|Species||Encephalization quotient (EQ)|
Encephalization Quotient (EQ), or encephalization level is a measure of relative brain size defined as the ratio between actual brain mass and predicted brain mass for an animal of a given size, which is hypothesized to be a rough estimate of the intelligence of the animal.
This is a more refined measurement than the raw brain-to-body mass ratio, as it takes into account allometric effects. The relationship, expressed as a formula, has been developed for mammals, and may not yield relevant results when applied outside this group.
Additionally to volume, mass or cell count, the energy expenditure of the brain could be compared with that of the rest of the body.
Brain-body size relationship 
|Species||Simple brain-to body ratio (E/S)|
Brain size usually increases with body size in animals (is positively correlated), 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 (1/40), while elephants have a comparatively small brain/body size (1/560), despite elephants being quite intelligent animals.
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 has been called the cephalization factor: E = CS2, where E and S are body and brain weights and C is the cephalization factor. To compensate for this factor, a formula has been devised by plotting the brain/body weight of various mammals against each other and a curve fitted so as to give best fit to the 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 Ew(brain) = 0.12w(body)2/3. 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.
EQ and intelligence in mammals 
Intelligence in animals is hard to establish, but the larger the brain is relative to the body, the more brain weight might be available for more complex cognitive tasks. The EQ formula, as opposed to the method of simply measuring raw brain weight or brain weight to body weight, makes for a ranking of animals that coincide better with observed complexity of behaviour.
Mean EQ for mammals is around 1, with carnivorans, cetaceans and primates above 1, and insectivores and herbivores below. This reflects two major trends. One is that brain matter is extremely costly in terms of energy needed to sustain them. Animals which live on relatively nutrient poor diets (plants, insects) have relatively little energy to spare for a large brain, while animals living from energy-rich food (meat, fish, fruit) can grow larger brains. The other factor is the brain power needed to catch food. Carnivores generally need to find and kill their prey, which presumably requires more cognitive power than browsing or grazing.
Another factor affecting relative brain size is sociality and flock size. Rabbits, being solitary animals, have lower EQ than horses, a social species. Similarly, dogs (a social species) have a higher EQ than cats (a mostly solitary species). Animals with very large flock size and/or complex social systems consistently score high EQ, with dolphins and orcas having the highest EQ of all cetaceans, and humans with their extremely large societies and complex social life topping the list by a good margin.
Comparisons with non-mammalian animals 
Manta rays have the highest for a fish, and either octopuses or jumping spiders have the highest for an invertebrate. Despite the jumping spider having a huge brain for its size, it is minuscule in absolute terms, and humans have a much higher EQ, despite having a lower raw brain-to-body weight ratio. Mean EQ for reptiles are about one tenth of the EQ for mammals. EQ in birds (and estimated EQ in dinosaurs) generally also falls below that of mammals, possibly due to lower thermoregulation and/or motor control demands. Estimation of brain size in the oldest known bird, Archaeopteryx, shows it had an EQ well above the reptilian range, and just below that of living birds.
Biologist Stephen Jay Gould has noted that if one looks at vertebrates with very low encephalization quotients, their brains are slightly less massive than their spinal cords. Theoretically, intelligence might correlate with the absolute amount of brain an animal has after subtracting the weight of the spinal cord from the brain. This formula is useless for invertebrates because they do not have spinal cords, or in some cases, central nervous systems.
EQ in paleoneurology 
Behavioural complexity in living animals can to some degree be observed directly, making the predictive power of the encephalization quotient less relevant. It is however central in paleoneurology, where the endocast of the brain cavity and estimated body weight of an animal is all one has to work from. The behaviour of extinct mammals and dinosaurs are typically investigated using EQ formulas.
Recent research indicates that whole brain size is a better measure of cognitive abilities than EQ for primates at least. The relationship between brain-to-body mass ratio and complexity of are not alone in influencing intelligence. Other factors, like the evolution of the recent cerebral cortex and different degrees of brain folding, which increases the surface of the cortex, is positively correlated to intelligence in humans.
See also 
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