Using Observed Residual Error Structure Yields the Best Estimates of Individual Growth Parameters

Obtaining the best possible estimates of individual growth parameters is essential in studies of physiology, fisheries management, and conservation of natural resources since growth is a key component of population dynamics. In the present work, we use data of an endangered fish species to demonstrate the importance of selecting the right data error structure when fitting growth models in multimodel inference. The totoaba (Totoaba macdonaldi) is a fish species endemic to the Gulf of California increasingly studied in recent times due to a perceived threat of extinction. Previous works estimated individual growth using the von Bertalanffy model assuming a constant variance of length-at-age. Here, we reanalyze the same data under five different variance assumptions to fit the von Bertalanffy and Gompertz models. We found consistent significant differences between the constant and nonconstant error structure scenarios and provide an example of the consequences using the growth performance index ϕ′ to show how using the wrong error structure can produce growth parameter values that can lead to biased conclusions. Based on these results, for totoaba and other related species, we recommend using the observed error structure to obtain the individual growth parameters.

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

Frontiers in Marine Science ◽

10.3389/fmars.2021.747382 ◽

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.

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An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f02-022 ◽

2002 ◽

Vol 59 (3) ◽

pp. 424-432 ◽

Cited By ~ 84

Author(s):

Graham M Pilling ◽

Geoffrey P Kirkwood ◽

Stephen G Walker

Keyword(s):

Random Effects ◽

Standard Method ◽

Growth Parameters ◽

Growth Parameter ◽

Individual Growth ◽

Reliable Estimate ◽

Random Effects Model ◽

Von Bertalanffy ◽

Data Set ◽

Growth Variability

A new method for estimating individual variability in the von Bertalanffy growth parameters of fish species is presented. The method uses a nonlinear random effects model, which explicitly assumes that an individual's growth parameters represent samples from a multivariate population of growth parameters characteristic of a species or population. The method was applied to backcalculated length-at-age data from the tropical emperor, Lethrinus mahsena. Individual growth parameter variability estimates were compared with those derived using the current "standard" method, which characterizes the joint distribution of growth parameter estimates obtained by independently fitting a growth curve to each individual data set. Estimates of mean von Bertalanffy growth parameters from the two methods were similar. However, estimated growth parameter variances were much higher using the standard method. Using the random effects model, the estimated correlation between population mean values of L[Formula: see text] and K was 0.52 or 0.42, depending on the marginal distribution assumed for K. The latter estimate had a 95% posterior credibility interval of 0.62 to 0.17. These represent the first reliable estimate of this correlation and confirm the view that these parameters are negatively correlated in fish populations; however, the absolute correlation value is somewhat lower than has been assumed.

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Consequences of assuming an incorrect error structure in von Bertalanffy growth models: a simulation study

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f07-036 ◽

2007 ◽

Vol 64 (4) ◽

pp. 602-617 ◽

Cited By ~ 40

Author(s):

J Paige Eveson ◽

Tom Polacheck ◽

Geoff M Laslett

Keyword(s):

Model Selection ◽

Growth Models ◽

Individual Variability ◽

Individual Growth ◽

Von Bertalanffy ◽

Selection Procedures ◽

Error Structure ◽

Growth Variability ◽

Length Data ◽

Data Coverage

The underlying sources of growth variability in a population cannot generally be known, so when modelling growth it is important to understand the consequences of assuming an incorrect error structure. In this study, four error models for a von Bertalanffy growth curve with asymptotic length parameter L∞ and growth rate parameter k are considered. Simulations are carried out in which data are generated according to one of the models and fitted assuming each of the models to be true. This is done for two types of data: direct age–length and tag–recapture. For direct age–length data, the consequences of not accounting for individual growth variability, or assuming the wrong source of variability, are minor, even when individual variability is high or data coverage is poor. For tag–recapture data, some substantial biases in growth estimates can arise when individual variability exists but is not accounted for. Importantly, however, incorporating variability in just one parameter (be it L∞ or k), even if the variability truly stems from the other or both parameters, generally leads to much smaller biases than assuming no individual variability. Often the alternative models cannot be distinguished using standard model selection procedures, so caution is warranted in using model selection to draw inferences about underlying sources of growth variability.

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Pertumbuhan dan Struktur Umur Kerang Kepah (Meretrix meretrix) di Kampung Nipah Desa Sei Nagalawan Kecamatan Perbaungan Kabupaten Serdang Bedagai

Journal of Marine and Aquatic Sciences ◽

10.24843/jmas.2018.v4.i02.316-323 ◽

2017 ◽

Vol 4 (2) ◽

pp. 316

Author(s):

Nafi Sakila ◽

Dinda Ayu Ramadhani ◽

Ani Suryanti

Keyword(s):

Natural Resources ◽

Random Sampling ◽

Growth Parameters ◽

Growth Parameter ◽

Sampling Technique ◽

Simple Random Sampling ◽

Sampling Time ◽

Size Group ◽

Age Group ◽

Von Bertalanffy

Sei Nipah has enormous potential for natural resources. Natural resources that serve as the main livelihood in fulfilling daily needs in Kampung Nipah is shellfish. Shellfish (M. meretrix) is one of the shells that many interested by the surrounding community. The purpose of this research is to know growth parameter and age group of shellfish (M. meretrix) in Kampung Nipah. The sampling technique was done randomly (simple random sampling). Sampling time is done at low tide. Sampling was conducted in March - May 2017. The results showed differences in the length of different shells each month. The size group of shellfish (M. meretrix) found only one size group during the three months of the study. Analysis of shellfish growth parameters based on data of long frequency distribution showed length of infiniti (L?) 33,10 mm and growth growth (K) that was 1,21 per month. Von Bertalanffy Growth Parameters Lt = 33.1 (1-e [-1.21 (t + 0.12)]) Long infiniti size is seen the growth of shellfish shells can no longer be worked Shells reach maximum length at the age of 13 months with a shell length of 33.10 mm.The youthful shells have rapid growth and as age increases, when it reaches old age the rate of growth will slow even.

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

International Journal of Agricultural and Environmental Information Systems ◽

10.4018/ijaeis.2019040103 ◽

2019 ◽

Vol 10 (2) ◽

pp. 49-81 ◽

Cited By ~ 1

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.

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Age and growth of the dog snapper Lutjanus jocu (Bloch & Schneider, 1801) in Abrolhos Bank, Northeastern Brazil

Neotropical Ichthyology ◽

10.1590/s1679-62252011005000024 ◽

2011 ◽

Vol 9 (2) ◽

pp. 393-401 ◽

Cited By ~ 9

Author(s):

Marília Previero ◽

Carolina V. Minte-Vera ◽

Matheus Oliveira Freitas ◽

Rodrigo Leão de Moura ◽

Claudenice Dei Tos

Keyword(s):

Growth Parameters ◽

Growth Models ◽

Fork Length ◽

Age And Growth ◽

Northeastern Brazil ◽

Constant Variance ◽

Males And Females ◽

Average Size ◽

Constant Coefficient Of Variation ◽

Estuarine Region

We determined the age and growth of the dog snapper (Lutjanus jocu), caught in the region of Abrolhos Bank, Bahia State, by the fishermen from coastal communities of Prado, Alcobaça, Caravelas, and Nova Viçosa. We examined 205 sectioned otoliths of fish caught by harpoon, longline, hand line, and gill nets (14.5 to 79.5 cm fork length). The formation of each ring was considered annual. The sectioned otoliths showed between 0 and 29 rings. Nearly half of the analyzed specimens had between 0 and 7 rings (88 of 205). Fish caught with nets in the estuarine region were the juvenile, while fish caught with lines and harpoons were the oldest. Two von Bertalanffy growth models were fitted to length-at-age data: one assuming constant variance of length-at-age (SVB) and another assuming constant coefficient of variation, i.e. variance increasing as a function of average size (CVVB). The SVB estimates were Loo = 87.82 cm, K = 0.10, and t0 = -1.486 and the CVVB estimates were Loo = 117.60 cm, K = 0.06, and t0 = -2.470. The largest Loo values estimated by the CVVB model are supported by reports from the literature of larger animals occurring in the deeper outer shelf of Abrolhos Bank. Growth parameters were also estimated for males and females separately (SVB model) (Loo = 92.80 cm, K = 0.099, and t0 = -1.680 for males, and Loo = 82.10 cm, K = 0.105, and t0 = -1.570 for females).

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

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f95-025 ◽

1995 ◽

Vol 52 (2) ◽

pp. 252-259 ◽

Cited By ~ 43

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.

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Are Growth Parameters Estimated from Tagging and Age–Length Data Comparable?

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f88-115 ◽

1988 ◽

Vol 45 (6) ◽

pp. 936-942 ◽

Cited By ~ 128

Author(s):

R. I. C. C. Francis

Keyword(s):

Growth Rate ◽

Growth Rates ◽

Growth Parameters ◽

Growth Models ◽

Maximum Length ◽

Fish Growth ◽

Data Sets ◽

Von Bertalanffy ◽

Length Data ◽

The Mean

The two most common ways of estimating fish growth use age–length data and tagging data. It is shown that growth parameters estimated from these two types of data have different meanings and thus are not directly comparable. In particular, the von Bertalanffy parameter l∞ means asymptotic mean length at age for age–length data, and maximum length for tagging data, when estimated by conventional methods. New parameterizations are given for the von Bertalanffy equation which avoid this ambiguity and better represent the growth information in the two types of data. The comparison between growth estimates from these data sets is shown to be equivalent to comparing the mean growth rate of fish of a given age with that of fish of length equal to the mean length at that age. How much these growth rates may differ in real populations remains unresolved: estimates for two species of fish produced markedly different results, neither of which could be reproduced using growth models. Existing growth models are shown to be inadequate to answer this question.

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Effects of intrapopulation variability on von Bertalanffy growth parameter estimates from equal mark–recapture intervals

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f97-110 ◽

1997 ◽

Vol 54 (9) ◽

pp. 2025-2032

Author(s):

E B Smith ◽

F M Williams ◽

C R Fisher

Keyword(s):

Growth Parameters ◽

Growth Parameter ◽

Parameter Estimates ◽

Growth Equation ◽

Size Distributions ◽

Von Bertalanffy ◽

Initial Size ◽

Estimation Errors ◽

Mark Recapture ◽

Intrapopulation Variability

The effects of intrapopulation variability on the parameter estimates of the von Bertalanffy growth equation have received discussion in the literature. Here we evaluated the effects of intrapopulation variability, using computer simulations, on four commonly used methods for estimating the von Bertalanffy growth parameters: the Ford-Walford plot, Ricker's method, Bayley's method, and Fabens' method. Intrapopulation variability in growth rates (k) and maximum sizes ( L infinity ) plus initial size distributions and measurement error, were tested for their effects on the accuracy of the parameter estimates using simulated mark-recapture data with equal recapture intervals. Fabens' method and a modified Ford-Walford plot provided the most accurate estimates in all cases, but when intrapopulation variability was large, they performed poorly. With moderate intrapopulation variability, the bias in estimates was small although between-sample variance was quite large. Biased initial size distributions without either small or large size classes cause a magnification of the estimation errors. Without knowledge of the degree of intrapopulation variability in a natural population, large errors of unknown magnitude in parameter estimation can result, and care should be taken when interpreting these estimates. However, if this variability can be quantified, then approximate parameter estimate errors can be obtained.

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