Susan L. Cooksley

The relative performance of AIC, AICC and BIC in the presence of unobserved heterogeneity

Summary Model selection is difficult. Even in the apparently straightforward case of choosing between standard linear regression models, there does not yet appear to be consensus in the statistical ecology literature as to the right approach. We review recent works on model selection in ecology and subsequently focus on one aspect in particular: the use of the Akaike Information Criterion (AIC) or its small-sample equivalent, AICC. We create a novel framework for simulation studies and use this to study model selection from simulated data sets with a range of properties, which differ in terms of degree of unobserved heterogeneity. We use the results of the simulation study to suggest an approach for model selection based on ideas from information criteria but requiring simulation. We find that the relative predictive performance of model selection by different information criteria is heavily dependent on the degree of unobserved heterogeneity between data sets. When heterogeneity is small, AIC or AICC are likely to perform well, but if heterogeneity is large, the Bayesian Information Criterion (BIC) will often perform better, due to the stronger penalty afforded. Our conclusion is that the choice of information criterion (or more broadly, the strength of likelihood penalty) should ideally be based upon hypothesized (or estimated from previous data) properties of the population of data sets from which a given data set could have arisen. Relying on a single form of information criterion is unlikely to be universally successful.

Impacts of flow regulation on freshwater pearl mussel (Margaritifera margaritifera) habitat in a Scottish montane river

The River Moriston in NW Scotland is a cobble-gravel bedded river that has been dammed and regulated for hydroelectric power (HEP) since 1956. The river supports a functional population of the critically endangered freshwater pearl mussel (Margaritifera margaritifera) in the lower part. In contrast the population in the upper reach is sparse and shows no signs of juvenile recruitment, leading to speculation that hydrological and geomorphic changes associated with HEP have degraded the habitat they depend on. A combination of historical analysis, field mapping and geomorphic survey of channel and active bar sites was used to assess habitat changes and current quality. During the post-dam period, the naturally stability of much of the channel has increased, active bars have been stabilised through vegetation colonisation, riparian tree cover has increased and the active channel width has significantly reduced locally (>50%); adjustments that are indicative of a reduction in the incidence of competent flows caused by flow regulation. However area and stability of habitat for freshwater pearl mussels have not been reduced greatly. The channel sites examined are characterised by mixed cobble-gravel substrates (D(50) range=46-188 mm), predicted to be highly stable, that provide suitable habitat for adult freshwater pearl mussels. However a degree of bed compaction at one site was observed that could be limiting the recruitment of juvenile mussels. It is hypothesised that the sparse, non-functional status of the freshwater pearl mussel population reflects significant historical pearl fishing and the limitation of recovery due to HEP related pressures of fish migration obstruction and bed compaction. The implications of these factors for conservation of the species are discussed.

Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.

Modelling species abundance in a river by Negative Binomial hidden Markov models

The investigation of species abundance in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, a Bayesian hierarchical model within the class of hidden Markov models is proposed to map the distribution of freshwater pearl mussels in the River Dee (Scotland). In order to model the overdispersed series of mussel counts, the conditional probability function of each observation, given the hidden state, is assumed to be Negative Binomial. Both the transition probabilities of the hidden Markov chain and the state-dependent means of the observed process depend on covariates obtained from a hydromorphological survey. Bayesian inference, model choice, and covariate selection based on Markov chain Monte Carlo algorithms are presented. The stochastic selection of the explanatory variables which are associated with a reduced chance of finding a local mussel population provides new evidence for the causes of the deterioration of a highly threatened species.