A mathematical modelization of the prosperity of an Apis Mellifera beehive

TL;DR

This paper develops a mathematical model to analyze how honeybee colonies balance resource collection for survival and reproduction, considering the spatial distribution of resources around the hive.

Contribution

It introduces a novel mathematical framework to optimize resource collection strategies of Apis Mellifera based on resource geometry.

Findings

Model predicts optimal foraging proportions for survival and reproduction.

Highlights importance of resource spatial distribution in hive prosperity.

Provides insights into bee foraging behavior and colony health.

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.