A Method for Finding the Limits of Application of the von Bertalanffy Growth Model and Statistical Estimates of the Parameters

1977 ◽  
Vol 34 (8) ◽  
pp. 1079-1084 ◽  
Author(s):  
Peter B. Bayley
Keyword(s):  
Growth Rate ◽  
Key Words ◽  
Growth Parameters ◽  
Instantaneous Growth Rate ◽  
Von Bertalanffy ◽  
Confidence Limits ◽  
Statistical Estimates ◽  
Length Relationship ◽  
Von Bertalanffy Growth Model ◽  
Age Range

The following expression is derived expressing the instantaneous growth rate (G) in terms of length (l) the power of the weight–length relationship (b), and the Bertalanffy growth parameters (K and L∞): G = bK(L∞/l − 1). Since this is valid for a length (or age) range in which growth conforms to the Bertalanffy model, a plot of G vs. 1/l should be linear with the intercept on the G axis being −bK and on the 1/l axis being 1/L∞. Since the variables can be measured independently, deviations of points from the regression can be tested and the limits of validity of the model ascertained. In addition, confidence limits of K and L∞ can be estimated. Two examples compare results with those using previous methods. Key words: method, Bertalanffy, growth, statistical, estimates, parameters

scholarly journals Fitting of von Bertalanffy growth model: Stochastic differential equation approach

2017 ◽  
Vol 64 (3) ◽  
Author(s):  
Prajneshu Gupta ◽  
Himadri Ghosh ◽  
N. N. Pandey
Keyword(s):  
Differential Equation ◽  
Rainbow Trout ◽  
Stochastic Differential Equation ◽  
Computer Code ◽  
Von Bertalanffy ◽  
Equation Approach ◽  
Length Relationship ◽  
Length Data ◽  
Von Bertalanffy Growth Model ◽  
Modelling Approach

In this paper, the well-known von Bertalanffy growth (VBG) model for estimating age-length relationship in fisheries is considered. It is emphasised that nonlinear estimation procedures should be adopted for fitting the von Bertalanffy nonlinear statistical (VBNS) model rather than the age-old Ford-Walford plot. Some limitations of employing VBNS modelling approach are highlighted. Employment of stochastic differential equation (SDE) approach, which does not suffer from these limitations, is advocated for fitting the VBG model. The methodology for fitting the von Bertalanffy SDE (VBSDE) model is described. Relevant computer code for fitting this model is written in SAS package and the same is included as an Appendix. Finally, as an illustration, superiority of VBSDE model over VBNS model for fitting and forecasting purposes is shown for rainbow trout (Onchorhynchus mykiss) age-length data.

scholarly journals In situ Growth Rate Assessment of the Hexactinellid Sponge Asconema setubalense Using 3D Photogrammetric Reconstruction

2021 ◽  
Vol 8 ◽  
Author(s):  
Elena Prado ◽  
Javier Cristobo ◽  
Augusto Rodríguez-Basalo ◽  
Pilar Ríos ◽  
Cristina Rodríguez-Cabello ◽  
...  
Keyword(s):  
Growth Rate ◽  
Marine Protected Area ◽  
Growth Parameters ◽  
Benthic Communities ◽  
Monitoring Program ◽  
Maximum Size ◽  
Point Clouds ◽  
Von Bertalanffy ◽  
3D Point Clouds ◽  
Novel Approach

We describe the first application of a non-invasive and novel approach to estimate the growth rate of Asconema setubalense (Porifera, Hexactinellida) through the use of 3D photogrammetric methodology. Structure-from-Motion techniques (SfM) were applied to videos acquired with the Politolana ROTV in the El Cachucho Marine Protected Area (MPA) (Cantabrian Sea) on three different dates (2014, 2017, and 2019) over six years. With these data, a multi-temporal study was conducted within the framework of MPA monitoring. A complete 3D reconstruction of the deep-sea floor was achieved with Pix4D Mapper Pro software for each date. Having 3D point clouds of the study area enabled a series of measurements that were impossible to obtain in 2D images. In 3D space, the sizes (height, diameter, cup-perimeter, and cup-surface area) of several A. setubalense specimens were measured each year. The annual growth rates recorded ranged from zero (“no growth”) for a large size specimen, to an average of 2.2 cm year–1 in cup-diameter, and 2.5 cm year–1 in height for developing specimens. Von Bertalanffy growth parameters were estimated. Taking into account the size indicators used in this study and based on the von Bertalanffy growth model, this sponge reaches 95% maximum size at 98 years of age. During the MPA monitoring program, a high number of specimens disappeared. This raised suspicions of a phenomenon affecting the survival of this species in the area. This type of image-based methodology does not cause damage or alterations to benthic communities and should be employed in vulnerable ecosystem studies and MPA monitoring.

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.

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

1988 ◽  
Vol 45 (6) ◽  
pp. 936-942 ◽  
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.

Sexual seasonal growth of the European anchovy (Engraulis encrasicolus) caught by mid-water trawl and purse seine in the southern Black Sea

2012 ◽  
Vol 93 (2) ◽  
pp. 333-339 ◽  
Author(s):  
Sabri Bilgin ◽  
Burak Taşçi ◽  
Hatice Bal
Keyword(s):  
Growth Rate ◽  
Black Sea ◽  
Growth Pattern ◽  
Growth Parameters ◽  
Purse Seine ◽  
Von Bertalanffy ◽  
Seasonal Growth ◽  
European Anchovy ◽  
Engraulis Encrasicolus ◽  
Males And Females

The seasonal growth pattern and size composition of the European anchovy, Engraulis encrasicolus caught by mid-water trawl and purse seine was studied in the southern Black Sea between October 2010 and April 2011. Total length (TL) and size distribution of females caught by purse seine was higher than males and females obtained from mid-water trawl (P < 0.05). The seasonal von Bertalanffy growth parameters, computed from monthly length–frequency distributions, were estimated as asymptotic length to which the fish grow (L∞) = 13.01 cm TL, growth-rate parameter (K) = 0.993 year−1, amplitude of the sinusoidal growth oscillations (C) = 0.800, and the time of the year when the growth rate is slowest, the winter period (WP) = 0.298 for males and as L∞ = 13.69 cm TL, K = 1.249 year−1, C = 0.950, and WP = 0.151 for females caught by mid-water trawl. The seasonal von Bertalanffy growth parameters for anchovy obtained from purse seine fishing in the Rize region were estimated as L∞ = 14.00 cm TL, K = 0.800 year−1, C = 0.980, and WP = 0.212 for males and as L∞ = 13.93 cm TL, K = 0.994 year−1, C = 0.725, and WP = 0.319 for females. The period of slowest growth for males and females estimated between February and April, which is the period with a relatively low water temperature and consequently anchovy in the southern Black Sea have a seasonal growth pattern.

scholarly journals Growth of European hake (Merluccius merluccius) in the Gulf of Lions based on conventional tagging

2009 ◽  
Vol 67 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Capucine Mellon-Duval ◽  
Hélène de Pontual ◽  
Luisa Métral ◽  
Loic Quemener
Keyword(s):  
Growth Rate ◽  
Sexual Maturity ◽  
Growth Parameters ◽  
Growth Parameter ◽  
Bay Of Biscay ◽  
Von Bertalanffy ◽  
Merluccius Merluccius ◽  
Size Frequency Distribution ◽  
Gulf Of Lions ◽  
European Hake

Abstract Mellon-Duval, C., de Pontual, H., Métral, L., and Quemener, L. 2010. Growth of European hake (Merluccius merluccius) in the Gulf of Lions based on conventional tagging. – ICES Journal of Marine Science, 67: 62–70. Growth of European hake was estimated from the results of a conventional tagging study in the Gulf of Lions, the first tagging experiment to have been undertaken on the species in Mediterranean waters. In all, 4277 hake 15–40 cm long were tagged and released on the inshore fishing grounds during spring 2006. The overall recapture rate was 6.5% and times-at-liberty ranged from 1 to 717 d. Growth rate in hake varied with size and sex. The estimated growth parameter (von Bertalanffy k) was estimated as double previously published values based on size frequency distribution in the area. Compared with recent growth parameters derived from the tagging experiments in the Bay of Biscay, k was estimated to be slightly lower in the Gulf of Lions. With this faster growth, hake would mature earlier than previously thought: at age 2 for both sexes, instead of at age 3 or 4 as currently accepted for the Mediterranean. Growth rate by sex decreased to a similar level once fish had attained sexual maturity.

Age and growth of a newly described barb, Capoeta coadi (Cyprinidae), in Beheshtabad River, Tigris basin

2020 ◽  
Vol 56 ◽  
pp. 26
Author(s):  
Yazdan Keivany ◽  
Masoud Siami
Keyword(s):  
Growth Rate ◽  
Life History ◽  
Sex Ratio ◽  
Age Groups ◽  
Fork Length ◽  
Age And Growth ◽  
Von Bertalanffy ◽  
Males And Females ◽  
Endemic Fish ◽  
Von Bertalanffy Growth Model

The Coad barb, Capoeta coadi Alwan, Zareian and Esmaeili, 2016, is a newly described endemic fish in Beheshtabad River, Tigris basin of Iran and little is known about its life-history. Life history characteristics were examined in 426 specimens collected monthly from Beheshtabad River (central Iran) during May 2013 to May 2014. The sex ratio was 1M:0.7F. Based on scale and opercular readings, the maximum ages of the population were 8+ years for females and 7+ for males. The most frequent age groups were 3+ and 4+ in males and females, respectively. Size varied from 8.94 to 42.95 cm in fork length and weight between 10.3 and 1255.5 g. Length–weight relationship implied that the growth was negatively allometric for both sexes. The von Bertalanffy growth model was estimated as Lt =35.97[1‑e‑0.205( t+0.586)] and Lt = 49.31[1‑e ‑0.162( t‑0.208)] for males and females, respectively. The growth performance index was estimated as 5.58 and 5.97 for males and females, respectively, indicating a faster growth rate for females.

scholarly journals Age and growth of the deep water mud shrimp Solenocera melantho (De Man, 1907) off Visakhapatnam coast, India

2016 ◽  
Vol 63 (4) ◽  
Author(s):  
P. R. C. Ganesh ◽  
Myla. S. Chakravarty
Keyword(s):  
Growth Model ◽  
Deep Water ◽  
Growth Parameters ◽  
Age And Growth ◽  
Von Bertalanffy ◽  
Males And Females ◽  
Von Bertalanffy Growth Model ◽  
Mud Shrimp ◽  
De Man ◽  
Visakhapatnam Coast

Age and growth of the deep water mud shrimp Solenocera melantho (De Man, 1907) was estimated using von Bertalanffy growth model employing modal progression analysis, Ford-Walford method for L∞ and K and t0 by Gulland’s method as well as ELEFAN I (FiSAT II software version 1.2.2) method. The growth parameters estimated by the former method were: L∞= 107.9 mm, K = 2.61 y-1, t0 = 0.1344, φ’ = 4.4825 for males and L∞ = 116.4 mm, K = 3.69 y-1, t0 = 0.1346, φ’ = 4.6997 for females and by the latter method were : L∞ = 106.1 mm, K = 2.17 y-1, t0 = -0.05, φ’ = 4.3879 for males and L∞ = 116.8 mm, K = 2.1 y-1, t0 = -0.05, φ’ = 4.4571 for females. The longevity estimated for both males and females of S. melantho was about 36 months. The females were observed to grow faster than the males.

scholarly journals DINAMIKA POPULASI DAN LAJU PEMANFAATAN IKAN BANDENG (Chanos chanos) DI WADUK SEMPOR, JAWA TENGAH

2018 ◽  
Vol 10 (1) ◽  
pp. 29
Author(s):  
Aisyah Aisyah Aisyah ◽  
Chairulwan Umar ◽  
Setiya Triharyuni ◽  
Husnah Husnah
Keyword(s):  
Growth Rate ◽  
Mortality Rate ◽  
Logistic Model ◽  
Condition Factor ◽  
Growth Parameters ◽  
Total Mortality ◽  
Von Bertalanffy ◽  
Chanos Chanos ◽  
Weight Relationship ◽  
Exploitation Rate

Ikan bandeng (Chanos chanos) di Waduk Sempor diintroduksi pada tahun 2014 melalui penerapan teknologi perikanan tangkap berbasis budidaya (Culture Based Fisheries, CBF). Penelitian ini bertujuan untuk mengevaluasi pertumbuhan bandeng melalui pengamatan parameter pertumbuhan dan biologi populasinya di Waduk Sempor, Jawa Tengah. Data yang dianalisis diperoleh dari hasil pencatatan enumerator periode September 2014 sampai– Desember 2015. Kajian dinamika populasi ikan bandeng yang meliputi laju pertumbuhan, laju kematian dan tingkat pemanfaatan mengacu pada persamaan Von Bertalanffy dan turunannya. Aspek biologi meliputi hubungan panjang berat mengacu pada model logistik, serta faktor kondisi, keseluruhan analisis dilakukan secara manual dengan program excel 2007. Hasil penelitian menunjukan bahwa parameter pertumbuhan panjang-asimtotik L∞ = 55,97 cm TL dan K= 0,38 per tahun. Laju kematian total (Z) = 1,17 per tahun, kematian alami (M) = 0,56 per tahun, kematian akibat penangkapan (F) = 0,61 per tahun serta laju eksploitasi (E) = 0,5. Pertumbuhan populasi dan laju pemanfaatan menunjukkan bahwa bandeng sudah dimanfaatkan secara optimal oleh masyarakat di sekitar Waduk Sempor.  Milkfish (Chanos chanos) was introduced at 2014 in Sempor Reservoir through culture based fisheries (CBF) technology. This study aims to evaluate population growth of the milkfish in Sempor Reservoir. Data were collected from September 2015 to December 2016, and were analyzed using excel 2007 programe manually. Analysis of length-weight relationship is refers to logistic model, population dynamic like growth rate, mortality and mortality rate are refers to Von Bertalanffy and differentiate of it. Biology of population like length-weight relationship are refers to logistic model, and condition factor. The results showed that growth parameters were L∞ = 55.97 cm TL and K = 0.38 year-1. Total mortality (Z) = 1.17 year-1; M = 0.56 year-1; F = 0.61 year-1; and E=0.5. The growth rate and exploitation rate of Milkfish (Chanos chanos) in Sempor Reservoir has been utilized optimally.

A stage-explicit expression of the von Bertalanffy growth model for understanding age at first reproduction of Great Lakes fishes

2002 ◽  
Vol 59 (2) ◽  
pp. 250-261 ◽  
Author(s):  
Ji X He ◽  
Donald J Stewart
Keyword(s):  
Growth Rate ◽  
Great Lakes ◽  
Body Length ◽  
Growth Parameters ◽  
Growth Potential ◽  
Growth Trajectories ◽  
Annual Growth Rate ◽  
Von Bertalanffy ◽  
Age At First Reproduction ◽  
First Reproduction

An initial annual growth rate of body length and its regular decrease with increasing age has general linkages with age at first reproduction (tR). We clarify their combinations and develop predictive functions. We use a complete Ford–Walford plot with yearling size (L1) on the y axis and show a slope transition between the relative yearling growth rate (ρy) and the Ford–Walford slope (ρ). The three stage-specific variables define a complete body-length trajectory over ages, including all von Bertalanffy growth parameters and the Ford–Walford intercept (Lint). The difference between asymptotic length (Linf) and yearling length is growth potential after the first annulus. Yearling growth is a transition period, so growth potential can be adjusted as ρLinf or Linf – Lint. Changes in the three life-stage variables have contrasting effects on growth potential and von Bertalanffy growth parameters, so they have contrasting relations with tR. For most invertebrate-eating fishes in the Laurentian Great Lakes, dominant changes in growth trajectories were reflected in ρ, so tR was predicted by the von Bertalanffy growth coefficient, K. For walleye (Stizostedion vitreum) populations around the Great Lakes, dominant changes in growth trajectories were from yearling size or yearling growth, so tR was predicted using Lint. Our results have clear implications for understanding fish population dynamics.

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