Brain-to-body mass ratio
Brain-to-body mass ratio, also known as the brain to body weight ratio, is the ratio of brain mass to body mass, which is hypothesised to be a rough estimate of the intelligence of an animal, although fairly inaccurate in many cases. A more complex measurement, encephalization quotient, takes into account allometric effects of widely divergent body sizes across several taxa.  The raw brain-to-body mass ratio is however simpler to come by, and is still a useful tool for comparing encephalization within species or between fairly closely related species.
Brain-body size relationship
Brain size usually increases with body size (positive correlation) in animals (i.e. large animals usually have larger brains than smaller animals). The relationship is not linear however. Small mammals like mice have a direct brain/body size similar to humans, while elephants have comparatively small brain/body size, despite elephants being obviously intelligent animals.
In animals it's hard to establish, but the larger the brain the more brain weight might be available for more complex cognitive tasks. However, large animals need more neurons to represent their bodies and control specific muscles, so that relative rather than absolute brain size makes for a ranking of animals that coincide better with observed complexity of behaviour. The relationship between brain-to-body mass ratio and complexity of behaviour is not perfect as other factors also influence intelligence, like the evolution of the recent cerebral cortex and different degrees of brain folding, which increase the surface of the cortex, which is positively correlated in humans to intelligence. The noted exception to this, of course, are those suffering from swelling of the brain which, while resulting in greater surface area, does not alter intelligence.
Comparisons between groups
mass ratio (E:S)
Dolphins have the highest brain-to-body weight ratio of all cetaceans. Monitor lizards, tegus and anoles and some tortoise species have the largest among reptiles. Among birds, the highest brain-to-body ratios are found among parrots, crows, magpies, jays and ravens. Among amphibians, the studies are still limited. Either octopuses or jumping spiders have some of the highest for an invertebrate, although some ant species have 14%-15% of their mass in their brains, the highest value known for any animal. Sharks have one of the highest for fish alongside manta rays (although the electrogenic elephantfish has a ratio nearly 80 times higher - about 1/32, which is slightly higher than that for humans). The tiny shrew, which holds about 10% of its body mass in its brain, has one of the highest brain-to-body mass ratios of any vertebrate.
It is a trend that the larger the animal gets, the smaller the brain-to-body mass ratio is. Large whales have very small brains compared to their weight, and small rodents like mice have a relatively large brain, giving the same brain-to-body mass ratio as a human. One explanation could be that as an animal's brain gets larger, the size of the neural cells remains the same, and more nerve cells will cause the brain to increase in size to a lesser degree than the rest of the body. This phenomenon has been called the encephalization quotient; E = CS2, where E and S are body and brain weights and C is the cephalization factor. Just focusing on the relationship between the body and the brain is not enough: one also has to consider the total size of the animal.
In the essay "Bligh's Bounty", Stephen Jay Gould noted that if one looks at vertebrates with very low encephalization quotient, 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.
Recent research indicates that, in non-human primates, whole brain size is a better measure of cognitive abilities than brain-to-body mass ratio. The total weight of the species is greater than the predicted sample only if the frontal lobe is adjusted for spatial relation. The brain-to-body mass ratio was however found to be an excellent predictor of variation in problem solving abilities among carnivoran mammals.
In humans, the brain to body weight ratio can vary greatly from person to person; it would be much higher in an underweight person than an overweight person, and higher in infants than adults. The same problem is encountered when dealing with marine mammals, which may have considerable body fat masses. Some researchers therefore prefer lean body weight to brain mass as a better predictor.
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- A graph of body mass vs. brain mass
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