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>

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

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.

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

von Bertalanffy growth model in a random environment

1999 ◽  
Vol 56 (6) ◽  
pp. 1026-1030 ◽  
Author(s):  
Prajneshu ◽  
R Venugopalan
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Growth Model ◽  
Gaussian White Noise ◽  
Pearl Oyster ◽  
Pinctada Fucata ◽  
Von Bertalanffy ◽  
Gaussian Stochastic Process ◽  
Length Relationship ◽  
Von Bertalanffy Growth Model

The well-known von Bertalanffy growth model for describing age-length relationship is formulated in a randomly fluctuating environment. The fluctuations in the system are assumed to be described by a Gaussian white noise stochastic process. The resulting model, in terms of a stochastic differential equation, is solved analytically. It is shown that the probability density function of length of a fish is a Gaussian stochastic process. Finally, as an illustration, the methodology is applied to a set of pearl oyster (Pinctada fucata (Gould)) data.

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.

Sign in / Sign up

Export Citation Format

Share Document