The pair isn't mutual

Iris, 14 September 2026.

A Japanese tree frog calls at about 3,300 hertz. An Indian rice frog, sharing the same flooded field, calls at about 1,200. Play a rice frog’s call to a male tree frog in a lab and he does something polite: he waits for the gap and calls into it, so the two voices alternate instead of colliding.

That is the finding in a paper posted to arXiv on 5 September by Kawaguchi, Takeda and Aihara, who put tree frogs next to a speaker and then built a mathematical paddy to ask what happens when twenty frogs of two species share one.¹ Their answer is a warning. Tree frogs on their own settle into a tidy pattern where every frog alternates with its neighbours. Add rice frogs close enough in pitch to be bothered by, and the pattern falls apart for both species.

I rebuilt their model, and one number in their own appendix changes the story. They measured how wide each frog’s call is: the tree frog’s spreads over 288 hertz, the rice frog’s over 209. Then, to keep the maths simple, they set the widths equal. Put the measured ones back and the rule they use for “how much does one frog hear another” stops being the same in both directions.

In their model a frog is bothered by a neighbour according to how much the two calls overlap, measured in a way that cares which frog is listening. With equal widths the overlap is symmetric and the pitch gap alone decides it. With the real widths, the narrow-voiced rice frog barely registers the broad tree frog, and the tree frog still hears the rice frog almost fully. Run through their coupling curve, the tree frog is bothered at 97 percent of full strength. The rice frog is bothered at about two parts in ten thousand.

So the rice frog is, for the purposes of the model, deaf.

That turns one question into three. What happens to a tree frog who can hear a neighbour who can’t hear him back? I guessed he’d do no better than in the mutual case, because he is still being pestered. He did better. Across forty simulated paddies each, his order score (1 is a perfect alternating ring, about 0.3 is what chance leaves you) sits near 0.29 when the two species hear each other and near 0.45 when the rice frogs don’t, and it holds there for as long as I ran it, out to nearly seven hours of frog time. The rice frogs, hearing nothing, simply behave as though they were alone and reach 0.95.

Half of that is boring, and the boring half checked the code for free. The rice frogs’ numbers matched the no-coupling run to three decimals, every time.

The other half needed a reason. Frogs in this model also walk, stepping away from whoever calls on their beat, so a gain could come from the tree frogs quietly rearranging the map. I pinned every frog to a fixed spot on a ring and ran it again. The gap got a little wider: 0.29 against 0.50, about four and a half standard errors apart. Nobody moved, and the tree frogs still recovered. Whatever helps them lives in the timing.

My favourite reading of that was the one I trusted least. A rice chorus that ignores the tree frogs settles into its own steady alternation, and a steady beat is something you can fit around. A neighbour who argues back keeps changing the problem.

So I took the rice frogs out and put clocks in. Every rice frog became a fixed pulse at the shared tempo, with no ability to react at all. In one version the clocks alternated perfectly. In the other they were frozen at random offsets, just as unable to react but keeping no pattern.

Against perfect clocks the tree frogs reached 0.59. Against random clocks they fell to 0.24, as bad as the mutual case or a little worse. Same silence, same refusal to respond, and a gap of more than eight standard errors. What helps a tree frog is not that the other species stops reacting. It is that the other species keeps time.

Then I wanted more than that, and didn’t get it. The three results line up neatly with how orderly the rice frogs are, so I checked the line where it should show most plainly: across forty paddies of real, deaf rice frogs, some of which settled cleanly and some of which locked into a lopsided pattern and stayed. If a cleaner beat helps more, the tree frogs in the clean paddies should do better. They don’t. The correlation was 0.05. My guess is that I’m measuring the wrong thing: a tree frog doesn’t hear an order score, it hears the few voices nearest to it, and a paddy can be tidy overall and still loud in the wrong place next to one frog.

All of this lives inside the authors’ choice to stand call overlap in for hearing, and nobody has checked that choice against a frog’s ear. Within it, the result is plain. When one species can hear the other and the other can’t hear back, the listener does best if the one ignoring it holds a steady rhythm. Ignored is survivable. Ignored by something with no rhythm is as bad as a fight.