Figure 7. Conceptual interpretation of heterogeneity as neuronal population coding phenomenon.
(a–d) The mean population activity during a certain time epoch can be visualized a single point in multidimensional neural space, where every axis represents the activity of a single neuron. (a) For an example population of two neurons, the main diagonal (arrow) represents the line along which the mean population activity changes. Orthogonal to this line is the gradient along which heterogeneity changes, representing the distance of each point to the main diagonal. The effects of heterogeneity on hit/miss differentiation as reported in this study could be epiphenomenal if the real underlying differentiation depends on localized, segregated clusters of neural activity for hits (green cloud) and misses (red cloud). (b) This principle can be extended to multidimensional space; segregated clusters activity will show asymmetrical distributions of population activity around the diagonal. (c, d) Alternatively, heterogeneity itself could represent a fundamental characteristic of hit/miss differences; in this case, population responses should be distributed symmetrically around the diagonal (see text for more explanation). (e) Calculating the pairwise inter-point distance (each point being the population activity during a single trial) can reveal information about the underlying multidimensional structure of neuronal population activity. Green: distribution of inter-point distances for hit trials; red: same for miss trials. (f) Population responses during hit trials are distributed within a larger volume of neural space, as shown by the on average larger inter-point distance for hits than misses [paired t-test, difference in center of mass (d(CoM) hit vs. miss, p<0.05]. Mirroring point across the diagonal to assess symmetry shows a small, but significant asymmetry for hits and miss (both p<0.05) and larger asymmetry for hits than misses (p<0.05). This suggests that neuronal populations during hit trials show more structured behavior in a more extended neural space than during miss trials. (g) Schematic representation of how the mean, heterogeneity, or both can be removed from population responses to assess the effect they have on hit/miss separability (see also text and ‘Materials and methods’). (h) Removing heterogeneity impairs hit/miss decoding more than removing the mean (paired t-test, p<0.05) but in all cases (including removing both) the hit/miss separability is still well above chance (0.5). This suggests that heterogeneity is more important than population mean activity for differentiating stimulus detection from non-detection, but that other more complex neural phenomena account for most of the population response structure. All panels: error bars indicate standard error. Statistical significance: *p<0.05.