  Spatial structure can arise in spatial point process models via a range of
mechanisms, including neighbour-dependent directionally biased movement. This
spatial structure is neglected by mean-field models, but can have important
effects on population dynamics. Spatial moment dynamics are one way to obtain a
deterministic approximation of a dynamic spatial point process that retains
some information about spatial structure. However, the applicability of this
approach is limited by the computational cost of numerically solving spatial
moment dynamic equations at a sufficient resolution. We present an asymptotic
expansion for the equilibrium solution to the spatial moment dynamics equations
in the presence of neighbour-dependent directional bias. We show that the
asymptotic expansion provides a highly efficient scheme for obtaining
approximate equilibrium solutions to the spatial moment dynamics equations when
bias is weak. This scheme will be particularly useful for performing parameter
inference on spatial moment models.
