Estimation of von Bertalanffy Growth Curve Parameters Using both Length Increment and Age–Length Data

1983 ◽  
Vol 40 (9) ◽  
pp. 1405-1411 ◽  
Author(s):  
G. P. Kirkwood
Keyword(s):  
Growth Curve ◽  
Full Range ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Ratio Test ◽  
Von Bertalanffy ◽  
Predictive Regression ◽  
Length Increment ◽  
Southern Bluefin Tuna ◽  
Length Data

Many fish species cannot be aged directly over their full range of lengths. Therefore, to estimate a growth curve, one often uses length increment data from a mark–recapture experiment, supplemented by whatever age–length data are available. I describe a new method for maximum likelihood estimation of the three von Bertalanffy growth curve parameters, using the length increment and age–length data jointly. Also, I describe a likelihood ratio test for determining whether the same growth curve fits both data sets adequately. The von Bertalanffy growth curve can be taken as a predictive regression with either length or age as the dependent variable. Here, age is taken as the dependent variable, as would be appropriate for estimation of age from length, but only minor modifications are necessary for the more common alternative predictive regression of length on age. As an illustration, the techniques are applied to data for southern bluefin tuna, Thunnus maccoyii.

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.

An integrated model for growth incorporating tag–recapture, length–frequency, and direct aging data

2004 ◽  
Vol 61 (2) ◽  
pp. 292-306 ◽  
Author(s):  
J Paige Eveson ◽  
Geoff M Laslett ◽  
Tom Polacheck
Keyword(s):  
Growth Curve ◽  
Bluefin Tuna ◽  
Fish Growth ◽  
Data Sources ◽  
Smooth Transition ◽  
Likelihood Method ◽  
Von Bertalanffy ◽  
Length Frequency ◽  
Direct Aging ◽  
Southern Bluefin Tuna

A maximum likelihood method for modelling fish growth is presented that integrates data from three key sources of growth information: tag–recapture studies, length–frequency samples from commercial catches, and direct aging data from hard-parts analyses. Previous studies have almost exclusively modelled growth using only one of these sources of information. Different data sources are often most informative about different portions of the life cycle. The development of an integrated approach allows for the different data sources to complement each other and provide more comprehensive and robust estimates of growth parameters. The integrated method is applied to data sets from southern bluefin tuna (Thunnus maccoyii) using the von Bertalanffy growth curve as well as a more sophisticated growth curve that makes a smooth transition between two von Bertalanffy curves with different growth rate parameters. The latter is found to provide a significantly better fit and supports previous findings that southern bluefin tuna experience a transition in growth during the juvenile stage of life. Many species exhibit a seasonal growth pattern, including southern bluefin tuna for which growth is fastest during the austral summer. A method for incorporating an annual seasonal component into the analysis is described and applied.

Statistical Properties of Alternative Parameterizations of the von Bertalanffy Growth Curve

1986 ◽  
Vol 43 (4) ◽  
pp. 742-747 ◽  
Author(s):  
D. A. Ratkowsky
Keyword(s):  
Linear Model ◽  
Growth Curve ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Data Sets ◽  
Von Bertalanffy ◽  
Marine Animals ◽  
Nonlinear Regression Models ◽  
Linear Behavior ◽  
Biological Interpretation

The von Bertalanffy growth curve is often used in fisheries research to describe the relationship between the weight or length of a fish and its age. The equation is also encountered in various other branches of science and applied science in a variety of different parameterizations and names; for example, it is also known as the asymptotic regression equation or the three-parameter exponential equation. Since these equations are all nonlinear regression models, the properties of the least squares estimators of the parameters of these models may be very different from their large-sample properties, where the estimators are unbiased, have the minimum attainable variance, and are normally distributed, the conditions that pertain in a linear model. Different parameterizations will have estimators which approximate the asymptotic properties to varying degrees of closeness. My study of eight parameterizations shows that one of them, a generalization which allows unequal age increments of a parameterization proposed by Schnute and Fournier, is far superior to any of the other models, which include the most commonly used parameterization, in that it exhibits close-to-linear behavior. Two of the three parameters in this model represent the expected mean lengths corresponding to the youngest and oldest ages, respectively, in the sample, and thus have a ready biological interpretation. I discuss why it is important to have a close-to-linear model when one wishes to make comparisons between two or more data sets. Methodology is briefly described for carrying out such comparisons, and some further remarks are made about why biologists should be concerned about the statistical properties of the models that they use. Although most data sets I used for illustration are obtained from marine animals, the conclusions are general and apply to all disciplines which make use of the von Bertalanffy model in whichever guise or form it appears.

scholarly journals A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 62
Author(s):  
Zhengwei Liu ◽  
Fukang Zhu
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Models ◽  
Superior Performance ◽  
Data Sets ◽  
Binomial Thinning ◽  
Free Case ◽  
Two Parameters ◽  
Conditional Maximum ◽  
Thinning Operator

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

Full-Coverage Film Cooling—Part II: Heat Transfer Data and Numerical Simulation

1980 ◽  
Vol 102 (4) ◽  
pp. 1006-1012 ◽  
Author(s):  
M. E. Crawford ◽  
W. M. Kays ◽  
R. J. Moffat
Keyword(s):  
Heat Transfer ◽  
Film Cooling ◽  
Numerical Procedure ◽  
Stanton Number ◽  
Data Sets ◽  
Blowing Ratio ◽  
Diameter Hole ◽  
Full Coverage ◽  
Sample Data ◽  
Length Data

Experimental research into heat transfer from full-coverage film-cooled surfaces with three injection geometries was described in Part I. This part has two objectives. The first is to present a simple numerical procedure for simulation of heat transfer with full-coverage film cooling. The second objective is to present some of the Stanton number data that was used in Part I of the paper. The data chosen for presentation are the low-Reynolds number, heated-starting-length data for the three injection geometries with five-diameter hole spacing. Sample data sets with high blowing ratio and with ten-diameter hole spacing are also presented. The numerical procedure has been successfully applied to the Stanton number data sets.

scholarly journals Spatial Heterogeneity of the Incidence of Powdery Mildew on Hop Cones

Plant Disease ◽  
2006 ◽  
Vol 90 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
David H. Gent ◽  
Walter F. Mahaffee ◽  
William W. Turechek
Keyword(s):  
Powdery Mildew ◽  
Spatial Heterogeneity ◽  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Disease Assessment ◽  
Cluster Sampling ◽  
Data Sets ◽  
Ratio Test ◽  
Frequency Distributions

The spatial heterogeneity of the incidence of hop cones with powdery mildew (Podosphaera macularis) was characterized from transect surveys of 41 commercial hop yards in Oregon and Washington from 2000 to 2005. The proportion of sampled cones with powdery mildew ( p) was recorded for each of 221 transects, where N = 60 sampling units of n = 25 cones assessed in each transect according to a cluster sampling strategy. Disease incidence ranged from 0 to 0.92 among all yards and dates. The binomial and beta-binomial frequency distributions were fit to the N sampling units in a transect using maximum likelihood. The estimation procedure converged for 74% of the data sets where p > 0, and a loglikelihood ratio test indicated that the beta-binomial distribution provided a better fit to the data than the binomial distribution for 46% of the data sets, indicating an aggregated pattern of disease. Similarly, the C(α) test indicated that 54% could be described by the beta-binomial distribution. The heterogeneity parameter of the beta-binomial distribution, θ, a measure of variation among sampling units, ranged from 0.01 to 0.20, with a mean of 0.037 and a median of 0.015. Estimates of the index of dispersion ranged from 0.79 to 7.78, with a mean of 1.81 and a median of 1.37, and were significantly greater than 1 for 54% of the data sets. The binary power law provided an excellent fit to the data, with slope and intercept parameters significantly greater than 1, which indicated that heterogeneity varied systematically with the incidence of infected cones. A covariance analysis indicated that the geographic location (region) of the yards and the type of hop cultivar had little effect on heterogeneity; however, the year of sampling significantly influenced the intercept and slope parameters of the binary power law. Significant spatial autocorrelation was detected in only 11% of the data sets, with estimates of first-order autocorrelation, r1, ranging from -0.30 to 0.70, with a mean of 0.06 and a median of 0.04; however, correlation was detected in only 20 and 16% of the data sets by median and ordinary runs analysis, respectively. Together, these analyses suggest that the incidence of powdery mildew on cones was slightly aggregated among plants, but patterns of aggregation larger than the sampling unit were rare (20% or less of data sets). Knowledge of the heterogeneity of diseased cones was used to construct fixed sampling curves to precisely estimate the incidence of powdery mildew on cones at varying disease intensities. Use of the sampling curves developed in this research should help to improve sampling methods for disease assessment and management decisions.

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