Age and Growth of Fishes: Principles and Techniques

Chapter 12: Growth Estimation: Growth Models and Statistical Inference

Derek H. Ogle, Travis O. Brenden, and Joshua L. McCormick


Growth models use mathematical functions to describe how fish size (length or weight) changes by age or over a fixed period of time. Parameters of these functions may describe growth characteristics such as maximum mean size attained, instantaneous growth rate at a particular age or time, maximum relative growth rate, or mean size at a specific age. Typical sources of data used to model growth are described in section 12.2, whereas several common functions used to model growth are described in section 12.3.

Statistical inference is the drawing of conclusions about a population based on a sample collected from that population. Herein, we use the term “population” in the statistical, rather than biological, sense, such that population may refer to any group of fish of interest (e.g., defined by location, time, sex, or species). Two major components of statistical inference are the estimation and testing of parameters. A parameter is an unknown quantity in a model that represents an attribute or process of the population, such as growth rate. Estimation involves computing a best value for the parameter along with a measure of the uncertainty of that estimate. Statistical tests are used to assess whether there is evidence that a parameter differs from a specific value or whether a parameter differs among two or more populations. Statistical methods to fit growth models to estimate growth-related parameters, compare the fit of two or more growth models, and compare growth model parameters between two or more populations are described in sections 12.4 and 12.5. Bayesian approaches to fitting growth models and hierarchical growth models are introduced in sections 12.6 and 12.7.

Most topics in this chapter are demonstrated in boxes using the R programming environment (R Development Core Team 2017). Setup of the R environment and descriptions of the data used in the boxes are in Box 12.1.