Statistical challenges in null model analysis

Abstract

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.

The ghost of nestedness in ecological networks

“…For both binary and quantitative matrices, we define three null models for constructing B 0 : (i) preserve |P|, |A| and place |E| edges at random within the matrix; (ii) as in (i), but accept only connected matrices; and (iii) as in (ii), but conserve the degree distribution (the row and column sums of B). As measures of nestedness can be very sensitive to matrix size, fill and configuration 10,11 , we used null model implementations that preserve |P|, |A| and |E| (null models (i) and (ii)) and degree distribution (iii) exactly, and not just their expected values.…”

“…In a nested bipartite network or graph, interactions are organized such that specialists (for example, pollinators that visit few plants) interact with subsets of the species with whom generalists (for example, pollinators that visit many plants) interact. A nested structure corresponds to a systematic arrangement of non-zero entries in the binary matrix used to represent a network, and existing detection methods are based on distinguishing the nested pattern from other possible arrangements of matrix elements 10,11 . However, these methods are often computationally expensive for large matrices and are not applicable to quantitative networks (binary metrics extended to work with quantitative data, such as WNODF 12 , do not make full use of the available quantitative information).…”

Phylogenetic fields of species: cross-species patterns of phylogenetic structure and geographical coexistence

“…Nonetheless, as in classical null model analyses, deviations from null expectations allowed us the interpretation of potential processes not included in our models (i.e. historical processes mentioned above [47,48]). …”

“…Non-random patterns are particularly informative, providing evidence that actual mechanisms act beyond stochasticity [47] and, in our case, beyond species richness and range size variation. Yet, depending on the specified null hypothesis or null model expectations, interpretations can still be made when observed patterns do not differ from such expectations [48]. We tested two null models with different constraints preserving some features of empirical data; observed species richness and range sizes.…”

Linking environmental filtering and disequilibrium to biogeography with a community climate framework

“…First, inferences from the scaled version of the framework are sensitive to the definition of the regional species pool and other attributes of the null model. Of most importance, the definition of the species pool affects the deviation of estimates and statistical power Graves 1996, Gotelli andUlrich 2012), both of which can lead to misinterpretation of the biological meaning of the results (Swenson et Lessard et al 2012b). The geographic extent and configuration of each community's regional pool may affect our results.…”