Correlation is a normalized measure of covariation. It has commonly been used to refer to two distinct phenomena. One use refers to tuning similarity, measured as the correlation in the mean responses of two neurons to an ensemble of stimuli (termed signal correlation or rsignal, see and Box 1). The second use of correlation—and our focus here—is as a measure of the degree to which trial-to-trial fluctuations in response strength are shared by a pair of neurons. This is typically quantified as the Pearson correlation of their spike count responses to repeated presentations of identical stimuli under the same behavioral conditions (spike count correlation or rSC, also called noise correlation; ).
Figure 1 Types of pairwise neuronal correlations. A Tuning curves for two hypothetical direction-selective neurons. Open circles show mean responses to different directions of motion, and small points show responses to individual presentations of a stimulus at (more ...)
Co-fluctuations in the responses of a pair of neurons can arise over a range of timescales 8, 12, 22, 23
, from the precise temporal alignment of spikes (i.e. synchrony) to slower changes in excitability (Box 1). The timescale over which correlated activity affects the responses of downstream neurons is unknown, but membrane time constants suggest that it is tens of milliseconds or less. However, most work on the relationship of spike count correlations to population coding and behavior has been based on responses measured over the duration of a stimulus presentation or behavioral trial (typically hundreds of milliseconds).
Over the past two decades, spike count correlations have been measured in many cortical areas under a variety of behavioral and stimulus conditions (). These studies have reported a range of values, but correlations are typically small and positive. They tend to be highest for pairs of neurons that are near each other 24-26
and have similar functional properties or tuning (high rsignal
; 6, 7, 12, 13, 15, 25-31
). Pairs recorded from opposite hemispheres have very low correlations7
. These properties suggest that correlations reflect co-fluctuations in the responses of restricted subsets of neurons, rather than global fluctuations that affect all cells.
Table 1 Summary of studies measuring spike count correlations in primates. These studies measured correlations in a variety of brain areas, behavioral and stimulus conditions, and measurement durations and between pairs of neurons that varied in the cortical (more ...)
Correlation strength is also likely to depend on local circuitry or architecture. For instance, rSC
is weak in the input layers of primary sensory cortex (32
; M.A. Smith and A. Kohn, personal communication; J. Hansen and V. Dragoi, personal communication). Correlations in motor areas seem to be consistently lower than those in sensory cortex (see ).
The influence of distance, tuning similarity, and architecture can explain some of the variability across studies, but even studies that sample similarly can arrive at quite different estimates of correlation strength. We show here that many of these discrepancies can be explained by differences in other factors that can systematically bias correlation estimates—namely, response strength, the time period for counting spikes, spike sorting, and fluctuations in internal states.
Why is it important to understand the influence of these factors and, more generally, differences in estimates across studies? It is not because the mean strength of correlations is a particularly critical quantity. Even very weak correlations can substantially affect the information encoded by a population of neurons, and the structure of correlations can have a much stronger influence than their mean strength2-6
. Furthermore, other properties of the distribution of correlation coefficients, such as its variance, may be more informative about the underlying circuit than the mean 33
. However, understanding differences in correlations across brain regions or in different stimulus or task conditions is critical both for elucidating their role in sensory processing and for making inferences about the circuitry and mechanisms that generate them. For this reason, we explore below the way that different experimental and physiological factors affect measurements of correlations and discuss guidelines for interpreting correlation data.