Multinomial models

The data on powerful owls allow for two possibilities for each bird (dead or alive). In such circumstances a binomial model is often appropriate. A greater number of possibilities may arise in other ecological examples. For example, habitats might be categorized into a number of different vegetation types, organisms might be classified into a number of different species, or individuals of a species might be placed into a number of age classes. The powerful owl example used a binomial model with two possible states (alive or dead). When there are more than two possible states, data can be analysed with a multinomial model.

An example of the use of the multinomial model is an analysis of the age structure of a koala population. The age structure of a population describes the distribution of individuals among age classes. This measure is important in population ecology because it can influence the rate of growth of species and the likely response to management.

The age of koalas is determined by assessing the degree of tooth wear, specifically, the degree of wear on the premolar. McLean (2003) recognized nine different tooth wear classes that define age. If we sampled a population of koalas and determined the tooth wear classes (e.g. see data in Table 3.1), what could we infer about the age structure of the population from which the sample was taken?

By using a multinomial model, in which it is assumed that each individual is assigned to one of the nine possible age classes and that each individual is a random and independent sample from the population, it is possible to estimate the age structure of the population (Box 3.14). Thus, animals in TWC II are predicted to make up 33% of the population, with 95% credible intervals of 28—37%. The upper bound of the 95% credible interval for TWC VII is approximately 1%, suggesting that the number of animals in this oldest TWC represents a very small proportion of the total population (Fig. 3.5).

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