a) We fitted three model families to an empirical dataset combined from 23 published experiments across 10 different research groups. The ‘Egocentric maps’ family (top three models) is the main topic of this paper, and the ‘Q-fields (Q-learning)’ model is the specific model described in the main text. The ‘Monotonous decay’ family (middle three models) contains purely empirical models that attempt to describe the data, but without having a theoretical a-priori reason for being appropriate models. The ‘Perceptual models’ (bottom two models) have previously been used to fit individual datasets, and are largely based on the notion that peripersonal fields arise due to uncertainty in visual and auditory input, while estimating the probability that the source of the visual input makes contact with the body. We calculated all quantities for each 5 × 5 × 5cm voxel around the upper body, and fit them to the data with at least the same number of parameters as we used for Q-value fitting. The exponential and linear falloffs required two additional parameters, to fit the size and slope of the receptive fields. We parametrised the uncertainty necessary for the perceptual models by taking the same values as reported in17,20. b) Mathematical description of each model. For the ‘Egocentric maps’ models family, we display the update equation for the Q values, and underline the part of the equation that is unique to each of the three models. c) Summed error when each model is fitted to the empirical data (red line). The error of all models other than egocentric maps is larger than the error expected from a model that appropriately describes the generative mechanism behind the data (blue distribution). Models with a summed error corresponding to p 10 for AIC and BIC (indicated by dashed black lines) is commonly taken to indicate that the considered model can be rejected in favour of the reference model.