Simple rules for establishment of effective marine protected areas in an age-structured metapopulation

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) aim to promote conservation by increasing population size and reducing its variability. To resolve how these effects depend on PA features, 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, organism preference for PAs, and size 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. The results from this study demonstrate that sufficiently reduced density-independent mortality in PAs and high site preference for PAs and immigration rate into PAs are likely to decrease the CV. However, different types of stochasticity induce rather different consequences: under demographic stochasticity, the CV is always reduced because 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.

On the spillover effect and optimal size of marine reserves for sustainable fishing yields

Marine reserves are an essential component of modern fishery management. Marine reserves, which represent a management tradeoff between harvesting and conservation, are fundamental to maintenance of fisheries. Finding optimal reserve sizes that improve fishing yields is not only of theoretical interest, but also of practical importance to facilitate decision making. Also, since the migratory behavior of some species influences the spillover effect of a marine reserve, this is a key consideration when assessing performance of marine reserves. The relationship between optimal reserve size and migration rate/mode has not been well studied, but it is fundamental to management success. Here, I investigate optimal reserve size and its management outcome with different levels of spillover via a simple two-patch mathematical model. In this model, one patch is open to fishing, and the other is closed. The two-patch model is aggregated by single-population dynamics when the migration rate is sufficiently larger than the growth rate of a target species. At this limit, I show that an optimal reserve size exists when pre-reserve fishing occurs at fishing mortality larger than f_MSY, the fishing mortality at the maximum sustainable yield (MSY). Also, the fishing yield at an optimal reserve size becomes as large as MSY at the limit. Numerical simulations at various migration rates between the two patches suggest that the maximum harvest under management with a marine reserve is achieved at this limit. This contrasts with the conservation benefit which is maximized at an intermediate migration rate. Numerical simulations show that the above-mentioned condition for an optimal reserve size to exist derived from the aggregated model is necessary when the migration rate is not sufficiently large, and that a moderate migration rate is further necessary for an optimal reserve size to exist. However, high fishing mortality reduces this requirement.

Harvesting induced stability and instability in a tri-trophic food chain

Non-equilibrium dynamics in the form of oscillations or chaos is often found to be a natural phenomenon in complex ecological systems. In this paper, we first analyze a tri-trophic food chain, which is an extension of the Rosenzweig-MacArthur di-trophic food chain. We then explore the impact of harvesting individual trophic levels to answer the following questions : a) when a non-equilibrium dynamics persists, b) whether it can locally be stabilized to a steady state, c) when the system switches from a stable steady state to a non-equilibrium dynamics and d) whether the Maximum Sustainable Yield (MSY) always exists when the top predator is harvested. It is shown that searching for a general theory to unify the harvesting induced stability must take into account the number of trophic levels and the degree of species enrichment, the outcomes that cannot be obtained from the earlier reports on prey-predator models. We also identify the situation where harvesting induces instability switching: the non-equilibrium state enters into a stable steady-state and then, upon more intensive harvesting, the steady-state again loses its stability. One of the new and important results is also that the MSY may not exist for harvesting the top predator. In general, our results contribute to biological conservation theory, fishery and ecosystem biodiversity management.