For some sex-changing parrotfish, math is really sexy

While we've all been busy crunching numbers for tax time, the female bucktooth parrotfish has been doing a little math, too. Only, instead of calculating write-offs, she's deciding whether or not to change sex.  In the world of fish, the right math can make or break your sex life.

Fish are some of the few vertebrates that have the ability to regularly change sex (other verts, such as some frogs, may do it under extreme circumstances). And while this is a pretty nifty party trick, changing sex takes a lot of energy- transforming one's genitals and gonads (external and internal sex parts) is no simple task. So why do fish bother? The answer is: reproductive success. It all comes down to how many offspring an individual can produce. Here's how it works:

The most common way fish change sex is from female to male. This is called (take a breath) sequential (one sex after another) protogynous (first female, then male) hermaphroditism (one individual, two sexes in a lifetime). In general, for species where big males can control access to females (think harem), it pays to be female when small (you get to reproduce with the dominant male) and then turn into a male when you are big enough to duke it out with a competing male to win access to a group of females.  There are also protandrous hermaphrodites, who start male and turn to female (brace yourselves, Finding Nemo fans, the folks at The Fisheries Blog don't mince fins on this one)—more on that strategy later.

Back to why switching to male can make sense: sperm are less expensive to manufacture than eggs, so one male will be able to make lots more sperm than a similar sized female can produce eggs—as long as there are enough females churning out enough eggs for the male to fertilize, he'll make more offspring. The female-to-male sex switching strategy allows for maximum reproduction during all stages of life, when small and when larger...if the conditions are right.

Bucktooth parrotfish. Photo credit:  Kevin Bryant .

Bucktooth parrotfish. Photo credit: Kevin Bryant.

And here's where a little math goes a long way.

Unlike us, the bigger the fish, the more eggs or sperm they can produce. For our species, every woman is born with a set number of eggs, no matter if she grows to be a towering 5'11" or petite 5'0". And a man's sperm count has little to do with body size.  Not so for fish. The bigger the female, the larger the number of eggs she produces (and often, the higher quality).  A fish that doubles in size may gain over 10x as many eggs. This fact alone has major implications for management: catching one large female fish can reduce the reproductive output of a school by the same amount as several smaller females. Accounting for that in setting quotas and size limits can be really complicated, but it is critical to effective management. Saving these Big Old Fat Fertile Female Fish (BOFFFS) has become a focused effort of some conservation initiatives, including design of marine protected areas.

Which takes us back to the arithmetic those bucktooth parrotfish females are constantly conducting.  As they grow larger, they have to weigh which choice will bring more babies: changing to male and gaining access to multiple females or staying female, and having your eggs fertilized by the dominant male.  If the sum total of all the eggs produced by all the other females is more than your total number of eggs, it pays to switch and be the male. But, if as a large female you make more eggs than all the other females combined, than you should stay female.

Photo credit: Flickr Creative Commons

Photo credit: Flickr Creative Commons

If (female 1 + female 2 + female 3) < eggs than female 4, female 4 stays female.

If (female 1 + female 2 + female 3) > eggs than female 4, female 4 will likely switch to male and take over the harem (and thus begin fertilizing all those eggs).

A large female is especially likely to skip sex change if there are other males around crashing the love nest. In some species, the dominant male is not as dominant as he looks: "sneaker" males that hide nearby can dash in and add their own sperm to the mix (remember, fish have external fertilization, casting sperm and eggs into the water) right when the dominant male spawns. These "sneakers" create high levels of sperm competition that dilute the dominant male's success rates.  This is good for females, whose eggs are bathed by plenty o'sperm (and a greater diversity of genes), but it is bad news for the male. Studies have shown that in species where this happens, large females often choose not to turn into males. Such is the case with bucktooth parrotfish.

Instead of the standard large size/status-triggered sex change of most protogynous hermaphrodites, large female bucktooth parrotfish are constantly sizing up the other females in the harem, noting the sneakers streaking in, and doing a little mental math to figure out whether its worth it to change sex. And you thought figuring out your taxes was hard.