Mantel test in population genetics

The comparison of genetic divergence or genetic distances, estimated by pairwise F_ST and related statistics, with geographical distances by Mantel test is one of the most popular approaches to evaluate spatial processes driving population structure. There have been, however, recent criticisms and discussions on the statistical performance of the Mantel test. Simultaneously, alternative frameworks for data analyses are being proposed. Here, we review the Mantel test and its variations, including Mantel correlograms and partial correlations and regressions. For illustrative purposes, we studied spatial genetic divergence among 25 populations of Dipteryx alata (“Baru”), a tree species endemic to the Cerrado, the Brazilian savannas, based on 8 microsatellite loci. We also applied alternative methods to analyze spatial patterns in this dataset, especially a multivariate generalization of Spatial Eigenfunction Analysis based on redundancy analysis. The different approaches resulted in similar estimates of the magnitude of spatial structure in the genetic data. Furthermore, the results were expected based on previous knowledge of the ecological and evolutionary processes underlying genetic variation in this species. Our review shows that a careful application and interpretation of Mantel tests, especially Mantel correlograms, can overcome some potential statistical problems and provide a simple and useful tool for multivariate analysis of spatial patterns of genetic divergence.     

濒危物种--巴东木莲等位酶遗传变异的空间自相关分析

采用空间自相关分析方法对巴东木莲目前残留的两个最大居群, 小溪居群的40个个体和桑植居群的28个个体等位酶遗传变异的空间结构进行了研究, 以揭示两居群遗传变异的空间模式, 并探讨其形成机制及与巴东木莲致濒原因、过程之间的关系。根据检测出来的8个酶系统的19个酶位点, 选择基因频率大于0 1小于0 9的等位基因, 运用等样本频率和等地理距离间隔两种方法分别计算两居群不同距离等级下的Moran’sI空间自相关系数。结果表明: 小尺度的小溪居群等位基因的遗传变异缺乏空间结构, 为随机分布模式。巴东木莲生境片断化的桑植居群则是相反的结果, 遗传变异存在明显的空间结构, 遗传变异空间分布为斑块状。造成这种差别的原因可能是桑植居群片断化和地理隔离造成的基因流的限制。上述结果为进一步制定有效的巴东木莲的保育措施提供科学的理论依据。     

GENETIC CONSEQUENCES OF SEED DISPERSAL IN THREE SYMPATRIC FOREST HERBS. II. MICROSPATIAL GENETIC STRUCTURE WITHIN POPULATIONS

Significant spatial genetic differentiation over short distances was detected by F-statistics and spatial autocorrelation within populations of the temperate forest herbs Cryptotaenia canadensis, Osmorhiza claytonii and Sanicula odorata (Apiaceae). Differences among the three species were consistent with estimates of their seed-dispersal abilities. Populations of Cryptotaenia, with the most limited seed dispersal, are characterized by genetic structure at smaller spatial scales than those of Osmorhiza or Sanicula, as indicated by higher estimates of θ(F_st), larger autocorrelation coefficients, and correlograms with more distant x-intercepts. Although spatial autocorrelation was somewhat more sensitive to the distribution of rare alleles than F-statistics, the two methods were generally concordant. Genetic structure was more pronounced, and inbreeding coefficients larger, in low-density, patchy populations than in a high-density site. Observed patterns of spatial autocorrelation, particularly for Cryptotaenia, were in agreement with expectations based on simulations of isolation by distance. The magnitude of observed autocorrelations was less than those typically produced in computer-simulation studies, but this discrepancy between empirical and theoretical results probably is derived from a lack of genetic and demographic equilibrium in natural populations. Isolation by distance can be an important evolutionary force organizing spatial genetic structure in plant populations, particularly in predominantly self-fertilizing species such as those studied here.     

Patchy population structure in a short-distance migrant: evidence from genetic and demographic data

Species often occur in subdivided populations as a consequence of spatial heterogeneity of the habitat. To describe the spatial organization of subpopulations, existing theory proposes three main population models: patchy population, metapopulation and isolated populations. These models differ in their predicted levels of connectivity among subpopulations, and in the risk that a subpopulation will go extinct. However, spatially discrete subpopulations are commonly considered to be organized as metapopulations, even though explicit tests of metapopulation assumptions are rare. Here, we test predictions of the three models on the basis of demographic and genetic data, a combined approach so far surprisingly little used in mobile organisms. From 2002 to 2005, we studied nine subpopulations of the wetland-restricted reed bunting ( Emberiza schoeniclus ) in the southeastern part of the Canton Zurich (Switzerland), from which local declines of this species have been reported. Here, wetlands are as small as 2.7 ha and separated through intensively used agricultural landscapes. Demographic data consisted of dispersal of colour-banded individuals among subpopulations, immigration rates and extinction-/recolonization dynamics. Genetic data were based on the distribution of genetic variability and gene flow among subpopulations derived from the analysis of nine microsatellite loci. Both demographic and genetic data revealed that the patchy population model best described the spatial organization of reed bunting subpopulations. High levels of dispersal among subpopulations, high immigration into the patchy population, and genetic admixture suggested little risk of extinction of both subpopulations and the entire patchy population. This study exemplifies the idea that spatially discrete subpopulations may be organized in ways other than a metapopulation, and hence has implications for the conservation of subpopulations and species.     

Phylogeography in continuous space: coupling species distribution models and circuit theory to assess the effect of contiguous migration at different climatic periods on genetic differentiation in Busseola fusca (Lepidoptera: Noctuidae)

Current population genetic models fail to cope with genetic differentiation for species with large, contiguous and heterogeneous distribution. We show that in such a case, genetic differentiation can be predicted at equilibrium by circuit theory, where conductance corresponds to abundance in species distribution models (SDMs). Circuit‐SDM approach was used for the phylogeographic study of the lepidopteran cereal stemborer Busseola fuscaFüller (Noctuidae) across sub‐Saharan Africa. Species abundance was surveyed across its distribution range. SDMs were optimized and selected by cross‐validation. Relationship between observed matrices of genetic differentiation between individuals, and between matrices of resistance distance was assessed through Mantel tests and redundancy discriminant analyses (RDAs). A total of 628 individuals from 130 localities in 17 countries were genotyped at seven microsatellite loci. Six population clusters were found based on a Bayesian analysis. The eastern margin of Dahomey gap between East and West Africa was the main factor of genetic differentiation. The SDM projections at present, last interglacial and last glacial maximum periods were used for the estimation of circuit resistance between locations of genotyped individuals. For all periods of time, when using either all individuals or only East African individuals, partial Mantel r and RDA conditioning on geographic distance were found significant. Under future projections (year 2080), partial r and RDA significance were different. From this study, it is concluded that analytical solutions provided by circuit theory are useful for the evolutionary management of populations and for phylogeographic analysis when coalescence times are not accessible by approximate Bayesian simulations.     

A heterogeneity test for fine-scale genetic structure

For organisms with limited vagility and/or occupying patchy habitats, we often encounter nonrandom patterns of genetic affinity over relatively small spatial scales, labelled fine-scale genetic structure. Both the extent and decay rate of that pattern can be expected to depend on numerous interesting demographic, ecological, historical, and mating system factors, and it would be useful to be able to compare different situations. There is, however, no heterogeneity test currently available for fine-scale genetic structure that would provide us with any guidance on whether the differences we encounter are statistically credible. Here, we develop a general nonparametric heterogeneity test, elaborating on standard autocorrelation methods for pairs of individuals. We first develop a 'pooled within-population' correlogram, where the distance classes (lags) can be defined as functions of distance. Using that pooled correlogram as our null-hypothesis reference frame, we then develop a heterogeneity test of the autocorrelations among different populations, lag-by-lag. From these single-lag tests, we construct an analogous test of heterogeneity for multilag correlograms. We illustrate with a pair of biological examples, one involving the Australian bush rat, the other involving toadshade trillium. The Australian bush rat has limited vagility, and sometimes occupies patchy habitat. We show that the autocorrelation pattern diverges somewhat between continuous and patchy habitat types. For toadshade trillium, clonal replication in Piedmont populations substantially increases autocorrelation for short lags, but clonal replication is less pronounced in mountain populations. Removal of clonal replicates reduces the autocorrelation for short lags and reverses the sign of the difference between mountain and Piedmont correlograms.     

The influence of niche and neutral processes on a neotropical anuran metacommunity

One of the most important questions in ecology is the relative importance of local conditions (niche processes) and dispersal ability (neutral processes) in driving metacommunity structure. Although many studies have been conducted in recent years, there is still much debate. We evaluated the processes (niche and neutral) responsible for variation in anuran composition in 28 lentic water bodies in southeastern Brazil. Because anurans depend heavily on environmental conditions, we hypothesized that environmental variables (niche processes) are the most important drivers of community composition. Additionally, as anurans have limited dispersal abilities, and the study region presents harsh conditions (high forest fragmentation, low rainfall and long dry season), we expected a lower, but significant, spatial signature in metacommunity structure, due to neutral dynamics. We used a partial redundancy analysis with variation partitioning to evaluate the relative influence of environmental and spatial variables as drivers of metacommunity structure. Additionally, we used a recently developed spatial autocorrelation analysis to test if neutral dynamics can be attributed to the pure spatial component. This analysis is based on predictions that species abundances are independent but similarly spatially structured, with correlograms similar in shape. Therefore, under neutral dynamics there is no expectation of a correlation between the pairwise distance of spatial correlograms and the pairwise correlation of species abundances predicted by the pure spatial component. We found that the environmental component explained 21.5%, the spatial component 10.2%, and the shared component 6.4% of the metacommunity structure. We found no correlation between correlograms and correlation of abundances predicted by the pure spatial component (Mantel test = ?0.109, P = 0.961). In our study, niche‐based processes are the dominant process that explained community composition. However, neutral processes are important because spatial variation can be attributed to pure neutral dynamics rather than to missing spatially structured environmental factors.     

Genetic diversity and population structure of Eugenia dysenterica DC. (``cagaiteira' – Myrtaceae) in Central Brazil: Spatial analysis and implications for conservation and management

Studies about the organization of the genetic variability and population structure in natural plant populations are used to support conservation and management programs. Among the Cerrado fruit tree species that possess potential economic importance in agriculture, the “Cagaiteira” (Eugenia dysenterica DC. – Myrtaceae), deserves an special position. We obtained information about allele and genotypic frequencies in 10 local populations, situated up to 250 km apart, from six isozymes that furnished a total of 8 loci. The average within-population fixation index (f) was 0.337, and the out crossing rate was 0.835, suggesting a mixed mating system for this species, which seems to be preferably alogamous. Based on genetic diversity and analysis of variance techniques, a high degree of population differentiation (θ_P = 0.154) was found, in comparison with other tropical tree species. Genetic divergence, analyzed by Nei's genetic distances, clustered with UPGMA and ordinated by non-metric multidimensional scaling, showed spatial patterns of clusters of local populations. Explicit spatial analyses, using Mantel tests and boundary tests, basically confirmed these patterns and revealed a complex pattern of genetic variation in geographic space. The intercept of the multivariate spatial correlograms was around 120 km, an indication of the minimum distance between samples needed to conserve genetic diversity among samples. This spatial scale can be used to define population genetics units for conservation programs or to establish sampling strategies. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new eigenfunction spatial analysis describing population genetic structure

Several methods of spatial analyses have been proposed to infer the relative importance of evolutionary processes on genetic population structure. Here we show how a new eigenfunction spatial analysis can be used to model spatial patterns in genetic data. Considering a sample of n local populations, the method starts by modeling the response variable (allele frequencies or phenotypic variation) against the eigenvectors sequentially extracted from a geographic distance matrix (n × n). The relationship between the coefficient of determination (R ²) of the models and the cumulative eigenvalues, which we named the spatial signal-representation (SSR) curve, can be more efficient than Moran’s I correlograms in describing different patterns. The SSR curve was also applied to simulated data (under distinct scenarios of population differentiation) and to analyze spatial patterns in alleles from microsatellite data for 25 local populations of Dipteryx alata, a tree species endemic to the Brazilian Cerrado. The SSR curves are consistent with previous phylogeographical patterns of the species, revealing combined effects of isolation-by-distance and range expansion. Our analyses demonstrate that the SSR curve is a useful exploratory tool for describing spatial patterns of genetic variability and for selecting spatial eigenvectors for models aiming to explain spatial responses to environmental variables and landscape features.     

Combined definition of seed transfer guidelines for ecological restoration in the French Pyrenees

Question: Can genetic tools combined with phytogeography help to define local plants and how geographically close the source population should be to the restoration site? Location: Subalpine and alpine French Pyrenees. Methods: The main phytogeographic boundaries in the French Pyrenees described by different authors were studied and this geographic pattern was compared with the results of genetic analysis for the four Pyrenean plants studied (Trifolium alpinum, Festuca eskia, Festuca gautieri and Rumex scutatus), based on random amplified polymorphic DNA (RAPD) marker analysis, unweighted pair‐group method with arithmetic averages (UPGMA) analysis and Mantel correlograms comparing geographic and genetic distances. Results: The genetic analysis allowed definition of two main evolutionarily significant units (ESUs) for the plants under study. Although the limit between the two zones was slightly variable according to the species considered, an eastern and a western ESU was consistently observed. This delineation was concordant with the main phytogeographic boundaries of the French Pyrenees. Conclusion: RAPD markers and associated Mantel correlograms can be useful to draw ESUs for individual species when the sampling intensity is relatively dense, and similarities were revealed between species sharing the same distribution range. This delineation allowed integration of infraspecific plant variation in the management of natural resources for revegetation in the Pyrenees. Nevertheless, caution is needed for the establishment of seed pools in order to maximize genetic diversity in each of the pools during collection and production.     

Periodicity in spatial data and geostatistical models: autocorrelation between patches

Several recent studies in landscape ecology have found periodicity in correlograms or semi-variograms calculated, for instance, from spatial data of soils, forests, or animal populations. Some of the studies interpreted this as an indication of regular or periodic landscape patterns. This interpretation is in disagreement with other studies that doubt whether such analysis is valid. The objective of our study was to explore the relationship between periodicity in landscape patterns and geostatistical models. We were especially interested in the validity of the assumption that periodicity in geostatistical models indicates periodicity in landscape pattern, and whether the former can characterize frequency and magnitude of the latter. We created maps containing various periodic spatial patterns, derived correlograms from these, and examined periodicity in the correlograms. We also created non-regular maps that we suspected would cause periodicity in correlograms. Our results demonstrate that a) various periodic spatial patterns produce periodicity in correlograms derived from them, b) the distance-lags at which correlograms peak correspond to the average distances between patch centers, c) periodicity is strongest when the diameter of patches is equal to the distance between patch edges, d) periodicity in omni-directional correlograms of complex spatial patterns (such as checkerboards) are combinations of several waves because inter-patch distances differ with direction; multiple directional correlograms can decompose such complexity, and e) periodicity in correlograms can also be caused when the number of patches in a study site is small. These results highlight that correlograms can be used to detect and describe regular spatial patterns. However, it is crucial to ensure that the assumption of stationarity is not violated, i.e., that the study area contains a sufficiently large number of patches to avoid incorrect conclusions.     

Global distribution of Polaromonas phylotypes--evidence for a highly successful dispersal capacity

Bacteria from the genus Polaromonas are dominant phylotypes in clone libraries and culture collections from polar and high-elevation environments. Although Polaromonas has been found on six continents, we do not know if the same phylotypes exist in all locations or if they exhibit genetic isolation by distance patterns. To examine their biogeographic distribution, we analyzed all available, long-read 16S rRNA gene sequences of Polaromonas phylotypes from glacial and periglacial environments across the globe. Using genetic isolation by geographic distance analyses, including Mantel tests and Mantel correlograms, we found that Polaromonas phylotypes are globally distributed showing weak isolation by distance patterns at global scales. More focused analyses using discrete, equally sampled distances classes, revealed that only two distance classes (out of 12 total) showed significant spatial structuring. Overall, our analyses show that most Polaromonas phylotypes are truly globally distributed, but that some, as yet unknown, environmental variable may be selecting for unique phylotypes at a minority of our global sites. Analyses of aerobiological and genomic data suggest that Polaromonas phylotypes are globally distributed as dormant cells through high-elevation air currents; Polaromonas phylotypes are common in air and snow samples from high altitudes, and a glacial-ice metagenome and the two sequenced Polaromonas genomes contain the gene hipA, suggesting that Polaromonas can form dormant cells.     

Effects of landscape and history on diversification of a montane, stream-breeding amphibian

Aim The aim of this study was to understand the roles of landscape features in shaping patterns of contemporary and historical genetic diversification among populations of the Andean tree frog (Hypsiboas andinus) across spatial scales. Location Andes mountains, north‐western Argentina, South America. Methods Mitochondrial DNA control region sequences were utilized to assess genetic differentiation among populations and calculate population pair‐wise genetic distances. Three models of movement, namely traditional straight‐line distance and two effective distances based on habitat classification, were examined to determine which of these explained the most variation in pair‐wise population genetic differentiation. The two habitat classifications were based on digital vegetation and hydrology layers that were generated from a 90‐m resolution digital elevation model (DEM) and known relationships between elevation and habitat. Mantel tests were conducted to test for correlations between geographic and genetic distance matrices and to estimate the percentage variation explained by each type of geographic distance. To investigate the location of possible barriers to gene flow, we used Monmonier’s maximum difference algorithm as implemented in barrier 2.2. Results At both geographic scales, effective distances explained more variation in genetic differentiation than did straight‐line distance. The least‐cost distances based on the simple classification performed better than the more detailed habitat classification. We controlled for the effects of historical range fragmentation determined from previous nested clade analyses, and therefore evaluated the effect of different distances on the genetic variation attributable to more recent factors. Effective distances identified populations that were highly divergent as a result of isolation in unsuitable habitats. The proposed locations of barriers to gene flow identified using Monmonier’s maximum difference algorithm corresponded well with earlier analyses and supported findings from our partial Mantel tests. Main conclusions Our results indicate that landscape features have been important in both historical and contemporary genetic structuring of populations of H. andinus at both large and small spatial scales. A landscape genetic perspective offers novel insights not provided by traditional phylogeographic studies: (1) effective distances can better explain patterns of differentiation in populations, especially in heterogeneous landscapes where barriers to dispersal may be common; and (2) least‐cost path analysis can help to identify corridors of movement between populations that are biologically more realistic.     

Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data

The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum-of-squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and canonical analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and canonical analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.     

Patterns of seed dispersal and pollen flow in Quercus garryana (Fagaceae) following post-glacial climatic changes

Aim We examined the genetic structure of Quercus garryana to infer post‐glacial patterns of seed dispersal and pollen flow to test the hypotheses that (1) peripheral populations are genetically distinct from core populations and from one another; (2) genetic diversity declines towards the poleward edge of the species’ range; and (3) genetic diversity in the chloroplast genome, a direct measure of seed dispersal patterns, declines more sharply with increasing latitude than diversity in the nuclear genome. We address our findings in the context of known historical oak distribution from pollen core data derived from previously published research. Location Oak–savanna ecosystems from southern Oregon, USA (core populations/non‐glaciated range) northward to Vancouver Island, British Columbia, Canada (peripheral populations/glaciated range). Methods We genotyped 378 trees from 22 sites with five chloroplast and seven nuclear microsatellite loci. For both sets of markers, we estimated genetic diversity and differentiation using an analysis of molecular variance and generated Mantel correlograms to detect genetic and geographical distance correlations. For the nuclear markers, we also used a Bayesian approach to infer population substructure. Results There was a large degree of population differentiation revealed by six chloroplast haplotypes, with little (≤ 3) or no haplotype diversity within sites. Peripheral island locations shared the same, maternally inherited chloroplast haplotype, whereas locations in mainland Washington had greater haplotype diversity. In contrast, genetic diversity of the nuclear markers was high at all locations sampled. Populations clustered into two groups and were significantly positively correlated over large spatial scales (≤ 200 km), although allele richness decreased significantly with latitude. Population substructure was observed between core and peripheral populations because rare alleles were absent in peripheral localities and common allele frequencies differed. Main conclusions The observed pattern of chloroplast haplotype loss at the northern periphery suggests restricted seed dispersal events from mainland sites to peripheral islands. This pattern was unexpected, however, as refugial oak populations remained near the current post‐glacial range even during the Last Glacial Maximum. Using nuclear markers, we found high within‐population diversity and population differentiation only over large spatial scales, suggesting that pollen flow is relatively high among populations.     

Genes mirror geography in Daphnia magna

Identifying the presence and magnitude of population genetic structure remains a major consideration in evolutionary biology as doing so allows one to understand the demographic history of a species as well as make predictions of how the evolutionary process will proceed. Next‐generation sequencing methods allow us to reconsider previous ideas and conclusions concerning the distribution of genetic variation, and what this distribution implies about a given species evolutionary history. A previous phylogeographic study of the crustacean Daphnia magna suggested that, despite strong genetic differentiation among populations at a local scale, the species shows only moderate genetic structure across its European range, with a spatially patchy occurrence of individual lineages. We apply RAD sequencing to a sample of D. magna collected across a wide swath of the species' Eurasian range and analyse the data using principle component analysis (PCA) of genetic variation and Procrustes analytical approaches, to quantify spatial genetic structure. We find remarkable consistency between the first two PCA axes and the geographic coordinates of individual sampling points, suggesting that, on a continent‐wide scale, genetic differentiation is driven to a large extent by geographic distance. The observed pattern is consistent with unimpeded (i.e. no barriers, landscape or otherwise) migration at large spatial scales, despite the fragmented and patchy nature of favourable habitats at local scales. With high‐resolution genetic data similar patterns may be uncovered for other species with wide geographic distributions, allowing an increased understanding of how genetic drift and selection have shaped their evolutionary history.     

Effect of landscape features on genetic structure of the goitered gazelle (<Emphasis Type="Italic">Gazella subgutturosa</Emphasis>) in Central Iran

The populations of goitered gazelle suffered significant decline due to natural and anthropogenic factors over the last century. Investigating the effects of barriers on gene flow among the remaining populations is vital for conservation planning. Here we adopted a landscape genetics approach to evaluate the genetic structure of the goitered gazelle in Central Iran and the effects of landscape features on gene flow using 15 polymorphic microsatellite loci. Spatial autocorrelation, isolation by distance (IBD) and isolation by resistance (IBR) models were used to elucidate the effects of landscape features on the genetic structure. Ecological modeling was used to construct landscape permeability and resistance map using 12 ecogeographical variables. Bayesian algorithms revealed three genetically homogeneous groups and restricted dispersal pattern in the six populations. The IBD and spatial autocorrelation revealed a pattern of decreasing relatedness with increasing distance. The distribution of potential habitats was strongly correlated with bioclimatic factors, vegetation type, and elevation. Resistance distances and graph theory were significantly related with variation in genetic structure, suggesting that gazelles are affected by landscape composition. The IBD showed greater impact on genetic structure than IBR. The Mantel and partial Mantel tests indicated low but non-significant effects of anthropogenic barriers on observed genetic structure. We concluded that a combination of geographic distance, landscape resistance, and anthropogenic factors are affecting the genetic structure and gene flow of populations. Future road construction might impede connectivity and gene exchange of populations. Conservation measures on this vulnerable species should consider some isolated population as separate management units.     

Spatial patterns of human gene frequencies in Europe

The aims of this study of spatial patterns of human gene frequencies in Europe are twofold. One is to present new methodology developed for the analysis of such data. The other is to report on the diversity of spatial patterns observed in Europe and their interpretation as evidence of population processes. Spatial variation in 59 allele and haplotype frequencies (26 genetic systems) for polymorphisms in blood antigens, enzymes, and proteins is analyzed for an aggregate of 3,384 localities, using homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices are reduced to reveal the principal patterns by clustering techniques. The findings of this study can be summarized as follows: 1) There is significant heterogeneity in allele frequencies among the localities for all but one genetic system. 2) There are significant spatial patterns for most allele frequencies. 3) There is a substantial minority of clinal patterns in these populations. Clinal trends are found more frequently in HLA alleles than for other variables. North-south and northwest-southwest gradients predominate. 4) There is a strong decline in overall genetic similarity with geographic distance for most variables. 5) There are few, if any, appreciable correlations in pairs of allele frequencies over the continent, and there is little interesting correlation structure in the resulting correlation matrix. 6) Few spatial correlograms are markedly similar to each other, yet they form well-defined clusters. Spatial variation patterns, therefore, differ among allele frequencies. Patterns of human gene frequencies in modern Europe are diverse and complex. No single model suffices for interpretation of the observed genetic structure. Some clinal patterns reported here support the Neolithic demic-expansion hypothesis, others suggest latitudinal selection. Most of the clinal patterns are in HLA alleles, but there is also evidence from ABO for east-west migration diffusion. The majority of patterns are patchy, consistent with hypotheses of isolation by distance or of settlement of genetically differing, subsequently expanding ethnic groups. While undoubtedly there has been an ongoing stochastic process of differentiation consistent with the isolation-by-distance model, this has not obscured the directional patterns caused by migration (demic diffusion), and has perhaps only reinforced the contribution from settlement of ethnic units to patterns of genetic variation. However, the impact of the latter is most difficult to discern and requires further methodological developments.     

Silene rothmaleri P. Silva (Caryophyllaceae), a rare, fragmented but genetically diverse species

Silene rothmaleri is an endemic Portuguese species considered extinct until 1992, when it was rediscovered in the wild with a highly fragmented distribution. These rare plants occur along the southwestern Portuguese coast in small populations, which in addition to phenological differences that occur along the north–south gradient could create a pattern of genetic isolation. To evaluate the degree of genetic diversity and estimate the relationship between population fragmentation and genetic variability, we analysed the five known populations of S. rothmaleri using random amplified polymorphic DNA. Degree of polymorphism and Shannon Index of phenotypic diversity revealed high levels of diversity, found mainly within populations. PCo and cluster analysis revealed a distinct north–south cline, which was confirmed by spatial autocorrelation (Mantel) analysis. This indicates the existence of gene flow between small nearby populations and its insufficiency between widely separated populations. Levels of gene flow (Nm) estimated from the Shannon Index reveal a pattern consistent with a larger past distribution that went through a period of contraction and lack of gene flow followed by population differentiation. The central and largest population probably acts as a core of genetic variability inherited as a relict from a larger and more diverse ancestral population.