Modeling Honey Bee Populations (original) (raw)
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A Quantitative Model of Honey Bee Colony Population Dynamics
PLoS ONE, 2011
Since 2006 the rate of honey bee colony failure has increased significantly. As an aid to testing hypotheses for the causes of colony failure we have developed a compartment model of honey bee colony population dynamics to explore the impact of different death rates of forager bees on colony growth and development. The model predicts a critical threshold forager death rate beneath which colonies regulate a stable population size. If death rates are sustained higher than this threshold rapid population decline is predicted and colony failure is inevitable. The model also predicts that high forager death rates draw hive bees into the foraging population at much younger ages than normal, which acts to accelerate colony failure. The model suggests that colony failure can be understood in terms of observed principles of honey bee population dynamics, and provides a theoretical framework for experimental investigation of the problem.
Modelling Food and Population Dynamics in Honey Bee Colonies
PLoS ONE, 2013
Honey bees (Apis mellifera) are increasingly in demand as pollinators for various key agricultural food crops, but globally honey bee populations are in decline, and honey bee colony failure rates have increased. This scenario highlights a need to understand the conditions in which colonies flourish and in which colonies fail. To aid this investigation we present a compartment model of bee population dynamics to explore how food availability and bee death rates interact to determine colony growth and development. Our model uses simple differential equations to represent the transitions of eggs laid by the queen to brood, then hive bees and finally forager bees, and the process of social inhibition that regulates the rate at which hive bees begin to forage. We assume that food availability can influence both the number of brood successfully reared to adulthood and the rate at which bees transition from hive duties to foraging. The model predicts complex interactions between food availability and forager death rates in shaping colony fate. Low death rates and high food availability results in stable bee populations at equilibrium (with population size strongly determined by forager death rate) but consistently increasing food reserves. At higher death rates food stores in a colony settle at a finite equilibrium reflecting the balance of food collection and food use. When forager death rates exceed a critical threshold the colony fails but residual food remains. Our model presents a simple mathematical framework for exploring the interactions of food and forager mortality on colony fate, and provides the mathematical basis for more involved simulation models of hive performance.
How to model honeybee population dynamics: stage structure and seasonality
Mathematics in Applied Sciences and Engineering, 2020
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 a...
Modeling the Interaction Dynamics between Honeybees and Food Availability
DEStech Transactions on Computer Science and Engineering, 2017
The success of honeybee (Apis mellifera) colonies is critical to the United States agriculture with 35% of American diets dependent on honeybee pollination. There are various complex factors that can contribute to a colonys failure, such as nutritional stress. Nutritional stressors primarily pertain to food scarcity, lack in diversity of food, and the availability of food with low nutritional value. Previous mathematical models have examined the impact of nutrition and the early recruitment on honeybee population dynamics. These models do not include the impact of a food supply with a limited storage space within a single hive. In this work, we use a mathematical model to investigate the impact of food scarcity and limited storage space on honeybee viability, early recruitment rates of workers into foragers, and the influence of these rates on the growth of a colony. A threshold, R d , was found for conditions when a colony will persist or collapse. We found conditions for the stable coexistence of a honeybee population and food supply as well as conditions for periodic behavior. Through sensitivity analysis we find that a honeybee colony is most sensitive to changes in the rate at which a worker bee encounters food and the rate food is entering the food supply. There are no qualitative differences between using a Holling Type I or Holling Type II functional response in honeybee population persistence when modeling the interaction between a honeybee colony and the availability of food.
Influence of brood deaths on Honey Bee population dynamics and the potential impact of insecticides
Honey bees (Apis mellifera) are responsible for pollinating nearly 80% of all food-producing plants, therefore, the success or failure of a colony is vital to global food production. However, Vector-borne diseases account for approximately the 20% of all infectious diseases leading to the use of insecticides to control them. These chemical products not only affect mosquitoes but other insects such as Honey bees, causing imbalances across most ecosystems around the world. Our goal is to describe the effect of insecticides over brood death rate and its possible effects over Honey Bee population dynamics. For this, we constructed a compartmental model using ordinary differential equations (ODE's) to describe brood birth, mortality, maturation and adult dynamics. To analyze our model we solved the equilibriums and performed stability and sensitivity analysis. We used data from 1975-76 in order to see how well our model fits the data and estimate the parameters. Besides, we implemented seasonality in our simulations to include the biological behavior of the queen's egg-laying rate. Our analytical results showed that for the population to become extinct, approximately half of the brood must die daily. The simulations obtained with the seasonality and the estimated parameters show that in order for the colony to collapse it is necessary that the 39.87% of the brood die at the moment of the birth if the pesticide is applied during the spring and 41.69% if the pesticide is applied during the summer. This is congruent with the theoretical result that tell us that if the 46.66% of the brood die the colony won't survive. If the insecticides applied during spring and summer affect half of the brood population in a hive, due to contamination, the total population will collapse. In future work, the effect of insecticides in the egg laying rate, in the brood-adult conversion, and in the adult lifespan should be taken in account to have more biologically accurate results.
Journal of Applied Ecology, 2014
A notable increase in failure of managed European honeybee Apis mellifera L. colonies has been reported in various regions in recent years. Although the underlying causes remain unclear, it is likely that a combination of stressors act together, particularly varroa mites and other pathogens, forage availability and potentially pesticides. It is experimentally challenging to address causality at the colony scale when multiple factors interact. In silico experiments offer a fast and cost-effective way to begin to address these challenges and inform experiments. However, none of the published bee models combine colony dynamics with foraging patterns and varroa dynamics. 2. We have developed a honeybee model, BEEHAVE, which integrates colony dynamics, population dynamics of the varroa mite, epidemiology of varroa-transmitted viruses and allows foragers in an agent-based foraging model to collect food from a representation of a spatially explicit landscape. 3. We describe the model, which is freely available online (www.beehave-model.net). Extensive sensitivity analyses and tests illustrate the model's robustness and realism. Simulation experiments with various combinations of stressors demonstrate, in simplified landscape settings, the model's potential: predicting colony dynamics and potential losses with and without varroa mites under different foraging conditions and under pesticide application. We also show how mitigation measures can be tested. 4. Synthesis and applications. BEEHAVE offers a valuable tool for researchers to design and focus field experiments, for regulators to explore the relative importance of stressors to devise management and policy advice and for beekeepers to understand and predict varroa dynamics and effects of management interventions. We expect that scientists and stakeholders will find a variety of applications for BEEHAVE, stimulating further model development and the possible inclusion of other stressors of potential importance to honeybee colony dynamics.
Modeling the Influence of Mites on Honey Bee Populations
Veterinary Sciences, 2020
The Varroa destructor mite has been associated with the recent decline in honey bee populations. While experimental data are crucial in understanding declines, insights can be gained from models of honey bee populations. We add the influence of the V. destructor mite to our existing honey bee model in order to better understand the impact of mites on honey bee colonies. Our model is based on differential equations which track the number of bees in each day in the life of the bee and accounts for differences in the survival rates of different bee castes. The model shows that colony survival is sensitive to the hive grooming rate and reproductive rate of mites, which is enhanced in drone capped cells.
Environmental science & technology, 2015
To simulate effects of pesticides on different honeybee (Apis mellifera L.) life stages, the BEEHAVE model was used to explore how increased mortalities of larvae, in-hive workers and foragers, as well as reduced egg-laying rate, could impact colony dynamics over multiple years. Stresses were applied for 30 days, both as multiples of the modelled control mortality and as set percentage daily mortalities to assess the sensitivity of the modelled colony both to small fluctuations in mortality and periods of low to very high daily mortality. These stresses simulate stylised exposure of the different life stages to nectar and pollen contaminated with pesticide for 30 days. Increasing adult bee mortality had a much greater impact on colony survival than mortality of bee larvae or reduction in egg laying rate. Importantly, the seasonal timing of the imposed mortality affected the magnitude of the impact at colony level. In line with the LD50, we propose a new index of 'lethal imposed ...