Cope's rule, named after American paleontologist Edward Drinker Cope, postulates that population lineages tend to increase in body size over evolutionary time. It was never actually stated by Cope, although he favoured the occurrence of linear evolutionary trends. It is sometimes also known as the Cope–Depéret rule, because Charles Depéret explicitly advocated the idea. Theodor Eimer had also done so earlier. (that he apparently had not read) from the English translation of Depéret's book. though it is possible that this perception may be a result of sample bias. If such a niche is already occupied, competitive pressure may oppose the directional selection.
Validity
Cope recognised that clades of Cenozoic mammals appeared to originate as small individuals, and that body mass increased through a clade's history. In other words, the maximum size increases, but the minimum size does not; this is usually a result of size varying pseudo-randomly rather than directed evolution. This does not fall into Cope's rule sensu stricto, but is considered by many workers to be an example of "Cope's rule sensu lato".
However, many palaeobiologists are skeptical of the validity of Cope's rule, which may merely represent a statistical artefact. Purported examples of Cope's rule often assume that the stratigraphic age of fossils is proportional to their "clade rank", a measure of how derived they are from an ancestral state; this relationship is in fact quite weak. Counterexamples to Cope's rule are common throughout geological time; although size increase does occur more often than not, it is by no means universal. For example, among genera of Cretaceous molluscs, an increase in size is no more common than stasis or a decrease. In many cases, Cope's rule only operates at certain taxonomic levels (for example, an order may obey Cope's rule, while its constituent families do not), or more generally, it may apply to only some clades of a taxon. Giant dinosaurs appear to have evolved dozens of times, in response to local environmental conditions.
Despite many counter-examples, Cope's rule is supported in many instances. For example, all marine invertebrate phyla except the molluscs show a size increase between the Cambrian and Permian. Collectively, dinosaurs exhibit an increase in body length over their evolution. Cope's rule also appears to hold in clades where a constraint on size is expected. For instance, one may expect the size of birds to be constrained, as larger masses mean more energy must be expended in flight. Birds have been suggested to follow Cope's law, although a subsequent reanalysis of the same data suggested otherwise.
An extensive study published in 2015 supports the presence of a trend toward larger body size in marine animals during the Phanerozoic. However, this trend was present mainly in the Paleozoic and Cenozoic; the Mesozoic was a period of relative stasis. The trend is not attributable simply to neutral drift in body size from small ancestors, and was mainly driven by a greater rate of diversification in classes of larger mean size. A smaller component of the overall trend is due to trends of increasing size within individual families.