Review on mathematical modeling of honeybee population dynamics

Abstract

<abstract><p>Honeybees have an irreplaceable position in agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally. Parasites, diseases, poor nutrition, pesticides, and climate changes contribute greatly to the global crisis of honeybee colony losses. Mathematical models have been used to provide useful insights on potential factors and important processes for improving the survival rate of colonies. In this review, we present various mathematical tractable models from different aspects: 1) simple bee-only models with features such as age segmentation, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We aim to review those mathematical models to emphasize the power of mathematical modeling in helping us understand honeybee population dynamics and its related ecological communities. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe the bee population dynamics in environments that include factors such as temperature, rainfall, light, distance and quality of food, and their effects on colony growth and survival. In addition, we propose a future outlook on important directions regarding mathematical modeling of honeybees. We particularly encourage collaborations between mathematicians and biologists so that mathematical models could be more useful through validation with experimental data.</p></abstract>

Bee pasture as a buffer against flower-mediated disease transmission

“…Fifth, our model does not consider complex inter-colony food competition between Colony A and C. Sixth, we assume that the number of flowers in each foraging area is dense enough to attract bees [25, 35-38, 38, 39]. Lastly, the model does not incorporate various other constraints that may influence disease transmission dynamics, such as the presence of bee chemical cues, complex barriers, differential floral preferences, floral fidelity, differential length of visitation, differential pathogen load, possible attraction to diseased plants, or the use of optic flow information as an odometer to estimate distance [20,[40][41][42][43][44][45][46][47][48]. These simplifications are made to streamline the analysis and focus on the core dynamics of disease transmission via food source visitation between colonies A and C, hence, enabling us to derive straightforward yet generalizable conclusions from our model.…”

Reconstruction coefficient analysis of honeybee collapse due to pesticide contamination

“…The models presented in [12,22,23] do not incorporate worker bees within the hive, despite them constituting the majority of the bee population and playing a crucial role in caring for juvenile bees. These worker bees stay inside the hive and, therefore, do not become contaminated by coming into contact with pesticides present outside the hive.…”

“…These factors collectively affect the timing, duration, and variability of seasonal events, see e.g. [1,2,4,8,12,18,19,25,26,28,30]. Numerous research studies are dedicated to exploring the reasons behind the global decline of the honeybee population, as documented in works like [25,26,30].…”

“…Consequently, the colony's foraging region experiences heterogeneous spatial pesticide contamination, leading to varying fractions of the forager bee population being affected. This model [12,22,23] is specifically tailored for application in managed colonies.…”

“…The reasons behind colony losses are attributed to several potential factors, including emerging pathogens and pests, diminished genetic diversity, pesticide usage, scarcity of highquality food, and alterations in the environment [3,6,9,12]. Notable pathogens and pests known to contribute to colony losses encompass Paenibacillus larvae and Melissococcus plutonius (causing American and European foulbrood, respectively), the parasitic mite Varroa destructor, parasitic microsporidia Nosema species, and various honeybee viruses [4,12,19,20].…”