The order of growth contains information

Finding 02 · Temporal-order null model

Keeping every observed increment but changing its position changes the developmental signal.

Question

Does Fire VASE retain information about sequence, or does only the total and multiset of growth increments matter?

Answer

Sequence matters. In a separately recorded 4,000-fire sample, observed histories are more front-loaded, less pulsed, and less frequently reactivated than within-fire permutations of exactly the same increments.

Observed orderlarge → small → small → large → small

shuffle the same increments

Permuted ordersmall → large → small → small → large

If only total growth mattered, rearranging the same increments would not systematically change order-sensitive developmental traits. Each permutation preserves the fire’s observation count, reconstructed total, and full increment multiset.

What to notice. Panel S2C compares observed trait means with the 95% range from temporal shuffles. Panel S2B shows an equally important boundary: other positive, mass-conserving allocation nulls compress as much as or more than the observed space. Ordering is informative; compression alone does not prove biological restriction. Technical caption

How to read this figure

- **Panels:** This supplementary figure assembles six challenges. The temporal ordering result is in S2C; observation depth is S2A and allocation nulls are S2B. - **Axes:** In S2C, dots are observed trait means and intervals are the 95% ranges obtained after shuffling increments within fires. - **Look here:** Front-loading, pulse count, and reactivation move outside or away from the shuffle references, while entropy stays unchanged—as it should for an order-insensitive quantity. - **Supported conclusion:** Sequence carries information beyond the increment multiset. The comparison does not identify why that ordering arose.

Challenge this result. If shuffling the same increments left every order-sensitive trait unchanged, Fire VASE would be encoding little beyond totals and increment distributions. Inspect the temporal-order challenge →

Evidence trail

ClaimObserved ordering carries information

FigureSupplementary Figure 2C · recorded N = 4,000

Analysis100 within-fire permutation replicates with invariants

ReproduceFigure script · notebooks

ValidateThreat, failure criterion, and result

PaperCurrent claim

0.541observed mean first-half allocation

0.500mean after temporal shuffling

1.249 vs 1.413observed vs shuffled detected pulses

0.038 vs 0.120observed vs shuffled reactivations

How well does it hold up?

One hundred replicates compare profile distances, trait distributions, landmark occupancy, and PCA summaries. Entropy remains unchanged by shuffling—as it should, because entropy ignores order. That invariant is a useful internal control on what the permutation changes.

What this does not show

The result does not prove that morphology is caused by biology, fuels, weather, suppression, or any other mechanism. The empirical tail tests are descriptive, have resolution 1/101, and are not multiplicity-adjusted. Positive normalized curves are constrained objects, so compression cannot carry the argument by itself.

Technical details

Read the null-model methods and frozen reanalysis evidence.