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Modeling Honey Bee Populations.

Torres DJ, Ricoy UM, Roybal S - PLoS ONE (2015)

Bottom Line: Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes.Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al.We also conduct sensitivity studies and show the effects of parameter variations on the colony population.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Physical Science, Northern New Mexico College, Espanola, NM, USA.

ABSTRACT
Eusocial honey bee populations (Apis mellifera) employ an age stratification organization of egg, larvae, pupae, hive bees and foraging bees. Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes. We first perform an analysis of steady state bee populations given mortality rates within each bee caste and find that the honey bee colony is highly susceptible to hive and pupae mortality rates. Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al. Our transient model based on differential equations accounts for the effects of pheromones in slowing the maturation of hive bees to foraging bees, the increased mortality of larvae in the absence of sufficient hive bees, and the effects of food scarcity. We also conduct sensitivity studies and show the effects of parameter variations on the colony population.

No MeSH data available.


Related in: MedlinePlus

Effect of time step on the accuracy of the model in predicting the number of adult bees.
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pone.0130966.g006: Effect of time step on the accuracy of the model in predicting the number of adult bees.

Mentions: To make the determination of how small △t should be, we perform a convergence study. We note that if ai = 3, the time step should be at least a third of a day to properly accelerate the maturation of hive bees. A 150 day simulation is performed with four different time steps: 16.8 hours, 12 hours, 6 hours and 2.4 hours. We use the seasonal equation from Schmickl et al. [13] to model the term s(t) used in (14) and (31),s(t)=1-max{1-11+x1exp(-[2t/x2])11+x3exp(-[2(t-x4)/x5])(32)with x1 = 385, x2 = 30, x3 = 36, x4 = 155, x5 = 30 and t is the day of the year. The egg laying rate is assumed to be B0 = 1600s(t) eggs per day. We begin with 8,000 hive bees. Our goal is to determine the time step below which the evolution of the adult bees is independent of the time step. Fig 6 shows the results of the simulations. On the horizontal axis, a value of t = 1 refers to January 1st and a value of t = 365 refers to December 31st. When the time step is 16.8 hours, the simulation becomes unstable. Below a time step of 6 hours, there no visual difference between the graph and the simulation that uses a time step of 2.4 hours. Therefore we believe that △t should be 6 hours or smaller. This is an important observation since many models [11, 12] use a time step of one day, although we acknowledge that their specific equations may not require as restrictive of a time step.


Modeling Honey Bee Populations.

Torres DJ, Ricoy UM, Roybal S - PLoS ONE (2015)

Effect of time step on the accuracy of the model in predicting the number of adult bees.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493160&req=5

pone.0130966.g006: Effect of time step on the accuracy of the model in predicting the number of adult bees.
Mentions: To make the determination of how small △t should be, we perform a convergence study. We note that if ai = 3, the time step should be at least a third of a day to properly accelerate the maturation of hive bees. A 150 day simulation is performed with four different time steps: 16.8 hours, 12 hours, 6 hours and 2.4 hours. We use the seasonal equation from Schmickl et al. [13] to model the term s(t) used in (14) and (31),s(t)=1-max{1-11+x1exp(-[2t/x2])11+x3exp(-[2(t-x4)/x5])(32)with x1 = 385, x2 = 30, x3 = 36, x4 = 155, x5 = 30 and t is the day of the year. The egg laying rate is assumed to be B0 = 1600s(t) eggs per day. We begin with 8,000 hive bees. Our goal is to determine the time step below which the evolution of the adult bees is independent of the time step. Fig 6 shows the results of the simulations. On the horizontal axis, a value of t = 1 refers to January 1st and a value of t = 365 refers to December 31st. When the time step is 16.8 hours, the simulation becomes unstable. Below a time step of 6 hours, there no visual difference between the graph and the simulation that uses a time step of 2.4 hours. Therefore we believe that △t should be 6 hours or smaller. This is an important observation since many models [11, 12] use a time step of one day, although we acknowledge that their specific equations may not require as restrictive of a time step.

Bottom Line: Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes.Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al.We also conduct sensitivity studies and show the effects of parameter variations on the colony population.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Physical Science, Northern New Mexico College, Espanola, NM, USA.

ABSTRACT
Eusocial honey bee populations (Apis mellifera) employ an age stratification organization of egg, larvae, pupae, hive bees and foraging bees. Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes. We first perform an analysis of steady state bee populations given mortality rates within each bee caste and find that the honey bee colony is highly susceptible to hive and pupae mortality rates. Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al. Our transient model based on differential equations accounts for the effects of pheromones in slowing the maturation of hive bees to foraging bees, the increased mortality of larvae in the absence of sufficient hive bees, and the effects of food scarcity. We also conduct sensitivity studies and show the effects of parameter variations on the colony population.

No MeSH data available.


Related in: MedlinePlus