**I’m writing a book about ants. It’s still many months from completion. A chapter on ant evolution must mention fossils, so I thought I’d throw this suggestion into the internet maelstrom to see how it should be honed. Or binned.**

**MIRACLES IN STONE — WHY ARE FOSSILS SO RARE?**

Recognizable ants have been around for at least 100 million years. We have exquisitely preserved fossils in amber to prove it. A quick internet search shows that ants preserved in amber are widely available from dealers. I was tempted by several in the £15–£30 price bracket. The ants were all tiny, 2–4 mm, but with low monetary value they were unlikely to be fakes. However I was not temped by the mating ‘queen and drone’ for sale from a US website at $49,500. If memory serves, this is the same item that I came across over 10 years earlier when I was researching ‘the most expensive insect’ (Jones, 2010, *Extreme insects*, HarperCollins), and which was then on offer for $100,000. No matter how rare such an event might be to get fossilized, this seems to be a fairly arbitrary sum, even if now knocked down by 50%.

But it at least got me thinking.

Dinosaurs have captured the popular imagination, but this las led to some completely silly and imaginary ideas about fossils. Fossils are real, but they are so rare that they do, actually, verge on the mythical. I casually wondered out loud what might be the chances of something getting fossilized. This seemed like quite a straightforward question to me, but I soon found out that nobody was willing to offer up any calculations. Taphonomists (fossil palaeontologists) openly mocked my question, claiming that ‘putting odds on it is impossible’. Having thought about it a bit more I’m tempted to agree with them. Nevertheless, having set the metaphorical ball of fiery curiosity rolling through my brain, I here offer some back-of-the-envelope calculations.

Firstly — how many ants have ever been available for fossilization? We have to start with a calculation from over half a century ago, by C.B. Williams (1960, The range and pattern of insect abundance, *The American Naturalist*,** 94:** 137-151). Extrapolating from bird counts, insect trapping surveys, log–normal biodiversity indices and world-wide species lists, he estimated 10^{18} insects on the planet at any given time, of which say 1% were ants; this would give us 10^{16}. Assuming some sort of conformity with modern faunas, and allowing each ant to live 1 year, the last 100 million (10^{8}) years would therefore have produced 10^{16 }x 10^{8} = 10^{24} ant individuals having crawled on planet Earth.

Secondly — how many fossils are known? It turns out that about 750 fossil ant species are described from, say, 10,000 ant fossils. At the final count this does not seem like very much at all.

Finally — what proportion of fossils have we humans found? Of course humans have only discovered a tiny fraction of the fossils buried in the soil. This is where the calculations and guesswork start to get a bit fanciful. For the sake of argument, I’d suggest that humans have only discovered 0.001% of ant fossils; this is a figure I admit to having arbitrarily plucked out of the air. I dare somebody to disagree with me.

So, if 10,000 known fossils represents 0.001% of the total, that total number might be 10^{9}. This would still give the ratio of all ants to fossil ants at something like 10^{24 }: 10^{9 } or in more conventional usage 10^{15 }: 1. These are incomprehensibly small odds.

Given that the chance of winning the UK’s National Lottery is reportedly 4.5 x 10^{7 }: 1 (45 million to one), the chances of an ant becoming fossilized are about on a par with the same person winning the lottery two weeks running. Given that 32 million people are reputed to do the lottery each week, my increasingly tenuous grip on mathematics suggests that it might take 613, 278 years for them all to have just a single win. For someone to win twice in a row seems mathematically (and morally) untenable. For an ant to become fossilized must be equally dubious.

It’s that unknown how-many-more-fossils-are-left-in-the-ground part of the equation that gives me most anxiety. But even if my guesstimate is out by a million-fold (even a billion-fold) the odds are still vanishingly small. Really, in any sensible world, fossils shouldn’t exist — each and every one of them is a tiny miracle of geological chance. Perhaps I was being a bit dismissive of that mating ant pair in amber.