A mathematical description of fossilization.

Fossils constitute an inestimable archive of past life on the Earth. However, the stochastic processes driving decay and fossilization and overwhelmingly distorting this archive, are challenging to interpret. Consequently, concepts of exceptional or poor preservation are often subjective or arbitrarily defined. Here, we offer an alternative way to think about fossilization. We propose a mathematical description of decay and fossilization relying on the change in the relative frequency and characteristics of biogenic objects (e.g. atoms, functional groups, molecules, body parts and organisms) within an organism-fossil system. This description partitions taphonomic changes into three categories: gain, loss and alteration of state. Although the changes undergone by organisms through decay, preservation and alteration vary a lot for different organisms under different conditions, we provide a unified formalism which can be applied directly in the comparison of different assemblages, experiments and fossils. Our expression is closely related to George R. Price's famous equation for the change in evolutionary traits and can be adapted to the study of palaeontological systems and many others.