Flexible allometry: leaf and sapwood as ODE states

[dfalster]

Frees leaf and sapwood area as ODE states, so replacement of turned-over
leaf becomes conditional on the marginal leaf's carbon balance and the stem
can track the Huber value that maximises growth.

Both are OFF at the defaults (a_pl0 = 0, a_sw = 0) and the model is then
bit-exact: the scenario gateway passes unmodified against develop.

TF24 v10 -> v11; TF24f v10.1 -> v11.1. Merges #617.

Draft: the demo's "thinning does not buy survival" section still quotes
pre-#617 numbers. Detail, measurements and retractions in the first comment.

[dfalster]

What this does

Two mechanisms, both defaulting to off.

1. Conditional leaf replacement (a_pl0). Leaf turnover is currently charged as a cost and the tissue restored unconditionally by the allometry, so a struggling plant cannot economise by carrying less leaf. Replacement now depends on whether the marginal leaf is paying for itself. Carbon not spent and leaf mass not replaced are two halves of one decision and conserve exactly by construction.

2. Sapwood tracks its growth optimum (a_sw). dψ/dt gains a_sw · R_s, an integral controller on the marginal growth return of sapwood area. It converges onto R_s = 0, and because integrating is averaging, a small a_sw makes the stem follow the long-run mean of a signal that swings with the weather — no extra tracked state.

States are carried as departures, log(actual/preferred), which is what makes the fixed-allometry model recoverable bit-for-bit rather than approximately.

The objective is growth, not production

This is the design decision everything else follows from. Against production, extra sapwood is nearly always worth building: it raises k_max, and nothing in P charges the plant for the leaf area it did not build instead. R_s subtracts that price. The optimum is not one number — after #617 it rises with height and again as soil dries:

stem area per leaf area, ×pipe model	5 m	10 m	16 m	20 m
soil 0.30	0.87	1.03	1.17	1.26
soil 0.20	0.89	1.05	1.21	1.30
soil 0.15	1.04	1.28	1.54	1.68

The defining correctness property is that R_s crosses zero exactly where dh/dt peaks — verified in all twelve cells above on a 0.01 grid in ψ. A controller built on production instead is still monotone, still converges, and is still wrong, so the test asserts the crossing on the grid rather than by interpolation.

⚠️ Two retractions

The envelope theorem does not apply here. I claimed the sensitivity was nearly free: profit is already maximised, so re-evaluate at the collar potential already found and the indirect term vanishes. That holds for opt_psi_stem_, which is genuinely maximised. It does not hold for opt_root_psi_, which is a root find — the collar potential where the soil-root network's supply matches the leaf's demand. A constraint is not an optimum, so d(profit)/d(collar) ≠ 0.

Holding it fixed under-reported d(profit)/d(k_max) by 15–19%, putting the controller's zero at 1.22× where growth peaks at 1.28×. A full re-solve matches a finite difference of the model's own assimilation to 0.09%. Consequence: a_sw > 0 costs a second full leaf solve per rate evaluation; a_sw = 0 skips the block. plant #614 (analytic d(profit)/d(k_max)) would remove that cost and is worth more than it looked.

Why it survived so long is worth its own warning. In wet soil the growth peak is nearly flat — at 16 m, dh/dt varies by 6e-4 relative between 1.13× and 1.22× — so a 0.025 scan grid could not resolve a 0.03 offset in ψ and the zero appeared to land exactly on the peak. A coarse grid here does not merely lose precision; it manufactures an exact-looking agreement.

Shedding's benefit is a function of size, and my first measurement was taken at one size. An early sweep at 10 m found 1.001–1.06× and I concluded thinning does not buy survival. That is true at 10 m and false at 20 m+.

What #617 changed, measured before and after

The benefit band sits at the height-resistance relation's viability ceiling, so replacing that relation moved both:

	before #617	after
viability ceiling (P > 0 in wet soil)	17–18 m	30–36 m
benefit at soil 0.16, 4 yr, any height ≤24 m	up to 4.4e9×	exactly 1.00
largest benefit found	6.1e9× (both arms dead)	84× at 30 m

TF24 is now much more drought-tolerant: a 4-year drought at soil 0.16 kills nothing up to 24 m, where before it took a 20 m plant to 3e-19. The size dependence survives, shifted — nothing below 13 m, 2.4× at 20 m, 84× at 30 m at soil 0.14.

Shedding still never converts death into survival. Zero cells of the post-#617 grid have the fixed plant dead and the shedding plant alive; the large ratios sit between two very small numbers. The benefit is also largest at moderate drought, not the harshest — at soil 0.12 everything dies whatever it does. This is the open scientific question, and it is why the demo carries a section on it.

Merge resolutions worth reviewing

• k_max takes Derive TF24 height-resistance from stem anatomy #617's path-integral denominator and this branch's actual Huber value as numerator, and is now stored rather than recomputed. The controller had been recomputing it on the old height-linear relation — wrong by a factor 0.35 at 16 m, and silent. This is the resolution I would most like a second pair of eyes on.
• scientific_version → 11. Both branches independently claimed v10; a merged TF24 carries both changes and is comparable to neither.
• Derive TF24 height-resistance from stem anatomy #617's exactness test is pinned to the height coordinate. This branch changes TF24's default, so a bare Control() compared two coordinates rather than two hydraulic models (404.5 against 30.2) — a failure that reads exactly like a broken exactness test.
• The TF24f k_acclim bracket moved rather than its threshold relaxed. The peak shifted from k≈0.1 to k≈1 under the birth-date coordinate, so 0.1-vs-10 straddled the maximum and read 3% — a badly-placed bracket, not weak acclimation. Spanning 0.001–1 gives 13.2%.

Also fixed along the way

• Sapwood turnover is gated, so its ψ-derivative is not k_s·m_s. The charge falls as exp((1 − 1/a_pl2)ψ). Differentiating the ungated cost dropped a term worth 6.8 of 13.1 kg/yr — invisible to any check on sign or monotonicity.
• The controller's denominator must stay positive, and profit is not: it goes negative in exactly the drought where the sign is most needed. It now divides by the maintenance bill.
• Re-proportioning has to be paid for. The reserve gate G is not the right switch — at soil 0.13 reserves are still full and it is production that has gone to zero.
• Deep-crown is refused, not skipped (prepare_strategy() throws). Skipping leaves the controller with only its negative cost term, and the stem shrinks without bound while the run looks plausible the whole way down.

Status

Full suite green at 3738, and the scenario gateway passes unmodified — the strongest available statement that a_sw = 0 is bit-exact against develop.

Draft because the demo's "thinning does not buy survival" section still quotes pre-#617 numbers. Its chunks run, so nothing fails; the prose beside them is what is stale.

[dfalster]

@itowers1 @elijahmagistrado — feedback welcome on this one, whenever suits.

Please run the demo rather than only reading the diff. It is the honest account of what this does and, more usefully, of where it does not yet work:

git fetch && git checkout feature/flexible-allometry-516
R CMD INSTALL --preclean .          # header + yml changed, so a clean build
quarto render overstorey_staging/TF24_flexible_allometry_demo.qmd

It runs in a few minutes and needs nothing beyond the branch. If you would rather not build it, say so and I will render and attach the HTML.

What I would most like challenged, in priority order:

1. The claim that shedding does not buy survival. Across a 90-cell grid of size, drought intensity and duration, there is no cell where the fixed plant dies and the shedding plant lives. That is the central negative result and I would like it attacked — either a regime I have not tried, or a reason the experiment is the wrong one. The demo's section on this is the part still carrying pre-Derive TF24 height-resistance from stem anatomy #617 numbers, so read the prose sceptically.

2. Whether the growth rate is the right objective. R_s is zero where dh/dt peaks. Height growth is one choice; dA_leaf/dt, or the relative rate (dA/dt)/A, are defensible and give different optima. Daniel's view is that this is ultimately an empirical question for evolutionary analysis of competing strategies, but if either of you has a prior I would rather hear it before we run that.

3. The merged k_max. It takes Derive TF24 height-resistance from stem anatomy #617's path-integral denominator with the plant's actual Huber value as numerator. I think that is right — supply per unit leaf area should follow the stem the plant actually has — but it is the one place where this branch and Derive TF24 height-resistance from stem anatomy #617 genuinely interact, and it was silently wrong once already.

4. Whether the parameters are the right ones to expose. a_pl0–a_pl4 and a_sw are all TF24_Pars fields and so settable as traits. Defaults reproduce the current model exactly. Whether any of them should instead be derived from an existing trait is open, and [TF24 allometry] Review empirical data on plasticity in allometry (height-to leaf area for individuals) in response to environment (light or water) #512 is the input.

The first comment above has the measurements and two retractions. No rush on any of this — it is draft and the demo needs a pass before it is merge-ready.

[dfalster]

Ready for review — the stale section is re-measured.

@itowers1 @elijahmagistrado the demo is now safe to read end to end. It renders clean and the full suite is green at 3753.

One argument in it is retracted outright, and it is worth knowing about before you read the section. It used to say that thinning "cuts income just as fast" — that shrinking the canopy shrinks both sides of the budget together, with per-leaf production worsening monotonically from −3.81 to −4.68 as the canopy went to a fiftieth. That is no longer true after #617. With resistance derived from stem anatomy, the remaining leaves inherit the whole stem's hydraulic supply, so thinning improves the per-leaf balance by 43% and there is an interior optimum near a tenth of full canopy:

canopy fullness	1.00	0.50	0.20	0.10	0.05	0.018
net production per m² leaf	−1.47	−1.17	−0.94	−0.84	−0.86	−0.99

The conclusion survives the argument being replaced: a struggling plant can now narrow its deficit by shedding, but it still cannot close it. Thinning slows the burn; it never reaches balance.

The stand-level cost also shrank a lot. Switching the mechanism on used to cost 0.55–0.64× lifetime offspring production on seasonal stands. It is now 0.92–1.00×, so the mechanism is close to free rather than expensive — but still buys no survival, which is what the section is about.

The decisive measurement is unchanged and now guarded. The two thresholds are in the wrong order in stress space: at soil 0.145 nothing thins because the leaves are still profitable, and by 0.140 a 10 m plant is at a survivorship of one in a million with its canopy still at 1.000. Mortality saturates at a milder drought than shedding begins at, so there is no intensity where a plant is both stressed enough to thin and alive enough to profit. Across the grid the largest gain is 20×, and it moves survivorship from 2.8e-08 to 5.6e-07 — both dead.

Why this rotted, and what stops it next time. The section's tables were prose, not chunks, so every number in it survived #617 while the page rendered clean. test-allometry-demo.R now asserts the ordering, the absence of any rescue cell, the interior optimum, and the trajectory's height cost — against demo_soil_history's own arguments, since quoting a number from a nearby-but-different run is how an earlier Huber-value claim went wrong.

The four things I would most like challenged are unchanged, in the comment above.

[itowers1]

Just adding my current understanding of how this all works via a flowchart, this can be edited in powerpoint as I learn more.

[itowers1]

In terms of optimisation of allometry, if the purpose of thinning is to stave off mortality in drought periods, would there be a functional difference to maximising survivorship as opposed to growth. Is survival maximised where height growth is greatest anyway?

[elijahmagistrado]

I think once the trees reach their height at maturation and af_1 = 1, then the purpose of thinning would be exclusively for reducing mortality. So in wet periods, survival would be the highest where height growth is also the highest when there is still room to grow, otherwise the trade-off is between survival and reproduction.