During the past 5 years there have been a number of important developments in the estimation of animal abundance and related parameters such as survival rates. Many of the new techniques need to be more widely publicized as they supplant previous methods. The aim of this paper is to review this literature and suggest further avenues for research.

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A review of estimating animal abundance.

We compared the von Bertalanffy growth function (VBGF) and five polynomial functions (PF) in modelling fish growth for 16 populations comprising six species of freshwater fishes. Ranked results of the variance explained by each growth function indicated that VBGF described growth data better than three- and four-parameter polynomial functions. Log-transforming length and age greatly improved the goodness-of-fit of the three-parameter polynomial function. Statistical comparison of growth between populations or sexes was done using a general linear model for polynomial functions. An analysis of residual sum of squares was proposed to compare the resultant VBGFs because the nonlinear formulation of the VBGF prevented traditional analysis of covariance procedures. Fitting of different growth functions to the same growth data set yielded the same result in the intra-species growth comparisons for three species (eight populations) but different results for two species (seven populations). Where ages of the fish...

A Comparison of von Bertalanffy and Polynomial Functions in Modelling Fish Growth Data

Likelihood ratio, t-, univariate χ2-, and T2-tests have been proposed to compare von Bertalanffy parameters among stocks. As commonly applied, all of these tests are approximate, with the accuracy ...

Interpretable Statistical Tests for Growth Comparisons using Parameters in the von Bertalanffy Equation

The relationship between size of calcified structures and the body of fish has been used widely in fisheries science to estimate body size at a younger age by “back-calculation.” I labeled the calcified tissue of northern pike Esox lucius with tetracycline to examine the concurrent linear growth of calcified structures and the body. I also conducted comparisons of the sizes of one or more calcified structures with body sizes of northern pike, lake trout Salvelinus namaycush, and muskellunge Esox masquinongy. Over a broad size and age range (juveniles and older), growth of scales, cleithra, and otoliths is only transitorily isometric in relation to body growth. Although scale growth is more strongly allometric than bone growth, allometry in both structures is positive during rapid growth and negative during slow growth. Slower-growing individuals have relatively smaller scales and cleithra. Calcified structure-body relations indicate that in older fish, growth of the scales virtually ceases while ...

Growth and Relative Size of Calcified Structures of Fish

http://www.bio.vu.nl/thb/research/bib/Kooy86a.pdf

Energy budgets can explain body size relations

If the von Bertalanffy growth model is used to statistically compare the properties of growth in two spatial regions by examination of the estimates of the growth parameter k and the asymptotic length parameter L∞, a possible compound null hypothesis H0, is H0: K1= k2 and L∞1 = L∞ 2 for regions 1 and 2. Since the results of this two-parameter test may be difficult to interpret, an alternative procedure is suggested. In addition, the interpretation of the test must be based upon the nature of the data as well as upon the parameter estimates. A regression fit of the model to real but “inappropriate” data may yield a very “good” statistical fit but unrealistic estimates. The use of a third parameter (for example, t0, the time when length is zero) is necessary to uniquely specify a solution; its inclusion always enhances the statistical fit. Because of the interdependence between parameters k and L∞, we reparameterize the von Bertalanffy model with a new parameter w = k˙L∞. The parameter corresponds ...

Reparameterizing, Fitting, and Testing a Simple Growth Model

The estimation of the abundance of animal populations with the line—transect sampling method requires that a sighting model be postulated to represent the decreased probability of a sighting as its distance from the transect line increases. The development of parametric sighting models and estimation techniques is reviewed, and general procedures for variance estimation are given. Two new models and their corresponding abundance estimators are developed. The half—normal model provides a useful alternative to the widely used exponential model. The generalized exponential model contains the half—normal and exponential models as special cases and has the flexibility to account for a wide range of sighting phenomena. The new models are applied to transect surveys of porpoise schools and the results are related to sampling and ecological conditions. Criteria for model selection and transect design are discussed. See full-text article at JSTOR

Terrance J. Quinn

Papers

Reparameterizing, Fitting, and Testing a Simple Growth Model

Parametric models for line-transect estimators of abundance'

Von Bertalanffy Growth Parameters