Null model analyses of presence–absence matrices need a definition of independence

Navarro-Alberto, Jorge; Manly, Bryan F. J.

doi:10.1007/s10144-008-0137-x

Cited by 14 publications

(12 citation statements)

References 14 publications

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“…In the first, the probability of converting a matrix element from 0 to 1 was based on the formula for null 8 in Table I, p ( X ij ) = S i T j / N 2 . Gotelli ( 15 ) is clear to indicate that this probability applies strictly to the first entry, and so this method is designated “null 8.” The second approach uses a statistical fitting procedure of Navarro‐Alberto and Manly ( 22 ) to derive p ( X ij ), designated “null 8 NM.” These authors note that the underlying species abundance data may be modeled with a log‐linear model where the expected value of abundance E ( A ij ) is given by a constant overall effect γ, a species effect δ j , and a location effect ϑ i . : …”

Section: Methodsmentioning

confidence: 99%

Biogeographical Analysis of Chemical Co‐Occurrence Data to Identify Priorities for Mixtures Research

2011

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A challenge with multiple chemical risk assessment is the need to consider the joint behavior of chemicals in mixtures. To address this need, pharmacologists and toxicologists have developed methods over the years to evaluate and test chemical interaction. In practice, however, testing of chemical interaction more often comprises ad hoc binary combinations and rarely examines higher order combinations. One explanation for this practice is the belief that there are simply too many possible combinations of chemicals to consider. Indeed, under stochastic conditions the possible number of chemical combinations scales geometrically as the pool of chemicals increases. However, the occurrence of chemicals in the environment is determined by factors, economic in part, which favor some chemicals over others. We investigate methods from the field of biogeography, originally developed to study avian species co-occurrence patterns, and adapt these approaches to examine chemical co-occurrence. These methods were applied to a national survey of pesticide residues in 168 child care centers from across the country. Our findings show that pesticide co-occurrence in the child care center was not random but highly structured, leading to the co-occurrence of specific pesticide combinations. Thus, ecological studies of species co-occurrence parallel the issue of chemical co-occurrence at specific locations. Both are driven by processes that introduce structure in the pattern of co-occurrence. We conclude that the biogeographical tools used to determine when this structure occurs in ecological studies are relevant to evaluations of pesticide mixtures for exposure and risk assessment.

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Section: Methodsmentioning

confidence: 99%

Biogeographical Analysis of Chemical Co‐Occurrence Data to Identify Priorities for Mixtures Research

2011

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“…However, very different types of association might be called random with respect to certain factors. Even with a precisely stated null hypothesis about randomness, it is still uncertain whether an associated randomization adequately approximates the pattern predicted by the null hypothesis (Navarro‐Alberto and Manly 2009).…”

Section: Benchmark Metric and Algorithm Performance In Null Model mentioning

confidence: 99%

“…For very large matrices, and for matrices sampled at large spatial scales, the homogeneity assumption cannot be justified and traditional null models should be applied with caution. Recently Navarro‐Alberto and Manly (2009) showed that any difference either in occurrence probabilities of species across sites (non‐uniform column degree distributions) or species (non‐uniform row degree distributions) causes some degree of spatial autocorrelation. Null models that do not correct for autocorrelation may therefore too often point to non‐randomness.…”

Section: Sample Size Effects In Null Model Analysismentioning

confidence: 99%

Statistical challenges in null model analysis

Gotelli¹,

Ulrich²

2011

Oikos

228

297

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This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson–Neyman tests (which require a fully‐specified null distribution) and specific process‐based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence–absence matrices to incorporate species‐level traits (such as abundance) and site‐level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years.

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“…No algorithm produces every possible matrix during the randomization, except perhaps for the smallest of matrices. This issue of biased randomizations has recently attracted the attention of ecologists and statisticians (Zaman & Simberloff, 2002;Miklós & Podani, 2004;Lehsten & Harmand, 2006;Navarro-Alberto & Manly, 2009;Sanderson et al, 2009;Fayle & Manica, 2010;Gotelli & Ulrich, 2011). In a greater context, the use of data randomization (as a null model and statistical test of inference) is not distribution-free.…”

Section: Introductionmentioning

confidence: 99%

A probabilistic model for analysing species co‐occurrence

Veech

2012

Global Ecology and Biogeography

425

484

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Aim To develop a new probabilistic model that can be used to test for statistically significant pair-wise patterns of species co-occurrence. The model gives the probability that two species would co-occur at a frequency less than (or greater than) the observed frequency if the two species were distributed independently of one another among a set of sites. The model can be used to classify species associations as negative, positive or random.Innovation Historically, the analysis of species co-occurrence has involved the use of data randomization. An observed species presence-absence matrix is compared with randomized matrices to determine if the observed matrix has structure, either an excess or deficit of species positively or negatively associated with each other. The computer algorithms used to randomize matrices can sometimes produce Type I and Type II errors (when the randomization algorithm produces a biased set of all possible matrices) due to the randomization process itself. The probabilistic model does not rely on any data randomization, hence it has a very low Type I error rate and is powerful having a low Type II error rate.Main conclusions When applied to 10 different data sets the probabilistic model revealed significant positive and negative species associations in most of the data sets. Compared with previous analyses the model tended to find fewer significant associations; this may indicate a generally low rate of Type I error in the model. The model is easy to implement and requires no special software. The model could potentially transform the way that ecologists test for species co-occurrence in a wide range of ecological studies.

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Null model analyses of presence–absence matrices need a definition of independence

Cited by 14 publications

References 14 publications

Biogeographical Analysis of Chemical Co‐Occurrence Data to Identify Priorities for Mixtures Research

Biogeographical Analysis of Chemical Co‐Occurrence Data to Identify Priorities for Mixtures Research

Statistical challenges in null model analysis

A probabilistic model for analysing species co‐occurrence

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