Stock-recruitment Relationship Research Articles

Circularity in fisheries data weakens real world prediction

The systematic substitution of direct observational data with synthesized data derived from models during the stock assessment process has emerged as a low-cost alternative to direct data collection efforts. What is not widely appreciated, however, is how the use of such synthesized data can overestimate predictive skill when forecasting recruitment is part of the assessment process. Using a global database of stock assessments, we show that Standard Fisheries Models (SFMs) can successfully predict synthesized data based on presumed stock-recruitment relationships, however, they are generally less skillful at predicting observational data that are either raw or minimally filtered (denoised without using explicit stock-recruitment models). Additionally, we find that an equation-free approach that does not presume a specific stock-recruitment relationship is better than SFMs at predicting synthesized data, and moreover it can also predict observational recruitment data very well. Thus, while synthesized datasets are cheaper in the short term, they carry costs that can limit their utility in predicting real world recruitment.

Multispecies yield and profit when exploitation rates vary spatially including the impact on mortality of ocean acidification on North Pacific crab stocks

A multi-species size-structured population dynamics model that can account for spatial structure and technical interactions between commercial fisheries was developed and applied to the snow and southern Tanner crab fisheries in the eastern Bering Sea. The model was then used as the basis for forecasts to calculate reference points related to yield and profit under the effects of ocean acidification on snow and southern Tanner crab. Stochastic projections that account for variation about the stock-recruitment relationship were undertaken for a constant F35% harvest strategy, a strategy that sets effort to maximize profit ignoring the effects of environmental variability such as ocean acidification, and the Acceptable Biological Catch control rule, which includes a reduction in fishing mortality rate when stocks are below target levels. Single- and four-area models led to similar fits to abundance and catch data, and provide similar estimates of time-trajectories of mature male biomass. The model is used to compute Maximum Sustainable Yield (MSY) and an upper bound on Maximum Economic Yield (uMEY). The effort levels that achieve MSY and uMEY were sensitive to whether a spatial or non-spatial model was used to calculate reference points and hence how technical interactions among species were accounted for. Dynamic projections based on various management strategies indicated that adopting a uMEY target level of effort leads to some robustness to the effects of ocean acidification, although similar results can be obtained using the Acceptable Biological Catch control rule, which reduces harvest rates as biomass levels decline.

Leveraging scientific uncertainty in fisheries management for estimating among-assessment variation in overfishing limits

AbstractFisheries management systems can utilize probability-based harvest control rules to incorporate scientific uncertainty and manager risk tolerance when setting catch limits. A precautionary buffer that scales with scientific uncertainty is used to calculate the acceptable biological catch from the overfishing limit (OFL) for US West Coast groundfish and coastal pelagic species. A previous analysis formed the basis for estimating scientific uncertainty as the among-assessment variation in estimates of historical spawning biomass time-series. This “historical biomass” approach may underestimate scientific uncertainty, because the OFL is a function of estimated exploitable biomass and fishing mortality. We developed a new approach that bases the calculation of scientific uncertainty on projected spawning biomass (SSB) and OFLs, accounting for uncertainty in recruitment and among-assessment variation. OFL projections yielded a higher estimate of uncertainty than SSB (0.502 vs. 0.413 for 25-year projections and 0.562 vs. 0.384 for a 1-year projection, assuming a deterministic stock-recruitment relationship). Assuming a stochastic stock-recruitment relationship produced smaller estimates of uncertainty (0.436, 25-year OFL projections; 0.452, 1-year OFL projections; 0.360, 25-year SSB projections; 0.318, 1-year SSB projections). The projection-based approach presented herein is applicable across stocks and regions that conduct assessments with sufficient and consistent outputs for calculating an OFL.

Evaluating Impacts of Time-varying Productivity in Stock-recruit Relationships on Biological Benchmarks

Evaluating Impacts of Time-varying Productivity in Stock-recruit Relationships on Biological Benchmarks

Numerical approach for evaluating impacts of biological uncertainties on estimates of stock–recruitment relationships in elasmobranchs: example of the North Pacific shortfin mako

Abstract Impacts of biological uncertainties on estimates of stock–recruitment relationships (SRRs) in elasmobranchs such as lamniform sharks were evaluated using a numerical approach based on an age-structured model considering reproductive ecology in elasmobranchs. The values of steepness were estimated using several combinations of life history parameters for North Pacific shortfin mako to elucidate whether the numerical approach could identify reasonable values for fundamental life history parameters as well as steepness. The results of the numerical approach indicated that the mean values of steepness and their 95% confidence intervals were highly sensitive to combinations of values for growth rate, maturity ogive, longevity, reproductive cycle, and natural mortality rate. Meanwhile, the most plausible combinations of the biological parameters and values of steepness were identified based on the numerical approach with biological knowledge. The mean values and their standard deviation (SD) for steepness with the Beverton-Holt-SRR model were 0.353 (SD=0.057) and 0.273 (SD=0.046) for 2- and 3-year reproductive cycles, respectively. The numerical approach therefore has high potential to become an important tool for estimating SRR in elasmobranchs such as lamniform sharks, and the application of this approach to other elasmobranchs could greatly contribute to improvements in stock assessment and management.

Stock-recruitment dynamics of a freshwater clupeid

The clupeid gizzard shad Dorosoma cepedianum is often the most abundant fish species in North American reservoirs, and this dominance can have cascading trophic effects on entire fish assemblages. Accordingly, a key aspect of managing reservoir fish assemblages involves controlling gizzard shad densities. We used a 33-year time series to evaluate the relative importance of parental stock density, winter temperature, and water regime on recruitment of age-0 gizzard shad in a large reservoir. Recruitment modeled with a Ricker-type curve increased with the size of the adult stock, peaked, and then decreased at high stock densities. This over-compensatory stock-recruitment relationship was made more dynamic by fluctuations in inflow, with recruitment increasing in years of high inflow, however there was no temperature effect at the latitude of the study site. The influence of stock size on recruitment was roughly twice as high as the influence of inflow. This study is the first to report stock-recruitment relationships for a clupeid species in a reservoir and concurs with analyses of marine fishes that have shown that most clupeids exhibit compensatory or over-compensatory patterns in their stock-recruitment relationships.

Understanding historical summer flounder (Paralichthys dentatus) abundance patterns through the incorporation of oceanography-dependent vital rates in Bayesian hierarchical models

Climate can impact fish population dynamics through changes in productivity and shifts in distribution, and both responses have been observed for many fish species. However, few studies have incorporated climate into population dynamics or stock assessment models. This study aimed to uncover how past variations in population vital rates and fishing pressure account for observed abundance variation in summer flounder (Paralichthys dentatus). The influences of the Gulf Stream Index, an index of climate variability in the Northwest Atlantic, on abundance were explored through natural mortality and stock–recruitment relationships in age-structured hierarchical Bayesian models. Posterior predictive loss and deviance information criterion indicated that out of tested models, the best estimates of summer flounder abundances resulted from the climate-dependent natural mortality model that included log-quadratic responses to the Gulf Stream Index. This climate-linked population model demonstrates the role of climate responses in observed abundance patterns and emphasizes the complexities of environmental effects on populations beyond simple correlations. This approach highlights the importance of modeling the combined effect of fishing and climate simultaneously to understand population dynamics.

Spawning stock recruitment creates misleading dynamics under predation release in ecosystem and multi-species models.

Ecosystem and multi-species models are used to understand ecosystem-wide effects of fishing, such as population expansion due to predation release, and further cascading effects. Many are based on fisheries models that focus on a single, depleted population, and may not always behave as expected in a multi-species context. The spawning stock recruitment (SSR) relationship, a curve linking the number of juvenile fish to the existing adult biomass, can produce dynamics that are counter-intuitive and change scenario outcomes. We analysed the Beverton–Holt SSR curve and found a population with low resilience when depleted becomes very productive under persistent predation release. To avoid implausible increases in biomass, we propose limiting recruitment to its unfished level. This allows for specification of resilience when a population is depleted, without sudden and excessive increase when the population expands. We demonstrate this dynamic and solution within an end-to-end ecosystem model, focusing on myctophids under fishing-induced predation release. We present one possible solution, but the specification of stock-recruitment models should continue to be a topic of discussion amongst multi-species and ecosystem modellers and empiricists going forward.

Model-free time series analysis detected the contributions of middle-age spawner biomass and the environment on Pacific bluefin tuna recruitment

Abstract The relationship between the biomass of Pacific bluefin tuna (PBF) spawners and the amount of recruitment (stock–recruitment relationship, SRR) is unclear. It is likely that environmental effects have masked the SRR of PBF. As the basis of constructing an effective SRR for PBF, we examined the effect of spawning biomass at different ages and the spatiotemporal patterns of environmental effects on the amount of recruitment, using a recently developed model-free nonlinear time series analysis method (empirical dynamic modelling, EDM). EDM revealed where, when, and how the environment affected the amount of recruitment. EDM also found a significant contribution of ages 8–9 spawners on recruitment dynamics and that the amount of recruitment plateaus with increase in ages 8–9 spawners. Based on knowledge obtained from EDM, we formulated several example SRRs that incorporated environmental effects (sea surface temperature). The newly developed SRR with information from EDM outperformed the SRR without this information. Finally, we interpreted the results based on preceding observational and experimental studies and discussed the potential of applying the combination of EDM and mathematical modelling towards the sustainable use of other stocks.

Non-linearity in stock–recruitment relationships of Atlantic cod: insights from a multi-model approach

Abstract The stock–recruitment relationship is the basis of any stock prediction and thus fundamental for fishery management. Traditional parametric stock–recruitment models often poorly fit empirical data, nevertheless they are still the rule in fish stock assessment procedures. We here apply a multi-model approach to predict recruitment of 20 Atlantic cod (Gadus morhua) stocks as a function of adult biomass and environmental variables. We compare the traditional Ricker model with two non-parametric approaches: (i) the stochastic cusp model from catastrophe theory and (ii) multivariate simplex projections, based on attractor state-space reconstruction. We show that the performance of each model is contingent on the historical dynamics of individual stocks, and that stocks which experienced abrupt and state-dependent dynamics are best modelled using non-parametric approaches. These dynamics are pervasive in Western stocks highlighting a geographical distinction between cod stocks, which have implications for their recovery potential. Furthermore, the addition of environmental variables always improved the models’ predictive power indicating that they should be considered in stock assessment and management routines. Using our multi-model approach, we demonstrate that we should be more flexible when modelling recruitment and tailor our approaches to the dynamical properties of each individual stock.

The state of Canada’s iconic Northern cod: A second opinion

Canada’s Northern cod stock (NAFO Divisions 2J3KL), once one of the world’s most important stocks, declined rapidly in the early 1990s and remains at historically low biomass despite a recent comeback. In contrast to many studies, recent stock assessments based on a new state-space model (hereafter Canada Department of Fisheries and Oceans, or NCAM model) concluded that natural (M) and not fishing mortality (F) was the main cause of stock depletion and has kept it at low levels since. Here we offer a second opinion on those conclusions, using the same catch and survey data, but based on a VPA model that allows for variability in M and unreported catch. This model posits that the biomass, both total and spawning from the NCAM model, is overestimated (35%), that fishing mortality was a major contributor to the early 1990s decline and slow rebuilding, and that the decline began in the late 1980s and was not as knife-edged as suggested by the NCAM. In agreement with the NCAM results, M has been variable and episodically elevated, but much less than suggested by the NCAM. VPA using a non-variable M did not fit well. In addition, the stock recruitment relationship suggests an asymptote at near 106 t, similar but slightly higher than the current limit reference point for spawning biomass. Of importance, the present analyses suggest that fishing has impacted rebuilding and will slow achievement of a spawning biomass that avoids recruitment overfishing.

The relative importance of sub-populations to the Gulf of Maine stock of Atlantic cod

AbstractDiscriminating among sympatric sub-populations is critical not only for the investigation of fish population structure, but also for effective fishery management. The Gulf of Maine stock of Atlantic cod contains two genetically distinct sub-populations whose spawning grounds overlap in space, but not season. Lack of a practical tool for discriminating between these spring and winter spawners has thus far prevented addressing metapopulation structure in stock assessments and fishery management plans. To address this issue, we developed a simple approach to discriminate between the sympatric sub-populations that relies on internal otolith structures. Using a logistic regression model fit to training data (n = 577) and evaluated through cross-validation, we correctly classified individuals with 81% accuracy and predicted the overall sub-population mixture within 1%. Applying the model to a broader population dataset (n = 1642) revealed that spring-spawned cod are more concentrated within closed fishing areas and therefore experience a lower mortality rate. However, despite dominating older age classes and comprising a large fraction of the spawning stock, these spring cod contribute little to recruitment. This apparent sub-population difference in the stock–recruitment relationship has important consequences for assessment models and the success of management measures designed to rebuild the stock.

Developing and evaluating a management strategy evaluation framework for the Gulf of Maine cod (Gadus morhua)

Management strategy evaluation (MSE) is an effective tool to evaluate the performance of harvest control rules (HCRs) and alternative management strategies. However, a comprehensive MSE framework advising management is still absent for the severely depleted Gulf of Maine (GoM) cod (Gadus morhua). In the present study, we developed a conceptual MSE framework and conditioned on this stock utilizing stock-specific parameterization. We highlighted the simulation of a few key processes with semi-independent sub-models and accounted for uncertainties from multiple sources. The simulated population dynamics was calibrated and validated against the historical trend in hindcasting. Forecasting simulations were also conducted and validated to examine the effectiveness in the context of uncertainty. Hindcasting results suggested that the calibrated MSE framework could capture the stock dynamics assuming different recruitment dynamics indicated by residuals lower than 5%. Forecasting stochastic runs demonstrated a minor disparity between management effects of fishing-mortality-based and catch-based HCRs when the segregated stock recruitment relationship was adopted with a difference in simulated spawning stock biomass lower than 10%. Additionally, the results were comparable to assessment and projections made in the stock assessment, indicating the robustness of the framework. The framework can potentially help disentangle complex issues related to the mixed fishery, decision-making, and performance evaluation of a monitoring system.

Re-evaluation of the environmental dependence of Pacific sardine recruitment

The environment influences the recruitment of small pelagic fishes, so environmental indices are used to match fishing mortalities to the stocks’ productivities. For example, the exploitation fraction for the northern stock of Pacific sardine in the Northeastern Pacific is a function of sea-surface temperature (SST). The functional relationship changes, however, because our perception of the environmental effects on sardine recruitment is based on assessment models that are periodically updated with new input data and assumptions. In this paper, we use data from recent stock assessments to re-examine previously identified correlations of sardine recruitment success (the logarithmic ratio of recruitment and spawning stock biomass) with indices of SST off Southern California and the Pacific Decadal Oscillation (PDO). We show that the earlier correlation with SST is likely invalid, and the persistent correlation with the PDO is weaker. Because many environmental stock-recruitment relationships fail upon re-examination, environmental proxies for fish productivity might not always prescribe the correct amount of fishing mortality and should be avoided. Alternatively, for species assessed periodically, dynamic fishing mortalities could be based on measurements of recent stock productivity inferred directly from surveys, or from the results of analytical assessments based on those observations.

Global warming impairs stock–recruitment dynamics of corals

Changes in disturbance regimes due to climate change are increasingly challenging the capacity of ecosystems to absorb recurrent shocks and reassemble afterwards, escalating the risk of widespread ecological collapse of current ecosystems and the emergence of novel assemblages1-3. In marine systems, the production of larvae and recruitment of functionally important species are fundamental processes for rebuilding depleted adult populations, maintaining resilience and avoiding regime shifts in the face of rising environmental pressures4,5. Here we document a regional-scale shift in stock-recruitment relationships of corals along the Great Barrier Reef-the world's largest coral reef system-following unprecedented back-to-back mass bleaching events caused by global warming. As a consequence of mass mortality of adult brood stock in 2016 and 2017 owing to heat stress6, the amount of larval recruitment declined in 2018 by 89% compared to historical levels. For the first time, brooding pocilloporids replaced spawning acroporids as the dominant taxon in the depleted recruitment pool. The collapse in stock-recruitment relationships indicates that the low resistance of adult brood stocks to repeated episodes of coral bleaching is inexorably tied to an impaired capacity for recovery, whichhighlights the multifaceted processes that underlie the global decline of coral reefs. The extent to which the Great Barrier Reef will be able to recover from the collapse in stock-recruitment relationships remains uncertain, given the projectedincreased frequency of extreme climate events over the next two decades7.

Management implications of modelling fisheries recruitment

The representation and parameterisation of the stock-recruitment relationship is highly influential in fisheries stock assessments. We overview important management implications arising from choices and assumptions made when modelling recruitment and propose pragmatic solutions. An age-structured population model is used to highlight some additional considerations including (1) incorrect assumptions about the source of recruits and (2) ways to account for environmental correlates in stock assessment models, either directly or indirectly. Existing stationary approaches ignore the sometimes considerable influence of the environment on population processes such as recruitment, growth and mortality, all of which are expected to shift under changing climate. We show that where environmental relationships are explicitly included in models, they need to be rigorously assessed and model parameterization carefully evaluated. Variability in annual recruitment estimates (specified by the standard deviation σR) must be adjusted to control the partitioning of total variation into environmental and unexplained variation, as reference point estimates are particularly sensitive to the choice of σR. Finally, we evaluate two recommended solutions to these issues: Harvest Control Rules (HCRs) that are robust to recruitment uncertainty and variability, and empirical HCRs that use pre-season survey inputs as a way to more directly provide forecasts without needing to quantify the complex underlying details of the environmental-recruitment relationships.

Ecological-economic sustainability of the Baltic cod fisheries under ocean warming and acidification

Human-induced climate change such as ocean warming and acidification, threatens marine ecosystems and associated fisheries. In the Western Baltic cod stock socio-ecological links are particularly important, with many relying on cod for their livelihoods. A series of recent experiments revealed that cod populations are negatively affected by climate change, but an ecological-economic assessment of the combined effects, and advice on optimal adaptive management are still missing. For Western Baltic cod, the increase in larval mortality due to ocean acidification has experimentally been quantified. Time-series analysis allows calculating the temperature effect on recruitment. Here, we include both processes in a stock-recruitment relationship, which is part of an ecological-economic optimization model. The goal was to quantify the effects of climate change on the triple bottom line (ecological, economic, social) of the Western Baltic cod fishery. Ocean warming has an overall negative effect on cod recruitment in the Baltic. Optimal management would react by lowering fishing mortality with increasing temperature, to create a buffer against climate change impacts. The negative effects cannot be fully compensated, but even at 3 °C warming above the 2014 level, a reduced but viable fishery would be possible. However, when accounting for combined effects of ocean warming and acidification, even optimal fisheries management cannot adapt to changes beyond a warming of +1.5° above the current level. Our results highlight the need for multi-factorial climate change research, in order to provide the best available, most realistic, and precautionary advice for conservation of exploited species as well as their connected socio-economic systems.

Global forage fish recruitment dynamics: A comparison of methods, time-variation, and reverse causality

The population dynamics of forage fish are often ‘boom or bust’, and variation in recruitment may be a contributing factor to changes in abundance. Here we applied several methods for identifying stock recruit relationships (SRR) to 52 forage fish stocks: a time-invariant Ricker model and two time-varying methods (dynamic linear models and regime-based models). A positive relationship between spawning biomass and recruitment existed for 28 stocks, with 14 of those being best fit by a Ricker curve. Time-varying models were preferred for 26 stocks over a time-invariant Ricker curve. We also showed through simulation that spurious, yet significant stock-recruit relationships can be generated if recruitment was environmentally driven, the lag between recruitment and spawning biomass was small, and autocorrelation in recruitment was high—a combination of characteristics that many forage fish stocks display. Based on our results, observed time-invariant SRRs can result from a reversed causality of ‘boom and bust’ dynamics in situations in which life histories are short (i.e., changes in recruitment are driving changes in spawning biomass). ‘Hidden’ SRRs are also possible because of time-variation in SRR parameters. Understanding when each of these potential failings of fitting SRRs can occur is a key challenge in forage fish management.

Modeling temporal variation in recruitment in fisheries stock assessment: A review of theory and practice

Recruitment is one of the most variable biological processes driving fisheries population dynamics and the characteristics and drivers of the variation differ among stocks. Understanding, describing (modeling), estimating, and predicting (forecasting) this variation is essential to appropriate stock assessment and fisheries management. Most modern stock assessments estimate annual variation in recruitment, particularly those that include age or size composition data. Changes over time are often partitioned into those related to the spawning biomass due to density dependence (the stock-recruitment relationship) and those related to other factors such as environmental conditions. Several methods have been used to model recruitment inside stock assessment models, and they differ by how recruitment is represented and how statistical inference is conducted. Virtual population analyses make few statistical assumptions about recruitment and instead calculate recruitment as the sum of the mortality-adjusted catches of a cohort while surplus production models generally imply a stock-recruitment relationship in their production function. Integrated statistical stock assessment models have modelled recruitment using a stock-recruitment relationship, autocorrelation, a function of covariates, regime shifts, or a combination of these. Statistical inference has typically been conducted using state-space (hierarchical) models, whether using Bayesian or maximum likelihood methods, or inferences are approximated using penalized likelihood approaches, which may not be statistically reliable. All these methods have specific issues that need to be addressed and there are tradeoffs in their use. Future temporal variation also needs to be considered when providing management advice. We review the theory and practice of modelling temporal variation in recruitment in fisheries stock assessment, provide advice on good practices, and recommend important research.

Implications of a climate-induced recruitment shift in the stock assessment of Patagonian grenadier (Macruronus magellanicus) in Chile

Patagonian grenadier (Macruronus magellanicus) is the most abundant demersal fisheries resource off Chilean Patagonia, and also is a key fisheries species off the south of Argentina and off the Falkland Islands. A Stock Synthesis assessment shows that this stock has declined in abundance off Chile, which has been attributed to a major change in recruitment strength, and subsequent production, after 1999. An assessment is conducted in which the change in recruitment is modelled as a shift in the stock-recruitment relationship. Management Strategy Evaluation is then used to examine the consequences of a mis-match between the assumptions related to recruitment in the assessment used to set the annual total allowable catch (TAC), and those in the operating model that represents the actual situation being managed. A management strategy that does not consider a shift in recruitment resulted in average TAC values of approximately 125,000 t, substantially larger than the sustainable yield of 45,000 t when there is a recruitment shift. A management strategy based on ignoring the shift in recruitment would thus lead to unsustainable catches, with major impacts on the ecosystem as well as the industry and coastal communities reliant on the fishery, if there was an actual shift in recruitment. Management of the fishery has not accounted for a recruitment shift, and annual landings have been consistently lower than the estimated annual TACs. The 2014 landings are similar to the long term TAC estimated by the assessment models under the Shift operating model. The history of the Patagonian grenadier fishery demonstrates the benefits of taking a precautionary approach that accounts for changes in fish productivity (whether climate-driven or otherwise). However, there can be considerable delays before a shift is observed in recruitment estimates or assessment model mis-specification is detected. The need for alternative approaches for providing more timely recruitment information is discussed.