A length-structured population model, which incorporates von Bertalanffy growth, is used to describe changes in population abundance over time. The model is incorporated into a catch-at-length algorithm that uses a nonlinear least squares approach to estimate relative abundance, fishing mortality, selectivity, and the von Bertalanffy growth parameters L∞ and k. The algorithm is applied to a simulated data set for Pacific cod (Gadus macrocephalus) and to catch data on Pseudotolithus typus and Decapterus russellii. The parameter estimates of Pacific cod obtained from this algorithm were comparable with the values that were originally used to simulate the data. Although the catch data of P. typus did not exhibit the full range of sizes present in the population due to differential vulnerability of the population to the fishery, the estimates of L∞ and k reflect the growth over the entire size range of the population. Other population estimates for P. typus were in agreement with observed biological information. The estimated growth parameters L∞ and k of D. russellii showed some discrepancy with the information available on mature individuals present in this fishery but appeared to adequately represent year 1 growth. The estimated population and exploitation parameters fit the observed catch-at-length. Estimates made with the catch-at-length approach can be improved by using auxiliary information that may be available on abundance, fishing effort, recruitment, and growth.
We conducted a meta-analysis of growth for 46 species of the genus Sebastes in the eastern Pacific Ocean using a Bayesian hierarchical model to estimate parameters, to investigate growth variability, and to elucidate meaningful biological covariates. Growth in terms of maximum attainable size (L∞) ranged from 12 to 80 cm, and instantaneous growth rates varied by over an order of magnitude (K; 0.03–0.34·year–1). Results from this method also confirm the theoretical, but often untested, view that growth parameters L∞ and K are negatively correlated among populations or species of fish; Bayesian credibility intervals for correlation ranged from –0.2 to –0.7, with the posterior median of –0.4. The Bayesian hierarchical growth model showed less variability in growth parameters and lower correlations among parameters than those from standard techniques used in population ecology, suggesting that the absolute value of the correlation between L∞ and K may be lower than the general perception in the ecological literature. Exploration of several covariates revealed that asymptotic size varied positively as a function of the size at 50% maturity. Finally, posterior probability distributions of the hyperparameters from this analysis provide plausible informative priors of growth for stock assessments of data-poor species.
This is the first age determination study for Cynoscion albus, a large tropical sciaenid, using otolith morphology and daily increment analysis. The practicality of both methods for age determination is illustrated by their consistent estimates of age and von Bertalanffy growth parameters. The daily increment analysis was used to validate the surface readings. An alternative, otolith morphometrics, is shown to hold promise for rapid prediction of fish age. Two multivariate linear regression models using gross otolith dimensions can estimate the age of C. albus to within 1 year. Growth parameter estimates are: from surface readings: L=127.5cm with K=0.12; from daily increment readings: L= 122.1 cm with K=0.17. Implications for the stock assessment of tropical fish using size instead of age are discussed.
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