Sequential Population Analysis Research Articles

AVALIAÇÃO DO ESTOQUE DE LAGOSTA VERMELHA Panulirus argus NA COSTA BRASILEIRA

O estudo trata da avaliação de estoque de lagosta vermelha Panulirus argus, recurso pesqueiro de considerável importância econômica na costa brasileira. As análises foram conduzidas com a utilização da Análise Sequencial de Populações, baseada na composição das capturas por idade, obtida a partir de dados de exportação por tipo comercial, amostras biológicas realizadas em empresas de pesca dos principais estados produtores e captura e esforço de pesca estimado para o período de 2005 a 2015. Os resultados indicam que, apesar das elevadas taxas de mortalidades por pesca e do comprometimento da estrutura por idade/comprimento da população, o estoque apresenta certa estabilidade quanto à sua composição em número e biomassa. A biomassa reprodutiva estimada, no entanto, se encontra bastante reduzida, com uma média 18% da biomassa sem pesca. Uma redução da mortalidade por pesca, especialmente sobre os indivíduos nas idades 4 e 5, seria fundamental para recuperar a estrutura da população e poderia resultar em melhores rendimentos da pescaria. Há indícios de resultados positivos neste sentido, a partir das medidas de ordenamento adotadas nos últimos 10 anos, que resultou em considerável diminuição do esforço de pesca.

Dependence of recruitment on parent stock of the spiny lobster, Panulirus argus, in Florida

AbstractDespite management practices to achieve sustainability, commercial landings for Florida spiny lobster (Panulirus argus) have experienced a drastic decline (57%) since 2000. This is cause for concern not only for economic reasons, but for issues of sustainability. An annual index of P. argus post‐larval (puerulus) abundance, estimated with a generalized linear model with significant mean sea‐level effects, shows a 36% decrease in annual puerulus supply since 1988. In addition, local Florida spawning stock biomass estimated from an age‐structured sequential population analysis decreased 57% since 1988. Puerulus abundance follows a highly correlated (R = 0.76) trend with a 12‐month delayed spawning stock abundance, which supports the contention that the Florida spawning population is a significant contributing factor to post‐larval recruitment in Florida. Residuals about the puerulus on spawning stock abundance function follow closely an interannual North Atlantic Oscillation Index signal. This residual effect is thought of as a secondary regional population effect on Florida puerulus recruitment. The Florida spiny lobster stock is exploited with no fishing mortality controls due to the Pan Caribbean recruitment concept adopted in Florida spiny lobster management. Therefore, the potential of recruitment overfishing exists if fishing mortality controls to protect local spawning stock abundance, such as catch quotas, are not introduced.

Detecting and correcting underreported catches in fish stock assessment: trial of a new method

Landings from fisheries are often underreported, that is, the true landings are greater than those reported. Despite this bias, reported landings are widely used in fish stock assessments, and this might lead to overoptimistic exploitation strategies. We construct a statistical stock assessment model that accounts for underreported landings using the theory of censoring with sequential population analysis (SPA). The new model is developed and implemented specifically for the cod stock ( Gadus morhua ) from the southern Gulf of St. Lawrence (Canada). This stock is known to have unreported overfishing during 1985–1992. We show in simulations that for this stock, the new censored model can correctly detect the problematic landings. These corrections are nearly insensitive to subjective boundaries placed on real catches and robust to modifications imposed in the simulation of landings. However, when surveys are too noisy, the new SPA for censored catches can result in increased uncertainty in parameters used for management such as spawning stock biomass and age-structured stock size.

Summing Up - Symposium on Reproductive and Recruitment Processes of Exploited Marine Fish Stocks

Variability in recruitment results in variability in catch from year-to-year, which is a problem for fishermen, for the processing industry and for fisheries managers. It is commonplace to read how large the interannual variability in recruitment can be and how difficult it is to determine the causes. However for an ecologist, the astonishing feature of recruitment variability is how small it is, given that fish produce thousands or millions of eggs each and that survival is extremely unlikely and uncertain. Among the pelagic and demersal stocks assessed in the NE Atlantic the smallest year-class is generally within a factor of 10 of the biggest. It is not infrequent for interannual recruitment variability to be less than the variability of the spawning biomass of the stock (Brander, 2003). How is the variability damped out? What are the compensatory mechanisms? Density dependence is necessary for populations to remain within feasible bounds (Reddingius, 1971) but as Ed told us “A little density dependence, especially in the relatively long juvenile stage, can regulate recruitment”. Density dependence should not be invoked without good evidence in relation to processes like adult growth, however appealing it is to biologists or convenient for modellers trying to keep their models stable. Fisheries assessment and management, at least in the North Atlantic, has focussed on year-to-year tracking of stock biomass in order to set annual catch limits. Questions about the role of recruitment were therefore also principally directed at annual prediction and the understanding of processes needed in order to do this. The biological book-keeping was done using sequential population analysis which gives estimates of both annual recruitment and spawning stock biomass (SSB). The latter is assumed to represent spawning output of the stock, but as many of the papers in this symposium show, fecundity, maturity, spawning frequency and egg quality, are not constant. The relevance of the symposium is therefore obvious, since strategies for sustainable management, using precautionary reference levels of SSB and fishing mortality, are based on the relationship between SSB and recruitment. We need to move on to a longer term view which includes a wider range of information about the biological state of fish, their environment and their interaction with the rest of the marine ecosystem. Ed once more: “’Solving the recruitment problem’ is no longer the holy grail of fishery science. Appreciating recruitment variability, explaining probable causes, considering implications for management, and understanding it in the context of broader variability in marine ecosystems are worthy goals.”

Simultaneous versus sequential pharmacokinetic‐pharmacodynamic population analysis using an Iterative Two‐Stage Bayesian technique

A method for simultaneous pharmacokinetic-pharmacodynamic (PK-PD) population analysis using an Iterative Two-Stage Bayesian (ITSB) algorithm was developed. The method was evaluated using clinical data and Monte Carlo simulations. Data from a clinical study with rocuronium in nine anesthetized patients and data generated by Monte Carlo simulation using a similar study design were analysed by sequential PK-PD analysis, PD analysis with nonparametric PK data and simultaneous PK-PD analysis. Both PK and PD data sets were 'rich' with respect to the number of measurements per individual. The accuracy and precision of the estimated population parameters were evaluated by comparing their mean error (ME) and root mean squared error (RMSE), respectively. The influence of PD model misspecification on the results was also investigated. The simultaneous PK-PD analysis resulted in slightly more precise population parameter estimates than the sequential PK-PD analysis and the nonparametric PK method. In the presence of PD model misspecification, however, simultaneous analysis resulted in poor PK parameter estimates, while sequential PK-PD analysis performed well. In conclusion, ITSB is a valuable technique for PK-PD population analysis of rich data sets. The sequential PK-PD method is better suited for the analysis of rich data than the simultaneous analysis.

Covariation between grey seal (Halichoerus grypus) abundance and natural mortality of cod (Gadus morhua) in the southern Gulf of St. Lawrence

More than 10 years after the collapse of Atlantic cod (Gadus morhua) fisheries in Canada, the role of increased seal populations in the decline and lack of recovery of the stocks continues to be discussed. Using removals and abundance indices from synthetic populations, we found that sequential population analysis can uncover trends in natural mortality. We used this approach to examine variation in natural mortality (M) of southern Gulf of St. Lawrence cod. M increased from the late 1970s to the mid-1990s but declined slightly recently. Results were consistent with previous work indicating that M increased in the 1980s. Changes in estimated M for this cod stock matched fluctuations in grey seal (Halichoerus grypus) abundance. The increase in grey seal abundance from the late 1970s to the mid-1990s corresponded with the increase in estimated M of cod over this time period. The correspondence between seal abundance and M of cod supports the hypothesis that seal predation may be a cause of increased M. However, the diet information available suggests that seals consume mainly juvenile cod, whereas our evidence for an increase in M is for larger cod (ages 3 years and older).

Local influence diagnostics for the retrospective problem in sequential population analysis

Abstract The retrospective problem involves systematic differences in sequential population analysis (SPA) estimates of stock size or some other quantity in a reference year. The differences occur as successively more data are used for estimation, and they appear to be structural biases caused by a mis-specification of the SPA. In some cases the retrospective problem is so severe that the SPA is considered to be too unreliable for stock assessment purposes. There are many possible sources of retrospective patterns, and it is usually difficult in practice to determine which are more likely. We propose diagnostics to help determine the more likely causes. We use local influence diagnostics to investigate whether small changes or perturbations to SPA input components such as catches or natural mortalities can remove or reduce retrospective patterns. We show, for the fall-spawning herring stock in the southern Gulf of St. Lawrence SPA, that relatively small age- and year-specific changes to the SPA assumptions about the proportional relationship between an abundance index and stock size can result in greatly reduced retrospective patterns. We therefore conclude primafacie that these assumptions are a plausible source of the retrospective pattern. Larger changes to catches, natural mortality assumptions, or estimation weights are required to reduce the retrospective pattern. These other factors seem to be less plausible sources of the retrospective pattern, although this is best assessed by the herring stock experts who are more knowledgeable about the fishery and other scientific information for this stock.

An application of generalized linear models in production model and sequential population analysis

In fitting production models and age-structured models to an index of the relative abundance of a fish population, errors are usually assumed to follow a log-normal or normal distribution, without any diagnostic analyses. A generalized linear model can readily deal with many types of error structures. In this paper, a generalized linear model is coupled with a production model and a sequential population model to assess the stock of the Atlantic cod (Gadus morhua) 2J3KL. This study suggests that the parameter estimates in these models can be greatly influenced by the assumption about the error structures in the estimation and that log-normal and gamma distributions are appropriate for the production model in assessing the Atlantic cod 2J3KL stock, whereas gamma distribution is appropriate for the sequential population model. We recommend that generalized linear models should be used to identify the appropriate error structure in modeling fish population dynamics.

Assessment methodology for Barents Sea capelin, Mallotus villosus (Müller)

The methods used to assess the Barents Sea capelin, Mallotus villosus (Muller), stock have always differed considerably from those used for most other stocks. Owing to the life history characteristics of capelin (short lifespan, considerable natural mortality, including spawning mortality), sequential population analysis (VPA, etc) cannot be applied to assess stock status and to generate catch prognoses. The assessment is based on an annual acoustic survey, which is regarded as an absolute measurement of stock size. The assessment methods have changed considerably since these activities started in the early 1970s. They have evolved from a relatively simple single-species model, used prior to the first major stock collapse in the early 1980s, through several steps towards the rather ambitious probabilistic model used at present, in which multispecies interactions and uncertainty in measured and modelled quantities are included. In this paper we review the history of stock assessment of Barents Sea capelin, describe current practice, and briefly outline the extensions to the model that will soon be implemented. Current management practice is evaluated in light of the history of the stock and the fishery, and is compared with that used with other capelin stocks. 2002 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd.

Generalized Local Influence with Applications to Fish Stock Cohort Analysis

Summary It is important to understand the influence of data and model assumptions on the results of a statistical analysis, and influence diagnostics are valuable tools for this. We consider local influence diagnostics for a statistical model that is fully parametric, and where estimation involves a fit function that is second order differentiable with respect to the parameters. Similarly to Cook, we study the local behaviour of influence graphs formed from perturbations to model components. However, the diagnostics that we develop are more general in that the type of model result that is used to assess influence is fairly arbitrary and must only be first order differentiable with respect to model parameters and the perturbations. This allows us to focus our influence analyses on important results, and to produce diagnostics that are meaningful to practitioners. The procedures that we propose are applied to sequential population analysis, a common method that is used to estimate the size of commercially exploited fish stocks. Our diagnostics reveal interesting patterns of influence that are not revealed by using Cook's likelihood displacement influence diagnostics. Our diagnostics lead to an increased understanding of how the data affect important estimates, and thereby provide information for assessing the potential effect of errors in model inputs. In addition, empirical comparisons illustrate that the local influence diagnostics proposed tend to provide a good description of global influence.

Estimated total abundance and numbers at age of longtail hake (<i>Macruronus magellanicus</i>) in the Southwest Atlantic during the years 1987-2000

Delta-based estimates of longtail hake biomass off Argentina were derived from the results of summer trawl surveys carried out on an irregular basis since 1987. Annual estimates of biomass within the whole area ranged from 1.2 to 4.5 million tons, consistent with those obtained by sequential population analysis. There was no clear trend throughout the period 1987-1995, but the 1987 estimate was higher than those for the same area during the years 1992-1995, and estimates since 1997 were much higher than the mean for the four-year period 1992-1995. Since 1992 the largest concentrations of fish have been between 50 and 100 m deep. Most of those were adults, small fish being scarce. Analysis of numbers-at-age showed the dominance of 4-8 year old fish in 1987 and from 1992 to 1994 and the existence of two very strong year-classes, those of 1993 and 1995.

Reference priors for Bayesian fisheries models

Bayesian models require the specification of prior distributions for all unknown parameters, and this formal utilization of prior knowledge (if any) can be used to great advantage in some fisheries. However, regardless of whether prior knowledge about model parameters is available, specification of prior distributions is seldom unequivocal. This work addresses the problem of specifying default priors for several common fisheries models. To maintain consistency of terminology with the statistical literature, such priors are herein called reference priors to recognize that they can be interpreted as providing a sensible reference point against which the implications of alternative priors can be compared. Here, the Jeffreys' prior is demonstrated for the Ricker and Beverton–Holt stock–recruit curves, von Bertalanffy growth curve, Schaefer surplus production model, and sequential population analysis. The Jeffreys' priors for relevant derived parameters are demonstrated, including the steepness parameter of the Beverton–Holt stock–recruit curve. The sequential population analysis example is used to show that the Jeffreys' prior should not be automatically accepted as a reference prior in all models—this needs to be decided on a case-by-case basis.

A comparison of gamma and lognormal maximum likelihood estimators in a sequential population analysis

We analyze the model used to assess most major commercial marine fish populations, namely, sequential population analysis (SPA). This model estimates population abundance by combining catch-at-age data with research surveys or commercial catch per unit effort indices of abundance. We examine two maximum likelihood estimators of SPA parameters. These estimators are based on assuming that the stock-size indices are from lognormal or gamma distributions. Using simulations, we find that both types of estimators can have significant biases; however, our results indicate that it is preferable to use the gamma model, because it tends to have lower bias and variability, even when the true distribution of the stock-size indices is lognormal.

A comparison of gamma and lognormal ma×imum likelihood estimators in a sequential population analysis

A comparison of gamma and lognormal ma×imum likelihood estimators in a sequential population analysis

Interpreting the collapse of the northern cod stock from survey and catch data

Sequential population analysis reconstructions of the northern cod (Gadus morhus) stock using survey and catch data formed the basis for the scientific advice for substantial reductions in catch quotas in the late 1980s. However, the model failed to provide acceptable reconstructions of the population in subsequent stock assessments when data for the 1990s were added. The model assumes constant age-independent instantaneous rate of natural mortality, accurate catch reporting, and a constant linear relationship between the survey index at age and the population size at age. It seems likely that one or more of these assumptions failed to hold around the time of the collapse. Diagnostic studies were carried out to determine the magnitude of the departure from the assumptions required to allow the model to fit the data. Information related to changes in natural mortality, fishing activity, and survey catchability is reviewed to evaluate the plausibility of departures from model assumptions of the magnitude estimated. It is concluded that unreported deaths caused by the offshore fishery may be most plausible as the main contributing factor to lack of model fit but that factors such as increased natural mortality, and possibly changes in survey catchability, also played a role.

Effect of water temperature on catchability of Atlantic cod (Gadus morhua) to the bottom-trawl survey in the southern Gulf of St Lawrence

Correlations between catch rates in bottom-trawl surveys and indices of environmental conditions or fish distribution have been attributed to effects of the environmental conditions or fish distribution on catchability to the survey. We tested this hypothesis using data on cod in the southern Gulf of St Lawrence. Survey catch rates of cod were significantly correlated with indices of bottom temperature and of cod temperature and depth distributions. Correlations were in the directions expected on the basis of predicted effects on catchability or availability to the survey. However, tests involving calibrations of sequential population analysis (SPA) or residuals from multiplicative analyses of the survey catch rates (with terms for yearclass, age and cumulative mortality) did not support the hypothesis that these correlations resulted from effects on catchability to the survey. These tests provided no support for an effect of cod temperature or depth distribution on catchability. They provided some support for an effect of bottom temperature conditions on availability to the survey, but this effect on availability was not reflected by the correlations observed between bottom temperature indices and survey catch rates. We conclude that adjustments for effects on catchability should be based on relationships with inconsistencies in survey catch rates instead of relationships with the catch rates themselves. These adjustments could be incorporated in calibration of the SPA or calculated based on relationships with residuals from models relating survey catch rate to yearclass, age and fishing mortality. However, such adjustments were negligible in the case of southern Gulf of St Lawrence cod. 2000 International Council for the Exploration of the Sea

Bayesian state-space modeling of age-structured data: fitting a model is just the beginning

Explicit modeling of process variability in the dynamics of fisheries is motivated by a desire to incorporate more realism into stock assessment models, and much recent research effort has been devoted to the computational features of fitting state-space models for this purpose. Here, we extend the Bayesian application of nonlinear state-space modeling to sequential population analysis of age-structured data using a model formulation that allows for unreported catches and incidental fishing mortality. It is shown that, once a familiarity with the general-purpose Bayesian software BUGS is acquired, implementing a state-space model is a relatively simple task. Indeed, this application requires just 18 lines of code in its entirety and does not require the programmer to know the formulae for any prior density functions or likelihoods. Consequently, we suggest that this methodology may permit the implementation phase of nonlinear state-space modeling to be relegated, thereby allowing more effort to be devoted to the challenging issues of model checking, selection/averaging, sensitivity, and prior specification.

The retrospective problem in sequential population analysis: An investigation using cod fishery and simulated data

The retrospective problem is a systematic inconsistency among a series of estimates of population size, or related assessment variables, based on increasing periods of data. In some stocks, this problem is of such magnitude that sequential population analyses (SPA) are deemed inapplicable. The eastern Scotian Shelf (ESS) cod fishery, which displays the retrospective problem, and simulated data are analysed to provide insight into the causes and potential solutions to this problem. The retrospective problem is shown to be a result of the traditional analysis techniques and a non-stationarity in the data used in the population analysis. A moving window analysis is developed which allows the non-stationarities to be identified and in some cases rectified. Recommendations are also made for ad hoc investigations of the data. The analysis suggests that failure to correct the retrospective problem for a stock with data like ESS cod could lead to catch-level advice that would be twice or more the intended level.

Estimating trends in fishing mortality at age and length directly from research survey and commercial catch data

Relative fishing mortality (R) is estimated directly as the ratio of commercial catch divided by a research vessel survey index of relative population abundance. If the survey is conducted near the middle of the fishing year, its catchability is constant, and the rate of catch reporting remains constant, R will be proportional to the actual fishing mortality (F). Trends in R will reflect trends in F. A case study is presented where R at age and length are compared with estimates obtained with sequential population analysis (SPA). They were found to be of similar magnitude and trend. This new method would be useful for stocks where SPA is not possible. It would also be a useful addition to analytical assessments where SPA is used; it provides estimates of relative F at length, it is insensitive to changes in natural mortality provided the research survey occurs close to the middle of the fishing year, and it provides useful diagnostics for interpreting SPA results.

A comparative analysis of recruitment variability in North Atlantic flatfishes — testing the species range hypothesis

The hypothesis that recruitment variation in flatfishes should be most variable at the northern edge of the species range, least near the centre of the range, and intermediate near the southern limit was tested using stock and recruitment data generated from sequential population analysis for several different flatfish stocks involving four species (plaice Pleuronectes platessa, sole Solea vulgaris from the eastern Atlantic, American plaice Hippoglossoides platessoides, and yellowtail flounder Limanda ferruginae from the western Atlantic). Several groundfish species have been found to conform to this so-called species range hypothesis with the suggestion that density-independent processes predominate at the edges of the distributional range and density-dependent processes dominate in the centre of the range. Our results were generally inconsistent with the hypothesis: the coefficient of variation (CV) of recruitment for plaice in the eastern Atlantic was independent of latitude, the CV of recruitment for sole exhibited a dome-shaped relationship with latitude with the highest CVs occurring at the mid-point of the range, and the CV of recruitment for the western Atlantic stocks exhibited a monotonic decrease with latitude. We extended our latitudinal analyses by assessing both the degree of dependency of recruitment on spawning stock biomass and the spatial and temporal scales of variability in recruitment and pre-recruit survival for the eastern Atlantic stocks. In general our analysis revealed no evidence of a strong stock and recruitment relationship for any of the stocks examined, and previously published analyses revealed no such patterns with latitude. Analysis of both de-trended recruitment and pre-recruit survival time series over the species ranges of sole and plaice revealed strong positive correlations among adjacent stocks and inverse correlations among stocks at the extremes of the range. Recruitment variation in the flatfish stocks examined appears to be dominated by density-independent factors, operating at a local scale, on the egg and larval stages.