Reflections on the stochastic niche

Background/Question/Methods

G.E. Hutchinson in 1958 proposed a famous concept of the ecological niche -- a specification of the environmental states permitting a species to persist indefinitely. This was formalized using a basic concept of population ecology, the intrinsic rate of increase r (the rate of per capita births b minus deaths d, r = b-d, with units 1/time), at low abundance. A niche response surface expresses r as a function of environmental states. In stage-structured populations in a constant environment, the dominant eigenvalue of a projection matrix describes long-term growth rate r, and can be used to formalize a species’ niche, given demographic parameters expressed as a function of environmental states. Yet species are often absent in habitats which seem to match their niche requirements. In this talk I will use stochastic population models to argue that absences in seemingly suitable habitats are expected, once one accounts for the impact of demographic stochasticity during colonization. The rich mathematical literature on branching processes provides techniques for analyzing the probability of successful establishment, both in constant and variable environments, and helps point to alternative formalizations of the Hutchinsonian niche.

Results/Conclusions

Branching process models show that rather than the intrinsic growth rate, r, other demographic quantities combining birth and death rates determine the probability of successful establishment. This point can be illustrated using even the simplest kind of population model, namely species with continuously overlapping generations and no stage or age structure (i.e., exponential growth or decline). For such a species, expected lifetime reproductive success of an individual, denoted R0 ( = b/d, which is unit-less), determines the probability of successful establishment for a colonizing propagule. If the niche is viewed as a probability surface of successful establishment during colonization, as a function of environmental states, the niche response surface can differ qualitatively from the niche surfaces defined by the intrinsic growth rate. In dispersal-limited species, these theoretical results suggest that it is reasonable to expect many absences of species in seemingly suitable habitats. Comparable (but more complex) results arise from branching process models for species with age- or stage-structure, and for species living in variable environments. I will end by noting that when species are found outside their niche (e.g., due to climate change), the potential for evolutionary rescue (i.e., niche evolution) also depends upon R0 , because this quantity scales the potential input of novel genetic variation into the population.