#### Efficiently quantifying spatial patterns of diversity over regional to continental extents (16894)

Spatial biodiversity patterns are increasingly being analysed using phylogenetic and trait based measures. Spatial patterns are typically assessed by calculating one or more indices for every spatial unit of analysis and then mapping them However, many of the diversity measures are computationally intensive, and the increasing availability of georeferenced specimen data sets mean that hundreds of thousands of index calculations are a real prospect. Exacerbating this is that many indices use permutation analyses which result in orders of magnitude increases in analysis duration. In this talk I will describe the spatialisation of a set of established phylogenetic and functional diversity indices, their implementation in the Biodiverse software, and the ways in which the calculations have been accelerated. The indices used are the Net Relatedness Index, Net Taxonomic Index and Trait Standardised Effect Size indices from PhyloCom. Code accelerants included caching strategies, taking advantage of the quadratic form of the calculations, early stopping when results have converged, and the use of power curve relationships for permutation analyses. A set of analyses using a continental extent data set of Australian rainforest plants shows that analyses can be implemented at least an order of magnitude faster than a simple implementation, with some inner components being several thousand percent faster. In summary, the spatialisation of diversity indices can be greatly accelerated by intelligent use of the properties of the indices themselves and their spatial variations. The approaches used are generic can be readily ported to other implementations of these indices.