Research frontiers in null model analysis

Null models are pattern-generating models that deliberately exclude a mecha nism of interest, and allow for randomization tests of ecological and bioge ographic data. Although they have had a controversial history, null models are widely used as statistical tools by ecologists and biogeographers. Thre e active research fronts in null model analysis include biodiversity measur es, species co-occurrence patterns, and macroecology. In the analysis of bi odiversity, ecologists have used random sampling procedures such as rarefac tion to adjust for differences in abundance and sampling effort. In the ana lysis of species co-occurrence and assembly rules, null models have been us ed to detect the signature of species interactions. However, controversy pe rsists over the details of computer algorithms used for randomizing presenc e-absence matrices. Finally, in the newly emerging discipline of macroecolo gy, null models can be used to identify constraining boundaries in bivariat e scatterplots of variables such as body size, range size, and population d ensity. Null models provide specificity and flexibility in data analysis th at is often not possible with conventional statistical tests.