Research Article with accompanied with R Code. The research group developed a mathematical model to quantify the loss of resilience in honeybee colonies experiencing a strong Allee effect. In their model, recruitment and mortality of adult bees are significantly influenced by social factors: recruitment is boosted, and the presence of more adult bees reduces mortality. This leads to an Allee effect, where the net per-individual rate of hive growth increases with the number of adult bees. The Allee effect establishes a critical minimum size for the adult bee population. If the population falls below this size, mortality surpasses recruitment, leading to the hive's decline. Under normal and favorable environmental conditions, this critical size is low, allowing hives to thrive and maintain large populations. These hives can produce new, viable swarms (naturally or through beekeeping) as they approach an upper stable equilibrium size or carrying capacity. However, the lower critical size and the upper stable size have been influenced by various parameters related to demographic rates and their enhancement through bee sociality. Environmental factors that increase mortality, decrease recruitment, or disrupt the social regulation of these rates exacerbate the Allee effect by raising the lower critical size and significantly reducing the upper stable size. Furthermore, the model shows that the basin of attraction to the upper stable size, defined by the potential function, becomes narrower and shallower under these conditions. This indicates a loss of resilience, as the hive becomes more vulnerable to dropping below the critical size. Severe environmental impacts can cause the two equilibria to converge, eliminating the basin of attraction to the upper stable size and leading to hive collapse regardless of initial size. The model suggests that various proximate causes, such as pesticides, mites, pathogens, and climate change, whether acting alone or in combination, could trigger hive collapse.
NOTE: To utilize their accompanied R code, I was required to adjust some of the code to apply it in RMarkdown
Asocial Hive Model
Social Hive Model
Allee Effect
Hive Collapse
Ecological Resilience
Allee Effect in HoneyBees
