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Stationary Gaussian

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STATIONARY GAUSSIAN.
Western end of the Matadero Trail, looking east.

Evolution of a trait along a branch of a tree is often modeled as Gaussian, so that the difference between a random value of a trait for a descendant taxon conditional on a fixed value for its ancestral taxon follows a Gaussian distribution. In a Gaussian process that is stationary, the value in the descendant taxon depends on the length of the branch connecting the ancestor and descendant, and not on the particular starting time and ending time for the branch. The Gaussian distribution has a bell shape.

Photo: Noah Rosenberg, July 28, 2018