The social structure of a bee hive is that of a matriarchal family headed by a queen. The queen has a potential life span of three years and during this time may continually lay eggs thereby establishing and maintaining a total colony population of approximately twenty five thousand bees. Almost 95% of the queens offspring are what are referred to as worker bees, with the remaining 5% developing into drones. The queen mates during one period of her life in a series of excursions called nuptial flights. She takes these flights shortly after emerging, and may mate with 7 to 17 male drones. It is estimated that the queen may receive up to 5,000,000 individual sperm during this short period of mating, all of which is stored in a pouch-like structure on her abdomen called the spermatheca. The queen accesses the sperm throughout her life, fertilizing eggs at a rate dictated by the needs of the hive.
The worker bees make up the majority of the population and are all females, but with undeveloped, or static reproductive systems. The worker-females are altruistic, for they take care of the queen at the expense of their ability to reproduce, and perform virtually all of the tasks necessary for the support of the hive. These worker-females have a short lifespan of approximately 30 days, and during this time will go through different developmental stages which dictates their role in the hive, as well as giving the hive its hierarchal character. Worker bees may be classified as housekeepers, which are responsible for the upkeep of the hive, or as foragers whose role is to collect the nectar, pollen, and water necessary to sustain life.
The primary cause of death for a worker bee is burnout. That is, their wing muscles only have a certain amount of flight, generally 800 kilometers, and when this point has been reached they are incapable of fulfilling their role and taking care of themselves.
The basis for the division of labor within the hive is the age of the worker. The worker begins its life taking care of the storage cells of the hive, then moves on to brood care and food storage, and ends its life as a forager. The adaptive significance of this labor schedule is that it extends the life of the worker by establishing a system whereby the young worker bees spend the majority of their lives inside the hive where they live in the protected environments of their colony. Once they become foragers, they are susceptible to predation, bad weather, and wing burnout.
The drones are the only males produced by the queen. Although few in number, they serve a singular, but important, role as mates for the queen. The lifespan of the male drone is very short, for after mating their abdomens explode which results in rapid death. Drones only serve as mates for the queen, and are not involved in feeding the colony, or the upkeep of the hive. Thus, if resources are scarce, worker bees do not like to keep the seemingly lazy males around and will often force them from the hive or kill them directly. Further, since the drones spend a great deal of time outside of the hive they are more susceptible to predation or death. All this results in an average drone lifespan of less than 25 days. The drones will often begin mating flights eight days after emerging, and within twelve days they may perform up to five mating flights per day.
The caste system functions as an integrated feedback system of interdependent elements. The growth of the colony, and the rearing of brood depend on the reproductive state of the queen, that is, the number of eggs she is capable of laying each day, and the worker population that is responsible for tending to the larvae. The amount of brood that can be effectively reared is directly proportional to the number of worker bees, resulting in a cycle whereby the greater the number of workers, the more a population may grow (assuming an abundance of resources). However, the ability of the colony to obtain resources, and the reproductive state of the queen are strongly influenced by factors such as the queen's age, the photoperiod (amount of light in a day), mean daily temperature, and the availability of resources.
These factors may be used to emulate the feedback system of interdependent elements and allow ecologists to create a mathematical model which may predict the population of a hive given a specific set of conditions. The most important factors used are the initial population size, the queen's reproductive state, and the weather. Yet, more information is needed to determine the significance of these factors. One must also know the developmental rates of the worker bees through their life cycle, the lifespan of drones, rate of brood production, amount of sperm obtained by queen during mating, and the average worker age before becoming a forager. This information has been developed by entomologists and reported in the scientific literature.
The first task in creating a population model for honey bees is to take the interdependent factors and determine their relationship to one another. This can be accomplished by creating a concept-map, or flow chart, visually depicting how these factors relate to one another, this is called free-body modeling. To do this, one can write out the variables that govern the functioning of the system, then draw lines between them to show how they influence each other. Further, one may then write on the lines just how it is that the factors affect each other. This is an extremely important tool that allows the modeler a graphic visualization of how the model will work. Next, equations can be created to describe the behavior of each variable. Finally, these equations can be entered into a computer program to see if they accurately represent what is seen in the empirical data.
In creating a model representing a month in the hive, we must be able to predict the number of eggs that may be laid by the queen on any given day. This is accomplished by determining through many observations the maximum number of eggs that a queen may lay in a day, and how factors such as the queen's age (the number of days that a queen has been laying eggs), ambient temperature (in degrees celsius or Fahrenheit), the photoperiod (in hours), and the adult population size. The maximum number of eggs that a queen may lay in a day has been estimated to be as large as 3000 eggs per day. However, a more realistic value under average conditions may be 1500 eggs per day.
After determining the number of eggs laid per day one must then determine the proportion of eggs that develop into either workers or drones. This is in part established by the amount of sperm that the queen has left in her spermatheca, which is dependent upon the number of days that the queen has been laying eggs, for as the queen nears the end of her supply she predominantly fertilizes drones. The second factor in predicting the number of drones is the product of egg fertilization responses to photoperiod and the population size of the colony. As the population becomes very large, the queen may reduce her egg laying to prevent an unnecessary strain on available resources. Further, as the photoperiod decreases, the colony anticipates the advent of winter and signal the queen to reduce or stop egg laying so that the hive will achieve a population size that is sustainable through the winter months. Using these factors it has been determined that fertilized drone brood may comprise no greater than 5% of the total brood, with the remaining 95% designated as workers. The different eggs have different rates by which they develop into adults. Worker brood takes an average of 21 days to mature into adults, whereas the drone brood takes 24.
Temperature plays a pivotal role in hive population dynamics. Honey bees will forage only when the average daily temperature exceeds 12 degrees celsius.
The photoperiod plays an important role as noted above. It has a strong affect on the number of eggs that a queen may lay. It is believed that a decrease in the photoperiod sends a signal to the hive that winter is approaching. This is supported by the logic that as daily low temperatures fall below freezing, the amount of available resources, such as pollen and nectar, falls dramatically. The decrease in resources means that the hive may not continue to grow, and may even need to reduce its population to sustain itself through the winter.
Honey bees will not forage if the wind velocity is greater than 34 km/hr, or if it is raining. The high winds prevent bees from being able to maneuver which may result in their being unable to return to the hive from foraging. Rain results in wet bees with the water increasing their weight to the extent that they can no longer support themselves in flight.
Weather conditions affect the size and functioning of the hive resulting in different population dynamics for different geographic regions. For example, in the midwest, photoperiod may range from 9.1 (December) to 15.25 (June) hours of light per day, with the temperature ranging from 0 to 31 degrees celsius. In contrast, the photoperiod in the southwest may range from 10 (December) to 14.5 (June) hours of light per day, with the temperature ranging from 0 to 39 degrees celsius. Under the midwestern conditions, the colony may be confined to the hive and will not produce brood from autumn to mid-winter, and nor will they forage from late October to late April. In contrast, colonies in the Southwest may produce brood and forage year round. From this information, it is easy to predict what times of the year will promote colony growth or decline.
The information thus far presented can be used to predict how the population of a colony may change over the course of a month.