Bees by the Numbers

Bee Arithmetic

A medium frame of 4.9 mm/cell comb has about 30 rows of 88 cells for a total of 2,640 on each face. The area of the face is about 65,800 sq mm. A worker bee occupies about 88 sq mm.

Ergo:

• A medium frame completely covered with bees would have some 750 bees on each face, total 1,500 bees.
• A queen might be expected to lay in about 2,000 cells (80%) in each face.

Consider that ALL of the bees will be in the hive overnight. The 'carrying capacity' of the hive will be 1,500 per frame times the number of frames. Each box of an 8-frame medium super can hold 12,000 bees. This has nothing to do with how much room the queen needs for laying or how much is needed for stores, it is merely the 'parking space' needed to keep all the bees out of the night air. One must plan the number of boxes based upon how many bees are expected/hoped for. Too little and the queen may stop laying while waiting for capped brood to be evacuated and cleaned up.

How many bees are ultimately in the hive depend crucially on how many eggs the queen lays per day. Death rates, will ultimately limit the final population as bees start dying at about the same rate they are being born (if the queen continues at the same rate – if she declines, the overall population will also decline).

We can model this with some basic assumptions:

• On the day the queen starts laying in earnest there will be some initial population, perhaps the survivors of winter and some limited brood that will hatch out over the next 21 days. We will be interested in the results 40 days out from when we start counting and these bees should all be dead by then.
• We assume the queen starts (or is) laying at a more-or-less constant rate of X per day.
• For the first 21 days there will be no 'new' bees – hive population will be more-or-less steady.
• Starting on day 22 there will be X 'new' bees every day – the population will start to climb.
• These newly hatched bees will spend about 10 days in the hive before venturing out to the risky business of foraging for nectar and pollen. At the end of the first 10 days the hive population will have increased by 10 times X.
• So, on day 11 after the first 'new' bees emerge X bees will become foragers and these bees can be expected to live for 30 more days. In the 30 days before the first foragers start dying (also at the rate of X per day) the hive population will add 30 times X more bees. From that time on the number of foragers that will die each day will be X and the total population will have leveled off.
• The leveling off point is 10X + 30X = 40X.
  
  

So, we see that X marks the spot! Or, at least, is the key figure in hive strength – but we knew that all along. Now we have some understanding of how to analyze any given hive and, maybe, what to do about it.

We've heard folks talk about queens that lay 2,000 or more eggs per day, of 'strong' hives, of hives 'full of bees.' From above we can see that such a wonderful queen would need at least 6 medium boxes to hold every one of her children in rainy weather. I would be suspicious of any claim that a 2,000 egg per day lady is happy in a 3-box setup. Likewise, it should be easy to quantify what 'strong' and 'full of bees' mean by simply counting frames covered with bees and estimating the percentage coverage of those not completely teeming with bees.

As to what to do about this new found knowledge of the state of one's hives it appears that the danger would be to hold a good queen back by not giving her and her babies enough room. We can estimate how well the queen is doing by counting frames of brood. We don't need to search for eggs and young larvae, it is enough to count the sealed brood because, once the first 21 days are past, there will be 12X cells of capped brood at all times. Assuming a 'full' frame is some 2,000 cells a 2,000 eggs per day lady will have 6 frames (both sides) of sealed brood. (If you saw 6 frames of capped brood early on before the first 30 days have past, would you prepare more boxes – the possible population could hit 80,000 bees? Hmmm, that also implies that there were some 15,000 bees in there to cover 10 ½ frames of brood to keep them warm.) Needless to say(?), only 3 frames would indicate a 1,000 eggs per day queen, etc.

Now all this last assumes that the queen has room to lay, the nurse bees have enough food to feed the larvae, there are enough bees to cover the brood to keep it warm in cool weather, etc. The first two are in the control of the beekeeper, the third is why a strong hive coming out of winter is so important (also explains how moving bees from a weak hive to an other-wise stronger hive makes sense).

Actually, there is another variable under control of the beekeeper that might advantageous – frame spacing. Michael Bush (http://www.bushfarms.com/beesframewidth.htm) reports that if the faces of two opposing brood combs will only allow one layer of bees, that number of bees will be sufficient to keep the brood warm, take care of the larvae, etc. That means a given number of bees can cover and care for twice as much brood as when there are bees on both faces of the brood. If the limitation on build up is the queen's capacity or lack of comb, the bees freed up can work on making more comb (or go out and forage).

BUT, hearkening back to the start of this post, there is still a need for 'roosting' surfaces to accommodate everyone at night or on rainy days. Squeezing the frames together cuts that 'roosting' space in half and the beekeeper will have to compensate somewhere. Perhaps the close spacing would only be used when the hive is not so populous (early Spring?) and would be relaxed as the numbers build up. Or, maybe extra supers might be provided. I'm thinking close spacing would be very useful with new splits or packages when brood rearing and comb making are paramount and there are no dangers of overcrowding.

Please comment if you have something to add.