Encephalization quotient

Encephalization quotient, encephalization level, or just encephalization is a relative brain size measure that is defined as the ratio between observed and predicted brain mass for an animal of a given size, based on nonlinear regression on a range of reference species. It has been used as a proxy for intelligence and thus as a possible way of comparing the intelligence levels of different species. For this purpose, it is a more refined measurement than the raw brain-to-body mass ratio, as it takes into account allometric effects. Expressed as a formula, the relationship has been developed for mammals and may not yield relevant results when applied outside this group.

Perspective on intelligence measures

Encephalization quotient was developed in an attempt to provide a way of correlating an animal's physical characteristics with perceived intelligence. It improved on the previous attempt, brain-to-body mass ratio, so it has persisted. Subsequent work, notably Roth, found EQ to be flawed and suggested brain size was a better predictor, but that has problems as well.
Currently the best predictor for intelligence across all animals is forebrain neuron count. This was not seen earlier because neuron counts were previously inaccurate for most animals. For example, human brain neuron count was given as 100 billion for decades before Herculano-Houzel found a more reliable method of counting brain cells.
It could have been anticipated that EQ might be superseded because of both the number of exceptions and the growing complexity of the formulae it used. The simplicity of counting neurons has replaced it. The concept in EQ of comparing the brain capacity exceeding that required for body sense and motor activity may yet live on to provide an even better prediction of intelligence, but that work has not been done yet.

Variance in brain sizes

Body size accounts for 80–90% of the variance in brain size, between species, and a relationship described by an allometric equation: the regression of the logarithms of brain size on body size. The distance of a species from the regression line is a measure of its encephalization. The scales are logarithmic, distance, or residual, is an encephalization quotient, the ratio of actual brain size to expected brain size. Encephalization is a characteristic of a species.
Rules for brain size relates to the number brain neurons have varied in evolution, then not all mammalian brains are necessarily built as larger or smaller versions of a same plan, with proportionately larger or smaller numbers of neurons. Similarly sized brains, such as a cow or chimpanzee, might in that scenario contain very different numbers of neurons, just as a very large cetacean brain might contain fewer neurons than a gorilla brain. Size comparison between the human brain and non-primate brains, larger or smaller, might simply be inadequate and uninformative – and our view of the human brain as outlier, a special oddity, may have been based on the mistaken assumption that all brains are made the same.

Limitations and possible improvements over EQ

There is a distinction between brain parts that are necessary for the maintenance of the body and those that are associated with improved cognitive functions. These brain parts, although functionally different, all contribute to the overall weight of the brain. Jerison has for this reason considered 'extra neurons', neurons that contribute strictly to cognitive capacities, as more important indicators of intelligence than pure EQ. Gibson et al. reasoned that bigger brains generally contain more 'extra neurons' and thus are better predictors of cognitive abilities than pure EQ among primates.
Factors such as the recent evolution of the cerebral cortex and different degrees of brain folding, which increases the surface area of the cortex, are positively correlated to intelligence in humans.
In a meta-analysis, Deaner et al. tested absolute brain size, cortex size, cortex-to-brain ratio, EQ, and corrected relative brain size against global cognitive capacities. They have found that, after normalization, only ABS and neocortex size showed significant correlation to cognitive abilities. In primates, ABS, neocortex size, and Nc correlated fairly well with cognitive abilities. However, there were inconsistencies found for Nc. According to the authors, these inconsistencies were the result of the faulty assumption that Nc increases linearly with the size of the cortical surface. This notion is incorrect because the assumption does not take into account the variability in cortical thickness and cortical neuron density, which should influence Nc.
According to Cairo, EQ has flaws to its design when considering individual data points rather than a species as a whole. It is inherently biased given that the cranial volume of an obese and underweight individual would be roughly similar, but their body masses would be drastically different. Another difference of this nature is a lack of accounting for sexual dimorphism. For example, the female human generally has smaller cranial volume than the male; however, this does not mean that a female and male of the same body mass would have different cognitive abilities. Considering all of these flaws, EQ should not be viewed as a valid metric for intraspecies comparison.
The notion that encephalization quotient corresponds to intelligence has been disputed by Roth and Dicke. They consider the absolute number of cortical neurons and neural connections as better correlates of cognitive ability. According to Roth and Dicke, mammals with relatively high cortex volume and neuron packing density are more intelligent than mammals with the same brain size. The human brain stands out from the rest of the mammalian and vertebrate taxa because of its large cortical volume and high NPD, conduction velocity, and cortical parcellation. All aspects of human intelligence are found, at least in its primitive form, in other nonhuman primates, mammals, or vertebrates, with the exception of syntactical language. Roth and Dicke consider syntactical language an "intelligence amplifier".

Brain-body size relationship

Brain size usually increases with body size in animals, i.e. large animals usually have larger brains than smaller animals. 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, while elephants have a comparatively small brain/body size, despite being quite intelligent animals. Treeshrews have a brain/body mass ratio of.
Several reasons for this trend are possible, one of which is that neural cells have a relative constant size. 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
where and are brain and body weights respectively, and is called the cephalization factor. 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.
The cephalization factor and the subsequent encephalization quotient was developed by H. J. Jerison in the late 1960s. The formula for the curve varies, but an empirical fitting of the formula to a sample of mammals gives
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.

Calculation

Snell's equation of simple allometry is
were is the weight of the brain, is the cephalization factor, is body weight, and is the exponential constant.
The "encephalization quotient" is the coefficient in Snell's allometry equation, usually normalized with respect to a reference species. In the following table, the coefficients have been normalized with respect to the value for the cat, which is therefore attributed an EQ of 1.
Another way to calculate encephalization quotient is by dividing the actual weight of an animal's brain with its predicted weight according to Jerison's formula.

Species	Encephalization quotient
Human	7.4–7.8
Northern right whale dolphin	5.55
Bottlenose dolphin	5.26
Orca	2.57–3.3
Chimpanzee	2.2–2.5
Raven	2.49
Domestic Pig	2.42
Rhesus macaque	2.1
Red fox	1.92
Elephant	1.75–2.36
Raccoon	1.62
Gorilla	1.39
California sea lion	1.39
Chinchilla	1.34
Dog	1.2
Squirrel	1.1
Cat	1.00
Hyena	0.92
Horse	0.92
Elephant shrew	0.82
Brown bear	0.82
Sheep	0.8
Taurine cattle	0.52–0.59
Mouse	0.5
Rat	0.4
Rabbit	0.4
Domestic Pig	0.38
Hippopotamus	0.37
Opossum	0.2

This measurement of approximate intelligence is more accurate for mammals than for other classes and phyla of Animalia.