DOI 10.1007/s00285-006-0044-8 Mathematical Biology Stochastic stable population growth in integral projection models: theory and application

Abstract Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative proper-ties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population struc-ture. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, Uni-versity of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411–440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325–344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple trait