Thursday, November 18, 2010

On optimal foraging, cod larvae and robot vacuum cleaners

On Monday I took part in a meeting of the Complex Systems Dynamics (CoSyDy) network in Warwick. The theme of the meeting was Movement in models of mathematical biology, and I heard amazing talks about (modelling) albatross flight patterns, e-coli locomotion, locust swarming and the spread of epidemics. (My contribution was about modelling an artificial system - a robot swarm.) Although a good deal of the maths was beyond me, I was struck by a common theme of our talks that I'll try and articulate in this blog post.

The best place to start is by (badly) paraphrasing a part of Jon Pitchford's brilliant description of optimal foraging strategies for cod larvae. Cod larvae, he explained, feed on patches of plankton. They are also very small and if the sea is turbulent the larvae have no chance of swimming in any given direction (i.e. toward a food patch), so the best course of action is to stop swimming and go where the currents take you. Of course the food patches also get washed around by the current so the odds are good that the food will come to you anyway. There's no point wasting energy chasing a food patch. Only if the sea is calm is it worthwhile for the cod larvae to swim toward a food patch. Thus, swim (toward food) when the sea is calm, but don't swim when it's rough, is the optimal foraging strategy for the cod larvae.

It occurred to me that there's possibly a direct parallel with robot vacuum cleaners, like the Roomba.  A robot vacuum cleaner is also foraging, not for food of course, but dirt in the carpet. For the robot vacuum cleaner the equivalent of a rough, turbulent, sea is a room with chaotically positioned furniture. The robot doesn't need a fancy strategy for covering the floor: it just drives ahead and every time it drives up to a wall or piece of furniture it stops to avoid a collision, makes a random turn and drives off again in a straight line. This is the robot's best strategy for reasonable coverage (and hence cleaning) of the floor in a chaotic environment (i.e. a normal room). Only if the room was relatively large and empty (i.e. a calm sea) would the robot (like the cod larvae) need a more sophisticated strategy for optimal cleaning - such as moving in a pattern across the whole area to try and find all the dirt.

Robot vacuum cleaners, like cod larvae, can exploit the chaos in their environment and hence get away with simple (i.e. stupid) foraging strategies. I can't help wondering - given the apparently unpredictable current economic environment - if there's really no point governments or individuals trying to invent sophisticated economic strategies. Perhaps the optimal response to economic turbulence is the KISS principle.


  1. In the case of companies in an economy or individuals in a group if the environment is quite unpredictable then it might be advantageous for the individual agents to simplify their behaviour or signal their intentions more unambiguously, allowing them to focus more of their resources on dealing with the environment and less on interpreting the actions of others.

  2. Thanks, Alan. Not often I see my name and brilliant in the same sentence, I’m printing it and framing it before you make any edits.

    I think I agree with your logic re. foraging, but moving the analogy towards social and economic systems isn’t necessarily easy. My foraging fish larvae are almost certain to die anyway, and natural selection is very happy about this - they end up following a high risk strategy (so-called risk sensitive foraging, or George Orwell’s miners having sugar in their tea). Governments do mind if large numbers of businesses fail, or if lots of individual people die, so it’s possible that the selection pressure is rather different. Nature isn’t always fussed about reliability and resilience in systems. This is something I’d like time to think more coherently about.

    Re. groups, information, and communication, Edd Codling and Steve Simpson and I once asked how fish might use the “many-wrongs principle” to navigate as groups. We all want to swim to the reef, we all get noisy information as to its location, and we’re all imperfect at orienting ourselves. If we go as a group then we average out our navigational deficiencies and get there quicker (therefore less chance of being eaten en route, good news for the fish). Big deal. But what was interesting was that when the ocean was really turbulent it was a BAD idea to be in a group - trying to follow a load of confused idiots is harmful even though they’re going the right way on average. In turbulent times it was best to forget the group, go it alone, and hope for the best.

    Anyroadup, it’s late on a Friday afternoon…

  3. Thank you Bob and Jon for your comments.

    Jon: thanks especially for further clarifying the 'high risk' strategy of fish larvae. Your very interesting description (and ref) of collective navigation in fish shoals clearly offers a much better (or at least more satisfying-to-the-cynical analogy) for economic systems in turbulent times.