Lessons from the wild

Indy, one of the tagged cuckoos whose migration flights are being tracked, has done a remarkable thing.  See here for details.  En route for winter quarters in Africa, flying over the Mediterranean, Indy turned through 180 degrees to fly back to feeding grounds 850 miles away.  The observers in the study have concluded that the bird realised that her energy levels were too low for the next stage in the migration, and chose to return to the last landfall to feed and top up with energy.

It was a little surprising that the bird did not try to search for food closer to the southern Mediterranean.  However, I think there is a logical decision here.  One of the less frequented corners of the O.R. library of techniques is sequential search.  A model of sequential search divides the search area into sections, in each of which there is a prior probability of finding the item that is being sought.  For Indy, a simple model would say that there were two areas to seek food.  Area A, where the bird had recently fed, had a prior probability of 1 of finding food quickly.  Area B, everywhere else, was unknown, and Indy did not know for sure that food could be found quickly.  It was better to use energy flying back rather than use energy searching for a new food source closer by.  It's not the first case of birds using sequential decision making.  I wrote an article for schools which mentions the research that ornithologists have carried out about the behaviour of pied flycatchers, seeking a mate.  it's a variant of a secretary problem, one of optimal stopping.  African weaverbirds choose their mates based on the quality of the nests that potential partners have constructed.  Doubtless other birds have behaviour which can be recognised as sequential decision making in one form or another.

Many years ago, I had a call from an animal psychologist, who was curious to see if the sheep in his study were following optimal paths when grazing.  He had set up a succession of feeding stations and observed the animals as they moved between these stations.  The observations were repeated, day after day, to see whether the sheep did learn to follow an optimal path.  Sadly, that study came to nothing.

But we can add one piece of animal behaviour which may be an optimal path.  (Recall that in dynamic programming, and optimal paths in general, one needs to define "optimal".  Is it the shortest path, the quickest path, the cheapest path, the one with the highest probability of passing a good bar, or what?)  Several houses in the road where we live have two gateways.  I watched one of our urban foxes walk down the pavement, turn into one gateway, walk through the plants in the front garden, and walk out of the other gateway.  It came to the next house with two gateways and did the same.  Now, it was clearly not going by the shortest route, nor the quickest.  But, the path taken would be safer, because it was out of sight of the road, and it also offered an increased chance of finding food.  So, was this urban fox following a route to minimise being seen?  Or maximising the chance of food?  Or some combination of these (and possibly other objectives)?  Here's another area where biological behaviour can be interpreted as practical operational research.


  1. Models of "optimal" animal behavior need to be done (and interpreted) carefully. Long ago, a doctoral student from entomology took a nonlinear programming course from me. He brought me a journal article that used an NLP to model the predation pattern of a female spider surrounded by "patches" with varying prey densities. The authors used Lagrange multipliers to find the spider's optimal search.

    The student wanted to know if the authors had done their math correctly. (They had not; they'd failed to account for the nonnegativity of time spent in each patch ... charitably assuming the spider lacked a time machine.) Beyond that, though, the solution was not entirely informative. The model posed a time limit T, and the optimal solution spent time in each patch proportional to the prey density of that patch. This raises at least a couple of questions, one being how the spider knows in advance how much time she has. (Another is, as T -> 0, how she achieves the infinite speed needed to change patches.)

    1. Thank you Paul. I agree, the link between animal behaviour and O.R. is not always proven. As far as I can see, the evidence for mating behaviour among birds is quite sound (why pied flycatchers have been so well studied is not clear!). The story about the European cuckoo is fresh research; until last year, nobody knew where they wintered (Cameroon) and so the data on their migrations is still to be fully evaluated. However, the ornithologists had raised the question of the logic of turning back along the track that the bird had taken and had reached a conclusion based on comparisons with other observations.

      The fox story is my own observation (and one should never take a sample of one to be indicative of the population!)


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