Lies, damned lies, and beekeeping statistics: Paul Honigmann

Introduction

Firstly I want to thank everyone for supporting this website. It’s fun to be number one for a week or so though I’m not sure how this rating really works, or it’s significance. Probably just all down to complicated algorithms. What is important about this blog is that readers find information that they can trust here. Keeping this blog fresh and interesting is down to teamwork and I am indebted to the many generous beekeepers who have written guest blogs over the last seven years, and to my trusty admin in Australia, Iain Wilson. Iain has spent hours recently troubleshooting the problems with Jetpack that caused the subscription button to fail.

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This Week’s Feature

This week, Paul Honigmann author of The Observant Beekeeper, and Beelistener blog supporter of many years, shares a bit of bee maths and beekeeping knowledge with us. Thank you very much, Paul, for sharing your work with us and contributing to the blog this week.

Inconventient Truths

Humans are habitually inclined to ignore inconvenient truths, especially those that contradict our preconceptions. But, fortunately, there are several rigorous mathematical concepts and analytical tools we can employ to reveal truths from underlying patterns. So, let’s examine some maths, see how it can be applied to bees, and whether what it reveals might contradict or confirm established beekeeping lore.

1. The Uncontroversial

Temperature control: Let’s start with something uncontentious, how maths relates to bees clustering – the square-cube law. In essence, this says that clustering keeps bees warm in cold weather by reducing their total surface area. To put this another way, bee colonies tune their surface area to mass ratioby huddling as a single large organism to conserve heat, or conversely, by dispersing to shed heat.

The flight puzzle: small creatures can get by with short wings because they don’t need to lift much mass. (It’s the square-cube law again: they have a relatively large wing surface area for their weight.) Even so, the sums implied bumblebee wings were too small to lift them. Then as fluid mechanics advanced, it was realised that their wings are not rigid, and don’t work by gliding through an airflow around them. Instead, bees’ wings flex in a figure-8 pattern and form vortices above them, which provide lift and permit flying backwards and hovering.

Air feels like a fluid to bees: Furthermore, fluid mechanics showed that at the scale of a bee, air feels very viscous, making them extremely sensitive to airflow and turbulence; this can be seen in the way they nibble off sharp edges at hive entrances to smooth airflow. One has to wonder whether bees find rectangular frames require more effort to pump air past.

Why do bees work together? Another widely discussed intersection of maths and bees is game theory: finding the best strategy for different circumstances. This shows cooperation is most efficient for ants and bees because pooling excess resources benefits the whole – a non zero sum game – and it maximises the spread of your genes if you can’t lay eggs yourself.

Finding wild nests: For years, many beekeepers denied that wild nests persisted. One way this has been disproven is using the mark and recapturedata gathering and analysis technique borrowed from ecology, to estimate the population of an animal in an area. This has been used to gauge how many hidden bee colonies are present. You mark drones from known colonies then catch drones at the nearest drone congregation area and see how many are unmarked.

2. The Unsettling

Why are some colonies swarmy? There are several potential drivers, but game theory and economics offer the following insight. If you live in unstable conditions the rational choice is to choose a short-term “terminal investment strategy” and have lots of children – no point saving for tomorrow if you might not live to see it, or a beekeeper keeps taking all your honey – better to create lots of highly variable swarms and hope some survive. Bees produce more child-swarms in stressful environments, like intensive farming.

Are big colonies always better? There’s an obvious lesson from business – employers don’t maintain a large permanent workforce when trade is intermittent. This is analogous to stationary hives which tend to experience forage gaps. For such hives, stimulating laying for constant maximum bees is unproductive, reduces queens’ lifespans, and encourages swarming. Some people end up feeding more sugar than they get back as a honey crop!

Can you have too many bees? Without continuous bounteous forage, a prolific colony, like Buckfasts or a very young split which is mainly nurse bees, is likely to eat everything it gathers to make more bees, requiring emergency feeding. Queens which never stop laying are a tool for migratory beekeepers, not for stationary hives.

Are commercial bees best for your apiary? Another game theory discovery, Parrondo’s paradox, describes how a population can be more resilient to catastrophic events, say climate change or a new pest, despite being less fit for the current conditions. That’s because being optimised for one single set of conditions may be an evolutionary dead end (think: dinosaurs; inbred bees) because you’ve sacrificed adaptability which would enable you to take advantage of changing opportunities. A wide range of mediocre generalist traits is advantageous in unstable environments – like British weather.

How much variability should we expect between colonies? The natural variation in populations of living creatures is described by Taylor’s Power Law. Simply put, it states the amount of genetic variability increases exponentially with population size: it’s a non linear relationship. For example, doubling colony numbers might give 4x the variability. This obviously evolved through natural selection, because it worked, giving the right balance of risk and variation to remain healthy in the face of rapidly mutating parasites and diseases. This implies that selecting queens and breeding from this year’s “best” will lead – quite rapidly – to susceptibility to pests and diseases. I note that the open mated wild colonies around me are extremely robust.

3. And the Obscure

Will varroa always be a problem? I first came across the Copernican Principle (see diagram) applied to the duration of current events, in 2020. That’s interesting, I thought: varroa arrived in Britain in 1992, so by this logic, I’m likely to be in the middle of its reign of terror and it will be a non-issue by 2048. And…. we’re already seeing the beginning of widespread resistance here, with 25% of UK beekeepers now reporting they are successfully treatment-free for at least some of their colonies.

Should you force your bees to work harder? Returning to economics, cost/benefit analyses are a common business tool. Perhaps you’ve used Pareto analysis (1) to optimise your beekeeping business. But there is a grim lesson from the days of forced labour:

Caribbean sugar plantations deliberately worked enslaved workers to death and then bought new ones – people were cheap and the profits on sugar were huge. At the same time, on inland US plantations, enslaved workers were more expensive and margins were lower; profit was maximised by working them less hard so they lasted longer. (2) This implies that competition from cheap fake honey, or the collapse of the almond pollination industry from water shortages and self pollinating cultivars, could actually be good for bees, as the balance shifts from buying queens and miticides, and working them intensively, to spreading reduced annual profits over several years with less invested time and cash: the extensive beekeeping model.

This is surprisingly common in biological systems, causing massive variation in e.g. colony losses in the long term. It resembles a baseline drift, but is inconsistent in direction. The cause is irrelevant – new diseases, pesticides, laws; fashionable bee race; war – statistically, there will be long term “1/f noise” which, just as gamblers can be fooled by a run of luck and not spot the small house percentage, masks true permanent changes.

Such long term noise can be identified and removed in a number of ways. You could alternate your management strategy annually; or hedge your bets by running different strategies in parallel. Chaos theory suggests false trends can be removed by using a different time series of results – i.e. parallel datasets recording data at different times. Researchers also do meta-analyses of different datasets to spot true trends. Projects like Europe’s BEE-GUARDS and Pollinera, and the UK’s National Honey Monitoring Scheme gather huge datasets for these purposes. (3)

Conclusions

Large data studies are valuable – so do contribute to those surveys if you can – the broader the range of data they cover, the more useful their results are. And, from the above, we can conclude:

• Question old beekeeping maxims: they can be based on unfounded assumptions or assertions, and on closer examination some are very misleading, applying in only very specific circumstances or environments.
• Micro-management has downsides: manipulations, such as stimulating laying, moving hives, disturbing the nest, etc. create cumulative stressors which actively degrade health.
• Genetic uniformity means death: Healthy bees require diversecolonies. Over-selection of single traits, e.g. for productivity, causes the loss of other valuable traits, like adaptability to pests, diseases and changing environments. This is why a local reservoir of varied survivor colonies is so desirable.

And finally, your lived experience, with your bees in your location, is the most valuable. Most advice is generic but beekeeping is always local. Enjoy observing your bees and learning their, and their environment’s, own ebb and flow, and allow yourself to be led by them.

Paul Honigmann, 2026

Author of The Observant Beekeeper

Notes

1. The 80/20 rule: 20% of a business generates 80% of the profit, so concentrate on that 20% (but which 20%?) The Pareto law is a power law, like Taylor’s. Power laws are ubiquitous across many fields from biology and economics to geology and physics.

2. Another parallel – a 30 year old skilled enslaved worker was more valuable than a fit 20 year old labourer… just as your older bees do most of the foraging.

3. Interestingly, I can’t find equivalent American examples of any large scale, detailed, cross-disciplinary ecological initiatives. I would be very interested to hear of any.