This paper takes an alternative approach to the problem of inferring patterns of phenotypic evolution in the fossil record. Reconstructing temporal biological signal from noisy stratophenetic data is an inverse problem analogous to subsurface reconstructions in geophysics, and similar methods apply. To increase the information content of stratophenetic series, available geological data on sample ages and environments are included as prior knowledge, and all inferences are conditioned on the uncertainty in these geological variables. This uncertainty, as well as data error and the stochasticity of fossil preservation and evolution, prevents any unique solution to the stratophenetic inverse problem. Instead, the solution is defined as a distribution of model parameter values that explain the data to varying degrees. This distribution is obtained by direct Monte Carlo sampling of the parameter space, and evaluated with Bayesian integrals. The Bayesian inversion is illustrated with Miocene stratigraphic data from the ODP Leg 174AX Bethany Beach borehole. A sample of the benthic foraminifer Pseudononion pizarrensis is used to obtain a phenotypic covariance matrix for outline shape, which constrains a model of multivariate shape evolution. The forward model combines this evolutionary model and stochastic models of fossil occurrence with the empirical sedimentary record to generate predicted stratophenetic series. A synthetic data set is inverted, using the Neighbourhood Algorithm to sample the parameter space and characterize the posterior probability distribution. Despite small sample sizes and noisy shape data, most of the generating parameter values are well resolved, and the underlying pattern of phenotypic evolution can be reconstructed, with quantitative measures of uncertainty. Inversion of a stratigraphic series into a time series can significantly improve our perception and interpretation of an evolutionary pattern.

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