Here we will derive a general solution near equilibrium (i.e. ) for the equation

Since is a function of , we will derive an equation for the time evolution of . We start by noting that

and

Taylor expansion up to first order around of this latter equation results in

Subtracting Eq. (58) and (60) and letting we arrive at

Thus as soon as we know the solution of

we can compute the solution for any . Solving (62) results in

or

in which the fictive age of a patch of size , i.e. the time needed to grow from 0 to under steady state conditions.

Wed Feb 26 07:30:07 EST 1997