We develop a novel dynamical method to examine spatial interaction models
(SIMs). For each SIM, we use our dynamical framework to model emigration
patterns. We look at the resulting population distributions to see if they are
realistic or not. We use the US census data from 2010 and various spatial
statistics to access the success or failure of each model. While we looked at
over eighty different SIMs, we will focus here on two examples: the production
constrained gravity model and the Radiation model. The results suggest that all
these models fail to produce realistic population distributions and we identify
the flaws within existing models. This leads us to suggest that we should
define site attractiveness in terms of a second short range SIM leading to a
new spatial interaction model - the Two-Trip model - which offers significant
improvements when examined via our method. We also note that our Two-Trip
adaptation can be used in any spatial modelling contexts, not just emigration.