Long-term conservation effects of protected areas in stochastic population dynamics

Terrestrial and marine protected areas are essential tools in mitigating anthropogenic impacts and promoting population persistence and resource sustainability. Adequately implemented protected areas (PAs) promote long-term conservation effects. Stochasticity causes fluctuations in the conservation effects of PAs, and so it is important to investigate the variabilities of these conservation effects to inform their long-term conservation effects. To investigate long-term conservation effects, I develop and analyze new models of stochastic processes that encompass the fluctuations generated by demographic or environmental stochasticity in PAs management. The stochastic model is built upon individual processes. In the model, density-independent mortality, migration between PAs and non-PAs, and site preferences characterize the features of the PA. The effect of PAs size is also examined. The long-term conservation effects are quantified using the coefficient of variation (CV) of population size in PAs, where a lower CV indicates higher robustness in stochastic variations. Typically, the results from this study demonstrate that sufficiently reduced density-independent mortality in PAs and high site preference and immigration rate of PA are likely to decrease the CV. However, different types of stochasticity induce rather different consequences: under demographic stochasticity, the CV is always reduced when PAs increase the population size therein, but an increased population size by PAs does not always decrease the CV under environmental stochasticity. The deterministic dynamics of the model are investigated, facilitating effective management decisions.