Mass-Gated Timing of the Pre-Spice Mass Transition: A Time-to-Event Analysis of Twenty-Three Sandtrout Aggregation Sequences, 10178–10224 AG

1. Introduction

The life cycle of Shai-Hulud was first set out systematically in the records of the Imperial Planetologists, Pardot Kynes and his son Liet-Kynes. In that account the sandtrout (the Fremen little makers) are the juvenile stage of the giant worm. They encapsulate free water, and the planet's surface dryness is their work. Where a body of water reaches the excretions of little makers deep under the sand, a fungoid growth called the pre-spice mass develops, ferments and builds gas until it erupts in a spice blow. Most sandtrout nearby perish in the eruption; the survivors encyst and later emerge as small worms.

This paper concerns only the first part of that sequence, from a visible aggregation of sandtrout to the blow that ends the pre-spice mass. We write from the Imperial era, in about 10246 AG, some decades after the Jihad of Muad'Dib, and all dates below are given in the Guild reckoning.

Survey observers have repeatedly noted that the interval between aggregation and blow is irregular. Two explanations are open. The transition might follow a fixed developmental programme, with the scatter arising from poor dating of onset. Alternatively, the transition might be gated by a quantity that accumulates at a rate set by the size of the aggregate, so that large aggregates reach it sooner. Earlier work by one of us described the field records but did not test these alternatives formally.

The membrane mechanism by which individual sandtrout take up water is relevant here, because it fixes how the uptake capacity of a colony scales with its size. Site conditions also matter: a comparative coring survey of open-erg sites found trace-element differences between sites that blew and sites where little makers gathered without result. We therefore treat soil and moisture conditions as site-level confounders and model the organism-level quantity that the field records can support, namely aggregate mass.

2. Methods

Sequences were drawn from the station logbooks and aggregation files of the Fremen Planetological Survey Archive at Sietch Tabr. A sequence qualified if an observer recorded the onset of a concentrated little-maker colony at a fixed location, described its extent, and returned to the location at least twice in the following year. Of 41 candidate files, 23 met these criteria. Onsets fall between 10178 and 10224 AG. Sequences from the planted basins of the greening programme were excluded, because dew precipitation there alters the moisture regime; every retained site lies in open erg.

Aggregate mass could not be measured directly. Observers recorded surface extent and, where soundings were taken, the depth band occupied by the colony. We converted these to mass with the packing coefficients tabulated in the Survey's field manual and rounded each estimate to the nearest 10 kg. Repeat descriptions of the same colony by different observers imply that an individual estimate is uncertain by roughly a factor of 1.3 in either direction. Such error in a predictor attenuates its estimated effect, so the slopes reported below are likely to be conservative. Across the 23 sequences, estimated mass had a mean of 840 kg (SD 560) and ranged from 120 to 2,100 kg.

Our outcome was the interval in standard months from recorded onset to the spice blow. The pre-spice mass itself develops underground and cannot be observed, so the blow serves as the observable end of the transition. Observers never sampled a developing mass, since the archive treats approach to a site in its final months as lethal. Five sequences ended without a blow, two because a station was abandoned and three because the observation window closed. The four censored aggregates under 500 kg had been followed for 74 to 96 months, and the single censored aggregate in the 500–999 kg band for 30 months. All five were treated as right-censored at the last recorded visit.

Each file also records the depth of the sequestered water stratum, sand moisture, surface temperature at onset and distance to the deep-erg margin. Stratum depth and moisture were available for only 14 of the 23 sequences, too few for adjusted modelling with 18 events.

For the primary analysis we fitted a Weibull accelerated-failure-time model with the base-2 logarithm of mass, centred at 850 kg, as its single covariate. The exponentiated coefficient is a time ratio per doubling of mass. The fixed-clock hypothesis corresponds to a model with no mass term, and we compared the two by likelihood ratio and by Akaike's information criterion. A Cox proportional-hazards model with the same log-mass covariate served as a check that did not depend on the Weibull form, and proportionality was assessed from scaled Schoenfeld residuals. For comparison with earlier descriptive work we also report a Pearson correlation between log mass and interval among the 18 sequences with a recorded blow, recognising that this complete-case figure ignores censoring. Secular drift in timing was tested by adding onset year to the accelerated-failure-time model using all 23 sequences, so that late onsets with short follow-up enter as censored observations and do not bias the comparison.

3. Results

Eighteen of the 23 sequences ended in a recorded blow. The Kaplan–Meier median interval for the whole archive was 41 months. Grouping sequences by estimated mass showed a clear gradient (Table 1). Among the eight lightest aggregates, only four blew within observation; because the four censored members of that band were all followed beyond 72 months, the Kaplan–Meier median for the band is 72 months, reached at its last recorded blow. All eight aggregates of 1,000 kg or more blew, with a median of 19 months.

In the accelerated-failure-time model each doubling of estimated mass multiplied the expected interval by 0.59 (95% CI 0.53–0.67; p < .001), a reduction of about 41%. The Weibull shape parameter was 3.2 (95% CI 2.2–4.6), indicating a hazard of blowing that rises steeply with time since onset. The model predicts median intervals of about 49 months at 500 kg, 33 months at 850 kg, 21 months at 1,500 kg and 17 months at 2,000 kg. We do not extrapolate below 250 kg, where most sequences were censored. On the same log-mass scale, the Cox model gave a hazard ratio of 4.9 per doubling (95% CI 2.4–10.1), close to the value of about 5.4 implied by the Weibull fit, and heavier aggregates therefore blew sooner. The residual test gave no evidence against proportional hazards (p = .48).

The fixed-clock model fitted the archive poorly. Adding mass to a mass-free Weibull model gave a likelihood-ratio χ²(1) of 47.9 (p < .001) and lowered the information criterion from 176.3 to 130.4. Among blown sequences the intervals ranged from 15 to 72 months, with a coefficient of variation of 0.50. Errors in dating onset, which the files suggest amount to a few months at most, cannot produce a nearly fivefold spread of that kind.

Among the 18 blown sequences, the complete-case correlation between log mass and interval was r = −0.83 (95% CI −0.93 to −0.59; R² = 0.69; F(1, 16) = 35.4), a strong inverse association. Onset year added to the accelerated-failure-time model had a time ratio of 1.04 per decade (95% CI 0.90–1.20; p = .59), and the mass coefficient was unchanged to two decimal places.

Thermal records offer a separate check on mechanism. Survey instruments registered subsurface temperatures above background at 14 blown sites, with a mean excess of 28 K (SD 8; range 14–44 K). We framed the check as a bound. Warming a kilogram of aggregate by 28 K at a specific heat near 1 kJ per kilogram per kelvin requires about 28 kJ. Assuming one litre of sequestered water per kilogram of aggregate, confining the heat to the aggregate alone and ignoring all loss to the surrounding sand, sequestration would have to release at least 28 kJ per litre to produce the mean anomaly, and at least 14 kJ per litre to produce the smallest. Qassem's calorimetric series on little-maker tissue measured an encapsulation enthalpy of 4.8 kJ per litre, with preparations ranging from 2.1 to 9.6 kJ per litre. That figure lies far below ordinary hydration energies because encapsulated water is held as bulk liquid within membrane pockets and forms few new bonds. Even the highest preparation falls short of the smallest recorded anomaly, and dissipation over months of accumulation would widen the gap.

4. Discussion

Across this archive, time to the blow depends strongly on how large the aggregation was, and a fixed-duration programme does not describe the record. The effect survives both parametric and semi-parametric treatment of censoring. Because mass estimates carry substantial error, the true dependence is probably somewhat steeper than the 0.59 time ratio we report.

A threshold-accumulation account explains the pattern most simply. If the transition requires that a colony gather a certain quantity of water, or of some product of its sequestration, before the mass can form, the time needed depends on the rate of accumulation. Sandtrout take up water by an active membrane process, so each individual contributes a limited rate. A colony's total rate then scales with its number of individuals, and so with its mass. The steeply rising hazard implied by the Weibull shape fits an accumulating quantity approaching a threshold. That threshold remains unmeasured, and the account is a hypothesis that fits the timing data; it is not an observed mechanism.

This bound weighs against proposals that water sequestration itself heats mass sites. Exothermic sequestration may occur, but at the measured encapsulation enthalpy it cannot produce warming of the size recorded. The fermentation and gas build-up that the planetological account attributes to the pre-spice mass itself is the more likely source. This conclusion depends on Qassem's value. Were encapsulation to bind water as tightly as ordinary hydration does, the required enthalpy would be exceeded many times over, so an independent calorimetric series is the decisive test.

For survey practice, repeated estimates of colony extent are worth more than a count of months since onset. Withdrawal should not be planned from the predicted median, since by definition half of aggregates blow before it. Using the 10th percentile of the fitted Weibull distribution, an aggregate estimated at 1,500 kg warrants withdrawal of observers and equipment within about 12 months of onset, and one of 500 kg within about 27 months. Because mass is underestimated as often as overestimated, stations should apply these figures to the upper end of a colony's plausible mass.

5. Limitations

Every mass in this study is an estimate derived from verbal and sketched descriptions of extent. The factor-of-1.3 uncertainty rests on few repeat descriptions, and packing coefficients may vary with sand type. We have corrected neither for this error nor for observer identity.

Censoring is assumed to be unrelated to the eventual outcome. That assumption may fail. Some sites where little makers gather never blow, and the coring survey found such sites chemically distinct from blow sites. If some of our five censored sequences were sites of that kind, a model that assumes every aggregate eventually blows will misstate the timing for small aggregates, which make up four of the five.

Site covariates were too incomplete for adjustment, so the association between mass and timing may be partly confounded by stratum depth or moisture. The archive also spans the years before and after the Jihad, when survey practice changed. The null onset-year term gives some reassurance on that point but does not exclude changes in which aggregations observers chose to follow. The thermal bound rests on assumed water content per kilogram and on one calorimetric series. Finally, the data end at the blow, and nothing here bears on encystment, the emergence of small worms or their later growth.