ETD system

Electronic theses and dissertations repository


Tesi etd-05222015-090117

Thesis type
Tesi di dottorato di ricerca
Formal Modelling for Population Dynamics
Settore scientifico disciplinare
Corso di studi
tutor Prof. Maggiolo Schettini, Andrea
relatore Dott. Cerone, Antonio
Parole chiave
  • stochastics
  • spatial
  • parallelism
  • formalism
Data inizio appello
Riassunto analitico
The spirit of sustainable development has inspired our research work. Ecologically sus-<br>tainable development needs preventative strategies and measures against environmental<br>degradation. In our work we focus on constructing a formalism that enables modellers to<br>model the population dynamics within an ecosystem and to analyse them. Furthermore,<br>preventative strategies can be put into the model so that their effectiveness for ecosystems<br>can be measured.<br>An ecosystem consists of many interacting components. These components have many<br>behaviours which are not easy to put together in a model. Work on such modelling started<br>a long time ago, and even more has been done recently. These approaches have been taken<br>from ordinary differential equations to stochastic processes. There are also some existing<br>formalisms that have already been used for this modelling. In ecosystems there are several<br>important aspects that need to be incorporated into the model, especially: stochasticity,<br>spatiality and parallelism. One formalism has strengths in a certain aspect but weaknesses<br>in others. Being motivated by this situation our work is to construct a formalism that<br>could accommodate these aspects. Besides this, the formalism is intended to facilitate the<br>modellers, who are generally biologists, to define the behaviours in the model in a more<br>intuitive way. This has led our work to adopt features from existing formalisms: Cellular<br>Automata and P Systems. Then, after adding new features, our work results in a new<br>formalism called Grid Systems.<br>Grid Systems have the spatiality of Cellular Automata but also provide a way to define<br>behaviours differently in each cell (also called membrane) according to the reaction rules<br>of P Systems. Therefore, Grid Systems have a richer spatiality compared to CA and<br>the parallelism and stochaticity of P Systems. Besides these, we incorporate stochastic<br>reaction duration for the reaction rules so that Grid Systems have stochasticity in rule<br>selection and stochasticity in reaction termination. This enables us to define scheduled<br>external events which are important aspects in modelling ecosystems.<br>In addition to these, we extend Grid Systems with a new feature called ‘links’. A link<br>is an object that can carry pointers. The pointer of a link can be used in the rule to<br>transfer objects to another membrane. Because a link is also an object, its existence as<br>well as its pointer are dynamic. By using the links, the membranes of Grid Systems can<br>be structured as a tree to imitate the membrane structure of P Systems, or even more as<br>a graph for a more general computation. The property of the links enables the structure<br>to be dynamic, in a similar way to the dissolving membrane in the P Systems.<br>The features of Grid Systems are defined in terms of syntax and semantics. The syntax<br>describes how the model should be expressed by the modeller. The semantics describes<br>what will happen to the model when the model evolves. From the semantics a software<br>tool can be developed for analysing the model.<br>In our research work we have developed the models in two case studies. In the first case<br>study, we focus on the interacting events and external events that affect the population<br>dynamics of mosquitoes. We observe how the impacts of events are propagated in space<br>and time. In the second case study, we focus on the spatiality movement created by the<br>seasonal migration of wildebeests. We observe that the pathways in the migration can be<br>modelled well using links.<br>The models of both case studies are analysed by using our simulation tool. From<br>both case studies we conclude that our formalism can be used as a modelling framework<br>especially for population dynamics, and in general for analysing the models of ecosystems.