Quantitative research

The role of quantitative research within ALARM

BioSS contributed directly to the scientific work of ALARM by engaging in collaborative inter-disciplinary research, mainly in the areas of applied statistics and mathematical modelling. Most of our work was integrative, spanning more than one module of the project, but with an overall emphasis towards work on invasive species.

Methods for analysing species atlas data

The majority of our quantitative research involved the development and application of new techniques for analysing species atlas data. Species atlas data record the presence or absence of a species with the cells a regular spatial grid, and are widely used to study the relationship between environmental variables (such as climate and land use) and the distributions of species.

Species atlas need to be interpreted with care, because they typically compiled from the set of available observational data, rather than from a designed experiment or systematic survey. This leads to various difficulties, which can, at least partly, be address using modern statistical techniques. Bierman et al. (submitted) use the technique of Bayesian image restoration to simultaneously address two specific issues: the fact that atlas data are susceptible to non-recording (since recorded absences may arise from the failure to detect a species that is actually present), and the fact that they are susceptible to spatial dependence (or spatial autocorrelation).

Species atlas data enable us to look not only at the spatial distribution of individual species, but also at the spatial distribution of species traits. The data now refer to the proportions of species at a particular location that adopt a particular trait. Data on proportions need to be analysed using special statistical methods (compositional data analysis) that deal with the fact that they need to lie between zero and one and need to sum to one. Kü et al. (2006) analyse spatial variations in the prevalence of different pollination strategies within Germany by applying a multivariate conditional autoregressive model to the log-ratios of the proportions.

Species atlas data for alien invasive species sometimes contain information on the year in which the species arrived at each location. These allow us, through the use of stochastic model for dispersal and colonisation to model the spatio-temporal spread of a species across a landscape. Cook et al. (2007) use this approach to model the expansion of the range of Giant Hogweed Heracleum mantegazzianum across the United Kingdom during the 19th and 20th centuries, and extend the methodology to allow for the effects of landscape heterogeneity.

Statistical treatment of complex models

The other main strand of ALARM research at BioSS focuses on the development of statistical methods to quantify uncertainties in the outputs from complex models. In September 2006 BioSS and Edinburgh University co-hosted a workshop on the topic of probabilistic future climate and climate impacts prediction. Butler et al. (2009) use model averaging to quantify the degree of uncertainty between simulations of future vegetation carbon stocks generated by a dynamic vegetation model. They focus upon quantifying the uncertainty associated with the choice of climate model.