Global warming, environmental change/degradation and human activities have led to an unprecedented threat to the world's biodiversity. How to quantify and estimate biodiversity change - how biodiversity is changing over time - has become one of the most pressing issues in biology, ecology, evolution, environmental science, bioinformatics, and related research fields. Robust and meaningful diversity measures that possess good mathematical/statistical properties and support biological reasoning about diversity are required. To date, most of the effort has been directed towards quantifying taxonomic diversity - i.e. species relative abundance and composition. However, it is now recognized that biodiversity has multiple dimensions and that it is essential to consider phylogenetic and functional diversity as well. Fortunately, remarkable progress in our understanding of phylogenies and the extensive collection of species traits opens the door to innovative approaches to the measurement and assessment of biodiversity change. At the same time, this is a complex challenge; collaboration among ecologists and mathematicians/statisticians is essential to tackle it. This project will bring together world experts in the assessment of biodiversity, in a new collaboration. Its goal is to develop an integrated mathematical and statistical framework to quantify and estimate changes in taxonomic, phylogenetic and functional diversity, focusing on the BioTIME database. The focus of the work will be ecological assemblages, and how they change through time. Project partners are Sandra Diaz (Argentina), a world leader in quantifying functional diversity, and Anne Chao (leading the MOST component of the work) who is globally renowned for her statistical contributions to the quantification of biodiversity. They will collaborate with the UK (St Andrews) team (Anne Magurran and Maria Dornelas) who have pioneered the quantification of biodiversity change in taxonomic diversity. The new methodology will permit rigorous analysis of diversity changes for alpha, beta and gamma diversities based on all three dimensions of biodiversity (taxonomic, functional, phylogenetic). Access to the BioTIME database (biotime.st-andrews.ac.uk), currently the world's largest repository of assemblage time series, will provide a proof of concept of the methodology. We will also develop appropriate user-friendly, self-interpreting software, complete with online versions, and maintain a website featuring all software and statistical tools developed in this project. By offering a number of short visiting fellowships to postdocs, who will have an opportunity to work on key components of the analyses, we will increase the global reach of the collaboration. A workshop will provide a further opportunity to disseminate findings and secure the future of the collaboration. The project will thus forge a strong partnership between researchers who have not had the opportunity to work together in the past, while providing innovative solutions to an urgent ecological challenge.