The role of environmental stochasticity in reducing the amplitude of population fluctuations

Background/Question/Methods   It has long been established, both theoretically and empirically, that temporal variation in environmental conditions is linked to temporal variation in population abundances. Much less attention has been paid to the role that temporal environmental variation plays in dampening population fluctuations. Recent studies have indicated that there are indeed situations in which this negative relationship between environmental variation and population variation occurs. This work attempts to provide theoretical and mathematical explanations for this phenomenon. A few simple models that exhibit cycling-like dynamics under constant environmental conditions are considered. Environmental conditions that change deterministically and stochastically over time are introduced to these standard systems. Situations in which the introduction of environmental variation decreases the amplitude of population fluctuations are analyzed. The primary tools used in this work are stochastic differential equations. Particular attention is paid to the ways in which demographic stochasticity, environmental stochasticity, and deterministic environmental fluctuations interact to control fluctuations in abundances of interacting populations. Emphasis is placed on studying the type of environmental stochasticity introduced to the system, especially to the color of environmental noise.

Results/Conclusions   The stochastic differential equation models are studied, both analytically and with numeric simulation. Sets of conditions under which stochastic variation reduces population variation are determined. These conditions are analyzed mathematically and explored with simulations. The ecological relevance of these conditions is discussed. Finally, the role of increased environmental variability due to global climate change in influencing population fluctuations is considered.