Random Walk Models of Worker Sorting in Ant Colonies

Sorting can be an important mechanism for the transfer of information from one level of biological organization to another. Here we study the algorithm underlying worker sorting in Leptothorax ant colonies. Worker sorting is related to task allocation and therefore to the adaptive advantages associated with an efficient system for the division of labour in ant colonies. We considered four spatially explicit individual-based models founded on two-dimensional correlated random walk. Our aim was to establish whether sorting at the level of the worker population could occur with minimal assumptions about the behavioural algorithm of individual workers. The behaviour of an individual worker in the models could be summarized by the rule “move if you can, turn always”. We assume that the turning angle of a worker is individually specific and negatively dependent on the magnitude of an internal parameter μ which could be regarded as a measure of individual experience or task specialization. All four models attained a level of worker sortedness that was compatible with results from experiments onLeptothorax ant colonies. We found that the presence of a sorting pivot, such as the nest wall or an attraction force towards the centre of the worker population, was crucial for sorting. We make a distinction between such pivots and templates and discuss the biological implications of their difference.