============================================================================== IGUANAS ON A RAFT: THE CLUB'S OWN FEASIBILITY CALCULATION Companion to Scarpetta et al. (2025) PNAS 122(12) e2318622122 master seed = 20250317 numpy = True Everything below is the club's simplified model, not the paper's analysis. The paper did the phylogenomics. We did the arithmetic. ============================================================================== ============================================================================== BLOCK 1 DRIFT TIME: HOW LONG IS THE VOYAGE? ============================================================================== Great-circle distance assumed : 8,000 km Path sinuosity factor (A1) : 1.35 Actual water distance travelled : 10,800 km Crossing time by current speed ------------------------------------------------------------------------------ case m/s km/day straight d with detour d months note slow 0.15 13.0 617.3 833.3 27.4 weak NEC limb, near the northern flank median 0.35 30.2 264.6 357.1 11.7 typical NEC / SEC surface speed fast 0.70 60.5 132.3 178.6 5.9 SEC core, plus windage on a canopied raft Comparison against a published drift estimate (not a validation) ------------------------------------------------------------------------------ Montenegro et al. (2008) model sweet-potato drift trajectories across the tropical Pacific and report transit times of 80-120 days for comparable distances in their fastest current. That is a different object (a tuber, not a raft carrying a lizard) on a different route, so this is a plausibility comparison, not an independent check of this model: nothing here is computed from a second, unrelated method. Our fast case lands at 179 days, which is 1.49x the top of that range, not inside it. We report the gap honestly rather than rounding it away. Plausible reasons a raft could run slower than a semi-submerged tuber include more wind and wave drag, a longer effective path than the great circle sinuosity factor assumes, and current speed varying along the route rather than sitting at the single fastest value used here. ============================================================================== BLOCK 2 ENERGY: HOW LONG CAN IT GO WITHOUT EATING? ============================================================================== Body mass (A3) : 70 g Air temperature along route : 27.0 C Body temperature on raft (A8) : 28.5 C Reptile FMR allometry 0.196*M^0.889 : 8.56 kJ/day at 30 C Resting fraction (A4) : 0.40 Q10 correction 30 C -> 28.5 C : 0.8716 Resting metabolic rate on the raft : 2.985 kJ/day Fat store 10% of mass, 80% usable, 39.3 kJ/g Usable energy reserve : 220.1 kJ SURVIVABLE DAYS WITH NO FOOD : 73.7 days Fat burned per day : 0.0759 g/day Fasting endurance against the three crossing times ------------------------------------------------------------------------------ case voyage d fast-only d shortfall d verdict slow 833.3 73.7 759.6 STARVES median 357.1 73.7 283.4 STARVES fast 178.6 73.7 104.8 STARVES The raft as food: a herbivore is eating its own vehicle ------------------------------------------------------------------------------ slow 833.3 d needs 2487.3 kJ = 710.7 g dry foliage (10.15 x its own body mass) median 357.1 d needs 1066.0 kJ = 304.6 g dry foliage ( 4.35 x its own body mass) fast 178.6 d needs 533.0 kJ = 152.3 g dry foliage ( 2.18 x its own body mass) A single uprooted tree carries kilograms of leaf. Energy is not the wall, provided the vegetation is alive and the animal is a herbivore. A carnivore on the same raft has nothing to eat but the raft's other passengers, and runs out. Block 2b: how long does the raft have to keep feeding it? ------------------------------------------------------------------------------ Mass of foliage is not the constraint. Freshness is. Model the raft as supplying phi(t) = exp(-t/TAU) of the daily requirement (A12), so the animal draws burn*(1 - phi) from fat. Solve for the TAU at which fat runs out exactly at landfall. case voyage d critical TAU d meaning slow 833.3 4427.1 raft must stay edible on this timescale median 357.1 741.3 raft must stay edible on this timescale fast 178.6 151.4 raft must stay edible on this timescale Read that carefully, because it is the most awkward number we found. Even in the fast current the raft has to go on being worth eating on a 151-day timescale, most of the length of the crossing. On the slow current it has to be 4427 days, which is not a raft, it is a small floating island with a working food web. The vegetation cannot be ballast. It has to be alive, or dead in a way a hindgut fermenter can still use. ============================================================================== BLOCK 3 WATER: HOW LONG WITHOUT A DRINK? ============================================================================== Air temperature : 27.0 C Relative humidity : 80% Skin temperature : 28.5 C Saturation density at skin : 27.91 g/m3 Vapour density of marine air : 20.55 g/m3 Vapour density deficit : 7.35 g/m3 Skin area 10*M^(2/3) : 169.8 cm2 Skin resistance (A7) : 300 s/cm Daily water ledger, grams ------------------------------------------------------------------------------ cutaneous evaporation -0.3596 respiratory evaporation -0.0354 urine and faeces -0.1343 metabolic water (credit) +0.0813 .............................................................................. NET LOSS -0.4480 g/day Total body water 70% of mass : 49.00 g Tolerable deficit at 25% loss : 12.25 g SURVIVABLE DAYS WITH NO WATER : 27.3 days Cutaneous loss is 68% of gross loss. The animal is leaking through its skin, slowly, and nothing else is close. Sensitivity: the water clock against air temperature ------------------------------------------------------------------------------ T air C T skin C deficit g/m3 net g/day days dry 24 25.5 6.26 0.3694 33.2 26 27.5 6.97 0.4200 29.2 27 28.5 7.35 0.4480 27.3 28 29.5 7.75 0.4781 25.6 30 31.5 8.60 0.5452 22.5 32 33.5 9.54 0.6229 19.7 34 35.5 10.55 0.7134 17.2 36 37.5 11.66 0.8195 14.9 Warm air is what kills, and it kills through the vapour deficit rather than through metabolism. Between 27 C and 36 C the dry-survival window falls from 27.3 days to 14.9 days. Sensitivity: body mass ------------------------------------------------------------------------------ mass g RMR kJ/d fat kJ fast d net H2O g/d dry d 20 0.980 62.9 64.2 0.1850 18.9 40 1.815 125.8 69.3 0.3014 23.2 70 2.985 220.1 73.7 0.4480 27.3 120 4.820 377.3 78.3 0.6579 31.9 200 7.590 628.8 82.8 0.9489 36.9 350 12.482 1100.4 88.2 1.4213 43.1 Bigger is better on both clocks, because reserves scale with mass and losses scale with surface area. A 350 g animal is a better boat than a 20 g one by roughly a factor of two on water and three on fuel. Monte Carlo: does rain on the raft rescue the voyage? ------------------------------------------------------------------------------ seed = 611, trials per cell = 20000, raft treated as food = yes Rain is an independent daily Bernoulli draw (A9). A drinking bout restores at most 12% of body mass in water (A10). p(rain) slow median fast 833 d 357 d 179 d .............................................................................. 0.00 0.0000 0.0000 0.0000 0.05 0.0000 0.0002 0.0174 0.10 0.0034 0.1051 0.3411 0.15 0.2423 0.5544 0.7642 0.20 0.7170 0.8727 0.9372 0.25 0.9364 0.9726 0.9872 0.30 0.9890 0.9958 0.9976 0.40 0.9998 0.9999 1.0000 0.50 1.0000 1.0000 1.0000 Read the zero row first. With no rain at all, every crossing kills the animal, at every current speed, without exception. The voyage is only possible because the route runs through the wettest air on the planet. Where the survivable window actually is ------------------------------------------------------------------------------ Minimum rainfall frequency for a 50% and a 90% chance of arrival, by current speed, at 27 C. case voyage d p for 50% p for 90% rain days/yr at p50 slow 833 0.18 0.24 66 median 357 0.15 0.21 55 fast 179 0.12 0.18 44 For scale: the Intertropical Convergence Zone and the South Pacific Convergence Zone, which sit across this route, deliver rain on a large fraction of days year-round. A raft crossing the tropical Pacific is not crossing a desert. It is crossing a rainforest with no floor. Deterministic voyage log at the median current (no rain, worst case) ------------------------------------------------------------------------------ day km route % water left % fat left % state 0 0 0.0 100.0 100.0 adrift 30 672 8.4 0.0 59.3 dead of thirst 60 1344 16.8 0.0 18.6 dead of thirst 90 2016 25.2 0.0 0.0 dead of thirst 120 2688 33.6 0.0 0.0 dead of thirst 180 4032 50.4 0.0 0.0 dead of thirst 240 5376 67.2 0.0 0.0 dead of thirst 300 6720 84.0 0.0 0.0 dead of thirst 357 7997 100.0 0.0 0.0 dead of thirst This is the pessimistic log: no rain, nothing edible. The water clock stops the voyage before the first tenth of the route is behind it. Voyage log: one seeded crossing, median current, 15% of days rainy ------------------------------------------------------------------------------ TAU_LEAF = 900 d (A12). Seed for this single voyage = 7711. Water reserve is what remains of the tolerable dehydration deficit. Energy reserve is what remains of the usable fat store. day km route % water % energy % log entry 1 22 0.3 96.3 100.0 adrift 36 806 10.1 78.1 99.0 adrift 72 1613 20.2 52.5 96.1 adrift 108 2419 30.2 92.7 91.5 adrift 143 3203 40.0 78.1 85.3 adrift 179 4010 50.1 100.0 77.3 adrift 215 4816 60.2 100.0 67.6 adrift 250 5600 70.0 70.7 56.8 adrift 286 6406 80.1 70.7 44.2 adrift 322 7213 90.2 88.1 30.2 adrift 358 8000 100.0 52.5 14.8 landfall rainy days on this crossing : 53 of 358 (14.8%) longest dry run : 23 days (lethal at 27.3) water reserve at landfall : 52.5% energy reserve at landfall : 14.8% outcome : ARRIVED [Block 4 input] survival at median current (357 d), p(rain)=0.15, 40000 trials: 0.5545 ============================================================================== BLOCK 4 DEEP TIME: NEAR-IMPOSSIBLE, DIVIDED BY THIRTY-FOUR MILLION YEARS ============================================================================== Per-voyage success is a product of four terms (A11). raft still afloat and vegetated at the far end 0.0200 animal survives water and energy budget 0.5545 raft actually intersects Fiji rather than ocean 0.0100 founding propagule viable (gravid female, or 2+) 0.0500 .............................................................................. PER-VOYAGE SUCCESS PROBABILITY q 5.545e-06 that is one voyage in 180,343 Expected waiting time for one successful colonisation ------------------------------------------------------------------------------ launches/century successes/century wait, centuries wait, Myr 0.1 5.545e-07 1,803,427 180.34 1.0 5.545e-06 180,343 18.03 5.0 2.773e-05 36,069 3.61 10.0 5.545e-05 18,034 1.80 50.0 2.773e-04 3,607 0.36 100.0 5.545e-04 1,803 0.18 Probability of at least one arrival inside the phylogenetic window ------------------------------------------------------------------------------ Window taken as 34 Myr (median split) and 42 Myr (upper interval). launches/century expected arrivals P(>=1) 34 Myr P(>=1) 42 Myr 0.1 0.189 0.1718 0.2078 1.0 1.885 0.8482 0.9026 5.0 9.427 0.9999 1.0000 10.0 18.853 1.0000 1.0000 50.0 94.265 1.0000 1.0000 100.0 188.530 1.0000 1.0000 The same fact said three ways ------------------------------------------------------------------------------ At 10 launches per century over 34 Myr, 3,400,000 rafts set out. At q = 5.545e-06, 18.85 of them are expected to succeed. Probability at least one does: 1.0000 A voyage that fails 99.99945% of the time is a near-certainty if you run it three million times. Deep time is not a long wait. It is a large sample. How hard is the conclusion? Sweep q over three orders of magnitude ------------------------------------------------------------------------------ q one in arrivals in 34 Myr P(>=1) (10 launches/century) 5.545e-08 18,034,265 0.189 0.1718 5.545e-07 1,803,427 1.885 0.8482 2.773e-06 360,685 9.427 0.9999 5.545e-06 180,343 18.853 1.0000 1.109e-05 90,171 37.706 1.0000 5.545e-05 18,034 188.530 1.0000 5.545e-04 1,803 1885.300 1.0000 A ten-fold pessimism about q still leaves an 85% chance of at least one arrival. A hundred-fold pessimism drops it to 17%, and that is where the conclusion finally becomes fragile. Everything hangs on q to within about two orders of magnitude, and q is a guess. ============================================================================== SUMMARY OF THE NUMBERS THE ARTICLE QUOTES ============================================================================== voyage, slow current 833 days voyage, median current 357 days voyage, fast current 179 days fasting endurance, 70 g, 28.5 C 73.7 days dry endurance, 70 g, 27 C 27.3 days net water loss 0.4480 g/day resting metabolic rate 2.985 kJ/day usable fat store 220.1 kJ survival, median + 15% rain 0.5545 critical raft-food TAU, median 741 days critical raft-food TAU, fast 151 days voyage-log landfall water/energy 52.5% / 14.8% Reproduce with: python analysis/iguana-raft.py