Spike Correlations in a Songbird Agree with a Simple Markov Population Model

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Abstract
The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups. To deal with the vast complexity of the brain and its many degrees of freedom, many reductionist methods have been designed that can be used to simplify neural interactions to just a few key underlying macroscopic variables. Despite these theoretical advances, even today relatively few population models have been subjected to stringent experimental tests. We explore whether second-order spike correlations measured in songbirds can be explained by single-neuron statistics and population dynamics, both reflecting hypotheses on network connectivity. We formulate a Markov population model with essentially two degrees of freedom and associated with different behavioral states of birds such as waking, singing, or sleeping. Excellent agreement between spike-train data and model is achieved, given a few connectivity assumptions that strengthen the view of a hierarchical organization of songbird motor networks. This work is an important demonstration that a broad range of neural activity patterns can be compatible at the population level with few underlying degrees of freedom.