Learning objectives consist in reaching a good level as of knowledge and skills, which are seen in a continuous interaction during the class work. Of particular importance, to this end, is the skill in modelling development, which requires capabilities in selecting the aspects of the real systems that deserve to enter in the modelling description, identifying their interactions and representing them appropriately. Knowledge and skills about modelling are framed in a dialectical view of the systems, that is wholes as contingent structures in reciprocal interactions with their own parts and with the greater whole of which they are parts.
Independence of judgment is vital for a discipline in which deciding which modelling representation of a real system is the most appropriate becomes crucial. Independence of judgment is needed to decide which elements and interactions in a system are really important and which ones can be instead discarded as irrelevant. In this framework independent judgment will be improved through:
1. creation of models to describe specific systems;
2. analysis of alternative model to highlight similarities and differences and identify the importance of variables and relationship in the dynamics of the models;
3. capturing robust results while analyzing alternative models of the same system.
Communication skills will be strengthened through:
1. the creation of cognitive maps to fix the concepts that are really important for a model representation;
2. debating around alternative choices for modelling representation of real systems: choice of variables, description of their relationships, weighting the dynamical factors, etc.
Course contents summary
The course can be thought as methodologicaly composed of three parts. In the first the focus is on classical two species models (predator-prey and competitive interactions) as they took shape according to the pioneering studies of Vito Volterra and Alfred Lotka. Also this part will focus on the management of natural populations. In the second part the focus will be on ecological networks and the food webs. Finally in the third part the qualitative analysis of complex systems will dominate the didactic landscape to provide a tool to investigate socio-ecological systems.
Part 1. Systems of differential equations, parameters and variables. Jacobian matrix and the Community Matrix. Population dynamics: density-dependent growth, exploiting populations. Competition models. Predator-prey models.
Part2. Ecological networks. Material and energy flows. Building a flow network: the case of the Santo Lake (Parma, Apennines). Input-output analysis. Trophic levels, cycles, indicators of growth and development: TST, AMI Ascendency, Overhead, Finn cycling Index. Application to an urban ecosystem: water flow networks and the idea of sustainability. A particular type of ecological network: the food web. Properties of the food webs: centrality, connectance. Secondary extinction in food webs. The dominator tree model. Allometric properties of the food webs.
Part 3. Qualitative modelling for the study of complex systems. Differential equations and signed digraphs. Stability and levels of feedback. Types of variability: fluctuations in the levels of the variables and parameter changes. Moving equilibrium. Predicting impacts of parameter changes. Prediction tables. The table of predictions a diagnostic tool. The controlling factors in ecological communities. Applications: the case of the Black Sea Ecosystem.
Puccia, C.J. and Levins, R. 1986. Qualitative modelling of complex systems. Harvard University Press, Cambridge, MA, USA.
Bodini, A., Bondavalli, S., Allesina, S. 2007. L'ecosistema e le sue relazioni. Franco Angeli, Milano.
Lecturing and exercises. The exercises will be organized within a problem-solving approach. In this framework the students will be asked to construct alternative models to solve a management problem. Models will be analyzed through the use of a dedicated software (Levins Analysis)
Assessment methods and criteria
The final examination will be inspired by a management question which should be solved through the construction and analysis of alternative models. This will guarantee the possibility to assess knowledge and skills.