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.     

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.     

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 in biology 2. Some biological implications and four applications of evolutionary and ecological interest

Spatial autocorrelation analysis tests whether the observed value of a variable at one locality is significantly dependent on values of the variable at neighbouring localities. The method was extended by us in an earlier paper to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities, and summarize the patterns of geographic variation exhibited by the response surface of any given variable. Identical variation patterns lead to identical correlograms, but different patterns may or may not yield different correlograms. Similarity in the correlograms of different variation patterns suggests similarity in the generating mechanism of the pattern.
The inferences that can be drawn from correlograms are discussed and illustrated. Examination and analysis of variation patterns of several characters or gene frequencies for one population, or of several populations in different places or at different times, permit some conclusions about the nature of the populational processes generating the observed patterns.
Autocorrelation analysis is applied to four biological situations differing in the nature of the data (interval or nominal), in the type of grid connecting the localities (regular or irregular), and the field of application (evolution or ecology). The examples comprise genotypes of individual mice, blood group frequencies in humans, gene frequency variation in a perennial herb, and the distribution of species of trees. The implications of our findings are discussed.     

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.     

Geographic variation of six dermatoglyphic traits in Eurasia

We describe the geographic variation patterns of six dermatoglyphic traits from 144 samples in Eurasia. The methods of analysis include computation of interpolated surfaces, one-dimensional and directional correlograms, correlations between all pairs of surfaces, and distances between correlograms. There are at least two, probably three, distinct and significant patterns of variation. 1) A general NW-SE trend for pattern intensity, the main line index, and frequency of hypothenar patterns. 2) A trend from the Middle East to the north and east for frequency of axial triradius and of accessory interdigital triradii. 3) A patchy pattern for frequency of the thenar-interdigital 1. The results are compatible with a diffusion process between Europe and the peoples of Northern Asia, and possibly with a radiation of populations from the Middle East. The hypothesis of diffusion processes is supported by substantial interpopulation correlations between dermatoglyphic traits that contrast sharply with largely negligible intralocality correlations. © 1993 Wiley-Liss, Inc.     

PEMPHIGUS REVISITED: CHANGES IN GEOGRAPHIC VARIATION BUT CONSTANCY IN VARIABILITY AND COVARIATION

Samples of the gall-forming aphids Pemphigus populicaulis and P. populitransversus (both elongate and globular morphs) were re-collected at sites in eastern North America after 13 to 16 years. Twenty-three morphometric characters of the galls, stem mothers, and alate fundatrigeniae were analyzed by univariate and multivariate methods. Varying proportions of the variance of each character are attributable to the four levels of variation—locality, year, year by locality interaction, and among galls (within one year and locality). The year by locality interaction level generally has the greatest variation and is highly significant. Year and locality effects tend to be lower and not significant. The variance components do not exhibit trends with time. Geographic variation patterns of single variables or factor scores in the original and revisited populations show significant spatial structure overall but lack clear-cut spatial patterns, especially clines. Observable patterns of variation match results of the spatial analyses: most characters lack clear trends; patterns in the revisited data do not resemble patterns for the same variables in the original data. Variability profiles for characters change little over the time span and are comparable among and within localities. Covariation among characters over localities is largely maintained during the time interval despite the changes in patterns. Fluctuating interclonal competition among aphids on secondary hosts is believed to cause the marked heterogeneity in space and time among the aphids in the galls.     

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.     

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.     

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.     

Effects of bird species-level environmental preference on landscape-level richness-heterogeneity relationships

The niche-based argument that species are filtered from environments in which they cannot sustain viable populations is the basis of the Richness-Heterogeneity Relationship (RHR). However, the multi-dimensionality of niches suggests that the RHR may take different shapes along different environmental axes, with potential confounding effects if filtering along the axes is not equally strong. Here, we explore how different structural and landscape variables drive the RHR as the accumulative outcome of environmental preferences at the species-level while considering the intercorrelation between heterogeneity levels along three niche axes. We used occurrence data of avifauna from 226 sites situated along a grassland-to-woodland gradient in a Midwestern USA study area. In each site, we quantified horizontal (habitat cover type), vertical (vegetation height structure), and spatial (habitat configuration) heterogeneity and explored the shape of the observed RHR at the landscape scale, as well as the correlations among heterogeneity levels at different axes. We then fitted species distribution models to environmental variables from the three axes separately and compared the stacked probabilities of occurrences of all species to the observed species richness. We found that predictions of richness patterns improved when more than one heterogeneity axis was included in RHR models, and that habitat suitability along different axes is not equally strong. Furthermore, a unimodal RHR along the vegetation height axis, which the species distribution models revealed to be a weak predictor for most species, may arise through intercorrelation with heterogeneity along the two other axes, along which we recorded stronger signals of environmental preference at the species level. Our results emphasize the importance of selecting relevant niche axes in studies of species richness patterns because ultimately, these patterns reflect the various environmental preferences of individual species.     

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.     

Temperature-related natural selection in a wind-pollinated tree across regional and continental scales

Adaptive genetic variation is a key factor in evolutionary biology, but the detection of signatures of natural selection remains challenging in nonmodel organisms. We used a genome scan approach to detect signals of natural selection in the Black alder (Alnus glutinosa), a widespread wind-pollinated tree. Gene flow through pollen dispersal is believed to be high in this species, and we therefore expected to find a clear response to natural selection. In combination with two different landscape genetic approaches, we determined which environmental variables were most associated with the inferred selection. This analysis was performed on a regional scale (northern Belgium) and on a continental scale (Europe). Because climate-related differences are much more pronounced at the continental scale, we expected to find more selection-sensitive genetic markers across Europe than across northern Belgium. At both spatial scales, a substantial number of genetic loci were considered outliers, with respect to neutral expectations, and were therefore identified as selective. Based on results from our combined approach, four putative selective loci (or 2.5%) were recovered with high statistical support. Although these loci seemed to be associated with different environmental variables, they were mainly temperature-related. Our study demonstrates that the use of complementary methods in landscape genetics allows the discovery of selective loci which otherwise might stay hidden. In combination with a genome scan, the selective loci can be verified and the nature of the selection pressure can be identified.     

林分光照空间异质性对水曲柳更新的影响

 光照是森林更新动态中极为关键的环境因子。本研究在东北天然次生林中选择样地,应用地统计学理论结合实验生态学方法,定量分析林分光照空间异质性特征,同时进行林下播种水曲柳（Fraxinus mandshurica）的更新实验,探测更新格局特征。通过空间关联性分析,研究探讨是否林分光照的空间变异对水曲柳更新有重要影响作用。研究结果表明： 1）生长季林分平均光照仅为全光照的4.2%～4.6%,在空间分布上呈现非常明显的异质性特征,空间自相关变异（62.5%～78.2%）主要体现在10.9～12.4 m的尺度上。2）林分光照不同的空间样点上,水曲柳更新幼苗发生数量和秋季幼苗存活数量均存在显著差异,光照相对强的微生境中,更新苗发生数量较多且存活率高,而在光照较弱的微生境中则更新较差,更新具有十分明显的空间格局。3）更新格局与林分光照空间异质性特征紧密关联。在光照空间异质性程度较高、空间变异较复杂的条件下,更新相应呈现出较复杂的空间格局,自相关的变异表现在较小尺度范围（2.12～6.97 m）。在光照空间异质性程度较低、空间变异复杂性较小的条件下,更新格局的复杂程度明显变小,空间自相关变异（>83%）表现在较大的尺度上（30 m）,对更新格局起主要的影响作用,随机变异的影响很小（<17%）。这些研究结果说明,林分光照环境在水曲柳更新中的作用十分关键,林分光照的空间异质性对更新格局起决定性作用。     

Is the spatial pattern of a tree population in a seasonally dry tropical climate explained by density‐dependent mortality?

Spatial pattern of tropical plants is initially generated by limited seed dispersal, but the role of density‐dependent and independent mechanisms as modifiers of these patterns across ontogeny is poorly understood. We investigated whether density‐dependent mortality (DDM) and environmental heterogeneity can drive spatial pattern across the ontogeny of a tree in a seasonally dry tropical climate. We used Moran's I correlograms and spatial analysis by distance indices (SADIE) to assess the spatial patterns of the pre‐ and post‐germinative stages of Cordia oncocalyx (Boraginaceae), an abundant tree endemic in the deciduous thorny woodland in the northeastern Brazilian semiarid region. We also used RDA to analyse the effect of DDM and environmental heterogeneity (measured by microtopography and canopy openness) in the mortality and recruitment. Seeds, seedlings, juveniles and adults showed aggregated spatial patterns; infants and immatures were randomly distributed; adults, seeds and seedlings attracted each other while adult, juveniles and immatures repulsed each other. Infant and seedling mortality rates were related to DDM and the recruitment from infant to juvenile was more influenced by spatial heterogeneity. Attraction was determined by local dispersal; repulsion was related to DDM and environment heterogeneity, which allowed the return to aggregation in adult stage. Together, these results indicated that spatial pattern can change across ontogeny, in which the initial stages are responsive to DDM and the final stages are influenced by spatial heterogeneity.     

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.     

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.     

Spatial autocorrelation and red herrings in geographical ecology

Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates ‘red herrings’, such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro‐scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least‐squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north–south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non‐detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de‐emphasized predictors with strong autocorrelation and long‐distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.