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A plant-pollinator system： How learning versus cost-benefit can induce periodic oscillations

International Journal of Biomathematics 2018年第2期11卷 189-215页

作者： Virgilio Vazquez Ignacio Barradas Instituto de Fisicay Matemdticas Universidad Tecnologica de la Mixteca Huajuapan de Leon Oaxaca 69000 Mexico Centro de Investigacion en Matemdticas Apartado Postal 302 Guanajuato Guanajuato 36000 Mexico

In this paper, we propose a model describing the interaction between two species： a plant population that gets pollinated by an insect population. We assume the plant population is divided into two groups： the first group in mutualistic relationship with the insect and the second group attracting the insects while deceiving them and not delivering any reward. In addition, we assume that the insect population reduces the number of visits to the plants after several unsuccessful visits. We are interested in the conditions for the coexistence of both species, especially in the appearance of damped or sustained oscillations. We focus the analysis on the parameters that measure the balance among deceit, the benefit that the insect gets from the plant, and the learning by the pollinators. We are especially interested in analyzing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants.

关键词： deceptive pollination mutualism learning oscillations Hopf bifurcation.

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A Preliminary Study on pollination Biology of an Endangered Orchid, Changnienia amoena, in Shennongjia

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Acta Botanica Sinica 2003年第9期45卷 1019-1023页

作者：孙海芹罗毅波葛颂中国科学院植物研究所系统与进化植物学重点实验室北京100093

Changnienia amoena Chien is a monotypic species and endemic to China, and was listed on the Chinese Red Book in 1992. The species was once abundant but has become rare and endangered in recent years because of the habitat fragmentation and unduly commercial collections. Previous observation showed that this species has very low and even no fruit set, and the pollinators are not observed before this report. The present observation was conducted at the Shennongjia, Hubei Province during the spring of 2002. The results showed that Bombus (Diversobombus) trifasciatus Smith, B. imitator Pittion and one species of Apis visited the flowers of the orchid, but only B. tritasciatus could carry pollinaria on its body and was the legitimate pollinators of C amoena. During 113 h of observation, only nine visitations were recorded. The bumblebees mainly appeared during 12:00-15:00 during the day. Bumblebees stayed in a flower only a few seconds and never more than ten seconds. The flowers would persist in fresh for about three weeks when they were not pollinated, but 3 or 4 d after pollinated, the pollinated flowers underwent a series of color and morphological changes including stalk elongation and ovary swelling. Therefore, stalk elongation can be considered an index of fruits set. Artificial pollination indicated that C amoena is a highly self-compatible and outcrossing species, but dependent on pollinators for fruit set. Based on the field observations, we concluded that pollination system of C amoena is deceptive. The fruit set in nature is not very low (26.98% on average) compared to other deceptive orchids, which may be related to small population sizes. The number of pollinia removal is much higher than that of fruit set, indicating that there are some degrees of pollinia wasting in C amoena.

关键词： Changnienia amoena Bombus (Diversobombus) trifasciatus deceptive pollination stalk elongation

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