A few weeks ago I blogged about the way the universe is doomed by the exponential growth in readership of an old post here on Scientist Sees Squirrel. That exercise was a bit silly, but I used it to make a non-silly point or two about biology. My blogging example reminded me that I used to use an almost-as-silly fruit fly example in my undergrad ecology courses. I thought you might enjoy it – so here it is. (And if you’re teaching, and want to borrow it, be my guest.)
Imagine that you return from the grocery store with some bananas. Unbeknownst to you, a single (inseminated) female fruit fly* has stowed away in there. If all her offspring survive, how many fruit flies will your kitchen have after just one year?
We can do this with hard math or easy math. I’ll make a few assumptions (conservatively) so we can use the easy math, but if you’d like to check me with the harder math, be my guest. A fruit fly takes about 10 days to develop from egg to adult, then can live another 80-ish days and lay about 600 eggs**. The early-laid eggs are the most influential in population growth rate (that’s part of the hard math). Let’s assume discrete, 21-day generations (egg to egg) and 200 eggs/female (this might actually underestimate growth potential, but as you’ll see below, that doesn’t matter). Of the 200 eggs, assume half are female; we can ignore the other half because as long as there are just enough to inseminate all the females, males don’t matter to population growth. We can proceed, then, with a female producing 100 new females about every 3 weeks.
Now we need the simple math, for unlimited population growth with discrete generations:
Nt = N0Rt, where R = 1 + b – d (b being the birth rate, and d the death rate).
For your fruit flies, N0 is one (the one female you started with), and R = 1 + 100 – 1 = 100 (b is 100 females per female, and d is 1 since the female dies after her allotted 3 weeks). There are 18 3-week generations in a year, so:
Nt =(1)(100)(18) = 1036 = 1,000,000,000,000,000,000,000,000,000,000,000,000 female fruit flies.***
How many fruit flies is that? Well, the technical term we ecologists use is “a metric crap-ton”.
Can we visualize this? Sort of. Imagine that your fruit flies pack themselves solidly through your kitchen, and then outside it, taking up the minimum space they need. A single fruit fly is about 3 mm long; we can estimate its volume as 3 mm3. So your year’s flies take up 3 x 1036 mm3, which is 3 x 1018 km3 (cubic kilometres). If they have about the density of water (which they do), they weigh about 3 x 1030 kg.
Yeah, I know, you can’t visualize that quite yet. How about this: if your flies are packed solid over the entire surface of the Earth, the solid mass of flies will be quite deep. How deep? Just over twice the distance to the Moon.
Now, perhaps you think your kitchen (and everywhere else on Earth) might be an unpleasant place to be, under all those flies. You don’t have to worry about that. That’s because the flies’ combined mass is about one and half times that of our Sun, and that’s more than enough mass for the fly ball to undergo spontaneous nuclear fusion and become a new star. Which you are in the middle of. Ouch.
Of course, we’ve been bringing home fruit flies with our bananas for many years, and haven’t found ourselves in the middle of a fruit-fly star yet. That’s because exponential growth can’t continue; resources always become limiting at some point. That’s why ecologists are so interested in density-dependent population regulation (understanding those limits to growth). Even more importantly, it’s why natural selection is such a powerful force****. If your one fruit fly replaces itself, a year later, with about one new fruit fly on average – then nature took 1,000,000,000,000,000,000,000,000,000,000,000,000 slightly different stabs at making a better fruit fly.
Give me 1,000,000,000,000,000,000,000,000,000,000,000,000 tries at improving anything, even if they’re totally random, and one of them will be pretty good. And then I can start with that pretty good one and take 1,000,000,000,000,000,000,000,000,000,000,000,000 stabs at improving it further the next year and the next, and on for the several billion years of life on Earth. That’s the key to evolution – which has brought us orchids, and great white sharks, and orangutans, and birds of paradise, and (for better or for worse) us. Astonishing, isn’t it, from beginning to end?
© Stephen Heard August 18, 2020
I did my original calculations many years ago. Since then, Randall Munroe has written an entire book of similarly silly-but-revealing hypothetical calculations: What If? It’s marvelous. However, while my take may have predated Munroe, no good idea is ever truly original. The very day after writing this post, I stumbled across the calculation at right (click on it, it will expand). It’s an exponential-growth-in-flies calculation by Antonie van Leeuwenhoek (1632-1723), here in English translation by Samuel Hoole and published in 1808. I ran across it in Ivan Valiela’s Doing Science, which I was reading for no reason even remotely related to this post. Serendipity is a marvelous thing.
Image: A female Drosophila melanogaster having a bad day. © Géry Parent CC BY-ND 2.0 via flickr.com.
*^Drosophila melanogaster, let’s say, since we know so much about that species. Ironically, one thing we know about fruit flies is that they aren’t fruit flies. The true fruit flies are in another fly family (the Tephritidae); the familiar “fruit fly” is a member of the Drosophilidae, the vinegar flies. The existence of this footnote tells you two things: that common names for organisms are an unreliable mess; and that I make poor time-management choices.
**^The life history numbers here are all estimates for flies under ideal conditions. For real flies, they depend on temperature, food, and lots of other things; there’s plenty of discussion and citation in Nguyen and Moehring 2015, Accurate Alternative Measurements for Female Lifetime Reproductive Success in Drosophila melanogaster. PLoS ONE 10(6): e0116679. https://doi.org/10.1371/journal.pone.0116679
***^Plus another 1,000,000,000,000,000,000,000,000,000,000,000,000 male fruit flies, because although we said we’d ignore them as unimportant to population growth, they’re still there. Having acknowledged that, though, let’s go back to ignoring them. The first 1,000,000,000,000,000,000,000,000,000,000,000,000 will suffice.
****^Assuming just two extra things: variation among offspring, and heritability of at least some of that variation from parents to offspring. Both of these extra things are broadly true.