scholarly journals On the exponent in the von Bertalanffy growth model

2017 ◽  
Author(s):  
Katharina Renner-Martin ◽  
Norbert Brunner ◽  
Manfred Kühleitner ◽  
Georg Nowak ◽  
Klaus Scheicher
Keyword(s):  
Information Criterion ◽  
Growth Function ◽  
Data Sets ◽  
Scaling Exponent ◽  
Von Bertalanffy ◽  
Metabolic Scaling ◽  
Von Bertalanffy Growth Function ◽  
Definition Of ◽  
Growth Of Animals ◽  
Best Fit

Bertalanffy proposed the differential equation m´(t) = p × m (t) a –q × m (t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Using the Akaike information criterion it proposes a testable definition of ‘weak universality’ for a taxonomic group of species. (It roughly means that a model has an acceptable fit to most data sets of that group.) This definition was applied to 60 data sets from literature (37 about fish and 23 about non-fish species) and for each dataset an optimal metabolic scaling exponent 0 ≤ a opt < 1 was identified, where the model function m(t) achieved the best fit to the data. Although in general this optimal exponent differed widely from a = 2/3 of the VBGF, the VBGF was weakly universal for fish, but not for non-fish. This observation supported the conjecture that the pattern of growth for fish may be distinct. The paper discusses this conjecture.

scholarly journals On the exponent in the von Bertalanffy growth model

2017 ◽  
Author(s):  
Katharina Renner-Martin ◽  
Norbert Brunner ◽  
Manfred Kühleitner ◽  
Georg Nowak ◽  
Klaus Scheicher
Keyword(s):  
Information Criterion ◽  
Growth Function ◽  
Data Sets ◽  
Scaling Exponent ◽  
Von Bertalanffy ◽  
Metabolic Scaling ◽  
Von Bertalanffy Growth Function ◽  
Definition Of ◽  
Growth Of Animals ◽  
Best Fit

Bertalanffy proposed the differential equation m´(t) = p × m (t) a –q × m (t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Using the Akaike information criterion it proposes a testable definition of ‘weak universality’ for a taxonomic group of species. (It roughly means that a model has an acceptable fit to most data sets of that group.) This definition was applied to 60 data sets from literature (37 about fish and 23 about non-fish species) and for each dataset an optimal metabolic scaling exponent 0 ≤ a opt < 1 was identified, where the model function m(t) achieved the best fit to the data. Although in general this optimal exponent differed widely from a = 2/3 of the VBGF, the VBGF was weakly universal for fish, but not for non-fish. This observation supported the conjecture that the pattern of growth for fish may be distinct. The paper discusses this conjecture.

scholarly journals On the exponent in the Von Bertalanffy growth model

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4205 ◽  
Author(s):  
Katharina Renner-Martin ◽  
Norbert Brunner ◽  
Manfred Kühleitner ◽  
Werner Georg Nowak ◽  
Klaus Scheicher
Keyword(s):  
Optimal Parameter ◽  
Growth Function ◽  
Model Parameters ◽  
Data Sets ◽  
Scaling Exponent ◽  
Von Bertalanffy ◽  
Large Variability ◽  
Metabolic Scaling ◽  
Main Observation ◽  
Parameter Values

Von Bertalanffy proposed the differential equation m′(t) = p × m(t)a − q × m(t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (Von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Based on 60 data sets from literature (37 about fish and 23 about non-fish species) it optimizes the model parameters, in particular the exponent 0 ≤ a < 1, so that the model curve achieves the best fit to the data. The main observation of the paper is the large variability in the exponent, which can vary over a very large range without affecting the fit to the data significantly, when the other parameters are also optimized. The paper explains this by differences in the data quality: variability is low for data from highly controlled experiments and high for natural data. Other deficiencies were biologically meaningless optimal parameter values or optimal parameter values attained on the boundary of the parameter region (indicating the possible need for a different model). Only 11 of the 60 data sets were free of such deficiencies and for them no universal exponent could be discerned.

Age and growth of the threatened endemic skate Rioraja agassizii (Chondrichthyes, Arhynchobatidae) in the western South Atlantic

2019 ◽  
Vol 70 (1) ◽  
pp. 84 ◽  
Author(s):  
F. P. Caltabellotta ◽  
F. M. Silva ◽  
F. S. Motta ◽  
O. B. F. Gadig
Keyword(s):  
Growth Parameters ◽  
Management Strategies ◽  
Information Criterion ◽  
Growth Function ◽  
South Atlantic ◽  
Age And Growth ◽  
Biological Information ◽  
Growth Coefficient ◽  
Von Bertalanffy Growth Function ◽  
Best Fit

The Rio skate Rioraja agassizii is a threatened endemic skate species frequently caught as bycatch in the western South Atlantic. However, there is no biological information about its age and growth parameters, which would be necessary to provide science-based information for the development of management strategies for this species. The aim of the present study was to provide information about the age and growth parameters of R. agassizii. In all, 138 vertebrae from individuals ranging in size from 9.0 to 53.2-cm total length (TL) were analysed. The edge analysis indicated a trend for annual band deposition in the vertebrae. Maximum ages estimated for males and females were 6 and 10 years respectively. Akaike’s information criterion indicated that the modified two-parameter form of the von Bertalanffy growth function (using length at birth L0=9.0cm TL) provided the best fit, with derived parameters of theoretical maximum length L∞=49.6cm TL and growth coefficient k=0.27 for males and L∞=59.0cm TL and k=0.22 for females. Our results are important to understanding the resilience of this skate species to harvest, which can contribute to the development of fisheries management strategies and conservation programs.

An Antarctic shelf population of the deep-sea, Pacific brachiopod Neorhynchia strebeli

1997 ◽  
Vol 77 (2) ◽  
pp. 399-407 ◽  
Author(s):  
David K.A. Barnes ◽  
Lloyd S. Peck
Keyword(s):  
Deep Sea ◽  
Growth Function ◽  
Weddell Sea ◽  
Von Bertalanffy ◽  
Growth Rings ◽  
Von Bertalanffy Growth Function ◽  
Annual Periodicity ◽  
A Site ◽  
The Antarctic ◽  
Order Rhynchonellida

Thirty-five specimens of the articulate brachiopod Neorhynchia strebeli were collected from a site at 814 m in the Weddell Sea. This was only the second species of the order Rhynchonellida to be found in Antarctica. Formerly N. strebeli was known solely from abyssal Pacific Ocean localities. A circumantarctic distribution is suggested in addition to the known deep-sea Pacific range. The specimens of this collection showed considerable commissure variation, suggesting that the previously proposed erection of two subspecies on the basis of this character is erroneous, and emphasises the phenotypic plasticity of some articulate brachiopods. The valve lengths and the number of alpha growth rings in the sample showed a normal distribution and a von Bertalanffy growth function was fitted to the data: Lt = 23 (1-exp[-0·228t]). If the alpha growth rings were of annual periodicity, the ages attained by the Antarctic N. strebeli of 11 y would be substantially lower than those reported for other Weddell Sea brachiopods. The epibiotic communities occurring on the valves of N. strebeli were impoverished, which is characteristic of deep water Antarctic brachiopods. The few specimens collected with their substratum were attached to small pebbles, but the typical attachment substrata may be different.

Age, Growth and Sex Ratio of the Azorean Rock-Pool Blenny, Parablennius Sanguinolentus Parvicornis

1995 ◽  
Vol 75 (3) ◽  
pp. 751-754 ◽  
Author(s):  
Ricardo Serrão Santos ◽  
Richard D. M. Nash ◽  
Stephen J. Hawkins
Keyword(s):  
Sex Ratio ◽  
Growth Function ◽  
Early Growth ◽  
Reproductive Season ◽  
First Year ◽  
Von Bertalanffy ◽  
Rock Pool ◽  
Total Length ◽  
Von Bertalanffy Growth Function ◽  
One Year

The age and population structure of Parablennius sanguinolentus parvicornis (Valenciennes) (Pisces: Blenniidae) from the Azores have been studied. Total length and weight relationships are given for each sex. Age study was based on otoliths readings. The von Bertalanffy growth function was applied to describe the growth in total length with age. At the end of the first year mean (±SD) total length was significantly different in males (7.1 ±1.5 cm) and females (6.1 ±1.2 cm). One-year-old males participate in reproduction as satellites, whereas females do not. The implications of this in early growth rate of the males is discussed. During the two most important months of the reproductive season (i.e. June and July), the sex ratio was significantly biased towards males, particularly in the larger size classes.

Comparing Polynomial and von Bertalanffy Growth Functions for Fitting Tag–Recapture Data

1994 ◽  
Vol 51 (8) ◽  
pp. 1689-1691 ◽  
Author(s):  
William S. Hearn ◽  
George M. Leigh
Keyword(s):  
Growth Function ◽  
Growth Increment ◽  
Bias Reduction ◽  
Release Time ◽  
Von Bertalanffy ◽  
Growth Functions ◽  
Straight Line ◽  
Von Bertalanffy Growth Function ◽  
Multiple Measurements ◽  
The One

The properties of polynomial and von Bertalanffy growth functions are compared for analysing data from tag–recapture experiments in which fish are recaptured once. For the quadratic and von Bertalanffy growth functions, explicit formulae are obtained for the expected growth increment in terms of length-at-release, time-at-liberty, and the function parameters. If the least-squares fitting technique is used the von Bertalanffy function fits tag–recapture data with no more bias (probably less) than any other growth function, including polynomial growth functions. A bias-reduction technique for fitting the von Bertalanffy growth function to tag–recapture data is not applicable to other growth functions. We conclude that, apart from the straight line, the von Bertalanffy growth function is the one with the most desirable mathematical and statistical properties for fitting to tag–recapture data. The matter of the function that best characterises the way a specific fish species grows can be adequately addressed only by analyses of multiple measurements of individual fish.

A new model accounting for seasonal cessation of growth in fishes

1992 ◽  
Vol 43 (5) ◽  
pp. 1151 ◽  
Author(s):  
S Pauly ◽  
M Soriano-Bartz ◽  
J Moreau ◽  
A Jarre-Teichmann
Keyword(s):  
Salmo Salar ◽  
Growth Function ◽  
Sine Wave ◽  
Smooth Transition ◽  
Von Bertalanffy ◽  
New Model ◽  
Von Bertalanffy Growth Function ◽  
Zero Growth ◽  
Key Features ◽  
Summer Growth

A modified version of the von Bertalanffy growth function (VBGF) is proposed in which a sine wave modifies a standard version of the VBGF, enabling a smooth transition between rapid summer growth and a variable period of zero growth (in length) during winter or during the dry season for aestivating fishes. The key features of a nonlinear routine for fitting this new model are also presented, with emphasis on the estimation of the period of zero growth. Application examples, to Salmo salar and Trisopterus esmarkii, are presented.

Age, growth and reproduction of the protandrous hermaphrodite fish, Sarpa salpa, from the Portuguese continental coast

2016 ◽  
Vol 98 (2) ◽  
pp. 269-281 ◽  
Author(s):  
Rafaela Barros Paiva ◽  
Ana Neves ◽  
Vera Sequeira ◽  
Ana Rita Vieira ◽  
Maria José Costa ◽  
...  
Keyword(s):  
Information Criterion ◽  
Growth Function ◽  
Population Parameters ◽  
Von Bertalanffy Growth Function ◽  
Protandrous Hermaphrodite ◽  
Sarpa Salpa ◽  
Back Calculation ◽  
First Maturity ◽  
Available Information ◽  
Growth And Reproduction

Salema, Sarpa salpa is a commercial exploited species in the Atlantic Ocean with little available information for the essential population parameters, such as age, growth and reproduction. The present study aims to describe these parameters for S. salpa obtained off the coast of Portugal. Ages were estimated from the whole otolith readings; the minimum and the maximum ages observed were 0 and 14 years, respectively, corresponding to 5.2 and 41.4 cm of total length (TL). Whole otolith readings and back-calculation approaches were used to estimate the parameters of the von Bertalanffy growth function and the Akaike's information criterion value suggested that the second approach was the best one to describe the growth of salema: L∞ = 45.07 cm, k = 0.14 year−1 and t0 = −1.43 year. The species is a protandric hermaphrodite and the sex change process occurred between 28.6 and 40.9 cm TL. A short spawning season was identified, extending from September to November. The estimated length at first maturity for males was 24.5 cm TL, corresponding to an age of 2 years at first maturity. This species exhibited a determinate fecundity type and the relative annual fecundity varied between 462 and 2662 oocytes per gram of gutted weight.

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