A Markov chain model of Daphnia motion.

This article focuses on modeling the two-dimensional locomotion of the planktonic crustacean *Daphnia magna* using a second-order Markov chain (SOMC) that incorporates the animal's morphology, specifically its antennae-whipping behavior which induces directional changes. The model simulates movement on a lattice grid, capturing the probabilistic nature of turns and steps based on empirical observations, and includes adjustments for boundary effects and random noise to better replicate real movement patterns. Results demonstrate that the simulated tracks closely match the statistical properties of observed tracks, and analyses of return and meeting times on lattices provide insights relevant to foraging behavior. The study presents this SOMC framework as a foundational step toward more complex three-dimensional models and agent-centered animation of aquatic locomotion, emphasizing adaptability to different species and environmental factors.