A late window names the wait it mostly saw

A plant’s buds forget the climate that grew them read branching plants from a late window — ten seasons of dated, sorted scars on a plant that had grown over its oldest — after a change of climate in their youth, and found two things. The wait a bud spends before it matures into a growing apex was named for 97 to 100 per cent of plants whatever the youth, from the steady-growth start that splits the window’s opening buds by age as steady growth at the window’s own survivals would. And the climate change could not be read off the plant’s age structure, because a steadily growing plant’s buds per apex barely depend on its survivals: the growth factor falls with the survivals as the buds do.

Every plant in that essay kept one wait for life, and the essay said that was what made its mix of buds and apices so stable. Its last question was a plant whose wait changes with its own size — a bud on a large plant taking a season longer to mature than a bud on a young one, as apical dominance strengthens — and whether a late window names the wait the plant has now, the wait it had, or neither; and whether the age structure, which forgets a climate, remembers a change of wait.

A wait that changes at a size #

The plant is the same plant, a branching count set by a delay: grown from one apex, each mature apex making a bud a season, each bud maturing into an apex after the wait, apices dying at 0.05 a season on average and buds at 0.15 — two ways to die, each counted — and one season in ten a drought with both chances five times a good year’s, which does not average out. With one change: its wait is two seasons until its living total first reaches a stated size, and three seasons from then on. The size at which the wait lengthens is 20, 50, 100, 200, 400 or 800 living points.

When the wait lengthens, every bud already waiting simply waits a season longer. The reverse plant, whose wait shortens from three seasons to two at the same sizes, is grown beside it, and there every bud already past the new wait matures at once. Two thousand plants of each kind are grown for thirty seasons at each size, and each is read from five windows of ten seasons, opening at seasons 0, 5, 10, 15 and 20. Only plants alive at the end of a window are read from it, as only those could be found.

One plant, five windows #

One plant reaches a hundred living points in its fifteenth season. Read from the windows that open at seasons 0 and 5, which close before the change, it is named a two-season plant. From the window opening at season 15, which opens as the wait changes, and the one at 20, it is named a three-season plant. The window opening at season 10 is the instructive one. The change falls in its fifth season, so the window saw five seasons of each wait — and it names two.

The window does not name neither, and it does not name the plant’s present. It is a description of the plant in one number, and a plant whose wait changed has two; the window chooses between them. It names a wait the plant actually had, and which one depends on how much of the window each wait occupied.

Before, inside and after #

Over every size and every window, readings fall into three groups. Where the change came before the window opened, the window names the new wait on 14,465 of 14,467 readings of a lengthening plant and on every one of 8,182 readings of a shortening one. Where it comes after the window closes, the window names the old wait on 98.6 per cent of lengthening plants and 93.8 per cent of shortening ones; the rest are the reading’s ordinary misses, mostly a wait one season too long, on plants that have stayed small enough not to change. Where the change falls inside the window, the readings split: 45 per cent name the new wait on lengthening plants and 35 per cent on shortening ones.

A reading naming a third wait — neither the plant’s old wait nor its new one — occurs on four readings in 34,144 of lengthening plants whose change came before or inside the window, and on 29 in 23,920 of shortening ones. The window does not average the two waits into something the plant never had.

Inside the window, the wait that held longer #

The split inside the window is not a coin toss; it is decided by when the change fell. A lengthening plant whose wait changed in the first, second or third season of a ten-season window is named a three-season plant on 99.6 per cent of readings or more; in the fourth season on 92 per cent; in the fifth, 18.5; from the sixth season on, 2 per cent or fewer. A shortening plant is the same with the turn a little earlier: 97.8 per cent or more up to the third season, 61 at the fourth, 5.5 at the fifth, 2 or fewer from the sixth.

So the window names the wait that held for most of it. The reading fits ten seasons of living totals with one wait at a time, and the wait that explains more of the seasons explains them better: a change in the fourth season leaves six seasons of the new wait and is read as it, one in the sixth leaves four and is not. At five seasons of each the old wait is named on most plants; why the tie goes that way is not traced here.

A census against size #

That rule has a consequence a field worker could use. The change happens at a size, and plants are found at all sizes. Gathered across plants and windows and sorted by how large the plant was when its window opened, the wait named turns from two seasons to three over one doubling of size: for plants whose wait lengthens at fifty living points, from 1.6 per cent naming three below 12.5 to 74.6 per cent between 12.5 and 25 and 98.8 between 25 and 50; at two hundred, from 2.2 per cent between 25 and 50 to 67.9 between 50 and 100 and 99.3 between 100 and 200; at eight hundred, from 1 per cent below 200 to 61 per cent between 200 and 400 and 100 above.

The turn comes between a quarter and a half of the size at which the wait changed. A two-season plant under this climate multiplies by about 1.34 a season, and so by about 3.2 over four seasons; a window opening at a third of the changing size meets the change in its first four seasons, early enough to name it. Read that way, a wait that lengthens with size is visible as exactly that — across plants, at a size a factor of two to four below the true one, which a worker who knows the reading’s rule can correct for.

The same census for a wait that shortens #

The rule behind the turn can be checked on the reverse plant. A three-season plant grows more slowly than a two-season one — about 1.25 a season under this climate against 1.34, so about 2.4 times over four seasons rather than 3.2 — and the same reading rule should put its turn nearer the size at which the wait changed. It does. For plants whose wait shortens at fifty living points, 26.2 per cent of readings name two seasons between 12.5 and 25 and 90.1 per cent between 25 and 50; at two hundred, 19.6 per cent between 50 and 100 and 92.9 between 100 and 200. The lengthening plants turned a doubling earlier: at a hundred living points, 65.3 per cent naming three between 25 and 50; at four hundred, 66.8 per cent between 100 and 200.

So the factor between the size a census turns at and the size the wait changed at is the plant’s own growth over the four seasons the window needs, and a worker who has read the plant’s growth rate off the same scars has the correction in hand: the growth over a season is the ratio of the living totals a season apart, which the dated scars give directly, as they have since a count first lost its growing points.

What the buds remember #

The climate essay’s detector asked whether a plant’s buds per apex at the window’s opening fall outside the middle ninety per cent of plants that never changed, read the same way, and found a climate change inside that range within a few seasons. Here it reads the change of wait, among plants whose window names the new wait.

A shortened wait is remembered, briefly. Read in the season the wait shortened, 59 per cent of plants fall outside the steady range; a season later, 76 per cent; two seasons later, 2.9 per cent, and about 2 per cent or less after. A lengthened wait is hardly remembered at all: 2.5 per cent in the season of the change, 19.6 a season later, 1.2 two seasons later, and under one per cent after.

The asymmetry is in what the change does to the buds. When the wait shortens, every bud past the new wait matures at once: the oldest of the plant’s three ages of bud become apices in one season, the buds per apex drop below anything steady growth at the new wait holds, and the deficit takes two seasons to refill. When the wait lengthens, the buds already waiting wait a season more and no bud is lost or advanced; the buds per apex rise by one season’s worth of new buds, which a steady three-season plant also carries, and most plants are within the steady range at once.

Why the wait is remembered where the climate was not #

The climate essay’s reason for forgetting was that the buds per apex barely depend on survival: across every survival a climate gives, the steady ratio moved by a few per cent. The wait is different. A two-season plant’s buds per apex and a three-season plant’s differ by a whole season’s buds, and the detector compares a plant against plants at its own named wait, so a plant that has caught up to the new wait’s proportion is inside the range and one that has not is outside it. A shortened wait leaves the plant out of proportion for exactly as long as its missing buds take to be replaced, which is the new wait. A lengthened wait puts it in proportion straight away. So the age structure does not forget a change of wait the way it forgot a climate — it records the change in the direction that removes buds, for as many seasons as the new wait, and then forgets it too.

Five windows on one plant #

A plant can be read more than once. A worker who comes back to the same plant every five seasons reads it through the five windows here, and the windows then see the change as a step. Of the lengthening plants that change at a hundred living points between their first and twenty-fifth seasons and survive every window, 1,790 of 1,838 read two seasons in every window up to some point and three in every window after; 36 step back once from three to two, a window in which the old wait still explained the seasons better. For plants changing at four hundred, 1,719 of 1,787 show the clean step and 32 a step back.

The step locates the change to within the five seasons between two windows’ openings, and the inside-the-window rule above narrows it further: the change almost always fell no earlier than four seasons after the last window naming the old wait opened, and no later than three seasons after the first window naming the new one opened. Two readings bracket what one cannot.

What a worker can and cannot read #

Read from a late window, a plant whose wait changes with size gives up its wait at the time of the window, near enough — the wait that held for most of the ten seasons — and never an average. That is enough to see a size-dependent wait across a population and to place it within a factor of two to four in size. What a single plant cannot give up is the moment of its own change: inside the window, the reading turns from one wait to the other within two seasons, and the buds per apex record a shortening for two seasons and a lengthening for barely one. A worker with one window per plant sees the waits and not the switch; a worker with several sees the switch too.

One step at one size #

Every plant here changes its wait once, in one step, when its total first passes a size. A real plant’s buds may lengthen their wait gradually, or differ by their position — a bud near a dominant apex waiting longer than one at the edge — and then the wait belongs to the bud rather than the plant, and a window would be reading a mixture of waits it has no way to name. Nor is the size threshold anything a plant is known to use; it is the simplest rule that makes a wait depend on size, chosen to put a change at a place the window can be set against.

The climate is the present one throughout. A change of wait and a change of climate together were not grown.

Readings that would undo it #

A change before the window read as the new wait on fewer than 999 readings in a thousand, or after it as the old on fewer than 93 per cent. A third wait named on more than three readings in a thousand whose change came before or inside the window. A change in a window’s first three seasons named the new wait on fewer than 97 per cent, or from its sixth season on on more than 2 per cent. A census against size that turns outside a quarter to a half of the changing size. A shortened wait flagged on fewer than half of plants in its first two seasons or on more than 3 per cent after, or a lengthened wait flagged on more than 21 per cent in any season. Each is checked against the grown plants whenever they are read.

The wait it mostly saw #

A late window reads a plant whose wait lengthens with its size as the wait that held for most of the window: the new wait if the change came in its first three seasons or before, the old one from its sixth season on, and never a third. Across plants that makes a size-dependent wait readable, turning at a quarter to a half of the true size. The buds per apex remember a shortened wait for two seasons, because the shortening matures a season’s worth of buds at once, and a lengthened one hardly at all.

Still open: a wait that belongs to the bud #

Every bud here waits the plant’s wait. A plant whose buds’ waits depend on where they sit — longer near a dominant apex, shorter at the edge — grows a mixture of waits at every size, and the window reads one wait from ten seasons of living totals. The next measurement grows plants whose buds wait two or three seasons by a stated share that depends on the plant’s size, reads them from late windows, and asks whether the window names the commoner wait, a wait weighted by the share, or something the plant never had — the case this essay’s single-step plants could not reach, since every one of them held exactly one wait at a time.