continuous low-level mite erosion

A London beekeeper friend gave me two monthly magazines that members of the Bromley Beekeepers receive as part of their membership. One of them was BeeCraft, and while flipping through it, I came across an article by Paul Honigmann.  The name caught my attention. Honigmann literally translates to "honey man," which seems wonderfully appropriate once you start reading his work.

In his article, Paul highlighted a fascinating graph originally developed by Gareth John. It compared two very different approaches to managing varroa mites: a single, one-time treatment versus a continuous daily reduction of just 2% in the mite population. The graph was simple, elegant, and memorable. As a treatment-free hobby beekeeper, it immediately grabbed my attention. There was just one problem—for me, at least. The graph didn’t include the underlying numbers. And if you’re anything like me, that’s unsettling. I don’t just want to see the curve; I want to understand what drives it. Without the math, it felt incomplete… almost like an itch I couldn’t scratch.

So, naturally, I went digging.  With a little help from a large language model (Perplexity), I tracked down a practical growth model used by Randy Oliver. That gave me the missing piece—and from there, the rest fell into place.

Building the Model Behind the Graph

To recreate Gareth John’s insight, we can start with a simple assumption: in the absence of intervention, varroa mites grow exponentially.

M(t)=M₀e^rt

Where:

M₀ is the initial mite population

r is the daily growth rate

t is time in days

Randy Oliver suggests a reasonable rule-of-thumb growth rate of r=0.021 per day during active brood rearing. That corresponds to a doubling time of about 33 days.

For example, if a colony starts with 10 mites:

M(33)=10⋅e^0.021⋅33≈20

What Happens With Continuous Control?

What if the colony continuously removes a small fraction of mites—say 2% per day?

We can model that by adjusting the growth rate:

M(t)=M₀e^(r−0.02)t

Using the same r=0.021

M(t)=M₀e^0.001t

That’s a dramatically slower growth rate.   In fact, when you run the numbers, the population barely increases over time. It’s not quite flat—but it’s close enough to feel like balance.

A Different Way to Think About Control

This is where Gareth John’s insight really lands.  A steady, modest continuous reduction—just 2% per day—can almost stabilize the mite population. Compare that to a one-time treatment, which often leads to a rebound as mites continue their exponential climb.

It raises an interesting question: are the bees themselves already contributing to this continuous “background” mite suppression?  Gareth suggests they might be. And it’s easy to imagine other colony behaviors or environmental factors playing a role as well—hygienic behavior, grooming, brood interruption, or even subtle ecological pressures within the hive.