Geometric speed limit for acceleration by natural selection in evolutionary processes

We derived a new speed limit in population dynamics, which is fundamental on the evolutionary rate. By splitting contributions of selection and mutation to rate, we obtained bound arbitrary observables, named bound, that can be tighter than conventional Cram\'er-Rao bound. Remarkably, much if contribution more dominant mutation. This tightness geometrically characterized by correlation between observable interest growth also numerically illustrate effectiveness transient dynamics processes discuss how test our experimentally.