Demographic projection of high-elevation white pines infected with white pine blister rust: a nonlinear disease model

Matrix population models have long been used to examine and predict the fate of threatened populations. However, the majority of these efforts concentrate on long-term equilibrium dynamics of linear systems and their underlying assumptions and, therefore, omit the analysis of transience. Since management decisions are typically concerned with the short-term (< 100 years), asymptotic analyses could lead to inaccurate conclusions or, worse yet, critical parameters or processes of ecological concern may go undetected altogether. We present a stage-structured, deterministic, nonlinear, disease model which is parameterized for the population dynamics of high-elevation white pines in the face of infection with white pine blister rust (WPBR). We evaluate the model using newly developed software to calculate sensitivity and elasticity for nonlinear population models at any projected time step. We concentrate on two points in time, during transience and at equilibrium, and under two scenarios: a regenerating pine stand following environmental disturbance and a stand perturbed by the introduction of WPBR. The model includes strong density-dependent effects on population dynamics, particularly on seedling recruitment, and results in a structure favoring large trees. However, the introduction of WPBR and its associated disease-induced mortality alters stand structure in favor of smaller stages. Populations with infection probability (beta) > or = 0.1 do not reach a stable coexisting equilibrium and deterministically approach extinction. The model enables field observations of low infection prevalence among pine seedlings to be reinterpreted as resulting from disease-induced mortality and short residence time in the seedling stage. Sensitivities and elasticities, combined with model output, suggest that future efforts should focus on improving estimates of within-stand competition, infection probability, and infection cost to survivorship. Mitigating these effects where intervention is possible is expected to produce the greatest effect on population dynamics over a typical management timeframe.