The Model-Free Analysis of Growth Curves

Abstract.

• 1) An incremental (graphical in this presentation) method for the analysis of growth curves has revealed actual, as opposed to modelled, growth rates. Here, we present data derived from the scallop Pecten maximus (L.). These actual rates exhibit differences in annual environmental conditions and differences between local populations.
• 2) Both first and second derivatives (growth rate and acceleration ? deceleration in growth rate, respectively) can be obtained from plotted size ? age data: here, size is represented by the height of the flat left valve.
• 3) The analysis of age class data from different years allows one to estimate maximum theoretical rates in any given year.
• 4) The analysis of individual data naturally reveals more than the analysis of average data, reinforcing the average nature of population growth parameters.
• 5) The departure of average data from the maxima revealed by the analysis of growth rate and acceleration allows one to identify changes in environmental conditions in different years.
• 6) The Von Bertalanffy growth curve has been used as an example because it is well known and widely used; however, any desired growth curve can be fitted by the method discussed here.