Canonical functions for dispersal-induced synchrony

Area of Science:

• Ecology
• Population Dynamics
• Spatial Statistics

Background:

• Spatial synchrony in population abundance is driven by dispersal and environmental stochasticity.
• Previous models show synchrony mirrors environmental correlation without dispersal.
• The relationship between synchrony and distance under dispersal remains less understood.

Purpose of the Study:

• To determine the functional relationship between spatial synchrony and distance in populations synchronized by density-independent dispersal.
• To model the time evolution of spatial covariance as a function of distance.
• To identify canonical functions for dispersal-induced synchrony.

Main Methods:

• Formulation of a continuous-space, continuous-time model.
• Explicit representation of the time evolution of spatial covariance.
• Analysis of covariance as a function of spatial distance.

Main Results:

• Two canonical functions describe dispersal-induced covariance in spatially extended populations.
• Rare dispersal: Covariance follows dispersal distance distribution locally, with exponential/Bessel tails at long distances.
• Common dispersal: Covariance follows a mixture distribution (Gaussian near origin, exponential/Bessel tails) irrespective of dispersal distance distribution.

Conclusions:

• Dispersal strongly dictates spatial synchrony patterns in populations.
• The frequency of dispersal relative to birth/death rates determines the specific functional form of synchrony decay with distance.
• Identified two universal functions for understanding dispersal-mediated population synchrony.