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.

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 Peach Rusty Spot Epidemics: Management with Fungicide, Effect on Fruit Growth, and the Incidence-Lesion Density Relationship

Plant Disease ◽  
2003 ◽  
Vol 87 (12) ◽  
pp. 1477-1486 ◽  
Author(s):  
Laura A. Furman ◽  
Norman Lalancette ◽  
James F. White
Keyword(s):  
Disease Incidence ◽  
Exponential Model ◽  
Rapid Decline ◽  
Model Parameters ◽  
Data Sets ◽  
Progress Curve ◽  
Significant Seasonal Variation ◽  
Density Relationship ◽  
Parameter Values ◽  
The Relationship

Different numbers of consecutive fungicide applications, beginning at petal fall and continuing into the summer, were examined for their effect on rusty spot epidemics. Disease progressions for each fungicide level were quantified by fitting either the logistic or monomolecular model. When the weighted absolute infection rate (ρ) and maximum disease level (Kmax) parameters were expressed as functions of the number of applications, the logistic decline model provided the best fit for five of six data sets. This model described a gradual decrease in ρ and Kmax in response to the initial fungicide application, a rapid decline in parameter values with the addition of one or two applications, and a diminished parameter response as fungicide applications continued toward the end of the epidemic. Based on examination of model behavior across all 3 years of the study, adequate management was achieved with a total of three to five fungicide applications. Additional analyses of area under the disease progress curve and final disease intensity at harvest supported these results and indicated that further reduction in fungicide usage may be possible. Unlike earlier findings, rusty spot did not significantly decrease fruit volume or weight at midseason or at harvest; as lesion density increased, fruit volume remained constant. The relationship between disease incidence and lesion density within any given year was best explained by the zero-intercept version of the exponential model. However, comparison of model parameters across years revealed significant seasonal variation. Nevertheless, the incidence-lesion density relationships were fairly uniform across years at incidence values below 0.5, where lesion density increased gradually and in a near-linear fashion.

scholarly journals Improving SWAT Model Calibration Using Soil MERGE (SMERGE)

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 2039 ◽  
Author(s):  
Kenneth J. Tobin ◽  
Marvin E. Bennett
Keyword(s):  
Great Plains ◽  
Assessment Tool ◽  
Root Zone ◽  
Optimal Parameter ◽  
Swat Model ◽  
Model Parameters ◽  
Highly Sensitive ◽  
Improved Performance ◽  
Parameter Values ◽  
Sensitive Parameters

This study examined eight Great Plains moderate-sized (832 to 4892 km2) watersheds. The Soil and Water Assessment Tool (SWAT) autocalibration routine SUFI-2 was executed using twenty-three model parameters, from 1995 to 2015 in each basin, to identify highly sensitive parameters (HSP). The model was then run on a year-by-year basis, generating optimal parameter values for each year (1995 to 2015). HSP were correlated against annual precipitation (Parameter-elevation Regressions on Independent Slopes Model—PRISM) and root zone soil moisture (Soil MERGE—SMERGE 2.0) anomaly data. HSP with robust correlation (r > 0.5) were used to calibrate the model on an annual basis (2016 to 2018). Results were compared against a baseline simulation, in which optimal parameters were obtained by running the model for the entire period (1992 to 2015). This approach improved performance for annual simulations generated from 2016 to 2018. SMERGE 2.0 produced more robust results compared with the PRISM product. The main virtue of this approach is that it constrains parameter space, minimizesing equifinality and promotesing modeling based on more physically realistic parameter values.

scholarly journals Optimal and near-optimal exponent-pairs for the Bertalanffy-Pütter growth model

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e5973 ◽  
Author(s):  
Katharina Renner-Martin ◽  
Norbert Brunner ◽  
Manfred Kühleitner ◽  
Werner-Georg Nowak ◽  
Klaus Scheicher
Keyword(s):  
Differential Equation ◽  
Growth Model ◽  
Gompertz Model ◽  
Optimal Growth ◽  
Growth Function ◽  
Bias Reduction ◽  
Model Complexity ◽  
Model Parameters ◽  
Von Bertalanffy ◽  
Data Set

The Bertalanffy–Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p * ma − q * mb. The special case using the von Bertalanffy exponent-pair a = 2/3 and b = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants p, q, and an initial value for the differential equation). For the general Bertalanffy–Pütter model, two more model parameters are optimized (the pair a < b of non-negative exponents). While this reduces bias in growth estimates, it increases model complexity and more advanced optimization methods are needed, such as the Nelder–Mead amoeba method, interior point methods, or simulated annealing. Is the improved performance worth these efforts? For the case, where the exponent b = 1 remains fixed, it is known that for most fish data any exponent a < 1 could be used to model growth without affecting the fit to the data significantly (when the other parameters were optimized). We hypothesized that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and we tested this conjecture for a data set (20,166 fish) about the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. To this end, we assessed the fit on a grid of 14,281 exponent-pairs (a, b) and identified the best fitting model curve on the boundary a = b of the grid (a = b = 0.686); it corresponds to the generalized Gompertz equation dm/dt = p * ma − q * ln(m) * ma. Using the Akaike information criterion for model selection, the answer to the conjecture was no: The von Bertalanffy exponent-pair model (but not the logistic model) remained parsimonious. However, the bias reduction attained by the optimal exponent-pair may be worth the tradeoff with complexity in some situations where predictive power is solely preferred. Therefore, we recommend the use of the Bertalanffy–Pütter model (and of its limit case, the generalized Gompertz model) in natural resources management (such as in fishery stock assessments), as it relies on careful quantitative assessments to recommend policies for sustainable resource usage.

scholarly journals Exploring the Parameters Space of the Regional Climate Model COSMO-CLM 5.0 for the CORDEX Central Asia Domain

2020 ◽  
Author(s):  
Emmanuele Russo ◽  
Silje Lund Sørland ◽  
Ingo Kirchner ◽  
Martijn Schaap ◽  
Christoph C. Raible ◽  
...  
Keyword(s):  
Central Asia ◽  
Parameter Uncertainty ◽  
Climate Models ◽  
Climate Model ◽  
Optimal Parameter ◽  
Regional Climate ◽  
Model Parameters ◽  
Study Results ◽  
Calibration Methods ◽  
Parameter Values

Abstract. The parameter uncertainty of a climate model represents the spectrum of the results obtained by perturbing its empirical and unconfined parameters used to represent sub-grid scale processes. In order to assess a model reliability and to better understand its limitations and sensitivity to different physical processes, the spread of model parameters needs to be carefully investigated. This is particularly true for Regional Climate Models (RCMs), whose performances are domain-dependent. In this study, the parameter space of the RCM COSMO-CLM is investigated for the CORDEX Central Asia domain, using a Perturbed Physics Ensemble (PPE) obtained by performing 1-year long simulations with different parameter values. The main goal is to characterize the parameter uncertainty of the model, and to determine the most sensitive parameters for the region. Moreover, the presented experiments are used to study the effect of several parameters on the simulation of selected variables for sub-regions characterized by different climate conditions, assessing by which degree it is possible to improve model performances by properly selecting parameter inputs in each case. Finally, the paper explores the model parameter sensitivity over different domains, tackling the question of transferability of an RCM model setup to different regions of study. Results show that only a sub-set of model parameters present relevant changes in model performances for different parameter values. Importantly, for almost all parameter inputs, the model shows an opposite behavior among different clusters and regions. This indicates that conducting a calibration of the model against observations to determine optimal parameter values for the Central Asia domain is particularly challenging: in this case, the use of objective calibration methods is highly necessary. Finally, the sensitivity of the model to parameters perturbation for Central Asia is different than the one observed for Europe, suggesting that an RCM should be re-tuned, and its parameter uncertainty properly investigated, when setting up model-experiments to different domains of study.

scholarly journals ALGORITMA GENETIK UNTUK OPTIMASI PARAMETER MODEL TANGKI PADA ANALISIS TRANSFORMASI DATA HUJAN-DEBIT

2012 ◽  
Vol 13 (1) ◽  
pp. 85 ◽  
Author(s):  
Sulianto Sulianto ◽  
Ernawan Setiono
Keyword(s):  
Genetic Algorithm ◽  
River Flow ◽  
Optimal Parameter ◽  
Optimization Process ◽  
Data Sets ◽  
Parallel Composition ◽  
Systems Of Equations ◽  
Optimal Model ◽  
Testing Data ◽  
Parameter Values

Fundamental weaknesses of the application of Tank Models is on so many parameters whose values should be set firstbefore the model is simultaneously applied. This condition causes the Tank Models is considered inefficient to solve practical problems. This study is an attempt to improve the performance of Tank Models can be applied to more practical and effective for the analysis of the data transformation of rainfall into river flow data. The discussion in this study focused on efforts to solve systems of equations Tank Models Series Composition, Parallel Composition and Combined Composition with the use of genetic algorithms in the optimization process parameters, so that the resulting system of equations to determine the optimal model parameter values are automatically in the studied watersheds. The results showed that the Wonorejo Watershed, Genetic Algorithm to solve the optimization process Tank Models parameter values as well. In the generation-150 showed the three models can achieve convergence with similar fitness values . Testing optimal parameter values by using the testing data sets show that the Tank Models Combined composition with Genetic Algorithm-based tend to be more consistent than the other two types of Tank Models.

Generalized Flexible Weibull Extension Distribution

2017 ◽  
Vol 2 (4) ◽  
pp. 68-75
Author(s):  
Zubair Ahmad ◽  
Brikhna Iqbal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Suggested Model ◽  
Proposed Model ◽  
Parameter Values ◽  
Family Of Distributions

In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

Parameter Estimation and Sensitivity Analysis of a Nonlinearly Elastic Static Lung Model

1985 ◽  
Vol 107 (4) ◽  
pp. 315-320 ◽  
Author(s):  
J. R. Ligas ◽  
G. M. Saidel ◽  
F. P. Primiano
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Least Squares ◽  
Static Pressure ◽  
Optimal Parameter ◽  
Elastic Strain Energy ◽  
Lung Model ◽  
Model Parameters ◽  
Least Squares Fit ◽  
Parameter Values

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.

Differential evolution based identification of automotive hydraulic engine mount model parameters

2000 ◽  
Vol 214 (3) ◽  
pp. 249-264 ◽  
Author(s):  
A Kyprianou ◽  
J Giacomin ◽  
K Worden ◽  
M Heidrich ◽  
J Bocking
Keyword(s):  
Differential Evolution ◽  
Optimal Parameter ◽  
Numerical Models ◽  
Differential Evolution Algorithm ◽  
Time History ◽  
Model Parameters ◽  
Engine Mount ◽  
Force Time ◽  
Parameter Values ◽  
Mean Square Errors

Hydraulic engine mounts are commonly used in automotive applications, and numerical models exist for performing full-vehicle noise, vibration and harshness (NVH) studies by means of multibody simulation. The parameters of these models are usually determined by the manufacturer from first-principle numerical calculations, or by means of direct testing of the individual components. This paper describes, instead, a four-step identification method developed to determine the parameter values of a specific hydromount numerical model, the Freudenberg hydromount equations, a set of highly non-linear piecewise-continuous differential equations. The identification procedure is based on two concepts, the first being the use of the differential evolution algorithm for determining optimal parameter values, while the second is the use of data obtained from a series of experimental tests of progressively higher displacement amplitude. Identified parameters provide models whose mean square errors between the calculated output force time history and the experimentally measured force time history are typically of the order of 1-2 per cent.

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