Staged Models for Interdisciplinary Research

Abstract

Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are thought relevant. The former ensures rigour, the latter relevance. We discuss a method that combines these two approaches, beginning with a complex model and then modelling the complicated model with simpler models. The resulting "chain" of models ensures some rigour and relevance. We illustrate this process on a complex model of voting intentions, constructing a reduced model which agrees well with the predictions of the full model. Experiments with variations of the simpler model yield additional insights which are hidden by the complexity of the full model. This approach facilitated collaboration between social scientists and physicists-the complex model was specified based on the social science literature, and the simpler model constrained to agree (in core aspects) with the complicated model.

Fig 1. From a single to a multi-stage abstraction process.

Fig 2. Diagrammatic representation of the full model processes.

The main pathway is shown in blue, with additional factors in red, and development of the agent population in green.

Fig 3. Comparison between the full model (black) and the reduced model (red).

Ten different values of the influence rate parameter (from 2 to 11) are shown. For each one, the steady state value of the turnout obtained is shown for 25 realisations (dots), together with the mean values (lines).

Fig 4. Schematic comparison between the full model network (left) and the synthetic network (network CN, right).

Agents are displayed as green circles. Lines connecting agents represent social links. In the full model red lines represent partners, blue lines represent families and green lines represent other kinds of relationships.

Fig 5. Comparison between the full model M₁, (dashed black), the reduced model, M₂ (red) and version M₂+CN (purple).

The synthetic network (network CN, see the main text) decreases turnout in the high-turnout regime and leads to a transition between low- and high-turnout at a lower influence rate.

Fig 6. Comparison between the full model, version M₂+CN (purple) and version M₂+CN+D (green).

Rewiring the network (with a probability of 0.15 per long-range link per year) increases turnout.

Fig 7. Comparison between version M₂+CN (purple) and version M₂+CN+HI (light blue).

When immigration occurs by households turnout is reduced.

Fig 8. Comparison between original model (black) and version M₂+CN+D+HI (blue).

Ten different values of the influence rate parameter (from 2 to 12) are shown. For each one, the steady state value of the turnout obtained is shown for 25 realisations (dots), together with the mean values (lines).