Growing a Stand, Not a Tree: Joint Canopy Generation Reproduces Crown Shyness

Guang Yang; Fengchen Liu

cs.CVAug 27, 2026

Growing a Stand, Not a Tree: Joint Canopy Generation Reproduces Crown Shyness

Authors: Guang Yang, Fengchen Liu

Organizations: Phi Lab Foundation · University of California, Berkeley

Abstract

In closed forests, neighboring tree crowns often stop short of touching, leaving a network of narrow gaps known as crown shyness. The pattern belongs to the stand rather than to any single tree, which makes it a natural probe of a question in generative modeling: can a learned model produce a set of objects whose defining structure exists only between them? We formulate stand-level canopy generation as set generation with a flow-matching model, in which attention between trees is the only channel through which coupling can arise. Trained on stands grown by a resource-competition simulation that is provably not reducible to per-tree geometry, the joint model halves the clearance distribution error of an identical-capacity model that generates each tree alone, and the advantage persists at stem densities outside the training range. Against field measurements of a tropical oak forest, a single calibrated scalar yields held-out agreement in gap magnitude and crown asymmetry. The directional statistics of the gaps are controlled by stem placement rather than by the growth rule, and match the field once stem jitter is calibrated. Crown shyness, in both the simulation and the learned model, is a property of the stand and not of the tree.

Figures & tables

Figure 1: Crown shyness from one growth rule, across the density range this paper studies. Each panel is a stand grown by the coupled simulation (Sec. 3 ) on hard-core Poisson stems, seen from above; color is height, gaps are unlit background. Columns: mean stem spacing 3.0 to 6.5 m (144 to 30 trees in the same footprint). Rows: the paper’s two operating points of the contact die-back fraction, 0.06 selected by the mechanism gate and used for all training data, and 0.16 calibrated to field measurements (Sec. 5 ); crown draws are shared within each column, so the only change down a column is the abrasion strength, and the channels widen accordingly. The channels follow the outline of both crowns that share them, at every density: the signature of crown shyness. The learning question of this paper is whether a generative model can produce these stands jointly (Sec. 5 ).

Figure 2: Crown shyness, real and generated, seen the same way: from above, coloured by height, gaps dark. (a) A 96 m window of an airborne lidar canopy height model, Maliau Basin, Borneo [ 22 ] , chosen by shape search for canopy cover matching (b); interpolation for display only. (b)–(d) The teacher at 5 m stem spacing held out of training (+0.328 m clearance), the trained joint model on the same stems (+0.029 m), and the same model with attention ablated (-0.389 m). Rings mark crowns that run into a neighbor: 9 of 24 for the joint arm, 15 for the ablated one. Both paint the same canopy area from the same mean crown radius, so they differ in crown shape, not size.

Figure 3: Shyness needs both mechanisms. Left to right: coupling off, abrasion off, both on; below each panel, nearest-neighbor clearance measured on the stand shown. Identical stems and crown draws across panels, on hard-core Poisson stems at 3.5 m; the gate itself is judged on the controlled lattice, and the rule behaves the same on both. Removing coupling interpenetrates the canopy; removing abrasion closes the gaps; only the full rule produces crown shyness.

Figure 4: The teacher is not a function of stem positions. Left: fraction of neighbors whose crowns respond when one tree is made 30% taller, by stem spacing; the dashed line marks the 50% gate. Right: the response under step refinement (circles) against the decay a discretization artifact would show (squares, dashed); the response converges instead of tracking the step.

Figure 5: Joint generation beats independent generation at matched capacity. Left: clearance distribution error on unseen stem spacings for the joint and independent arms over 12 seeds; the dotted line is the direction-blind baseline. Right: relative advantage of joint over independent at spacings outside the training range; the dashed line is the preregistered 20% gate.

Figure 6: Field validation calibrates one scalar and holds out the rest. Left: the calibration curve; the die-back fraction is chosen where the simulated median clearance meets the field median (dashed). Center: held-out clearance spread against the preregistered band (shaded); the uncoupled control lands at 31.3

\times

the field spread and is correctly rejected. Right: held-out crown elongation against the observed field band; crown shape was never calibrated, so this is a prediction.

Figure 7: The gap network across stem densities, drawn as the point cloud a scan would return. (a–c) Coupled stands at 5, 4 and 3 m mean stem spacing (51 to 144 stems), with 85, 92 and 96% of crowns contacting a neighbour. Stems are hard-core Poisson draws; the controlled experiments (Fig. 5 ) keep the jittered lattice. The channels are an artefact of neither. (d) The stand in (c) regrown with coupling off, from identical stems and crown draws: the canopy closes. (e) Nearest-neighbour clearance for (c) and (d), moving from -7.034 m to +0.180 m.

Figure 8: Directional gap statistics are controlled by stem placement. Clearance anisotropy against stem jitter amplitude (circles: calibration sweep; square: the controlled lattice used in the learning experiments; star: held-out evaluation at the calibrated amplitude). The shaded band is the field’s observed range and the dotted line its median. Raising jitter from 4% to 8% moves anisotropy into the field band; gap magnitude and crown shape remain inside their own bands.

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