Generalised Complementarity Analysis: identifying the most precious places for the conservation of Species, Functional and Phylogenetic Diversity

The most precious places for conservation are those that make the largest contribution to regional, national or global biodiversity. The two key concepts for determining the contribution of a specific site are Complementarity (the gain in diversity achieved when adding that site to a set of other sites) and Irreplaceability (here defined as the overall complementarity of that site when compared to a range of possible combinations of other sites). Generalised Complementarity Analysis (GCA) is a mathematical framework that provides an exact analytical solution for the expected complementarity (gain in diversity) of a focal site, when added to a set of other sites of a given size (m). Diversity is defined very generally to allow for complementarity to be calculated for species richness, Functional Diversity or Phylogenetic Diversity. The expected irreplaceability of a focal site is then defined in GCA as the area under the curve of expected complementarity values for all possible values of m. GCA is much more computationally efficient than existing algorithmic approaches and is scalable to very large numbers of sites. Because complementarity and irreplaceability are calculated for all possible combinations of sites, GCA serves as a null model for systematic conservation planning algorithms that seek to optimise site selection. However, because truly irreplaceable sites remain so under all possible site selections, GCA is a powerful conservation planning tool in its own right, providing an efficient means of identifying the world’s most precious places for conservation.