Buzz pollination: A theoretical analysis via scaling invariance

Nearly half of the bee species can perform a fascinating stereotyped behavior to collect pollen grains by vibrating flowers, known as buzz pollination. During the floral visit, these bees mechanically transfer the vibrations produced by their thoracic indirect flight muscles to the flower anther, inducing the movement of the pollen grains and leading them to be released through a small pore or slit placed at the tip of the anther in poricidal flowers. In such flowers, pollen release is affected by the vibrational behavior of buzzing bees, primarily their duration and velocity amplitude. However, we know little about how poricidal anther morphology may influence it. In this work, we investigated through a theoretical and numerical point of view the buzz pollination process considering a typical poricidal anther of a tomato flower (Solanum lycopersicum), which in our work will be approached by a rectangular billiard, experiencing vibrations applied by a bumblebee (Bombus terrestris). Our primary goals in this paper are (i) to understand the mechanism behind the pollen release in this model, (ii) to observe some scale effects associated with morphological variations of the anther (as pore size and anther shape), and (iii) analyze how these results are related to natural buzz pollination systems.