Time and Knowability in Evolutionary Processes (1301.6470v2)

Abstract: Historical sciences like evolutionary biology reconstruct past events by using the traces that the past has bequeathed to the present. The Markov Chain Convergence Theorem and the Data Processing Inequality describe how the mutual information between present and past is affected by how much time there is in between. These two results are very general; they pertain to any process, not just to the biological processes that occur in evolution. To study the specifically biological question of how the present state of a lineage provides information about its evolutionary past, we use a Moran process framework and consider how the kind of evolutionary process (drift, and selection of various kinds) at work in a lineage affects the epistemological relation of present to past.