Exact Steady-State Distributions of Multispecies Birth-Death-Immigration Processes: Effects of Mutations and Carrying Capacity on Diversity
Exact Steady-State Distributions of Multispecies Birth-Death-Immigration Processes: Effects of Mutations and Carrying Capacity on Diversity
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DOI：
10.1007/s10955-018-2128-4
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发表时间：
2018-10-01
影响因子：
1.6
通讯作者：
Chou, Tom
中科院分区：
文献类型：
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作者：
Dessalles, Renaud;D'Orsogna, Maria;Chou, Tom
包含出生、死亡和移民的随机模型(也称为出生-死亡模型和创新模型)无处不在，适用于生态种群中物种大小的量化、基因家族大小的描述、体内淋巴细胞进化的建模等问题。其中许多应用涉及到新物种进入系统的移民。我们考虑了与多物种出生-死亡-迁移相关的全高维随机过程，并在稳态下给出了一些精确的渐近结果。我们进一步通过承载能力包括随机突变或相互作用，并得到总个体数量、总物种数量、物种大小分布和各种多样性指数的统计数据。我们的结果包括对这些系统在快速移民极限下的行为的严格分析，结果表明，在不同的多样性指数中，物种丰富度最能区分不同类型的出生-死亡-移民模型。我们还发现，在简单的不相互作用的生灭移民模型和通过死亡实现承载能力的生死移民模型中保持了详细的平衡。令人惊讶的是，当通过出生率来实施承载能力时，细节平衡被打破了。
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many problems such as quantifying species sizes in ecological populations, describing gene family sizes, modeling lymphocyte evolution in the body. Many of these applications involve the immigration of new species into the system. We consider the full high-dimensional stochastic process associated with multispecies birth-death-immigration and present a number of exact and asymptotic results at steady state. We further include random mutations or interactions through a carrying capacity and find the statistics of the total number of individuals, the total number of species, the species size distribution, and various diversity indices. Our results include a rigorous analysis of the behavior of these systems in the fast immigration limit which shows that of the different diversity indices, the species richness is best able to distinguish different types of birth-death-immigration models. We also find that detailed balance is preserved in the simple noninteracting birth-death-immigration model and the birth-death-immigration model with carrying capacity implemented through death. Surprisingly, when carrying capacity is implemented through the birth rate, detailed balance is violated.