The Asymptotic Behaviour of the Extinction Probabibity in Bisexual Galton-Watson Branching Processes with Independent and Identically Distributed Random Environments

In bisexual Galton-Watson branching process with independent and identically distributed random environments, it is shown that under certain conditions there exists 0<\alpha<+\infty and 0<c<+\infty such that the extinction probability starting with k individuals is bounded above by ck^-\alpha for sufficiently large k.