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Catch-AGE Analysis with Auxiliary Information
Canadian Journal of Fisheries and Aquatic Sciences
Abstract
We examined the use of catch-at-age data for estimating population abundance, productivity, and year-class abundance. A review section is included where various published models and our new models are shown to form a cohesive theory of catch-at-age analysis linked by level of model complexity. We developed three new models with different error structures: a log-normal measurement error model, a multinomial measurement error model, and a log-normal process error model. By application to data on Pacific halibut (Hippoglossus stenolepis), we show that moderate amounts of auxiliary information, such as fishing effort data or the assumption of a spawner–recruit relationship, are needed to stabilize estimates. The models performed very similarly with moderate amounts of auxiliary information, suggesting a degree of robustness to the underlying error structure. We also developed an extension to classic catch-curve analysis that estimates relative year-class strength reasonably well.
... The current assessment is done by the integrated catch analysis (ICA) method. This method has been evolved from the theory described by Fournier and Archibald (1982) to the practical applications described by Deriso et al. (1985), and to new applications by Patterson in recent herring assessments (Patterson and Melvin 1996). The approach is fundamentally to build a model to describe the data. ...
... The assessment model used is the integrated catch analysis (ICA) method. This method has been evolved from the theory described by Fournier and Archibald (1982) to the practical applications described by Deriso et al. (1985), and to new applications by Patterson in recent herring assessments (Patterson and Melvin 1996). On the basis of samples from the fishery, the catch is split in numbers per age group. ...
... , where λ 2 is the value of the explained variance of each index (Deriso et al. 1985, Methot 1989, Punt and Hilborn 1996. The maximization procedure was performed using the Excel Solver routine with the nonlinear generalized reduced gradient solving method. ...
... , donde λ 2 es el valor de varianza explicada de cada indicador (Deriso et al. 1985, Methot 1989, Punt y Hilborn 1996. El procedimiento de maximización se realizó mediante la rutina Solver de Excel con el método de resolución gradiente reducido generalizado no lineal. ...
Se evaluó el estado de explotación del marlin rayado en el Pacífico mexicano con datos históricos (1963-2014) de captura y esfuerzo de flotas comerciales y deportivas, incluso datos de captura incidental. Se estimaron 8 indicadores de abundancia relativa independientes para ajustar un modelo dinámico de biomasa por máxima verosimilitud. Para el periodo más reciente (2015-2019), se evaluó el estado de explotación a través de simulaciones hechas con el modelo ajustado, y se tomó como referencia los datos disponibles de captura por unidad de esfuerzo de las flotas deportivas. Los resultados indicaron que hasta 2014, la abundancia del marlin rayado ha pasado por 3 etapas diferentes. La primera fue una tendencia decreciente de 1964 a 1977, donde las capturas y el esfuerzo de las flotas comerciales excedieron, respectivamente, el máximo rendimiento sostenible (MRS) y el esfuerzo para alcanzar el MRS. La segunda ocurrió de 1977 a 1990, y fue una tendencia estable de baja abundancia, inferior a la abundancia cuando se alcanza el MRS; este cambio se relacionó con la reducción del esfuerzo de las flotas comerciales, aunque con capturas superiores al MRS. La tercera ocurrió de 1990 a 2014, y mostró una tendencia al incremento de la abundancia, debido al cese de operaciones de las flotas comerciales. Este incremento ha sido lento debido al desarrollo de la pesca deportiva y al incremento de las capturas incidentales. Después de 2014, el indicador para las flotas deportivas sugirió un cambio en la abundancia; de acuerdo con las simulaciones, la mortalidad por pesca fue insuficiente para explicar dicho cambio. Se plantea como hipótesis que la mortalidad natural del marlin rayado ha sido alta desde la década de 2010. Se discuten las condiciones que pudieron influir en esta situación y sus implicaciones en el manejo pesquero.
... When integrated analysis are used, they provide estimates of population parameters based on processes like recruitment, catchability, the adult stock-recruitment relationship, and fishing and natural mortality. Deriso et al. (1985) showed that the addition of auxiliary information (e.g., fishing effort) is typically required to constrain the analysis; therefore, the inclusion of fishery-dependent and fishery-independent data can be used for obtaining reliable population parameter estimates. The stock assessment is relevant for management purposes, because in Mexico, the Small Pelagic Species Fishery Management Plan establishes as reference point the maximum sustainable yield for Pacific sardine, and the control rule is defined according to this management quantity (DOF, 2012). ...
... ASAP is a forward-projection method following the standard and known equations of population dynamics proposed by Units: 1) average annual catch rate (tons); 2) annual tons (x 10 3 ); 3) number of Pacific sardine eggs and larvae standardize to 10 m 2 of sea surface; 4) number of egg and larvae sampled through cruises covering the central Gulf of California; 5) proportion (%) of Pacific sardine in the diet of Heermann's gulls and Elegant terns estimated from seabird regurgitations. Fournier and Archibald (1982); Deriso et al. (1985), and Methot (1989) for statistical catch-at-age analysis. The basic equations describing the population dynamics implemented in ASAP are contained in Table 2. ASAP is a multi-fleet stock assessment model; therefore, the catches and fishing mortalities can be fleetspecific. ...
Knowledge of the population dynamics and changes in the abundance of Pacific sardine fishery is relevant for fishery management. In this study, an integrated catch-at-age model (ASAP) was performed on 47 fishing seasons (1971−2018) of Sardinops sagax in the Gulf of California, including five indices of relative abundance (survey catch rate, acoustic surveys, egg and larvae, spawning probability, and bird diet index). The ASAP model showed the importance of age group 0 (recruits); this is the most important age group in the Pacific sardine fishery, and its abundance has consequences for the variability of the total abundance of the species. In this study, the spawning and acoustic indices denoted the changes in abundance of Pacific sardine population better than the survey catch rate and bird diet ratio. Historically, the total biomass is estimated to have varied from 461 thousand to 4.82 million t. In the 1970s and 1980s, a peak biomass close to three million tons was reached, and in the second peak from the mid-1990s to the late 2000s, the total biomass varied between 3.26 and 4.82 million t. When the spawning biomass was at least 750 x 10³ t, the recruitment (age group 0) showed high values, promoting high catches in the subsequent years. The annual fishing mortality estimates did not show a rise related to the periods of high harvestable biomass; therefore, the catch records were low in comparison to the harvestable biomass estimated from ASAP, and the annual fishing mortalities were less than 0.22 during periods of high abundance. The changes in biomass and the variability observed in the Pacific sardine fishery were validated for the model diagnostics; the retrospective patterns did not identify poor fits to data, therefore the robustness of the model can be used for management purposes. According to the Kobe phase plot, the Pacific sardine fishery in the Gulf of California has been fully exploited with an apparent stable level of harvest.
... From the age-structured matrix representation of Leslie (1945) and statistical catch-at-age analyses, dynamic length and stage-structured models were developed (Doubleday, 1976;Fournier and Archibald, 1982;Deriso et al., 1985;Gudmundsson, 1986Gudmundsson, , 1994Kimura, 1989). These were made general so that the model might be divided into categories for size, developmental stage, sex, or area (Usher, 1966(Usher, , 1971Sainsbury, 1982;Caswell, 1989;Sullivan et al., 1990;Sullivan, 1992). ...
This paper explores the possible options for quantitative fishery stock assessment in tropicalwaters and is composed of four layers viz., concepts, methodologies, data and indicators.The concept promotes the fundamental theory that has been popular in research on stockdynamics, including the possibility of combining it with various doses of intrinsicallybiological information, from individual fish to regional stocks. After reviewing the concepts,tools and their evolution, an attempt has also been made to propose a few guidelines as thebest ways to approach stock assessment and formulate input control or output regulationstrategies in the most pragmatic yet scientific manner, thereby ensuring minimal impact onthe fishery, fishers and stocks in the medium term. Keywords:Bayesian approach, Capture fisheries, Fish stockassessment, Models
... The shell length selectivity coefficient was analyzed using a gamma probabilistic density function, which provides greater flexibility to the curve allowing different selectivity patterns (Deriso et al., 1985). Thus, the selectivity function was expressed as follows (Carlson and Cortés, 2003): ...
The green abalone fishery in Mexico has showed declines in the availability of the resource, but the current state of the population is unknown. The aim of this study was to analyze inter-annual variation in recruitment, mortality, total and vulnerable biomass, selectivity, and harvest rate of Haliotis fulgens. A size-structured model was used to assess changes in the population dynamics and management quantities from 2010 to 2019. The model describes the exploitation and growth of individuals in the population, and incorporates a stochastic growth matrix that defines the variation in the length increments of individual to individual. Key results indi- cated that the recruitment failures occurred in infrequent pulses of varying intensity. Moreover, a slight recovery of total biomass during 2017 (791 t), 2018 (1496 t), and 2019 (1274 t) was observed after a slight increase in recruitment and a decrease in harvest rate. The vulnerable biomass increased 44.38% from 2010 to 2019. The harvest rate revealed that individuals larger than the minimum legal size of 145 mm were under high fishing pressure. The stock assessment model highlights an adverse effect in the population; given the deteriorating conditions of the green abalone fishery, it is imperative to transition fully to a recovery strategy, including all the administrative zones in the assessment and management. The adoption of proactive strategies such as the establishment of reference points, no-fishing reserves, and the implementation of a farming system would facilitate the protection of critical abalone populations, contributing to their medium-term recovery, and would be an economic alternative for local fishers.
... To estimate annual mortality, an age-structured model allowing for inter-annual variability in relative recruitment (Deriso et al. 1985; see also Smith et al. 2022) was fitted to age-composition data collected, each year, using gill nets in 2016-2018 in the SCE and in 2017-2018 in the PHE. The analysis assumed 'knife-edge' at Age 4 years, on the basis of selectivity analyses conducted by Smith et al. (2022), which showed N. vlaminghi becoming fully vulnerable to the gillnet sampling gear at ~180 mm. ...
Context
Fishing can reduce population biomass, allowing remaining individuals to grow faster and mature earlier because of greater resource availability, which potentially compensates for lost reproductive output over a shortened lifespan resulting from fishing mortality.
Aims
To compare life-history traits of Nematalosa vlaminghi, a long-lived (20 years), semi-anadromous fish endemic to south-western Australia, in exploited and unexploited populations living in similar environments.
Methods
Populations were sampled in 2016–2018. Total mortality (Z) was estimated using catch-curve analyses, allowing for annual recruitment variability. Maturation age and length was estimated by logistic regression analysis. Growth curves were fitted to length-at-age data.
Key results
Compared to the unexploited population, Z was 2.6 times greater, juvenile growth was more than twice as fast, and maturity was attained at least 3 years earlier in the unexploited population.
Conclusions
Results supported the hypothesis of faster growth in exploited populations because of density-dependent processes. Environmental factors may also have contributed to trait differences between populations.
Implications
Faster growth and earlier maturation may partly compensate for lost reproductive output in exploited populations, although severe age truncation owing to fishing is still likely to decrease population resilience in this species, irrespective of any compensatory density-dependent processes.
... Additionally, the CPUE index (catch/fishing trip) of the fleet during the fishing years 2000-2021 was incorporated into the model. This, as auxiliary information to stabilize the model and increase the precision in the estimation of the parameters (Deriso et al., 1985;Methot, 1989;Hilborn and Walters, 1992;Hilborn et al., 1994). Assuming observed CPUE is proportional to population abundance: ...
... The coefficient of variation was i i i CV according to the bootstrap approach. The mean of the bootstrap analysis represents the mean of the original parameter estimated (in this case M for time-interval) (Deriso et al., 1985), therefore the standard deviation of the bootstrap represents the standard error of estimated M. Our characterization of uncertainty was measured from standard error and mean in relation to M estimates. ...
The gnomonic-interval natural-mortality model (GIM) that provides an indicative vector of natural mortality (M) and of life history stage duration was applied to the jumbo squid (Dosidicus gigas) of the Gulf of California, Mexico. Estimate of M incorporated uncertainty because of fecundity variation. The variability in longevity and first stage duration were also explored for the estimations of M. We observed that M declines with age, independently of the duration of egg stage and of the longevity values and approached an asymptotic value for adult stage (M 5 per year). Compared with another iteroparous species, we found that jumbo squid which is assumed to be a semelparous species have relatively lower mortality rates during their early life stages and higher ones in their adult stages. The magnitude of the M values is greater when for its estimation the value of life spans is increased. A comparison of the G parameters (constant probability of death within each gnomonic interval) obtained with GIM for various species: jumbo squid (Dosidicus gigas), pink shrimp (Farfantepenaeus duorarum) and Pacific sardine (Sardinops caeruleus) reveals how differences in life-history strategy, fecundity and natural mortality might be related. Mortalidad natural y duración de los estadios del ciclo de vida del calamar gigante (Dosidicus gigas) en el Golfo de California, México, usando intervalos de tiempo gnomónico El modelo de intervalos gnomónicos (GIM) que proporciona índices del vector de mortalidad natural (M) y de la duración de los estadios del ciclo de vida fue aplicado al calamar gigante (Dosidicus gigas) del Golfo de California, México. Las estimaciones del vector de M incorporaron incertidumbre debida a la variación de la fecundidad. La variabilidad en la longevidad y en la duración del primer estadio del ciclo de vida fue también explorada para las estimaciones de M. Se observó que M declina con la edad independientemente de la duración del estadio huevo y de los valores de longevidad y, se aproxima a un valor asintótico en el estadio adulto (M 5 por año). Comparados con otras especies iteróparas, nuestros resultados indican que el calamar gigante, que se asume como especie semélpara, tiene bajas tasas de mortalidad durante los estadios tempranos del ciclo de vida y altas en los estadios de adulto. La magnitud de los valores de M es mayor cuando para su estimación se incrementa el valor de longevidad. La comparación del parámetro G (la probabilidad de muerte se mantiene constante dentro de cada intervalo gnomónico) obtenido con GIM para varias especies: calamar gigante (Dosidicus gigas), camarón rosado (Farfantepenaeus duorarum) y sardina del Pacífico (Sardinops caeruleus), explica cómo las diferencias en la estrategia del ciclo de vida, la fecundidad y la mortalidad natural pueden ser relacionadas. Palabras clave: Mortalidad natural, duración de los estadios del ciclo de vida, especie semélpara, especie iterópara.
... This could be explored using multi-year approaches to catch curve analysis involving approaches that estimate recruitment variability among year classes (e.g. relative abundance analysis, Deriso et al. 1985). If there is a strong link between juvenile recruitment, as measured from recruitment surveys, and recruitment strength as measured in the adult stock from catch curve analysis, this would suggest that the recruitment survey data are useful to management for predicting years of future high or low abundance. ...
Age validation is commonly based on the marginal increment ratio (MIR). This procedure has been used to validate the annual periodicity of growth band deposition. In this study, MIR data from geoducks Panopea globosa and Panopea generosa were analyzed using a new method for age validation based on a sinusoidal model. The model used four parameters, including the amplitude |d|, defined as half the distance between the highest and the lowest values of the function; r, which is the cycle from 0–2p; t, which is the horizontal shift; and l, which is the vertical shift, or displacement. When the parameters in the
Hulson, P-J. F., Hanselman, D. H., and Quinn, T. J. II. 2011. Effects of process and observation errors on effective sample size of fishery and survey age and length composition using variance ratio and likelihood methods. – ICES Journal of Marine Science, 68: 1548–1557.
Observations of age or length composition from fisheries or research surveys are modelled frequently with the multinomial distribution. Violations of multinomial assumptions in data collection usually cause overdispersion of observations and consequent underestimation of uncertainty. This has led to the adoption of an effective sample size less than the actual sample size to approximate the likelihood function for age or length composition better in, for example, fishery stock assessment models. The behaviour of effective sample size is examined under different scenarios for population age distribution and sampling design. Effective sample size was approximated with three approaches: (i) the ratio of multinomial to empirical variance; (ii) sampling estimation; and (iii) the Dirichlet likelihood. The most significant changes in effective sample size were attributable to process error involving aggregation of ages within schools. In terms of observation error, effective sample size can be increased by increasing the number of tows from which samples are obtained for age or length composition, then, because of the reduced uncertainty in effective sample size, the Dirichlet likelihood can be integrated into the objective function of fishery stock assessment models to estimate the effective sample size in future assessments.
Hulson, P-J. F., Hanselman, D. H., and Quinn II, T. J. 2012. Determining effective sample size in integrated age-structured
assessment models. – ICES Journal of Marine Science, 69:281–292.
Effective sample size (ESS) is a quantity that allows for overdispersion of variance and is used commonly in integrated age-structured
fishery assessment models to fit age-and-length-composition datasets. Owing to the sources of measurement, observation, process,
and model-specification errors, the ESS is smaller than the actual sample size. In this study, methods to set a priori or to estimate the ESS when confronted with datasets that include these sources of error were investigated. In general, a
number of methods previously proposed to incorporate the ESS resulted in accurate estimation of population quantities and
parameters when different sources of error were included in the data on age and length compositions. Three objective methods
to incorporate the ESS resulted in unbiased population quantities: (i) using sampling theory to derive the ESS from actual
age and length compositions, (ii) iteratively estimating the ESS with the age-structured assessment model, and (iii) estimating
the ESS as a parameter with the Dirichlet distribution.
A modified DeLury method to estimate fish population size from relative abundance data was developed. The method may be applied either with or without knowledge of the age composition of catch. In addition to estimating catchability coefficients, the technique accounts for error in the measurement of relative abundance. The technique is demonstrated using Northeast Fisheries Center bottom trawl survey data as a measure of relative abundance. Fitting was carried out for 4 fish populations: Georges Bank and Southern New England yellowtail flounder Limanda ferruginea; Georges Bank and NAFO SA 4X haddock Melanogrammus aeglefinus.-from Authors
The abundance of many stocks is estimated by fitting an age-structured model to catch-at-age and relative abundance data from the commercial fishery and scientific surveys. The natural mortality rate used in the model is usually estimated externally and its value is uncertain. An erroneous natural mortality rate will bias the stock size estimates obtained by fitting the model and will also bias the yield calculations that are done to choose a harvest rate and recommend quotas. This paper describes the general features of both effects by analyzing a simple age-structured model fitted to artificial data. It is shown that an erroneous natural mortality rate mainly affects the estimates of fishing mortality and hence abundance but not the estimates of age-specific selectivity. Errors in estimated abundance and target harvest rate are always in the same direction, with the result that, in the short term, extremely high exploitation rates can be recommended (unintentionally) in cases where the natural mortality rate is overestimated and historical exploitation rates in the catch-at-age data are low. A conservative (low) estimate of natural mortality can avoid that danger. Long-term yield under either an F-MSY or F-35% strategy is not very sensitive to error in natural mortality rate unless it is grossly underestimated.
Geoduck (Panopea globosa and Panopea generosa) fisheries regulations in the Gulf of California and Baja California Peninsula, Mexico, are based on a minimum legal size (shell length, 130 mm), limited bed harvests with densities greater than 0.4 geoduck/m2, maximum allowable catch, and restrictions on fishing activity on identified beds. Data on age structure and growth rate for geoducks could greatly improve fisheries management in the region; however, variability in size-at-age data for geoducks has made it difficult to develop a sound management strategy, and the presence of outliers in the data have influenced parameter estimates significantly. Different probability density functions can be applied as fat-tail distributions in mixture probability distributions. In the current study, outlier effects on candidate growth models in P. globosa were analyzed, as well as model performance when parameters were estimated using a two-component mixture probability distribution function. The best candidate growth model was selected based on the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Results suggest that growth models analyzed yielded an estimated asymptotic length larger than 160 mm in shell length. The logistic growth model was selected following the AIC, whereas the von Bertalanffy growth model was based on the BIC. A lack of congruence between the two statistics indicated insufficient evidence in P. globosa size-at-age data to support a best candidate growth model. It is suggested that growth compensation (when cohort size-at-age variability decreases with time or age) was operating in the population evaluated. Consequently, the size-at-age data were more scattered for younger individuals compared with older ones.
SURBAR is a survey-based fisheries stock assessment model that is used to indicate relative stock dynamics and provide advice for both data-rich and data-poor fisheries. It is a relatively simple separable model that requires only a survey index-at-age to determine stock trends (although data on weights and maturity can also be included). This paper evaluates the characteristics and potential utility of SURBAR by applying it to data generated by the model itself, considering the impact of three parameters (survey noise, smoothing, and the time of year of the survey) on the ability of the model correctly to reconstruct self-generated populations. We show that, while SURBAR is generally able to achieve this reconstruction, errors can be induced by either of the three tested parameters that may not be detectable by standard goodness-of-fit measures, and which could lead to inappropriate management advice. The analysis emphasises the importance of understanding the likely characteristics and behaviour of the model before using it to provide advice on fisheries stock dynamics.
Over a 7-year period more than 50 000 smolts were tagged in the Rivers Usk, Wye, and Severn. A total of 228 of these fish
was subsequently recaptured: 19 were taken at West Greenland; 3 were taken in British waters away from the Bristol Channel;
and a further 100 fish were taken in tidal waters in the Severn estuary and Bristol Channel area. Of the remaining 106 salmon
recaptured above tidal limits in home waters, 97 (92 %) were in their parent rivers, while 9 (8 %) had strayed to the freshwater
reaches of other rivers.
Punt, A. E., Huang, T., and Maunder, M. N. 2013. Review of integrated size-structured models for stock assessment of hard-to-age crustacean and mollusc species. – ICES Journal of Marine Science, 70:16–33.
Crustaceans and molluscs such as crabs, rock lobsters, prawns, abalone, and oysters constitute large and valuable fisheries. However, assessments of these species are hampered because they cannot be production aged, in contrast to many teleosts. The major data sources for these species, in addition to catch and abundance index data, are the size compositions of the catches and of any fishery-independent indices. Assessments of such species have been conducted using age-based methods of stock assessment, as well as surplus production models. However, size-structured methods are now preferred because they can make full use of size-composition data, are able to integrate multiple sources of data, and produce the types of outputs which are needed for management purposes. An advantage of size-based models over age-based models is that all processes can be size-based, and these processes can modify the (unmodelled) size-at-age distribution. We review these methods, highlighting the choices that need to be made when developing integrated size-structured stock assessments, the data sources which are typically available and how they are used for parameter estimation, and contrast a number of such assessments worldwide.
Interpretation of data used in fisheries assessment and management requires knowledge of population (e.g. growth, natural
mortality, and recruitment), fisheries (e.g. selectivity), and sampling processes. Without this knowledge, assumptions need
to be made, either implicitly or explicitly based on the methods used. Incorrect assumptions can have a substantial impact
on stock assessment results and management advice. Unfortunately, there is a lack of understanding of these processes for
most, if not all, stocks and even for processes that have traditionally been assumed to be well understood (e.g. growth and
selectivity). We use information content of typical fisheries data that is informative about absolute abundance to illustrate
some of the main issues in fisheries stock assessment. We concentrate on information about absolute abundance from indices
of relative abundance combined with catch, and age and length-composition data and how the information depends on knowledge
of population, fishing, and sampling processes. We also illustrate two recently developed diagnostic methods that can be used
to evaluate the absolute abundance information content of the data. Finally, we discuss some of the reasons for the slowness
of progress in fisheries stock assessment.