= Two-season seed-bank recurrence
{title2=$X_{n+1}=aX_n+bX_{n-1}$}
A seed-producing population with first-season and second-season recruitment leads to nonnegative recurrence coefficients $a,b$. Its characteristic roots are $(a\pm\sqrt{a^2+4b})/2$. The nonnegative dominant root is below one precisely when $a+b<1$, giving deterministic decay of every finite initial population. This is a mean-population model; literal integer extinction requires a stochastic interpretation or a separate integer-population argument.
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