The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population...The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species will elbow out all the initial species very quickly. Small-time behavior in thls case seems to be the key to understand this fast transition. The small-time asymptotic results related to time scale t and a（O）t, where lim0→∞θ θa（θ） = O, are obtained by Dawson and Shni （1998, 2001）, Shui and Xiong （2002）, and Xiang and Zhang （2005）, respectively. Only the behavior under the scale t（θ）, where limθ→∞θt（θ） = 0 and limθ→∞（O） =∞ was left untouched. In this paper, the weak limits under various small-time scales are obtained. Of particular interest is the large deviations for the small-time transient sam- pling distributions, which reveal interesting phase transition. Interestingly, such a phase transition is uniquely determined by some species diversity indices.展开更多
基金supported by Fundamental Research Fund of Zhongnan University of Economics and Law (Grant No. 31541411208)
文摘The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species will elbow out all the initial species very quickly. Small-time behavior in thls case seems to be the key to understand this fast transition. The small-time asymptotic results related to time scale t and a（O）t, where lim0→∞θ θa（θ） = O, are obtained by Dawson and Shni （1998, 2001）, Shui and Xiong （2002）, and Xiang and Zhang （2005）, respectively. Only the behavior under the scale t（θ）, where limθ→∞θt（θ） = 0 and limθ→∞（O） =∞ was left untouched. In this paper, the weak limits under various small-time scales are obtained. Of particular interest is the large deviations for the small-time transient sam- pling distributions, which reveal interesting phase transition. Interestingly, such a phase transition is uniquely determined by some species diversity indices.
