ECOLOGY

The course is included in the batchelor degree programme “Engineering for the ecological transition” .The main objective of the programme is to train highly skilled professionals, who could put into use their interdisciplinary knowledge for identifying and solving complex problems, related to the implementation of national and European Union strategies for the ecological transition. In particular, the programme aims at providing an integrated and systemic view of environmental dynamics, in order to enable master graduates to deal with global environmental challenges, in the context of sustainable development. To this regard, the challenges connected to adaptation and mitigation to Climate Changes are extremely significant, the implementation of the energy transition being a most relevant one. In this context, this course provides the basic knowledge for simulating ecosystems functioning, by means of process based models. These tools allow one to turn conceptual models into mathematical ones, whose output can be compared with field observations, thus enabling the elucidation of the mechanisms which generate the system output, on the basis of the flow of energy and matter at its boundaries and of the interactions among its main variables. This systemic approach is of paramount importance for developing predictive models, which could orient the implementation of environmental policies aimed at implementing the ecological transition.

Attending the classes, thoroughly studying the course notes and reading materials, carrying out homework and assignments will enable the students to achieve the following learning outcomes.
1) Knowledge and comprehension
Knowledge of the terminology and of the main concepts of dynamic system theory. In line with the learning objectives of the programme, this knowledge will enable students to characterize and model the time series of environmental, economic and energetic data, thus providing a back ground for science-based policy making and management actions.
Understanding the relevance of the systemic approach for the investigation of ecosystem dynamics and the prediction of their evolution.
2) Capacity of applying knowledge and comprehension
To be able to apply dynamic system theory in case studies concerning: 1) the modelling of the effects of pollutant loads on ecosystems, with focus on acquatic ones. 2) the management of renewable resources under different exploitation regimes.
To be able to plan management actions, aimed at mitigating the impacts of local and global antropic pressures.
3) Assessment capacity
To be able to assess the environmental benefits brought about by the implementation of alternative scenarios of management actions, such as wildlife restoking, reduction of the loads of pollutants and nutrients, limitation of the exploitation of alieutic resources .

Basic knowledge of calculus: function, most common functions of real variables (exponential, logarithm, trigonometric functions), derivative, derivation and differentiation rules, antiderivative, integrals, basic integrals and integration rules. Basic knowledge of linear algebra: matrix/vector operations,eigenvalues, eigenvectors.

1) Main principle of ecosystem ecology: ecosystem structure, trophic levels, ecosystem functioning, energy flows, biogeochemical cycles..
2) Overview of the main environmental directives for the protection of the environment, with focus on acquatic ecosystems: Water Framework Directive, Marine Strategy Framework Directive, Maritime Spatial Planning. Relevance of the biological quality elements for the definition of the Good Environmental Status. Systemic approach: state variable and forcings.

3) Ordinary Differential Equations (ODE). Order of an ODE. 1st order ODE. Initial value problem. Existence and uniqueness theorem. Particular and general solution. Autonomous equations: stationary points and qualitative asymptotic analysis. General solution of a 1st order separable ODE. First order linear ODE. General solution of a homogeneous linear ODE. Solution of non-homogeneous linear ODE: 1) constant forcing; 2) the variation of constant method. Solution of a linear first order ODE for three time dependent forcing functions: linear , periodic , exponential. Linear combination of forcings: the superposition principle.

Applications – separable ODE

Radioactive decay and radionuclide half-life.
Penetration of light in a water body.
Micropollutant contamination: half-life of pollutants in environmental media.
Population dynamics: Malthus equation, the logistic equation.

Applications: linear ODE
Modelling the dynamics of a pollutant in a waterbody. Input-output relationship. Inverse problem and its relevance for the implementation of the environmental legislation.
Modelling the individual growth of aquatic organisms.
Modelling organic micropollutant bioaccumulation in aquatic organisms.

4) 1D Dynamic systems. State variables. Definition of a dynamic system. 1D autonomous systems. Direction field and phase portrait of autonomous equation. Orbits and trajectories. Phase portraits: stationary points and their stability. Local stability analysis.
Applications – 1D dynamic systems
Renewable resources. Open access resources. Management policies: controlling quotes and efforts. Example: the logistic model revisited.

5) 2D dynamic systems. State vector and state space. Autonomous 2D systems. Vector field. Existence and uniqueness Theorem in 2D. 2D linear systems. Particular solutions of a 2D linear dynamic system. General solution. Properties of the general solution. Trajectories and orbits for real eigenvalues. Numerical examples. Numerical solution of dynamic systems using "R" programming environment. Constructing phase portraits using numerical solutions. Classification of orbits of 2D systems: typical phase portraits for complex eigenvalues. Periodic orbits. Summing up: classification of orbits of linear systems.
Applications: 2D linear systems
The Streeter-Phelps model for simulating the dynamic of Dissolved Oxygen in a waterbody.
Multimedia environmental models for predicting the contamination in several abiotic compartment.
Applications: 2D non linear systems
Interactions among population in ecosystems. Predator-prey interactions. The Lotka-Volterra model. Stability of an equilibrium point. Stability analysis of 2D linear systems. Local stability analysis of non-linear systems. Stability analysis of the Lotka-Volterra model. More complex dynamics: predator functional response Holling I,and II. Emerging of periodical oscillation in predator-prey systems.
6) Guidelines for model building. Steps in model building: identification of model structure, a priori parameter estimation, calibration, validation, assessment of model performance: Goodness of Fit (GoF) indices and graphical methods.

Corse notes, slides and reading materials provided by the lecturer.

The achievement of the learning objectives if verified by means of a written test and of a report. The written test account for 24/30 to the final mark. The test includes 5 questions, aimed at ascertaining that a student has understood the main theoretical background and is able to apply it. The report presents the results of the coding of a simple model and of the comparison of model output with a set of observations, provided by the lectures. This assignement contributes for 6/30 to the final mark.

Lectures, based on the notes which are provided weekly to the students, in which power point presentations will also be used. The relevance of all topics in understanding and modelling environmental processes is underlined and illustrated by means of examples. Simple numerical problems, similar to those proposed in the final test, are solved and discussed during classes. Correction of homework. Use of software tools for the numerical solution of dynamic systems: these tools allow students to check the analytical solutions and to explore the system dynamics in real world situation, in which the forcings are estimated from time series of observations.

Italian

written

This subject deals with topics related to the macro-area "Natural capital and environmental quality" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development