Optimal conservation effort for a population in a stochastic environment

We study the optimal conservation effort for a population in a fluctuating environment. The survivorship of a population is affected by unpredictable environmental fluctuation (noise) and can be improved by conservation effort accompanied by a cost. The optimal effort level is the one that minimizes the total cost, defined as the weighted sum of the population extinction risk and the economic cost of conservation effort. The optimal effort depends on the variance and the probability distribution of the noise, the relative importance of the population's survival vs. the economic cost, the effectiveness of conservation effort, and the time scope over which we optimize. The analysis of dynamic programming illustrates that the choice of extinction risk function greatly affects the optimal effort level. The conservation effort level that is the best solution of a multiple-year optimization may be higher than that for the corresponding single-year optimization, if the population is relatively safe. However, the conservation level for the multiple-year optimization becomes lower than for the single-year optimization if the population is endangered. In a similar manner, the optimal conservation effort level for the problem with a short time scope is either higher or lower than that for the problem with a long time scope, depending on the extinction risk of the population. Next, for each parameter of the model, we define five different sensitivities of extinction probability or of the total cost. We then study the mean increase in the total cost caused by the uncertainty of parameters. To achieve the best conservation result, we need to invest the limited research effort to the parameter with the largest effect to the optimal effort level, rather than to those with large impacts on the extinction probability or on the total cost. The recommended policy should depend critically on the choice of the criterion to optimize, which shows the importance of theoretical study of the relationship in performing proper decision making in conservation practice.