Seed-bank population recurrence ($M_{n+1}=N(a{M}_n+b{M}_{n-1})$)

A seed-bank population recurrence includes delayed recruitment from seeds that survive more than one season. For $a,b\ge 0$, recruitment function $N$ with $N(0)=0$ and $N^{\prime }(0)=1$ gives extinction multipliers solving ${\lambda }^2-a\lambda -b=0$. If $N$ is strictly concave, bounded and increasing, a positive fixed point exists uniquely exactly when $a+b>1$; it solves $M=N((a+b)M)$. The dominant extinction multiplier then exceeds one.