The Use of Graphical Methods to Estimate Demographic Parameters

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Abstract
The demographic parameters of a population (the number of age-classes present; growth rates; mortality as a function of age and recruitment levels) are of considerable interest to marine biologists. If individuals can be aged from growth rings in their hard parts, then the estimation of demographic parameters is relatively straightforward. If this is not possible, the next best alternative is to tag or mark individuals and use data on the recapture of these to give the information required. For many marine invertebrates, neither of these options is practical and we must resort to estimating the demographic parameters by making assumptions about recruitment and the size variation between individuals of the same age and then infer the age structure of the population from its size structure. This was first done by Petersen (1891) who interpreted each mode on a size/ frequency histogram as representing a single age-class. More recently, extensive use has been made of methods which assume that the sizes of individuals of the same age will be normally distributed. The size/frequency histogram can then be decomposed into a number of normal distributions, each of which represents a single age-class. This can be done graphically (Harding, 1949; Cassie, 1954; Bhattacharya, 1967) or with computerbased numerical methods (Macdonald & Pitcher, 1979). The graphical methods seem to be the most popular and are frequently taught to undergraduate students. The same methods can be used to dissect a size/frequency distribution into components other than age-classes (Harding, 1949), but the principles are the same.