What happens when the modern evolutionary theory of punctuated equilibrium collides with the older theory of mosaic evolution? That's the issue addressed by paleobiologists Melanie J Hopkins at the Museum fuer Naturkunde Berlin and Scott Lidgard at the Field Museum in Chicago.  

While processes of evolution are largely studied by observation and experiment in the living world, evolutionary tempo and mode – rates and patterns of change, respectively – are mostly revealed by studying the fossil record.

Paleontologists measure parts of the hard skeletal fossil remains of once-living organisms that they believe best represent the morphology, or form, of those organisms and then analyze the variation in these traits through successive layers of rock that were laid down over longs spans of geologic time in order to determine the tempo and mode of species evolution.

Punctuated equilibrium postulates that most evolutionary change takes place in relatively short periods of time during the origination of new species, while species themselves mostly undergo stasis, or little change, over longer periods. Mosaic evolution is the tendency for different parts within species to evolve in different ways or at different rates. 
Several recent studies have indicated that stasis is much more common than gradual directional change in the fossil record.

A new study based on data taken from hundreds of sequences of fossil samples previously reported in the scientific literature compared models describing different modes of change, namely stasis, random change, and directional change, to each fossil series and found that different traits generally showed different, conflicting evolutionary modes within the same species. Many kinds of life were represented, including mammals, fish, mollusks, arthropods, and single-celled organisms.

This large comparative study validates the ubiquity of mosaic evolution but also raises questions about the evidence for different evolutionary modes, since the great majority of previous studies that quantify stasis, punctuated equilibrium, and gradual or "random" patterns in the fossil record are based on measurements of single traits, not on combined analyses of many traits.

 Further research will be required to establish the underlying processes driving the patterns of mosaic evolution and fossil species change.