Glenn De’ath, AIMS
CSIRO Auditorium, Hobart
Friday 20^th January, 2 pm

Abstract:
The multinomial diversity model, MDM, is a new method for relating Shannon diversity to complex environmental, spatial and temporal predictors. Based on a novel link between Shannon entropy and the likelihood of the multinomial logit model, the MDM estimates the relationships between multivariate-species data and their predictors, and simultaneously minimises the Shannon diversity of the estimated species values.
By formulating diversity as a statistical model and working in terms of entropy, diversity is simplified both conceptually and analytically, and diversity analyses extend beyond traditional simple hierarchies of \(\alpha\), \(\beta\), \(\gamma\) and measures of turnover. Entropy can be partitioned within and between models, and changes in entropy attributed to model predictors. All entropies translate into diversity for meaningful ecological interpretation. A weighted version of the Shannon diversity model is proposed in order to extend the MDM to non-Shannon diversities. Two example analyses, based on simulated and field data, illustrate the theoretical concepts and the analytical methods. Software to implement the model is freely available.