Wednesday, 1 February 2017

Games that Trees Play

I never expected to find the term "Game theory" in a book about trees, but - I was wrong.  Reading Max Adams' "The Wisdom of Trees" I read the following:
Seeds and their germination ... are hailed as an example of so-called game theory, whereby (in its biological context) evolution tests all possibilities to find successful strategies for an optimum number of best-fit species. (page 59)
I'm not happy with "so-called" applied to game theory - users of the subject know what it is, and because of my faith, I would be inclined to apply the mind of God to evolution as well, but the idea is intriguing.  Adams lists six characteristics of the seeds of trees which vary to fill niches in ecology: seed size; quantity of seeds; age of first production; method or means of distribution; how the seed germinates; frequency of seed production.  The OR person spots that four of those are numerical, even if slightly fuzzy. 

The author goes on to discuss some of the varied combinations of those six characteristics which may be observed with different species.  An oak tree produces medium to large seeds, in a quantity which is somewhere between the fine dust of tens of thousands of hazel seeds and the dozens of giant nuts of a coconut palm, and starts to produce when the tree is forty years old or more - while the fruit trees in my garden produce their first crop after four or five years.

The qualitative characteristics are extremely varied.  Seed that is spread by the wind, by birds which bury the nuts and forget (or die), by being buried until there is a fire or a flood.  There are so many possibilities, and so many subtle differences between them.  As a challenge, consider two native trees that you know growing close together, and see how they compete to survive.  (Theey ought to be native, because imported plants may not fit the ecological niche here that they belong to at home.)

Adams goes on to discuss yet another dimension to ecological niches; the variation from year to year in the number of edible seeds produced by trees.  This leads into another topic from OR - predator-prey models.  If a tree species produced the same number of seeds every year, then the population of a bird or animal that fed on those seeds would tend to a stable value by Lotka–Volterra models.  The predator would consume the harvest and there would be very few seeds left to be the potential for the next generation.  So trees do not yield similar crops every year.  In some years there is a bumper harvest for future plants and the predator species, in others, the predator may be starved.  The plum trees in my garden vary in their yield, partly through natural variation from the species, partly through my intervention in pruning, and partly through the random effect of climate at the time of the plum blossom.  And my story could be repeated over countless orchards and plantations of fruit. 

Now, what is the game theory approach to weeding my garden?


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