Engelstädter Jan, Telschow Arndt, Hammerstein Peter
Institute for Theoretical Biology, Humboldt University, Invalidenstrasse 43, 10115 Berlin, Germany.
J Theor Biol. 2004 Dec 7;231(3):345-55. doi: 10.1016/j.jtbi.2004.06.029.
Wolbachia are widespread intracellular symbionts of arthropods which are known to cause several reproductive manipulations in their hosts, the commonest of which being cytoplasmic incompatibility (CI), male killing (MK), and the induction of parthenogenesis (PI). Strains of endosymbionts inducing one of these effects can be referred to as 'Wolbachia-types'. Here, we try to ascertain whether two of these Wolbachia-types can stably coexist within one population. We investigate this question by means of two discrete-time mathematical models which describe the dynamics of an infection of a host population with either CI- and MK- or CI- and PI-Wolbachia. We derive analytical solutions for two special cases of each model showing that stable coexistence of the respective Wolbachia-types is not possible if no doubly infected individuals occur within the population and that stable coexistence is possible when doubly infected hosts do exist and transmission of the endosymbionts is perfect. Moreover, we show that a population infected with either CI- or MK-Wolbachia at equilibrium can resist invasion of the respective other Wolbachia-type as a single infection. In contrast, a population infected with CI-Wolbachia can be invaded by PI-Wolbachia as a single infection with the CI-Wolbachia going extinct. Computer simulations confirmed these findings for the general models. We discuss our results with respect to the prevalence of the Wolbachia-types considered here and the emergence of PI- from CI-Wolbachia.
沃尔巴克氏体是节肢动物中广泛存在的细胞内共生菌，已知会在其宿主中引发多种生殖操控，其中最常见的是细胞质不亲和（CI）、雄性致死（MK）和孤雌生殖诱导（PI）。诱导这些效应之一的内共生菌菌株可被称为“沃尔巴克氏体类型”。在此，我们试图确定这两种沃尔巴克氏体类型是否能在一个种群中稳定共存。我们通过两个离散时间数学模型来研究这个问题，这两个模型描述了宿主种群被CI和MK型或CI和PI型沃尔巴克氏体感染的动态过程。我们推导了每个模型两种特殊情况的解析解，结果表明，如果种群中不存在双重感染个体，相应的沃尔巴克氏体类型就不可能稳定共存；而当存在双重感染宿主且内共生菌传播完美时，稳定共存是可能的。此外，我们表明，处于平衡状态下被CI或MK型沃尔巴克氏体感染的种群能够抵御另一种沃尔巴克氏体类型作为单一感染的入侵。相比之下，被CI型沃尔巴克氏体感染的种群可能会被PI型沃尔巴克氏体作为单一感染入侵，同时CI型沃尔巴克氏体灭绝。计算机模拟证实了这些一般模型的结果。我们根据这里所考虑的沃尔巴克氏体类型的流行情况以及CI型沃尔巴克氏体中PI型的出现来讨论我们的结果。
