Scenarios and scenario models

As formalised by Keppens and Shen [20], a compositional modeller takes two inputs and produces one output. The first input is a representation (which is itself a model) that describes the system of interest by means of an accessible formalism. This model, which normally consists of (mainly) real-world participants and their interrelationships, is called the scenario. The second input is the task description. It is a formal description of the criteria by which the adequacy of the output is evaluated. The output is a new model that describes the scenario in a more detailed formalism, usually a set of variables and equations, which the model-based reasoner can employ readily. Such a model, which normally contains conceptual participants and interrelationships, is called a scenario model. The aim of any compositional modeller is to translate the scenario into a scenario model, by means of the task description.

In this work, a model is formally defined by a tuple $\langle P,R\rangle$, where $P$ is a set of participants and $R$ is a set of relations over the participants in $P$. This definition applies to both the scenario and the scenario model. A typical example of a scenario is a description of a predator population, a prey population and a predation relation between the predator and the prey. This scenario is a model $\langle P,R\rangle$ with:

$$\begin{split}P&=\{\texttt{predator},\texttt{prey}\}\\ R&=\{\texttt{(predation predator prey)}\} \end{split}$$

Figure 3: Stock flow diagram of predator prey scenario model

Table 1: Variables in the stock flow diagram and the mathematical model

Symbol	Variable name
$N_{\text{predator}}$, $N_{\text{prey}}$	number of predators, prey
$B_{\text{predator}}$, $B_{\text{prey}}$	natality of predators, prey
$D_{\text{predator}}$, $D_{\text{prey}}$	mortality of predators, prey
$P_{\text{prey}}$	predation of prey
$b_{\text{predator}}$, $b_{\text{prey}}$	natality-rate of predators, prey
$d_{\text{predator}}$, $d_{\text{prey}}$	mortality-rate of predators, prey
$C_{\text{predator}}$, $C_{\text{prey}}$	capacity of predators, prey
$s_{\text{(prey,predator)}}$	search-rate
$t_{\text{(prey,predator)}}$	prey-handling-time
$r_{\text{(predator,prey)}}$	prey-requirement

The aim of the compositional model repository is to translate a scenario into a scenario model. Within this work, both systems dynamics stock-flow formalism [12] and ordinary differential equations (ODEs) will be employed as the modelling formalisms. For example, a scenario model that corresponds to the above scenario is depicted in Figure 3. Formally, a scenario model is another model $\langle P,R\rangle$ and in this case

$$\begin{split}P=\{ &N_{\text{predator}},B_{\text{predator}},D_... ...ext{predator})},r_{(\text{predator},\text{prey})}\} \end{split}$$

$$\begin{split}R=\{ &\frac{d}{dt}N_{\text{predator}}=B_{\text{p... ...\text{prey}},\\ &C_{\text{prey}}=N_{\text{prey}} \} \end{split}$$

The relation between the variables of the mathematical model and those used in the stock-flow diagram is given in table 1. Generally speaking, stock-flow diagrams are graphical representations of systems of (ordinary or qualitative) differential equations. In the automated modelling literature in general, and engineering and physical systems modelling in particular, more sophisticated representational formalisms have been developed to enable the identification of mathematical models of the behaviour of dynamic systems from observations. Examples include bond graphs [17] and generalised physical networks [9]. However, the potential benefits of these more advanced formalisms are not exploited here, but remain as an interesting future work. Instead, stock-flow diagrams are employed throughout this paper as they are far more commonly used in ecological modelling [11].

It is often possible to construct multiple scenario models from a single given scenario, and the task specification is employed to guide the search for the most appropriate one(s). In this work, scenario models are selected on the basis of hard constraints and user preferences. The hard constraints stem from restrictions imposed on compositionality by the representational framework (see section 3.2.3) and from properties the scenario model is required to satisfy (see section 3.2.3). The user preferences express the user's subjective view as to which modelling approaches are more appropriate in the context of the current scenario (see section 2.2).