Biodiversity, Mathematics and Sustainability: Maintaining the Planet’s Biotic Resources

Abstract

Our planet is replete with living systems that provide the essential infrastructure for human civilization. All life processes on the planet rely upon the photosynthetic capacity of aquatic and terrestrial plants and microbes to produce the high-energy carbon compounds upon which all non-photosynthetic organisms depend for their energetic needs. The complex, interwoven linkages between diverse organisms from numerous taxa have arisen via biological evolution over a long time span relative to the recent advent of human civilization, yet the direct actions and indirect influences of humanity have created great strains on the planetary biota. Mathematical methods are one of the key tools used to assess the current impacts of human actions, project how modifications of anthropogenic forcing might affect living systems over the future, and suggest hypotheses to assist in teasing apart the interactions and feedbacks between environment and biotic systems to better inform science and public policy. These are all key questions addressed by sustainability science in determining how we might appropriately modify human actions and impacts in order to sustain and support human societies and the living systems upon which they depend. In common parlance, biodiversity refers to the collection of species present in a region, but in practice it includes the variety of life present at a location including the connections and systems of which the species are a part. Mathematical methods have been used to characterize components of biodiversity, as a means of determining whether these are changing at a location, comparing these across locations, and evaluating hypotheses about the factors that affect biodiversity. The simplest metric used is species richness which is simply a count of the number of species, typically from some restricted set of taxa such as plants or vertebrates, present at a location. This provides some useful information to compare locations, but does not account for the differences in abundance of the species present. A location with a very large number of individuals or biomass of a single species and only a few individuals of other species is quite different from a location with about equivalent numbers of all the species present. If many species at a location are rarely occurring, then a major disturbance such as a fire could potentially greatly reduce the biodiversity at the location quickly. In this sense, a location with higher evenness of distribution of species abundances is more resilient.