  An ongoing challenge in the mathematical modeling of biological aggregations
is to strengthen the connection between models and biological data by
quantifying the rules that individuals follow. We model aggregation of the pea
aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the
motion of aphids walking in a featureless circular arena in order to deduce
individual-level rules. We observe that each aphid transitions stochastically
between a moving and a stationary state. Moving aphids follow a correlated
random walk. The probabilities of motion state transitions, as well as the
random walk parameters, depend strongly on distance to an aphid's nearest
neighbor. For large nearest neighbor distances, when an aphid is essentially
isolated, its motion is ballistic with aphids moving faster, turning less, and
being less likely to stop. In contrast, for short nearest neighbor distances,
aphids move more slowly, turn more, and are more likely to become stationary;
this behavior constitutes an aggregation mechanism. From the experimental data,
we estimate the state transition probabilities and correlated random walk
parameters as a function of nearest neighbor distance. With the
individual-level model established, we assess whether it reproduces the
macroscopic patterns of movement at the group level. To do so, we consider
three distributions, namely distance to nearest neighbor, angle to nearest
neighbor, and percentage of population moving at any given time. For each of
these three distributions, we compare our experimental data to the output of
numerical simulations of our nearest neighbor model, and of a control model in
which aphids do not interact socially. Our stochastic, social nearest neighbor
model reproduces salient features of the experimental data that are not
captured by the control.
