School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China.
Bull Math Biol. 2013 Jul;75(7):1138-56. doi: 10.1007/s11538-013-9846-1. Epub 2013 May 4.
This paper considers plant-pollinator systems in which plants are divided into two categories: The plants that secret a substantial volume of nectar in their flowers are called secretors, while those without secreting nectar are called nonsecretors (cheaters). The interaction between pollinators and secretors is mutualistic, while the interaction between pollinators and nonsecretors is parasitic. Both interactions can be described by Beddington-DeAngelis functional responses. Using dynamical systems theory, we show global dynamics of a pollinator-secretor-cheater model and demonstrate mechanisms by which nectarless flowers/nonsecretors can invade the pollinator-secretor system and by which the three species could coexist. We define a threshold in the nonsecretors' efficiency in translating pollinator-cheater interaction into fitness, which is determined by parameters (factors) in the systems. When their efficiency is above the threshold, non-secretors can invade the pollinator-secretor system. While the nonsecretors' invasion often leads to their persistence in pollinator-secretor systems, the model demonstrates situations in which the non-secretors' invasion can drive secretors into extinction, which consequently leads to extinction of the nonsecretors themselves.
本文考虑了植物-传粉者系统，其中植物分为两类：在花朵中分泌大量花蜜的植物称为分泌者，而不分泌花蜜的植物称为非分泌者（骗子）。传粉者和分泌者之间的相互作用是互利共生的，而传粉者和非分泌者之间的相互作用是寄生的。这两种相互作用都可以用 Beddington-DeAngelis 功能反应来描述。本文使用动力系统理论，展示了传粉者-分泌者-骗子模型的全局动力学，并演示了无花蜜花/非分泌者如何入侵传粉者-分泌者系统，以及这三个物种如何共存。我们定义了非分泌者将传粉者-骗子相互作用转化为适应度的效率的一个阈值，该阈值由系统中的参数（因素）决定。当它们的效率高于阈值时，非分泌者就可以入侵传粉者-分泌者系统。虽然非分泌者的入侵通常会导致它们在传粉者-分泌者系统中持续存在，但该模型也展示了非分泌者的入侵会导致分泌者灭绝的情况，而这又会导致非分泌者自身的灭绝。
