Characterising extinction debt following habitat fragmentation using neutral theory

Habitat loss leads to species extinctions, both immediately and over the long term as 'extinction debt' is repaid. The same quantity of habitat can be lost in different spatial patterns with varying habitat fragmentation. How this translates to species loss remains an open problem requiring an understanding of the interplay between community dynamics and habitat structure across temporal and spatial scales. Here we develop formulas that characterise extinction debt in a spatial neutral model after habitat loss and fragmentation. Central to our formulas are two new metrics, which depend on properties of the taxa and landscape: 'effective area', measuring the remaining number of individuals and 'effective connectivity', measuring individuals' ability to disperse through fragmented habitat. This formalises the conventional wisdom that habitat area and habitat connectivity are the two critical requirements for long-term preservation of biodiversity. Our approach suggests that mechanistic fragmentation metrics help resolve debates about fragmentation and species loss.