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.     

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.