Analysis of the spawning stock–recruitment relationship of vendace (Coregonus albula (L.)) with evaluation of alternative models, additional variables, biases and errors

Abstract –  Spawning biomass and recruitment data for vendace from a central Finnish lake were analysed by fitting various recruitment models and comparing the fits statistically. The compensatory models of Ricker, Cushing and Beverton & Holt fitted the data better than the H ₀ hypothesis of constant proportionality, but model and parameter uncertainties were high. Additional variables were included in an attempt to reduce uncertainties. Heavy wind forcing during the first month after hatching of larvae reduced the recruitment success. For the Ricker and the Cushing models, recruitment seemed to be also negatively associated with the density of the previous year-class. The r ² increased considerably with inclusion of these additional variables, but the precision of model parameters remained low. Monte Carlo simulation of a vendace stock was applied to evaluate the interference of biases from the measurement error (ME) and time series error (TSE) in the analysis. Especially in the case of the Cushing model, compensatory density dependence can be overestimated severely. Increasing the number of observations decreases the biases in some cases. In view of potential biases and uncertainties, a precautionary management policy is recommended.     

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

Maintaining 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 (F_MSY). Because MSY is achieved in the long term only if an F proxy is happenstance with F_MSY, 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.     

Impacts of the nonlinear relationship between abundance and its index in a tuned virtual population analysis

The abundance index used in a tuned virtual population analysis (VPA) is usually assumed to be proportional to actual abundance. However, the actual abundance and abundance index do not always have a linear relationship. Such nonlinearity can cause biases in abundance estimates as well as retrospective biases arising from systematic differences in abundance estimates when more data are successively added. Severe retrospective biases can damage the reliability of stock assessments. In this study, we use an approach to estimate an additional parameter that controls the nonlinearity in a tuned VPA. A performance test using simulated data revealed that the tuned VPA was able to accurately estimate the nonlinearity parameter and thus yielded less biased abundance estimates and smaller retrospective biases. We also found that estimating the nonlinearity parameters was effective even under other model misspecification scenarios, such as disregarding historical increases in catchability and time-varying natural mortality. Moreover, we applied this approach to some Japanese fish stocks and evaluated its validity. We found that estimating the nonlinearity parameters in the tuned VPA enhances the reliability of fisheries stock assessments.     

Evaluation of a spatially sex‐specific assessment method incorporating a habitat preference model for blue marlin (Makaira nigricans) in the Pacific Ocean

Blue marlin, widely distributed throughout the Pacific Ocean, are sexually dimorphic, have certain preferred habitats, and migrate seasonally. These characteristics have been ignored in previous stock assessment models. A population dynamics model that includes spatial structure, and sex and age structure was therefore constructed and fitted to fisheries data for blue marlin, along with information on the relative density of the population over space derived from a habitat preference model that uses the oceanographic and biological variables sea‐surface temperature, mixed layer depth, sea‐surface height anomaly, and chlorophyll‐a concentration. Monte Carlo simulation was then used to examine the estimation performance of the stock assessment method. Estimates of management‐related quantities including current spawning stock biomass are substantially biased when the assessment method ignores seasonal movement and sexual dimorphism. We also found that (i) uncertainty about the relationship between catch rate and abundance influences estimation performance to a larger extent than uncertainty in catches, (ii) the outcomes of the assessment are sensitive to the values assumed for natural mortality and stock‐recruitment steepness, and (iii) the ratio of current spawning stock biomass to that at pre‐exploitation equilibrium appears to be the most robust among the quantities considered. We conclude that assessment methods for blue marlin in the Pacific Ocean need to take account of seasonal migration and sex structure to improve stock assessments.     

The interim management procedure approach for assessed stocks: Responsive management advice and lower assessment frequency

Stock assessments are often used to provide management advice, such as a total allowable catch (TAC), to fishery managers. Many stocks are not assessed annually, and the TAC from the previous assessment is often maintained in years between assessments. We developed two interim management procedures (MPs) that update the estimate of current vulnerable biomass from a surveyed index of abundance to adjust the TAC from a previous assessment. These MPs differ in how they handle uncertainty in observed indices. Using closed‐loop simulation, we evaluated the two interim MPs (with 10‐ and 5‐year assessment intervals) against several “status quo” approaches: (1) an annual assessment, and (2) a stock assessment every 5 or 10 years with (a) fixed TACs or (b) projections between assessments. We evaluated performance across three life‐history types and six operating model scenarios. The interim MPs performed similarly to annual assessments in terms of trends in biomass and yield, regardless of the assessment interval of the interim MPs. The interim MPs often produced more yield than the Fixed TAC MP with 10‐year assessment intervals, for example, in depleted scenarios. The Fixed TAC MP performed more similarly to interim MPs when the assessment interval for the Fixed TAC MP was decreased to five years. The interim MPs can also perform well when circumstances arise that are not accounted for in the Projection MP. Our results show that interim MPs should be considered for infrequently assessed stocks or rebuilding stocks, and highlight potential cost savings of interim MPs over annual assessments.     

A stochastic surplus production model in continuous time

Surplus production modelling has a long history as a method for managing data‐limited fish stocks. Recent advancements have cast surplus production models as state‐space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous‐time state‐space model formulation include the ability to provide estimates of exploitable biomass and fishing mortality at any point in time from data sampled at arbitrary and possibly irregular intervals. We show in a simulation that the ability to analyse subannual data can increase the effective sample size and improve estimation of reference points relative to discrete‐time analysis of aggregated annual data. Finally, subannual data from five North Sea stocks are analysed with particular focus on using residual analysis to diagnose model insufficiencies and identify necessary model extensions such as robust estimation and incorporation of seasonality. We argue that including all known sources of uncertainty, propagation of that uncertainty to reference points and checking of model assumptions using residuals are critical prerequisites to rigorous fish stock management based on surplus production models.     

Biomass limit reference points are sensitive to estimation method,time‐series length and stock development

Biomass limit reference points are widely used in fisheries management and define the biomass threshold (BT) below which stock productivity (i.e. recruitment) is likely to be impaired. Scientifically sound and transparent methods for estimating BTs are therefore needed together with ways of quantifying uncertainties. The main focus of the study was placed on two methods currently applied to several small‐bodied pelagic species in the Northeast Atlantic. These methods have not formerly been described in the scientific literature and are in the present study being compared with some already described methods, of which one is broadly applied outside the Northeast Atlantic. Using a combination of data simulations and data from 51 small‐bodied pelagic fish stocks, we analysed the sensitivity of estimated BTs to (a) the choice of method, (b) time‐series length and (c) stock development (e.g. rebuilding or declining). It was demonstrated that estimated BTs are associated with considerable uncertainty not previously quantified. Furthermore, the level of the estimated threshold and the amount of uncertainty depended on choice of method, time‐series length and stock development trends. Hence, this study contributes to improving the quality of future biomass limit reference points by providing guidance regarding choice of method and how to demonstrate stock‐specific uncertainties.     

Do albacore exert top‐down pressure on northern anchovy? Estimating anchovy mortality as a result of predation by juvenile north pacific albacore in the California current system

Quantifying the mortality of marine fishes is important for understanding spawner–recruit relationships, predicting year‐class strength, and improving fishery stock assessment models. There is increasing evidence that pelagic predators can exert a top‐down influence on prey, especially during critical early life‐history stages. The objective of this study was to quantify predation by North Pacific albacore on Northern anchovy in the California current system (CCS). I estimated the abundance of juvenile albacore in the CCS from 1966–2005 using stock assessment models and spatially explicit catch‐per‐unit‐effort time series. Anchovy abundance (1966–93), both recruitment and total biomass, was obtained from a stock assessment model. Annual rates of anchovy consumption by albacore were calculated using diet studies of albacore in the CCS, an age‐structured bioenergetics model, and regional estimates of albacore abundance. The range of estimates was large: albacore may remove from less than 1% to over 17% of anchovy pre‐recruitment biomass annually. Relationships between predation and recruitment biomass were consistent with expectations from top‐down effects, but further study is required. This is the first attempt to quantify a specific source of mortality on anchovy recruits and to demonstrate potential top‐down effects of predation on anchovy.     

渔获量不确定性对印度洋大眼金枪鱼资源评估的影响

大眼金枪鱼(Thunnus obesus)是最具经济价值的热带金枪鱼类,其资源状况一直是区域性金枪鱼渔业管理组织关注的重点。由于多种渔业作业、捕捞船队构成复杂,印度洋大眼金枪鱼的历史渔获量统计存在一定的偏差(Bias),但国际上近些年开展资源评估时都忽略了这一偏差。本研究根据1979~2015年的年渔获量、年龄结构渔获量及相对丰度指数数据,运用年龄结构资源评估模型(ASAP)对印度洋大眼金枪鱼资源进行评估,重点考查渔获量的不确定性(观测误差和统计偏差)对资源评估结果的影响。结果显示,印度洋大眼金枪鱼当前资源总体没有过度捕捞,但2015年初显示轻微的过度捕捞,通过对比基础模型与8个灵敏度分析模型的评估结果发现,渔获量观测误差(CV)的预设对资源开发状态的判断有一定的影响。当渔获量统计偏差调整量为15%时(即历史渔获量被低估了),评估结果与基础模型基本一致;统计偏差调整量为20%时,评估结果有过度捕捞的趋势。本研究结果表明,资源评估模型中渔获量观测误差的设定和历史渔获量统计偏差均会对评估结果产生影响,后者更为明显,因此,二者均不能忽略。     

Classifying tagging experiments for commercial fisheries into three fundamental types based on design,data requirements and estimable population parameters

Mark–recapture experiments have the potential to provide direct estimates of fundamental parameters required for fishery stock assessment and provision of subsequent management advice in fisheries. The literature on mark–recapture experiments is enormous, with a variety of different experimental designs and estimation models; thus, it can be difficult to grasp the primary features of different approaches, the inter‐relationship among them and their potential utility in different situations. Here, we present an overview of the tagging experimental designs that are appropriate for use in commercial fishery situations. We suggest that most mark–recapture experiments in a large‐scale fishery context can be classified into one of three basic types – Petersen, tag‐attrition or Brownie – based on the fundamental design employed for releases and recaptures. The release and recapture strategy (e.g. the number of release events, whether the size of the sample examined for recaptured tags is known) determines which parameters can be estimated and from where the information for estimating them arises. We conclude that an integrated Brownie and Petersen approach is the most powerful of the different approaches in terms of the range of parameters that can be estimated without underlying assumptions or constraints on parameters. Such an approach can provide direct estimates of fishing mortality, natural mortality and population size, which are the main population dynamics parameters that traditional fishery stock assessments attempt to estimate.     

Developing robust frequentist and Bayesian fish stock assessment methods

Errors in fitting models to data are usually assumed to follow a normal (or log normal) distribution in fisheries. This assumption is usually used in formulating likelihood functions often required in frequentist and Bayesian stock assessment modelling. Fisheries data are commonly subject to atypical errors, resulting in outliers in stock assessment modelling. Because most stock assessment models are nonlinear and contain multiple variables, it is difficult, if not impossible, to identify outliers by plotting fisheries data alone. Commonly used normal distribution‐based frequentist and Bayesian stock assessment methods are sensitive to outliers, resulting in biased estimates of model parameters that are vital in defining the dynamics of fish stocks and evaluating alternative strategies for fisheries management. Because of the high likelihood of having outliers in fisheries data, frequentist or Bayesian methods robust to outliers are more desirable in fisheries stock assessment. This study reviews three approaches that can be used to develop robust frequentist or Bayesian stock assessment methods. Using simulated fisheries as examples, we demonstrate how these approaches can be used to develop the frequentist and Bayesian stock assessment approaches that are robust to outliers in fisheries data and compare the robust approaches with the commonly used normal distribution‐based approach. The proposed robust approaches provide alternative ways to developing frequentist or Bayesian stock assessment methods.     

印度洋长鳍金枪鱼资源评估的影响因素分析

多个模型被用于印度洋长鳍金枪鱼(Thunnus alalunga)的资源评估,但这些模型的评估结果均存在较大的不确定性,为此,本文对影响印度洋长鳍金枪鱼资源评估的因素进行了分析。分析结果认为:(1)由于渔业数据存在不报、漏报或混报及采样样本数过低、采样协议出现变化等问题,造成印度洋长鳍金枪鱼渔业的渔获量、体长组成或年龄组成数据存在质量问题;(2)尽管对单位捕捞努力渔获量(catch per unit effort,CPUE)进行了标准化,但目标鱼种变化及捕捞努力量空间分布变化仍严重影响了标准化CPUE数据的质量;(3)印度洋长鳍金枪鱼的种群生态学及繁殖生物学研究仍比较薄弱,种群结构、繁殖、生长、自然死亡信息比较缺乏,在资源评估中,相关参数设置需借用其他洋区的研究结果;(4)海洋环境对印度洋长鳍金枪鱼的资源变动与空间分布具有显著影响,但评估模型较少考虑海洋环境的影响。由于上述问题的存在,导致当前评估结果存在较大不确定性。未来,应继续探索提高资源评估质量的方法,同时研究建立管理策略评价框架,以避免渔业资源评估结果的不确定性对该渔业可持续开发的影响。     

运用SS3评估东太平洋大眼金枪鱼(Thunnus obesus)资源——复杂模型和简化模型的比较

大眼金枪鱼(Thunnus obesus)是东太平洋最重要的商业性金枪鱼鱼种,其资源评估采用的是结构复杂的Stock Synthesis 3模型(SS3).模型简化是提高资源评估效率的必要手段,但对大眼金枪鱼简化模型的效果尚未开展研究.本研究尝试从渔业数据结构的角度,将SS3复杂模型的23个渔业简化为仅含围网和延绳钓2个渔业,从而比较简化模型的评估能力.结果显示,简化模型能较为准确地描述大眼金枪鱼补充量、亲体量、捕捞死亡系数等主要时间序列的历史动态变化,对传统生物学参考点FMSY的估计也较为准确,且受陡度和自然死亡系数的影响较小,但对其他参考点的估算误差较大.陡度参数对简化模型基于Kobe图判断资源状态的准确性有重要影响,陡度较低时,简化模型能较为准确地判断资源状态.研究表明,权衡模型的评估能力和降低模型结构的复杂性,是大眼金枪鱼资源评估今后需要重点研究的任务之一.此外,对模型简化的效果评价,与采用的生物学参考点和资源状况判断标准的选择有关.     

Density dependence in total egg production per spawner for marine fish

A paradigm of fisheries science holds that spawning stock biomass (SSB) is directly proportional to total egg production (TEP) of fish stocks. This “SSB–TEP proportionality” paradigm has been a basic premise underlying the spawner–recruitment models for fisheries management and numerous studies on recruitment mechanisms of fish. Studies on maternal effects on reproductive potential of a stock have progressed during the last few decades, leading to doubt concerning the paradigm. Nonetheless, a direct test of the paradigm at multidecadal scales has been difficult because of data limitations in the stock assessment systems worldwide. Here, we tested the paradigm for marine fish based on a novel combination of two independent 38‐year time series: fishery‐dependent stock assessment data and fishery‐independent egg survey data. Through this approach, we show that the SSB–TEP proportionality is distorted by density dependence in total egg production per spawner individual (TEPPS) or spawner unit weight (TEPPSW) at a multidecadal scale. The TEPPS/TEPPSW exponentially declined with biomass and thus was density‐dependent for Japanese sardine, a small pelagic species exhibiting a high level of population fluctuation, in the western North Pacific. By contrast, the TEPPS/TEPPSW was sardine‐density‐dependent for Japanese anchovy, another small pelagic species exhibiting a moderate level of population fluctuation well‐known for being out of phase with sardine. Our analysis revealed intraspecific (sardine) and interspecific (anchovy) density dependence in TEPPS/TEPPSW, which was previously unaccounted for in spawner–recruitment relationships. Such density‐dependent effects at the time of spawning should be considered in fisheries management and studies on recruitment mechanisms.     

Global fishery dynamics are poorly predicted by classical models

Fisheries dynamics can be thought of as the reciprocal relationship between an exploited population and the fishers and/or managers determining the exploitation patterns. Sustainable production of protein of these coupled human‐natural systems requires an understanding of their dynamics. Here, we characterized the fishery dynamics for 173 fisheries from around the globe by applying general additive models to estimated fishing mortality and spawning biomass from the RAM Legacy Database. GAMs specified to mimic production models and more flexible GAMs were applied. We show observed dynamics do not always match assumptions made in management using “classical” fisheries models, and the suitability of these assumptions varies significantly according to large marine ecosystem, habitat, variability in recruitment, maximum weight of a species and minimum observed stock biomass. These results identify circumstances in which simple models may be useful for management. However, adding flexibility to classical models often did not substantially improve performance, which suggests in many cases considering only biomass and removals will not be sufficient to model fishery dynamics. Knowledge of the suitability of common assumptions in management should be used in selecting modelling frameworks, setting management targets, testing management strategies and developing tools to manage data‐limited fisheries. Effectively balancing expectations of future protein production from capture fisheries and risk of undesirable outcomes (e.g., “fisheries collapse”) depends on understanding how well we can expect to predict future dynamics of a fishery using current management paradigms.     

Status of white croaker Micropogonias furnieri exploited in southern Brazil according to alternative hypotheses of stock discreetness

The exploitation status of white croaker Micropogonias furnieri in southern Brazil is assessed using a production model constructed according to three hypotheses of stock discreetness: an isolated stock in southern Brazil; a straddling stock shared between Brazil and Uruguay; and a straddling stock shared among Brazil, Uruguay and Argentina. Estimates of virgin stock size and maximum sustainable yield were more sensitive to the hypothesis assumed correct, the posterior means varying respectively from 177,648 to 1,007,256 tonnes and from 7459 to 38,677 tonnes. Estimates of stock status in relation to management reference points were more robust to the uncertainties in stock discreetness and indicate that the species in currently overfished (biomass at 60% of B_msy) and under heavy overfishing (F between approximately 2 and 6 times higher than F_msy). Results suggest that the relative stability of catches in the region occurs at the expense of a steady decline in stock abundance and that concerted management actions by the three countries are needed to bring the stock to safer levels of exploitation.     

What makes fisheries data informative?

Informative data in fisheries stock assessment are those that lead to accurate estimates of abundance and reference points. In practice, the accuracy of estimated abundance is unknown and it is often unclear which features of the data make them informative or uninformative. Neither is it obvious which model assumptions will improve estimation performance, given a particular data set. In this simulation study, 10 hypotheses are addressed using multiple scenarios, estimation models, and reference points. The simulated data scenarios all share the same biological and fleet characteristics, but vary in terms of the fishing history. The estimation models are based on a common statistical catch‐at‐age framework, but estimate different parameters and have different parts of the data available to them. Among the findings is that a ‘one‐way trip’ scenario, where harvest rate gradually increases while abundance decreases, proved no less informative than a contrasted catch history. Models that excluded either abundance index or catch at age performed surprisingly well, compared to models that included both data types. Natural mortality rate, M, was estimated with some reliability when age‐composition data were available from before major catches were removed. Stock‐recruitment steepness, h, was estimated with some reliability when abundance‐index or age‐composition data were available from years of very low abundance. Understanding what makes fisheries data informative or uninformative enables scientists to identify fisheries for which stock assessment models are likely to be biased or imprecise. Managers can also benefit from guidelines on how to distribute funding and manpower among different data collection programmes to gather the most information.     

Estimating fisheries reference points from catch and resilience

This study presents a Monte Carlo method (CMSY) for estimating fisheries reference points from catch, resilience and qualitative stock status information on data‐limited stocks. It also presents a Bayesian state‐space implementation of the Schaefer production model (BSM), fitted to catch and biomass or catch‐per‐unit‐of‐effort (CPUE) data. Special emphasis was given to derive informative priors for productivity, unexploited stock size, catchability and biomass from population dynamics theory. Both models gave good predictions of the maximum intrinsic rate of population increase r, unexploited stock size k and maximum sustainable yield MSY when validated against simulated data with known parameter values. CMSY provided, in addition, reasonable predictions of relative biomass and exploitation rate. Both models were evaluated against 128 real stocks, where estimates of biomass were available from full stock assessments. BSM estimates of r, k and MSY were used as benchmarks for the respective CMSY estimates and were not significantly different in 76% of the stocks. A similar test against 28 data‐limited stocks, where CPUE instead of biomass was available, showed that BSM and CMSY estimates of r, k and MSY were not significantly different in 89% of the stocks. Both CMSY and BSM combine the production model with a simple stock–recruitment model, accounting for reduced recruitment at severely depleted stock sizes.     

Generic solutions for data‐limited fishery assessments are not so simple

The majority of the world's fisheries, by number, are data‐poor/limited, and there is a growing body of literature pertaining to approaches to estimate data‐limited stock status. There are at least two drivers for assessing the status of data‐limited fisheries. The first is to try to understand and report on the global or regional status of fisheries across many stocks. The second is to attempt to assess individual data‐limited stocks, for status reporting and/or guiding management decisions. These drivers have led to attempts to find simple, generic, low‐cost solutions, including the broad application of generically parameterised models, and the blanket application of a single, or limited number of possible, analytical approach(es). It is unclear that generic methods function as intended, especially when taken out of their original design context or used without care. If the intention is to resolve individual stock status for the purposes of management, there is concern with the indiscriminate application of a single method to a suite of stocks irrespective of the particular circumstances of each. We examine why caution needs to be exercised, and provide guidance on the appropriate application of data‐limited assessment methods (DLMs). We recommend: (a) obtaining better data, (b) using care in acknowledging and interpreting uncertainties in the results of DLMs, (c) embedding DLMs in harvest strategies that are robust to the higher levels of uncertainty in the output of DLMs by including precautionary management measures or buffers and (d) selecting and applying DLMs appropriate to specific species’ and fisheries’ data and context.     

Stock assessment on fishery-dependent data: Effect of data quality and parametrisation for a red snapper fishery

Data availability, and unreported and unregulated fishing are significant obstacles to evaluating stock status, especially in tropical areas. Limitations in data quantity and quality can lead to model misspecification and erroneous data treatments, potentially causing important changes in model outputs and subsequent management implications. Red snapper Lutjanus purpureus (Poey) in French Guiana provides an example of a stock with a long-time series of fishery-dependent data subject to large uncertainty. A flexible catch-at-age model (Stock Synthesis) was applied to the available data and compared to an historically applied assessment approach. Inter-model variability based on different model specifications and data treatments were compared to identify better the status of the resource. Results showed that a major source of uncertainty in the model was the inclusion of a catch-per-unit-effort abundance index with questionable ability to track abundance. The Stock Synthesis model provided a more flexible and viable method than the virtual population analysis approach. Despite large uncertainty, models depicted a similar trend with a notable stock depletion in the late 1990s but with two distinct biomass trends in more recent years depending on the treatment. To reduce uncertainty and preserve this important economic resource, new data collection programmes and management policies are needed.