Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.