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

2002 ◽  
Vol 59 (3) ◽  
pp. 424-432 ◽  
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.

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

Fishes ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 35
Author(s):  
Marcelo V. Curiel-Bernal ◽  
E. Alberto Aragón-Noriega ◽  
Miguel Á. Cisneros-Mata ◽  
Laura Sánchez-Velasco ◽  
S. Patricia A. Jiménez-Rosenberg ◽  
...  
Keyword(s):  
Fish Species ◽  
Gulf Of California ◽  
Growth Parameters ◽  
Growth Models ◽  
Growth Parameter ◽  
Individual Growth ◽  
Von Bertalanffy ◽  
Error Structure ◽  
Endangered Fish ◽  
Constant Variance

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.

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

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.

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 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.

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.

scholarly journals Global Versus Non-Global Banks: A Capital Ratios-Based Analysis

2021 ◽  
Vol 10 (2) ◽  
pp. 5-22
Author(s):  
Konstantinos Drakos ◽  
Ioannis Malandrakis
Keyword(s):  
Panel Data ◽  
Financial Crisis ◽  
Random Effects ◽  
Financial Institutions ◽  
Random Effects Model ◽  
Data Set ◽  
Leverage Ratio ◽  
Total Capital ◽  
Capital Ratios ◽  
Global Banks

Abstract This paper examines the Leverage Ratio and Total Capital Ratio of global versus non-global banks in both the pre- and post-crisis periods. A panel data set of 165 global and non-global financial institutions from 38 countries is used for the period 1999-2015 and a random effects model is employed to examine whether global banks perform better or not compared to their non-global counterparts. This study comes up with two important findings. First, global banks do not exhibit heterogeneous behaviour with respect to both ratios neither in the pre- and especially nor in the post-crisis period. Second, the Leverage Ratio is crisis-insensitive, but the Total Capital Ratio is not. Our findings encourage further research on the topic of the contribution of global banks to the financial crisis propagation (at least as far as leverage is concerned).

scholarly journals 690Growth in childhood and age at menarche: Insights from individual trajectory modelling

2021 ◽  
Vol 50 (Supplement_1) ◽  
Author(s):  
Lynne Giles ◽  
Melissa Whitrow ◽  
Alice Rumbold ◽  
Michael Davies ◽  
Vivienne Moore
Keyword(s):  
Random Effects ◽  
Growth Parameters ◽  
Growth Parameter ◽  
Hazard Ratio ◽  
Age At Menarche ◽  
Parameter Estimates ◽  
Early Puberty ◽  
Random Effects Models ◽  
Childhood Growth ◽  
Menstrual History

Abstract Background The relationship between patterns of weight gain across childhood and the onset of puberty remains unclear. We aimed to derive growth parameters (size, tempo, and velocity) from models of weight across childhood and to estimate their effects on age at menarche. Methods Serial height and weight measurements from birth to age 9.5 years for 557 children who took part in the Generation 1 cohort study were used, along with girls’ menstrual history at age 12-13 years. Shape invariant random effects models were fit to log(weight+1) for all available participants’ data (282 girls, 260 boys), and AIC used to identify the best-fitting model. In time-to-event models subsequently fit to the girls’ data to estimate effects of the growth parameters on menarcheal age, a censoring age of 12 years was used to define early puberty. Results A model with 4df and fixed and random effects for size and tempo and a fixed effect for velocity was preferred. Some 19% of girls began menstruating before age 12 years. Size and tempo were each associated with an increased hazard of earlier menarche; a 0.1 unit gain in size was associated with a hazard ratio of 1.75 (95%CI 1.32–2.33), and a 0.1 unit gain in tempo with a hazard ratio of 7.84 (95%CI 3.41–18.05). Conclusions Using all participants’ data gave more precise growth parameter estimates. Key messages Understanding mechanisms that drive increased size and tempo of childhood growth may help to elucidate the links between obesity and girls’ risk of early puberty.

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

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.

scholarly journals Estimating growth parameters and growth variability from length frequency data using hierarchical mixture models

2019 ◽  
Vol 76 (7) ◽  
pp. 2150-2163
Author(s):  
Luke Batts ◽  
Cóilín Minto ◽  
Hans Gerritsen ◽  
Deirdre Brophy
Keyword(s):  
Mixture Models ◽  
Growth Parameters ◽  
Growth Parameter ◽  
Melanogrammus Aeglefinus ◽  
Parameter Estimates ◽  
Frequency Data ◽  
Length Frequency ◽  
Frequency Distributions ◽  
Growth Variability ◽  
Length Frequency Data

Abstract Analysis of length frequency distributions from surveys is one well-known method for obtaining growth parameter estimates where direct age estimates are not available. We present a likelihood-based procedure that uses mixture models and the expectation–maximization algorithm to estimate growth parameters from length frequency data (LFEM). A basic LFEM model estimates a single set of growth parameters that produce one set of component means and standard deviations that best fits length frequency distributions over all years and surveys. The hierarchical extension incorporates bivariate random effects into the model. A hierarchical framework enables inter-annual or inter-cohort variation in some of the growth parameters to be modelled, thereby accommodating some of the natural variation that occurs in fish growth. Testing on two fish species, haddock (Melanogrammus aeglefinus) and white-bellied anglerfish (Lophius piscatorius), we were able to obtain reasonable estimates of growth parameters, as well as successfully model growth variability. Estimated growth parameters showed some sensitivity to the starting values and occasionally failed to converge on biologically realistic values. This was dealt with through model selection and was partly addressed by the addition of the hierarchical extension.

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

2007 ◽  
Vol 64 (4) ◽  
pp. 602-617 ◽  
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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