A Test of Spatial Autocorrelation Analysis Using an Isolation-by-Distance Model

Using the isolation-by-distance model as an example, we have examined several assumptions of spatial autocorrelation analysis applied to gene frequency surfaces. Gene frequency surfaces generated by a simulation of Wright's isolation-by-distance model were shown to exhibit spatial autocorrelation, except in the panmictic case. Identical stochastic generating processes result in surfaces with characteristics that are functions of the process parameters, such as parental vagility and neighborhood size. Differences in these parameters are detectable as differences in spatial autocorrelations after only a few generations of the simulations. Separate realizations of processes with identical parameters yield similar spatial correlograms. We have examined the inferences about population structure that could have been made from these observations if they had been real, rather than simulated, populations. From such inferences, we could have drawn conclusions about the presence of selection, migration and drift in given natural systems.     

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.     

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.     

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.     

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0–2 migrations, 0–2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39.3% (weak) to 3.6% (strong), far lower than the expected rate of 88.9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.     

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.     

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。     

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.     

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.     

Analysis of within-population spatial genetic structure in Antirrhinum microphyllum (Scrophulariaceae)

Random amplified polymorphic DNA (RAPD) markers were used to study the spatial genetic structure in two populations (Bolarque and Entrepe?as) of endangered cliff specialist Antirrhinum microphyllum Rothm. (Scrophulariaceae). Mantel tests found no significant linear correlations between geographic and genetic data. However, redundancy analysis (RDA) models developed using the spatial data as the constraining matrix were highly significant, and spatial data explained 13.6% and 11.1% of total genetic variation in Bolarque and Entrepe?as, respectively. Moran's I correlograms and Mantel correlograms revealed a positive autocorrelation in the first distance class (15 m), which suggests a patchy distribution of genetic diversity. This distribution is consistent with the genetic vicinities that are expected from the territorial behavior of main pollinator Rhodanthidium sticticum (Megachilidae), the predominant short-distance seed dispersal, and the patchy spatial distribution of available safe sites. The gradient pattern obtained in Entrepe?as was consistent with standard isolation-by-distance models. However, a differential sinusoidal pattern was obtained in Bolarque, which would indicate a more frequent gene flow between patches and might be due to lower plant density there. The spatial genetic structure coexists with a strict self-incompatibility system in the species. Simplified RDA models obtained using a stepwise forward selection comprised the easting component in Entrepe?as and the easting and northing components in Bolarque. Similar results were obtained with directional correlograms. These differential patterns can be explained by the distinct spatial arrangement of the populations (linear and bidimensional in Entrepe?as and Bolarque, respectively).     

The Genetic Structure of a Tribal Population, the Yanomama Indians. Xv. Patterns Inferred by Autocorrelation Analysis

Fifteen allele frequencies have previously been determined for 50 villages of the Yanomama, an Amerindian tribe from southern Venezuela and northern Brazil. These frequencies were subjected to spatial autocorrelation analysis to investigate their population structure. There are significant spatial patterns for most allele frequencies. Clinical patterns, investigated by one-dimensional and directional spatial correlograms, were relatively few in number and were moderate in strength. Overall, however, there is a marked decline in genetic similarity with geographic distance. The results are compatible with a hierarchic population structure superimposed on the geography, and generated by a stochastic fission-fusion model of village propagation, followed by localized gene flow. Strong temporal autocorrelations of allele frequencies based on linguistic-historical distances representing time since divergence were also found. There appears to be a stronger relation between geography and linguistic-historical hierarchic subdivisions than between either feature and genetic distances. These findings confirm by different approaches the results of earlier analyses concerning the important roles of both stochastic and social factors in determining village allele frequencies and the occurrence within this tribe of some allele frequency clines most likely due to the operation of chance historical processes.     

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     

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.     

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.     

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.     

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.     

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.     

The consequences of spatial structure for the design and analysis of ecological field surveys

In ecological field surveys, observations are gathered at different spatial locations. The purpose may be to relate biological response variables (e.g., species abundances) to explanatory environmental variables (e.g., soil characteristics). In the absence of prior knowledge, ecologists have been taught to rely on systematic or random sampling designs. If there is prior knowledge about the spatial patterning of the explanatory variables, obtained from either previous surveys or a pilot study, can we use this information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables?
The specific questions addressed in this paper are: a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse field survey data? b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer the last question, we compared regular regression analysis to a modified t‐test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation.
Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and 2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created).
Our results indicate that: 1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance. 2) A broad‐scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error. 3) Dutilleul's modified t‐test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation.
The presence of a broad‐scale deterministic structure may, in some cases, reduce the power of the modified t‐test.     

Testing for spatial autocorrelation in ecological studies

We describe a statistical method appropriate for the analysis of spatial autocorrelation in data varying in time as well as space. In particular, the technique was developed lo address the issue of geographic synchrony in ecological variables that may change markedly from year to year such as population density of animals or seed production of trees. The method yields 'modified correlograms" that test for significant autocorrelation between sites located within any given range of distances apart. This technique facilitates detecting and understanding spatial processes m a variety of ecological phenomena, including testing the plausibility of causational hypotheses using cross-correlational analyses. Several examples are discussed, including population densities of squirrels in Finland, winter densities of two hawk species in California, and acorn production and radial growth by individual blue oak Quercus douglasii trees in central coastal California.