Determining individual phase response curves from aggregate population data

Phase reduction is an invaluable technique for investigating the dynamics of nonlinear limit cycle oscillators. Central to the implementation of phase reduction is the ability to calculate phase response curves (PRCs), which describe an oscillator's response to an external perturbation. Current experimental techniques for inferring PRCs require data from individual oscillators, which can be impractical to obtain when the oscillator is part of a much larger population. Here we present a simple methodology to calculate PRCs of individual oscillators using an aggregate signal from a large homogeneous population. This methodology is shown to be accurate in the presence of interoscillator coupling and noise and can also provide a good estimate of an average PRC of a heterogeneous population. We also find that standard experimental techniques for PRC measurement can produce misleading results when applied to aggregate population data.