In this paper we extend PALPS, a process calculus proposed for the spatially-explicit individual-based modeling of ecological systems, with the notion of a policy. A policy is an entity for specifying orderings between the different activities within a system. It is defined externally to a PALPS model as a partial order which prescribes the precedence order between the activities of the individu- als of which the model is comprised. The motivation for introducing policies is twofold: one the one hand, policies can help to reduce the state-space of a model, on the other hand, they are useful for exploring the behavior of an ecosystem under different assumptions on the ordering of events within the system. To take account of policies, we refine the semantics of PALPS via a transition relation which prunes away executions that do not respect the defined policy. Furthermore, we propose a translation of PALPS into the probabilistic model checker PRISM . We illustrate our framework by applying PRISM on PALPS models with policies for conducting simulation and reachability analysis.
Population ecology is a subfield of ecology that deals with the dynamics of species populations and their interactions with the environment. Its main aim is to understand how the population sizes of species change over time and space. It has been of special interest to conservation scientists and practitioners who are interested in predicting how species will respond to specific management schemes and in guiding the selection of reservation sites and reintroduction efforts, e.g. [22,33].
One of the main streams of today’s theoretical ecology is the individual-based approach to modeling population dynamics. In this approach, the modeling unit is that of a discrete individual and a system is considered as the composition of individuals and their environment. Since individuals usually move from one location to another, it is common in individual-based modeling to represent space explicitly. There are four different frameworks in which spatially-explicit individual-based models can be defined [7]. They differ in the way space and time are modeled: each can be treated either discretely or continuously. The four resulting frameworks have been widely studied in Population ecology and they are considered to complement as opposed to compete with each other.
In this paper, we extend our previous work on a process-calculus framework for the spatially-explicit modeling of ecological systems. Our process calculus, PALPS follows the individual-based modeling and, in particular, it falls in the discrete-time, discrete-space class of Berec’s taxonomy [7]. PALPS associates processes with information about their location and their species. The habitat is defined as a graph consisting of a set of locations and a neighborhood relation. Movement of located processes is then modeled as the change in the location of a process, with the restriction that the originating and the destination locations are neighboring locations. In addition, located processes may communicate with each other by exchanging messages upon channels. Communication may take place only between processes which reside at the same location. Furthermore, PALPS may model probabilistic events, with the aid of a probabilistic choice operator, and uses a discrete treatment of time. Finally, in PALPS, each location may be associated with a set of attributes capturing relevant information such as the capacity or the quality of the location. These attributes form the basis of a set of expressions that refer to the state of the environment and are employed within models to enable the enunciation of location-dependent behavior.
The extension presented in this paper is related to the issue of process ordering inside each time unit. In particular, simulations carried out by ecologists impose an order on the events that may take place within a model. For instance, if we consider mortality and reproduction within a single-species model, three cases exist: concurrent ordering, reproduction preceding mortality and reproduction following mortality. In concurrent ordering, individuals may reproduce and die simultaneously. For reproduction preceding mortality, the population first reproduces, then all individuals, including new offspring, are exposed to death. For reproduction following mortality, individuals are first exposed to death and, subsequently, surviving individuals are able to reproduce.
Ordering can have significant implications on the simulation. Thus, alternatives must be carefully studied before conclusions are drawn.
In order to capture process ordering in PALPS, we define the notion of a policy, an entity that imposes an order on the various events that may take place within a system. Formally, a policy, σ, is defined as a partial order on the set of events in the system where, by writing ( β) ∈ σ, we specify that, whenever there is a choice between executing the activities $andβ, β is chosen. As a result, a policy is defined externally to a process description. This implies that one may investigate the behavior of a system under different event orderings simply by redefining the desired policy without redeveloping the system’s description. To capture policies in the semantics of PALPS we extend its transition relation into a prioritized transition relation which prunes away all transitions that do not respect the defined policy. Furthermore, we present a methodology for analyzing models of PALPS with policies via the probabilistic model checker PRISM [1]. To achieve this, we describe a method for translating models of PALPS with policies into the PRISM language and we prove its correctness. We then apply our methodology on simple examples that demonstrate the types of analysis that can be performed on PALPS metapopulation models via the PRISM tool. By contrasting our results with our previous work of [37], we observe that policies achieve a significant reduction in the size of models and may thus enable the analysis of larger systems.
Various formal framewo
This content is AI-processed based on open access ArXiv data.
