Abstract
ABSTRACTThe study of the role of environmental variation in community dynamics has traditionally assumed that the environment is a stationary stochastic process or a periodic deterministic process. However, the physical environment in nature is nonstationary. Moreover, anthropogenically driven climate change provides a new challenge emphasizing a persistent but frequently ignored problem: how to make predictions about the dynamics of communities when the nonstationarity of the physical environment is recognized. Recent work is providing a path to conclusions with none of the traditional assumptions of environmental stationarity or periodicity. Traditional assumptions about convergence of long-term averages of functions of environmental states can be replaced by assumptions about temporal sums, allowing convergence and persistence of population processes to be demonstrated in general nonstationary environments. These tools are further developed and illustrated here with some simple models of nonstationary community dynamics, including the Beverton-Holt model, the threshold exponential and the lottery model.
Highlights
How should one realistically model the dynamics of populations and communities? There will never be agreement on the most important features of nature even when a common question or goal has been agreed upon
Despite its major implications for the structure of populations and communities, it remains a highly specialized topic within theoretical ecology [14]. Even within this specialized area, the physical environmental fluctuations considered in most models are distinctly lacking in realism
The concept of the aedt reflects a common type of generalization in mathematics where a Euclidean point is generalized to a function
Summary
How should one realistically model the dynamics of populations and communities? There will never be agreement on the most important features of nature even when a common question or goal has been agreed upon. Note that in both the threshold exponential and in the Beverton-Holt model, rt0 = lnRt. In a stationary environment, the persistence of a process is commonly investigated by studying r0 = E[rt0], (10)
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