Appendix figure 2. The effect of lesioning grid modules on the distribution over location for hierarchical vs non-hierarchical grid schemes.

For the hierarchical scheme, we assume that four one-dimensional grid modules are related by a scale factor r (r = 2.7), that is, $\frac{{\lambda }_i}{{\lambda }_{i+1}}=2.7$, i = 1, 2, 3, and the ratio $\frac{{\lambda }_i}{{\sigma }_i}=9.1$, i = 1, 2, 3, 4. We assume that the animal is at x = 0 and construct the probability distribution over location given the activity in each grid module as described in Optimizing the grid system: probabilistic decoder, ‘Materials and methods’. For the non-hierarchical scheme, we again assume four grid modules and set the periods of the four modules to be 1/105 (fourth), 1/70 (third), 1/42 (second), 1/30 (first) of the whole range, respectively. We set the width of the composite likelihood after combining all four modules to be 1/210 of the range [−5000, 5000].

DOI: http://dx.doi.org/10.7554/eLife.08362.009