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. 'A null model is a pattern generating model that is based on randomization of ecological data or random sampling from a known or imagined distribution. The null model is designed with respect to some ecological or evolutionary process of interest'. (Gotelli and Graves 1996) From its origins in the analysis of species/genus ratios Hypothesis testing and constraints in null model analysis Classical Pearson-Neyman hypothesis testing The null hypothesis varies depending on the details of the test, but it is often a parsimonious expectation that the data are drawn from a single distribution, so that any patterns in the data arise only from random sampling processes. The alternative hypothesis is that patterns in the data are not the result of random variation generated by H 0 . Erroneous rejection of H 0 occurs with probability a and represents a type I statistical error. Conversely, erroneous acceptance of a false null hypothesis is a type II error and occurs with probability b. The quantity 1 -b is the power of the test, the probability of correctly rejecting H 0 given that it is false In ecological null model analysis, 'Null hypotheses entertain the possibility that nothing has happened, that a process has not occurred, or that change has not been produced by a cause of interest&apos
