Not all plant-pollinator interactions are mutualistic, and in fact deceptive pollination systems are widespread in nature. The genus Arisaema has a pollination system known as lethal deceptive pollination, in which plants not only attract pollinating insects without providing any rewards, but also trap them until they die. Many Arisaema species are endangered from various disturbances, including reduction in forest habitat, modification of the forest understorey owing to increasing deer abundance, and plant theft for horticultural cultivation. We aimed to theoretically investigate how lethal deceptive pollination can be maintained from a demographic perspective and how plant and pollinator populations respond to different types of disturbance. We developed and analysed a mathematical model to describe the population dynamics of a deceptive plant species and its victim pollinator. Calibrating the model based on empirical data, we assessed the conditions under which plants and pollinators could coexist, while manipulating relevant key parameters. The model exhibited qualitatively distinct behaviours depending on certain parameters. The plant becomes extinct when it has a low capability for vegetative reproduction and slow transition from male to female, and plant-insect co-extinction occurs especially when the plant is highly attractive to male insects. Increasing deer abundance has both positive and negative effects because of removal of other competitive plants and diminishing pollinators, respectively. Theft for horticultural cultivation can readily threaten plants whether male or female plants are frequently collected. The impact of forest habitat reduction may be limited compared with that of other disturbance types. Our results have emphasized that the demographic vulnerability of lethal deceptive pollination systems would differ qualitatively from that of general mutualistic pollination systems. It is therefore important to consider the demographics of both victim pollinators and deceptive plants to estimate how endangered Arisaema populations respond to various disturbances.
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