A Markov chain model of Daphnia motion

Abstract

Daphnia magna make turns through an antennae-whipping action. This action occurs every few seconds, so during the intervening time, the animal either remains in place or it continues movement roughly along its current course. We view their movement in two dimensions as being on a lattice, and construct a second-order Markov chain model to make predictions about which region of the lattice the animal moves to based on where it was at the last two time points. This model accounts for the animal’s morphology with respect to the antennae-whipping behavior.