Effectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we investigate problems where optimal control theory has been implemented. We show that transforming these problems from state-costate systems to state-control systems provides the complete qualitative description of the optimal solution and leads to its theoretical expression for free terminal time problems. 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. (C) 2019 The Authors. Published by Elsevier Ltd.

Routine in linguaggio R per il controllo ottimo delle specie invasive

We present a modified version of an existing lake ecosystem model, describing a trophic chain generated by nutrients, phytoplankton and zooplankton (NPZ model). The NPZ model takes into account the vertical dynamics of the biomasses of the main species. We tailor the model to specific ecosystems by including seasonality in the dynamics of the various compartments. Moreover, different species exhibit a different behaviour with respect to diffusion and to the rate of vertical movement. With this model, we simulate the ecosystem dynamics of Alpine lakes located in study sites of the H2020 ECOPOTENTIAL project.

Presentazione orale al side event - GEO Week 2018 - Sede: Kyoto (JP) - La GEO WEEK è la conferenza scientifica internazionale di GEO che precede il summit annuale dei 200 membri di GEO. Si tiene alternativamente in America, Asia, Europa, Africa e Oceania.

Terrestrial and marine ecosystems provide essential goods and services to human societies. In the last decades, however, anthropogenic pressure has produced a loss of ecosystem services that can seriously affect human wellbeing and climate processes at local and regional scale. In order to improve ecosystem benefits, knowledge-based conservation, management and restoration policies are urgently needed. Fundamental to all these is effective monitoring of the state and trends in ecosystem conditions and services. New monitoring methodologies are now available, combining approaches in geo- and bioscience, earth observation data, and in situ data. This digital poster synthesizes the objectives and methods of the ECOPOTENTIAL project, a European Horizon 2020 project started in June 2015, which has been designed to reach significant progress beyond the state of the art on ecosystem services. The project focuses its activities and pilot actions on a targeted set of internationally recognized protected areas (PA) in Europe, European Territories and beyond, over a broad range of habitats, ecosystems and landscapes, including wetlands, arid and mountain ecosystems. Gli ecosistemi terrestri e marini forniscono beni e servizi essenziali alle società umane. Negli ultimi decenni, tuttavia, la pressione antropica ha prodotto una perdita di servizi ecosistemici che può seriamente influenzare il benessere umano e i processi climatici su scala locale e regionale. Al fine di migliorare i benefici degli ecosistemi, sono urgentemente necessarie politiche di conservazione, gestione e ripristino basate sulla conoscenza. Fondamentale per tutto questo è il monitoraggio efficace dello stato e delle tendenze delle condizioni e dei servizi ecosistemici. Sono ora disponibili nuove metodologie di monitoraggio che combinano approcci in geo- e bioscienze, dati di osservazione della terra e dati in situ. Questo poster digitale sintetizza gli obiettivi e i metodi del progetto ECOPOTENTIAL, un progetto europeo Horizon 2020 iniziato nel giugno 2015, che è stato progettato per raggiungere progressi significativi oltre lo stato dell'arte sui servizi ecosistemici. Il progetto concentra le sue attività e azioni pilota su un insieme mirato di aree protette (PA) riconosciute a livello internazionale in Europa, nei territori europei e oltre, su una vasta gamma di habitat, ecosistemi e paesaggi, comprese le zone umide, gli ecosistemi aridi e montani.

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).

Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction-diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well-posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species.

We propose novel positive numerical integrators for approximating predator-prey models. The schemes are based on suitable symplectic procedures applied to the dynamical system written in terms of the log transformation of the original variables. Even if this approach is not new when dealing with Hamiltonian systems, it is of particular interest in population dynamics since the positivity of the approximation is ensured without any restriction on the temporal step size. When applied to separable M-systems, the resulting schemes are proved to be explicit, positive, Poisson maps. The approach is generalized to predator-prey dynamics which do not exhibit an M-system structure and successively to reaction-diffusion equations describing spatially extended dynamics. A classical polynomial Krylov approximation for the diffusive term joint with the proposed schemes for the reaction, allows us to propose numerical schemes which are explicit when applied to well established ecological models for predator-prey dynamics. Numerical simulations show that the considered approach provides results which outperform the numerical approximations found in recent literature.

Protected Areas are subject to long-term modifications associated with climate and environmental change, enhancing the risk of ecosystem collapse, tipping points and unexpected responses to droughts, fires, floods and other individual events. One of the goals of the EU H2020 Project ECOPOTENTIAL and of the GEO ECO Initiative of the Group on Earth Observations (GEO) is to quantify ongoing and expected changes in the drivers and the characteristics of Protected Areas in Europe and beyond, using gridded climatic datasets, in situ meteo-climatic and biological data and Remote Sensing observations. Several statistical approaches are used to this goal, with the aim of determining the patterns and properties of the changes currently affecting Protected Areas. Use of suitably downscaled climate scenarios allows for estimating how such changes are projected into the next decades. Here we report the results on the changes in meteo-climatic drivers and in some remotely-sensed variables for the set of Protected Areas participating in the ECOPOTENTIAL project, focusing on a few specific examples encompassing mountain, arid/semi-arid and coastal ecosystems.

The large H2020 project ECOPOTENTIAL (2015-2019, 47 partners, contributing to GEO and GEOSS http://www.ecopotential-project.eu/) is devoted to making best use of remote sensing and in situ data to improve future ecosystem benefits, adopting the view of ecosystems as one physical system with their environment, focusing on geosphere-biosphere interactions, Earth Critical Zone dynamics, Macrosystem Ecology and cross-scale interactions, the effect of extreme events and using Essential (Climate, Biodiversity and Ocean) Variables as descriptors of change. In ECOPOTENTIAL, remote sensing and in situ data are collected, processed and used for a betterunderstandingoftheecosystemdynamics,analysingandmodellingtheeffectsofglobalchangesonecosystem functions and services, over an array of different ecosystem types, including mountain, marine, coastal, arid and semi-arid ecosystems. The project focuses on a network of Protected Areas of international relevance, that is representative of the range of environmental and biogeographical conditions characterizing Europe. Some of the activitiesoftheprojectaredevotedtodetectandquantifythechangestakingplaceintheProtectedAreas,through the analysis of remote sensing observations, in-situ data and gridded climatic datasets. Likewise, the project aims atprovidingestimatesofthefutureecosystemconditionsindifferentclimateandenvironmentalchangescenarios. In all such endeavours, one is faced with cross-scale issues: downscaling of climate information to drive ecosystem response, and upscaling of local ecosystem changes to larger scales. So far, the analysis has been conducted mainly by using traditional methods, but there is wide room for improvement by using more refined approaches. In particular, a crucial question is how to upscale the information gained at single-site scale to larger, regional or continental scale, an issue that could benefit from using, for example, complex network analysis.

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

This poster has been presented at the first ILTER Open Science Meeting in Skukuza, Kruger National Park, South Africa, 9-13 October 2016 (https://na.eventscloud.com/ehome/156435), and describes the general purposes and organization of the H2020 project ECOPOTENTIAL (http://www.ecopotential-project.eu/) Questo poster è stato presentato al primo ILTER Open Science Meeting a Skukuza, Kruger National Park, Sud Africa, 9-13 ottobre 2016 (https://na.eventscloud.com/ehome/156435), e descrive gli scopi generali e l'organizzazione del progetto H2020 ECOPOTENTIAL (http://www.ecopotential-project.eu/)

We apply the Z-control approach to a generalized predator prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter A. for the successful application of the method is stressed and related to specific dynamical properties of the Z-controlled model. Critical values of the design parameter are also found, delimiting the lambda-range for the effectiveness of the Z-method. Analytical results are then numerically validated by the means of two ecological models: the classical Lotka-Volterra model and a model related to a case study of the wolf wild boar dynamics in the Alta Murgia National Park. Investigations on these models also highlight how the Z-control method acts in respect to different dynamical regimes of the uncontrolled model. (C) 2016 The Authors. Published by Elsevier Inc.

tProtected areas are experiencing increased levels of human pressure. To enable appropriate conserva-tion action, it is critical to map and monitor changes in the type and extent of land cover/use and habitatclasses, which can be related to human pressures over time. Satellite Earth observation (EO) data andtechniques offer the opportunity to detect such changes. Yet association with field information and expertinterpretation by ecologists is required to interpret, qualify and link these changes to human pressure.There is thus an urgent need to harmonize the technical background of experts in the field of EO dataanalysis with the terminology of ecologists, protected area management authorities and policy makers inorder to provide meaningful, context-specific value-added EO products. This paper builds on the DPSIRframework, providing a terminology to relate the concepts of state, pressures, and drivers with the appli-cation of EO analysis. The type of pressure can be inferred through the detection of changes in state (i.e.changes in land cover and/or habitat type and/or condition). Four broad categories of changes in stateare identified, i.e. land cover/habitat conversion, land cover/habitat modification, habitat fragmentationand changes in landscape connectivity, and changes in plant community structure. These categories ofchange in state can be mapped through EO analyses, with the goal of using expert judgement to relatechanges in state to causal direct anthropogenic pressures. Drawing on expert knowledge, a set of pro-tected areas located in diverse socio-ecological contexts and subject to a variety of pressures are analysedto (a) link the four categories of changes in state of land cover/habitats to the drivers (anthropogenic pres-sure), as relevant to specific target land cover and habitat classes; (b) identify (for pressure mapping) themost appropriate spatial and temporal EO data sources as well as interpretations from ecologists andfield data useful in connection with EO data analysis. We provide detailed examples for two protectedareas, demonstrating the use of EO data for detection of land cover/habitat change, coupled with expertinterpretation to relate such change to specific anthropogenic pressures. We conclude with a discussionof the limitations and feasibility of using EO data and techniques to identify anthropogenic pressures,suggesting additional research efforts required in this direction

It is known that symplectic algorithms do not necessarily conserve energy even for the harmonic oscillator. However, for separable Hamiltonian systems, splitting and composition schemes have the advantage to be explicit and can be constructed to preserve energy. In this paper we describe and test an integrator built on a one-parameter family of symplectic symmetric splitting methods, where the parameter is chosen at each time step so as to minimize the energy error. For second-degree polynomial Hamiltonian functions as the one describing the linear oscillator, we build up second and fourth order symmetric methods which are symplectic, energy-preserving and explicit. For non-linear examples, it is possible to construct schemes with minimum error on energy conservation. The methods are semi-explicit in the sense that they require, as additional computational effort, the search for a zero of a scalar function with respect to a scalar variable. Therefore, our approach may represent an effective alternative to energy-preserving implicit methods whenever multi-dimensional problems are dealt with as is the case of many applications of interest.

We evaluate a mathematical model of the predator-prey population dynamics in a fragmented habitat where both migration processes between habitat patches and prey control policies are taken into account. The considered system is examined by applying the aggregation method and different dynamical scenarios are generated. The resulting implications are then discussed, their primary aim being the conservation of the wolf population in the Alta Murgia National Park, a protected area situated in the Apulian Foreland and also part of the Natura 2000 network. The Italian wolf is an endangered species and the challenge for the regional authorities is how to formulate conservation policies which enable the maintenance of the said wolf population while at the same time curbing that of the local wild boars and its negative impact on agriculture. We show that our model provides constructive suggestions in how to combine wild boar abatement programs awhile maintaining suitable ecological corridors which ensure wolf migration, thus preserving wolves from extinction.

We examine spatially explicit models described by reaction-diffusion partial differential equations for the study of predator-prey population dynamics. The numerical methods we propose are based on the coupling of a finite difference/element spatial discretization and a suitable partitioned Runge-Kutta scheme for the approximation in time. The RK scheme here implemented uses an implicit scheme for the stiff diffusive term and a partitioned RK symplectic scheme for the reaction term (IMSP schemes). We revisit some results provided in the literature for the classical Lotka-Volterra system and the Rosenzweig-MacArthur model. We then extend the approach to metapopulation dynamics in order to numerically investigate the effect of migration through a corridor connecting two habitat patches. Moreover, we analyze the synchronization properties of subpopulation dynamics, when the migration occurs through corridors of variable sizes.

The ECOPOTENTIAL project focuses its activities and pilot actions on a targeted set of internationally recognised protected areas (PA) in Europe, European Territories and beyond, including mountain, arid and semi-arid, and coastal and marine ecosystems. Building on the knowledge gained in individual PAs, the ECOPOTENTIAL project addresses cross-scale ecological interactions and landscape-ecosystem dynamics at regional to continental scales, using geostatistical methods and the emerging novel approaches in Macrosystems Ecology, which is addressing long-term and large-scale ecological challenges. ECOPOTENTIAL addresses the entire chain of ecosystem-related services, by (a) developing ecosystem data services, with special emphasis on Copernicus services; (b) implementing model output services to distribute the results of the modelling activities; and (c) estimating current and future ecosystem services and benefits, combining ecosystem functions (supply) with beneficiaries needs (demand). In ECOPOTENTIAL all data, model results and acquired knowledge are made available on common and open platforms, coherent with the Global Earth Observation System of Systems (GEOSS) data sharing principles and fully interoperable with the GEOSS Common Infrastructure (GCI).