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

Abstract

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 fMSY, 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.

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

“…However, ineffective PAs managements are often associated with failure to reduce human activities [6,29], which may amplify population fluctuation. The immigration and emigration rates are not purely biological parameters but can be controlled by the configuration of PAs [32]. Protecting favored sites by a target species is desirable to increase conservation benefit in PAs [16].…”

“…(3). With multiplying by n 1 both sides and summing over all probabilities, we recover a deterministic two-patch dynamics (Appendix A.2) discussed, for example, in [32,33] with some arrangements.…”

Long-Term Conservation Effects of Protected Areas in Stochastic Population Dynamics

“…where E[x] represents the average of x. This model is discussed, for example, in Takashina et al (2017) and Takashina (2020) with some arrangements.…”

“…However, ineffective PA management is often associated with a failure to reduce human activities (Craigie et al, 2010;Schulze et al, 2018), which may amplify population fluctuations. The immigration and emigration rates are not purely biological parameters, but can be controlled by the configuration of the PAs (Takashina, 2020). Protecting the favored sites of a target species is desirable as a means of increasing the conservation effects of PAs (Hunt et al, 2020).…”