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.

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.

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.

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.

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.

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 Growth parameters of Poecilia latipinna (Lesueur, 1821) (Actinopterygii, Poeciilidae) – an introduced species in brackish water of Wadi Al-Bahayes (Oman)

2021 ◽  
Vol 50 (3) ◽  
pp. 269-277
Author(s):  
Salim Serkan Güçlü ◽  
Saud M. Al Jufaili ◽  
Laith A. Jawad
Keyword(s):  
Growth Performance ◽  
Alien Species ◽  
Condition Factor ◽  
Growth Parameters ◽  
Growth Equation ◽  
Von Bertalanffy ◽  
Poecilia Latipinna ◽  
Weight Relationship ◽  
The Mean ◽  
Von Bertalanffy Growth Equation

Abstract This work is one of the first studies on the growth of Poecilia latipinna outside its natural habitat. The objective of our study was to investigate the growth parameters of the population of P. latipinna, which is an alien species in Oman (Wadi Al-Bahayes). The population structure of P. latipinna in Wadi Al-Bahayes (Oman; 23°40′47″N; 58°11′36″E) was studied in June and August 2020, using 124 fish. In the course of this study, the number of individuals of each sex, age, weight and size composition were determined. In addition, the total length–weight relationship (LRW) was calculated, as well as the von Bertalanffy growth equation. The mean growth performance (phi prime) and the condition factor were calculated. Males accounted for 37.10% and females for 62.90% of the population. The length–weight relationship and the von Bertalanffy growth equation were W = 0.0214 × L 2.7889 R2 = 0.9212, Lt = 11.46 (1 − e −0.127 (t + 2.71)) for males and Lt = 14.51 (1 − e−0.072 (t + 3.98)) for females. The mean growth performance and the condition factor were calculated as 1.22 for males and 1.18 for females and 1.54 for all specimens. The study shows that the population of the species is characterized by a wide age range. Consequently, monitoring of this alien species is highly recommended.

scholarly journals Several Growth Characteristics of an Invasive Cyprinid Fish (Carassius gibelio Bloch, 1782)

2013 ◽  
Vol 5 (2) ◽  
pp. 133-138 ◽  
Author(s):  
Sait BULUT ◽  
Ramazan MERT ◽  
Beklan ALGAN ◽  
Musa ÖZBEK ◽  
Bülent ÜNAL ◽  
...  
Keyword(s):  
Condition Factor ◽  
Growth Parameters ◽  
Gibel Carp ◽  
Growth Equation ◽  
Von Bertalanffy ◽  
Age Composition ◽  
Carassius Gibelio ◽  
The Mean ◽  
Von Bertalanffy Growth Equation ◽  
Index Value

Age composition, length-weight relationships, growth, and condition factors of the gibel carp (Carassius gibelio Bloch, 1782) were determined using specimens collected from Seyitler Reservoir between July 2005 to June 2006. A total of 149 gibel carp were observed and examined. The age composition of the samples ranged between I and VII years of age. It has been determined than 82.55% of the obtained samples are comprised of females, 16.11% is comprised of males and 1.34% is comprised of immature. The population is dominated by females able to reproduce gynogenetically. The mean fork lengths and mean weights of the population were 14.8-32.5 cm and 43.1-807.3 g respectively. The length-weight relation were calculated as W = 0.0696 L2.132, r=0.838 for females, for males W = 0.2942 L2.6417 r=0.784 and W = 0.0274 L2.9382, r=0.813 for all samples. The mean Fulton Condition Factor was calculated as 2.342 for females, 2.064 for males and 2.276 for all samples. Age-length and age-weight relations were determined according to von Bertalanffy growth equation formula. Growth parameters of the population were Lt = 48.09 [1-e-0.093(t+0.29)], and Wt=2323.62 [1-e-0.093(t+0.29)]2.9382. The growth performance index value (Ø´) was computed as 5.37 for all specimens.

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