Spatial uncertainty provides a unifying account of navigation behavior and grid field deformations

Abstract

To localize ourselves in an environment for spatial navigation, we rely on vision and self-motion inputs, which only provide noisy and partial information. It is unknown how the resulting uncertainty affects navigation behavior and neural representations. Here we show that spatial uncertainty underlies key effects of environmental geometry on navigation behavior and grid field deformations. We develop an ideal observer model, which continually updates probabilistic beliefs about its allocentric location by optimally combining noisy egocentric visual and self-motion inputs via Bayesian filtering (A, B). This model directly yields predictions for navigation behavior and also predicts neural responses under Fisher-optimal population coding of location uncertainty (C). We simulate this model numerically under manipulations of a major source of uncertainty, environmental geometry, and support our simulations by analytic derivations for its most salient qualitative features. We show that our model correctly predicts a wide range of experimentally observed effects on homing behavior and grid field deformations: 1. Anisotropic environmental geometries result in anisotropic uncertainty, which in turn leads to deformations of homing response distribution & grid fields. In an asymmetric environment (e.g., trapezoid-shaped), spatial uncertainty is larger with less visual parallax (e.g., along the long axis; D), which leads to lower homing accuracy and anisotropic expansion of grid fields (E; [1,2]). 2. Model mismatch due to covert changes in the environment results in rescaling of homing response distribution & grid fields: when a room is covertly scaled along an axis, homing response distribution and grid fields show a partial rescaling along that axis, and paradoxically, an opposite scaling along the unchanged axis (F; [3-5]). 3. Cue conflict between visual & self motion inputs results in simultaneous rescaling & tethering of homing responses: homing in rescaled rooms show “tethering” (in addition to rescaling), whereby responses are biased such that their distance from the starting position is partially preserved between the original and rescaled rooms (G; [6]). Thus, our model provides a unifying, normative account for the dependence of homing behavior and grid fields on environmental geometry, and identifies the unavoidable uncertainty in navigation as a key factor underlying these diverse phenomena.