An investigation of matrix population model assumptions: wrens (Troglodytes troglodytes) as a case study

Abstract

A simulation matrix population model of a small population of wrens (Troglodytes troglodytes) is presented. The field work methods used to obtain and analyse the demographic rates are provided. This includes a description of the use of miniature radio tags to track juvenile (post-fledging) survival and dispersal, and capture mark recapture analysis of an eight year dataset to estimate adult survival rates, taking into account environmental variation and density dependence. Age related reproductive rates were obtained from detailed nest surveys. Using these demographic rates (means and variances), and information on density dependence in survival and breeding, a simulation matrix model was developed using Matlab (The MathWorks, Inc.). The operation of this model and its outputs are explained in detail, with particular reference to the methods employed to incorporate both density dependent survival and reproduction and environmental and demographic stochasticity. This model is then used to illustrate how, under plausible conditions of density dependence and stochasticity, large discrepancies are obtained between the deterministic, density independent elasticities of the population growth rate (λ) and the stochastic, density dependent elasticities of the equilibrium population size, extinction probability and invasion exponent. Since the elasticities of λ are often used to guide the management of endangered species, these results are particularly relevant to workers in the field of rare species conservation. While the importance of including environmental variation in the form of stochastic population simulations seems to now be generally accepted, the role of density dependent population regulation is still infrequently considered. Since one of the most common causes of population decline is habitat destruction, leading to an increase in population density within the remaining areas of habitat, this omission may rarely be justified. It is recommended that when elasticity analysis is conducted as part of species conservation efforts, both density dependence and stochasticity are included. Failure to do so may result in the misguided management of endangered species.