![]() However, limited research has been undertaken to identify sustainable harvest rates that account for spatial structure and dynamics in a manner that matches spatial assessment assumptions. This echoes the findings from the previously mentioned simulation studies, and suggests that assumptions regarding the timing and locality of density dependence (recruitment) can influence the degree to which an assessment model diverges from the spatially-structured reality (Cadrin et al., 2019). As a corollary, assessing yellow croaker as a single stock, with the assumption of global recruitment, led to a high probability of local depletion. (2011) found that assessing and managing three mixed stocks of small yellow croaker ( Larimichthys polyactis) off the coast of China as independent populations led to a high probability of overexploitation. (2020) found that applying single-area models separately to each of two connected stocks in a simulation framework (i.e., ignoring spatial mixing) resulted in biased estimates of recruitment and spawning biomass for both stocks. ![]() Ignoring spatial structure in the assessment and management processes for such species may lead to local depletion (Benson et al., 2015 Goethel and Berger, 2017). For example, Atlantic bluefin tuna ( Thunnus thynnus) are comprised of two demographically distinct stocks inhabiting different areas with connectivity between them (National Research Council (NRC), 1994). 1 A stock can be defined by both its demography and the spatial area it inhabits. Problems for sustainable management can arise from a mismatch between management regions, which are often political, and the spatial extent of demographic population units, or stocks. They also can evaluate other types of spatial control mechanisms for fisheries management such as spatial closures within management zones, protected areas, and Territorial Use Rights for Fishing reserves (e.g., Kapur and Franklin, 2017 McGilliard et al., 2015 Field et al., 2006). Spatially-structured assessments can inform rules for setting catch limits that respond to local dynamics (Bosley et al., 2019, McGarvey et al., 2017). Accounting for spatial structure can provide a greater degree of biological realism by 1) allowing for spatial variation in demographic parameters, 2) reducing the variance of fixed effect parameter estimates, and 3) more accurately reflecting the spatial dynamics of the fishing fleet(s), which may differ from those of fish population dynamics (Punt, 2019a). Ignoring spatial structure in assessments can lead to bias in estimated management quantities (Booth, 2000, Fay et al., 2011, Punt, 2019a see Online Supplementary Material for a discussion of the definition of “spatial structure”). The interaction of biological and environmental processes, and spatial exploitation patterns, can lead demographic rates (i.e., growth, death, immigration, and emigration) to vary across space, resulting in observable spatial patterns in fish populations and yields. Finally, we address areas of research and development needed to integrate spatially-structured population dynamics models within existing management systems.įisheries scientists have long recognized the need to appropriately account for spatial heterogeneity in stock assessments (e.g., Beverton and Holt, 1957 Schaefer, 1968). ![]() Results suggest that our method for calculating reference points under the assumption of local density-dependence can be performed using a straightforward optimization routine, and provide clearer understanding of the effects of fishing on a spatially-structured population. We compare those values to equivalent situations when density-dependence in recruitment is global, thereby extending the set of population dynamics models on which spatially-structured stock assessments could be based. ![]() We outline how to calculate equilibrium quantities within spatially-structured models where density-dependence in recruitment is local. However, the calculation process can be challenging for spatially-structured population dynamics models. Reference points (e.g., limit or target harvest rates and their associated biomass) are inherent to stock assessments and are often calculated under equilibrium conditions. Accounting for spatial structure accurately and easily is a major goal for the next generation of stock assessment software development. Fish populations with spatial structure inherently violate the assumption of a single well-mixed stock, necessitating the use of spatially-structured population dynamics models. ![]()
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