Population density, reaction-diffusion process

In conclusion, we have shown that the neutral response approach can be extended to inhomogeneous, space-dependent reaction-diffusion systems. For labeled species (tracers) that have the same kinetic and transport properties as the unlabeled species, there is a linear response law even if the transport and kinetic equations of the process are nonlinear. The susceptibility function in the linear response law is given by the joint probability density of the transit time and of the displacement position vector. For illustration we considered the time and space spreading of neutral mutations in human populations and have shown that it can be viewed as a natural linear response experiment. We have shown that enhanced (hydrodynamic) transport due to population growth may exist and developed a method for evaluating the position of origin of a mutation from experimental data. 

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