Box 1. Chesson theoretical framework
In Chesson's theoretical framework, niche differences (more formally called stabilizing processes) and fitness differences are quantified by their contributions to population growth rates when a species is rare. In many mathematical models of competing species, the number of individuals produced per individual (logged) when the invader is rare and the resident community is at its stochastic equilibrium can be expressed as follows:
r = s[FitnessDifference + Niche Difference](eqn 1)
where r is the per capita growth rate and s is a scaling term that converts the units of the niche and fitness differences to per capita growth rate units. The fitness difference term can be positive or negative, depending on whether the invader or the resident community has the greater average fitness. The niche difference term is always positive, because it describes advantages due to the resident community limiting itself more than the invader. See Chesson & Kuang (2008) for a specific model decomposed into niche and fitness differences.
Successful invasion requires that the invader has a positive growth rate when rare, which in turn requires the term in bracket to be positive. Invasion can thus result from a fitness advantage (a positive fitness difference term) or a niche difference strong enough to exceed the fitness disadvantage. These two scenarios form the basis of the ‘niche opportunities’ in Shea & Chesson (2002).
Equation 1 can be used to understand impact by treating the invader as the abundant resident and evaluating native species growth when rare. If positive, the latter persist. If the invader has greater average fitness, native persistence rests on the niche difference term being sufficiently positive. More generally, the native residents and exotic invader will coexist if both can increase when rare, which depends on a positive niche difference term.