Understanding the multifaceted effects of the matrix on species persistence in fragmented landscapes

Nicholas Kortessis and Robert Holt, Department of Biology, University of Florida, Gainesville, FL, Thomas Smith and Robert J. Fletcher Jr., Wildlife Ecology and Conservation, University of Florida, Gainesville, FL

Background/Question/Methods
Land conversion poses a serious threat to global biodiversity because it reduces habitat prevalence and continuity over space. Converted land – termed the matrix – is often of a markedly different character and has many effects on populations, both regional and local. Regionally, the matrix can alter dispersal likelihood, speed, and risk of death. Locally, matrix conditions can affect demographic rates inside remaining habitat, called edge effects. What is the cumulative outcome of regional and local effects of the matrix? And do these effects depend the distribution of remaining habitat, in terms of size and location?
We answer these questions in reference to species persistence in a spatially implicit Lotka-Volterra model of population growth in habitat fragments of varying size. We model local matrix effects as changes in the intrinsic rate of increase as a function of habitat size. We model regional matrix effects as mortality during dispersal. We model habitat loss as changes in total habitat amount and fragmentation as the distribution of fragment sizes. We defined persistence as a positive rate of increase when the population is rare on the landscape.

Results/Conclusions
We developed a persistence criterion in the case where individuals have equal density in all fragments. It compares the effects of the matrix with a measure of the distribution of fragment sizes on the landscape – which we call the effective habitat size. The two matrix effects of interest – edge effects and mortality during dispersal – interact with one another. Persistence is minimally affected by dispersal mortality when edge effects are strong but is greatly affected by dispersal mortality when edge effects are weak.
Species persist when matrix effects are smaller than effective habitat size on the landscape, which we define as the mean habitat size times 1 + the squared coefficient of variation in fragment size. Effective habitat size declines with fragment number and increases with variation in fragment size. Hence, landscapes with many small and few large fragments have greater effective size than an equivalent landscape with the same number of fragments, each the same size. This suggests that species are more robust to matrix effects in landscapes with variable fragment size, given fixed fragment number. The biological reason is that larger fragments house more individuals and these fragments are buffered from the negative effects of the matrix.