  We investigate the boundary between chemotaxis driven by spatial estimation
of gradients and chemotaxis driven by temporal estimation. While it is well
known that spatial chemotaxis becomes disadvantageous for small organisms at
high noise levels, it is unclear whether there is a discontinuous switch of
optimal strategies or a continuous transition exists. Here, we employ deep
reinforcement learning to study the possible integration of spatial and
temporal information in an a priori unconstrained manner. We parameterize such
a combined chemotactic policy by a recurrent neural network and evaluate it
using a minimal theoretical model of a chemotactic cell. By comparing with
constrained variants of the policy, we show that it converges to purely
temporal and spatial strategies at small and large cell sizes, respectively. We
find that the transition between the regimes is continuous, with the combined
strategy outperforming in the transition region both the constrained variants
as well as models that explicitly integrate spatial and temporal information.
Finally, by utilizing the attribution method of integrated gradients, we show
that the policy relies on a non-trivial combination of spatially and temporally
derived gradient information in a ratio that varies dynamically during the
chemotactic trajectories.
