Abstract
Seabirds breeding on islands are vulnerable to introduced predators, such as rats and cats, and the removal of such predators is generally viewed as a priority for seabird conservation and restoration. However, multiple invasive mammal species interacting may generate unexpected outcomes following the removal (eradication) of one species. Generally these indirect interactions are not well understood or demonstrated. We propose and study a prey (seabird)-mesopredator (rat)-superpredator (cat) model, taking into account the juvenile stages in the prey population, in order to direct conservation management for seabird conservation. We give a more biologically realistic differential system than those studied before (Courchamp et al. [1999]; Fan et al. [2005]), in particular for long-lived seabird species. We present a theoretical study and show existence and uniqueness of a positive solution as well as a qualitative study of the equilibria that may appear. Because standard numerical methods, usually implemented in scientific softwares, can fail to give the right biological approximations (Anguelov et al. [2009]), we propose a reliable algorithm that preserves most of the qualitative properties of the continuous system, using the theory of nonstandard finite difference methods. Finally, we use biologically realistic parameters available for the representative Barau's petrel (Pinet et al. [2008]), an endemic species from Reunion island, to present numerical simulations that support the theoretical study. Cats play the major role in seabird prey population dynamics. Seasonality in seabird breeding delays but does not prevent extinction. In all scenarios, cat control (or preferably eradication) is imperative to prevent extinction of vulnerable long-lived seabirds, like the Barau's petrel
Highlights
Biodiversity is undergoing a dramatic decline, attributable entirely to the impact of humans (Vitousek et al [1997])
We simulate a scenario similar to Reunion Island considering the dynamics of petrels without predation, i.e., without rats and cats: in Figure 3, we show that petrel dynamics tend slowly to the nontrivial equilibrium, E∗
We have presented an extension of previous mesopredator release models (Courchamp et al [1999]; Fan et al [2005]), with a particular focus on an endangered endemic seabird: the Barau’s petrel in Reunion Island
Summary
Biodiversity is undergoing a dramatic decline, attributable entirely to the impact of humans (Vitousek et al [1997]). Conservation and management of natural ecosystems has become an important and necessary task in order to preserve as much as possible of the biological diversity in many places around the world Le Corre [2008]. This is so on oceanic islands, which house a disproportionate amount of the world’s biodiversity relative to their area. Isolated islands have been disproportionately impacted by the introduction of non-native species. The introduction of alien species is recognized as directly or indirectly responsible for 42% of bird extinctions on islands (King [1985]). Mathematics has become a powerful tool giving prospective insight into the dynamics of interacting populations, helping conservation managers make informed and appropriate choices about the outcomes of control programmes
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