Numerical Modeling of the Collective Behavior of Scarab Beetles Transporting Dung Balls and Competing for Them on Complex Terrain

To avoid competition for the same food resource, scarab beetles form dung ball and roll it away from the dung pile. They randomly choose direction which they strictly follow. According to previous results, the dynamic behavior of the beetle rolling dung ball is essentially defined by the complexity of the surface. The typical real surface is combined from a universal scale invariant (fractal) component and another component having a well-defined characteristic scale. If the transported dung ball has a size comparable with the dimensions of peculiarities of the surface, it strongly influences the motion trajectory. On the flat terrain and at the absence of competitors, beetles manage to roll the ball along a nearly perfect straight path. However, even if the beetle is alone, on a more realistic terrain, the motion is more complex. The motion becomes much more complicated in the realistic situation, when the beetles complete for the balls. In this study, a numerical model is developed which combines 1 ) attraction of the beetles to the dung, (2) production of the balls of different sizes depending on the size/fitness of the animals, 3) the ball transportation on complex terrains, and 4) the competition between the beetles for already existing balls. A strong correlation between typical radius of the ball and the size of the relief minimums and the results of the competitions, as well as possible optimal strategies of the beetle behavior are found.