Mating Mathematics

Math or Maths?
Math or Maths?

In 2005 some researchers studying matings in the Hope Valley (England) found out some interesting stats on mating distance. Mating distance is the distance between the hive from which the virgin queen flew and the colonies from which the successful drones came. 50% of matings were at a mating distance of up to 2.5km. 90% were at 7.5km or less.

Other work referred to in ‘Mating Biology of honey bees’ (Wicwas Press) showed that drone congregation areas (DCAs) were visited by an average of 14,644 drones per day from over 200 colonies in the surrounding area.

It seems that drones from a colony tend to fly to the nearby DCA whilst the virgin queen flies further afield.

Drone Congregation Area
Drone Congregation Area

50+ million years of evolution

In short, nature has seen to it that there is very little chance of inbreeding. The queen typically mates with 17 drones. Those lucky 17 drones are from a group of 14,000 drones in the DCA, from over 200 hives in the surrounding area. There are multiple DCAs within flying distance of our virgin queen’s hive. Every site will be different, but you get the picture.

The majority of successful matings seem to happen with drones from colonies that are 1km to 1.5km from the mating apiary. Many beekeepers who raise queens place their drone donor colonies in a circle around the mating apiary at distances of around 1km to 1.5km. However, drones from further afield are also present at the DCAs.

Isolation Station

Unless you happen to have access to an island with no bees on it, and you take both virgin queens and drone donor hives there for mating, you can see how unlikely it is to have control. It can work with a peninsula or with an inhospitable place where bees would not usually go, such as high up on Dartmoor. How many people even know where their DCAs are, or how many there are? This study used radar to detect 26 DCAs in an area 5km x 2km which was adjacent to a commercial apiary. That’s 2.6 DCAs per square kilometre. Seems like a lot. I’m going to assume 2 DCAs per sq km for my area.

What’s more, in lands with few defining features, like plains, the DCAs are not necessarily fixed. My bees are in the flatlands of Cheshire, which has an average of about 2 colonies per km across the whole county. However, typically beekeepers are hobbyists with around 3 colonies per ‘apiary’, and these are located around the edges of towns and villages. There are also a few commercial beekeepers with 20 to 40 colonies per apiary in the more rural parts. Nothing is ever simple!

Most matings occur within a 7.5km distance
Most matings occur within a 7.5km distance

Insurmountable Odds

Based on the data available on Bee Base plus a recent survey of CBKA members, combined with research papers I’ve seen, I reckon a virgin queen in my area has access to over 350 DCAs and about 650 drone donor colonies (see diagram). The idea that I can have much control over matings is farcical. Even if I find 10 great colonies, give them lots of drone comb and place them in a circle around 1 km from my mating apiary, what chance do I really have? Probably about a 5% chance of one of my drones mating with my chosen queen. To even have a 50/50 chance I’m going to need 100+ drone donor colonies in the area.

Michael Palmer

When I visited Mike Palmer in Vermont, he showed me several apiaries, and it was clear that he is the dominant bee farmer on his patch. He floods his mating area with drones from his colonies; he has hundreds of them all across the mating area surrounding his mating apiary. Mike can be pretty confident that most of his virgin queens will be mating with drones from his colonies.

Mike Palmer is improving his bees; he is a queen producer rather than a queen breeder. Even though he knows that matings are between his selected queens and his drones (mostly) he can’t say which drones from which colony, and they are all different lines.

Summary of Mike Palmer's Set Up
Summary of Mike Palmer’s Set Up

Bee Improvement

I too am an improver, not a breeder. I just pick my best queens, graft from them, and hope for the best. I’m at the mercy of the local beekeepers – their drones will mate with my lovely queens, and I’m not the dominant beekeeper around. The results are variable. Mostly I’m happy with the queens that I raise, but I have to accept that some will be better than others. I have to be ready to continually cull the poor queens and scrape out the drone comb in poor colonies. I promote the qualities I want and try to suppress those I don’t, and this will go on forever because I cannot possibly control the drone side of the mating equation.

Enter instrumental insemination – the only realistic way for most UK beekeepers to actually breed bees. It’s not for me, at least not yet. One problem is that when you have the perfect thoroughbred honeybee queen, you know her workers will be fantastic, but if you graft from her and open mate the daughters you are back to the random drone thing.

For most of us, the only thing to do is continually try to improve our stock by grafting from our best queens and culling the worst. If everybody does this, the quality of the drones in our mating areas will inevitably improve, and we will all benefit. I’m not interested in the colour or type of bee, I’m interested in great bees that thrive in my area. The culling of poor queens is just as crucial as raising daughters from our best queens. This is why I feel sad when people use swarm cells to make their queens…I don’t want excessively swarmy genetics in my local drones. There’s not much I can do about it though.

5 thoughts on “Mating Mathematics

  1. BeeBase claims there are hundreds of apiaries within 10km of me. I know a lot of the beekeepers round here and no, there are nowhere near that many. I think BeeBase has a problem in that people never delete data from it, so it may indeed show that e.g. my neighbour has an apiary, but I know she moved away a few years ago.

    I could not access the full paper. Did they glue little ariel transponder thingies on the drones (powered by the radar pulse) or could they get enough resolution from plain old radar? (I’m not just interested in bees)

    • Hi Paul. It’s difficult to get accurate info as you say. Some people quit but stay on BeeBase, others never register. The general point remains true; that for most beekeepers in the UK we cannot control the drone side of the mating equation. I believe the radar research uses transponders but I didn’t access the full text either.

  2. I think that ’92 paper predates transponders by several years. It’s worth noting that there are studies earlier than 1992 that show matings over much greater distances ( Peer DF & Farrar CL (1956) The mating range of the honey bee. Journal of Economic Entomology 49: 254–256 and Peer DF (1957) Further Studies on the Mating Range of the Honey Bee, Apis mellifera. The Canadian Entomologist 89:108-110 … one or other of these shows matings over more than 10 miles separation of drone and queen.

    I’m not sure how much DCA’s “move about”. I thought they were geographically defined and that queens/drones had evolved to identify the relevant geographic areas (horizon dips, hedgerows etc) and home in on them. If they move the bees wouldn’t know where to go?!


    PS Perhaps time that BIBBA bought one of those infrequently available Scottish islands to establish a mating outstation …

    • Hi David, thanks for the input. I thought that about DCAs too, but in the Koeniger book, chapter 6.6 they refer to studies on featureless plains. The drones seemed to be just dispersed over an area with higher density closer to their hives. They were attracted to queens by scent and quickly congregated wherever the artificial queen was placed, rather than in specific DCAs. I’m not sure how rigorous the science on that is.

      I was thinking an island somewhere around the Canaries might be nice! 🙂

  3. […] queens is designed to lower inbreeding and increase the mixing up of genetics. The queen mates with lots of drones and mixes up their sperm which she retains in her spermatheca. This leads to multiple patrilines in […]

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