title: Social aggregation in pea aphids: experiment and random walk modeling.
abstract: From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of 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.
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: Christa
authors.initials: C
authors.lastname: Nilsen
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: John
authors.initials: J
authors.lastname: Paige
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: Olivia
authors.initials: O
authors.lastname: Warner
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Mayhew
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: Ryan
authors.initials: R
authors.lastname: Sutley
authors.affiliation: Department of Mathematics, Harvey Mudd College, Claremont, California, United States of America.
authors.forename: Matthew
authors.initials: M
authors.lastname: Lam
authors.affiliation: Department of Mathematics, Harvey Mudd College, Claremont, California, United States of America.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Bernoff
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Macalester College, Saint Paul, Minnesota, United States of America.
authors.forename: Chad M
authors.initials: CM
authors.lastname: Topaz
mesh_terms: D000818:Animals; D001042:Aphids / Q000502:physiology*; D003441:Crowding; D008124:Locomotion / Q000502:physiology*; D015233:Models, Statistical; D018532:Pisum sativum / Q000469:parasitology; D013269:Stochastic Processes