- Here we review recent advances in characterizing pattern of variation in community structure in space and time based on parametric approaches utilizing the full distribution of abundances of species rather than some summary indices.
- Assessment of biodiversity based on the structure of rank-abundance plots or simple species diversity indices, which describe properties of the sample of individuals, may reveal limited information about the underlying species abundance distribution of the community because the number of individuals counted are dependent on the sampling intensity. For instance, assuming Poisson sampling and an underlying lognormal species abundance distribution implies that observed abundances (counts) are a sample from a Poisson lognormal distribution. A convenient property of this distribution is that the estimate of σ2 can be used as an inverse measure of species diversity in a community as well as the number of unobserved species can be estimated approximately without bias for unknown sampling intensities.
- If two communities can be described by a bivariate lognormal species abundance model, then the correlation between the log abundances of species in the two communities is an index of similarity that can be estimated without knowledge of sampling intensities using the bivariate Poisson lognormal distribution. This method is even applicable as an approximation when the abundance distribution deviates from the lognormal.
- An analysis of the interrelationship between the parameters of the lognormal species abundance distribution in communities of species from a wide variety of taxa shows that the canonical hypothesis of Preston in general, for a given number of species, gives far too large variances in the distribution of log abundances.
- A general feature in community dynamics is that a large component of the variance in the species abundance distribution is caused by heterogeneity among species in the population dynamics as well as environmental noise. This pattern is in contrast to the assumptions of the neutral theory of community dynamics.
- The choice of species abundance distribution should be a consequence of specific assumptions about the dynamics of the species. We suggest that such specific assumptions for the choice of species abundance model will facilitate more robust comparisons of changes in community structure in time and space.