Segregated shrimp, sexual dimorphism, the law of small numbers

On our trip to the Big Island last July, Hai showed us a beautiful Marbled Shrimp tucked into a cauliflower coral on one of the pilings in (where else?) Kawaihae Harbor. It was a female. The shrimp was still there on our recent return to the island, and it had been joined by another one, also female.

On the February trip, Wendy showed us where another Marbled Shrimp had taken up residence along the quay at Mahukona. This one was male. Wendy said she’d seen other Marbled Shrimp at this site, all male.

Marbled Shrimp display considerable sexual dimorphism—biospeak for overt, non-reproductive differences between the sexes. This is a female we saw at Kawaihae. Females have conspicuous tufts (setae in biospeak) on body and legs, and their front pincers (chelae) are shorter than those of males. This little beauty is about an inch and a half long.

Here’s one of the males from Mahukona. Males have absurdly long chelae that they apparently use to fight one another. Though this species belongs to the broken-back cleaner shrimp family (Hippolytidae), they don’t engage in that family’s characteristic fish-cleaning behavior, but are instead opportunistic detritivores. The species is broadly distributed through the Indo-Pacific.

And now for some martini-fueled rambling:

It’s tempting to think that Marbled Shrimp generally tend to live in single-sex domiciles. One could invoke the law of small numbers to verify this if only there were a law of small numbers. There is not; there is only a law of large numbers. This statistical law basically states that if you flip a coin one thousand times you will get very nearly fifty percent heads and fifty percent tails. If not, you can conclude that the coin has been tampered with. But since there is no law of small numbers, five heads up coin tosses in a row mean nothing. And two same-sex Marbled Shrimp homes also mean nothing.

Irrational species that we are, we tend to believe in the law of small numbers. You see it all the time: “Two of my friends got the vaccine and they both got sick.” The result is that many of us embrace untruths, guided more by what we feel than what we know.

The difference between small and large number is not necessarily clear though. There are statistical tools for this, but there’s always a bit of subjectivity involved because you need to decide how sure you want to be. Very sure needs a much larger number of observations than just a little sure.

Anyway, maybe, just maybe, despite its biological unlikeliness, Marbled Shrimp actually do live sexually segregated lives, at least when they’re not reproducing. As lots of research papers (including a couple of mine) conclude: further study is needed.