An explicit solution for calculating optimum spawning stock size from Ricker’s stock recruitment model

Scheuerell, Mark D.

doi:10.7717/peerj.1623

Cited by 13 publications

(12 citation statements)

References 11 publications

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“…Under perfect management control the harvest rate, U , experienced by stock n in year y was:

U_{y, n} = \{\begin{matrix} 0 & {\overset{N}{true}}_{y, n} ‐ E_{n} \leq 0 \\ (N_{y, n} ‐ E_{n}) false/ N_{y, n}, & {\overset{N}{true}}_{y, n} ‐ E_{n} > 0 \end{matrix}

where

{\overset{false^}{N}}_{y, n}

, the forecasted run size, is equal to the true run size ( N y , n ) plus forecast error

ε_{n}

which was lognormally distributed with a mean of zero and variance equal to

σ_{f}^{2}

, where the f subscript differentiates this variance from other variance terms in the simulation. The escapement goal for a given stock, E n , is the spawner abundance expected to produce maximum sustainable yield based on the stock specific α n and β n (Scheuerell, 2016), such that “surplus” production above the escapement goal is harvested when the forecasted run size is larger than it. Total harvest by stock, H y , n , is then:

H_{y, n} = U_{y, n} N_{y, n}

and total escapement, by stock, is:

S_{y, n} = N_{y, n} ‐ H_{y, n}

…”

Section: Methodsmentioning

confidence: 99%

Conservation risks and portfolio effects in mixed‐stock fisheries

2021

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Fish biodiversity sustains the resilience and productivity of fisheries, yet this biodiversity can be threatened by overharvest and depletion in mixed‐stock fisheries. Thus, the biodiversity that provides benefits may also make sustainable resource extraction more difficult, a key challenge in fisheries management. We simulated a mixed‐stock fishery to explore relationships between different dimensions of biodiversity and fishery performance relative to conservation and fishery objectives. Different dimensions of biodiversity (number of stocks, evenness, asynchrony among stocks, heterogeneity in stock productivity) exacerbated trade‐offs between fishery and conservation objectives. For example, fisheries targeting stock‐complexes with greater asynchrony, and to a lesser extent richness, had greater stability in harvest through time but also greater risks of overfishing weak stocks and reduced yield compared to less biodiverse stock‐complexes. These trade‐offs were ameliorated by increasing management control—the capacity of fishery managers to harvest specific stocks. To explore these trade‐offs in real‐world fisheries, we contrasted the fishing and population status of individual stocks within three major mixed‐stock sockeye salmon (Oncorhynchus nerka, Salmonidae) fisheries—Bristol Bay, Fraser River, and Skeena River. In general, the fisheries with lower management control had individual stocks that were more often being over‐ or under‐fished, compared with those with higher management control, though variation among regions in biodiversity, scale of management, and magnitude of habitat alteration likely also contribute to these relationships. Collectively, our findings emphasize that there is a need to extract less or regulate better in order to conserve and benefit from biodiversity in fisheries and other natural resource management systems.

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“…Under perfect management control the harvest rate, U , experienced by stock n in year y was:

U_{y, n} = \{\begin{matrix} 0 & {\overset{N}{true}}_{y, n} ‐ E_{n} \leq 0 \\ (N_{y, n} ‐ E_{n}) false/ N_{y, n}, & {\overset{N}{true}}_{y, n} ‐ E_{n} > 0 \end{matrix}

where

{\overset{false^}{N}}_{y, n}

, the forecasted run size, is equal to the true run size ( N y , n ) plus forecast error

ε_{n}

which was lognormally distributed with a mean of zero and variance equal to

σ_{f}^{2}

H_{y, n} = U_{y, n} N_{y, n}

and total escapement, by stock, is:

S_{y, n} = N_{y, n} ‐ H_{y, n}

…”

Section: Methodsmentioning

confidence: 99%

Conservation risks and portfolio effects in mixed‐stock fisheries

2021

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“…For all models we estimated population size at maximum sustained yield (S MSY ) using Scheuerell’s method, where W is the solution to Lambert’s function, implemented in the R-package gsl (Scheuerell 2016) (Equation 6). Posterior density distributions of S MSY for each population were estimated using 10,000 randomly sampled α and β values from the MCMC, and mean and confidence intervals were estimated using the R-package HDInterval (Meredith and Krushke 2020).…”

Section: Methodsmentioning

confidence: 99%

Linking habitat and population dynamics to inform conservation benchmarks for data-limited salmon stocks

Atlas

Ca²,

et al. 2021

Preprint

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Management of data-limited populations is a key challenge to the sustainability of fisheries around the world. For example, sockeye salmon (Oncorhynchus nerka) spawn and rear in many remote coastal watersheds of British Columbia (BC), Canada, making population assessment a challenge. Estimating conservation and management targets for these populations is particularly relevant given their importance to First Nations and commercial fisheries. Most sockeye salmon have obligate lake-rearing as juveniles, and total abundance is typically limited by production in rearing lakes. Although methods have been developed to estimate population capacity based on nursery lake photosynthetic rate (PR) and lake area or volume, they have not yet been widely incorporated into stock-recruit analyses. We tested the value of combining lake-based capacity estimates with traditional stock-recruit based approaches to assess population status using a hierarchical-Bayesian stock-recruit model for 70 populations across coastal BC. This analysis revealed regional variation in sockeye population productivity (Ricker α), with coastal stocks exhibiting lower mean productivity than those in interior watersheds. Using moderately-informative PR estimates of capacity as priors reduced model uncertainty, with a more than five-fold reduction in credible interval width for estimates of conservation benchmarks (e.g. SMAX - spawner abundance at carrying capacity). We estimated that almost half of these remote sockeye stocks are below one commonly applied conservation benchmarks (SMSY), despite substantial reductions in fishing pressure in recent decades. Thus, habitat-based capacity estimates can dramatically reduce scientific uncertainty in model estimates of management targets that underpin sustainable sockeye fisheries. More generally, our analysis reveals opportunities to integrate spatial analyses of habitat characteristics with population models to inform conservation and management of exploited species where population data are limited.

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“…Deterministic forms of the (a) Ricker and (b) Beverton-Holt models used in the analyses (thick lines), including equations for carrying capacity ( K ) and the number of recruits corresponding to the maximum sustained yield ( R MSY ). The parameter α defines the slope at the origin, the constant e is Euler’s number, and W (·) is the Lambert function (see Scheuerell 2016 for details). The gray line is where R t = S t .…”

Section: Methodsmentioning

confidence: 99%

An integrated population model for estimating the relative effects of natural and anthropogenic factors on a threatened population of Pacific trout

Scheuerell

Ruff

Beamer

2019

Preprint

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1 1. Assessing the degree to which at-risk species are regulated by density dependent versus 2 density independent factors is often complicated by incomplete or biased information. If not 3 addressed in an appropriate manner, errors in the data can affect estimates of population 4 demographics, which may obfuscate the anticipated response of the population to a specific 5 action. 6 2. We developed a Bayesian integrated population model that accounts explicitly for interannual 7 variability in the number of reproducing adults and their age structure, harvest, and 8 environmental conditions. We apply the model to 41 years of data for a population of threatened 9 steelhead trout Oncorhynchus mykiss using freshwater flows, ocean indices, and releases of 10 hatchery-born conspecifics as covariates. 11 3. We found compelling evidence that the population is under strong density dependence, despite 12 being well below its historical population size. In the freshwater portion of the lifecycle, we 13 found a negative relationship between productivity (offspring per parent) and peak winter flows, 14 and a positive relationship with summer flows. We also found a negative relationship between 15 productivity and releases of hatchery conspecifics. In the marine portion of the lifecycle, we 16 found a positive correlation between productivity and the North Pacific Gyre Oscillation. 17 Furthermore, harvest rates on wild fish have been sufficiently low to ensure very little risk of 18 overfishing.19 4. Synthesis and applications. The evidence for density dependent population regulation, 20combined with the substantial loss of juvenile rearing habitat in this river basin, suggests that 21 habitat restoration could benefit this population of at-risk steelhead. Our results also imply that 22 hatchery programs for steelhead need to be considered carefully with respect to habitat 23 3 availability and recovery goals for wild steelhead. If releases of hatchery steelhead have indeed 24 limited the production potential of wild steelhead, there are likely significant tradeoffs between 25 providing harvest opportunities via hatchery steelhead production, and achieving wild steelhead 26 recovery goals. 27 28 Managing at-risk species requires an understanding of the degree to which population 29 dynamics are self-regulated versus driven by external factors. However, the data used to identify 30 potentially important density-dependent and population-environment relationships are rarely, if 31 ever, fully comprehensive or error free. Rather, imperfect detection, misidentification, and non-32 exhaustive sampling all lead to a somewhat distorted view of the true state of nature. For 33 example, when not addressed in an appropriate manner, errors in population censuses may cause 34 underestimates of recruitment (Sanz-Aguilar et al. 2016) or overestimates of the strength of 35 density dependence (Knape & de Valpine 2012). Similarly, imprecision in the estimated age 36 composition of the population also biases the estimated strength of density depe...

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An explicit solution for calculating optimum spawning stock size from Ricker’s stock recruitment model

Cited by 13 publications

References 11 publications

Conservation risks and portfolio effects in mixed‐stock fisheries

Conservation risks and portfolio effects in mixed‐stock fisheries

Linking habitat and population dynamics to inform conservation benchmarks for data-limited salmon stocks

An integrated population model for estimating the relative effects of natural and anthropogenic factors on a threatened population of Pacific trout

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