BBSRC International Workshop on The Mathematics of Biodiversity
The global biodiversity crisis is one of the outstanding scientific problems of our time. The dramatic loss of habitats, populations and species has led some writers to compare the current crisis with the five mass extinctions in the history of life on earth. It is a problem of enormous magnitude and the most pressing concern. There is a correspondingly vast literature on the subject. However, quantitative methods have not kept up. To any community – the fish in a river, the trees in a forest, or the bacteria in a human digestive system – one would like to be able to assign a number, measuring the community’s diversity. This is not a problem of statistics: even assuming that we have complete information on all the organisms in the community, it is far from clear what the best measure is.
The question "what measure of diversity to use?" has been debated in ecology journals for nearly fifty years. The results have not been satisfactory. Lou Jost, author of some of the most important recent papers on diversity measurement, put it bluntly: "The biological literature about diversity and similarity indices is a mess." Partly, it is a mess because many of the issues arising are fundamentally mathematical in nature, but many of those writing are ecologists with little mathematical training. Partly, it is because of convention: field ecologists typically use whatever measure of diversity is most popular, so that bad choices become quickly entrenched. Partly, it is because of genuine variation in the priorities of different ecologists: one person might attach great importance to rare species, while another, focused on the functioning of whole ecosystems, might attach more importance to common species. But it is also because there are deep, unanswered mathematical questions that need to be resolved before progress can be made.
This proposal is about rethinking diversity measurement. The fifty years of existing work certainly has a part to play, but should not be treated uncritically: complaints about the lack of rigour in the subject have been expressed since as long ago as 1971, when Hurlbert published a now-famous Ecology paper on the "nonconcept" of diversity. Our plan is predicated on the belief that coming at the subject with full mathematical rigour will be of benefit to life scientists and mathematicians, but it is critical that those involved communicate well with each other, or we will not derive as much benefit as possible from the activity.