Model space

Figure 11: Model space for the 1 predator and 2 competing prey scenario

A model space is constructed when the knowledge base is instantiated with respect to a given scenario. Consider for example the following scenario, which describes a predator population that preys on two other populations, prey1 and prey2, whilst the two prey populations compete with one another:

(defScenario pred-prey-prey-scenario
  :entities ((predator :type population)
             (prey1 :type population)
             (prey2 :type population))
  :relations ((predation predator prey1)
              (predation predator prey2)
              (competition prey1 prey2)))

The full specification of the model space is too unwieldy to present here but an abstract graphical representation of the model space for this scenario is shown in Figure 11. This model space contains the following knowledge:

• From each of the three populations in the scenario, a set of three population growth models (i.e. exponential, logistic and other) is derived. This inference is dependent upon a relevance assumption of the population growth phenomenon, and a model assumption that corresponds to one of the three population growth models.
• From both predation relations (i.e. (predation predator prey1) and (predation predator prey2)), and the populations related by them, a set of two predation models (i.e. Lotka-Volterra and Holling) is derived. This inference is dependent upon a relevance assumption of the predation phenomenon and a model assumption that corresponds to one of the two predation models.
• From the competition relation (competition prey1 prey2), and the populations related by it, a competition model is derived. Because there is only one competition model, the inference of the competition model is only dependent upon a relevance assumption that corresponds to the competition phenomenon.

In addition to the hypergraph of Figure 11, the model space also contains a number of constraints on the conjunctions of assumptions that are consistent. As explained earlier, these stem from two sources: 1) non-composable relations and 2) purpose-required properties. An example will be given of each type.

Let predation-phen-1 be the predation phenomenon between predator and prey1, and prey1-size be the variable representing the size of the prey1 population. In this example, the model fragments exponential-population-growth and Lotka-Volterra will each generate an equation for computing the value of a variable representing the change in prey1-size. Because both equations can not be composed, the following inconsistency is generated:

$$\begin{split}&\texttt{(relevant growth prey1)}\wedge\texttt{(... ...el predation-phen-1 lotka-volterra)}\rightarrow\bot \end{split}$$

Inconsistencies also arise from purpose-required properties. For example, if the model fragment predation-phenomenon is applicable and the predation relation is deemed relevant, then the purpose-required property (has-model ?pred-phen) will become a condition for consistency. Under certain combinations of assumptions, this property may not be satisfied. Say, when the Holling predation and exponential growth models are both selected, the Holling model is not generated because there is no ?capacity for which (capacity ?capacity ?pred) is true. No predation model is created in this case (because the Holling model fragment can not be instantiated), even though the predation phenomenon is deemed relevant under this set of assumptions. This is inconsistent with the has-model purpose-required property in the predation-phenomenon model fragment, and the responsible combination of assumptions is therefore marked as nogood.

$$\begin{split}&\texttt{(relevant growth predator)}\wedge\textt... ...tt{(model predation-phen-1 holling)}\rightarrow\bot \end{split}$$