Guaranteeing population growth under uncertainty for structured population models∗

Structured population models are increasingly used in decision making, but typically have many entries that are unknown or highly uncertain. We present an approach for the systematic analysis of the effect of uncertainties on long-term population growth or decay. Many decisions for threatened and endangered species are made with poor or no information. We can still make decisions under these circumstances in a manner that is highly defensible, even without making assumptions about the distribution of uncertainty or limiting ourselves to discussions of single, infinitesimally small changes in the parameters. Suppose that the model (determined by the data) for the population in question predicts long-term growth. Our goal is to determine how uncertain the data can be before the model loses this property. Some uncertainties will maintain long-term growth, and some will lead to long-term decay. The uncertainties are typically structured, and can be described by several parameters. We show how to determine which parameters maintain long-term growth. We illustrate the advantages of the method by applying it to a peregrine falcon population. The US Fish and Wildlife Service recently decided to allow minimal harvesting of peregrine falcons after their recent removal from the Endangered Species List. Based on published demographic rates, we find that population growth (λ > 1) is guaranteed with 5% harvest rate up to 3% error in adult survival if no two year olds breed, and up to 11% error if all two year olds breed. If a population growth rate of 3% or greater is desired, the acceptable error in adult survival decreases to between 1 and 6% depending of the proportion of two year olds that breed. These results clearly show the interactions between uncertainties in different parameters, and suggest that a harvest decision at this stage may be premature without solid data on adult survival and the frequency of breeding by young adults.