Honeybees survive winter by forming a thermoregulating cluster: bees on the outside pack tightly as an insulating shell while the core shivers its flight muscles to generate heat. When it's cold, the whole cluster contracts to cut heat-losing surface area — visible here as the ball shrinking and glowing hotter at its core.
Q_generated = Q_lost = h·A(T_cluster − T_out)
fondant burn rate ∝ colony_size × max(0, T_ref − T_out)
survival ∝ logistic(T_cluster − T_critical) × [fondant remaining > 0]
- Outside temperature — colder air forces a tighter cluster and faster fondant burn.
- Fondant amount — starting emergency sugar-feed mass on the candy board.
- Colony size — more bees generate more heat but also eat through fondant faster.
- Time speed — fast-forwards the simulated winter to see long-run survival.
Beekeepers place a fondant slab directly on top of the frames in late winter, when stored honey often runs low but it's too cold to feed liquid syrup — the bees can reach solid sugar without leaving the warmth of the cluster.