INTERACTIVE COMPANIONFIELD NOTEBIOGEOGRAPHY

The Voyage Simulator

A live model accompanying “Eight Thousand Kilometres on a Raft of Weeds”

← Read the full articleThe same model in Python

Study: Field note
Review: Peer-edited by the club review board
Article: 12 sectionsabout 34 min
Files: LaTeX source34 kB
Analysis code33 kB
Raw output16 kB

Fiji's iguanas are sister to the desert iguana of the Mojave, which means their ancestors crossed more than 8,000 km of open Pacific on floating vegetation. The paper that established the relationship did the genomics. It did not ask whether an animal could physically survive the trip. We did, and the two calculators below are that arithmetic, made adjustable.

Both are the club's own simplified model rather than the paper's analysis. Every number printed here can be checked by hand against the equations beside it, and the defaults reproduce the figures quoted in the article exactly.

Model 1. Launch a raft

Set the current, the animal, the weather. Press launch and watch the two reserves run down. Water is the fast clock and energy is the slow one, and the raft itself is food, so the fat only starts falling once the vegetation stops being worth eating.

Rain is the whole game. A dry raft kills the animal in under a month at every current speed we tried. Start at the defaults, press launch a few times, and then pull the rainfall slider down to 0.05 and watch what happens.

Current speed0.35m/s0.35 m/s is a typical surface speed for the North and South Equatorial Currents, and it gives a 357-day crossing. Push it to 0.70 for the core of the South Equatorial Current with a bit of windage, which halves the voyage to 179 days. Drop it to 0.15 and the crossing takes 833 days, which almost nothing survives.Body mass70gA mid-sized adult desert iguana is about 70 g. Bigger is better on both clocks, because reserves scale with mass while losses scale with surface area. Try 350 g and watch the dry-survival window go from 27 days to 43.Rain, fraction of days0.15The route crosses the Intertropical Convergence Zone, the rainiest belt on the planet. At 0.15 the animal has roughly a coin-flip chance at the median current. Set it to 0 and the voyage becomes impossible no matter what else you do.Air temperature27°CWarmth kills through the vapour deficit rather than through metabolism. Every extra degree widens the gap between the water in the skin and the water in the air. At 36 °C the dry window falls to under 15 days.

voyage: –dry survival: –fasting limit: –net water loss: –

Press launch.

resting metabolic rate: –
usable fat store: –
tolerable water deficit: –
vapour density deficit: –
dry foliage needed: –

The two budgets underneath the animation are these. Resting metabolism follows the reptile field-metabolic-rate allometry, scaled to 40% for an animal that is not foraging and corrected for temperature:

\text{RMR} = 0.40 \times 0.196\,M^{0.889} \times 2.5^{(T_b - 30)/10}\ \text{kJ day}^{-1}

and evaporative loss through the skin is the vapour density difference across a diffusion barrier of resistance $r = 300$ s/cm over an area $A = 10M^{2/3}$ :

\dot{m}_{\text{cut}} = \frac{A\left[\rho_{\text{sat}}(T_s) - \text{RH}\,\rho_{\text{sat}}(T_a)\right]}{r}

At the defaults those give 2.985 kJ per day and a net loss of 0.4480 g of water per day, which is exactly what the article quotes. The 70 g animal carries 220.1 kJ of usable fat and 12.25 g of water margin, so it fasts for 73.7 days and dehydrates in 27.3.

Model 2. The deep time lottery

Suppose the crossing really is close to impossible. An almost-impossible event with millions of chances is a different kind of object from an almost-impossible event with one.

Let $\lambda$ be the number of rafts per century that leave North America with an iguana aboard and enter the westward current system, and let $q$ be the probability that any one voyage ends with a breeding population on Fiji. Successful colonisations then arrive as a Poisson process with rate $\lambda q$ per century, and the expected wait between them is $1/(\lambda q)$ .

Set the two sliders and press the button. Ten million years will go past. Try the defaults first, then push $q$ two decades lower and see whether the lineage still gets across.

Rafts launched per century10Nobody knows this number. A coastline with hurricanes and flooding rivers plausibly launches many vegetation rafts a century, but only a fraction carry an iguana and enter the right current. Ten is our working guess. Drop it to 1 and the expected wait becomes 18 million years.Survival probability per voyage5.545e-6The slider moves our baseline

q

by powers of ten. At the default it sits at 5.545 × 10⁻⁶, one crossing in 180,343. Slide it to −1 for ten-fold pessimism and the argument still holds. Slide to −2 and it finally breaks.Window10.0MyrThe phylogeny allows about 34 million years between the split from Dipsosaurus and the present. Ten is the default here because it is a stingier test. Set it to 34 to see the window the paper actually gives you.

rafts launched: –expected arrivals: –arrivals this run: –expected wait: –

Press the button.

At the defaults, ten launches per century over ten million years is 1,000,000 rafts, and 5.545 of them are expected to succeed. Stretch the window to the 34 million years the phylogeny allows and the expectation rises to 18.85, which is the number quoted in the article. The expected wait between successes is 18,034 centuries, or 1.80 million years. Absurd on a human scale. Unremarkable on a geological one.

One warning about Model 2, and it matters. Three of the four terms in our $q$ are guesses rather than calculations: the chance that a raft is still afloat and vegetated at the far end, the chance that it intersects Fiji rather than empty ocean, and the chance that whatever steps ashore can found a population. Only the animal's own survival comes out of a model. The slider exists so you can register your own scepticism about the other three.