Comparison of the simulated effects of scaling track size versus scaling place field size on mean and sparsity of firing rate distributions for 100 Gaussian place fields distributed at random as in Figure 10
| WALK | CAR | WORLD | |
|---|---|---|---|
| Variable track | |||
| Rad | 0.45 | 0.15 | 0.05 |
| SD | 0.10 | 0.10 | 0.10 |
| Mean | 1 | 1 (0.02) | 1 (0.006) |
| Sparsity | 0.763 | 0.223 | 0.118 |
| Variable place fields | |||
| Rad | 0.45 | 0.45 | 0.45 |
| SD | 0.10 | 0.20 | 0.30 |
| Mean | 1 | 3 | 5.4 |
| Sparsity | 0.763 | 0.966 | 0.983 |
The place field size parameter (SD) and the track size parameter (Rad) for the variable-track size condition are as used for the simulations in Figure 10. Mean rates are shown relative to the putative WALK condition. The numbers in parentheses in the variable-track condition represent the relative rates, assuming that firing probability scales linearly with simulated running speed, if the lap time was held constant and the track diameter varied. Thus, under the hypothesis of a loss of gain in the speed parameter, firing rates decrease and the firing rate distribution becomes more sparse (smaller sparsity index), which is what is actually observed in the data. Under the hypothesis that all place fields simply get bigger, the mean rates increase substantially, and the firing rate distributions become less sparse (larger sparsity index).