Coexistence mechanisms pose major challenges for empirical testing. The recognition that stabilizing effects are necessary to counteract inevitable average fitness differences between species means that credible tests of species coexistence need to demonstrate stabilizing effects, but such demonstrations are rare. Moreover, although stabilizing effects might be demonstrated through density manipulations, associating those stabilizing effects with specific mechanisms is a critical issue given the likely simultaneous action of multiple coexistence mechanisms in most natural systems. The most common approaches to testing species coexistence aim to show that species partition the environment in some way, for example have different resource use patterns or are most active at different times or in different places (i.e. differ in their niches), but such differences need not lead to stabilizing effects unless the factors that distinguish species are coupled appropriately with density dependence processes. Showing that appropriate coupling is present is therefore key to strong tests of coexistence mechanisms. To develop a methodology for strong tests of species coexistence mechanisms, I developed general mathematical expressions that partition the density-dependent components of population growth rates into contributions from different mechanisms.
Results/Conclusions
Partitioning the density-dependent components of population growth rates into contributions from different mechanisms provides formulae revealing how the mechanisms function, and how the factors that species partition become coupled with density-dependent processes. Moreover, the measures show how specific mechanisms lead to intensification of intraspecific interactions relative to interspecific interactions, which is key to their stabilizing roles. In many cases, the relevant coupling of environmental factors and density dependence emerges a statistical covariance, which can in principle be measured in nature through appropriate manipulations and observations. This outcome is illustrated by three mechanisms that arise in spatially variable environments (the spatial storage effect, fitness-density covariance and nonlinear competitive variance) in addition to classical resource partitioning, which does not require spatial environmental variation. The spatial storage effect is easiest to understand and indeed to measure as a statistical covariance from field experiments. Although other mechanisms are more challenging empirically with current technology, recent advances in field methods hold much promise. Moreover, demonstrating that a mechanism provides the appropriate coupling of density dependence processes and environmental factors, without full estimates of the measure, is much less challenging, and may often be sufficient.