This paper considers a pollination-mutualism system in which flowering plants have strategies of secreting and cheating: secretors produce a substantial volume of nectar in flowers but cheaters produce none. Accordingly, floral visitors have strategies of neglecting and selecting: neglectors enter any flower encountered but selectors only enter full flowers since they can discriminate between secretors and cheaters. By combination of replicator equations and two-species dynamical systems, the games are described by a mathematical model in this paper. Dynamics of the model demonstrate mechanisms by which nectarless flowers can invade the secretor-pollinator system and by which a cyclic game between nectarless flowers and pollinators could occur. Criteria for the persistence of nectarless flowers are derived in terms of the given parameters (factors), including the nectar-producing cost and cheaters' efficiency. Numerical simulations show that when parameters vary, cheaters would vary among extinction, persistence in periodic oscillations, and persistence without secretors (i.e., cheaters spread widely). We also consider the evolution of plants in a constant state of pollinator population, and the evolution of pollinators in a constant state of plant population. Dynamics of the models demonstrate conditions under which nectarless flowers (resp. selectors) could persist.

中文翻译：

---

无花蜜授粉-互惠系统中的分叉

本文考虑了一种授粉-互惠系统，其中开花植物具有分泌和欺骗的策略：分泌物在花朵中产生大量的花蜜，而欺骗者则不产生。因此，花艺访客有忽略和选择策略：忽略者输入遇到的任何花朵，但选择者仅输入完整的花朵，因为他们可以区分分泌者和作弊者。通过复制器方程和两种种群的动力学系统的组合，用数学模型描述了博弈。该模型的动力学证明了无花蜜可以侵入分泌物-授粉系统的机制，以及无花蜜和授粉媒介之间的周期性博弈。根据所给定的参数（因素），得出了无花蜜的持久性的标准，包括花蜜的生产成本和作弊者的效率。数值模拟表明，当参数变化时，作弊者会在灭绝，周期性振荡的持久性和没有分泌物的持久性（即作弊者广泛传播）之间发生变化。我们还考虑了授粉媒介种群处于恒定状态的植物进化，以及处于授粉种群种群处于恒定状态的授粉媒介的进化。模型的动力学表明无花蜜（分别选择器）可以持续存在的条件。和没有分泌物的持久性（即骗子广泛传播）。我们还考虑了授粉媒介种群处于恒定状态的植物进化，以及处于授粉种群种群处于恒定状态的授粉媒介的进化。模型的动力学表明无花蜜（分别选择器）可以持续存在的条件。和没有分泌物的持久性（即骗子广泛传播）。我们还考虑了授粉媒介种群处于恒定状态的植物进化，以及处于授粉种群种群处于恒定状态的授粉媒介的进化。模型的动力学表明无花蜜（分别选择器）可以持续存在的条件。