We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density. Remote sensing and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. The approach has been applied to the plant species Ailanthus altissima (Mill.) Swingle within the Alta Murgia National Park. This area is one of the Natura 2000 sites under the study of the ongoing National Biodiversity Future Center (NBFC) funded by the Italian National Recovery and Resilience Plan (NRRP), and pilot site of the finished H2020 project ECOPOTENTIAL, which aimed at the integration of modeling tools and Earth Observations for a sustainable management of protected areas. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data provided by the EU Life Alta Murgia project (LIFE12 BIO/IT/000213), a project aimed at the eradication of Ailanthus altissima in the Alta Murgia National Park

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, typically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas [11]. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL).

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, tipically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach ; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas [11]. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL).

We develop a modelling approach for the optimal spatiotemporal control of invasive species in natural protected areas of high conservation value. The proposed approach, based on diusion equations, is spatially explicit, and includes a functional response (Holling type II) which models the control rate as a function of the invasive species density. We apply a budget constraint to the control program and search for the optimal eort allocation for the minimization of the invasive species density. Both the initial density map and the land cover map used to estimate the habitat suitability to the species diusion, have been generated by using very high resolution satellite images and validated by means of ground truth data. The approach has been applied to the Alta Murgia National Park, one of the study site of the on-going H2020 project ECOPOTENTIAL: Improving Future Ecosystem Benets Through Earth Observations' (http://www.ecopotential-project.eu) which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 641762. All the ground data regarding Ailanthus altissima (Mill.) Swingle presence and distribution are from the EU LIFE Alta Murgia Project (LIFE12 BIO/IT/000213) titled Eradication of the invasive exotic plant species Ailanthus altissima from the Alta Murgia National Park funded by the LIFE+ nancial instrument of the European Commission.

The threat, impact and management problems associated with alien plant invasions are increasingly becoming a major issue in environmental conservation. Invasive species cause significant damages, and high associated costs. Controlling them cost-effectively is an ongoing challenge, and mathematical models and optimizations are becoming increasingly popular as a tool to assist managers. The aim of this study is to develop a modelling approach for the optimal spatiotemporal control of invasive species in natural protected areas of high conservation value. Typically, control programs are either distributed uniformly across an area, or applied with a given fixed intensity, although there is no guarantee that such a strategy would be cost-effective at the conservation asset. The proposed approach, based on diffusion equations, is spatially explicit, and includes a functional response (Holling type II) which models the control rate as a function of the invasive species density. We apply a budget constraint to the control program and search for the optimal effort allocation for the minimisation of the invasive species density. Remote sensing derived input layers and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data. The approach has been applied to the Alta Murgia National Park, where the EU LIFE Alta Murgia Project is underway with the aim to eradicate Ailanthus altissima, one of the most invasive alien plant species in Europe. The Alta Murgia National Park is one of the study site of the on-going H2020 project ECOPOTENTIAL which aims at the integration of modelling tools and Earth Observations for a sustainable management of protected areas. The H2020 project 'ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations' (http://www.ecopotential-project.eu) has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 641762. All ground data regarding Ailanthus altissima (Mill.) Swingle presence and distribution are from the EU LIFE Alta Murgia Project (LIFE12 BIO/IT/000213 titled "Eradication of the invasive exotic plant species Ailanthus altissima from the Alta Murgia National Park" funded by the LIFE+ financial instrument of the European Commission).

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages, and associated costs, that stem from invasive species are well known, as is the benefit from their removal. We investigate problems where optimal control theory has been implemented, and we show that these problems can easily become hypersensitive, making their numerical solutions unstable. We show that transforming these problems from state-adjoint systems to state-control systems can provide useful insights into the system dynamics and simplify the numerics. We apply these techniques to two case studies: one of feral cats in Australia, where we use logistic growth; and the other of wild-boars in Italy, where we include an Allee effect. A further development is to optimize the control strategy by taking into account the spatio-temporal features of the invasive species control problems over large and irregular environments. The approach is used in a management scenario where the invasive species to be controlled with an optimal allocation of resources is the deciduous tree Ailanthus Altissima, infesting the Alta Murgia National Park in the south of Italy. This work has been carried out within the H2020 project ECOPOTENTIAL (http://www.ecopotential-project.eu), coordinated by CNR-IGG. The project has received funding from the European Union's Horizon 2020 research and innovation programme (grant agreement No 641762).

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