Persistence of pollination systems

Pollination systems are composed of flowering plants and flower visitors, engaging into mutualistic interactions. However, the flower visitors include true pollinators, which pollinate the flower by visiting it through the legitimate way, and also by cheaters, which use the flower′s resources (e.g. nectar and pollen) without pollinating it or been just marginally efficient on pollination. On the one hand, plants have different flower structures, as shallow and tubular flowers, which can provide some protection agains the cheaters effects or higher efficiency when visited by pollinators. Even though cheaters can damage flowers, there is evidence that cheaters can have a positive effect on the pollination service. In fact, the existence of cheaters decreases the amount of reward provided by plants in a given environment. Therefore, pollinators travel further in order to visit more flowers or even spend a longer time in each flower to collect enough resources. It increases the cross-pollination rate and the pollination success, especially to auto-incompatible plant species. The presence of cheaters in these systems represent a delicate trade-off when mutualistic interactions when cheaters effects are taken into account. In this work, we are interested to understand how pollination systems allow the persistent coexistence of the two types of visitors and plants. We developed a mean field analytical model relying on game theory, with a bipartite network of two kinds of plants (shallow and tubular flowers) and two kinds of visitors (pollinators and cheaters). Our analytical and numerical results confirm the presence of metastable states of persistent coexistence of the above-mentioned visitors and plants. In order to better describe additional real-world features of pollination systems (i.e. the spatial distribution of flowers, the depletion of resources, and the crossing pollination effect) we also implement an agentbased model. In this case, we observed coexistence of the two visitors and two plants when we included the space. We are still studying the agentbased mode approach to understand, for instance, how spatial structures (as the ones resulting from mankind actions) can affect pollination systems. ∗corresponding author: [email protected]