Stock-recruitment Curve Research Articles

Simulation Analyses Testing the Robustness of Productivity Determinations from West Coast Pacific Ocean Perch Stock Assessment Data

The estimated stock size and recruitment data from assessment models provide a way to evaluate the history of a fishery relative to the expected response given a target fishing mortality rate. For example, if recruitment estimates are below the fishing mortality replacement line, then further reductions in spawning biomass can be expected. However, recruitment variability, serial correlation, and variable historical harvest rates can create misleading perceptions of sustainable harvest rates when they are derived from these simple replacement-line curves. Careful analysis of the stock–recruitment relationship given the available data is required in order to evaluate stock productivity in age-structured modeling. In this study, simulation–estimation procedures were developed to evaluate stock productivity estimates given the level of information and historical fishing mortality currently reported for the Pacific ocean perch Sebastes alutus stock off the coast of Washington, Oregon, and California. Two scenarios were designed with significantly different optimum yield calculations, one with moderate productivity and one with relatively low productivity. Within each productivity scenario, two types of simulations were performed, one with recruitment values identical to the original estimates (the observation-error-only case) and one with recruitment varying about the stock–recruitment curve (the observation-and-process-error case). For each of the two scenarios and two cases, 100 simulated stock assessment data sets were generated. Each was then analyzed using the stock assessment model used in 1998. The results suggest that if the actual stock–recruitment productivity of this stock is low, the assessment model estimates will have a slight positive bias (estimated productivity will be higher than actual productivity). Conversely, if the actual stock–recruitment productivity is moderate, estimates are likely to have a negative bias given the observed sequence of recruitments and fishing mortality history. Including time series effects (simple autocorrelation) is shown to be a reasonable step toward remedying this problem.

Impacts of demographic variation in spawning characteristics on reference points for fishery management

Parametric relationships of recruitment to an index of parental stock size assume the latter is proportionally related to spawning potential, irrespective of the demographic composition of adults. Recent empirical information, however, suggests that reproduction by older and experienced females is more successful than by young and inexperienced females. New models are developed incorporating the proportion of each age group spawning for the first, second, etc., time (from information contained in the maturity ogive) and differences in the survival of eggs and larvae in relation to the demography of spawners (based on experimental results). A series of spawning metrics [spawning-stock biomass (SSB), egg production, hatched egg production, viable larval production] and associated recruitment-based fishing mortality reference points (Fmed, Fcrash, and the F that allows at least one lifetime spawning per recruit) are contrasted for the Georges Bank Atlantic cod (Gadus morhua) stock. The time-series of spawning intensity is significantly altered when hatched eggs or viable larvae are used as the metric, reflecting the contribution of first- and second-time spawners in some years, and the increasing trend in F. The effect of reduced average maternal size in relation to egg viability was a more important factor contributing to discrepancies with SSB than was spawning experience in relation to hatching success. Percent maximum spawning potential (%MSP) per recruit curves in relation to F are steeper (i.e. result in lower values of %MSP for a given F) for hatched eggs and viable larvae than for SSB or egg production per recruit. Lifetime expected numbers of spawnings per recruit are significantly reduced when the effects of spawning experience on egg hatching success are included. And finally, although point estimates of Fmed and Fcrash are similar using SSB and viable larval production, the median Fcrash estimated from 5000 bootstrap realizations of the Beverton-Holt stock recruitment curve for viable larvae is much lower than that from SSB, with narrower confidence bounds. Our results suggest that traditional approaches to F-based reference points using SSB systematically overestimate the resiliency of stocks to fishing. If age-at-spawning is at least partially heritable, then intense fishing on younger ages may exert high levels of selection for early maturity with negative impacts on net reproductive effort and trait diversity.

Recruitment of cod and haddock in the North Atlantic: a comparative analysis

We examined recruitment patterns of cod (Gadus morhua) and haddock (Melanogrammus aeglefinus) from eight regions in the North Atlantic (Georges Bank, Browns Bank, the Eastern Scotian Shelf, the Faroe Plateau, Iceland, the Barents Sea, the North Sea, and West of Scotland). The selection was based on the availability of contemporaneous estimates of stock and recruitment for both species within each location. We considered the following metrics for both species by region: recruitment variability (measured as absolute numbers at age 1 and as deviations from a fitted stock-recruitment curve), the rate of recruitment at low spawning stock sizes (the maximum reproductive rate, a measure of resilience of the stock to exploitation) and autocorrelation in recruitment adjusted for spawning stock size. We also examined the correlation of cod and haddock recruitment within regions. Differences in recruitment variability and resilience between cod and haddock in paired comparison tests were highly significant. Haddock consistently exhibited higher recruitment variability and lower resilience than cod. Autocorrelation in recruitment of the two species within region was related, possibly indicating serial correlation in forcing mechanisms affecting both species. Cod and haddock exhibited moderate synchrony in recruitment patterns within regions. In six out of the eight regions, the correlation between recruitment (adjusted for spawning stock size) was ∼0.5, suggesting that common environmental conditions experienced by both species did affect recruitment. Research-vessel survey information available for three of the regions (North Sea, Barents Sea, and Georges Bank) and one additional location (Gulf of Maine) were analyzed for evidence of density dependence and for levels of post-larval abundance variability. Cod exhibited stronger density-dependent mortality in three out of four regions. Post-larval abundance variability was not different between the two species.

Modelling the effects of drought on the population of brown trout in Black Brows Beck

Records from a 30-year study of the population of migratory brown trout, Salmo trutta L., in Black Brows Beck (English Lake District) are used to construct a model for predicting population numbers during normal rainfall conditions and under the influence of drought. Twice-yearly samples of different age-groups of trout were recorded, together with a more detailed set of records for a further 8 years. These data are used to develop and calibrate a time-dependent population model. A concurrent record of rainfall data for Windermere is aggregated to form seasonal averages and used as an indicator of drought for the region. Drought conditions result in lower than expected stock which can be identified as outliers from the Ricker stock-recruitment curves for each sample. A set of five difference equations, which describe the overlapping trout age-groups, is identified and used to forecast the trout population up to a few years ahead. The model is particularly successful at forecasting population numbers 1-year ahead if the following years drought is taken into account. Incorporation of drought effects into the model significantly improves model forecasts. A linearised stability analysis suggests that long-term drought conditions will have the effect of increasing population stability, although a particularly severe drought, or series of severe droughts, may lead to population decline.

Using nonlinear functional relationship regression to fit fisheries models

Functional relationship regression refers to that class of statistical model where a functional relationship is assumed to exist between two arithmetic variables, but the two arithmetic variables can only be viewed with measurement error and (or) natural variability. The goal is to estimate the underlying functional relationship when observing only the variables containing error or natural variability. While statistical details need to be worked out, some general approaches to this class of problem can be recommended. First of all, nonlinear least squares can provide maximum likelihood estimates when the error variance ratio, λ;, is assumed known. Furthermore, the usual estimates of standard errors from nonlinear least squares, while theoretically flawed for this class of model, appear to provide usable estimates for many practical problems. Next, a K-sample F test, for testing the equality of nonlinear functional relationship regression curves, is proposed. Finally, computer memory-saving algorithms are suggested for situations where sample sizes are large. Methods proposed here are applied to three types of functional curves commonly estimated in fisheries biology: a stock-recruitment curve, allometry, and the von Bertalanffy growth curve.

Using nonlinear functional relationship regression to fit fisheries models

Functional relationship regression refers to that class of statistical model where a functional relationship is assumed to exist between two arithmetic variables, but the two arithmetic variables can only be viewed with measurement error and (or) natural variability. The goal is to estimate the underlying functional relationship when observing only the variables containing error or natural variability. While statistical details need to be worked out, some general approaches to this class of problem can be recommended. First of all, nonlinear least squares can provide maximum likelihood estimates when the error variance ratio, λ;, is assumed known. Furthermore, the usual estimates of standard errors from nonlinear least squares, while theoretically flawed for this class of model, appear to provide usable estimates for many practical problems. Next, a K-sample F test, for testing the equality of nonlinear functional relationship regression curves, is proposed. Finally, computer memory-saving algorithms are suggested for situations where sample sizes are large. Methods proposed here are applied to three types of functional curves commonly estimated in fisheries biology: a stock-recruitment curve, allometry, and the von Bertalanffy growth curve.

Sustainable recruitment: the bottom line

This paper develops a single-species perspective on the limits of sustainable fishing. Given uncertain data and assessments, the problem is to determine lower confidence limits for the minimum fishing mortality rate Ft that, if maintained indefinitely, would drive the stock to extinction. For non-depensatory stocks, Ft is determined by the slope of the stock–recruitment curve at the origin. The paper reviews three different approaches to making inferences about Ft : recruit-per-biomass relationships (e.g. F high ), parametric curves (e.g. Ricker), and nonparametric curves (e.g. LOWESS fits; Cook 1998). Of these, nonparametic curves are potentially the best, but existing implementations suffer from operational difficulties and do not always give biologically sensible fits. These problems can be circumvented by two new nonparametric methods, CONCR (Concave Recruitment) and DIMPOS (Diminishing returns, Positive recruitment), which are described and applied to several ICES stocks. Finally, the paper explores issues surrounding the use of sustainable recruitment measures in assessment and management.

Chance fluctuations and the survival of small salmon stocks

In this paper, we use a Markovian approach to demonstrate that stocks with modest growth potential at low abundance can be driven quite rapidly to extinction. Under relatively benign conditions, stock survival rates may be high, but even a modest increase to the amount of chance variation in recruitment can reduce survival rates dramatically. Survival rates also depend on the form of the stock-recruitment curve, including depensation that takes hold only at extremely low abundances. Fortunately, small amounts of straying among adjacent populations can push the survival rate substantially toward the value for a combined, homogeneous unit. Our analysis also suggests modifications to existing approaches of establishing minimum target levels for spawning densities and the near impossibility of reliably estimating extinction rates.

Pink Shrimp, Farfantepenaeus duorarum, Recruitment Variability as an Indicator of Florida Bay Dynamics

Florida Bay exhibits highly dynamic hydrographic regimes that influence variability in the retention, survivorship, and migration of pink shrimp,Farfantepenaeus duorarum, larvae and juveniles. Florida Bay is the nursery habitat for pink shrimp and since a large fishery is based on the adult population in the Dry Tortugas region, Florida Bay plays a fundamental role in the health of the pink shrimp fishery in South Florida. Conversely, the level of shrimp recruitment to the fishery can act as an indicator of the health of Florida Bay integrating multiple biological, physical, and environmental variables. We examined 372 mo of data on commercial landings of pink shrimp to estimate monthly recruitment. We found recruitment occurs throughout the year, there are one or more seasonal peaks, and the magnitude and monthly position of the peaks changed through decades. These changes may be explained by a varying spawning population producing different levels of eggs, by environmental changes in the nursery grounds that modulate a nearly constant supply of eggs, or a combination of these. Recruitment estimates and the residuals about stock-recruitment relationships were compared over three decades (1965–1995) in terms of annual and monthly trends and average patterns. Significant differences found between the decades could be due to ecological changes in Florida Bay, specifically to loss of recruitment peaks, with an associated overall decline in pink shrimp recruitment. For the lates years of the study, recruitment and residuals about the stock-recruitment curve are increasing, which may indicate an improvement in Florida Bay as a nursery ground for pink shrimp, and thus as habitat for other organisms as well.

Application of least median of squared orthogonal distance (LMD) and LMD-based reweighted least squares (RLS) methods on the stock-recruitment relationship

Analysis of stock-recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD-based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

Patterns of covariation in survival rates of British Columbian and Alaskan sockeye salmon (Oncorhynchus nerka) stocks

We used a multi-stock comparison to identify spatial and temporal characteristics of environmentally driven sources of variability across four decades in the productivity of 29 sockeye salmon (Oncorhynchus nerka) stocks from British Columbia (B.C.) and Alaska. We examined patterns of covariation among indices of survival rate (residuals from the best-fit stock-recruitment curve) and found positive covariation among Fraser River sockeye stocks (southern B.C.) and, to a greater extent, among Bristol Bay stocks (western Alaska) but no evidence of covariation between these two regions or with stocks of other regions in B.C. and Alaska. This indicates that important environmental processes affecting variation in sockeye survival rate from spawners to recruits operate at regional spatial scales, rather than at the larger, ocean-basin scale. The observed covariation in survival rates of Bristol Bay stocks appears to be due to a combination of both freshwater and, to a greater degree, marine processes. Bristol Bay sockeye stocks showed a dramatic and persistent increase in survival rates coinciding with the abrupt changes in the North Pacific environment in the mid-1970s; however, there was little evidence of a similar response for Fraser River stocks.

EFFECTS OF STREAM CHANNEL MORPHOLOGY ON GOLDEN TROUT SPAWNING HABITAT AND RECRUITMENT

Populations of stream-dwelling salmonids (e.g., salmon and trout) are generally believed to be regulated by strong density-dependent mortality acting on the age-0 life stage, which produces a dome-shaped stock-recruitment curve. Although this paradigm is based largely on data from anadromous species, it has been widely applied to stream-resident salmonids despite the fact that the processes limiting or regulating stream-resident populations remain poorly understood. The purpose of the present study was to determine whether stream channel morphology affects the availability of spawning habitat for California golden trout, and whether spawning habitat availability influences the production of age-0 trout and recruitment into the adult population. Wide stream reaches contained significantly more spawning habitat and a higher density of nests and age-0 trout than did narrow reaches. In contrast to the idea that salmonid populations are regulated by density-dependent mortality of age-0 fish, we found that the mortality of age-0 trout was largely density independent. In addition, over most of the range of observed fish densities, the density of a particular cohort was positively correlated between years for age-0, age-1, and age-2 trout. Therefore, our golden trout study population was limited by spawning habitat, with spawning habitat availability influencing the production of age-0 trout as well as recruitment into the adult population. Grazing by cattle has widened the study streams, and our current findings help to explain why stream sections subject to grazing had more spawning habitat and higher golden trout densities than ungrazed sections. Individual growth rates of golden trout are apparently negatively density dependent, and these grazing-related increases in trout density have likely resulted in decreased growth rates. Our study demonstrates that it is only by gaining an understanding of how processes operate that we will be able to predict the effects of habitat alteration on populations.

Fish, Fact and Fantasy: a Long View

This paper suggests ways forward from the widely perceived present failures of fishery assessment and management. A history of fishery yield modelling is presented from the carefree days of the 1950s to the depressing series of stock collapses and depletions of the 1980s. Underlying this gruesome story has been the failure of management by quotas to arrest overcapacity in fishing power, the lack of robust and informative reference points and the inadequacy of methods dealing with some multispecies fisheries. The paper refines the use of the concept of Fext, defined as the minimum value of F in a self-regenerating yield model that leads to eventual extinction in a family of yield curves generated with a range of stock recruitment curves. Model reconstructions for North Sea cod and Icelandic herring make evident calamitous losses in catches forgone as result of the failure of rational management. An optimistic agenda that may achieve more effective fishery management in the future is presented. In some ways, we may have been trying to be too clever. A simple management system based on careful monitoring of fishing effort, biological targets such as F95, and exploitation of a diversity of fish resources may suffice to avert further disaster and hedge against uncertainty.

On the stock–recruitment relationships in fish population models

The framework of this article is modeling applied to fisheries. It aims at relating some classical stock–recruitment curves to a dynamic structured model, consisting of the adults stages of the stock and a pre-recruits stage (i.e., eggs, larvae, juveniles). The main result is that no functional stock–recruitment relationship can be found, unless further restrictive assumptions are added to the model (slow–fast dynamics and uniformity). Among the curves thus obtained is the Beverton–Holt curve, but not Ricker's.

A generalized stock-recruitment relationship fitted to the observed yield: implications for the recruitment dynamic

The present study presents a method of assessing and fitting a stock-recruitment relationship. The method is based on a combination of an equilibrium production model and a yield per recruit model. It does not use recruitment data which are, in general, highly dispersed, but production data. Thus, the relationship obtained is not of the parametric form of classical stock-recruitment relationship such as those of the Beverton and Holt (1957) and Ricker (1954), however, in some cases, the resulting stock-recruitment curve resembles models currently used in fisheries science. It is interpreted as an expectation of the recruitment conditionally to stock spawning biomass and stock demographic structure. However, for some realistic values of the parameters, the curve thus obtained describes a loop which suggests that two different recruitment levels may be expected from the same stock spawning biomass level. This theoretical property is illustrated with simulations. As an illustrative example, the method is applied to North-West Atlantic gadoid stocks. The significance of the method, its originality, the validity of the underlying assumptions and their conceptual consequences are discussed.

Herring stock-recruitment relationships and recruitment patterns in the North Atlantic and Northeast Pacific oceans

Understanding the recruitment dynamics of marine fish stocks is crucial in selecting harvest strategies. Revealing the recruitment patterns is the first step to understanding recruitment dynamics. In this study, stock-recruitment data for 19 Atlantic and Pacific herring stocks from the north Atlantic and northeast Pacific oceans were examined for density-dependent effects on recruitment and for recruitment patterns over spatial scales. Two parametric and one nonparametric tests indicate that the survival rates from eggs to recruits from 15 out of 19 stocks are related to spawning biomass, with high spawning biomass resulting in low survival rates. Seven out of 19 stocks show that year class strengths are associated with spawning biomass. Most stocks have compensatory, dome-shaped or asymptotic stock-recruitment curves. Positive correlations are generally found among the geographically close neighbor stocks. The recruitment patterns suggest that each environmental process may play an important role in recruitment dynamics of herring only within a certain spatial scale.

A review of stock-recruitment relationships with reference to flatfish populations

The relationship between stock and recruitment in fish populations has been a subject of many studies and some controversy, even to the extent that it has been questioned whether the two can be related in any meanignful way. The denial of a meaningful stock-recruitment relationship has profound and disturbing influences on the science of fish population dynamics and would seem to be something of a policy of despair. A more constructive approach is to acknowledge the difficulties in establishing a stock-recruitment relationship from the available information but still to seek the best interpretation of the data for the purposes for which the analysis is intended. Among the models that have been developed to fit stock-recruitment curves to data sets are the well-known Beverton-Holt and Ricker curves, both of which have two parameters. Less commonly used is the two-parameter model of Cushing. These two-parameter models have been generalized to give three-parameter models whose shape can be varied by settings of the parameters so as to model a wide range of observed stock-recruitment curves. In this paper these models and their underlying assumptions are described. Statistical methods of fitting the curves to data are reviewed with emphasis on the appraisal of the fitted curve, concentrating on the use for which the fitted curve is intended. Methods of choosing between different curves are discussed. The review is illustrated with examples of stock-recruitment data derived for various flatfish stocks. Among the questions that are discussed is whether there are any features of stock-recruitment relationships for flatfish that differentiate them from those of other species. Methods for testing the null hypotheses that there is no relationship between stock and recruitment and that recruitment in flatfish is not influenced by environmental or other biological factors are described. Of the 20 flatfish stocks for which suitable stock and recruitment data are available, it is shown that in six cases there is a statistically significant relationship between stock size and recruitment. In one of these cases the relationship is significantly strengthened by the incorporation of an environmental measurement. Of the six significant stock-recruitment relationships one is strongly domed and three are the right-hand arm of a domed curve. In the other two cases average recruitment increases with increasing stock size, but it is not possible to differentiate between a domed and an asymptotic curve. This evidence of density-dependence in the stock-recruitment relationships for flatfish is further strengthened by an examination of those cases in which the model of constant recruitment, independent of stock size, is not rejected. In eight of these stocks it is shown that the model of constant recruitment is favoured in preference to a model in which recruitment is directly proportional to stock size. Although recruitment may vary about a constant average level over a restricted range of stock size, it is not biologically possible for a population to sustain a high level of recruitment at low stock sizes. Thus in these eight cases there is further evidence of an underlying, but as yet unidentified, stock-recruitment relationship.

How to Behave Around Cannibals: A Density-Dependent Dynamic Game

The fate of a cannibalistic cohort developing in a seasonal environment hinges on a complex array of interacting features, prominently including a size-specific, density-dependent trade-off between growth and survival, mediated by activity and constrained by a seasonal time horizon. The dynamic size structure of such a cohort is partly self-imposed and partly determined by alternative prey availability, noncannibalistic sources of mortality, and other factors. In the work reported here, we derive a new model of cannibalism that incorporates these features and requires us to obtain numerical solutions of a density-dependent dynamic game between stages within the developing cohort. The convergence method used to find the solutions should prove useful for other dynamic ecological models as well. The results indicate that the optimal levels of predator activity predicted by the model are particularly sensitive to parameter shifts; changes in activity mediate and damp growth, survival, and fitness responses. The ratio of mortality rate to growth rate may be approximately minimized (as predicted in other theoretical analyses) even within cannibalistic cohorts constrained by seasons, unless there is no advantage to reaching intermediate or larger sizes during the season. Except when cannibalism is particularly intense overall or increases in intensity with the absolute size of the potential cannibal, within-cohort cannibalism should generally tend to synchronize the cohort, yielding survivors more uniform in size than would result at lower intensities. Finally, stock-recruitment curves derived from the results imply stable generation-to-generation dynamics, though low alternative prey availabilities and high fecundities can generate oscillatory behavior consistent with published observations.

Modeling of Recruitment Patterns in Pacific Cod (Gadus macrocephalus) in Hecate Strait, British Columbia

We combined published recruitment hypotheses into a single modeling framework and explored the relative contributions of the hypothesis factors to recruitment variation in Pacific cod (Gadus macrocephalus). Our five hypotheses were (1) recruitment decreased with increasing transport during the larval period; (2) recruitment was related to percentage hatching success as a dome-shaped curve with a peak between 4.0 and 5.0 °C; (3) recruitment was positively related to abundance of age-0 juvenile Pacific herring (Clupea harengus pallasi) hatched in the same year as the cod; (4) recruitment was positively related to abundance of age-0 and age-1 herring in the year prior to spawning; and (5) a dome-shaped curve related recruitment to adult stock size. We used new records for temperature, and a new index of advection based on measures of current in Hecate Strait. For fitting a response surface with age-3 cod recruitment as the independent variable, we used a 20-yr data series of variables from 1962 to 1981 inclusive and reserved data for the years 1982–85 for a prediction test. Only hypotheses 1 and 5 were supported by both the response surface fit and prediction tests. The stock–recruitment curve can be fitted only when the transport curve is fitted simultaneously.

A Comparison of Preseason Forecasting Methods for Returns of Two British Columbia Sockeye Salmon Stocks

Preseason forecasts of salmon returns are crucial to the management of coastal Pacific salmon fisheries. Forecasts are used by both fishery managers and industry to plan harvest strategies for the coming season. Forecasts are also of considerable importance in deciding the allocation of catch among different areas and user groups. This paper outlines several models currently used to generate preseason forecasts of salmon returns. In addition, several forecasting models that have proven useful for modeling other resources are presented. The ability of these models to produce accurate forecasts was tested with data from fisheries for sockeye salmon Oncorhynchus nerka in the Adams and Chilko rivers, British Columbia. Results of the forecasting study indicated that simple time-series models may provide more accurate forecasts of run size than currently used methods, such as Ricker stock-recruitment curves. In addition, naive combinations of forecasts from the competing models appear to perform at least as well as any single model. For both river systems, the commonly used sibling model performed poorly. On a gross level, the value of the differences in forecasting accuracy between the models is on the order of Can$30 million/year.