!VAR HAGENDOORN

Fish Trajectories

In chapter 20 of "The Ancestor's Tale" Richard Dawkins tells the cichlid's tale. It turns out that there are between 200 and 500 endemic cichlid species in Lake Victoria. Yes, the world is full of surprising facts. The Lake Victoria cichlids are completely different from Lake Malawi cichlids, which are completely different from Lake Tanganyika cichlids. What is even more interesting though from an evolutionary point of view is that Lake Victoria is only about 100,000 years old. How did so many species emerge in such a short period of time within a confined area?

As Dawkins writes from the fish's point of view there are lots of 'islands' within a large lake defined by underwater ridges. Although the fish could swim all across the lake they like to stay within a certain area where they can feed on the algae that live on the ridges. As the water level in Lake Victoria decreased from time to time, these 'islands' became separated from the rest of the lake creating the conditions for speciation. Then as the water level rose again some fish would spread all over the lake again.

This set me thinking. For how do fish in the oceans move about? Do they also stay within a confined area? It could be that they stay within certain temperature zones. Some fish and whales are migratory, that I know. But then what pattern do they follow when they are just swimming around? I consulted the invaluable Mathematical Biology by J.D. Murray, but it doesn't have a chapter on spatial movement. Perhaps this is because the answer is trivial. They can't follow a random walk, else they wouldn't get very far from where they start, so they must follow some kind of a Lévy flight within a bounded space. But fish can move up and down, they don't stay on a plane, so it would be a 3 dimensional Lévy flight.

It turns out my intuition made sense, since others had thought of this before, except that after a brief search I came across this article from Nature (2007), Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer, which disputes earlier findings that the data are described by a Lévy flight. But if these animals don't follow a Lévy flight, then which model best describes their behavior? It must be somewhere between random walk and Lévy flight.

The chapter by Richard Dawkins reminded me how little I actually know about the world I live in. These findings remind me how little is actually known.

The Ancestor's Tale is a dazzling book by the way. I wish there were more illustrations, so I wouldn't have to google every animal that I've never heard of.