The ablation a plant would survive

This site has one experiment it can specify rather than merely wish for. Take a plant with a settled spiral arrangement, remove a single primordium, and record whether the next one appears where it was going to. The number of positions for which the answer is no is the larger parastichy number — a spiral count with no angles, no coordinates and no counting of rows.

It was specified at one rise, on one kind of stem. Measured across three rungs and through a transition it survives, and it acquires conditions. This is the specification with those conditions in it.

What the experiment measures, restated #

The prediction is a step. Removing an organ k places back moves the next organ by tens of degrees for every k out to n, and by less than a degree for every k past it.

The rival account — organs at exact multiples of a divergence, with errors passed between neighbours — predicts zero at every offset, by construction rather than by fitting, since in it no organ’s intended position is a function of whether an earlier organ exists. So this is a one-sided test with an effect size of tens of degrees against a null of tenths.

Why this experiment rather than a photograph #

The case for spending a scalpel on a plant that could simply be counted is worth restating, because it is the whole reason the specification exists.

Every other instrument on this site reads an arrangement that is already there. A counter shown the positions returns a pair; a spectrum of the divergence sequence returns a pair; a fit to the hop lengths returns the rise and the divergence. All of them are measurements of form, and the site’s own results have shown, twice, that form does not separate the accounts: a kinematic lattice with transported errors reproduces the comb, the second comb and the pair, and the ratio that once separated them follows the disturbance rather than the rule.

The intervention is not a measurement of form. It asks what the plant does when its arrangement is changed, and the two accounts differ about that by construction — one has a rule that recomputes, the other has positions that were never computed. This is the only observable on this site that a photograph cannot supply, which is why it is worth the conditions.

Condition one: the plant must be finely enough patterned to be damaged #

The intervention has a second half — whether the stem recovers — and that half is where the ladder matters.

At the 8/13 rung, five of the thirteen offsets never recover in three hundred organs. At 5/8, two of eight. At 3/5, none: every single-organ ablation is undone within forty organs, at three cut points four dozen organs apart.

For an experimenter that is a selection criterion, and it is the first thing the specification did not have. A study of whether ablation permanently disturbs phyllotaxis, done on material with a low count — a young shoot, a small cone, a seedling — would return no and would be right about its material and wrong about the rule.

The counts to work with are 8/13 and finer. Below that, healing is the expected outcome, and the count the work was done at has to be reported with it so that two results can be told apart.

Which condition binds on which half #

The two conditions are not conditions on one experiment, and saying so changes who can run it.

The intervention has two results. The first is a count: how many offsets move the next organ, which equals the larger parastichy number. The second is a susceptibility: which removals the pattern never undoes.

Condition one binds only on the second. A plant counted 3 and 5 has a front of five organs and a perfectly clean step — the displacements run from a few degrees to a whole divergence inside the front and under 1.4° outside it — so it returns the count as well as any finer plant does. What it will not return is a permanent disturbance, because a front of five has no middle to sever.

So a coarse specimen is not an unsuitable subject; it is a suitable subject for one of the two readings. The specification should say which reading a given plant can supply rather than admitting or excluding the plant, and the deciding number — the count — is readable from a photograph before anything is cut.

That also says which experiment to run first on scarce material. The count needs sixteen apices and any rung; the susceptibility needs a fine rung as well. If a laboratory has one species and it is coarse, the count is available and the robustness question is not.

Condition two: not near a transition #

The clean form of the result — the response is the offsets one to n, and nothing past — holds in the middle of a rung. Within about a fifth of a rung of a transition the response is an interval plus one isolated offset, with silent organs in between: at a rise of 0.008 the felt offsets are one to eight and twelve, with nine, ten and eleven moving the next organ by under a degree.

That condition has a property the first one does not: the experiment checks it itself. A plant in the middle of a rung gives a run of felt offsets and silence past it; a plant near a transition gives the run, a stretch of silence, and then a lone offset felt as strongly as anything. So there is no need to establish in advance where on its rung a specimen sits — the shape of the answer says.

The cost of the self-check is stated elsewhere and it is small: cut past the first silence rather than stopping at it, which is four more apices at a count of eight. What comes back is either a clean run — the plant is mid-rung and the count is the run’s length — or a run with a lone responder behind it, in which case the count is still the run’s length and the plant is additionally known to be approaching its next rung.

So condition two is not a condition at all once the design cuts past the first silence. It is a second reading that the same apices supply, and the only way to fail it is to stop cutting too early.

An experimenter who took the largest felt offset as the count would report thirteen minus one on a plant with eight rows. The condition is therefore: test the offsets past the front as well, and report the response as a set rather than as a maximum.

Done that way the transition is not a nuisance but a second measurement — the lone offset names the pair the plant is climbing towards, which is information no photograph of the same plant contains.

Condition three: the count is the yeses, not the largest yes #

Which follows from the second, and is the sentence the original specification got slightly wrong.

In the middle of a rung the two are the same number. Near a transition they are not: the count is the length of the run from the tip, and the largest felt offset is one place inside the incoming count. Reported as a run, the answer is right at every rise measured; reported as a maximum, it is wrong at four of thirteen.

The three questions, and what each one is worth #

Setting the questions out in order of value rather than in order of cost is worth doing once, because they are usually run together and they are not equally important.

The count by intervention. A parastichy count obtained without counting. This is the least surprising of the three and the most useful, because it is a number an experimenter can compare directly with a photograph of the same plant. Agreement is a check on the whole picture; disagreement is a defect in one of two instruments, and cheap to chase.

The boundary as evidence about mechanism. The step’s existence, rather than its position, is what separates the accounts. It is worth more than the count and is harder to report convincingly, because the null it is being tested against — no response at any offset — has to be established with the plant’s own scatter measured on the same material.

The second attractor. Whether a cut in the middle of the front leaves the plant permanently on a different arrangement is the most striking prediction here and the least likely to survive contact with a real meristem, because it is the one that depends on the model’s behaviour hundreds of organs after the intervention. It also has the most distinctive signature: a two-ranked arrangement with a slow twist, whose block length is the plant’s old smaller count.

An experiment that answered only the first question would still be worth doing. An experiment that answered the third would be remarkable, and it would take a season.

What it costs in specimens #

Three questions, three sample sizes, and they differ by an order of magnitude.

Is the response a step at all? One specimen, if the ablations can be done at enough offsets on it. The effect is tens of degrees against a null of tenths, so a single clean series of fifteen ablations either shows the step or does not.

Where does the step end? The same series, read as a run. The boundary is one organ wide in the model, so the precision is set by how many offsets are tried rather than by how many plants.

Does the stem recover? This is the expensive one. Recovery has to be watched for over roughly three hundred organs after the cut, which on a real apex is a season rather than an afternoon, and the fates of neighbouring offsets differ — one offset heals in seven organs and its neighbour never does. A study of the recovery question needs several plants per offset and a plant that will keep producing organs for long enough to see it.

What would refute the rule #

Worth stating plainly, because an experiment whose every outcome is consistent with the model is not an experiment.

A response with no step. Displacements of tens of degrees at offsets far behind the front — thirty, fifty — would say the rule’s neighbourhood is not what it is modelled as.

A response that ends at the wrong number. A run ending at the smaller parastichy number, or at neither, on a plant well inside a rung.

No response at all. Every offset moving the next organ by less than the plant’s own scatter is the transported account’s prediction, and it is the outcome that would end the placement rule as a model of that material.

And a recovery pattern with no middle. If cuts anywhere in the front heal on a plant with thirteen contact rows, the second attractor is an artefact of the model rather than a property of a placement rule.

What a null result would and would not mean #

The experiment can come back empty in three ways, and they are not the same failure.

No response at any offset. This is the transported account’s prediction and would be the strongest possible result — against the placement rule, and worth publishing on its own.

A response with the wrong shape. Displacements that decay with offset rather than stopping, or a response that ends at the smaller number, would say the rule is roughly right about recomputation and wrong about its neighbourhood. That is the most likely interesting outcome, because the neighbourhood is the part of the model with the least evidence behind it.

Healing everywhere. On material at 8/13 or finer this contradicts the model; on coarser material it contradicts nothing, which is why the selection criterion is a condition rather than a suggestion. A study that reported “ablation does not permanently disturb phyllotaxis” without stating its counts would be uninterpretable, and this is the specific thing this essay exists to prevent.

Two ways the model could be right and the experiment still fail #

Both are about the difference between a deletion and a wound, and neither is addressable from here.

The hole may not stay a hole. The model’s ablation removes an organ and the gap remains a gap for ever. On a real apex the surrounding tissue grows, and if it closes the gap faster than the next primordium is initiated, the rule sees an arrangement with no vacancy in it and does nothing. That would produce a null result on a plant that computes its positions exactly as modelled.

The wound may inhibit. A damaged region may itself act as an inhibitor, in which case removing an organ adds to the field rather than subtracting from it, and the next primordium is pushed away from the vacancy rather than into it. The model predicts a displacement into the hole, of a whole divergence at some offsets — so the sign of the displacement is itself a test, and a next organ that moves away from the vacancy would be evidence that the wound dominates.

That second one is a gift rather than a difficulty: the prediction is directional and large, so an experiment that measures the sign has already learned something whichever way it comes out.

What the model still cannot tell an experimenter #

Two things, and both are honest limits rather than to-do items.

How long a real apex takes to do any of this. The model’s time is organs, not days, and the mapping between them is the plastochron — which varies with temperature, light and the plant’s own age.

What a wound does. Removing a primordium from a real meristem is surgery: it leaves damaged tissue, a wound response, and a hole that is not simply an absence of inhibition. The model’s ablation is a clean deletion, and the difference is the largest single reason a real result might differ from the prediction.

The specification is therefore: a plant at 8/13 or finer, well inside a rung, ablated at fifteen offsets, with the response reported as a set of yeses; and, if the recovery question is being asked, several plants per offset and a season.

That is a smaller and more specific experiment than the one written down in the essay that first specified it, and every one of the conditions came from a measurement rather than from a worry.

The check #

The conditions are asserted where the stems are grown, which is what stops them becoming advice.

The coarsest rung must heal every ablation at every cut point — the criterion in condition one, stated so that it fails if a coarse stem ever fails to recover.

The response must be an interval at every rung rise and must not be one at the transition rises, which is conditions two and three together.

And the isolated offset must be the incoming count less one, predicted from the hop lengths of the undisturbed stem rather than fitted after the fact. If that prediction failed, the second measurement this specification offers would be worth nothing, and the specification would go back to being about one number.

Two of the conditions have moved #

The condition that reads most like a restriction — the plant must not be too coarsely patterned, or nothing will go wrong at all — is now about the intervention rather than about the plant. A stem carrying 3/5 heals every single-organ removal and does not heal every two-organ one, so the experiment reaches coarse arrangements at the cost of one more primordium.

A second condition has been added in its place, and it is about whorled shoots. On a stem with two organs at every node the displacement has to be read modulo half a turn, or the response never appears to end; read that way the boundary is the larger count as usual, and removing either organ of one node gives the same answer to the last digit — a control internal to one shoot.