Scienze Naturali, Scienze dei Sistemi Naturali,
Evoluzione del comportamento animale e dell’uomo

The aim of this course is to introduce the basic mathematical models for evolution:

- Classical models in ecology and evolutionary biology: logistic and malthusian growth
- Models for interacting species (Lotka Volterra) and epidemiological models
- Basic evolutionary game theory applied to animal and human behavior

Specific software, such as Wx-maxima and spreadsheets, will be introduced and used for simulations.

Knowledge and learning skills: Knowledge of the most important game-theoretical population-dynamical models for the evolution of behavior; Students are expected to acquire the capability to construct and study models for simple conflict problems
using game theory, and to develop operational knowledge of different mathematical models in evolutionary biology. Futher, the students will be able to understand and work on the scientific literature on the subjects.

Ability to apply the acquired knowledge: applying and studying mathematical modes described on the course; ability of determining the solution methods and analyse the results of the models, possibly with the aid of computer packages such as Excel. Understanding and interpreting scientific papers on the topics treated in the course.

Critical thought: understanding, interpreting and discussing the results of the models and of scientific papers.

Communication skills: to be able to present the results of a model possibly with diagrams, graphs, and  so on.

Learning skills: ability of focusing on the most relevant aspects of scientific information.

The  oral examination is preceded by a quiz test to determine the knowledge of the minimal objectives of the course. In order to access the oral exam it is necessary to pass the quiz, that will have to be repeated in case of failure to pass the oral exam. The oral exam is based both on questions regarding the theory and the solution of exercises, and is aimed at verifying both the understanding of the basic theoretical principles underlying the mathematical models, as well as the capability of formulating, solving and discussing problems arising in the study of human and animal behavior.

1) Discrete dynamical systems with examples on the logistic and malthusian growth; Fibonacci models.
2) Dynamical systems in continuous time, specifically exponential and logistic models; multi-variable dynamical
systems and interacting population models (epidemiological and Lotka-Volterra models).
3) Introduction to game theory; the basic strategic games and Nash equilibrium: Prisoner's dilemma, the battle of sexes, chicken and stag-hunt; evolutionary stability: hawk and doves and variants; extended games and perfect equilibrium. Iterated Prisoner's dilemma and decisional automata: tit for tat, grim, and others.
Applications to animal behavior:  the handicap principle, mating strategies, cooperation.
4) Evolution of animal behavior: the replicator dynamics.
5) Population genetics: Hardy-Weinberg equilibrium and Fisher's equation; stability of negative traits.