Evidence for pattern development; power laws (Introduction)

by David Turell , Sunday, November 08, 2015, 16:16 (3303 days ago) @ David Turell

Much of our reality can be understood in mathematics. Einstein's theories showed this beautifully. Now an ecologist shows this in his article:-http://nautil.us/issue/29/scaling/the-hidden-power-laws-of-ecosystems-"Brown and Maurer had been influenced heavily by regularities in many ecological phenomena. One of these, called the species-area curve, was discovered back in the 19th century, and formalized in 1921. That curve emerged when naturalists counted the number of species (of plants, insects, mammals, and so on) found in plots laid out in backyards, savannahs, and forests. They discovered that the number of species increased with the area of the plot, as expected. But as the plot size kept increasing, the rate of increase in the number of species began to plateau. Even more remarkable, the same basic species-area curve was found regardless of the species or habitat. To put it mathematically, the curve followed a power law, in which the change in species number increased proportionally to the square root of the square root of the area.-***-"Bacteria seemed like the obvious subject, partly because they're incredibly abundant, and partly because DNA sequence data gives us a window into their evolutionary history. Our plan was to count numbers of species, just as was done in species-area curves. But instead of area, we'd use some measure of time.-"We constructed that measure by comparing DNA sequences among our bacteria, and drawing trees of life. Each branch of a tree represented a new bacterial lineage—some kind of diversification of life deep in the past. The average evolutionary distance (or branch length) between the species on the tree quantified their relatedness through time. The microbes we sampled came from about 25 different habitats, including the nasal cavity of humans, human feces, the surface of plant leaves, the Antarctic Ocean, and water from the English Channel.-***-"When we plotted average evolutionary distance against species number, we found the power law lurking in yet another dimension of ecology: The distance increased rapidly at first, then began to slow in the same manner as the species-area curve. The reasons for this behavior are not clear at the moment. One possibility is that both spatial and temporal scaling behaviors are affected by a “burstiness,” in which periods of stasis are punctuated by rapid periods of diversification. In our bacterial trees we found that these bursty expansions have a fractal distribution, also described by a power law, and they could point to radiations of species through both time and space.-"The power laws we see for evolutionary distance and diversification point once again to a simple, mechanistic, and relatively detail-free view of ecology at the biggest scales. They're just not quite as simple as what has been proposed for spatial patterns. They take at least one step back down the spectrum toward needing real ecological and evolutionary mechanisms to explain macroecological patterns."-Comment: What if God is really a mathematician. It sure looks that way.