Stock-recruitment Relationship Research Articles

Coping with information gaps in stock productivity for rebuilding and achieving maximum sustainable yield for grouper–snapper fisheries

AbstractMaintaining fish stocks at optimal levels is a goal of fisheries management worldwide; yet, this goal remains somewhat elusive, even in countries with well‐established fishery data collection, assessment and management systems. Achieving this goal often requires knowledge of stock productivity, which can be challenging to obtain due to both data limitations and the complexities of marine populations. Thus, scientific information can lag behind fishery policy expectations in this regard. Steepness of the stock–recruitment relationship affects delineation of target biomass level reference points, a problem which is often circumvented by using a proxy fishing mortality rate (F) in place of the rate associated with maximum sustainable yield (FMSY). Because MSY is achieved in the long term only if an F proxy is happenstance with FMSY, characterizing productivity information probabilistically can support reference point delineation. For demersal stocks of equatorial and tropical regions, we demonstrate how the use of a prior probability distribution for steepness can help identify suitable F proxies. F proxies that reduce spawning biomass per recruit to a target percentage of the unfished quantity (i.e., SPR) of 40% to 50% SPR had the highest probabilities of achieving long‐term MSY. Rebuilding was addressed through closed‐loop simulation of broken‐stick harvest control rules. Similar biomass recovery times were demonstrated for these rules in comparison with more information‐intensive rebuilding plans. Our approach stresses science‐led advancement of policy through a lens of information limitations, which can make the assumptions behind rebuilding plans more transparent and align management expectations with biological outcomes.

Assessment of the Relationship of Stock and Recruitment in the Atlantic Surfclam Spisula solidissima in the Northwestern Atlantic Ocean

Atlantic surfclams support a major commercial fishery in the western North Atlantic Ocean with landings consistently between 15,000 and 25,000 metric tons since 1982. The stock is not and historically has not been overfished nor has overfishing occurred; however, in recent years landings per unit effort have declined. Surfclams are a biomass dominant on the continental shelf and a bellwether of climate change in the northwestern Atlantic. This study investigated the relationship of broodstock and recruitment during a period when Mid-Atlantic warming initiated a shelf-wide shift in the surfclams range. A species distribution function model was used to assess the effective area occupied by surfclams for five study regions (Delmarva, New Jersey, Long Island, Southern New England, and Georges Bank). The effective area occupied by small surfclams was consistently much greater than that for large (≥120 mm) surfclams. Three independent statistical analyses of the stock-recruitment relationship found little evidence of a significant association in any of the five regions, suggesting that factors besides spawning stock biomass (SSB) are primary determinants of recruitment success. Interannual variability in recruitment, in part associated with variations in larval transport and in part associated with spatially different rates of mortality post-settlement, is an important source of uncertainty and warming bottom waters driving surfclams into new habitat may decouple any inherent interaction between recruits and SSB. A recruitment index obtained from a fishery-independent survey across the range of the stock, as a consequence, is unlikely to usefully presage changes in abundance of the fishable stock. The wider distribution of settlers relative to the fishable stock, however, positions the species well to respond to changing bottom water temperatures as Mid-Atlantic warming continues.

The influence of metrics for spawning output on stock assessment results and evaluation of reference points: An illustration with yellowfin tuna in the eastern Pacific Ocean

Reference points are used to determine whether overfishing is occurring, a stock is overfished, or the abundance of the stock is approaching an undesirable level. Reference points are often classified as limit reference points, which indicate an undesirable state, or target reference points, which specify a desirable one. Limit reference points frequently indicate a state for which the reproductive potential of the stock is impacted, and are thus based on spawning output. Spawning output is also used in the stock-recruitment curve, which is a key component of stock-assessment models. We investigated the effect on stock assessment results of metrics of spawning output that are used either in the stock-recruitment relationship or to evaluate reference points. We use yellowfin tuna (Thunnus albacares) in the eastern Pacific Ocean as an example. The metrics biomass of mature females and fecundity attribute higher reproductive potential to the older ages, while numbers of mature females and summary biomass attribute more to the younger ages. Both the stock assessment results and the evaluation of reference points are sensitive to the metric used. The most optimistic perceptions of stock status are obtained when using numbers of mature females, female summary biomass or summary biomass to evaluate the reference points. The choice of metric may be as important as the uncertainty about steepness of the stock-recruitment curve. Given the difficulty in determining the appropriate measure of spawning output and the fact that populations fluctuate naturally, it is recommended that fishing mortality-based reference points are given more consideration for management advice aiming to maintain stocks at desirable states (target reference points) and that harvest control rules based on both types of reference points be compared for their relative effectiveness in avoiding recruitment overfishing and achieving other fisheries objectives using Management Strategy Evaluation.

Four-year decline in Ostrea chilensis recruits per spawner in Foveaux Strait, New Zealand, suggests a diminishing stock-recruitment relationship

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 600:85-98 (2018) - DOI: https://doi.org/10.3354/meps12641 Four-year decline in Ostrea chilensis recruits per spawner in Foveaux Strait, New Zealand, suggests a diminishing stock-recruitment relationship Keith P. Michael1,2,3,*, Jeffrey S. Shima1,2 1School of Biological Sciences, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand 2Victoria University Coastal Ecology Laboratory (VUCEL), PO Box 600, Wellington 6140, New Zealand 3National Institute of Water and Atmospheric Research (NIWA), PB 14901, Wellington 6021, New Zealand *Corresponding author: k.michael@niwa.co.nz ABSTRACT: Rebuilding and maintaining sufficient spawning stock to ensure recruitment is a key strategy for fisheries management and ecological restoration. We evaluated variation in Ostrea chilensis recruitment across seasons and sites over 4-6 yr in Foveaux Strait (New Zealand) to infer the relative importance of determinants of population recruitment. Recruitment varied significantly between seasons (p < 0.001). Most recruitment in any given year (97.8 ± 0.9%, mean ± SE) occurred in the austral spring and summer (November to February). Recruitment also varied significantly between years (p < 0.001). In a separate fishery-wide study, we investigated the effect of spawner densities on recruitment, relative to other climatic and biological factors. We deployed spat collectors at 6 sites across 3 discrete fishery areas, and estimated densities of spawning-sized oysters from dredge samples. We modelled counts of oyster spat and spawners with a negative binomial regression to evaluate the stock-recruitment relationship. Recruitment varied between years (50.8% of the deviance explained), spawner densities (13.8%), and areas (11.6%), with further 2-way interactions among these factors. Importantly, our analysis showed a continued decline in recruits per spawner, despite similar or increasing densities of spawning-sized oysters. Average recruitment for 2010-11 when spawner densities were highest was 4.6% of the level observed in 2007-08. Our data suggest that factors other than densities of oysters play a major role in the numbers of competent larvae available for settlement. Managing oyster fisheries as a single stock and maintaining oyster densities above management reference points alone may not be sufficient to ensure recruitment to rebuild populations. KEY WORDS: Recruitment variability · Oysters · Spatial management · Foveaux Strait · Stock-recruitment relationship Full text in pdf format Supplementary material PreviousNextCite this article as: Michael KP, Shima JS (2018) Four-year decline in Ostrea chilensis recruits per spawner in Foveaux Strait, New Zealand, suggests a diminishing stock-recruitment relationship. Mar Ecol Prog Ser 600:85-98. https://doi.org/10.3354/meps12641 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 600. Online publication date: July 30, 2018 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2018 Inter-Research.

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.

Effects of walleye predation on variation in the stock-recruitment relationship of Lake Erie yellow perch

Abstract Stock-recruitment relationships (SRRs) may vary over time due to temporal variation in ecological conditions, reducing confidence in projections from stock-recruitment models. We examined whether the time-varying SRRs detected for yellow perch (Perca flavescens) in the western basin of Lake Erie between 1977 and 2013 could be attributed to variation in yearling walleye (Sander vitreus) predation, indexed by variation in density. Annual variation in yearling walleye density was strongly associated with yellow perch recruitment dynamics, and positively correlated with temporal variation in density-dependence of yellow perch SSRs. However, non-stationary SRRs persisted after accounting for effects of yearling walleye density, and the extent of temporal variation in SRRs actually increased. In simulations, we showed that time-varying SRRs may result more from variation in low-frequency ecological factors on the order of decades, than from variation in high-frequency ecological factors on the order of years (e.g., yearling walleye density) and thus may not be distinguishable from noise. Hence, of these two types of factors, the systematic identification, characterization and incorporation of those of low-frequency factors into stock-recruitment models (e.g., exotic mussel invasions and eutrophication, in the case of Lake Erie) may offer greater promise to improve the reliability of long-term forecasts for sustainable harvests in this and other fisheries in dynamic ecosystems.

Ecosystem‐based forecasts of recruitment in two menhaden species

AbstractGulf (Brevoortia patronus, Clupeidae) and Atlantic menhaden (Brevoortia tyrannus, Clupeidae) support large fisheries that have shown substantial variability over several decades, in part, due to dependence on annual recruitment. Nevertheless, traditional stock–recruitment relationships lack predictive power for these stocks. Current management of Atlantic menhaden explicitly treats recruitment as a random process. However, traditional methods for understanding recruitment variability carry the very specific hypothesis that the effect of adult biomass on subsequent recruitment occurs independently of other ecosystem factors such as food availability and predation. Here, we evaluate the predictability of menhaden recruitment using a model‐free approach that is not restricted by these strong assumptions. We find that menhaden recruitment is predictable, but only when allowing for interdependence of stock with other ecological factors. Moreover, while the analysis confirms the presence of environmental effects, the environment alone does not readily account for the complexity of menhaden recruitment dynamics. The findings set the stage for revisiting recruitment prediction in management and serve as an instructive example in the ongoing debate about how to best treat and understand recruitment variability across species and fisheries.

Effects of Water-Level Management and Hatchery Supplementation on Kokanee Recruitment in Lake Pend Oreille, Idaho

Abstract Resource managers have been attempting to recover the kokanee (Oncorhynchus nerka) population in Lake Pend Oreille, Idaho for more than three decades using an annual stocking program and an experimental water-level management strategy. This study evaluated the effect of both management actions on kokanee recruitment. A bootstrap-based generalized Ricker model was used to test if wild kokanee recruitment was significantly influenced by water-level management, while accounting for error due to sampling variability and differential survival of wild- and hatchery-origin fish within age-classes. Wild kokanee exhibited a compensatory stock-recruitment relationship, whereas hatchery recruitment was positively and linearly related to stocking. The model did not identify a significant relationship between water level and wild kokanee recruitment. Density dependence and variable stocking appeared to explain the synchronized and cyclic recruitment of wild and hatchery fry.

Steepness for West Coast rockfishes: Results from a twelve-year experiment in iterative regional meta-analysis

Theoretical and applied research suggests that survival rates during early life stages will increase when spawning biomass is reduced in marine fishes (termed “recruitment compensation”). However, the magnitude of recruitment compensation is generally difficult to estimate for individual fish stocks, and its average value for marine fishes remains highly contested. Scientists and managers for Pacific rockfishes (Sebastes spp.) on the US West Coast have used a regional meta-analysis to estimate the likely distribution of the steepness parameter of the Beverton-Holt stock-recruit relationship using stock assessment models since 2007, and the method has been updated every two years as new assessments are conducted (i.e., five biennial updates). Here, we provide a short history of this approach, its methodological assumptions, changes in results over time, and ongoing efforts to validate its assumptions. While the regional meta-analysis has been successful in ensuring a consistent approach to treatment of steepness across assessments, the estimates of mean steepness have been unexpectedly variable as the meta-analysis has been updated. Specifically, we show that the estimated average value of steepness for West Coast rockfish increased markedly from 2007 (average: <0.6) to 2011 (average:>0.75), before decreasing somewhat again in the 2017 update. We also show that this value has a strong impact on rockfish rebuilding plans, and showcase the example of canary and widow rockfishes, where the estimated rates of rebuilding are strongly influenced by the assumed value of steepness. We conclude by discussing the bias-variance tradeoff between using global and regional meta-analysis, as well as the likely implications of difficult-to-validate assumptions including: (1) no recruitment autocorrelation within each stock; (2) no correlations among stocks; and (3) no bias from individual stocks resulting from mis-specification of the stock assessment models used in the meta-analysis.

Implications of late-in-life density-dependent growth for fishery size-at-entry leading to maximum sustainable yield

AbstractCurrently applied fisheries models and stock assessments rely on the assumption that density-dependent regulation only affects processes early in life, as described by stock–recruitment relationships. However, many fish stocks also experience density-dependent processes late in life, such as density-dependent adult growth. Theoretical studies have found that, for stocks which experience strong late-in-life density dependence, maximum sustainable yield (MSY) is obtained with a small fishery size-at-entry that also targets juveniles. This goes against common fisheries advice, which dictates that primarily adults should be fished. This study aims to examine whether the strength of density-dependent growth in actual fish stocks is sufficiently strong to reduce optimal fishery size-at-entry to below size-at-maturity. A size-structured model is fitted to three stocks that have shown indications of late-in-life density-dependent growth: North Sea plaice (Pleuronectes platessa), Northeast Atlantic (NEA) mackerel (Scomber scombrus), and Baltic sprat (Sprattus sprattus balticus). For all stocks, the model predicts exploitation at MSY with a large size-at-entry into the fishery, indicating that late-in-life density dependence in fish stocks is generally not strong enough to warrant the targeting of juveniles. This result lends credibility to the practise of predominantly targeting adults in spite of the presence of late-in-life density-dependent growth.

The True Mechanism That Controls the Stock-Recruitment Relationship

I propose a mechanism that controls the stock-recruitment relationship (SRR), which should replace traditional SRR models. The difference between the traditional SRR models and the model proposed herein is whether or not a density-dependent effect is assumed. The new mechanism elucidates the following: 1) why clockwise loops or anticlockwise loops are commonly observed in an actual SRR, and 2) the age at maturity (not a density-dependent effect) determines the slope of the regression line for the SRR. These cannot be explained by the traditional SRR models, the basis of which is a density-dependent effect. The new SRR mechanism can well explain the SRRs for Pacific stocks of Japanese sardine, Pacific bluefin tuna and Arctic bluefin tuna. The new SRR mechanism proposed herein should be used as a valid SRR model when the management of fishery resources is discussed. Without the adaptation of this new mechanism, fishery resource management may continue to be troubled by the lack of validity of the traditional SRR models.

The Caribbean spiny lobster (Panulirus argus) fishery in Cuba: current status, illegal fishing, and environmental variability

Spiny lobster, Panulirus argus (Latreille, 1804), is the most valuable fishery resource in Cuba. Despite strong management, the population shows signs of decline. The objectives of the present study were to complete a literature review and to evaluate spiny lobster status, including illegal fishing. A statistical catch-at-age analysis, considering the addition of two environmental indices in the stock-recruitment relationship, was applied for two separate scenarios: one with data (the official model), and a second including illegal fishing (the model). Combined analysis of yield-per-recruit, spawning biomass-per-recruit, and stock-recruitment relationship was used to estimate equilibrium conditions at fixed levels of fishing mortality rate (F) and environmental conditions. Annual illegal catch represented 18.4% of total harvest. Recruitment and stock size estimates in both models showed similar historical behavior with a decreasing trend and a recovery in the last 5 yrs. F estimates of the total model are higher than those of the model. There were considerable differences in stock production for reference points associated with environmental conditions, and the observed catch trajectory follows an average equilibrium curve. Incorporating illegal fishing led to lower maximum sustainable yield (MSY) and fishing mortality rate for the MSY (F MSY) values than the model. If not taken into account, illegal activities can lead to the establishment of reference points that are higher than those that are sustainable for current populations. Despite the uncertainty associated with illegal fishing estimates, it is more precautionary to include them in stock assessments, which can lead to management decisions that result in more sustainable fisheries.

Modeling White Sucker (Catostomus commersonii) populations to assess commercial harvest influence on age structure

Commercial harvest of White Suckers Catostomus commersonii for bait in the American Lobster Homarus americanus industry is minimally regulated in Maine and there are concerns as to the influence of increasing harvest. We built a population model using parameters (i.e. age-specific mortality, age at maturity, and size-specific fecundity) from literature and field studies to investigate the theoretical effects of harvest mortality on age structure. Because stock-recruitment relations are poorly characterized for this species, we explored the influence of both Beverton-Holt and Ricker recruitment processes. Our base model closely resembled the empirical age structures reported from three unfished lakes in Maine, with four percent of fish in the modeled spawning run being age-10 or older. We assessed the additive effects of harvest mortality on age structure using the full range of possible mortalities. As expected, increased harvest mortality in the model resulted in a decline and disappearance of older age-classes such that few fish greater than age-10 remained in the population under a realistic harvest mortality scenario. This age-truncation was qualitatively comparable to data from aggregate age distributions reported from three commercially harvested lakes in Maine. Because the loss of older fish may compromise population viability, this model is a valuable guidance tool for managers to craft regulation of this growing fishery.

Estimating steepness of the stock-recruitment relationship in Chilean fish stocks using meta-analysis

Steepness (h) is a fundamental metric in population dynamics because it defines the relationship between parental stock and offspring. h represents a direct measurement of resilience and is therefore crucial in the management of harvested populations. However, h represents one of the most difficult parameters to estimate, even for data-rich stocks. It is usually estimated using indirect methods based on meta-analysis. Existing meta-analyses use all available estimates of h from different sources of information (i.e., from outside or within the stock assessment model) and report non-significant relationships between h and other life history traits, even though several theoretical analyses suggest the contrary. We conducted a two-stage meta-analysis, firstly selecting suitable h estimates from stock assessment models for fish stocks worldwide. 42 estimates of h were collected and several life history attributes were used as explanatory variables within generalised linear models (GLMs). We found a significant relationship (p < 0.05) between h and the ratio between length at 50% maturity (L50) and asymptotic length (L∞). The second stage of our meta-analysis was to apply this relationship to 19 fish stocks harvested off Chile to estimate species-specific h and the associated uncertainty. We discuss the assumptions of the proposed meta-analysis, the reliability of the estimated uncertainties and outline the potential application in the assessment and management of fish resources in Chile.

Stock-recruitment relationships in elasmobranchs: Application to the North Pacific blue shark

Stock-recruitment relationships in elasmobranchs are uncertain due to a lack of data, especially regarding pre-recruit survivorship. A pre-recruit survival model for the early life history of elasmobranchs was developed and parameterized using biological data. Then, an existing age-structured model for the reproductive ecology of teleost fishes was modified for elasmobranchs and combined with the pre-recruit model. The combined model was then applied to the North Pacific blue shark (Prionace glauca). The stock-recruitment relationships of this species were clarified using the biological data collected from wide areas of the western North Pacific. The model provides a point estimate for steepness, which represents a fraction of the unfished recruitment when spawning stock biomass is 20% of the unfished spawning stock biomass. Numerical simulations were conducted to incorporate uncertainties in the biological parameters and produce the variance of steepness. The mean value and its standard deviation for steepness with the Beverton-Holt model were 0.584 (standard deviation=0.099). The results suggest that the stock-recruitment relationship in North Pacific blue shark remains highly density-dependent and that its productivity is higher than that of other viviparous elasmobranchs.

A parametrized stock-recruitment relationship derived from a slow-fast population dynamic model

The Beverton–Holt, Ricker and Deriso functions are three distinct descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish population.This paper presents a model consisting of a system of ordinary differential equations, which couples a stage of young fish with several adult stages. The slow-fast dynamics captures the different time scales of the dynamics of the population and leads to a singular perturbation problem.The novelty of the model presented here is its capability to replicate a rich class of the stock-recruitment relationship, including the Beverton–Holt, Ricker and Deriso dynamics. The results are explained using geometric singular perturbation theory and illustrated by numerical simulations.

Assessing causal links in fish stock–recruitment relationships

Abstract Understanding whether recruitment fluctuations in fish stock arise from stochastic forcing (e.g. environmental variations) rather than deterministic forces (e.g. intrinsic dynamics) is a long standing question with important applied consequences for fisheries ecology. In particular, the relationship between recruitment, spawning stock biomass and environmental factors is still poorly understood, even though this aspect is crucial for fisheries management. Fisheries data are often short, but arise from complex dynamical systems with a high degree of stochastic forcing, which are difficult to capture through classic modelling approaches. In the present study, recent statistical approaches based on the approximation of the attractors of dynamical systems are applied on a large dataset of time series to assess (i) the directionality of potential causal relationships between recruitment and spawning stock biomass and potential influence of sea-surface temperature on recruitment and (ii) their performance to forecast recruitment. Our study shows that (i) whereas spawning stock biomass and sea surface temperature influence the recruitment to a lesser extent, recruitment causes also parental stock size and (ii) that non-linear forecasting methods performed well for the short-term predictions of recruitment time series. Our results underline that the complex and stochastic nature of the processes characterizing recruitment are unlikely to be captured by classical stock–recruitment relationships, but that non-linear forecasting methods provide interesting perspectives in that respect.

Implementing a model for data-poor fisheries based on steepness of the stock-recruitment relationship, natural mortality and local perception of population depletion. The case of the kelp Lessonia berteroana on coasts of north-central Chile

Abstract Over the past decade, it has become increasingly important to develop and utilize specific methods for modeling fisheries with limited data. The sustainable development of aquatic resources and fisheries management requires an understanding of species exploitation despite limited knowledge or poor data. Many data-limited assessment methods are based on catch data and assumptions, with little consideration given the biological aspects of the species under study. Herein, a population depletion model is reparametrized to simplify biological reference point estimates related to a maximum sustainable yield. This model includes biological aspects (parameter probability distributions), the fishery history, and levels of population depletion as perceived by the fishers. This approach was used with landings data (2000–2014) for Lessonia berteroana, a brown kelp harvested off north-central Chile (25°17′S–29°30′S). Management of this kelp is in its early stages, with no formal procedures established for assessment. We estimated population variables and reference points for three zones and considered beached seaweed to represent biomass mortality due to natural causes. The results, which accounted for uncertainty in resilience (steepness of the stock-recruitment relationship), natural mortality, process error, and minimum proportions of beached kelp, contributed to our understanding of this fishery and allowed us to propose an assessment tool for fisheries with poor or limited data.

Ecosystem change and decadal variation in stock–recruitment relationships of Lake Erie yellow perch (Perca flavescens)

Abstract Fish stock–recruitment relationships (SRRs) may vary in response to ecosystem change, increasing uncertainty for fisheries management. We defined three periods between 1975 and 2015 over which Lake Erie, a Laurentian Great Lake, underwent significant ecosystem changes: before zebra mussel (Dreissena polymorpha) establishment, after zebra mussel establishment and before re-eutrophication, and after re-eutrophication. To examine the extent to which SRRs of Lake Erie yellow perch (Perca flavescens) also varied over these periods, we compared the performance of Baseline (constant recruitment), Ricker (constant SRR), Periodic Ricker (different SRRs among three periods) and Random-walk Ricker (annually varying SRRs) models fitted to data for yellow perch stocks corresponding to three lake basins. Periodic and Random-walk Ricker models performed better for stocks in the western and eastern basins, but the Baseline model performed best in the central basin. Annual variation in the SRRs coincided with the timing of zebra mussel establishment and re-eutrophication in the shallower western basin, but not in the deeper eastern basin, where quagga mussels (Dreissena bugensis) established later and conditions are less eutrophic. These results underscore that temporally and spatially varying SRRs associated with ecosystem change should be taken into account in models of fish population dynamics.

Extending integrated stock assessment models to use non-depensatory three-parameter stock-recruitment relationships

Stock assessments based on the integrated paradigm often include an underlying stock-recruitment relationship. This, along with estimates of fishery selectivity and biological parameters, allows the biomass and fishing mortality associated with Maximum Sustainable Yield (BMSY and FMSY respectively) to be calculated. However, the estimates of these quantities may differ from the proxies assumed in the harvest control rules that are used to provide management advice. Moreover, the estimated values for BMSY and FMSY are related functionally in population dynamics models based on 2-parameter stock-recruitment relationships such as the commonly used Beverton-Holt or Ricker relationships. Use of 2-parameter stock-recruitment relationships (SRRs) consequently restricts the ability to fully quantify the uncertainty associated with estimating BMSY and FMSY because 2-parameter SRRs restrict the potential range of values for BMSY/B0. In principle, BMSY/B0 and FMSY can be more independent if the stock-recruitment relationship is more general than these 2-parameter SRRs. This paper outlines eleven potential 3-parameter stock-recruitment relationships and evaluates them in terms of whether they are able to match a wide range of specifications for BMSY (expressed relative to unfished spawning stock biomass, B0) and FMSY (expressed relative to natural mortality, M). Of the eleven 3-parameter stock-recruitment relationships considered, the Ricker-Power stock-recruitment relationship is found to best satisfy the characteristics of (a) being able to mimic a wide range of BMSY/B0 and FMSY/M values, (b) not to lead to negative recruitment for biomasses between 0 and B0, and (c) not to lead to increasing recruitment while approaching the limit of zero population size. Bayesian assessments of three example groundfish species off the US west coast (aurora rockfish, petrale sole, and cabezon) are conducted using Simple Stock Synthesis based on the Beverton-Holt and Ricker-Power stock-recruitment relationships to illustrate some of the impacts of allowing for a 3-parameter stock-recruitment relationship.