Spatial Autocorrelation Analysis of Trend Residuals in Biological Data

Bocquet‐Appel, Jean‐Pierre; Sokal, Robert R.

doi:10.2307/2992399

Cited by 22 publications

(16 citation statements)

References 24 publications

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“…Results of the spatial analysis identified small scale clustering and weak directional gradients for several stand characteristics in each time period. While there is no direct evidence to suggest the presence of a true gradient, Bocquet-Appel and Sokal (1989) point out that the weak directional gradients such as the ones observed in this study may be due to a simple autocorrelated processes at the local level. In this study, the significant long distance negative spatial correlation of basal area growth and site index was due to a cluster of slow growing plots in northern part of the state.…”

Section: Discussioncontrasting

confidence: 63%

Spatial cross-correlation of undisturbed, natural shortleaf pine stands in northern Georgia

1994

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In this study a cross-correlation statistic is used to analyse the spatial relationship among stand characteristics of natural, undisturbed shortleafpine stands sampled during 1961-72 and 1972-82 in northern Georgia. Stand characteristics included stand age, site index, tree density, hardwood competition, and mortality. In each time period, the spatial cross-correlation statistic was used to construct cross-correlograms and cumulative crosscorrelograms for all significant pairwise combination of stand characteristics. Both the cross-correlograms and cumulative cross-correlograms identified small-scale clustering and weak directional gradients for different stand characteristics in each time period. The cumulative cross-correlograms, which are based on inverse distance weighting were more sensitive in detecting small-scale clustering than the cross-correlograms based on a 0-1 weighting. Further analysis suggested that the significant cross-correlation observed among basal area growth and other stand characteristics were due, in a large part, on a subset of sample plots located in the northern part of the state, rather than regional or broad-scale variation as first thought. The ability to analyse the spatial relationship between two or more response surfaces should provide valuable insight in the development of ecosystem level models and assist decision makers in formulating pertinent policy on intelligent multiresource management.

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Section: Discussioncontrasting

confidence: 63%

Spatial cross-correlation of undisturbed, natural shortleaf pine stands in northern Georgia

1994

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“…This is a multivariate generalization of the linear trend surface (mTSA) analysis (see Wartenberg, 1985; Bocquet-Appel and Sokal, 1989). The coefficient of determination R 2 of the RDA was equal to 0.251 (that of the Mantel test was equal to 0.249).…”

Section: Alternatives To Mantel Testmentioning

confidence: 99%

Mantel test in population genetics

et al. 2013

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The comparison of genetic divergence or genetic distances, estimated by pairwise FST and related statistics, with geographical distances by Mantel test is one of the most popular approaches to evaluate spatial processes driving population structure. There have been, however, recent criticisms and discussions on the statistical performance of the Mantel test. Simultaneously, alternative frameworks for data analyses are being proposed. Here, we review the Mantel test and its variations, including Mantel correlograms and partial correlations and regressions. For illustrative purposes, we studied spatial genetic divergence among 25 populations of Dipteryx alata (“Baru”), a tree species endemic to the Cerrado, the Brazilian savannas, based on 8 microsatellite loci. We also applied alternative methods to analyze spatial patterns in this dataset, especially a multivariate generalization of Spatial Eigenfunction Analysis based on redundancy analysis. The different approaches resulted in similar estimates of the magnitude of spatial structure in the genetic data. Furthermore, the results were expected based on previous knowledge of the ecological and evolutionary processes underlying genetic variation in this species. Our review shows that a careful application and interpretation of Mantel tests, especially Mantel correlograms, can overcome some potential statistical problems and provide a simple and useful tool for multivariate analysis of spatial patterns of genetic divergence.

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“…Replicate subplots only a meter apart differed, often quite dramatically. Failure to anticipate this variability may lead to poor performance of field experiments (Bocquet‐Appel & Sokal 1989; Ball et al. 1993; Edwards et al 1996).…”

Section: Discussionmentioning

confidence: 99%

Design and analysis of biodiversity field experiments

Deutschman¹

2001

Ecological Research

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The design and analysis of field experiments have figured prominently in the current debate about biodiversity and ecosystem function. These debates have identified important issues about species traits, functional groups, and community assembly, but a broader debate needs to include discussions about the scale (grain and extent) of experiments relative to natural spatial and temporal heterogeneity. In addition, alternative statistical analyses need to be explored that focus on comparison among several statistical models rather than simple hypothesis testing. Analyses of the first 2 years of data from a new biodiversity field experiment are used to illustrate these concepts. A traditional one‐way ANOVA demonstrates the expected increase in aboveground biomass with higher levels of vascular plant diversity. Further analysis demonstrates that this relationship is absent when the community contains either Arrhenatherum elatius or Holcus lanatus, two dominant species of grass. Variance in biomass is also a function of diversity and both spatial and temporal heterogeneity are significant factors in the analysis despite precautions taken to minimize them. These examples illustrate the degree to which the analysis of a field experiment influences the interpretation of the observed results. Ultimately, results from field experiments must be validated through continued comparisons among field experiments, mathematical models, laboratory trials, and mesocosm experiments.

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Spatial Autocorrelation Analysis of Trend Residuals in Biological Data

Cited by 22 publications

References 24 publications

Spatial cross-correlation of undisturbed, natural shortleaf pine stands in northern Georgia

Spatial cross-correlation of undisturbed, natural shortleaf pine stands in northern Georgia

Mantel test in population genetics

Design and analysis of biodiversity field experiments

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