Optimal conservation strategy in fluctuating environments with species interactions: resource-enhancement of the native species versus extermination of the alien species.

Alien species are often a major threat to native species. We consider optimal conservation strategies for a population whose viability is affected both by an alien species (such as a competitor, a predator, or a pathogen) and by random fluctuations of the environment (e.g. precipitation, temperature). We assume that the survivorship of the native population can be improved by providing resources such as food and shelter, and also by an extermination effort that decreases the abundance of the alien species. These efforts decrease the extinction probability of the native population, but they are accompanied by economic costs. We search for the optimal strategy that minimizes the weighted sum of the extinction probability and the economic costs over a single year. We derive conditions under which investment should be made in both resource-enhancement and extermination, and examine how the optimal effort levels change with parameters. When the optimal strategy includes both types of efforts, the optimal extermination effort level turns out to be independent of the density and economic value of the native species, or the variance of the environmental fluctuation. Furthermore, the optimal resource-enhancement effort is then independent of the density of the alien species. However, the parameter dependencies greatly change if one of the efforts becomes zero. We also examine the situation in which the impact of the alien species is uncertain. The optimal extermination effort increases with the uncertainty of this impact except when the cost of extermination is very high.