CONDITIONAL DISTRIBUTIONS AND WAITING TIMES IN MULTITYPE BRANCHING PROCESSES
CONDITIONAL DISTRIBUTIONS AND WAITING TIMES IN MULTITYPE BRANCHING PROCESSES
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DOI：
10.1239/aap/1377868535
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发表时间：
2013-09-01
影响因子：
1.2
通讯作者：
Alexander, H. K.
中科院分区：
文献类型：
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作者：
Alexander, H. K.
本文给出了离散时间和马尔可夫连续时间多类型分支过程的一些新结果。随着种群的发展，我们感兴趣的是等待时间，直到特定类型的兴趣（如逃逸突变体）出现，以及个体的分布如何依赖于这种类型是否已经出现。具体地说，在一种或多种特定类型不出现的条件下，导出了特定类型种群规模随时间分布的正向和反向方程。同时，还推导出一种或多种特定类型尚未出现的概率方程。举例说明数值方法和这些结果在进化生物学和流行病学中的潜在应用。
In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes overtime, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.