Fast family partition and slow family balance
= Fast family partition and slow family balance
For $X\rightleftharpoons Y$ with forward and reverse first-order rates $a,b$, the closed-family partition relaxes at rate $a+b$. Adding losses changes the relaxation eigenvalues. If family abundance evolves much more slowly, a quasi-equilibrium ratio can be useful; setting the entire family derivative to zero needs a separate timescale comparison.