[math-fun] A Quercus point with Geo-location
According to science news articles, in order to accomplish their yearly dismissals, deciduous trees have specially-evolved abscission cells. The release of used-up leafs is not a passive firing, rather it is an active process involving climate-dependent chemical signals. Naively we could hypothesize that the spatial distribution of active abscission cells is uniform random on the entire canopy volume at every instant of time; however, a walk around the block, and I could easily find many counterexamples--especially oaks, including the Pin Oak (Quercus Palustris). Here is a picture taken today, of tree T1438 (with a day moon in the background, and now with GPS metadata, cool!): https://0x0.st/z3Ma.jpg https://0x0.st/z3Mm.png Most of the tree remains green, but already a few branches have gone entirely bare. Then there are a few working groups of mostly bronze color, which seem likely to fall soon. This data suggests that distribution function for chemical signalling is highly correlated on the small scale of a single leaf, but remains at least partially random on the large scale of the entire tree. It seems impossible to derive chemical equations of motion and the ensuing statistics, but still I am curious, is there a better available empirical explanation as to what the signals are, where they come from, and how they flow through the tree's network of branches? And how much do these effects depend on species? --Brad [1] https://www.npr.org/templates/story/story.php?storyId=114288700 [2] https://www.esf.edu/pubprog/brochure/leaves/leaves.htm
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Brad Klee