Two Things on One Leaf

It is probably the most reproduced pairing in pond imagery. Storybook, cartoon, garden ornament, clip art. The frog and the pad arrive together, and the picture implies they belong together.

The pairing is so settled that it is hard to notice it is making a claim. It says: this animal and this plant go with each other. Something is being provided; something is being used; there is an arrangement.

We went looking for the arrangement. What we found instead was two entirely separate things happening on the same object — one of them genuinely extraordinary, and neither of them about the other.

A note on where this started. This zine began as a request to write about frogs and their relationship with lily pads, and the first draft of the argument was wrong twice before a person with an actual pond corrected it. Both corrections are on the page rather than quietly absorbed, because the way we got it wrong is the thing the zine is about.

Not a wild pond. A round steel water trough, about ten feet across, at Irie Smial Preserve in Dripping Springs, Texas — a place named for the springs at the Milk House Branch of the Edwards Aquifer.

Somebody put the tank there. Somebody put the plants in it: water lily, water pennywort webbing across the surface on long runners, elephant ear standing out of the water, rocks stacked at one edge.

Nobody put the frogs in it. They are wild Lithobates sphenocephalus, southern leopard frogs, and there have been more than thirty full-grown ones counted in that tank at one time.

Ten feet across is roughly 7.3 square metres, so thirty animals is about four frogs per square metre. That arithmetic is ours, not a measurement.

This is the sentence that took the zine apart and rebuilt it.

The frogs are not lily-pad specialists. They sit on the lily pads, yes — fully up on top of a mature leaf, taking the whole animal's weight, exactly as the picture has always shown. The picture is not a lie.

But they also sit on the pennywort. On the elephant ear. On the rocks. On the rim of the tank. Every structure the water offers gets used.

Which means the lily pad has no special claim on the frog, and the frog has no particular interest in the lily pad. Take the lilies out and the frogs would sit on whatever was left.

Not a plant. A platform, and the requirements are geometric rather than botanical.

Above the water. A frog at the surface is inside the strike zone of everything that hunts from below. Up on a leaf it is not.

In the sun. Ranids are ectotherms that actively thermoregulate, moving between warm and cool to hold a working body temperature. A leaf in daylight is a place to be warm without leaving the water behind.

Facing the air. Insects come to the surface and to the leaves. A pad is a hunting position with a view.

One jump from home. Whatever arrives, the answer is directly below.

Every one of those is satisfied by a rock. By a stem. By a steel rim in the sun. The lily pad is not being chosen as a lily pad. It is being chosen as a flat thing at the right height, and it happens to be the flat thing this pond has the most of.

The most interesting thing anybody has said about this pond is a throwaway clause.

Mostly on the big leaves, but also on smaller ones — especially when there are lots of frogs in the pond at the same time.

That is a preference revealed by crowding. When there is room, the good perches are taken. When thirty animals are in a tank ten feet across, the marginal ones end up on leaves that barely hold them.

Which means the number of frogs this pond can hold is not a fact about the frogs. It is a count of surfaces that will bear one. Add a plant and the capacity goes up. Take one out and it goes down, and the animals do not change at all.

The shape of that is well described, and the description is a model rather than a measurement. Under the ideal free distribution, consumers spread across a patchy landscape as the good patches fill. Avgar, Betini and Fryxell (2020) revisit it precisely to show how consumer density produces the shifting, context-dependent patterns that habitat-selection studies keep running into.

There is an obvious reading of the last spread, and we are not going to print it as a finding.

The obvious reading is that the frogs on the good leaves won and the frogs on the bad leaves lost. The theory that describes the pattern says the opposite. The ideal free distribution assumes animals are “omniscient, equally competitive and freely moving,” and predicts they distribute themselves so that fitness is equalised across the population — the crowding on the good patch is exactly what makes the poor patch worth taking.

The same authors say plainly that those assumptions are “clearly unrealistic to some degree.” So the honest position is that two readings are available and nobody counted. Under one, the small-pad frog is doing fine. Under the other, it is paying for arriving late.

What survives either way is the part that is not about the frog at all: which pad you are on is a fact about how full the pond is.

Everything so far has been about an animal that would be just as happy on a rock. Take the animal off the page.

What is left is a leaf lying flat on the surface of a pond, attached by a long stalk to something buried in the mud at the bottom.

And the mud is the problem. Pond sediment is anaerobic — the oxygen is used up in the top few millimetres and below that there is effectively none. A rhizome down there is a living organ in a place with nothing to breathe.

So the plant has a logistics problem that the frog does not have and will never know about: it has to get air from the surface to a part of itself that cannot reach the surface.

It solves it. The solution is the reason this zine exists.

In 1980 John Dacey published a paper in Science with a title that sounds like a metaphor and is not one: “Internal winds in water lilies.”

Dacey measured a “pressurized flow-through system which forces oxygen to the roots and rhizome buried in the anaerobic sediment.” Several litres of air a day enter the young, newly emerged leaves and travel down their petioles “at rates up to 50 centimeters per minute” to the rhizome.

The pump is not a pump. It runs, in his words, by “the purely physical processes of thermal transpiration and hygrometric pressure” — small differences in temperature and humidity across a leaf's internal pores, doing work. Sunlight and dry air, and the plant inhales.

Read at the abstract. The publisher returned 403 to us and the record came through Europe PMC; every quoted phrase above is verbatim from Dacey's own abstract. We have not read his methods.

This is the part that makes it a circuit rather than a straw.

The air going down does not stay down. Dacey's sentence continues: the incoming flow forces “a simultaneous flow of gas (rich in carbon dioxide) from the rhizome up the petioles of the older emergent leaves to the atmosphere.”

So the plant has an intake and an exhaust, and they are different leaves of different ages. The new growth breathes in. The old growth breathes out.

Neither half works alone. A lily with only young leaves has nowhere to vent; a lily with only old ones has nothing driving the flow. The circuit closes across the whole plant, and it closes across time — between the leaf that arrived this week and the leaf that is going yellow at the edges.

Dacey worked on Nuphar luteum, a yellow water lily. The plant in the stock tank is a Nymphaea — a different genus, and it would have been easy to quietly assume the finding carried over.

It does, and somebody checked. Richards, Kuhn and Bishop (2012) describe Nymphaea odorata as having “a convective flow system that moves gases from younger leaves through submerged parts to older leaves, aerating submerged parts” — the same architecture, in the genus floating in the tank.

They measured the plumbing:

Canals are added in pairs, outward from the centre, each pair smaller than the last — and both petiole and canal area increase with water depth, because a deeper leaf has further to push.

And the sentence that matters most for the previous spread: in their model, the rate of flow “varied with depth and with the balance of influx to efflux leaves.” How well the plant breathes depends on how many young leaves it has relative to old ones.

On 11 November 2021 the same pond produced a photograph, and its caption is the closest this zine comes to a punchline.

Leopard frogs attach their egg clusters to vegetation just under the surface, and in that tank the vegetation to hand was a water lily petiole. Which is to say: a tube that is roughly a quarter air by cross-section, carrying a current of gas down past the eggs toward the mud, or back up past them toward the sky, depending on the age of the leaf on the far end.

It would be very easy to write that the frog chose the stem because it is a pipe. Nothing supports that and we are not going to write it. The frog chose a stem because it was a stem, exactly as it chose a leaf because it was a leaf.

The coincidence does not resolve. It just gets more exact.

Two systems occupy one object. Neither is about the other.

The frog is on the leaf because the leaf is a surface at a height, and it would take a rock instead without noticing the difference. The leaf is running a pressurised air circuit into anaerobic mud, and it would run it just the same with nothing sitting on it.

They are not partners. There is no exchange, no service, no arrangement. What there is, is proximity — and proximity is the thing we are worst at looking at without adding a story to it.

That is worth naming because it is not a small error, and it is not unique to ponds. It is the same move that turned mycorrhizal symbiosis into a forest-wide network of elder trees feeding their young — a story so good it outran what anybody had shown, until Karst, Jones and Hoeksema went back and found the evidence for the popular version insufficient. We have made that error ourselves, in three pieces, and said so.

Here it is in miniature and much more cheaply: a frog sat down on a leaf and we wrote a relationship.

What is lost by giving up the pairing: nothing. The frog is still there, on the pad, exactly as the picture always had it. The leaf is still moving litres of air a day into airless mud, which is a stranger fact than any partnership we were going to invent for it. Two remarkable things, unrelated, on one leaf. That is not a smaller result. It is just an honest one.