Length-at-Age Analysis: Can You Get What You See?

1992 ◽  
Vol 49 (4) ◽  
pp. 632-643 ◽  
Author(s):  
T. J. Mulligan ◽  
B. M. Leaman
Keyword(s):  
Growth Model ◽  
Time Trend ◽  
Single Point ◽  
Mortality Rates ◽  
Individual Growth ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Model Ambiguity ◽  
Von Bertalanffy Growth Model ◽  
Single Set

Observations at a single point in time of length-at-age (LAA) for a long-lived rockfish (Sebastes alutus) show that old fish are shorter than intermediate-aged fish. Fitting of a von Bertalanffy growth model to these data produces a systematic trend in the residual of observed versus calculated LAA. We examined how such LAA data can lead to erroneous conclusions about individual growth, and whether asymptotic growth can give rise to such data. We considered two hypotheses: (i) that a time trend in growth rate resulted in larger fish in more recent years and (ii) that there are multiple growth types, where growth and mortality rates are directly related. Using a general growth model that incorporated both (i) and (ii), we show that both hypotheses can generate data identical to those for the rockfish. A single set of LAA data is inadequate for describing individual growth; however, if sufficient data are available, model ambiguity can be resolved and reasonable parameter estimates obtained. Analysis of the rockfish data indicates that (ii) is more likely to explain the observations than (i). We show how fisheries on such species may preclude our understanding these biological relationships.

Inferring the Distribution of the Parameters of the von Bertalanffy Growth Model from Length Moments

1988 ◽  
Vol 45 (10) ◽  
pp. 1779-1788 ◽  
Author(s):  
Robert L. Burr
Keyword(s):  
Growth Model ◽  
Joint Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Future Research ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Animal Populations ◽  
Von Bertalanffy Growth Model ◽  
Joint Probability Distributions

A theoretical approach is described for determining the joint distribution of the parameters of the von Bertalanffy growth model from statistical moments of length. The approach extends the work of K. J. Sainsbury, who had demonstrated that different mean parameter estimates are obtained by assuming that the von Bertalanffy equation applies to individual fish rather than to groups of fish. Sainsbury articulated the goal of studying the joint probability distributions of K and L∞ in animal populations and developed a maximum likelihood procedure for estimating the parameters of particular distributional forms describing K and L∞, which were assumed for mathematical convenience to be statistically independent. The primary goal of the present paper is to provide a framework for future research in generalizing Sainsbury's approach by considering (K, L∞) to be a random vector described by a joint probability density function and by allowing broader classes of distributions to be considered. Minimum cross-entropy (MCE) inversion, an information–theoretic methodology for approximating probability distributions, is shown to be effective in selecting a reasonable and unique joint distribution corresponding to observable length moments. Appealing features of the MCE methodology include the ability to include prior knowledge of uncertain applicability and the capacity of the resulting approximate distribution to represent potential stochastic dependencies between the von Bertalanffy parameters. Several numerical examples, using simulated and historical data, are presented to illustrate how information about the variation and covariation of L∞ and K can be inferred from a minimal set of length moments. The directions developed in this paper are far from a practical and useful methodology. The MCE inversion procedure is a "method of moments," with no statistical assessment of reliability. Further research is needed to make this promising pdf approximation scheme better suited for real fisheries problems.

Muskellunge Management: Fifty Years of Cooperation Among Anglers, Scientists, and Fisheries Biologists

2017 ◽  
Keyword(s):  
Growth Model ◽  
Mortality Rates ◽  
Fish Mortality ◽  
Minimum Length ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Mark Recapture ◽  
Passive Integrated Transponder ◽  
Reliable Parameter ◽  
Spring Lake

<em>Abstract</em>.—Accurate estimates of growth and mortality are important for management of recreational fisheries. Accurate age estimates often require the sacrifice of fish; thus, assessments of growth and mortality rates of trophy fishes such as Muskellunge <em>Esox masquinongy </em>often lack sufficient data. Mark–recapture history can be used as a nonlethal alternative to estimate growth and mortality in fishes. To determine the utility of this approach, we used data from a 17-year Muskellunge mark–recapture program conducted on two Illinois reservoirs (Kinkaid Lake and North Spring Lake). Von Bertalanffy parameter estimates by sex, lake, and tag type (passive integrated transponder and T-bar anchor tags) were obtained using a novel modification of the Fabens growth model and compared to von Bertalanffy growth estimates using known- or scale-aged fish. Mortality was calculated using both age- and length-based methods. Fabens growth model estimates of asymptotic length (<em>L</em><sub>∞</sub>) and growth coefficient (<EM>K</EM>) were within 6% (≤62 mm) and 23% (≤0.11) of corresponding von Bertalanffy growth model parameter estimates from known- or scale-aged fish by lake and sex. Provided that all sizes of fish are sampled, 4 years of mark–recapture data with more than 100 recaptures were found to be sufficient to produce reliable parameter estimates. Growth parameters differed between male fish tagged with passive integrated transponder or T-bar anchor tags but did not differ by tag type for females. Differences in Muskellunge growth and mortality rates between the two study lakes suggest that changing from a regionally applied minimum length limit to lake-specific minimum length limits may be warranted. Our results highlight the feasibility of mark–recapture data as a nonlethal technique to estimate population-specific growth and mortality rates for Muskellunge and the potential value of this approach in facilitating lake-specific Muskellunge management.

Growth of the saucer scallop, Amusium japonicum balloti Habe, in central eastern Queensland

1981 ◽  
Vol 32 (4) ◽  
pp. 657 ◽  
Author(s):  
MJ Williams ◽  
MCL Dredge
Keyword(s):  
Growth Model ◽  
Larval Stage ◽  
Size Range ◽  
Von Bertalanffy ◽  
Commercial Fishery ◽  
Long Distance ◽  
Von Bertalanffy Growth Model ◽  
Central Eastern

Tag-recapture data were used to determine growth and movement of A. japonicum balloti. The von Bertalanffy growth model was found to be suitable for describing growth in the latter half of the size range for A. japonicum balloti, and estimated S∞ of scallops varied with year and area. A. japonicum balloti grows rapidly, being recruited to the commercial fishery at about 6 months of age in some cases. Recapture data indicated that A. japonicum balloti does not undergo long-distance displacements in its post-larval stage.

Modelling individual variability in growth of bull trout in the Walla Walla River Basin using a hierarchical von Bertalanffy growth model

2016 ◽  
Vol 27 (1) ◽  
pp. 103-115 ◽  
Author(s):  
Julianne E. Harris ◽  
Courtney Newlon ◽  
Philip J. Howell ◽  
Ryan C. Koch ◽  
Steven L. Haeseker
Keyword(s):  
River Basin ◽  
Growth Model ◽  
Individual Variability ◽  
Bull Trout ◽  
Von Bertalanffy ◽  
Von Bertalanffy Growth Model ◽  
Walla Walla

scholarly journals Two-step Procedure Based on the Least Squares and Instrumental Variable Methods for Simultaneous Estimation of von Bertalanffy Growth Parameters

2019 ◽  
Vol 10 (2) ◽  
pp. 49-81 ◽  
Author(s):  
Ivelina Yordanova Zlateva ◽  
Nikola Nikolov
Keyword(s):  
Least Squares ◽  
Instrumental Variable ◽  
Initial Conditions ◽  
Growth Parameters ◽  
Individual Growth ◽  
Simultaneous Estimation ◽  
Parameter Estimates ◽  
Growth Equation ◽  
Von Bertalanffy ◽  
Step Procedure

Advanced in the present article is a Two-step procedure designed on the methods of the least squares (LS) and instrumental variable (IV) techniques for simultaneous estimation of the three unknown parameters L∞, K and t0, which represent the individual growth of fish in the von Bertalanffy growth equation. For the purposes of the present analysis, specific MATLAB-based software has been developed through simulated data sets to test the operational workability of the proposed procedure and pinpoint areas of improvement. The resulting parameter estimates have been analyzed on the basis of consecutive comparison (the initial conditions being the same) between the results delivered by the two-step procedure for simultaneous estimation of L∞, K and t0 and the results obtained via the most commonly employed methods for estimating growth parameters; first, use has been made of the Gulland-and-Holt method for estimating the asymptotic length L∞and the curvature parameter K, followed by the von Bertalanffy method for estimation of t0.

scholarly journals Evaluación de la pesquería de Lutjanus peru (Pisces: Lutjanidae) de . Guerrero, México

1969 ◽  
pp. 571-580
Author(s):  
Apolinar Santamaría ◽  
Ernesto A Chávez
Keyword(s):  
Growth Model ◽  
Population Analysis ◽  
Small Fish ◽  
Natural Mortality ◽  
Von Bertalanffy ◽  
Cohort Size ◽  
Virtual Population ◽  
Von Bertalanffy Growth Model ◽  
Parameter Values ◽  
Yield Per Recruit

Red snapper (Lutjanus peru) fishery was analyzed from landings and catch records. Stock age structure was reconstructed after the parameter values of the von Bertalanffy growth model, the length-weight relationship, ages and the natural mortality coefficient through each of nine years of cateh records. The Pisat software package was applied to assess population parameters, whose estimates are, for the von Bertalanffy growth model, K = 0. 1 442 to 0.38; lo = -0.2; L = 87 cm; W = 9.4 Kg, and the natural mortality coefficient (M) afier several methods (0. 14 to 0.38). Cohort size was assessed by the virtual population analysis (VPA), estlmating population size in 5.2* 1 06 fish with a biomass of 8 454 tonnes. Current fishing mortality P, ranges from 0.06 to 1 . 1 3, depending upon the chosen M value; according to this, when the M value used is low, the results suggest that the stock is nnderexploited, and vice versa. The yield per recruit model applied suggests improvements to the management strategy. The model indicates recruit overfishing because very small fish are the main target (te

scholarly journals Conditional Ulam stability and its application to von Bertalanffy growth model

2022 ◽  
Vol 19 (3) ◽  
pp. 2819-2834
Author(s):  
Masakazu Onitsuka ◽  
Keyword(s):  
Numerical Simulations ◽  
Growth Model ◽  
Von Bertalanffy ◽  
Ulam Stability ◽  
Von Bertalanffy Growth Model

<abstract><p>The purpose of this paper is to apply conditional Ulam stability, developed by Popa, Rașa, and Viorel in 2018, to the von Bertalanffy growth model $ \frac{dw}{dt} = aw^{\frac{2}{3}}-bw $, where $ w $ denotes mass and $ a &gt; 0 $ and $ b &gt; 0 $ are the coefficients of anabolism and catabolism, respectively. This study finds an Ulam constant and suggests that the constant is biologically meaningful. To explain the results, numerical simulations are performed.</p></abstract>

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