Species richness estimation for benthic data

This thesis addresses species richness estimation for benthic data by describing the clustering of individuals within a species using a Neyman Type A distribution, and incorporating this into species richness estimates. A review of current species richness estimation methods is included. The maximum-likelihood approach to species richness estimation is extended to incorporate the Neyman Type A model, with a gamma mixing distribution on the mean abundance of individuals within a species. Species richness estimates of this model are compared to those of the simpler negative binomial and Poisson models. The use of a penalised-likelihood is applied to avoid spuriously large estimates of species richness that can be associated with the "boundary problem". The Bayesian approach to species richness is considered, using uninformative and informative priors. Informative priors are elicited using expert opinion obtained from a number of benthic ecologists at the Centre for Environment, Fisheries and Aquaculture Science. These are incorporated into species richness estimation in the form of priors, and also converted into penalties for use in the frequentist approach. Several benthic data sets are analysed throughout, along with a Lepidoptera data set, and a data set from a common bird census carried out in the USA. In addition, several simulation studies are undertaken to illustrate the performance of the estimators. The research culminates in the application of species richness estimators to estimate species mortality due to dredging carried out off the Norfolk coast. Several estimators can be considered to gain a picture of the effect of dredging, and I recommend that species richness estimators should reflect the underlying distribution of the data. I also recommend that a precautionary approach should be taken when using these estimators in practical applications.