Fig. 3: Computational modeling results.

a Path integration errors of two example participants (error bars) versus model fits (solid lines). Error bars represent mean ± SEM over trials. See Supplementary Fig. 2 for all participants. b Average path integration errors per age group (error bars) versus model fits (solid lines). Error bars represent mean ± SEM over participants. c Single-trial path integration error vectors versus error vectors predicted by the model. Predicted position is computed individually per participant per trajectory; datapoints show the per-trajectory predicted position, averaged across participants of the same age group on the same trajectory and trial (to reduce scatter). Error bars represent mean ± SEM at a single trial across participants. Dashed black lines indicate perfect prediction; solid lines represent the best-fitting linear regression fit. Units are meters. d Model comparison: negative log-likelihood scores using LOOCV between models, with higher bars indicating a poorer model fit. *** Denotes “very strong” evidence against the model relative to the full model (ΔBIC or ΔLOOCV ≫ 10; see also “Methods” section on model comparison, and Supplementary Fig. 3). Key to model names: The “full model” (Full) is our default, with ongoing “accumulating noise” (AN) that is proportional to the length of the traveled path, nonzero additive bias (AB) and velocity gain bias parameters, and reporting noise (RN) that is proportional to the magnitude of the reported variable. CN refers to when the non-reporting portion of the noise is constant rather than accumulating. +/− refers to the addition/removal of that contribution to the model, respectively. e Impact of model parameters on the predicted path integration error. Relative influence measures the predicted reduction in square error by setting a parameter to its ideal value corresponding to noiseless and unbiased integration. Note that due to the nonlinearity of the model, the relative influences do not have to sum to 100%, and that a parameter’s relative influence can be negative if the reduced square error is larger than the square error of the full model (see “Methods” section).