Accounting for individual variability in the von Bertalanffy growth model

1995 ◽  
Vol 52 (7) ◽  
pp. 1368-1375 ◽  
Author(s):  
Yoy-Gan Wang ◽  
Mervyn R. Thomas
Keyword(s):  
Growth Parameters ◽  
Research Effort ◽  
Growth Increment ◽  
Individual Variability ◽  
Individual Growth ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Full Account ◽  
Conditional Expectations ◽  
The Individual

Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury (1980, Can. J. Fish. Aquat. Sci. 37: 241–247) much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation. This bias is found to be similar to that of the Fabens method. Such methods would be appropriate only under the assumption that the individual growth parameters that generate the growth increment were independent of the growth parameters that generated the initial length. However, such an assumption would be unrealistic. The results are derived analytically, and illustrated with a simulation study. Until techniques that take full account of the appropriate conditioning have been developed, the effect of individual variability on growth has yet to be fully understood.

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.

A maximum likelihood approach for estimating growth from tag–recapture data

1995 ◽  
Vol 52 (2) ◽  
pp. 252-259 ◽  
Author(s):  
You-Gan Wang ◽  
Mervyn R. Thomas ◽  
Ian F. Somers
Keyword(s):  
Maximum Likelihood ◽  
Growth Parameters ◽  
Profile Likelihood ◽  
Individual Variability ◽  
Maximum Length ◽  
Individual Growth ◽  
Von Bertalanffy ◽  
Maximum Likelihood Approach ◽  
Penaeus Semisulcatus ◽  
Likelihood Approach

The Fabens method is commonly used to estimate growth parameters k and l∞ in the von Bertalanffy model from tag–recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use of the measurements at tag and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag–recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

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 Growth Parameters and Spawning Season Estimation of Four Important Flyingfishes in the Kuroshio Current Off Taiwan and Implications From Comparisons With Global Studies

2022 ◽  
Vol 8 ◽  
Author(s):  
Shui-Kai Chang ◽  
Tzu-Lun Yuan ◽  
Simon D. Hoyle ◽  
Jessica H. Farley ◽  
Jen-Chieh Shiao
Keyword(s):  
Growth Parameters ◽  
Growth Models ◽  
Growth Parameter ◽  
Optimal Growth ◽  
Kuroshio Current ◽  
Parameter Estimates ◽  
Special Importance ◽  
Von Bertalanffy ◽  
Multiple Model ◽  
The Kuroshio

Growth shapes the life history of fishes. Establishing appropriate aging procedures and selecting representative growth models are important steps in developing stock assessments. Flyingfishes (Exocoetidae) have ecological, economic, and cultural importance to many coastal countries including Taiwan. There are 29 species of flyingfishes found in the Kuroshio Current off Taiwan and adjacent waters, comprising 56% of the flyingfishes taxa recorded worldwide. Among the six dominant species in Taiwan, four are of special importance. This study reviews aging data of these four species, documents major points of the aging methods to address three aging issues identified in the literature, and applies multi-model inference to estimate sex-combined and sex-specific growth parameters for each species. The candidate growth models examined included von Bertalanffy, Gompertz, Logistic, and Richards models, and the resulting optimal model tended to be the von Bertalanffy model for sex-combined data and Gompertz and von Bertalanffy models for sex-specific cases. The study also estimates hatch dates from size data collected from 2008 to 2017; the results suggest that the four flyingfishes have two spawning seasons per year. Length-weight relationships are also estimated for each species. Finally, the study combines the optimal growth estimates from this study with estimates for all flyingfishes published globally, and statistically classifies the estimates into clusters by hierarchical clustering analysis of logged growth parameters. The results demonstrate that aging materials substantially affect growth parameter estimates. This is the first study to estimate growth parameters of flyingfishes with multiple model consideration. This study provides advice for aging flyingfishes based on the three aging issues and the classification analysis, including a recommendation of using the asterisci for aging flyingfishes to avoid complex otolith processing procedures, which could help researchers from coastal countries to obtain accurate growth parameters for many flyingfishes.

scholarly journals Individual growth of Drepanotrema cimex (Pulmonata: Planorbidae) from Arenalcito pond, natural reserve multiple uses Martin García Island, Buenos Aires, Argentina

2013 ◽  
Vol 73 (4) ◽  
pp. 835-833
Author(s):  
M Martín-Stella ◽  
C Díaz-Ana ◽  
A Rumi
Keyword(s):  
Buenos Aires ◽  
Size Structure ◽  
Neotropical Region ◽  
Individual Growth ◽  
Buenos Aires Province ◽  
Von Bertalanffy ◽  
Natural Reserve ◽  
Multiple Uses ◽  
The Individual ◽  
Measured Water

The species of the genus Drepanotrema, most of them endemic to the Neotropical region, belong to the Planorbidae. Of the nine species of this genus, six are found in Argentina. The present investigation analysed the individual growth of Drepanotrema cimex in Arenalcito pond (34°11′ S, 58°15′ W), Martín García Island Natural Reserve of Multiple Uses, Buenos Aires Province, Argentina. A total of 14 samples were collected (n = 1931) from February 2006 to June 2007. Five environmental variables were measured: water temperature, dissolved oxygen (mg L–1), electrical conductivity (µS cm–1), total dissolved solids, and pH. The individual growth of the species was analysed mathematically by means of the von Bertalanffy equation, where: Lt = 5,6(1-e–2,0592 (t–0,293)). The parameter L∞ was estimated by the Ford-Walford Method. The population of D. cimex was characterised by a complex and dynamic size structure throughout the annual cycle. The analysis of the curves revealed unimodal (2006) and polymodal (April to June 2007) distributions, which pattern served to identify the existence of cohorts within the population studied.

Improved estimation of size-transition matrices using tag–recapture data

2014 ◽  
Vol 71 (9) ◽  
pp. 1385-1394 ◽  
Author(s):  
Luke R. Lloyd-Jones ◽  
Hien D. Nguyen ◽  
You-Gan Wang ◽  
Michael F. O’Neill
Keyword(s):  
Growth Model ◽  
Stock Assessment ◽  
Growth Increment ◽  
Individual Variability ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Transition Matrices ◽  
Time Step ◽  
Relative Age ◽  
Negative Growth

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Age and growth of forkbeard, Phycis phycis, in Portuguese continental waters

2013 ◽  
Vol 94 (3) ◽  
pp. 623-630 ◽  
Author(s):  
Ana Rita Vieira ◽  
Ana Neves ◽  
Vera Sequeira ◽  
Rafaela Barros Paiva ◽  
Leonel Serrano Gordo
Keyword(s):  
Growth Parameters ◽  
Growth Zone ◽  
Growth Increment ◽  
Age And Growth ◽  
Von Bertalanffy ◽  
Commercial Species ◽  
Marginal Increment ◽  
Slow Growing ◽  
Annual Growth Increment ◽  
Phycis Phycis

The forkbeard, Phycis phycis, is an important commercial species in Portugal; however, little information is available on its biology. Age and growth of the forkbeard from Portuguese continental waters were studied using 687 otoliths from specimens caught between May 2011 and December 2012. Otoliths were transversally sectioned, and assigned ages were validated by marginal increment analysis and edge analysis, and indices of precision were also calculated to corroborate ageing within and between readers. Validation techniques showed that an annual growth increment is formed every year, corresponding to the succession of an opaque and a translucent growth zone. Specimens ranged from 15.5 to 67.1 cm total length (TL), and their estimated ages ranged between 0 and 18 years. The forkbeard is a relatively slow growing, long lived species, that does not show sexual dimorphism in growth. The von Bertalanffy growth parameters estimated for forkbeard from the Portuguese continental waters were L∞ = 75.14 cm TL, k = 0.10 yr−1 and t0 = −2.09 yr.

Well-Being Curves Across Transitions

2010 ◽  
Vol 69 (1) ◽  
pp. 15-29 ◽  
Author(s):  
Sonja Perren ◽  
Roger Keller ◽  
Marco Passardi ◽  
Urte Scholz
Keyword(s):  
Convergent Validity ◽  
Growth Parameters ◽  
Well Being ◽  
Situational Factors ◽  
Individual Growth ◽  
Personality Factors ◽  
Subjective Well Being ◽  
Retrospective Design ◽  
The Individual ◽  
Adaptation Processes

A newly developed instrument (retrospective well-being curves: WBC) was applied in two studies. In Study 1, a sample of 145 adults (M = 26.6 years) completed the WBC twice for different normative transitions. In Study 2, 151 university freshmen (M = 21.5 years) reported on their subjective well-being at 9 consecutive measurement points during their transition to university and completed the WBC at T10. In both studies, personality factors were assessed. Retest reliability of the individual growth parameters (intercept, linear, and quadratic change) was moderate to high (Study 1), whereas convergent validity of the growth parameters was moderate (Study 2). The results demonstrated distinct well-being trajectories for different transitions. Situational factors (e.g., timing) and personality factors (neuroticism and extraversion) were significantly associated with well-being. The results indicate that, although the use of the WBC may be limited by its retrospective design, the instrument provides a time-efficient way of measuring hedonic adaptation processes.

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