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.
