Colony entropy-Allocation of goods in ant colonies.

Allocation of goods is a key feature in defining the connection between the individual and the collective scale in any society. Both the process by which goods are to be distributed, and the resulting allocation to the members of the society may affect the success of the population as a whole. One of the most striking natural examples of a highly successful cooperative society is the ant colony which often acts as a single superorganism. In particular, each individual within the ant colony has a "communal stomach" which is used to store and share food with the other colony members by mouth to mouth feeding. Sharing food between communal stomachs allows the colony as a whole to get its food requirements and, more so, allows each individual within the colony to reach its nutritional intake target. The vast majority of colony members do not forage independently but obtain their food through secondary interactions in which food is exchanged between individuals. The global effect of this exchange is not well understood. To gain better understanding into this process we used fluorescence imaging to measure how food from a single external source is distributed and mixed within a Camponotus sanctus ant colony. Using entropic measures to quantify food-blending, we show that while collected food flows into all parts of the colony it mixes only partly. We show that mixing is controlled by the ants' interaction rule which implies that only a fraction of the maximal potential is actually transferred. This rule leads to a robust blending process: i.e., neither the exact food volume that is transferred, nor the interaction schedule are essential to generate the global outcome. Finally, we show how the ants' interaction rules may optimize a trade-off between fast dissemination and efficient mixing. Our results regarding the distribution of a single food source provide a baseline for future studies on distributed regulation of multiple food sources in social insect colonies.