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.     

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.     

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.     

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.     

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。     

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.     

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 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.     

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.     

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.