Measurement of Diversity and Dissimilarity for Stochastic Populations

The existing measures of diversity within a population and of dissimilarity between two populations postulate a static population with unchanging probabilistic structure. We assume that the measurements associated with an individual change with time according to a stochastic process. General measures of diversity and of dissimilarity when the underlying process is a finite Markov chain are developed. An aportionment of these measures based on a partition of the state-space is provided. Their asymptotic behaviour is investigated. The spectral analysis of measures of diversity is carried out. Some specific measures of diversity and dissimilarity are obtained when the underlying stochastic process is a general vector-valued process. An indication of directions for future work is provided.