Why Evolution Plays the Lottery
The unexpected virtue of being a little bit disorganised
Imagine a bird who lays two perfect eggs. Every spring she chooses the same sheltered hedge, makes a nest from the same weight of twigs, and lays eggs with the same precise shade of blue.
Her sister, on the other hand, is a shambles. She lays three eggs one year, six the next, scatters them between a hedge, a wall and the rafters of an old barn, and some of her chicks hatch a fortnight after the others. To any sensible observer, the first bird is the paragon. She has found the ideal way of doing things, and she sticks to it. The second looks confused, as if she can never make up her mind.
Follow them for long enough, though, and it is the shambles who wins.
To see why, forget birds for a moment and think about money. Suppose I offer you a wager on a fair coin. Heads, I increase your stake by 50%. Tails, I take 50% of your stockpile. The expected gain on each flip is handsome — the average outcome sees you breaking even, but hey, you just might get lucky and heads comes up a lot. After all, the average of 150% and 50% leaves you back where you started at 100%, right?
So you play. You compound your winnings, flip after flip, trusting the average to carry you home.
You will go broke. That’s right. I’m not saying you might go broke. I’m saying you will. The arithmetic mean flatters you; what actually determines your fortune is the geometric mean, which is the running product of each outcome, not the running sum. A win followed by a loss does not break even. Over time, it multiplies to a nothing. Variance eats the gambler alive, however flattering the expected value.
Evolution discovered this long before mathematicians did. Natural selection is not interested in the average fate of your offspring this year. It is interested in the long-run growth rate of your lineage, compounded across centuries of drought, plague, storm and plenty. A strategy that wins big in good years and loses everything in a bad one is not a strategy, it is extinction with a long fuse.
In 1956 a Bell Labs physicist called John Kelly figured out how to calculate the wager that maximises the long-run growth rate of a gambler’s bankroll. It turns out to be far more cautious than the strategy that maximises expected winnings. The Kelly bettor sizes their bets to the edge, not the payoff, and they never bet the farm even when they are sure they are right. Every hedge fund manager that has lasted more than a decade is, knowingly or not, a Kelly bettor. So, more impressively, are large parts of the biological world.
Consider the water flea, Daphnia. Through the good months she breeds clonally (asexually), throwing off copies of herself at a blistering rate. But as the pond begins to foul, or winter approaches, she switches tack. She produces a handful of tough, dark, sexually-produced resting eggs, called ephippia, that sink into the mud. Some will hatch the following spring, while others will remain sleeping for two years. A stubborn minority will sit in the sediment for a decade, ignoring perfectly good spring after perfectly good spring, before finally emerging from dormancy. To a naïve optimiser those laggard eggs look like wasted ammunition. To a Kelly bettor they are the only reason the lineage is still here. One freak summer, one desiccation that kills every active Daphnia for miles, and the mud-hoarded eggs are suddenly the entirety of the gene pool.
The annual killifish of East Africa do something comparable. The pools they live in dry out every year, and every adult dies. Everything depends on the eggs in the sunbaked mud, and those eggs have been arranged not to hatch all at once when the rains come. Some hatch after the first shower, while others wait for the second. Some, perversely, sit through the whole wet season and take their chances with the next one. If there is a single false rainstorm in a drought year it can wipe out an entire generation.
Insects are full of the same trick. A fraction of every brood of fruit flies enters diapause (the pause gestation for a bit) even in laboratory conditions where there is no winter coming. Parasitic wasps that lay twenty eggs in a caterpillar don’t leave twenty eggs with identical developmental clocks, they have a spread. The desert locust produces eggs that will hatch over a range of rainfall thresholds. These are not failures of precision. In fact, I would say that precision is easy, and evolution is good at it. They are the optimal solution for survival in an unreliable world.
A great tit could, in principle, settle on the single clutch size that maximises her expected fledglings in an average year, but she doesn’t. In some years she undershoots, in others she overshoots, but this is not the great tit being sloppy, it is a diversified portfolio of bets against an unpredictable climate.
Natural selection does not always see the individual, it sees the lineage. An animal that bets everything on one answer, whether it is one clutch size or one hatching date, is an animal whose descendants can be erased by a single unlucky roll of the meteorological dice.
An animal whose offspring are variable, or whose resting stages sleep for different decades, has stapled a thousand little insurance policies to her genome. She will, on average, have fewer children than her tidy sister. She will, on average, be outbred this year and next and probably the year after that. But in the long run (and evolution runs very long indeed) she is the one still here.