Public parks management via mathematical tools

Abstract

In this paper, we consider a mathematical model for the interaction of wild and domestic herbivores with a natural or man-maintained landscape. We focus our attention on parks in Piedmont (NW Italy), which are characterized by the presence of meadows, woods and herbivore populations, such as deer and sheep. Even if herbivores consume mainly grass, they can occasionally debark trees. This behaviour occurs especially in the winter season, when grass availability is reduced, and may cause the death of trees. Our model evaluates some possible policies for dealing with this problem. The results of this study show that it is wise to keep the number of herbivores in environments in which young trees are present in check. Grazing of domestic herbivores should be prohibited in newly planted tree areas.

Keywords:

• mathematical models
• herbivores
• predator–prey systems
• tree debarking

2010 AMS Subject Classifications :

• 92D25
• 92D40
• 92D50

Acknowledgements

The authors thank Fabio Schiari for the photograph of deer debarking, Figure 1 right, and Elisa Ramassa, a ranger of the ‘Gran Bosco di Salbertrand’ park, for the useful information provided. The authors are indebted also to the referee for his valuable remarks that contributed to markedly improving the paper.