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 tended to hypothesize the occurrence of linear evolutionary trends. It is sometimes also known as the Cope-Depéret rule, because Charles Depéret explicitly advocated the idea[a] (Theodor Eimer had also done so earlier). While the rule has been demonstrated in many instances, it does not hold true at all taxonomic levels, or in all clades. Larger body size is associated with increased fitness for a number of reasons, although there are also some disadvantages both on an individual and on a clade level: clades comprising larger individuals are more prone to extinction, which may act to limit the maximum size of organisms.
Effects of growth
Directional selection appears to act on organisms' size, whereas it exhibits a far smaller effect on other morphological traits, though it is possible that this perception may be a result of sample bias. This selectional pressure can be explained by a number of advantages, both in terms of mating success and survival rate.
For example, larger organisms find it easier to avoid or fight off predators and capture prey, to reproduce, to kill competitors, to survive temporary lean times, and to resist rapid climatic changes. They may also potentially benefit from better thermal efficiency, increased intelligence, and a longer lifespan.
Offsetting these advantages, larger organisms require more food and water, and shift from r to K-selection. Their longer generation time means a longer period of reliance on the mother, and on a macroevolutionary scale restricts the clade's ability to evolve rapidly in response to changing environments.
Left unfettered, the trend of ever-larger size would produce organisms of gargantuan proportions. Therefore, some factors must limit this process. At one level, it is possible that the clade's increased vulnerability to extinction, as its members become larger, means that no taxon survives long enough for individuals to reach huge sizes. There are probably also physically imposed limits to the size of some organisms; for instance, insects must be small enough for oxygen to diffuse to all parts of their bodies, flying birds must be light enough to fly, and the length of giraffes' necks may be limited by the amount of pressure it is possible for their hearts to generate. Finally, there may be a competitive element, in that changes in size are necessarily accompanied by changes in ecological niche. For example, terrestrial carnivores over 21 kg almost always prey on organisms larger, not smaller, than themselves. If such a niche is already occupied, competitive pressure may oppose the directional selection. The three Canidae clades show a trend towards larger size before becoming extinct.
Cope recognised that clades of Cenozoic mammals appeared to originate as small individuals, and that body mass increased through a clade's history. Discussing the case of canid evolution in North America, Blaire Van Valkenburgh of UCLA and coworkers state:
Cope's rule, or the evolutionary trend toward larger body size, is common among mammals. Large size enhances the ability to avoid predators and capture prey, enhances reproductive success, and improves thermal efficiency. Moreover, in large carnivores, interspecific competition for food tends to be relatively intense, and bigger species tend to dominate and kill smaller competitors. Progenitors of hypercarnivorous lineages may have started as relatively small-bodied scavengers of large carcasses, similar to foxes and coyotes, with selection favoring both larger size and enhanced craniodental adaptations for meat eating. Moreover, the evolution of predator size is likely to be influenced by changes in prey size, and a significant trend toward larger size has been documented for large North American mammals, including both herbivores and carnivores, in the Cenozoic.
— 20, 20, Van Valkenburgh et al.
In some cases, the increase in body size may represent a passive, rather than an active, trend. 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". In other cases, an increase in size may in fact represent a transition to an optimal body size, and not imply that populations always develop to a larger size.
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.
Despite many counter-examples, Cope's rule does hold in many instances. For example, all marine invertebrate phyla except the molluscs show a size increase between the Cambrian and Permian. And 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. However, birds have been suggested to follow Cope's law, although a subsequent reanalysis of the same data suggested otherwise 
- Rensch, B. (September 1948). "Histological Changes Correlated with Evolutionary Changes of Body Size". Evolution 2 (3): 218–230. JSTOR 2405381.
- Stanley, S. M. (March 1973). "An Explanation for Cope's Rule". Evolution 27 (1): 1–26. JSTOR 2407115.
- Hone DW, Benton MJ (2005). "The evolution of large size: how does Cope's Rule work?". Trends Ecol. Evol. (Amst.) 20 (1): 4–6. doi:10.1016/j.tree.2004.10.012. PMID 16701331.
- Polly, P. D.; Alroy, J. (1998-10-02). "Cope's Rule". Science 282 (5386): 50–51. Bibcode:1998Sci...282...47P. doi:10.1126/science.282.5386.47f.
- Monroe, M. J.; Bokma, F. (2010-07-12). "Little evidence for Cope’s rule from Bayesian phylogenetic analysis of extant mammals". Journal of Evolutionary Biology 23 (9): 2017–2021. doi:10.1111/j.1420-9101.2010.02051.x.
- Charles Jean Julien Depéret (1907). Les transformations du monde animal. E. Flammarion. Retrieved 6 August 2013.
- Cope, E. D. (February 1885). "On the Evolution of the Vertebrata, Progressive and Retrogressive". The American Naturalist 19 (2): 140–148. JSTOR 2450032.
- Ibid. (3). March 1885. pp. 234–247. JSTOR 2450075.
- Ibid. (4). April 1885. pp. 341–353. JSTOR 2450836.
- Kingsolver, J. G.; Pfennig, D. W. (2004). "INDIVIDUAL-LEVEL SELECTION AS A CAUSE OF COPE'S RULE OF PHYLETIC SIZE INCREASE". Evolution 58 (7): 1608–1612. doi:10.1554/04-003. PMID 15341162.
- Van Valkenburgh, B.; Wang, X; Damuth, J (2004). "Cope's Rule, Hypercarnivory, and Extinction in North American Canids". Science 306 (5693): 101–4. Bibcode:2004Sci...306..101V. doi:10.1126/science.1102417. PMID 15459388.
- Finarelli, John A. (2008). "Testing hypotheses of the evolution of encephalization in the Canidae (Carnivora, Mammalia)". Paleobiology 34: 35. doi:10.1666/07030.1.
- Alroy, J. (1998). "Cope's Rule and the Dynamics of Body Mass Evolution in North American Fossil Mammals". Science 280 (5364): 731–734. Bibcode:1998Sci...280..731A. doi:10.1126/science.280.5364.731. PMID 9563948.
- Carrano, M.T. (2006). "Body-Size Evolution in the Dinosauria". Amniote Paleobiology: Perspectives on the Evolution of Mammals, Birds, and Reptiles: a Volume Honoring James Allen Hopson (University of Chicago Press). ISBN 978-0-226-09478-6. Retrieved 2008-05-12.
- Jablonski, D. (1997). "Body-size evolution in Cretaceous molluscs and the status of Cope's rule". Nature 385 (6613): 250–252. Bibcode:1997Natur.385..250J. doi:10.1038/385250a0.
- Stephen Jay Gould (1997). "Cope's rule as psychological artefact". Nature 385 (6613): 199–200. Bibcode:1997Natur.385..199G. doi:10.1038/385199a0.
- Sereno et al. 1998[full citation needed]
- Laurin, M. (2004), The evolution of body size, Cope's rule and the origin of amniotes. Systematic Biology, 53: 594-622. doi:10.1080/10635150490445706
- Novack-Gottshall (2008). "Ecosystem-wide body-size trends in Cambrian–Devonian marine invertebrate lineages". Paleobiology 34 (2): 210. doi:10.1666/0094-8373(2008)034[0210:EBTICM]2.0.CO;2. ISSN 0094-8373.
- Hone, W.; Dyke, J.; Haden, M.; Benton, J. (Mar 2008). "Body size evolution in Mesozoic birds". Journal of Evolutionary Biology 21 (2): 618–624. doi:10.1111/j.1420-9101.2007.01483.x. ISSN 1010-061X. PMID 18194232.
- BUTLER, R. J. and GOSWAMI, A. (2008), Body size evolution in Mesozoic birds: little evidence for Cope’s rule. Journal of Evolutionary Biology, 21: 1673–1682. doi:10.1111/j.1420-9101.2008.01594.x