  The area of population dynamics has a rich history of the development and
analysis of models of biological and social phenomena using ordinary
differential equations. This paper describes a method for understanding the
influence one variable exerts on another in such models as a force, with the
relative effects of these forces providing a narrative explanation of the
curvature in variable behaviour. Using the stock/flow form of a model, a
symbolic notation is developed that identifies the forces with the causal
pathways of the model's feedback loops. A force is measured by its impact,
defined as the ratio of acceleration to rate of change, computed by
differentiation along its associated pathway between variables. Different
phases of force dominance are determined to enhance the standard stability
analysis of the models, providing an explanation of model behaviour in
Newtonian mechanical terms. The concepts developed are applied to well-known
models from mathematical biology: the Spruce Budworm model, where force
dominance identifies scenarios that give clarity to intervention points; and
the Lotka-Volterra predator-prey model where the analysis highlights the
importance of dissipative forces in achieving stability. Conclusions are drawn
on the explanatory power of this approach, with suggestions made for future
work.
