Inferring phenotypic evolution in the fossil record by Bayesian inversion

Paleontological reconstructions of phenotypic evolution are based on highly incomplete data, comprised of morphological measurements from stratigraphic successions of fossil samples, referred to as stratophenetic series. This thesis presents an analytical method that recognizes stratophenetic series as a stratigraphic rendition of an underlying time series and evaluates the uncertainty involved in its reconstruction. This method can significantly improve the way we perceive and interpret evolutionary patterns in the fossil record.; Chapter 1 provides a literature review, highlighting some important analytical challenges and micropaleontological case studies. Chapter 2 presents a numerical model that simulates stratophenetic series by combining a sedimentary basin-fill model with stochastic paleobiological models. Numerical experiments show (1) the detrimental effects of sampling and depositional architecture on observed patterns, and (2) the inability of common statistical tests to correctly identify evolutionary mode.; Chapter 3 formulates the inference of pattern from stratophenetic series as an inverse problem, the solution to which is defined as a Bayesian posterior probability distribution (PPD) obtained by direct Monte Carlo sampling of the parameter space, and evaluated with Bayesian integrals. This inversion method is illustrated with Miocene stratigraphic data from an ODP borehole and a synthetic stratophenetic data set. Despite small sample sizes and very noisy data, most parameters can be resolved, and the generating model of phenotypic evolution can be reconstructed, with quantitative measures of uncertainty.; Chapter 4 expands the Bayesian inversion to perform model comparison, and applies the technique to a stratophenetic series of Miocene Pseudononion pizarrensis from ODP Leg 174AX cores Bethany Beach (Delaware) and Ocean View (New Jersey). P. pizarrensis shows subtle changes in the mean shape of its peripheral outline, associated with final whorl expansion. Different principal components of shape variation show different patterns, including directional change, stasis, and ecophenotypy. Several important caveats are discussed. The model comparison technique evaluates the relative merit of different models (multiple working hypotheses) by quantifying their relative predictive ability, or weight. These weights are used to sample the joint PPD for all the models, and multimodel inference is then used to reconstruct the best supported temporal pattern of mean shape evolution.