Scaling up: how do exogenous fluctuations in individual-based resource competition models re-emerge in aggregated stochastic population models?

In applied population dynamics the choice of stochastic per capita growth function has implications for population viability analyses, management recommendations, and pest control. This model choice is often based on statistical criteria, mathematical tractability or personal preferences, and general ecological guidelines are either too vague or entirely missing. To identify such guidelines, it is important to understand how exogenous and endogenous factors interact at the individual level and re-emerge at the aggregated population level. We therefore study different types of resource competition (contest vs. scramble competition) and different types of exogenous fluctuations (food and weather fluctuations) at the individual level in a simple individual-based simulation model. We statistically fit the resulting time series to find out (1) which functional form of the growth function (‘hyperbolic’ or ‘exponential’) better describes contest and scramble competition and (2) whether the pattern of population fluctuations resulting from the simulations can be assigned to vertical, lateral or nonlinear perturbations in the stochastic growth function (a classification scheme suggested by Royama 1992, Analytical Population Dynamics, Chapman and Hall, London). We found that the same type of competition can result in ‘hyperbolic’ or ‘exponential’ functional forms, depending on the type of exogenous fluctuations. So it is the interplay between exogenous variability and endogenous resource competition that affects model performance. In contrast to the widespread assumption of vertical (additive) perturbations, our findings highlight the importance of (non-additive) lateral and nonlinear perturbations and their combinations with vertical perturbations. The choice of the stochastic growth function should therefore consider not only statistical criteria but also ecological guidelines. We derive such ecological guidelines from our analysis.

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