A mathematical modelization of the prosperity of an Apis Mellifera beehive

Abstract

Aesop's famous fable The Ant and the Grasshopper emphasizes the choice that living beings have to make between survival (the Ant) and reproduction (the Grasshopper). Apis Mellifera colonies face the same dilemma : must they rather collect nectar in order to produce honey that will enable them to endure the cold of winter or should they choose to bring pollen back to the hive so as to raise young bees ? Both, of course, but in which proportion ? And where should they fly to find the best resources ? We adress these question through a mathematical perspective, by considering the geometry of resources around the hive.