Generalized Measures of Population Synchrony
arxiv(2024)
Abstract
Synchronized behavior among individuals is a ubiquitous feature of
populations. Understanding mechanisms of (de)synchronization demands
meaningful, interpretable, computable quantifications of synchrony, relevant to
measurements that can be made of dynamic populations. Despite the importance to
analyzing and modeling populations, existing notions of synchrony often lack
rigorous definitions, may be specialized to a particular experimental system
and/or measurement, or may have undesirable properties that limit their
utility. We introduce a notion of synchrony for populations of individuals
occupying a compact metric space that depends on the Fréchet variance of
the distribution of individuals. We establish several fundamental and desirable
mathematical properties of this synchrony measure, including continuity and
invariance to metric scaling. We establish a general approximation result that
controls the disparity between synchrony in the true space and the synchrony
observed through a discretization of state space, as may occur when observable
states are limited by measurement constraints. We develop efficient algorithms
to compute synchrony in a variety of state spaces, including all finite state
spaces and empirical distributions on the circle, and provide accessible
implementations in an open-source Python module. To demonstrate the usefulness
of the synchrony measure in biological applications, we investigate several
biologically relevant models of mechanisms that can alter the dynamics of
synchrony over time, and reanalyze published data concerning the dynamics of
the intraerythrocytic developmental cycles of Plasmodium parasites.
We anticipate that the rigorous definition of population synchrony and the
mathematical and biological results presented here will be broadly useful in
analyzing and modeling populations in a variety of contexts.
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