Mathematical tools for controlling invasive species in Protected Areas

A challenging task in the management of Protected Areas is the conservation of natural habitats and native endangered species through the optimization of control strategies for invasive plant or animal species, typically competing for the use of resources in a fragmented habitat [1]. We review two cases of control strategies on the wolf-wild boar populations in a Southern Italy Protected Area belonging to the Natura 2000 network [2,3]. The challenge for the regional authorities is to plan conservation policies able to maintain the population of wolves while limiting the presence of wild boars, here considered invasive because of their harmfulness on cultivated areas. The first strategy [2] considers the impact of control policies on predator-prey dynamics in fragmented habitats by simulating different dynamical scenarios theoretically analysed with the aggregation method. The key warning from the model is that a very careful combination of control - through proper planning programs - and migration processes among patches of habitats - through the existing suitable ecological corridors - must be used in order to limit the wild-boar population while preserving wolves from extinction. The second strategy has been developed to apply the Z-control approach to a generalized predator-prey system [3]. It considers the specific case of indirect control of the prey (invasive) population. The key role of the model design parameter is stressed and the critical values of the design parameter are found, delimiting the parameter range for the successful application of the Z-method. A further development is the optimization of a control strategy by taking into account the spatio-temporal data related to the control problem of an invasive species over a wide natural protected area. That approach will be applied to the Alta Murgia National Park, where a EU LIFE+ project is underway to eradicate Ailanthus altissima, included in the list of the most invasive alien plant species in Europe causing serious damages both in protected and urban areas [4]. The Alta Murgia National Park is one of the study site of an on-going H2020 project (ECOPOTENTIAL). This work has been carried out within the H2020 project `ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations', coordinated by CNR-IGG (http://www.ecopotential-project.eu). The project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 641762. Bibliography 1)Baker, C. M., Target the Source: Optimal Spatiotemporal Resource Allocation for Invasive Species Control, CONS. LETTERS, pp 1-8, 2016, doi: 10.1111/conl.12236 2)Lacitignola, D.; Diele, F.; Marangi, C., Dynamical scenarios from a two-patch predator-prey system with human control - Implications for the conservation of the wolf in the Alta Murgia National Park ECOLOGICAL MODELLING, Vol. 316, pp 28-40, 2015, doi: 10.1016/j.ecolmodel.2015.07.027 3)Lacitignola, D.; Diele, F.; Marangi, C.; Provenzale A., On the dynamics of a generalized predator-prey system with Z-type control, MATHEMATICAL BIOSCIENCES, vol. 280, pp 10-23, 2016, doi: 10.1016/j.mbs.2016.07.011 4)Casella F., Vurro M. , Ailanthus altissima (tree of heaven): Spread and harmfulness in a case-study urban area, Arboricultural Journal: The International Journal of Urban Forestry, 35(3), pp 172-181, 2013, doi: 10.1080/03071375.2013.852352