Editing Encephalization quotient (section)

== Brain-body size relationship ==
{| class="wikitable sortable" style="float: right; clear: right; margin-left:1em;"
!Species
!Simple brain-to-body <br/>ratio (''E''/''S''){{citation needed|date=February 2020}}
|-
|[[Treeshrew]] || 1/10
|-
|Small [[birds]] || 1/12
|-
|[[Human]] || 1/40
|-
|[[Mouse]] || 1/40
|-
|[[Dolphin]] || 1/50
|-
|[[Cat]] || 1/100
|-
|[[Chimpanzee]] || 1/113{{Undue precision}}
|-
|[[Dog]] || 1/125{{Undue precision}}
|-
|[[Frog]] || 1/172{{Undue precision}}
|-
|[[Lion]] || 1/550
|-
|[[Elephant]] || 1/560
|-
|[[Horse]] || 1/600
|-
|[[Shark]] || 1/2496{{Undue precision}}
|-
|[[Hippopotamus]] || 1/2789{{Undue precision}}
|}
Brain size usually increases with body size in animals (is [[correlation|positively correlated]]), i.e. large animals usually have larger brains than smaller animals.<ref name=Serendip /> The relationship is not linear, however. Generally, small mammals have relatively larger brains than big ones. [[Mice]] have a direct brain/body size ratio similar to humans (1/40), while [[elephant]]s have a comparatively small brain/body size (1/560), despite being quite intelligent animals.<ref>{{cite journal |last1=Hart |first1=Benjamin L. |last2=Hart |first2=Lynette A. |last3=McCoy |first3=Michael |last4=Sarath |first4=C.R. |title=Cognitive behaviour in Asian elephants: use and modification of branches for fly switching |journal=Animal Behaviour |date=November 2001 |volume=62 |issue=5 |pages=839–847 |doi=10.1006/anbe.2001.1815 |s2cid=53184282 }}</ref> [[Treeshrew|Treeshrews]] have a brain/body mass ratio of (1/10).<ref>{{Cite web |last=Feltman |first=Rachel |date=2018-03-15 |title=What does brain size have to do with intelligence? |url=https://www.popsci.com/what-does-brain-size-have-to-do-with-intelligence/ |access-date=2024-02-28 |website=Popular Science |language=en-US}}</ref>

Several reasons for this trend are possible, one of which is that [[neuron|neural cells]] have a relative constant size.<ref>{{cite book |last1=Oxnard |first1=C. |last2=Cartmill |first2=M. |last3=Brown |first3=K.B. |title=The human body: Developmental, functional and evolutionary bases |year=2008 |publisher=Wiley |location=Hoboken, NJ |isbn=978-0471235996 |page=274 |url=https://books.google.com/books?id=6W7gCAAAQBAJ&pg=PA274}}</ref> Some brain functions, like the brain pathway responsible for a basic task like drawing breath, are basically similar in a mouse and an elephant. Thus, the same amount of brain matter can govern breathing in a large or a small body. While not all control functions are independent of body size, some are, and hence large animals need comparatively less brain than small animals. This phenomenon can be described by an equation <math>C = E/S^{2/3},</math> 
where <math>E</math> and <math>S</math> are brain and body weights respectively, and <math>C</math> is called the cephalization factor.<ref name="Gould 1977 Ever since Darwin, c7s1"/> To determine the value of this factor, the brain and body weights of various mammals were plotted against each other, and the curve of such formula chosen as the best fit to that data.<ref name=Jerison>{{cite book |title=Advances in the Study of Mammalian Behavior |url=https://archive.org/details/advancesinstudyo00eise |year=1983 |series=Special Publication |publisher=[[American Society of Mammalogists]] |volume=7 |location=Pittsburgh, PA |author=Jerison, H. J. |author-link=The evolution of the mammalian brain as an information-processing system |editor1=Eisenberg, J. F. |editor2=Kleiman, D. G. |pages=[https://archive.org/details/advancesinstudyo00eise/page/113 113]–146}}</ref>

The cephalization factor and the subsequent encephalization quotient was developed by H.&nbsp;J.&nbsp;Jerison in the late 1960s.<ref name=Dinosaur_Paleoneurology>{{cite book |editor1-last=Brett-Surman |editor1-first=Michael K. |editor2-first=Thomas R. |editor2-last=Holtz |editor3-first=James O. |editor3-last=Farlow |others=Illustrated by Bob Walters |title=The complete dinosaur |publisher=Indiana University Press |location=Bloomington, Ind. |isbn=978-0-253-00849-7 |pages=191–208 |edition=2nd |date=27 June 2012 }}</ref> The formula for the curve varies, but an empirical fitting of the formula to a sample of mammals gives<ref name=Moore/>
<math display="block">
 \frac{w(\text{brain})}{1~\text{g}} = 0.12 \left(\frac{w(\text{body})}{1~\text{g}}\right)^{\frac{2}{3}}.
</math>
As this formula is based on data from mammals, it should be applied to other animals with caution. For some of the other [[vertebrate]] classes the power of 3/4 rather than 2/3 is sometimes used, and for many groups of [[invertebrates]] the formula may give no meaningful results at all.<ref name=Moore/>