Age-structured Assessment Models Research Articles

Analyses of the composite yield per recruit model CYPR14 for inferring plausible fishing mortality targets of fish in the tropics

Stocks' yield and size per recruit are widely used to provide fisheries management guidance. This study provides details for analyzing the composite (i.e. age-aggregated or stage-structured) yield per recruit (CYPR) model CYPR14, and proposes CYPR14 as a management tool for tropical fisheries. The fishing mortality rates maximizing CYPR (FCYPR) and associated with the marginal increase in CYPR (F0.1) and a target composite spawning potential ratio (CSPR;F35%CSPRorF40%CSPR) were suggested as candidate fishing mortality targets, provided assessments employ the delay-differential model underlying CYPR14. Using Monte Carlo (MC) simulations relying on growth parameters and natural mortality of Lake Tanganyika'sLates stappersiiand Lake Victoria'sLates niloticus, CYPR14 analyses involving maximum survivorship or declining survivorship were carried out to show howFCYPR,F0.1,F35%CSPR, andF40%CSPRcould be generated, given an age of knife-edge recruitment (r). Baseline MC employedr = 1 year and yielded mean annual rates ofFCYPR = 0.52,F0.1 = 0.33, andF35%CSPR = 0.51 forL. stappersiiandFCYPR = 0.23,F0.1 = 0.14, andF40%CSPR = 0.16 forL. niloticus. CYPR14 with maximum survivorship produced CYPR isopleths such that the CYPR maximized at an infiniterand finite, higherF. For CYPR14 involving a declining survivorship, the CYPR declined with increasedrand maximized with innermost closed-loop contours at lowerFand an optimal age. The CSPR isopleths from both types of CYPR14 analyses were first concave down, and the optimal age served as their inflection point. In terms of benchmarks based on the maximum sustainable yield and of proxies thereof, CYPR14 should be for its underlying delay-differential model what the age-structured pool models are for age-structured assessment models.

A new semi-parametric method for autocorrelated age- and time-varying selectivity in age-structured assessment models

Selectivity is a key parameter in stock assessments that describes how fisheries interact with different ages and sizes of fish. It is usually confounded with other processes (e.g., natural mortality and recruitment) in stock assessments and the assumption of selectivity can strongly affect stock assessment outcome. Here, we introduce a new semi-parametric selectivity method, which we implement and test in Stock Synthesis. This selectivity method includes a parametric component and an autocorrelated nonparametric component consisting of deviations from the parametric component. We explore the new selectivity method using two simulation experiments, which show that the two autocorrelation parameters for selectivity deviations of data-rich fisheries are estimable using either mixed-effect or simpler sample-based algorithms. When selectivity deviations of a data-rich fishery are highly autocorrelated, using the new method to estimate the two autocorrelation parameters leads to more precise estimations of spawning biomass and fully selected fishing mortality. However, this new method fails to improve model performance in low data quality cases where measurement error in the data overwhelms the pattern caused by the autocorrelated process. Finally, we use a case study involving North Sea herring (Clupea harengus) to show that our new method substantially reduces autocorrelations in the Pearson residuals in fit to age composition data.

Evaluating evidence for alternative natural mortality and process error assumptions using a state-space, age-structured assessment model

State-space models explicitly separate uncertainty associated with unobserved, time-varying parameters from that which arises from sampling the population. The statistical aspects of formal state-space models are appealing and these models are becoming more widely used for assessments. However, treating natural mortality as known and constant across ages continues to be common practice. We developed a state-space, age-structured assessment model that allowed different assumptions for natural mortality and the degree of temporal stochasticity in abundance. We fit a suite of models where natural mortality was either age-invariant or an allometric function of mass and interannual transitions of abundance were deterministic or stochastic to observations on Gulf of Maine – Georges Bank Acadian redfish (Sebastes fasciatus). We found that allowing stochasticity in the interannual transition in abundance was important and estimating age-invariant natural mortality was sufficient. A simulation study showed low bias in annual biomass estimation when the estimation and simulation model matched and the Akaike imformation criterion accurately measured relative model performance, but it was important to allow simulated data sets to include the stochasticity in interannual transitions of abundance-at-age.

Exploring the effect of sampling, protogyny, and larval advection on stock estimates subject to no-take closures in a spatially complex coral reef line fishery on the Great Barrier Reef, Australia

Simulation is used to evaluate the ability of a two-region, age-structured assessment model to provide accurate and precise estimates of stock status (i.e., the ratio of female spawning biomass to unfished female spawning biomass) for coral trout (Plectropomus leopardus) on the Great Barrier Reef (GBR), Australia. The model used to generate the simulated data used by the assessment model is a spatially complex age- and sex-structured population dynamics model that captures the protogynous nature of coral trout. Stock status is underestimated (negatively biased), with the extent of negative bias related to mis-specification of the breeding strategy of the target fish stock, the impact of the amount of larval connectivity among reefs, the number of reefs closed to fishing, as well as exploitation rates. The estimates of stock status were less negatively biased when fishery-independent index and age- and length-composition data were available from closed areas. The results will inform the development of management strategies for coral trout in the GBR and highlight the importance of basing evaluations of estimation and management performance on operating models that capture ecologically important processes such as metapopulation dynamics and protogynous life history.

A state-space approach to incorporating environmental effects on recruitment in an age-structured assessment model with an application to southern New England yellowtail flounder

The state-space model framework provides a natural, probabilistic approach to stock assessment by modeling the stochastic nature of population survival and recruitment separately from sampling uncertainty inherent in observations on the population. We propose a state-space assessment model that is expanded to simultaneously treat environmental covariates as stochastic processes and estimate their effects on recruitment. We apply the model to southern New England yellowtail flounder (Limanda ferruginea) using data from the most recent benchmark assessment to evaluate evidence for effects of the mid-Atlantic cold pool and spawning stock biomass on recruitment. Based on Akaike’s information criterion, both the cold pool and spawning stock biomass were important predictors of recruitment and led to annual variation in estimated biomass reference points and associated yield. We also demonstrate the effect of the stochasticity of the mid-Atlantic cold pool on short-term forecasts of the stock size, biomass reference point, and stock status.

The potential impact of time-variation in vital rates on fisheries management targets for marine fishes

Fisheries scientists are increasingly concerned about changes in vital rates caused by environmental change and fishing impacts. Demographic parameters representing individual growth, maturity, mortality, and recruitment have previously been documented to change over decadal time scales. However, there has been relatively little comparison regarding which vital rates cause relatively greater or lesser impacts on commonly used fisheries management targets. We therefore use a life table (based on age-structured assessment models) to explore the sensitivity of fishing mortality, spawning biomass, and catch targets to changes in parameters representing growth, mortality, recruitment, and maturation rates for three representative life histories representing long-, medium-, and short-lived species. The elasticity analysis indicates that demographic changes can result in substantial variation in fisheries management targets, but that changes in mortality rates are particularly important for spawning biomass and catch targets while maturity and recruitment compensation are also important for fishing mortality targets. We conclude by discussing the importance of improved data repositories to address covariation among maturity, growth, and mortality parameters.

ASSESSING UNCERTAINTY IN A MULTISPECIES AGE-STRUCTURED ASSESSMENT FRAMEWORK: THE EFFECTS OF DATA LIMITATIONS AND MODEL ASSUMPTIONS

Performance of a multispecies age-structured assessment (MSASA) model in the Gulf of Alaska (GOA) relative to changes in data and model assumptions was examined through simulation exercises. Species included arrowtooth flounder (Atheresthes stomias), Pacific cod (Gadus macrocephalus), walleye pollock (Theragra chalcogramma), Pacific halibut (Hippoglossus stenolepis), and Steller sea lion (Eumetopias jubatus). Age-specific predation mortality was estimated as a flexible function of predator and prey abundances and fitted to diet data. Simulated data sets were constructed by applying random error to estimates of catch, survey, and diet data from an operating model, whose structure was identical to that of the estimating model. Simulations explored the effects of data variability, mismatched assumptions regarding model structure, and lack of diet data on model performance. Model misspecification and uninformative diet data had the greatest influence on model performance. Given the current emphasis on the development of ecosystem-based models and management, prioritizing the rigorous sampling of diet data would best facilitate the development of predation models useful to management agencies.

Tradeoffs between bias, robustness, and common sense when choosing selectivity forms

Selectivity, as a combination of gear vulnerability and fish availability, can be modeled in age-structured assessment models with simple functions that range from those that employ a small number of parameters to those that use complex and highly parameterized functions. We conducted simulations across two life history types to test whether allowing more complicated selectivity forms is both estimable and justified when compared to simpler selectivity curves with a lower number of parameters. Operating models were constructed with asymptotic and dome-shaped fishery and survey selectivity and estimation models were evaluated that used a range of complexity in fishery selectivity from the 2-parameter logistic to the highly parameterized double normal function. Results indicated that in general, uncertainty and bias in final year spawning biomass was not consistent across the life history types, the parameterizations employed, or fishing to the left or right side of the maturity curve. For instance, estimating a dome shaped selectivity for the survey when the true selectivity was asymptotic did not result in positive bias in all cases, and, estimating asymptotic fishing selectivity was not always conservative. Overall, we find that more complex selectivity functions and even time-dependent parameterizations of selectivity may be robust for short-lived species, but may not be robust when applied to long-lived species.

A comparison of parametric, semi-parametric, and non-parametric approaches to selectivity in age-structured assessment models

Integrated assessment models frequently track population abundance at age, and hence account for fishery removals using a function representing fishery selectivity at age. However, fishery selectivity may have an unusual shape that does not match any parametric function. For this reason, previous research has developed flexible ‘non-parametric’ models for selectivity that specify a penalty on changes in selectivity as a function of age. In this study, we describe an alternative ‘semi-parametric’ approach to selectivity, which specifies a penalty on differences between estimated selectivity at age and a pre-specified parametric model whose parameters are freely estimated, while also using cross-validation to select the magnitude of penalty in both semi- and non-parametric models. We then compare parametric, semi-parametric, and non-parametric models using simulated data and evaluate the bias and precision of estimated depletion and fishing intensity. Results show that semi- and non-parametric models result in little decrease in precision relative to the parametric model when the parametric model matches the true data-generating process, but that the semi- and non-parametric models have less bias and greater precision when the parametric function is misspecified. As expected, the semi-parametric model reverts to its pre-specified parametric form when age-composition sample size is low but performs similarly to the non-parametric model when sample size is high. Overall, results indicate few disadvantages to using the non-parametric model given the range of simulation scenarios explored here, and that the semi-parametric model provides a selectivity specification that is intermediate between parametric and non-parametric forms.

Spatial modeling of Bering Sea walleye pollock with integrated age-structured assessment models in a changing environment

Climate change may affect the spatial distribution of fish populations in ways that would affect the accuracy of spatially aggregated age-structured assessment models. To evaluate such scenarios, spatially aggregated models were compared with spatially explicit models using simulations. These scenarios were based on hypothetical climate-driven distribution shifts and reductions in mean recruitment of walleye pollock (Gadus chalcogrammus) in the eastern Bering Sea. Results indicate that biomass estimates were reasonably accurate for both types of estimation models and precision improved with the inclusion of tagging data. Bias in some aggregated model scenarios could be attributed to unaccounted-for process errors in annual fishing mortality rates and was reduced when estimating effective sample size or time-varying selectivity. Spatially explicit models that allow estimation of variability in movement and ontogenetic parameters (specified as a random walk process) were shown to be feasible, whereas models that misspecified ontogenetic movement and climate change effects resulted in biased biomass and movement parameter estimates. These results illustrate that more complex models may characterize processes better but may be less robust for management advice.

Determining effective sample size in integrated age-structured assessment models

Abstract Hulson, P-J. F., Hanselman, D. H., and Quinn II, T. J. 2012. Determining effective sample size in integrated age-structured assessment models. – ICES Journal of Marine Science, 69:281–292. Effective sample size (ESS) is a quantity that allows for overdispersion of variance and is used commonly in integrated age-structured fishery assessment models to fit age-and-length-composition datasets. Owing to the sources of measurement, observation, process, and model-specification errors, the ESS is smaller than the actual sample size. In this study, methods to set a priori or to estimate the ESS when confronted with datasets that include these sources of error were investigated. In general, a number of methods previously proposed to incorporate the ESS resulted in accurate estimation of population quantities and parameters when different sources of error were included in the data on age and length compositions. Three objective methods to incorporate the ESS resulted in unbiased population quantities: (i) using sampling theory to derive the ESS from actual age and length compositions, (ii) iteratively estimating the ESS with the age-structured assessment model, and (iii) estimating the ESS as a parameter with the Dirichlet distribution.

Performance of a fisheries catch-at-age model (Stock Synthesis) in data-limited situations

Limited data are a common challenge posed to fisheries stock assessment. A simulation framework was applied to examine the impact of limited data and data type on the performance of a widely used catch-at-age stock-assessment method (Stock Synthesis). The estimation method provided negatively biased estimates of current spawning-stock biomass (SSB) relative to the unfished level (final depletion) when only recent survey indices were available. Estimation of quantities of management interest (unfished SSB, virgin recruitment, target fishing mortality and final depletion) improved substantially even when only minimal-length-composition data from the survey were available. However, the estimates of some quantities (final depletion and unfished SSB) remained biased (either positively or negatively) even in the scenarios with the most data (length compositions, age compositions and survey indices). The probability of overestimating yield at the target SSB relative to the true such yield was ~50%, a risk-neutral result, for all the scenarios that included length-composition data. Our results highlight the importance of length-composition data for the performance of an age-structured assessment model, and are encouraging for the assessment of data-limited stocks.

Illegal and unreported fishing on abalone—Quantifying the extent using a fully integrated assessment model

Illegal, unregulated and unreported (IUU) fishing is a major problem in many of the world's fisheries. The stocks most severely impacted centre on those characterised by high economic value, such as abalone, as well as long lived and slow growing species such as Patagonian toothfish ( Dissostichus eleginoides). Effective management of these stocks as well as assessment of the impacts of IUU fishing on the resources is impeded by the technical difficulties associated with determining the magnitude of the IUU catches. The South African abalone Haliotis midae fishery rates as an extreme example of extraordinarily high levels of illegal and unreported (IU) catch. To assess the level and trends in IU catches, we used a combination of approaches that included collation of confiscation records from law enforcement, development of a novel index (the confiscations per unit policing effort—CPUPE), estimation of illegal catches using a spatial and age-structured assessment model, and cross-checking of model outputs through comparison with trade data on abalone imports in destination countries. The model-predicted 2008 IU estimate was 860 tonnes, more than 10 times the total allowable catch (TAC) for that year, and implied that, on average, 14% of all IU catches are confiscated. Associated management responses included the listing of H. midae on Appendix III of CITES (the Convention on International Trade in Endangered Species of Wild Fauna and Flora), and a temporary closure of the commercial fishery. We summarise both technical and management lessons to be learnt from this integrated approach to assess and verify the magnitude of IU fishing.

A spatial- and age-structured assessment model to estimate the impact of illegal fishing and ecosystem change on the South African abalone Haliotis midae resource

The management of abalone stocks worldwide is complicated by factors such as illegal fishing combined with the difficulties of assessing a sedentary (but not immobile) resource that is often patchily distributed. The South African abalone Haliotis midae fishery is faced with an additional problem in the form of a relatively recent movement of rock lobsters Jasus lalandii into much of the range of the abalone. The lobsters have heavily reduced sea urchin Parechinus angulosus populations, thereby indirectly negatively impacting juvenile abalone which rely on the urchins for shelter. A model is developed for abalone that is an extension of more standard age-structured assessment models because it explicitly takes spatial effects into account, incorporates the ecosystem change effect described above and estimates the magnitude of substantial illegal (‘poached’) catches. The model is simultaneously fitted to catch per unit effort and Fishery-Independent Abalone Survey abundance data, as well as to several years of catch-at-age (cohort-sliced from catch-at-size) data for the various components of the fishery and different spatial strata. It constitutes the first quantitative approach applied to the management of this commercially valuable resource in South Africa and has provided a basis for management advice over recent years by projecting abundance trends under alternative future catch levels.

A multispecies age-structured assessment model for the Gulf of Alaska

Predation is the largest source of mortality for marine fish and may be an important process in regulating population size. Recent population models have attempted to quantify predation separately from other sources of natural mortality. Building upon such work, a multispecies age-structured assessment model (MSASA) for the Gulf of Alaska was developed, which included arrowtooth flounder ( Atheresthes stomias ), Pacific cod ( Gadus macrocephalus ), and walleye pollock ( Theragra chalcogramma ). Predation mortality was a flexible function of predator and prey abundances that was fitted to stomach-content data. A proof of concept illustration is presented here, assessing model outputs against a set of single-species models. The MSASA model was able to successfully estimate predation between species and integrate it into total mortality. Significant predation occurred on younger pollock and flounder. Results indicate a significant change in predation over time on pollock as a function of increased arrowtooth flounder abundance. Estimating mortality and other parameters for three species simultaneously is complex, and the advantage of greater biological realism of MSASA comes at the expense of greater uncertainty in parameter estimation.

Failure of population recovery in relation to disease in Pacific herring

Following an estimated 60% decline in population abundance in early 1993, recovery of the Pacific herring Clupea pallasii population of Prince William Sound, Alaska, USA, has been impaired by disease. Comprehensive epidemiological study from 1994 through 2002 validated an age-structured assessment (ASA) model of disease and population abundance; from 2003 to 2006, the impact of disease was modeled by analyzing only 2 lesions: ulcers and white foci in the heart. The ASA model identified increased natural mortality since 1993 that can be explained by (1) epidemics associated with ulcers (prevalence about 3%) and the North American strain of viral hemorrhagic septicemia virus (VHSV Type IVa; prevalence up to 14%) in 1994 and 1998 and (2) relatively high prevalence of the mesomycetozoean Ichthyophonus hoferi from 1994 through 2006, including epidemics with the greatest sample prevalence in 2001 (38%, by histopathology) and 2005 (51%, estimated histopathology prevalence). Fourteen other parasites occurred at prevalence > 10%, but none were considered significant contributors to fish mortality. We predict that if natural mortality after 1994 had returned to background levels that best fit the model from 1980 to 1992 (0.25 yr(-1)), population biomass in 2006 would have been 3 times the best estimate, despite relatively poor recruitment since 1994. In conclusion, disease information can be used to explain and predict changes in populations that have confounded traditional fisheries assessment.

Evaluating Management Actions for Spotted Seatrout, Cynoscion nebulosus, in Mississippi with an Age-Structured Projection Model

Spotted seatrout, Cynoscion nebulosus, is an important recreational fishery in the coastal waters of the Gulf of Mexico and is the most sought after gamefish in coastal Mississippi. The management of C. nebulosus is state-specific, and unlike other similarly managed species, data on both population structure and movement support the existence of local sub-stocks. It is important for each state to clearly examine its own sub-stock in the context of its own state fishery in order to properly manage for local sustainability. We used an age-structured assessment model to examine the status (1993–2005) of the Mississippi C. nebulosus population and to project forward several probable management actions (i.e., length limits) while also accounting for uncertainty in both fishing mortality and annual recruitment. Model results suggest annual fishing mortality for Mississippi C. nebulosus is close to Fmsy, but that spawning stock biomass (SSB) is not below SSBmsy. This suggests the sub-stock is currently stable, but with high fishing pressure and a high dependence on annual recruitment to the fishery. Projections suggest that when uncertainty in angler effort and annual recruitment are included in the analysis, more conservative management actions are warranted in order to achieve both higher fishery yield and stable SSB.

Parameterizing age-structured models from a fisheries management perspective

Age-structured models are widely used in fisheries stock assessments and contain two very important parameters that determine the rate and amount of harvest that can be safely taken: the compensation rate in juvenile survival (κ) and the unfished biomass (Bo). These two parameters are often confounded. It is common for relative abundance indices to lack contrast, and the use of informative priors, or fixing at least one of these parameters, is necessary to develop management advice. Providing management advice proceeds by transforming estimates of biological variables such as Boand κ into management variables such as the maximum sustainable yield (C*) and the fishing mortality rate that would achieve this yield (F*). There is no analytical solution for the transformation of Bo, κ to C*, or F* for age-structured models with commonly used stock–recruitment functions and therefore must be done numerically. The opposite transition, however, does have an analytical solution for both the Beverton–Holt and Ricker recruitment models with partial selectivities for all age classes. Use of these analytical solutions allows for age-structured assessment models to be directly parameterized in terms of the management variables C* and F*. The effects of informative priors on C* and F* on the results of the assessment model are completely transparent to management.

Assessment and bioeconomic analysis of the Majorca (NW Mediterranean) trammel net fishery

Trammel net is the main fishing gear used by artisanal fishers in Majorca Island (NW Mediterranean), and is representative of Mediterranean small-scale fisheries using static gear. The use of static gears close to the coast, where seasonal variability and spatial heterogeneity are high, promotes the diversification of fishing practices or metiers .W e analyze the seasonal dynamics of the nets used, target species (red and black scorpionfish, red mullet and cuttlefish) exploitation patterns and the socio-economic conditions under which this fishery takes place, based on General Fisheries Directorate daily sale records (2002-2006). Additional personal socioeconomic interviews allowed the characterization of the trammel net fishery, its fishing behaviour, cost structure and conflicts. Catch and effort data and market surveys are used to evaluate the level of exploitation of the target species and allowed describing Majorca trammel net fishery as an activity based on a sustainable resource. The main target species were found to be near their maximum sustainable yield both by means of a surplus production model (with parameters estimated by CEDA-Catch Effort Data Analysis, software) and an age structured assessment model based on yield-per-recruit analysis. Management actions currently debated by local administration and fishers focus on improving fishers' economic situation, rather than on protecting a threatened resource. One of the management actions proposed is a one day effort reduction, which was analyzed here with the help of a bioeconomic simulation model. A 15-year (2005-2020) simulation allows providing advice to local managers to focus on the commercialization aspects, in order to obtain a higher value to the fish production, rather than expecting to obtain higher profits only by a reduction of the offer.

Data conflicts in fishery models: incorporating hydroacoustic data into the Prince William Sound Pacific herring assessment model

Abstract Hulson, P-J. F., Miller, S. E., Quinn, T. J. II, Marty, G. D., Moffitt, S. D., and Funk, F. 2008. Data conflicts in fishery models: incorporating hydroacoustic data into the Prince William Sound Pacific herring assessment model. – ICES Journal of Marine Science, 65: 25–43. Data conflicts present difficulties in running integrated assessment models as shown by the age-structured assessment (ASA) model for the Pacific herring population in Prince William Sound (PWS), Alaska. After the 1989 “Exxon Valdez” oil spill in PWS, the Pacific herring (Clupea pallasi) ASA model indicated a significant decline in the population, starting in winter 1992. Back-calculated estimates from hydroacoustic abundance surveys that started in 1993 suggested that the ASA model overestimated herring biomass from 1990 to 1992 and that the population decline actually began in 1989. To expose data conflicts, we incorporated the hydroacoustic survey information with all available spawning population indices directly into the age-structured model. In this way, the substantial uncertainty about population parameters from 1989 to 1992 attributable to data conflicts was quantified. Consequently, the magnitude of declines for that period estimated from both linear and ASA models depend on the type of integrated datasets and weighting, particularly with indices of male spawners. Our view is that a major decline started in 1992 when disease affected a large population that was in weakened condition. Other views are consistent with the existing data too.