Spatial autocorrelation in biology 1. Methodology

Spatial autocorrelation analysis tests whether the observed value of a nominal, ordinal, or interval variable at one locality is independent of values of the variable at neighbouring localities. The computation of autocorrelation coefficients for nominal, ordinal, and for interval data is illustrated, together with appropriate significance tests. The method is extended to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities being considered, and summarize the patterns of geographic variation exhibited by the response surface of any given variable.
Autocorrelation analysis is applied to microgeographic variation of allozyme frequencies in the snail Helix aspersa. Differences in variational patterns in two city blocks are interpreted.
The inferences that can be drawn from correlograms are discussed and illustrated with the aid of some artificially generated patterns. Computational formulae, expected values and standard errors are furnished in two appendices.     

Spatial Autocorrelation Analysis of Migration and Selection

We test various assumptions necessary for the interpretation of spatial autocorrelation analysis of gene frequency surfaces, using simulations of Wright's isolation-by-distance model with migration or selection superimposed. Increasing neighborhood size enhances spatial autocorrelation, which is reduced again for the largest neighborhood sizes. Spatial correlograms are independent of the mean gene frequency of the surface. Migration affects surfaces and correlograms when immigrant gene frequency differentials are substantial. Multiple directions of migration are reflected in the correlograms. Selection gradients yield clinal correlograms; other selection patterns are less clearly reflected in their correlograms. Sequential migration from different directions and at different gene frequencies can be disaggregated into component migration vectors by means of principal components analysis. This encourages analysis by such methods of gene frequency surfaces in nature. The empirical results of these findings lend support to the inference structure developed earlier for spatial autocorrelation analysis.     

Dermatoglyphic variation in Europe

We describe the geographic variation patterns of 236 dermatoglyphic variables (118 for each sex) for 74 samples in Europe. Using principal components analysis and rotating to simple structure, we simplified these patterns to the first 20 axes, representing 74.2% of covariation. We then used heterogeneity tests, interpolated surfaces, one-dimensional and directional correlograms, and distances between correlograms to analyze the factor scores of these 20 axes. We also ordinated the 74 localities. The data are remarkable for showing little spatial autocorrelation, despite significant heterogeneity among localities. Only three factor axes exhibit consistently significant correlograms, indicating that there are few spatial patterns in the original variables in Europe. Almost all correlations between pairs of variables occur within serially homologous character sets and are thus developmentally determined. There is some support for demic diffusion from the southeast in finger patterns and ridge counts. We compare these results to those of previous studies and note that Lapps and Icelanders are outliers with respect to both genetics and finger tip variables, whereas Tatars are outliers with respect to craniometrics and dermatoglyphics. © 1996 Wiley-Liss, Inc.     

Geographic variation in Pemphigus populicaulis (Insecta: Aphididae) in Eastern North America*,†

The geographic variation of 33 morphological characters of the gall-forming aphid Pemphigus populicaulis is studied for 118 localities east of 100^oW longitude. Variation can be partitioned into within-gall, among-gall and among-locality components. Among localities variation ranges from 26 to 54%, being significant for all characters. Variation among galls within localities ranges from 24 to. 56%, that within-galls from 8 to 4796. The design of the study permits computation of character correlation matrices within and among localities. Gall size is correlated with tnorphometric characters only on an interlocality but not on an intralocality basis. Interlocalily correlations are a function of intralocality correlations, confirming earlier predictions. There is little correlation between characters of stem mother and alate morphotypes within localities, whereas among localities such correlation is appreciable. This phenomenon may be caused by aspects ol the environment that vary among localities but remain reasonably constant through the earlv life cycle of the aphid. When subjected to factor analysis both correlation matrices yield four factors. Multiple discriminant analysis of the data set results in five interpretable significant axes. Maps are furnished for characters representing the independent dimensions of variation and for discriminant function scores. The patterns of variation can be shown to be significantly nonrandom by Mantel's test and by spatial autocorrelation analysis. All variables are significantly positively autocorrelated at 200 km, many at 400 km and a few at 600 km; few general statements can be made about significant autocorrelations at higher distances. The positive autocorrelation at relatively short distances may be related to the pool of clones from which the genotypes of any one locality sample are taken. There are three correlogram patterns that can be associated with four clusters of variation patterns of characters. The separate patterns presumably cannot be explained by a single microevolutionary process.     

Detecting clinal and balanced selection using spatial autocorrelation analysis under kin-structured migration

Recently spatial autocorrelation has been employed to infer microevolutionary processes from patterns of genetic variation. In theory, different processes should show characteristic signature correlograms; e. g., clinal selection should produce correlograms decreasing from positive to negative autocorrelation, whereas uniform balanced selection should lead to no spatial autocorrelation. The ability of a statistical method such as spatial autocorrelation analysis to distinguish between these selective regimes or even to detect departures from neutrality is dependent on the strength of the evolutionary force and the population structure. Weak selection or migration will not be apparent against the expected background of stochastic noise. Moreover, the population structure may generate sufficient stochastic variation such that even strong evolutionary forces may fail to be detected. This study uses computer simulation to examine the effects of kin-structured migration and three different selective regimes on the shape of spatial correlograms to assess the ability of this technique to detect different microevolutionary processes. Genetic variation among 8 loci is simulated in a linear set of 25 artificial populations. Kin-structured stepping-stone migration among adjacent populations is modeled; directional, balanced, and clinal selection, as well as neutral loci are considered. These experiments show that strong selection produces correlograms of the predicted shape. However, with an anthropologically reasonable population structure, considerable stochastic variation among correlograms for different alleles may still exist. This suggests the need for caution in inferring genetic process from spatial patterns. © 1994 Wiley-Liss, Inc.     

Pattern‐oriented modelling of population genetic structure

Although several statistical approaches can be used to describe patterns of genetic variation and infer stochastic differentiation, selective responses, or interruptions of gene flow due to physical or environmental barriers, it is worthwhile to note that similar processes, controlled by several parameters in theoretical models, frequently give rise to similar patterns. Here, we develop a Pattern‐Oriented Modelling (POM) approach that allows us to determine how a complex set of parameters potentially driving empirical genetic differentiation among populations generate alternative scenarios that can be fitted to observed data. We generated 10 000 random combinations of parameters related to population size, gene flow and response to gradients (both driven by dispersal and selection) in a spatially explicit model, and analysed simulated patterns with F_ST statistics and mean correlograms using Moran's I spatial autocorrelation coefficients. These statistics were compared with observed patterns for a tree species endemic to the Brazilian Cerrado. For a best match with observed F_ST (equal to 0.182), the important parameters driving simulated scenario are mainly related to population structure, including low population size with closed populations (low N_m), strong distance decay of gene flow, in addition to a strong effect of the initial variance of allele frequencies. These scenarios present a low autocorrelation of allele frequencies. Best matching of correlograms, on the other hand, appears in simulations with a large population size, high N_m and low population differentiation and F_ST (as well as more gene flow). Thus, targeting the two statistics (correlograms and F_ST) shows that best matches with empirical data with two distinct sets of parameters in the simulations, because observed patterns involve both a relatively high F_ST and significant autocorrelation. This conflict can be resolved by assuming that initial variance in allele frequencies can be interpreted as reflecting deep‐time historical variation and evolutionary dynamics of allele frequencies, creating a relatively high level of population differentiation, whereas current patterns in gene flow creates spatial autocorrelation. This make sense in terms of the previous knowledge on population differentiation in D. alata, especially if patterns are explained by a combination of isolation‐by‐distance and allelic surfing due to range expansion after the last glacial maximum. This reveals the potential for more complex applications of POM in population genetics. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1152–1161.     

Geographic variation in Pemphigus populitransversus (Insecta: Aphididae)*†

The geographic variation of 33 morphological characters of two morphs of the gall-forming aphid Pemphigus populitransversus is studied in 214 locality samples. Among-locality variation ranges from 1 to 69% in the elongate morph and from 0 to 44% in the globular morph. The design of the study permits separation of interlocality correlations from intralocality correlations. The former are partly a function of the latter, confirming early observations on another Pemphigus species and on ticks. Factor analyses of both correlation matrices for both morphs yield four factors. Within localities these factors agree for the two morphs; among localities only one factor corresponds. Multiple discriminant analyses among localities of the two data sets do not correspond. There is little correlation between characters of stem mother and alate morphotypes within localities but such correlations are strong among localities. Maps are furnished for characters representing the independent dimensions of variation for each morph. Patterns of variation are shown to be significant by spatial autocorrelation analysis for both morphs but are much more marked in the elongate morph. Significant positive autocorrelation occurs up to 1000 km in the elongate morph – mostly only up to 200 km in the globular morph. There are two to three geographic variation patterns in the elongate morph, whereas in the globular morph the classes of patterns are less well defined and involve few characters. The environmental factors to which the globular and elongate morphs are adapting would appear to have different autocorrelation patterns. In each morph the patterns are clearly different and cannot be explained by a single microevolutionary process. The findings are compared with an earlier study in the related and largely sympatric P. populicaulis.     

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.     

水杉孑遗居群AFLP遗传变异的空间分布

本研究采用空间自相关分析方法对水杉 (Metasequoiaglyptostroboides)孑遗居群AFLP遗传变异的空间结构进行了研究 ,以探讨水杉孑遗居群遗传变异的分布特征及其形成机制。根据 6对AFLP选择性引物扩增的 46个多态性位点 ,选择了其表型频率在 2 5 %～ 75 %的 2 7个AFLP标记 ,运用等样本频率方法和等地理距离间隔方法分别对 3 9株和 3 7株原生母树进行了空间自相关系数Moran’sI值计算。结果表明 :水杉孑遗居群缺乏空间结构 ,绝大多数AFLP位点变异为随机分布的空间模式 ,但也有少数位点存在显著性随机相关 ,在 4～ 8km地理距离间隔显示负相关 ,说明该间隔可能是水杉孑遗居群的部分基因交流的有效屏障。水杉原生母树分布存在 12～ 2 8km的明显距离间隔空挡 ,说明人类从迁入该区域起就影响着水杉孑遗居群的原始生境 ,导致其生境片断化、景观破碎 ,进而形成岛屿状分布格局 ,并引起了水杉残留居群的随机遗传漂变。根据本研究结果 ,结合水杉孑遗居群较低的遗传多样性 ,分析探讨了水杉孑遗居群濒危的机理 ,并提出了相应的保育策略 ,为水杉的有效保育提供了科学依据     

EVOLUTION AND POPULATION STRUCTURE OF AFRICANIZED HONEY BEES IN BRAZIL: EVIDENCE FROM SPATIAL ANALYSIS OF MORPHOMETRIC DATA

In recent years, studies based on isoenzymatic patterns of geographic variation have revealed that what is usually called the Africanized honey bee does not constitute a single population. Instead, several local populations exist with various degrees of admixture with European honey bees. In this paper, we evaluated new data on morphometric patterns of Africanized honey bees collected at 42 localities in Brazil, using univariate and multivariate (canonical) trend surface and spatial autocorrelation analyses. The clinal patterns of variation found for genetically independent characters (wing size characters and some wing venation angles) are concordant with previous studies of malate dehydrogenase (MDH) allelic frequencies and support the hypothesis that larger honey bees in southern and southeastern Brazil originated by racial admixture in the initial phases of African honey bee colonization. Geographic variation patterns of Africanized honey bee populations reflect a demic diffusion process in which European genes were gradually lost because of the higher fitness of the African gene pool in Neotropical environmental conditions.     

Modern European cranial variables and blood polymorphisms show comparable spatial patterns

Spatial patterns in cranial traits for modern European populations are compared with patterns described by Sokal et al. (1989) for blood polymorphisms. Spatial patterns in these variables are described from both one-dimensional and directional autocorrelation correlograms. Manhattan distances computed among one-dimensional correlograms are used (1) to cluster variables with similar patterns and (2) to test the hypothesis that these clusters are to some extent accounted for by the type of variable. The one-dimensional correlograms for cranial traits do not show a significant contrast with either red cell antigens or the set of blood polymorphisms that excludes HLA. The only contrast that accounts for any of the cluster structure among one-dimensional correlograms is that between HLA and non-HLA variables. A cluster analysis of the directional correlograms demonstrates that cranial traits reflect patterns comparable to those for blood polymorphisms. This finding implies that patterns in cranial variables can be accounted for by the same, or similar, population processes as those inferred from patterns in blood polymorphisms. The implications of this finding for the likely origin of the northwest-southeast cline seen in some modern blood polymorphisms and modern cranial variables, but not in Neolithic cranial variables, are discussed.     

Cranial variation in European populations: a spatial autocorrelation study at three time periods

This study reports on spatial variation of 10 cranial variables in European populations at 3 time periods. Means for these variables, based on 137, 108, and 183 samples from the Early Medieval, Late Medieval, and Recent periods, were subjected to one-dimensional and directional spatial autocorrelation analyses. Significant spatial structure was found for most variables. It becomes more pronounced as time progresses. The spatial patterns are not strongly clinal. Correlograms based on distances computed from all variables are monotonic only to 900, 1,650, and 1,350 km for the three periods. Regional patterns are seen for most variables and become more structured and significant with time. There is little similarity among the correlograms of the variables at any one period and virtually none among periods. Inferences about spatial structure of these populations, based on spatial autocorrelation analysis, suggest a pattern dominated by migration, followed by expansion and admixture rather than selection or chance fluctuations. The patterns of morphometric change seem to reflect the patterns of linguistic change in these areas.     

Spatial autocorrelation analysis allows disentangling the balance between neutral and niche processes in metacommunities

One of the most popular approaches for investigating the roles of niche and neutral processes driving metacommunity patterns consists of partitioning variation in species data into environmental and spatial components. The logic is that the distance decay of similarity in communities is expected under neutral models. However, because environmental variation is often spatially structured, the decay could also be attributed to environmental factors that are missing from the analysis. Here, we use a spatial autocorrelation analysis protocol, previously developed to detect isolation‐by‐distance in allele frequencies, to evaluate patterns of species abundances under neutral dynamics. We show that this protocol can be linked with variation partitioning analyses. Moreover, in an attempt to test the neutral model, we derive three predictions to be applied both to original species abundances and to abundances predicted by a pure spatial model species abundances will be uncorrelated; Moran's I correlograms will reveal similar short‐distance autocorrelation patterns; an increasing degree of non‐neutrality will tend to generate patterns of correlation among abundances within groups of species with similar correlograms (i.e. within species with neutral and non‐neutral dynamics). We illustrate our protocol by analyzing spatial patterns in abundance of 28 terrestrially breeding anuran species from Central Amazonia. We recommend that researchers should investigate spatial autocorrelation patterns of abundances predicted by pure spatial models to identify similar patterns of spatial autocorrelation at short distances and lack of correlation between species abundances. Therefore, the hypothesis that spatial patterns in abundances are primarily due to pure neutral dynamics (rather than to missing spatiallystructured environmental factors) can be confirmed after taking environmental variables into account.     

HOW SEDENTARY ARE GREYWING FRANCOLINS (FRANCOLINUS AFRICANUS)?

Phasianids are considered to be sedentary birds with limited dispersal so that populations may be expected to show genetic isolation by distance. To test this, we examined genetic variability in 618 greywing francolins (Francolinus africanus) at 24 localities over a 1,500 km² area. We subdivided the samples to measure genetic population structure among localities separated by 6–60 km, and among coveys separated by 0.1–6 km. Thirteen of 30 (43%) allozyme loci were polymorphic, and heterozygosity ranged from 5.3 to 8.5% over 24 localities and averaged 7.0%, a value much larger than that found for other phasianids. Significant allele-frequency heterogeneity was detected among localities and among coveys at several localities for several loci. Mantel's test, however, showed that there was no correlation between geographical distance and the allele-frequency difference between localities for all but one allele. Although spatial autocorrelation was detected with Moran's I and Geary's c for two alleles, the geographical patterns of I in correlograms of 18 independent alleles showed a “crazy-quilt” pattern of allele-frequency patches. This shows that the isolation-by-distance model of subpopulation structure is inappropriate for these birds. Individuals, therefore, appear to disperse far beyond neighboring populations. “Private-allele” and F_ST estimates of migration under the island model were 8–9 individuals between localities of each generation. Allele-frequency heterogeneity, large amounts of gene flow, and the general lack of spatial autocorrelation imply that the small, socially-structured populations of greywing are subject to high rates of turnover, founder effects, and random drift.     

Elephants in space and time

Autocorrelation in animal movements can be both a serious nuisance to analysis and a source of valuable information about the scale and patterns of animal behavior, depending on the question and the techniques employed. In this paper we present an approach to analyzing the patterns of autocorrelation in animal movements that provides a detailed picture of seasonal variability in the scale and patterns of movement. We used a combination of moving window Mantel correlograms, surface correlation and crosscorrelation analysis to investigate the scales and patterns of autocorrelation in the movements of three herds of elephants in northern Botswana. Patterns of autocorrelation of elephant movements were long‐range, temporally complicated, seasonally variable, and closely linked with the onset of rainfall events. Specifically, for the three elephant herds monitored there was often significant autocorrelation among locations up to lags of 30 days or more. During many seasonal periods there was no indication of decreasing autocorrelation with increasing time between locations. Over the course of the year, herds showed highly variable and complex patterns of autocorrelation, ranging from random use of temporary home ranges, periodic use of focal areas, and directional migration. Even though the patterns of autocorrelation were variable in time and quite complex, there were highly significant correlations among the autocorrelation patterns of the different herds, indicating that they exhibited similar patterns of movement through the year. These major patterns of autocorrelation seem to be related to patterns of rainfall. The strength of correlation in movement patterns of the different herds decreased markedly at the cessation of major rain events. Also, there was a strong crosscorrelation between strength of autocorrelation of movement and rainfall, peaking at time lags of between three and four weeks. Overall, these approaches provide a powerful way to explore the scales and patterns of autocorrelation of animal movements, and to explicitly link those patterns to temporally variable environmental attributes, such as rainfall or vegetation phenology.     

Patterns of gene flow inferred from genetic distances in the Mediterranean region.

The analysis of population structure may lead to inferences about demographic phenomena. In particular, regions of sharp genetic differentiation suggest the existence of factors that impaired gene flow and increased the evolutionary role of genetic drift. Here, we present an analysis of a data set of 10 allele frequencies in 39 populations of the Mediterranean region. As a preliminary step, we describe spatial patterns of allele frequencies using spatial autocorrelation analysis. We then construct a network connecting localities and estimate genetic distances along the edges of the network. By applying specific algorithms, we locate on the map the areas of sharpest genetic differentiation, or genetic boundaries. The main boundaries separate the northern and the southern coasts, especially in their western portions; in addition, several localities appear genetically isolated. The comparatively high genetic differentiation across the western Mediterranean, where the sea distances between localities are shorter, strongly suggests that the sea distance by itself can hardly be regarded as a major isolating factor among these populations. On the contrary, the decrease in genetic resemblance between populations of the 2 coasts as one proceeds westward may reflect an increased genetic exchange in the eastern Mediterranean basin or independent human dispersal along the 2 coasts or both.     

Spatial autocorrelation as a tool for identifying the geographical patterns of aphid annual abundance

Abstract 1 A spatial autocorrelation analysis was undertaken to investigate the spatial structure of annual abundance for the pest aphid Myzus persicae collected in suction traps distributed across north‐west Europe. 2 The analysis was applied at two different scales. The Moran index was used to estimate the degree of spatial autocorrelation at all sites within the study area (global level). The contributions of each site to the global index were identified by the use of a local indicator of spatial autocorrelation (LISA). A hierarchical cluster analysis was undertaken to highlight differences between groups of resulting correlograms. 3 Similarity between traps was shown to occur over large geographical distances, suggesting an impact of phenomena such as climatic gradients or land use types. 4 The presence of outliers and zones of similarity (hot‐spots) and of dissimilarity (cold‐spots) were identified indicating a strong impact of local effects. 5 Several groups of traps characterized by similarities in their local spatial structure (correlograms, value of Moran's I_i) also had similar values for land use variables (the area occupied by agricultural zones, forest and sea). 6 It is concluded that trap data can provide information about Myzus persicae that is representative of large geographical areas. Thus, trap data can be used to estimate the aerial abundance of this species, even if the suction traps are not regularly and densely distributed.     

TESTING INFERENCES ABOUT MICRO-EVOLUTIONARY PROCESSES BY MEANS OF SPATIAL AUTOCORRELATION ANALYSIS

We generated numerous simulated gene-frequency surfaces subjected to 200 generations of isolation by distance with, in some cases, added migration or selection. From these surfaces we assembled six data sets comprising from 12 to 15 independent allele-frequency surfaces, to simulate biologically plausible population samples. The purpose of the study was to investigate whether spatial autocorrelation analysis will correctly infer the microevolutionary processes involved in each data set. The correspondence between the simulated processes and the inferences made concerning them is close for five of the six data sets. Errors in inference occurred when the effect of migration was weak, due to low gene frequency differential or low migration strength; when selection was weak and against a background with a complex pattern; and when a random process—isolation by distance—was the only one acting. Spatial correlograms proved more sensitive to detecting trends than inspection of gene-frequency surfaces by the human eye. Joint interpretation of the correlograms and their clusters proved most reliable in leading to the correct inference. The inspection and clustering of surfaces were useful for determining directional components. Because this method relies on common patterns across loci, as many gene frequencies as feasible should be used. We recommend spatial autocorrelation analysis for the detection of microevolutionary processes in natural populations.     

Genetic variation and population structure of cod, Gadus morhua L., in some fjords in northern Norway

Biochemical genetic polymorphism in cod from several fjords in Troms, northern Norway was analysed. Gene frequencies at several polymorphic loci ( Hb, Pgi, Ldh, Pgm, Gpd and Idh ) are given. Significant variation was found both within and between fjords, and even between samples from the same locality sampled in different years, indicating a mosaic structure of the cod population in the area studied. The results of the haemoglobin variation are compared to similar results obtained more than 20 years ago in the same and adjacent areas. The biochemical genetic variation is discussed in relation to stability of gene frequencies, isolation mechanisms and migration patterns.     

Genetic population structure of Italy. I. Geographic patterns of gene frequencies

The diversity of spatial patterns of 61 allele frequencies for 20 genetic systems (15 loci) in Italy is presented. Blood antigens, enzymes, and proteins were analyzed. The total number of data points over all systems and localities was 1119. We used homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices were reduced by clustering techniques to reveal the principal patterns. Only a few allele frequency surfaces are strongly correlated across loci. All systems but one (ADA) exhibit significant heterogeneity in allele frequencies among the localities. Significant spatial patterns are shown by 27 of the 61 surfaces. Only one pattern (cde; system 4.19) is clinal; another (PGM1) exhibits a pure isolation by distance pattern; the others show long-range differentiation in addition to the short-distance decline of autocorrelation expected under isolation by distance. There is a marked decline in overall genetic similarity with distance for most variables. The 27 spatially significant alleles in Italy are also significantly patterned in Europe, but in all but 2 cases the country-wide and continent-wide patterns differ. The Italian patterns are due to forces specific to Italy. Differential selection for alleles associated with malaria is still evident. Whereas short-range differentiation can with malaria is still evident. Whereas short-range differentiation can be explained by isolation by distance, long-range differentiation appears to be due to demographic changes in certain populations that may be maintained by physical and linguistic isolation.