Parity-subsequence extinction conjecture for the inter-stage Ricker model

Let $\{x_n\}$ be a positive solution of equation (4ab), and assume that condition (fxp0) holds. Consider its even subsequence $\{x_{2n}\}$ and odd subsequence $\{x_{2n-1}\}$. Parity-subsequence extinction conjecture. At least one of the two subsequences $\{x_{2n}\}$ or $\{x_{2n-1}\}$ converges to zero. This claim is proposed as potentially relevant to determining the extinction and survival sets when condition (fxp0) holds; no resolution is supplied in the excerpt.