(A) Schematic overview of the model describing the rat’s swimming dynamics in the Morris Water maze. x, y is the rat’s location, α is the rat’s actual heading, αdesired the rats desired heading, e the heading error, ê the rat’s estimate of the heading error, and η and Δrt the Gaussian and Rayleigh distributed random variables, respectively. The variable z arises from the z-Transform of the system, and can be understood as a time shift operator, i.e., z−ix(t) = x(t − i Δt). The model parameters F, K, A1, and A2, and the distributions of η and Δrt have been identified earlier (see Fey et al. 2011 for further details). (B) Using the dynamic model to analyze the effectiveness of different strategies. Distribution of mean (number) and median (line) escape latencies and % unsuccessful trials in various groups: (N RND) random swimming movements, (CA) approach a cue in Near (N) or Far position (F), (F CA-RND) approach a cue in Far position and turn away into a random direction, (F CA-180) approach a cue in Far position and turn away at 180°, (CA-DC) approach cues in Far position and turn away with directional error, (DC) approach cues in Far position on first trial only and turn away from cues with directional error. See Methods for details on all groups. (C) Modeling the effect of decreasing the number of steps that an animal swims toward the cues ncue (for 30° directional uncertainty and zero distance uncertainty) on escape latency. Therefore, as an animal learns the location of the platform relative to the cues, it does not need to keep approaching the cues, rather it can start moving directly toward the platform location. The figure shows this idea. Animals alternate between swimming toward the cues (in order to orientate—this parameter changes from 25 steps to 0 steps) and swimming into the direction of the platform (in order to escape—this parameter remains constant). Note, a step of 25 indicates an animal swimming toward the cue, and 0 indicates a minimum movement toward the cues.
