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SimBee

The following page represents a mixture of 2 posters presented at a meeting of the British IUSSI Section in December 2001 in Cambridge, UK and on the international meeting of IUSSI in September 2001 in Berlin, Germany. This compilation explains the basic functionality of SimBee and shows some basic results.

INTRODUCTION:

Honeybees form monogynous societies, where a mated queen lays fertilized eggs which build up the worker population. We could expect the population size to be directly derived from the queens egg laying activity. Although the queens egg laying is mainly influenced by season, there are also other factors determining the colony size and age structure as well.

The life of an individual undergoes discrete developmental stages: egg larvae pupae  adult. As immature stages, the bees need a steady care by “nurse bees”, which feed them and generate a favorable ambient climate. The mortality of the immature stages depend mainly on the colony’s state and the efficiency (number and physiological state) of the nurse bees. Our studies showed, that a key factor determining larval mortality is the pollen state of the hive.

In contrast to the immature stages, the life as an adult can differ significantly between individuals. During the adult phase, the individuals again undergo several physiological and behavioral transitions, a phenomenon we call “age polyethism”. This describes the fact that several age divided castes perform a specific range of tasks preferentially. During this adult phase, the mortality risk mainly depends on the task the bees perform. But the tasks also influence the longevity of the bees. Because the task decisions are not only age based but also demand based, the adult mortalities indirectly also reflect the nutritional state of the colony.

So if we assume that population dynamics mainly depend on the queens oviposition rate minus the mortalities of immature and adult stages, we see a system of several combined and delayed feedback loops to be present in a honeybee colony. Additional delayed effects can be expected due to the fact, that adult population is a descendent of the former immature population. The loss of immature stages leads delayed to a loss of a specific age group in the later adult population.

From this conceptual point of view, the division of labor between age groups and the ratio between nutritional demand and supply are crucial for the prediction of the population dynamics. The model we present here tracks the number of bees in discrete age groups, their function and working effort in tasks like nursing and foraging as well as a pollen management system that enables the modeled honeybee colony to collect pollen based on the current demand.

Please note: You can click on all figures of this page to zoom them to full size.

METHODS:

SimBee is an age structured population model tracking the number of bees in the colony in one-day-wide age cohorts. Time is treated in discrete steps of 1 day.

The model consists of 85 difference equations, treating the number of bees in each separate cohort, the number of bees in the functional groups of nurse bees and foragers, as well as treating the number of available pollen cells. A recruitment system (see figure 1) models the plasticity of the honeybee society to recruit additional workforce from other age groups, in times of higher demand.

The model was first implemented in Microsoft® Excel™, detailed analysis of the model was performed after porting the model to Mathematica™.

RESULTS:

The model is able to predict the population dynamics of the modeled colony after a variety of events like swarming, brood removal or pollen removal. We show here the results of 3 severe rain periods (preventing the bees from foraging for 5 consecutive days) on the stored pollen resources and on the colony’s population.

Fig. 2 shows that the rain periods immediately decrease the pollen stores, because the brood in the hive has still a high demand. During the rain periods, cannibalism of brood is high, what is indicated by the sudden drop of larvae and the delayed minima of adult bees in figure 4.

Fig. 3 shows the way the modeled colony performs the pollen foraging and storage management. Before the rain periods, the colony performs just as much pollen foraging as is steady consumed by the hive (=pollen stores stay on a quite constant level). During rain periods there is a steady pollen loss. But as the periods proceed, the daily loss gets smaller due to the shortage of demand by cannibalism and a lower nursing strategy of nurses. After the end of the rain periods, pollen is foraged up to a certain level. This level is lower than the level before the rain experiment, because the hive now contains less brood, has a lower demand and therefore lower pollen foraging motivation.

DISCUSSION:

Our model shows that the population structure of a honeybee colony is deeply influenced by the supply and demand state of the colony. The possibility to save resources by cannibalizing brood and therefore reducing demand very quickly seems to be very important for the adaptive collective behavior. But though this short term “escape strategies” are favorable for compensating sudden environmental changes, they also imply delayed costs in form of a later workforce loss. We can assume that the simulated rain periods lead to a significant shift of the ratio of young bees to old bees during the preceding month (Fig. 4). Although the total population size is not affected that much (Fig.4), division of labor may be influenced deeply.

As demonstrated here, our model is a valuable tool for a view into the age structured honeybee society, especially during experiments that deal with the issues of age polyethism, division of labor and task partitioning.

We currently extend the model using Mathematica™ by modeling honey collection, food handling and food processing as well as extending the modeled period throughout 356 days. Further elaboration will include swarming decisions (we only cover the results of swarming yet), supersedure decisions as well as the extension of the model’s time scale up to several years. This will enable us to investigate long-term collective strategies like the reproduction process on colony level.

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