## Gotelli, N. J., and A. M. Ellison. 2006. Forecasting extinction risk with non-stationary matrix models. *Ecological Applications* 16: 51-61.

Abstract

Matrix population growth models are standard tools for forecasting population change and for managing rare species, but they are less useful for predicting extinction risk in the face of changing environmental conditions. Deterministic models provide point estimates of λ, the finite rate of increase, as well as measures of matrix sensitivity and elasticity. Stationary matrix models can be used to estimate extinct risk in a variable environment, but they assume that the matrix elements are randomly sampled from a stationary (= nonchanging distribution). Here we outline a method for using non-stationary matrix models to construct realistic forecasts of population fluctuation in changing environments. Our method requires three pieces of data: 1) field estimates of transition matrix elements. 2) experimental data on the demographic responses of populations to altered environmental conditions. 3) forecasting data on environmental drivers. These three pieces of data – transition elements, experimental results, and forecasting data – are combined to generate a series of sequential transition matrices that emulate a pattern of long-term change in environmental drivers. Realistic estimates of population persistence and extinction risk can be derived from stochastic permutations of such a model. We illustrate the steps of this analysis with data from two populations of *Sarracenia purpurea* growing in northern New England. *Sarracenia purpurea* is a perennial carnivorous plant that is potentially at risk of local extinction because of increased nitrogen deposition. Long-term monitoring records or models of environmental change can be used to generate time series of driver variables under different scenarios of changing environments. Both manipulative and natural experiments can be used to construct a linking function that describes how matrix parameters change as a function of the environmental driver. This synthetic modeling 3 approach provides quantitative estimates of extinction probability that have an explicit mechanistic basis.