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摘要:
Moran or Wright–Fisher processes are probably the most well known models to study the evolution of a population under environmental various effects.Our object of study will be the Simpson index which measures the level of diversity of the population,one of the key parameters for ecologists who study for example,forest dynamics.Following ecological motivations,we will consider,here,the case,where there are various species with fitness and immigration parameters being random processes(and thus time evolving).The Simpson index is difficult to evaluate when the population is large,except in the neutral(no selection)case,because it has no closed formula.Our approach relies on the large population limit in the“weak”selection case,and thus to give a procedure which enables us to approximate,with controlled rate,the expectation of the Simpson index at fixed time.We will also study the long time behavior(invariant measure and convergence speed towards equilibrium)of the Wright–Fisher process in a simplified setting,allowing us to get a full picture for the approximation of the expectation of the Simpson index.
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篇名 On the Simpson index for the Wright–Fisher process with random selection and immigration
来源期刊 生物数学学报:英文版 学科 数学
关键词 Simpson index multidimensional Wright-Fisher process random selection random immigration moment’s closure
年,卷(期) 2020,(6) 所属期刊栏目
研究方向 页码范围 77-111
页数 35页 分类号 O17
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Simpson
index
multidimensional
Wright-Fisher
process
random
selection
random
immigration
moment’s
closure
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生物数学学报:英文版
其它
1793-5245
Singapore596224,or 2
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68
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0
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