Beverton Holt Stock Recruitment Research Articles

River Runoff as a Major Driver of Anchovy (Engraulis ringens) Recruitment but Not of Common Sardine (Strangomera bentincki) in Central-South Chile

River runoff to the coastal zone is one of the most important environmental variables that influences the structure and functioning of the neritic trophic web and modulates temporal fluctuations of coastal fishery production in many ecosystems worldwide. The relationship between recruitment of anchovy (Engraulis ringens) and common sardine (Strangomera bentincki) in central-south Chile (34°–40°S) and fluctuations in river runoff was analyzed during the last two decades (1999–2018) using linear and nonlinear regression models. River runoff was also incorporated as a co-variate in Beverton-Holt (BH) stock-recruitment models. Anchovy recruitment was found to be positive and significantly associated with river runoff for all analyzed rivers both for the runoff calculated during its main reproductive period (July–October) and for each single month during this period. This detected nonlinear relationship remained significant when runoff was analyzed for the central macrozone (CMZ) and southern macrozone (SMZ). In contrast, no relationship between runoff and recruitment was detected for the common sardine in any river or macrozone (CMZ, SMZ), for each month of the main reproductive season or for the whole reproductive period (July–October). No density-dependent regulation was detected using BH stock-recruitment models for either species, with or without total freshwater input (i.e., the joint discharge of all rivers; RIVSUM index) as a covariate. Our results highlight the relevance of river runoff as a major driving factor in anchovy recruitment variability, suggesting that high (low) monthly runoff anomalies during the main reproductive period of anchovy populations markedly affect the survival of its early stages, altering recruitment success. For common sardine the runoff effect was not significant, which suggests that other oceanographic/climatic factors (wind-driven upwelling, sea surface temperature, El Niño) are more relevant in driving the variability of its recruitment than river runoff.

Stock-recruitment models from the viewpoint of density-dependent survival and the onset of strong density-dependence when a carrying capacity limit is reached

When viewed on a discrete time step (e.g., one year) rather than instantaneously, the Ricker and Beverton-Holt stock recruitment relationships describe a strong influence of changes in adult abundance on juvenile survival even at low biomass levels. In fact, they describe a stronger influence at lower adult abundance than at high adult abundance. This is not consistent with a simplistic interpretation of carrying capacity, where survival reduces more rapidly as the juvenile abundance approaches its carrying capacity due to resource limitation. It implies that other processes (e.g., changes in predation risk with increased abundance as described by arena theory) control density dependence. A simple habitat limitation model suggests that a similar relationship can occur if the number of juveniles produced by the adults is always more than the juvenile carrying capacity. However, the resulting stock-recruitment relationship is constant recruitment, while that of the Beverton-Holt is increasing asymptotically and the Ricker is dome shaped. Fluctuations around an average recruitment level for a wide range of adult abundance levels is common for highly fecund pelagic spawners (e.g., tuna), suggesting that the survival and recruitment relationships implied by the simple habitat limitation model might be appropriate for these species. Underpinning this argument is the concept that the adult population will saturate the juvenile carrying capacity unless the adult population is fished to extremely low levels. However, it is reasonable to expect that survival should be density independent, or possibly even decompensatory, at some low level of adult abundance. Ignoring depensation, the survival relationship would therefore be well described by a general logistic equation where the decline in survival initially accelerates as abundance increases and then deaccelerates. The resulting stock-recruitment relationship would be a hockey stick shape with the possibility of reduced recruitment at large stock sizes. The model could also be used for low fecund species (e.g., sharks) for which the juvenile carrying capacity is not saturated until the adult abundance is large (i.e., survival is density-independent for a wide range of adult population sizes). In our model, particularly for high fecund species, temporal variation in recruitment would be controlled by changes in the juvenile carrying capacity. We provide equations for the generalized logistic survival stock-recruitment model and investigate the yield consequences. We suggest that an important management consideration is the level of adult abundance at which the juvenile carrying capacity becomes saturated (i.e., when does density dependence become influential on juvenile survival).

The changing times of Europe's largest remaining commercially harvested population of eel Anguilla anguilla L.

This study quantifies the processes involved in regulating the European eel population of Lough Neagh, a lake in Northern Ireland. The relationship between glass eel input and silver eel output for the 1923–1997 cohorts was best described by a Beverton–Holt stock recruitment model. Glass eel input time series was not complete and was thus derived from the relationship between catches elsewhere in Europe and Lough Neagh, together with the addition of stocked glass eel. Silver eel output was the sum of silver eel escapement, catch and yellow eel catch converted to silver eel equivalents. Natural mortality increased with glass eel density, ranging from 0.017 to 0.142 year−1. The mean carrying capacity increased from ≈3.25 M silver eels (≈26 kg ha−1) for the 1923–1943 cohorts to ≈5.0 M (≈40 kg ha−1) for the 1948–1971 cohorts before regressing back to ≈3.25 M. The total silver eel output was highest during the late 1970s/early 1980s at 35–45 kg ha−1 year−1 and lowest during the early years of the 20th century and is currently at 10–15 kg ha−1 year−1. The findings are discussed in relation to (a) the ecological changes that have occurred within the lough, associated with eutrophication and the introduction of roach (Rutilus rutilus L.), and (b) the decline of the wider European eel stock across its distribution range. The findings from this study have relevance for the wider management of the European eel stock.

Demographic and harvest analysis for blue shark (Prionace glauca) in the Indian Ocean

An estimate of the population growth rate (γ) is an essential biological information that can be input into stock assessment models to estimate management quantities for commercial fisheries. Demographic analysis conducted using the Leslie matrix method was used to estimate γ for Indian Ocean blue shark (Prionace glauca), with Monte Carlo simulation used to quantify uncertainty. A harvest analysis was conducted with various selectivity patterns. The results indicated that the productivity of the blue shark was high, with γ=0.26–0.32 y−1 under the assumption of a one-year reproductive cycle. The steepness of the Beverton–Holt stock-recruitment model was estimated to be 0.72 (0.24–0.87) when the Castro and Mejuto fecundity formular was assumed, and 0.80 (0.65–0.88) when the Fujinami et al. fecundity formular was assumed. Harvest analysis with tuna longline selectivity led to lower sustainable harvest rates, but a higher proportion of biomass removed compared to the selectivity patterns for other fisheries. This study provides crucial prior information on the population growth rate and steepness parameters, which can be incorporated into stock assessments for blue shark. Besides, harvest analysis could be a supplement for data-poor stock assessment and risk analysis, to evaluate a tradeoff among different fisheries when considering a management strategy.

Sidney Holt on principles for the conservation of wild living resources, whaling in the Antarctic, and the Beverton–Holt stock–recruitment relationship

Abstract I review my interactions with Sidney Holt concerning principles for the conservation of wild living resources, the whaling case between Australia and Japan in the International Court of Justice, and the Beverton–Holt stock–recruitment relationship (BH-SRR). Holt and Lee Talbot published a monograph on principles for conservation in 1977; I lead the publication of an update ∼20 years later. I compare the two versions and discuss Holt’s contributions. Holt was active in the world-wide campaign to cease whaling and in efforts to have the Japanese special permit whaling programme in the Antarctic recognized as violating the moratorium on commercial whaling. I describe my involvement in the case and my interactions with him during oral arguments in the case and when the International Court of Justice rendered its decision that the Japanese programme of special permit whaling contravened the international treaty for the regulation of whaling because it was not for purposes of scientific research. In response to a paper of mine concerning steepness, Holt wrote to me that the BH-SSR is a one-, not two-, parameter function. I explain my current understanding of his reasoning, which involves how we use the SRR in fishery management.

Effects of recruitment variability and fishing history on estimation of stock-recruitment relationships: Two case studies from U.S. West Coast fisheries

The Beverton-Holt stock-recruitment (SR) relationship has typically been reparameterized such that a single parameter, “steepness,” can be used to define recruitment compensation along a common scale. However, “steepness” is notoriously difficult to estimate in stock assessment models, particularly for the integrated analysis models used to assess groundfish stocks along the U.S. West Coast, due in part to the high levels of recruitment variability observed in the California Current Ecosystem. Additional complicating factors include the effects of exploitation history and subsequent level of contrast in stock abundance, which also influence the extent to which the SR function can be adequately estimated. We conducted a simulation study to explicitly evaluate the effects of recruitment variability on the ability to estimate the steepness parameter. We used two case study models to represent relatively short- and long-lived species of rockfish (Sebastes spp.), and for each we also evaluated effects of two fishing histories, reflecting high and moderate levels of exploitation and historical stock depletion. Not surprisingly, we found that even in data rich scenarios, using appropriately parameterized models, increasing recruitment variability alone can lead to high uncertainty in the estimation of steepness. Perhaps more importantly, with high recruitment variability steepness is frequently estimated to be near or at the upper boundary of the potential range of this value, and there is a bias towards overestimation of steepness in the face of increasing recruitment variability. This over-estimate of steepness occurred less frequently in high fishing scenario, suggesting that recruitment variability has less effects on estimation of steepness if the population has had greater contrast in relative abundance levels. The same results were found in both the relatively short and the long-lived species models. Inclusion of informative priors, either correctly or incorrectly specified, had a greater influence on estimated steepness values at higher levels of recruitment variability, further demonstrating the challenges and risks associated with the application of informative priors when recruitment variability is high.

Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system

The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton–Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton–Holt model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economic issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.

Stock-recruitment resilience of North Pacific striped marlin based on reproductive ecology

The resilience of a stock-recruitment relationship is a key characteristic for modeling the population dynamics of living marine resources. Steepness determines the expected resiliency of a fish stock to harvest and is fundamentally important for the estimation of biological reference points such as maximum sustainable yield. Stock-recruitment steepness was the primary uncertainty for the determination of stock status and biological reference points in recent stock assessments of Western and Central North Pacific striped marlin (Kajikia audax). We therefore applied the method of Mangel et al. to estimate probable values of steepness for striped marlin using new information on the mean batch fecundity, spawning frequency, and spawning season duration under an assumption of Beverton–Holt stock-recruitment dynamics. Results indicated that the median steepness was 0.87 with an 80% probable range of (0.38, 0.98). It is very likely that North Pacific striped marlin is highly resilient to reductions in spawning potential. Variation in reproductive and life history parameters had an important influence on the distribution of steepness. Sensitivity analyses showed that steepness was most sensitive to body girth, mean egg weight, and most importantly, early life history stage survival. Sensitivity analyses also confirmed that the effects of changes in life history parameters on steepness were consistent with expected increases or decreases in reproductive output due to changes in body weight or fecundity. Our approach can be applied to pelagic fish species to directly assess the probable distribution of stock-recruitment resiliency when sufficient information on reproductive ecology and life history parameters is available.

How variable is recruitment for exploited marine fishes? A hierarchical model for testing life history theory

Recruitment often varies substantially in fish populations, and residual variability may have serial autocorrelation due to environmental effects even after accounting for a stock–recruitment relationship. However, the likely magnitude of variability and autocorrelation in recruitment has yet to be formally estimated. We therefore developed a hierarchical model for recruitment variability and autocorrelation and applied it to data for 154 fish populations. Results were similar when using either the Ricker or Beverton–Holt stock–recruitment model, and showed that autocorrelated recruitment has a marginal standard deviation of 0.74 (SD = 0.35) and a mean autocorrelation of 0.43 (SD = 0.28) when predicting for an unobserved taxonomic order. Estimates differed somewhat among taxonomic orders and stocks, and also supported a hypothesized positive relationship between age at maturity and autocorrelation in recruitment. Our results can be used as a Bayesian prior for recruitment variability in models for data-poor stocks and to distinguish recruitment from other process errors in models for data-rich stocks. Estimates can also be used in the design of future simulation models and management strategy evaluations and in theoretical research regarding life history variation.

개체 수 변화에 대한 이산적 모델의 역사적 개요와 컴퓨터 소프트웨어를 이용하는 시각적 분석 방법

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.

A perspective on steepness, reference points, and stock assessment

We provide a perspective on steepness, reference points for fishery management, and stock assessment. We first review published data and give new results showing that key reference points are fixed when steepness and other life history parameters are fixed in stock assessments using a Beverton–Holt stock–recruitment relationship. We use both production and age-structured models to explore these patterns. For the production model, we derive explicit relationships for steepness and life history parameters and then for steepness and major reference points. For the age-structured model, we are required to generally use numerical computation, and so we provide an example that complements the analytical results of the production model. We discuss what it means to set steepness equal to 1 and how to construct a prior for steepness. Ways out of the difficult situation raised by fixing steepness and life history parameters include not fixing them, using a more complicated stock–recruitment relationship, and being more explicit about the information content of the data and what that means for policy makers. We discuss the strengths and limitations of each approach.

A stock–recruitment model for highly fecund species based on temporal and spatial extent of spawning

A stock–recruitment model is described for highly fecund species based on the contraction of the spatial and temporal extent of spawning when a population is reduced in size: R=αK(1−exp[−S/(mK)]), where S is the number of spawners, K is the carrying capacity in units of the number of habitat patches that can produce recruits, α is the average number of recruits per unit of habitat, and m is the number of spawners that group together to spawn. The model is based on three simplifying assumptions: (1) the environment is divided into K units; (2) the presence of one spawner provides sufficient eggs to fill the capacity of that unit, any additional spawners in that unit will not increase recruitment; and (3) groups of fish are randomly distributed over the environment. The model allows for a flat top curve, which is consistent with highly fecund species that are continuous spawners and do not aggregate to spawn. It also allows for a strong relationship between spawners and recruits, which is more consistent with species that aggregate in time and space to spawn. This stock–recruitment model can be approximated in terms of parameters commonly used in contemporary stock assessment models (virgin recruitment, R0, and steepness of the stock–recruitment relationship, h, virgin spawning biomass, S0): R=R0(1−exp(5ln(1−h)S/S0)). The functional form is compared with the Beverton–Holt stock–recruitment model.

Construction of biological reference points for management of the Dungeness crab, Cancer magister, fishery in the Fraser River Delta, British Columbia, Canada

The objective of this study was to define two biological reference points, the Upper Stock Reference Point (USR) and the Limit Reference Point (LRP), to facilitate management of the Fraser River delta commercial Dungeness crab (Cancer magister) fishery in a precautionary manner. The USR is the stock level below which the removal rate is progressively reduced to avoid reaching the LRP. The LRP is the stock level below which productivity is sufficiently impaired to cause serious harm. Currently, the commercial Dungeness crab fishery in the Fraser River delta is managed with a minimum size limit (165mm carapace width point-to-point), non-retention of females and soft-shell crabs, and a restricted fishing season (June to November) to protect large males during the winter/spring moult period. We evaluated variations in legal male, sublegal male, and female Dungeness crab abundances using fishery-independent trap surveys from 1988 to 2010. We also examined proportions of soft-shell legal male and female crabs using survey data and information collected from commercial fishing. A relationship existed between female abundance and corresponding legal male abundance five years later, which is well described by the Beverton–Holt stock–recruitment model. We conducted simulations to assess possible adverse impacts of fishing on the crab population. We assumed the population would stabilize at the existing abundance upon suspension of commercial harvesting if abundance has been steadily declining. Using the stock–recruitment relationship along with information on commercial catch compositions and soft-shell proportions, we assessed the potential reduction in legal male and female crab abundances, given persistent fishing, before the population reaches a lower equilibrium. The amount of reduction to legal male and female crabs increases with decreasing population size. If legal male crab abundance is 50% and 20% of maximum possible recruitment, then fishing would reduce female abundance by 20% and 48%, respectively, before the population is stabilized. We propose these two female abundance levels as the USR and LRP for managing the Fraser River commercial Dungeness crab fishery.

Can steepness of the stock–recruitment relationship be estimated in fishery stock assessment models?

Steepness of the stock–recruitment relationship is one of the most uncertain and critical quantities in fishery stock assessment and management. Steepness is defined as the fraction of recruitment from a virgin population obtained when the spawners are at 20% of the virgin level. Steepness directly relates to productivity and yield and is an important element in the calculation of many management reference points. Stock–recruitment relationships have traditionally been estimated from time series of recruitment and spawning biomass, but recently interest has arisen regarding the ability to estimate steepness inside fishery stock assessment models. We evaluated the ability to estimate steepness of the Beverton–Holt stock–recruitment relationship using simulation analyses for twelve US Pacific Coast fish stocks. A high proportion of steepness estimates from the simulated data and the original data occur at the bounds for steepness and the proportion decreased as the true steepness decreased. The simulation results indicate that, in most cases, steepness was estimated with moderate to low precision and moderate to high bias. The poorly estimated steepness indicates that often there is little information in the data about this quantity. However, reliable estimation is attainable with a good contrast of spawning stock biomass for relatively unproductive stocks when the model is correctly specified.

Evaluating the stock–recruitment relationship and management reference points: Application to summer flounder (Paralichthys dentatus) in the U.S. mid-Atlantic

The stock–recruitment relationship is one of the most uncertain processes of fish population dynamics, and is highly influential with respect to fisheries management advice. The stock recruitment relationship has a direct impact on reference points commonly used in contemporary fisheries management. Simulation analysis has shown that the steepness of the Beverton–Holt stock–recruitment relationship is difficult to estimate for most fish stocks, which has led to the use of proxy reference points. Proxy maximum sustainable yield reference points based on spawning biomass-per-recruit, which are commonly used when the stock–recruitment relationship is uncertain, are a linear function of steepness. Risk in terms of lost yield is generally lower when steepness is underestimated compared to when steepness is overestimated because the yield curve is flat when steepness is high (close to one: recruitment is independent of stock size), indicating that using a lower value of steepness might be appropriate. Simulation analysis based on data for summer flounder in the US mid-Atlantic indicates that steepness can be estimated from the data. Steepness is estimated to be close to one and a high steepness is supported by estimates for related species and from life history theory. Current target (F35%) and threshold (F40%) spawning biomass-per-recruit reference points used for summer flounder imply steepness values of 0.73 and 0.66, respectively, for the Beverton–Holt stock–recruitment relationship.

Analysis of Compensatory Responses in Land‐Locked Alewives to Walleye Predation: A Tale of Two Lakes

AbstractWe compared one established population (Cayuta Lake) and one expanding population (Canadarago Lake) of landlocked alewives Alosa pseudoharengus to evaluate compensatory responses of alewives to predation by walleyes Sander vitreus. Alewives have been present in Cayuta Lake since at least 1977, and during the years 1995 to 2009 the population ranged from 24,470 fish/ha in 2000 to 3,800 fish/ha in 2007. Alewives were first observed in Canadarago Lake during 1999, and the population remained at low densities (<26 fish/ha) until reaching 370 fish/ha in 2006 and 1,050 fish/ha in 2009. Differences in zooplankton reflected higher planktivory rates in Cayuta Lake than in Canadarago Lake. Density of age‐3 and older walleyes was higher in Canadarago Lake (21–24 fish/ha) than in Cayuta Lake (12–14 fish/ha), despite elevated stocking rates of fingerling walleyes in Cayuta Lake during 2002–2006. Alewife density explained 77–84% of the variation in alewife length at age and 48–84% of the variation in condition (ages 0, 1, and 2) among years and lakes. Alewife length at age under low densities in Canadarago Lake was similar to observations in anadromous populations. Alewife recruitment (number of fall age‐0 recruits/spawner) was higher in Canadarago Lake than in Cayuta Lake. The combined data yielded a Beverton–Holt stock–recruitment curve that rose rapidly at low alewife densities, and 50% of the maximum recruitment was predicted to occur at 400 spawners/ha. Compensatory responses of alewives at low densities include decreased cannibalism and increased growth rates of both adults and age‐0 fish. Compensatory responses should be considered when evaluating the piscivore levels needed to control alewife populations or, conversely, when evaluating the risk of alewife population collapse in response to increased predation rates. Although alewife abundance declined in response to the experimental walleye stocking in Cayuta Lake, we were unable to increase the walleye population sufficiently to decrease alewife recruitment.

Statistical catch-at-age analysis vs. ADAPT-VPA: the case of Gulf of Maine cod

Abstract Butterworth, D. S., and Rademeyer, R. A. 2008. Statistical catch-at-age analysis vs. ADAPT-VPA: the case of Gulf of Maine cod. – ICES Journal of Marine Science, 65: 1717–1732. In 2003, given an estimate of a spawning-stock biomass (Bsp) of 27% of the maximum sustainable yield (MSY) level based on an adaptive framework-virtual population analysis (ADAPT-VPA) assessment using data only after 1981, the Gulf of Maine cod (Gadus morhua) stock was deemed “overfished” under the US Magnuson–Stevens Act. However, an alternative statistical catch-at-age assessment (SCAA) at the time, using survey data from 1964, indicated Bsp above . This is investigated, together with other (sometimes conflicting) suggestions made during a number of recent assessment reviews of this stock. The primary reason for the different result is that the ADAPT-VPA assessment imposed asymptotically flat selectivity-at-age when there was strong statistical evidence for dome-shaped selectivity. Once adjusted for this, either assessment method robustly estimates Bsp relatively close to rather than below the “overfished” threshold of 0.5 . SCAA allows the longer series of survey data available to be incorporated, providing a better basis to estimate MSY-related targets and doubling the related precision in some cases. As such targets are important when implementing the Magnuson–Stevens Act, SCAA seems preferable to ADAPT-VPA for assessing this stock. Some broader inferences to be drawn from this comparative process include the need for: (i) careful treatment of the plus-group, especially if selectivity may be dome-shaped; (ii) flexible parameterizations of selectivity-at-age in SCAA to avoid false perceptions of the precision of results; and (iii) care in the use of the Beverton–Holt stock–recruitment function, as it gives inappropriately low estimates of if there is an overall negative trend in the estimates of recruitment plotted against Bsp.

A bio-economic evaluation of different management measures for the Mediterranean swordfish

The biological and economic implications of different management measures concerning the Mediterranean swordfish stock were evaluated by means of simulations performed under the Fisheries Language in R (FLR) framework. Six different scenarios were examined including Mediterranean-wide seasonal closures of different duration and an effort reduction scheme. Recruitment was assumed to vary in levels either predicted by a Beverton–Holt stock–recruitment relationship or around an average value estimated from the latest assessment accomplished by the International Commission for the Conservation of Atlantic Tunas (ICCAT). Simulations projected the levels of landings, spawning stock biomass (SSB), gross and net revenue for a period of twenty years. Considering the estimated statistical uncertainty, gains in terms of landings and SSB from short fishery closures (e.g. one month) will be negligible. On the contrary, seasonal closures of at least four months would result in important long-term gains, which are more profound in the case of SSB and net revenue. The ICCAT convention objectives concerning SSB, can only be met with drastic closures (i.e. six months). However, drastic closures would result in short-term decreases in landings and revenues, which should be taken into account before such measures are adopted.

Escapement goal analysis and stock reconstruction of sockeye salmon populations (Oncorhynchus nerka) using life-history models

We compare life-history models with the Beverton–Holt approach of escapement goal analysis. We model the life history of a sockeye salmon ( Onchorhynchus nerka ) population from a spawning stage, through juvenile and adult stages, and ending with adults that return to spawn. We fit models to data by statistically comparing predicted and observed numbers of four dominant adult ages. Posterior estimates of parameters from Markov chain Monte Carlo simulations are then used to assess optimal harvest policies. We search for policies that produce the highest average yield. We find that it is possible to detect density dependence with a life-history model where analysis of Beverton–Holt stock–recruitment relationship fails to do so. We find that Beverton–Holt relationships produce policies and long-term yield estimates that are inconsistent with empirical trends. Conversely, we find that optimal spawning stock sizes and maximum sustained yield estimates using the life-history model estimate are consistent with the historical behavior of fisheries examined. Adding smolt data to the analysis does not substantially change predicted optimal spawning stock size, but decreases the variance in estimated posterior parameter distributions and policy variable distributions.

Using age-structured models to develop a stock recovery strategy for Kuwait's shrimp fishery

Shrimps are the most important fisheries resources in Kuwait. Shrimp resources have been decreasing due mostly to over-fishing. For protection of Kuwait's shrimp resources and to encourage a sustainable shrimp fishery, age-structured models were used to develop a stock recovery strategy. Age-structured models, including a modified Beverton–Holt stock–recruitment relationship, growth function and equations for catch-at-age analysis were used to fit the fisheries data from 1965 to 2004 and estimate four parameters: a, b and ɛ from the modified Beverton–Holt equation and the catchability q. The model fitting was conducted through comparing the estimated catches with the observed catches using the maximum log-likelihood method. The results showed a declining trend for both the recruitment and biomass before and after the 1991 Gulf War. The estimated maximum sustainable yield (MSY) for Kuwait's shrimp fishery is 2298 t with a corresponding fishing effort ( f MSY) of 9730 boat-days using a median natural mortality 2.9 per year. The model fitting with different natural mortalities and catchabilities showed that both parameters had limited effects on the MSY and f MSY. The trends in recruitment, biomass, catch and catch-per-unit-effort (CPUE) to year 2020 under different fishing effort were simulated by the fitted models. The simulations demonstrated that reducing the fishing effort will only slightly decrease the catch, but increase the recruitment, greatly increase biomass, and CPUE. Increasing the fishing effort, however, will result in a decline of recruitment, biomass, catch, and CPUE. The simulations also showed different season opening dates and duration affect the fishery. Delaying the season opening or advancing the close date will increase MSY and f MSY and reduce CPUE. While opening earlier and closing later will reduce the MSY, f MSY and increase the CPUE. We suggested that a good season management strategy should balance the high MSY, CPUE values and the size (price) of the shrimp catch. Based on the model fitting and simulation results, a management strategy to recover the shrimp stock was provided.