Signs of stabilisation and stable coexistence.

Many empirical studies motivated by an interest in stable coexistence have quantified negative density dependence, negative frequency dependence, or negative plant-soil feedback, but the links between these empirical results and ecological theory are not straightforward. Here, we relate these analyses to theoretical conditions for stabilisation and stable coexistence in classical competition models. By stabilisation, we mean an excess of intraspecific competition relative to interspecific competition that inherently slows or even prevents competitive exclusion. We show that most, though not all, tests demonstrating negative density dependence, negative frequency dependence, and negative plant-soil feedback constitute sufficient conditions for stabilisation of two-species interactions if applied to data for per capita population growth rates of pairs of species, but none are necessary or sufficient conditions for stable coexistence of two species. Potential inferences are even more limited when communities involve more than two species, and when performance is measured at a single life stage or vital rate. We then discuss two approaches that enable stronger tests for stable coexistence-invasibility experiments and model parameterisation. The model parameterisation approach can be applied to typical density-dependence, frequency-dependence, and plant-soil feedback data sets, and generally enables better links with mechanisms and greater insights, as demonstrated by recent studies.