Energetic thresholds and hygienic cannibalism govern claustral ant colony founding under fungal challenge

Claustral ant queens found colonies in sealed, food-free chambers, making colony founding both energetically constrained and vulnerable to fungal disease. Recent experiments show that queens cannibalise infected larvae, thereby removing potential sources of conidia while recovering nutrients for further oviposition. We develop a deterministic four-compartment model for queen reserves, healthy brood, infected brood, and environmental spores to investigate how hygienic cannibalism shapes founding success under fungal challenge. The analysis reveals a nested threshold structure. An energetic persistence threshold determines whether brood recycling can offset maintenance and brood-production costs in the absence of infection; conditional on energetic viability, a pathogen invasion threshold determines whether a rare fungal infection can grow from the disease-free founding state. When energetic support is sufficient, the coexistence conditions reduce to a scalar equation for infected brood density, implying that at most two endemic equilibria can occur and yielding explicit criteria for a unique endemic state versus bistability between extinction and a high-infection endemic state. Bifurcation analysis further shows that varying cannibalism can generate a forward invasion transition, saddle-node bistability between extinction and endemic infection, and, in some regimes, stable infection oscillations. Simulations show that stronger hygienic cannibalism shifts founding outcomes from collapse to chronic but viable infection and, for low-yield pathogens, to infection clearance, whereas increasing conidial yield enlarges the region of founding failure. Sensitivity analysis identifies recycling efficiencies, cannibalism rate, brood-production cost, transmission, conidial yield, and spore decay as the strongest determinants of reserves, brood, infection, and successful founding. Together, these results show how energetic constraints and hygienic cannibalism jointly determine whether claustral founding clears infection, persists under chronic disease, or collapses under fungal challenge.