. pennsylvanicus, each reared in two environments. We used three matrix comparison approaches, including the Flury hierarchy, to improve our ability to perceive all aspects of matrix variation. Our results demonstrate that different methods perceive different aspects of the matrices, which suggests that, until more is known about these methods, future studies should use several different statistical approaches. We also found that the differences in G matrices within a species can be larger than the differences between species. We conclude that the expression of the genetic architecture can vary with the environment and that future studies should compare G matrices across several environments. We also conclude that G matrices can be conserved at the level of closely related species.     

Limited plasticity in the phenotypic variance‐covariance matrix for male advertisement calls in the black field cricket,Teleogryllus commodus

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent study, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance‐covariance matrix ( P ) stability are sparse, and largely focused on morphological traits. Here, we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild‐caught crickets from each of the populations and then a second subset after rearing crickets under common‐garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high‐ and low‐nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit.     

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance–covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.     

There is more than one way to skin a G matrix

Because of its importance in directing evolutionary trajectories, there has been considerable interest in comparing variation among genetic variance-covariance (G) matrices. Numerous statistical approaches have been suggested but no general analysis of the relationship among these methods has previously been published. In this study, we used data from a half-sib experiment and simulations to explore the results of applying eight tests (T method, modified Mantel test, Bartlett's test, Flury hierarchy, jackknife-manova, jackknife-eigenvalue test, random skewers, selection skewers). Whereas a randomization approach produced acceptable estimates, those from a bootstrap were typically unacceptable and we recommend randomization as the preferred method. All methods except the jackknife-eigenvalue test gave similar results although a fine-scale analysis suggested that the former group can be subdivided into two or possibly three groups, hierarchical tests, skewers and the rest (jackknife-manova, modified Mantel, T method, probably Bartlett's). An advantage of the jackknife methods is that they permit tests of association with other factors, such as in this case, temperature and sex. We recommend applying all the tests described in this article, with the exception of the T method, and provide R functions for this purpose.     

A note on simulating null distributions for G matrix comparisons

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G . We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti‐conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.     

The constancy of the G matrix through species divergence and the effects of quantitative genetic constraints on phenotypic evolution: a case study in crickets

Long-term phenotypic evolution can be modeled using the response-to-selection equation of quantitative genetics, which incorporates information about genetic constraints (the G matrix). However, little is known about the evolution of G and about its long-term importance in constraining phenotypic evolution. We first investigated the degree of conservation of the G matrix across three species of crickets and qualitatively compared the pattern of variation of G to the phylogeny of the group. Second, we investigated the effect of G on phenotypic evolution by comparing the direction of greatest quantitative genetic variation within species (g(max)) to the direction of phenotypic divergence between species (Delta(z)). Each species, Gryllus veletis, G. firmus, and G. pennsylvanicus, was reared in the laboratory using a full-sib breeding design to extract quantitative genetic information. Five morphological traits related to size were measured. G matrices were compared using three statistical approaches: the T method, the Flury hierarchy, and the MANOVA method. Results revealed that the differences between matrices were small and mostly caused by differences in the magnitude of the genetic variation, not by differences in principal component structure. This suggested that the G matrix structure of this group of species was preserved, despite significant phenotypic divergence across species. The small observed differences in G matrices across species were qualitatively consistent with genetic distances, whereas ecological information did not provide a good prediction of G matrix variation. The comparison of g(max) and Delta(z) revealed that the angle between these two vectors was small in two of three species comparisons, whereas the larger angle corresponding to the third species comparison was caused in large part by one of the five traits. This suggests that multivariate phenotypic divergence occurred mostly in a direction predicted by the direction of greatest genetic variation, although it was not possible to demonstrate the causal relationship from G to Delta(z). Overall, this study provided some support for the validity of the predictive power of quantitative genetics over evolutionary time scales.     

The evolution of the phenotypic covariance matrix: evidence for selection and drift in Melanoplus

Phenotypic variation in trait means is a common observation for geographically separated populations. Such variation is typically retained under common garden conditions, indicating that there has been evolutionary change in the populations, as a result of selection and/or drift. Much less frequently studied is variation in the phenotypic covariance matrix (hereafter, P matrix), although this is an important component of evolutionary change. In this paper, we examine variation in the phenotypic means and P matrices in two species of grasshopper, Melanoplus sanguinipes and M. devastator. Using the P matrices estimated for 14 populations of M. sanguinipes and three populations of M. devastator we find that (1) significant differences between the sexes can be attributed to scaling effects; (2) there is no significant difference between the two species; (3) there are highly significant differences among populations that cannot be accounted for by scaling effects; (4) these differences are a consequence of statistically significant patterns of covariation with geographic and environmental factors, phenotypic variances and covariances increasing with increased temperature but decreasing with increased latitude and altitude. This covariation suggests that selection has been important in the evolution of the P matrix in these populations Finally, we find a significant positive correlation between the average difference between matrices and the genetic distance between the populations, indicating that drift has caused some of the variation in the P matrices.     

Similarity in G matrix structure among natural populations of Arabidopsis lyrata

Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories; yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half‐sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display, and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape, and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.     

Population differentiation in G matrix structure due to natural selection in Rana temporaria

The additive genetic variance-covariance matrix (G) is a concept central to discussions about evolutionary change over time in a suite of traits. However, at the moment we do not know how fast G itself changes as a consequence of selection or how sensitive it is to environmental influences. We investigated possible evolutionary divergence and environmental influences on G using data from a factorial common-garden experiment where common frog (Rana temporaria) tadpoles from two divergent populations were exposed to three different environmental treatments. G-matrices were estimated using an animal model approach applied to data from a NCII breeding design. Matrix comparisons using both Flury and multivariate analysis of variance methods revealed significant differences in G matrices both between populations and between treatments within populations, the former being generally larger than the latter. Comparison of levels of population differentiation in trait means using Q(ST) indices with that observed in microsatellite markers (F(ST)) revealed that the former values generally exceeded the neutral expectation set by F(ST). Hence, the results suggest that intraspecific divergence in G matrix structure has occurred mainly due to natural selection.     

糖蛋白G 基因在基因组P-M 位的插入重组表达对狂犬病毒Flury LEP 致病力的影响

【目的】研究狂犬病病毒Flury鸡胚低代毒株(Flury LEP)在基因组P-M位增加糖蛋白基因(G基因)的重组表达对病毒致病力的影响。【方法】利用反向遗传操作技术,构建了P、M基因之间额外插入G基因的重组狂犬病病毒Flury LEP株(rLEP-PGM),并对重组病毒的生物学特性及对小鼠的致病性进行了初步研究。【结果】亲本株和重组病毒具有相似的生长特性,LEP和rLEP-PGM在BHK-21细胞的生长滴度分别为4×106 FFU/mL和2.5×106 FFU/mL,在小鼠神经母细胞(NA)的生长滴度分别为4×107 FFU/mL和2.5×107 FFU/mL;嗜神经指数均为1;Western blot显示,rLEP-PGM在感染细胞的G蛋白表达量比LEP显著提高;小鼠感染试验显示,rLEP-PGM与LEP脑内注射小鼠的LD50分别为3 FFU和1 FFU,肌肉注射途径的LD50分别为4×104 FFU和3.2×105 FFU。【结论】P、M基因之间插入一个额外的G基因能够提高G蛋白的表达水平,同时增强重组病毒外周侵入中枢神经系统的能力。     

The effect of temperature and wing morphology on quantitative genetic variation in the cricket Gryllus firmus, with an appendix examining the statistical properties of the Jackknife-MANOVA method of matrix comparison

We investigated the effect of temperature and wing morphology on the quantitative genetic variances and covariances of five size-related traits in the sand cricket, Gryllus firmus. Micropterous and macropterous crickets were reared in the laboratory at 24, 28 and 32 degrees C. Quantitative genetic parameters were estimated using a nested full-sib family design, and (co)variance matrices were compared using the T method, Flury hierarchy and Jackknife-manova method. The results revealed that the mean phenotypic value of each trait varied significantly among temperatures and wing morphs, but temperature reaction norms were not similar across all traits. Micropterous individuals were always smaller than macropterous individuals while expressing more phenotypic variation, a finding discussed in terms of canalization and life-history trade-offs. We observed little variation between the matrices of among-family (co)variation corresponding to each combination of temperature and wing morphology, with only one matrix of six differing in structure from the others. The implications of this result are discussed with respect to the prediction of evolutionary trajectories.     

From micro- to macroevolution through quantitative genetic variation: positive evidence from field crickets

Quantitative genetics has been introduced to evolutionary biologists with the suggestion that microevolution could be directly linked to macroevolutionary patterns using, among other parameters, the additive genetic variance/ covariance matrix (G) which is a statistical representation of genetic constraints to evolution. However, little is known concerning the rate and pattern of evolution of G in nature, and it is uncertain whether the constraining effect of G is important over evolutionary time scales. To address these issues, seven species of field crickets from the genera Gryllus and Teleogryllus were reared in the laboratory, and quantitative genetic parameters for morphological traits were estimated from each of them using a nested full-sibling family design. We used three statistical approaches (T method, Flury hierarchy, and Mantel test) to compare G matrices or genetic correlation matrices in a phylogenetic framework. Results showed that G matrices were generally similar across species, with occasional differences between some species. We suggest that G has evolved at a low rate, a conclusion strengthened by the consideration that part of the observed across-species variation in G can be explained by the effect of a genotype by environment interaction. The observed pattern of G matrix variation between species could not be predicted by either morphological trait values or phylogeny. The constraint hypothesis was tested by comparing the multivariate orientation of the reconstructed ancestral G matrix to the orientation of the across-species divergence matrix (D matrix, based on mean trait values). The D matrix mainly revealed divergence in size and, to a much smaller extent, in a shape component related to the ovipositor length. This pattern of species divergence was found to be predictable from the ancestral G matrix in agreement with the expectation of the constraint hypothesis. Overall, these results suggest that the G matrix seems to have an influence on species divergence, and that macroevolution can be predicted, at least qualitatively, from quantitative genetic theory. Alternative explanations are discussed.     

RAPD variation in relation to population size and plant fitness in the rare Gentianella germanica (Gentianaceae)

We investigated the distribution of genetic variation and the relationship between population size and genetic variation in the rare plant Gentianella germanica using RAPD (random amplified polymorphic DNA) profiles. Plants for the analysis were grown from seeds sampled from 72 parent plants in 11 G. germanica populations of different size (40-5000 fruiting individuals). In large populations, seeds were sampled from parents in two spatially distinct subpopulations comparable in area to the total area covered by small populations. Analysis of molecular variance revealed significant genetic variation among populations (P <0.001), while genetic variation among subpopulations was marginally significant (P <0.06). Average molecular variance within subpopulations in large populations did not differ significantly from whole-population values. There was a positive correlation between genetic variation and population size (P <0.01). Genetic variation was also positively correlated with the number of seeds per plant in the field (P <0.02) and the number of flowers per planted seed in a common garden experiment (P <0.051). We conclude that gene flow among natural populations is very limited and that reduced plant fitness in small populations of G. germanica most likely has genetic causes. Management should aim to increase the size of small populations to minimize further loss of genetic variation. Because a large proportion of genetic variation is among populations, even small populations are worth preserving.     

Q(St) meets the G matrix: the dimensionality of adaptive divergence in multiple correlated quantitative traits.

The Q(ST)-F(ST) comparison has become an increasingly common method for inferring adaptive quantitative trait divergence among populations. For cases in which there is divergence in multiple traits, most studies have applied the method by performing multiple univariate Q(ST)-F(ST) comparisons. However, because traits are often genetically correlated, such univariate analyses are likely to paint a simplified picture of adaptive divergence. Here we show how the multivariate analogue of Q(ST), F(STq), which accounts for genetic correlations among traits, can be used to supply a more detailed picture of multitrait divergence. We apply the method to naturally occurring genetic variation for a suite of sexually selected display traits in Drosophila serrata. The analyses suggest the operation of divergent multivariate selection that has influenced multiple independent axes of genetic variance in a sex-specific manner. Finally, we show how a comparison of the components of F(STq), the average within and among population genetic variance-covariance matrices, G(W) and G(B), can be used as an additional test of the null expectation of neutral divergence, and allows for an investigation of whether natural populations have diverged along major or minor axes of genetic variance.     

贵州省野生皂荚种实表型性状多样性分析

为深入了解贵州省野生皂荚(Gleditsia sinensis)荚果表型性状的遗传多样性及其变异类型,为皂荚的遗传改良、种质鉴定、亲本选择以及品种培育奠定理论基础。该研究以贵州省7个野生皂荚群体70个个体为研究对象,采用方差分析、主成分分析、相关性分析及多性状综合评价等方法对皂荚群体的10个种实表型性状进行系统分析和综合评价。结果显示：(1)所测皂荚的表型性状差异在群体内均达到极显著水平(P＜0.01);在群体间,除每荚粒数、种子宽、种子长宽积以及种子长宽比之外,其余表型性状的差异均达极显著水平(P＜0.01)。(2)7个居群野生皂荚各性状平均变异系数为21.16%,其中凯里市(P4)居群的变异系数最高(24.44%);居群间荚果的变异(29.22%)高于种子的变异(11.04%),且变异主要来自于群体内。(3)相关分析显示,皂荚种实各性状之间存在不同程度的关联性;主成分分析显示,前4个主成分(皂荚种子大小、单个荚果出籽数量、种子形态指数因子、与荚果长和种子厚相关的因子)的累积贡献率达69.783%,可基本反映皂荚表型性状的大部分信息;以10个种实性状对皂荚野生群体进行综合评价发现,来自于惠水县(P7)群体的皂荚种实性状综合评价最高。研究表明,贵州省野生皂荚在群体间及群体内具有丰富的表型变异,且群体内的变异大于群体间的变异,变异主要来自于群体内。     

Structure and stability of genetic variance–covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three‐spined stickleback

The genetic variance–covariance matrix ( G ) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G ‐matrices is limited for two reasons. First, phenotypes are high‐dimensional, whereas traditional statistical methods are tuned to estimate and analyse low‐dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high‐dimensional G ‐matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half‐sib breeding design of three‐spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low‐temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability—as well as the similarity among G ‐matrices—may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G ‐matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G , they also illustrate that by enabling the estimation of large G ‐matrices, the BSFG method can improve predicted evolutionary responses to selection.     

Genetics of body shape and armour variation in threespine sticklebacks

Patterns of genetic variation and covariation can influence the rate and direction of phenotypic evolution. We explored the possibility that the parallel morphological evolution seen in threespine stickleback (Gasterosteus aculeatus) populations colonizing freshwater environments is facilitated by patterns of genetic variation and covariation in the ancestral (marine) population. We estimated the genetic (G) and phenotypic (P) covariance matrices and directions of maximum additive genetic (g(max) ) and phenotypic (p(max) ) covariances of body shape and armour traits. Our results suggest a role for the ancestral G in explaining parallel morphological evolution in freshwater populations. We also found evidence of genetic constraints owing to the lack of variance in the ancestral G. Furthermore, strong genetic covariances and correlations among traits revealed that selective factors responsible for threespine stickleback body shape and armour divergence may be difficult to disentangle. The directions of g(max) and p(max) were correlated, but the correlations were not high enough to imply that phenotypic patterns of trait variation and covariation within populations are very informative of underlying genetic patterns.     

Allozyme variation in the endangered insular endemic Castilleja grisea

BACKGROUND AND AIMS: Genetic diversity in Castilleja grisea, an endangered, perennial herb endemic to San Clemente Island, California was investigated. Subsequent to the elimination of goats from the island in 1992, many populations of C. grisea have reappeared and have been increasing in size. METHODS: Nineteen populations were surveyed for their genotype at 19 allozyme loci. KEY RESULTS: At the taxon level, 57.9 % of loci are polymorphic with A(P) = 3.09 and H(E) = 0.137. Populations averaged 33.0 % polymorphic loci with A(P) = 2.43 and H(E) = 0.099. Most variation is found within rather than among populations (G(ST) = 0.128), although differentiation among populations is significant. Genetic identities range from I = 0.960 to I = 1.000 with mean I = 0.990. There is no significant relationship between genetic and geographic distance. Gene flow among populations is Nm = 2.50 based on private alleles and Nm = 1.70 based on F(ST). Outcrossing rates based on fixation indices average t = 1.01, indicating a primarily out-crossed mating system. CONCLUSIONS: The observed genetic variation is moderately high, unusually so for an insular endemic species, suggesting that C. grisea may not have lost substantial genetic variation during 150 years of overgrazing, and indicating that it is unlikely to be endangered by genetic factors.     

ISSR variation in the endemic and endangered plant Cycas guizhouensis (Cycadaceae)

BACKGROUND AND AIMS: Cycas guizhouensis (Cycadaceae) is a rare and endangered species endemic to the southwest of China. An investigation was undertaken into the genetic variation of wild populations. METHODS: ISSR markers were used to determine the genetic variation within and between 12 extant populations of this species. KEY RESULTS: Low genetic diversity (at population level, P = 14.21 %, H(E) = 0.0597; at species level, P = 35.90 %, H(T) = 0.1082) and a high degree of differentiation among populations (G(ST) = 0.4321) were detected. CONCLUSIONS: This genetic structure is considered to be due to the combined effects of slow biochemical evolution, genetic drift, inbreeding and limited gene flow between populations. Based on these findings, strategies are proposed for the genetic conservation and management of the species.