Methods for calculating coexistence mechanisms: beyond scaling factors

How do species coexist? A framework known as modern coexistence theory can ‘measure coexistence' by partitioning invasion growth rates into mechanisms, terms which correspond to classes of explanations for coexistence. There are several reasonable ways define each depending on exactly how a perturbed low density (the invader) is compared other that remain at their typical densities residents). Using conceptual arguments and two case studies, we compare five methods calculating mechanisms: 1) scaling factors, the traditional approach attempts eliminate linear effects regulating factors; 2) simple comparison, gives equal weight all resident species; 3) generation time scaling, novel method corrects intrinsic differences in population-dynamical speed; 4) β where scaled measure relative sensitivity competition; 5) invader–invader previously obscure focal itself high versus density. We find conventional factors lead nonsensical results when have strong asymmetric niche differences; though be useful certain theoretical they not recommended explaining real communities. Invader–invader comparisons also problematic, effectively specialization or differentiation. The universally-applicable comparison often works well, but give counterintuitive disparate times. well models, faces implementation problems complex models. tentatively recommend all-purpose mechanisms.