About The Model Of Asymptotically Optimal Strategy Of Birds Reproducing In Random Environments

In this paper the evolution of bird's populations is simulated as a branching process in random environment. An optimal strategy mathematic model is set up, in which birds oppose the influence of different states of random environment to young bird's survival probability by choosing the distribution of clutch-sizes. Under the model, the probability distribution of clutch-size is chosen, when the original num of birds Z0 increases, the corresponding extinction probability qk ( ) draws to 0 at the most speed. When the clutch-size is distributed as Poisson distribution, and there is at least one subcritical state in the supercritical environment with extinction probability less one, the following works are done:1. After the detailed discussion of the corresponding collection , this paper proves that the non-empty strategy collection is composed of one interval or the union of two mutual exclusion intervals.2. Deliver the sufficient and necessary condition of the corresponding non-empty strategy collection.3. Establish the confirmation: as to each ,there is the only constant term >0 , and (1) F( ) = 1 , (2) F'( )) < , (3) E(l - (0)) < . Besides, if , then the strategy * is the asymptotically optimal strategy opposing the random environment { }.This conclusion provides a mathematic explanation to the phenomenon that each bird species has a characteristic frequency distribution of clutch-sizes in nature.