Connecting fitness landscapes with trait distribution reshaping

Of central importance to evolutionary dynamics is the relationship between the traits and the fitness of an organism, which drives natural selection and changes population structure over time. The Price equation offers a mathematical description connecting these quantities; using the equation, the change in population trait mean can be calculated across generations. However, using the equation requires a priori characterization of the fitness landscape. In many cases this is not known, especially when it could take nontrivial, e.g. nonmonotone, shape. We present a method for determining how trait distribution reshaping relates to the underlying fitness landscape, estimated as a polynomial function. We show generalized Price relations that predict the change in higher-order moments of a population characteristic across generations. We then invert the problem to determine the fitness landscape from the observed changes via a linear system of equations. To determine the landscape to nth polynomial order it suffices to measure the change in the first n moments of the population trait distribution.