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

Optimal reproductive phenology under size‐dependent cannibalism

Intra-cohort cannibalism is an example of a size-mediated priority effect. If early life stages cannibalize slightly smaller individuals, then parents face a trade-off between breeding at the best time for larval growth or development and predation risk from offspring born earlier. This game-theoretic situation among parents may drive adaptive reproductive phenology toward earlier breeding. However, it is not straightforward to quantify how cannibalism affects seasonal egg fitness or to distinguish emergent breeding phenology from alternative adaptive drivers. Here, we devise an age-structured game-theoretic mathematical model to find evolutionary stable breeding phenologies. We predict how size-dependent cannibalism acting on eggs, larvae, or both changes emergent breeding phenology and find that breeding under inter-cohort cannibalism occurs earlier than the optimal match to environmental conditions. We show that emergent breeding phenology patterns at the level of the population are sensitive to the ontogeny of cannibalism, that is, which life stage is subject to cannibalism. This suggests that the nature of cannibalism among early life stages is a potential driver of the diversity of reproductive phenologies seen across taxa and may be a contributing factor in situations where breeding occurs earlier than expected from environmental conditions

Developing generalized sampling schemes with known error properties: the case of a moving observer

Pattern in space and time is central to ecology, and adequately designed ecological sampling is needed to resolve those patterns, pursue ecological questions and design conservation strategies. Recently, there has been an explosion of various ecological data due to the proliferation of online data‐sharing platforms, citizen science programs and new technology such as unmanned aerial vehicles (UAVs), but data reliability, consistency and the error properties of the sampling method are usually uncertain. While there are a number of standard survey protocols for different taxa, they often subjectively designed and standardization is meant to facilitate repeatability rather than produce a quantitative evaluation of the data (e.g. error properties). Here, we describe an ecological survey scheme consisting of an ‘algorithm\u27 to be followed in the field that will result in a standard set of data as well as the error properties of the data. While many such sampling schemes could be developed that target different types of organisms, we focus on one case of a moving observer attempting to detect a species in the field (e.g. a birder, UAV, etc.) with the goal of producing a presence–absence map. The multiscale model developed is spatially explicit and accommodates inherent survey tradeoffs such as sampling speed, detectability and map resolution. Given a set of sampling parameters, the model provides estimates of the total sampling time and map accuracy translated into the probability of false negative. Additionally it also provides an actual and sampled occupancy–area curve across mapping resolutions that can be utilized to discuss sampling effects. While the proposed sampling framework is simple, the same general approach could be adapted for other conditions to meet the needs of a particular taxon. If a set of ‘canonical\u27 sampling algorithms could be developed with known mathematical properties, it would enhance reliability and usage of ecological datasets

Effect of marine reserve establishment on non-cooperative fisheries management

Introducing effective marine reserves is a critical issue in fisheries management and marine ecosystem conservation. In recent years, a number of marine reserves or no-take marine protected areas (MPAs) have been implemented worldwide, and some MPAs have shown ecological and economic benefits. However, consideration for coordinated competition between institutions, a central for successful resource management, is often omitted in research on effective MPA management. Given increasing discussions on implementing MPAs in the high seas, where international fisheries often exemplify the tragedy of the commons, understanding potential competition between institutions can affect MPA management. With this in mind, we aimed to gain generic insight into non-cooperative fisheries management with MPAs. Specifically, we explored the effect of MPA establishment on (1) competition strength between fishery institutions, (2) fish population abundance resulting from the competition, and (3) distribution of the gross fishery profit between institutions. To approach these questions, we developed a minimal model that accounts a non-cooperative behavior of fishery institutions and population dynamics under the MPAs management. We demonstrate that, given a small price-to-cost ratio, a prominent increase in fishery competition could occur as a result of introducing an MPA, leading to reductions in fisheries profits and fish population abundance, and greater unevenness in distribution of the gross fishery profit. Intensified fishery competition was typically observed in the case where the rate of population exchange between the fishing grounds and the MPA is not large, and the fraction of the MPA is intermediate, suggesting that regulation agreements will be required to coordinate the competitive harvesting

A geometric approach to scaling individual distributions to macroecological patterns

Understanding macroecological patterns across scales is a central goal of ecology and a key need for conservation biology. Much research has focused on quantifying and understanding macroecological patterns such as the species-area relationship (SAR), the endemic-area relationship (EAR) and relative species abundance curve (RSA). Understanding how these aggregate patterns emerge from underlying spatial pattern at individual level, and how they relate to each other, has both basic and applied relevance. To address this challenge, we develop a novel spatially explicit geometric framework to understand multiple macroecological patterns, including the SAR, EAR, RSA, and their relationships. First, we provide a general theory that can be used to derive the asymptotic slopes of the SAR and EAR, and demonstrates the dependency of RSAs on the shape of the sampling region. Second, assuming specific shapes of the sampling region, species geographic ranges, and individual distribution patterns therein based on theory of stochastic point processes, we demonstrate various well-documented macroecological patterns can be recovered, including the tri-phasic SAR and various RSAs (e.g., Fisher\u27s logseries and the Poisson lognormal distribution). We also demonstrate that a single equation unifies RSAs across scales, and provide a new prediction of the EAR. Finally, to demonstrate the applicability of the proposed model to ecological questions, we provide how beta diversity changes with spatial extent and its grain over multiple scales. Emergent macroecological patterns are often attributed to ecological and evolutionary mechanisms, but our geometric approach still can recover many previously observed patterns based on simple assumptions about species geographic ranges and the spatial distribution of individuals, emphasizing the importance of geometric considerations in macroecological studies

A theory for ecological survey methods to map individual distributions

Spatially explicit approaches are widely recommended for ecosystem management. The quality of the data, such as presence/absence or habitat maps, affects the management actions recommended and is, therefore, key to management success. However, available data are often biased and incomplete. Previous studies have advanced ways to resolve data bias and missing data, but questions remain about how we design ecological surveys to develop a dataset through field surveys. Ecological surveys may have multiple spatial scales, including the spatial extent of the target ecosystem (observation window), the resolution for mapping individual distributions (mapping unit), and the survey area within each mapping unit (sampling unit). We developed an ecological survey method for mapping individual distributions by applying spatially explicit stochastic models. We used spatial point processes to describe individual spatial placements using either random or clustering processes. We then designed ecological surveys with different spatial scales and individual detectability. We found that the choice of mapping unit affected the presence mapped fraction, and the fraction of the total individuals covered by the presence mapped patches. Tradeoffs were found between these quantities and the map resolution, associated with equivalent asymptotic behaviors for both metrics at sufficiently small and large mapping unit scales. Our approach enabled consideration of the effect of multiple spatial scales in surveys, and estimation of the survey outcomes such as the presence mapped fraction and the number of individuals situated in the presence detected units. The developed theory may facilitate management decision-making and inform the design of monitoring and data gathering

Optimal reproductive phenology under size-dependent cannibalism

Intra-cohort cannibalism is an example of a size-mediated priority effect. If early life stages cannibalize slightly smaller individuals, then parents face a trade-off between breeding at the best time for larval growth or development and predation risk from offspring born earlier. This game-theoretic situation among parents may drive adaptive reproductive phenology toward earlier breeding. However, it is not straightforward to quantify how cannibalism affects seasonal egg fitness or to distinguish emergent breeding phenology from alternative adaptive drivers. Here, we devise an age-structured game-theoretic mathematical model to find evolutionary stable breeding phenologies. We predict how size-dependent cannibalism acting on eggs, larvae, or both changes emergent breeding phenology and find that breeding under inter-cohort cannibalism occurs earlier than the optimal match to environmental conditions. We show that emergent breeding phenology patterns at the level of the population are sensitive to the ontogeny of cannibalism, that is, which life stage is subject to cannibalism. This suggests that the nature of cannibalism among early life stages is a potential driver of the diversity of reproductive phenologies seen across taxa and may be a contributing factor in situations where breeding occurs earlier than expected from environmental conditions