Evidence for adaptation from standing genetic variation on an antimicrobial peptide gene in the mussel Mytilus edulis

Genome scans of population differentiation identify candidate loci for adaptation but provide little information on how selection has influenced the genetic structure of these loci. Following a genome scan, we investigated the nature of the selection responsible for the outlying differentiation observed between populations of the marine mussel Mytilus edulis at a leucine/arginine polymorphism (L31R) in the antimicrobial peptide MGD2. We analysed DNA sequence polymorphisms, allele frequencies and population differentiation of polymorphisms closely linked to L31R, and pairwise and third‐order linkage disequilibria. An outlying level of population differentiation was observed at L31R only, while no departure from panmixia was observed at linked loci surrounding L31R, as in most of the genome. Selection therefore seems to affect L31R directly. Three hypotheses can explain the lack of differentiation in the chromosomal region close to L31R: (i) hitchhiking has occurred but migration and recombination subsequently erased the signal, (ii) selection was weak enough and recombination strong enough to limit the hitchhiking effect to a very small chromosomal region or (iii) selection acted on a pre‐existing polymorphism (i.e. standing variation) at linkage equilibrium with its background. Linkage equilibrium was observed between L31R and linked polymorphisms in every population analysed, as expected under the three hypotheses. However, linkage disequilibrium was observed in some populations between pairs of loci located upstream and downstream to L31R, generating a complex pattern of third‐order linkage disequilibria which is best explained by the hypothesis of selection on a pre‐existing polymorphism. We hypothesise that selection could be either balanced, maintaining alleles at different frequencies depending on the pathogen community encountered locally by mussels, or intermittent, resulting in sporadic fluctuations in allele frequency.     

Robust indices of Hardy-Weinberg disequilibrium for QTL fine mapping

Hardy-Weinberg disequilibrium (HWD) measures have been proposed using dense markers to fine map a quantitative trait locus (QTL) to regions < approximately 1 cM. Earlier HWD measures may introduce bias in the fine mapping because they are dependent on marker allele frequencies across loci. Hence, HWD indices that do not depend on marker allele frequencies are desired for fine mapping. Based on our earlier work, here we present four new HWD indices that do not depend on marker allele frequencies. Two are for use when marker allele frequencies in a study population are known, and two are for use when marker allele frequencies in a study population are not known and are only known in the extreme samples. The new measures are a function of the genetic distance between the marker locus and a QTL. Through simulations, we investigated and compared the fine mapping performance of the new HWD measures with that of the earlier ones. Our results show that when marker allele frequencies vary across loci, the new measures presented here are more robust and powerful.     

Population genetic history of the dreissenid mussel invasions: expansion patterns across North America

This study tests population genetic patterns across the Eurasian dreissenid mussel invasions of North America—encompassing the zebra mussel Dreissena polymorpha (1986 detection) and the quagga mussel D. rostriformis bugensis (detected in 1990, which now has largely displaced the former in the Great Lakes). We evaluate their source-spread relationships and invasion genetics using 9–11 nuclear microsatellite loci for 583 zebra mussels (21 sites) and 269 quagga mussels (12 sites) from Eurasian and North American range locations, with the latter including the Great Lakes, Mississippi River basin, Atlantic coastal waterways, Colorado River system, and California reservoirs. Additionally, mtDNA cytochrome b gene sequences are used to verify species identity. Our results indicate that North American zebra mussels originate from multiple non-native northern European populations, whereas North American quagga mussels trace to native estuaries in the Southern Bug and Dnieper Rivers. Invasive populations of both species show considerable genetic diversity and structure (zebra F _ST = 0.006–0.263, quagga F _ST = 0.008–0.267), without founder effects. Most newer zebra mussel populations have appreciable genetic diversity, whereas quagga mussel populations from the Colorado River and California show some founder effects. The population genetic composition of both species changed over time at given sites; with some adding alleles from adjacent populations, some losing them, and all retaining closest similarity to their original composition. Zebra mussels from Kansas and California appear genetically similar and assign to a possible origin from the St. Lawrence River, whereas quagga mussels from Nevada and California assign to a possible origin from Lake Ontario. These assignments suggest that overland colonization pathways via recreational boats do not necessarily reflect the most proximate connections. In conclusion, our microsatellite results comprise a valuable baseline for resolving present and future dreissenid mussel invasion pathways.     

Population genetic structure of the endangered crayfish Austropotamobius pallipes in France based on microsatellite variation: biogeographical inferences and conservation implications

1. One important goal in conservation biology is to characterise evolutionary lineages within endangered species before management decisions are taken. Here, we assess population differentiation in the freshwater crayfish Austropotamobius pallipes, an endangered species endemic to western Europe and provide valuable information for the conservation of French populations. 2. Analysis of five microsatellite loci in 44 populations revealed very different within population levels of genetic diversity (0.000 < H₀ < 0.564). Two groups, corresponding to northern and southern French populations, showed a high degree of genetic differentiation in both allele frequencies and allele sizes. Comparison of these results with previous studies of A. pallipes strongly suggests that the divergence between northern and southern populations could have occurred during the last glaciation period of the Pleistocene from one Atlantic and one Mediterranean refuge. 3. Evidence for genetic admixture between these two lineages was revealed by correspondence analyses in southern populations, probably as the result of artificial translocations. 4. French populations appeared significantly differentiated among the different river drainages and were highly structured within rivers. The impact of population size, population bottlenecks and founder events on the population genetic differentiation are discussed. 5. Based on these results, we propose the designation of two evolutionarily significant units for A. pallipes in France. Our data also support the maintenance of separate demographic management strategies for crayfish inhabiting different river systems. However, genetic analyses will have to be combined with demographic and ecological data for sustainable conservation programmes.     

Population structuring in mountain zebras (<Emphasis Type="Italic">Equus zebra</Emphasis>): The molecular consequences of divergent demographic histories

The endangered mountain zebra (Equus zebra) is endemic to the semi-arid inhospitable mountainous escarpments of southern Africa. The species is divided taxonomically into two geographically separated subspecies, each with differing recent population histories. In Namibia, Hartmann’s mountain zebra (E. z. hartmannae) is common and occurs in large free-ranging populations, whereas in South Africa, prolonged hunting and habitat destruction over the last 300 years has decimated populations of the Cape mountain zebra (E. z. zebra). In this study, we investigate the consequences of these divergent demographic histories for population genetic diversity and structure. We also examine the phylogeographic relationship between the two taxonomic groups. Genetic information was obtained at 15 microsatellite loci for 291 individuals from a total of 10 populations as well as 445 bp of the mitochondrial control region sequence data from 77 individuals. Both model-based and standard analytical approaches were used to examine the data. Both types of marker returned levels of diversity and structure that were consistent with population history. Low genetic variation within individual Cape mountain zebra populations, the characteristic indicator of population fragmentation and drift, was offset by moderate variation in the entire E. z. zebra sample. This implies that higher levels of diversity still exist within the Cape mountain zebra gene pool. A management strategy that entailed the mixing of aboriginal populations is therefore advocated in order to halt the further loss of Cape mountain zebra genetic diversity. Allele frequencies in Hartmann’s mountain zebra were relatively resilient to demographic fluctuations. Due to the high incidence of mitochondrial haplotype sharing between populations, the hypothesis that Cape and Hartmann’s mountain zebra mitochondrial lineages were reciprocally monophyletic was not supported. However, the presence of private alleles at nuclear loci rendered the two subspecies genetically distinct evolutionary significant units.     

一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

Population genetic structure of mussels from the Baltic Sea

In a macrogeographic survey, the population genetic structure of mussels from various regions of the Baltic Sea, a large semi-enclosed brackish-water basin, was examined with reference toMytilus edulis andM. galloprovincialis samples from the North Sea, Irish coast and southern Portugal. Electrophoretically detectable variation was analysed at 6 polymorphic enzyme loci (Ap, Est-D, Lap-2, Odh, Pgi andPgm). Evidence was provided of a remarkably large amount of biochemical genetic differentiation among ecologically and morphologically divergent mussel populations in the Baltic. Patterns of allele frequencies in low-salinity populations from the area of the Baltic Proper were demonstrated to be widely homogeneous but contrast strongly with those of the western Baltic, the latter resembling populations from marine habitats of the North Sea. Associated with a pronounced salinity gradient, the spatial heterogeneity in gene-pool structure is indicated by steep clines of allele frequency changes in the area of the eastern Danish isles. The adaptive significance of the observed allozymic variation is suggested. From genetic distance estimates, the subdivision of population structure is discussed in relation to the significant amount of differentiation detected withinMytilus populations to date and to the evolutionary time required for the divergence of Baltic mussel populations. The allozymic data provide evidence for the genetic distinctiveness of mussels from the low-salinity areas of the Baltic. Their position at the specific or subspecific level of classification requires further consideration.     

Genetic structure of five susceptibility gene regions for coronary artery disease: disequilibria within and among regions

We analyzed two-locus disequilibria for 16 polymorphic loci of seven susceptibility genes for coronary artery disease located in five chromosomal regions distributed across four chromosomes. Included were the genes coding for apolipoprotein B (ApoB, chromosome 2, four marker loci), lipoprotein lipase (LPL, chromosome 8, three marker loci), apolipoproteins AI, CIII, AIV (ApoAI–CIII–AIV, chromosome 11, three marker loci), apolipoprotein E (ApoE, chromosome 19, two marker loci), and the low density lipoprotein receptor (LDLR, chromosome 19, four marker loci). Our sample included 540 unrelated individuals from the Rochester, Minn. population. There were no statistically significant deviations of single-locus genotypes from Hardy-Weinberg equilibrium. The strongest associations within genes were for composite diallelic disequilibria; 17/19 were significant (13 at Pr <0.001, 1 at Pr <0.01, 3 at Pr <0.05). These observations suggest marker alleles within genes have a shared evolutionary history reflected by disequilibria that have not been dissipated by recombination. Disequilibrium was not generally concordant with the physical orderings of markers. Only two significant higher-order disequilibria were observed although 12 triallelic disequilibria were at maximum possible values. We observed 19 statistically significant disequilibria (Pr <0.05; 4 composite diallelic, 13 triallelic, and 2 quadriallelic) between 101 pairs of marker loci, where each locus in a pair was from a different unlinked region. These unexpected results are most likely explained by recent historical factors, including worldwide population expansion and amalgamation with continuous admixture, that influence the genetic structure (organization of alleles and non-alleles into genotypes) of a population. We conclude that disequilibria between loci from unlinked regions may be more extensive than is commonly assumed. Our findings also suggest that it is, on average, at least 15 times more likely to not detect significant disequilibrium among unlinked loci when it is really present than to make a false positive inference. Disequilibria between functional loci within or between regions will impact estimates of genetic variance associated with particular functional mutations within a susceptibility gene region. Received: 15 January 1998 / Accepted: 24 June 1998     

The Genetical Response to Natural Selection by Varied Environments. IV. Gametic Disequilibrium in Spatially Varied Environments

Gametic disequilibria between allozyme loci were related to spatial variation of the environment in caged populations of Drosophila melanogaster . Two experiments, one with flies collected at "Chateau Tahbilk," South Australia, and the other with flies from "Groningen," The Netherlands, were sampled at generations 16 and 32. Spatial variation of the environment was stimulated using three food media. Eight polymorphic allozyme loci were used to estimate gametic disequilibria from digenic combinations of allotypes. All populations were duplicated within an environment and maintained at about 2500 adults. Standardized gametic disequilibria were compared by a weighted least squares analysis of the z-transformed statistical correlation of allele frequencies. Gametic disequilibria were strongly dependent upon food niche and food-niche interactions. The effects also varied with sampling time and were similar in duplicate populations. Gametic disequilibria were most often detected in the "Groningen"-derived populations and their strength was not strongly associated with recombination fraction. Many of the disequilibria concerned unlinked loci. The strength of selection was probably considerable and populations were evolving genetic architectures which reflected niche selection by the different foods without marked genetic isolation between foods; gene frequencies did not vary between niches within a population cage.     

Genetic variability and phylogeographical patterns of a nonindigenous species invasion: a comparison of exotic vs. native zebra and quagga mussel populations

There have been few investigations of the number of founding sources and amount of genetic variability that lead to a successful nonindigenous species invasion, although genetic diversity is believed to play a central role. In the present study, population genetic structure, diversity and divergence patterns were analysed for the zebra mussel Dreissena polymorpha [n=280 samples and 63 putative randomly amplified polymorphic DNA (RAPDs) gene loci] and the quagga mussel D. bugensis (n=136 and 52 loci) from 10 nonindigenous North American and six Eurasian sampling sites, representing their present‐day ranges. Results showed that exotic populations of zebra and quagga mussels had surprisingly high genetic variability, similar to those in the Eurasian populations, suggesting large numbers of founding individuals and consistent with the hypothesis of multiple colonizations. Patterns of genetic relationships indicate that the North American populations of D. polymorpha likely were founded by multiple source populations from north‐western and northcentral Europe, but not from southcentral or eastern Europe. Sampling areas within North America also were significantly divergent, having levels of gene flow and migration about twice those separating long‐established Eurasian populations. Samples of D. bugensis in Lakes Erie and Ontario were significantly different, with the former being more closely related to a native population from the Dnieper River, Ukraine. No evidence for a founder effect was discerned for either species.     

Contrasting population genetic structures using allozymes and the inversion polymorphism in Drosophila buzzatii

Second chromosome inversion and genotypic frequencies at seven allozyme loci, differentially associated with inversions, were determined in seven natural populations of Drosophila buzzatii. The patterns of variation of allozymes and the inversion polymorphisms were significantly different, indicating the role of adaptive differentiation for the latter. Moreover, the patterns of population structure varied among allozyme loci, suggesting the operation of diversifying selection for certain loci. Differentiation was negligible for Leucyl‐amino peptidase (Lap) and Peptidase‐2 (Pep‐2), low to moderate for Aldehyde oxidase (Aldox), Peptidase‐1 (Pep‐1) and Esterase‐1 (Est‐1) and high for Esterase‐2 (Est‐2) and Xanthine dehydrogenase (Xdh). Significant linkage disequilibria were detected between inversions and Aldox, Est‐1, Est‐2 and Xdh. Multiple regression analyses of inversion and allele frequencies on environmental variables revealed the existence of clines for inversions, Est‐1, Est‐2, Xdh and Aldox along altitudinal, latitudinal and/or climatic gradients. Tests using conditional allele frequencies showed that Est‐1 and Aldox clines could be accounted for by hitchhiking with inversions, whereas natural selection should be invoked to explain the clines observed for Est‐2 and Xdh.     

Temporal variation of allele frequencies in a natural population of wild Vigna unguiculata

Abstract

Temporal variation in allele frequencies in a natural population of wild Vigna unguiculata was studied by making monthly collections of seeds over a two-year period. Using starch gel electrophoresis, four out of seven loci analysed were shown to be polymorphic (Enp, Fdh, Fle₃ and Pgd₂ ). These four loci showed significant variation in allele frequencies over time. Changes in population structure over time were analysed using F-statistic estimators. Although heterogeneity was evident between loci, the analysis showed significant differentiation among months within a year for all polymorphic loci. Fixation indexes were all positive and statistically different from zero, highlighting a significant departure from random mating. Using analysis of variance (ANOVA), the pattern of inbreeding (f) showed significant changes over time (season); among the polymorphic loci, Enp most strongly contributed to this significance. Significant correlations were found between allele frequencies at different loci. The monthly average gene diversity (He) and allele frequencies at the Enp locus were found to be significantly correlated with weather conditions (temperature and rainfall distribution). These allele frequency deviations over time can be attributed to changes in pollinator behaviour, and frequent genetic bottlenecks that are associated with changes in environmental conditions.     

Multilocus structure in Pinus contorta Dougl.

We studied isozyme variation at 21 loci in 66 populations from three subspecies of Pinus contorta Dougl.; 35 in spp. latifolia, 20 in spp contorta and 11 in spp. murrayana. The objectives were to assess gametic disequilibria and multilocus structure. There was considerable differentiation of allele frequencies at 19 polymorphic loci across the 66 populations and within the subspecies. Allele frequencies at many loci correlated with geographic variables. Genetic variability varied considerably among populations within subspecies but the subspecies means were similar. The mean number of polymorphic loci and the mean heterozygosity over 19 polymorphic loci were, respectively, 13 and 0.194 in latifolia, 12 and 0.196 in murrayana, and 12 and 0.180 in contorta. The mean heterozygosity correlated with longitude and altitude across the 66 populations and with latitude in latifolia. Gametic disequilibria were evident in 40 populations; 29 in latifolia, eight in murrayana and three in contorta. Gametic disequilibria correlated with latitude across the 66 populations and with longitude in latifolia. The single-locus F _ST averaged 0.0339 in latifolia, 0.0567 in murrayana, and 0.0764 in contorta. The multilocus F _STM was 0.1227 in latifolia, 0.2926 in murrayana, and 0.3328 in contorta. Multilocus Wahlund and founder effects, migration patterns, and natural selection, probably played significant roles in generating and maintaining the multilocus genetic structure in P. contorta in general and the subspecies latifolia in particular.     

Allozyme Diversity among Different Size Cohorts of Spat of Mytilus trossulus (Bivalvia,Mytilidae) Dwelling together in Amursky Bay,Sea of Japan

Allozyme variability in 16 polymorphic loci in two size cohorts of large (30.0 ± 6.3 mm) and small (9.8 ± 2.3 mm) spat of the mussel Mytilus trossulus (Gould) coinhabiting the intertidal zone in Brazhnikov Bay (Amursky Bay, Sea of Japan) was studied 1988–1989. It was determined that the size cohorts compared were highly similar genetically; Nei's minimum distances were 0.014 and 0.016 in 1988 and in 1989. However, statistically significant differences in allele frequencies were found at 2 loci, both in 1988 and in 1989. The loci differing by allele frequencies in 1988 did not coincide with those in 1989. Significant differences by heterozygosity between the cohorts were found only at the Idg-1 and Est-3 loci, 1988; and at the Aat-1, 6-Fgd, Est-3 loci, 1989; but the average heterozygosity was not significantly different in the cohorts for both years. A deficiency of heterozygotes (Dg) was observed almost at all loci in both cohorts. The mean Dg values were significantly higher in the cohort of small size individuals. Since the environmental conditions for both cohorts were similar, the allozyme differences between them were not a result of natural selection. A possible cause of the allozyme and size differences among the mussel cohorts is the gap in the settling time of larvae, which entails the formation of two size cohorts of mussels. Such a gap was caused by protraction of spawning period of M. trossulus and by the formation of segregate larval pools from various mussel populations differing in allele frequencies.     

Assessing natural and disturbed population structure in European grayling Thymallus thymallus: melding phylogeographic,population genetic and jurisdictional perspectives for conservation planning

Natural and human‐mediated population structure of European grayling Thymallus thymallus was assessed in primarily Austrian reaches of the Danube River catchment. Data on phylogeographic structure based on mitochondrial DNA (mtDNA) were combined with variation found across 13 microsatellite loci to assess introgression stemming from stocking activities. Populations north of the Alps generally showed no signs of long‐term introgression from allochthonous stocks, although one population comprised two distinct genotypic groups, one of which may stem from recently stocked material. South of the Alps, levels of introgression with stocks from the north were extensive and only one of six populations is believed to represent a reference state. Allelic diversity and expected heterozygosity were positively correlated with mtDNA admixture supporting more recent introgression and that there is little or no reproductive barrier between these two major lineages north and south of the Alps. A third unrelated mtDNA lineage is described from the Lafnitz, a tributary of the Raab drainage. The high lineage diversity in the upper Austrian Danube is not concordant with an existing model of T. thymallus evolutionarily significant units in Europe. Caveats in naming such units or following a strict hierarchical conservation unit structure for broadly distributed species with complex phylogeographic distributions stretching over various jurisdictions are discussed. The necessity of using both phylogeographic and population genetic approaches in evaluating the history and conservation value of populations in a conservation context is additionally highlighted.     

Multivariate Analysis of Gametic Disequilibrium in the Yanomama

The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.     

Genetic diversity and multilocus associations in Cunninghamia lanceolata (Lamb.) Hook from The People's Republic of China

Open-pollinated seeds were assayed for allozyme polymorphisms at 24 loci to assess genetic diversity and multilocous associations in 16 populations of Cunninghamia lanceolata (Lamb.) Hook in the People's Republic of China. On average, the percentage of polymorphic loci was 88.0, the number of alleles per locus was 3.0, and the expected heterozygosity was 0.394. The distribution of genetic diversity was not correlated with the geographic and climatic variables of the populations. However, allele frequencies correlated linearly with the mean annual temperature of the populations at Mdh-1, Mdh-2, Mnr-2, Pgi-1, and Skdh-1 and with the altitude of the populations at Aph-4 and 6Pg-2. Of the total gene diversity 6% was attributed to among-population differentiation; 94% resided within populations. Two-locus gametic disequilibria were found in 15 of the 16 populations, and higher-order gametic disquilibria were significant in most populations. The gametic disequilibria did not correlate with geographic and climatic variables. The results suggest that population subdivision, founder effect, occurrence across diverse environments, a mating system dominated by inbreeding, and historical events from 2000 years of cultivation are contributing factors in the generation and maintenance of the multilocus genetic structure in this conifer.     

ASSOCIATIONS BETWEEN MITOCHONDRIAL AND NUCLEAR GENOTYPES IN CUTTHROAT TROUT HYBRID SWARMS

We examined mtDNA and nuclear allozyme genotypes in hybrid populations formed from interbreeding of westslope cutthroat trout (Oncorhynchus clarki lewisi) and Yellowstone cutthroat trout (O. c. bouvieri). These subspecies show substantial genetic divergence (Nei's D = 0.30; mtDNA P = 0.02). Diagnostic alleles at multiple nuclear loci and two distinct mtDNA haplotypes segregate in the hybrids. Nuclear and mtDNA genotypes are largely randomly associated, although there is slight disequilibrium in both nuclear and cytonuclear measures in some samples. Consistent positive gametic disequilibria for three pairs of nuclear loci confirm one previously reported linkage, and indicate two more. Allele frequencies provide no evidence for selection on individual chromosome segments. However, westslope mtDNA haplotype frequencies exceed westslope nuclear allele frequencies in all samples. This may be explained by differences in the frequency of occurrence of reciprocal F₁ matings, by viability, fertility, or sex ratio differences in the progeny of reciprocal matings, or by weak selection on mtDNA haplotypes.     

Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy–Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.     

Admixture and the organization of genetic diversity in a butterfly species complex revealed through common and rare genetic variants

Detailed information about the geographic distribution of genetic and genomic variation is necessary to better understand the organization and structure of biological diversity. In particular, spatial isolation within species and hybridization between them can blur species boundaries and create evolutionary relationships that are inconsistent with a strictly bifurcating tree model. Here, we analyse genome‐wide DNA sequence and genetic ancestry variation in Lycaeides butterflies to quantify the effects of admixture and spatial isolation on how biological diversity is organized in this group. We document geographically widespread and pervasive historical admixture, with more restricted recent hybridization. This includes evidence supporting previously known and unknown instances of admixture. The genome composition of admixed individuals varies much more among than within populations, and tree‐ and genetic ancestry‐based analyses indicate that multiple distinct admixed lineages or populations exist. We find that most genetic variants in Lycaeides are rare (minor allele frequency <0.5%). Because the spatial and taxonomic distributions of alleles reflect demographic and selective processes since mutation, rare alleles, which are presumably younger than common alleles, were spatially and taxonomically restricted compared with common variants. Thus, we show patterns of genetic variation in this group are multifaceted, and we argue that this complexity challenges simplistic notions concerning the organization of biological diversity into discrete, easily delineated and hierarchically structured entities.