Sensitivity analysis of equilibrium population size in a density-dependent model for Short-tailed Shearwaters

Sensitivity and elasticity analysis of a Lur'e system used to model a population subject to density-dependent reproduction

Sensitivity and elasticity analyzes have become central to the analysis of models in population biology and ecology. While much work has been done applying sensitivity and elasticity analysis to study density-independent (linear) matrix and integral projection models, little work has been done to study the sensitivity and elasticity of density-dependent models, especially integral projection models. In this paper we derive sensitivity and elasticity formulas for the equilibrium population n^* of a structured population modeled by a Lur'e system, which consists of a linear system plus a nonlinearity modeling density-dependent fecundity. Sensitivity and elasticity formulas are easy to interpret ecologically, and we apply these formulas to published models for Chinook Salmon and Platte thistle (Cirsium canescens). In the C. canescens example we show that models with identical equilibrium populations can have sensitivities that are an order-of-magnitude apart, depending on the functional form for the nonlinearity.

Annual plants under cyclic disturbance regime: better understanding through model aggregation

In their application for conservation ecology, "classical" analytical models and individual-based simulation models (IBMs) both entail their specific strengths and weaknesses, either in providing a detailed and realistic representation of processes or in regard to a comprehensive model analysis. This well-known dilemma may be resolved by the combination of both approaches when tackling certain problems of conservation ecology. Following this idea, we present the complementary use of both an IBM and a matrix population model in a case study on grassland conservation management. First, we develop a spatially explicit IBM to simulate the long-term response of the annual plant Thlaspi perfoliatum (Brassicaceae), claspleaf pennycress, to different management schemes (annual mowing vs. infrequent rototilling) based on field experiments. In order to complement the simulation results by further analyses, we aggregate the IBM to a spatially nonexplicit deterministic matrix population model. Within the periodic environment created by management regimes, population dynamics are described by periodic products of annual transition matrices. Such periodic matrix products provide a very conclusive framework to study the responses of species to different management return intervals. Thus, using tools of matrix model analysis (e.g., loop analysis), we can both identify dormancy within the age-structured seed bank as the pivotal strategy for persistence under cyclic disturbance regimes and reveal crucial thresholds in some less certain parameters. Results of matrix model analyses are therefore successfully tested by comparing their results to the respective IBM simulations. Their implications for an enhanced scientific basis for management decisions are discussed as well as some general benefits and limitations of the use of aggregating modeling approaches in conservation.