Below are two Java applets intended to illustrate the improbability of life forms colonizing remote oceanic islands. These are gross simplifications but are fun to watch.
In these models, the green dot just above the center represents Hawaii. The blue ellipse is supposed to be the Pacific Ocean. The black background is supposed to look vaguely like the Pacific Rim land masses. The (1,000) yellow dots represent propagules moving around, perhaps toward Hawaii. The first model assumes that the propagules move randomly. The second one includes assumes that the movement is biased by typical wind directions. Clicking in a model suspends it. Clicking again sets it running again.
There is room for much improvement in these models. Oahu is not drawn to scale (but then neither are the propagules). Oahu is about 608 square miles and the area of the Pacific is about 640,000,000 square miles. Further geographic realism could involve including the effects of continents on both ocean and atmospheric circulation, and doing something to have velocities realistic, both in terms of the currents and the propagules. Biological realism might include species' life-spans, speeds, and the sex of potential colonizers, as well as the probability of finding suitable footing when hitting land.
For now, enjoy these.
The first model uses a simple "random walk" mechanism. In it, potential colonizers are started off at random locations along the edges of the map. At each time step, they each move to one of the adjacent locations (pixels) with equal probability. Their halting progress is sometimes called a "drunkard's walk". Anthopomorphizing and projecting just a little bit of intent onto these glowing dots often has one hoping for a successful landing.
For the sake of discussion, what do you think the odds are of any individual propagule hitting a specific pixel in this 600 x 400 pixel map?
The basic notion here was to include (albeit crudely) wind and ocean currents. This was done by slightly modifying the random walk model. Depending on the latitude, it was about twice as likely to move in one of the eight possible directions as in each of the others (2/9 vs 1/9). The latitudes were divided into six ranges, loosely based on Hadley Cells and the Coriolis effect, and the more likely direction in each range was:
|Latitude Range||Biased Toward:|
|90N - 60N||Southwest|
|60N - 30N||Northeast|
|30N - 0N||Southwest|
|0S - 30S||Northwest|
|30S - 60S||Southeast|
|60S - 90S||Northwest|
These give us something like directional biases for the Trade Winds, the Horse latitudes, and the Northern and Southern Westerlies. The result is that 'bands' of flotsam develop. One of these moving westward along the equator (the ITC), and two juddering about around the sub-polar lows at about 60 degrees north and south latitude. In this model, those bands tend to keep things away from Hawaii. Is this really realistic?
Would anyone like to help me add more realistic surface winds and currents?
Getting here is only part of the battle. Landed plants and animals would have to find suitable habitat, sustenance, and perhaps mates to establish breeding populations and colonize the island. (We could model that next.)
For now, just let these run and see how unlikely life on these islands really is.