A modelling approach to study landscape effects on abundance from patch demographic processes

Biodiversity loss is one of the great challenges to be faced by the current and the future generations. Habitat loss and fragmentation are important sources of concern. A recent debate over the effects of habitat fragmentation on biodiversity led to contradictory results. Some argue that habitat fragmentation has profound negative effects on biodiversity, while others challenge this view and advocate that those effects are usually negligible and mostly positive when significant. One source of disagreement comes from the scale of investigations made so far. Initial studies investigated the patch-scale mechanisms by which habitat fragmentation affects biodiversity and generally supported negative effects, for example by means of edge effects, vulnerability of small populations to stochasticity, etc. Recently, however, studies seeking a landscape-scale pattern of how habitat fragmentation impacts biodiversity failed to reach consistent results. This apparent contradiction between mechanisms and observed pattern highlighted the need for mechanistic understanding on how patch-scale mechanisms lead to landscape-scale patterns. In this study we link patch-scale mechanisms to landscape-scale abundance patterns by means of a patch model consisting of a system of ordinary differential equations. The equations describe the populations of the patches, which are interdependent and affected by four basic demographic processes: births, deaths, immigration and emigration. We promote the link between scales by deriving an insightful expression for the landscape equilibrium abundance and a necessary and a sufficient condition for landscape extinction, all of them integrating the demographic processes of all patches. As a second step, we sought to describe birth, death, immigration and emigration rates in terms of characteristics of the patches, like patch areas and inter-patch distances. This translates our landscape equilibrium abundance expression and extinction conditions in terms of landscape traits commonly used in Landscape Ecology, like habitat amount (sum of the areas of all patches) and landscape configuration metrics (functions of the traits of all patches). We use data collected from an Individual Based Model (IBM) to illustrate each of the steps of this study.