Formal Modelling for Population Dynamics

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