Western honeybees (Apis Mellifera) serve extremely important roles in our ecosystem and economics as they are responsible for pollinating $ 215 billion dollars annually over the world. Unfortunately, honeybee population and their colonies have been declined dramatically. The purpose of this article is to explore how we should model honeybee population with age structure and validate the model using empirical data so that we can identify different factors that lead to the survival and healthy of the honeybee colony. Our theoretical study combined with simulations and data validation suggests that the proper age structure incorporated in the model and seasonality are important for modeling honeybee population. Specifically, our work implies that the model assuming that (1) the adult bees are survived from the egg population rather than the brood population; and (2) seasonality in the queen egg laying rate, give the better fit than other honeybee models. The related theoretical and numerical analysis of the most fit model indicate that (a) the survival of honeybee colonies requires a large queen egg-laying rate and smaller values of the other life history parameter values in addition to proper initial condition; (b) both brood and adult bee populations are increasing with respect to the increase in the egg-laying rate and the decreasing in other parameter values; and (c) seasonality may promote/suppress the survival of the honeybee colony.
more »
« less
Review on mathematical modeling of honeybee population dynamics
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.
- NSF-PAR ID:
- 10311210
- Date Published:
- Journal Name:
- Mathematical Biosciences and Engineering
- Volume:
- 18
- Issue:
- 6
- ISSN:
- 1551-0018
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Abstract Social insect colonies exhibit a variety of life history strategies, from the annual, semelparous colonies of temperate bees and wasps to the long-lived colonies of many ants and honeybees. Species introduced to novel habitats may exhibit plasticity in life history strategies as a result of the introduction, but the factors governing these changes often remain obscure. Vespula pensylvanica , a yellowjacket wasp, exhibits such plasticity in colony longevity. Multi-year (perennial) colonies are relatively common in introduced populations in Hawaii, while source populations in the western United States are typically on an annual cycle. Here, we use experiments and observational data to examine how diet, disease, nest thermal environment, and nest location influence colony longevity in a population with both annual and perennial colonies. Counter to our predictions, experimental feeding and warming did not increase colony survival in the winter in the introduced range. However, Moku Virus load and wasp colony density predicted colony survival in one year, suggesting a potential role for disease in modulating colony phenology. We also found that local V. pensylvanica colony density was positively correlated with Moku Virus loads, and that Arsenophonus sp. bacterial loads in V. pensylvanica colonies were positively associated with proximity to feral honeybee ( Apis mellifera ) hives, suggesting potential transmission routes for these poorly understood symbionts. The factors influencing colony longevity in this population are likely multiple and interactive. More important than food availability, we propose winter precipitation as a critical factor that may explain temporal and spatial variation in colony longevity in these invasive wasps.more » « less
-
Host temperature and gut chemistry can shape resistance to parasite infection. Heat and acidity can limit trypanosomatid infection in warm-blooded hosts and could shape infection resistance in insects as well. The colony-level endothermy and acidic guts of social bees provide unique opportunities to study how temperature and acidity shape insect–parasite associations. We compared temperature and pH tolerance between three trypanosomatid parasites from social bees and a related trypanosomatid from poikilothermic mosquitoes, which have alkaline guts. Relative to the mosquito parasites, all three bee parasites had higher heat tolerance that reflected body temperatures of hosts. Heat tolerance of the honeybee parasite Crithidia mellificae was exceptional for its genus, implicating honeybee endothermy as a plausible filter of parasite establishment. The lesser heat tolerance of the emerging Lotmaria passim suggests possible spillover from a less endothermic host. Whereas both honeybee parasites tolerated the acidic pH found in bee intestines, mosquito parasites tolerated the alkaline conditions found in mosquito midguts, suggesting that both gut pH and temperature could structure host–parasite specificity. Elucidating how host temperature and gut pH affect infection—and corresponding parasite adaptations to these factors—could help explain trypanosomatids' distribution among insects and invasion of mammals.more » « less
-
more » « less
Abstract Vairimorpha (=Nosema) ceranae is a widespread pollinator parasite that commonly infects honeybees and wild pollinators, including bumblebees. Honeybees are highly competentV. ceranae hosts and previous work in experimental flight cages suggestsV. ceranae can be transmitted during visitation to shared flowers. However, the relationship between floral visitation in the natural environment and the prevalence ofV. ceranae among multiple bee species has not been explored. Here, we analyzed the number and duration of pollinator visits to particular components of squash flowers—including the petals, stamen, and nectary—at six farms in southeastern Michigan, USA. We also determined the prevalence ofV. ceranae in honeybees and bumblebees at each site. Our results showed that more honeybee flower contacts and longer duration of contacts with pollen and nectar were linked with greaterV. ceranae prevalence in bumblebees. Honeybee visitation patterns appear to have a disproportionately large impact onV. ceranae prevalence in bumblebees even though honeybees are not the most frequent flower visitors. Floral visitation by squash bees or other pollinators was not linked withV. ceranae prevalence in bumblebees. Further,V. ceranae prevalence in honeybees was unaffected by floral visitation behaviors by any pollinator species. These results suggest that honeybee visitation behaviors on shared floral resources may be an important contributor to increasedV. ceranae spillover to bumblebees in the field. Understanding howV. ceranae prevalence is influenced by pollinator behavior in the shared floral landscape is critical for reducing parasite spillover into declining wild bee populations. -
more » « less
Abstract Bee–fungus associations are common, and while most studies focus on entomopathogens, emerging evidence suggests that bees associate with a variety of symbiotic fungi that can influence bee behavior and health. Here, we review nonpathogenic fungal taxa associated with different bee species and bee-related habitats. We synthesize results of studies examining fungal effects on bee behavior, development, survival, and fitness. We find that fungal communities differ across habitats, with some groups restricted mostly to flowers (Metschnikowia), while others are present almost exclusively in stored provisions (Zygosaccharomyces). Starmerella yeasts are found in multiple habitats in association with many bee species. Bee species differ widely in the abundance and identity of fungi hosted. Functional studies suggest that yeasts affect bee foraging, development, and pathogen interactions, though few bee and fungal taxa have been examined in this context. Rarely, fungi are obligately beneficial symbionts of bees, whereas most are facultative bee associates with unknown or ecologically contextual effects. Fungicides can reduce fungal abundance and alter fungal communities associated with bees, potentially disrupting bee–fungi associations. We recommend that future study focus on fungi associated with non-honeybee species and examine multiple bee life stages to document fungal composition, abundance, and mechanistic effects on bees.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/mbe.2021471
