By definition, an average mammal should have an EQ of 1. The formula breaks if we try to apply it to non-mammalian animals, such as birds, probably because their brain architecture is different from ours at quite a fundamental level. Even for mammals, there is some debate as to exactly what formula we should be using; most older studies have determined that brain size typically rises as the 2/3 power of body size (that is, as the cube root of the square) but a 2019 study argued that it's perhaps more accurate to base it on the 3/4 power and this seems to be a growing consensus.
The formula that you choose will inevitably change the number that you get when you look at specific animals. But, whatever method you use, two groups of mammals consistently score higher than any others: the primates and the cetaceans (dolphins and whales). The latter are, of course, often particularly large animals to start with, so that their brain is large shouldn't come as a surprise. But it is accurate to say that it's even larger than we'd expect it to be, all other things being equal.
Indeed, in terms of raw size, the brains of whales are the largest brains of any animals that have ever existed, and, in terms of EQ, they can get surprisingly close to the values of humans. Which doesn't necessarily mean that they are as "intelligent" as humans, since that would also depend on the fine details of the neural architecture... but it's still significant.
When did cetaceans develop these unusually large brains? Cetaceans are, as I've discussed before, a specialised evolutionary branch within what we'd otherwise call the "cloven-footed animals". And the other cloven-footed animals tend to have rather low EQ values, as is typical for non-primate herbivores. So, at some point, something has changed, perhaps because of the change in diet, the nature of their new habitat, or just going hand-in-hand with the development of more complex social structures.
One way of answering the question as to when this happened is to estimate the EQ of various fossil species of whale, and see what pattern emerges. There are, obviously a couple of problems here that don't apply to living animals - measuring the size of the brain and determining the weight of the entire animal. With regard to the latter, fossils are rarely complete so that, even if we assume that all whales and dolphins are approximately the same shape, we may not even know exactly how long the animal was to use that as the starting point for guessing the weight.
There certainly have been attempts to do this, based on the size of parts of the spine we do have, but a more common technique uses the distance between the outer edges of the occipital condyles. These are the two bumps at the rear of the skull (or the base of it, in upright animals such as humans) that articulate with the first of the neck vertebrae, thus connecting the skull to the backbone. This distance, apparently, correlates well with the overall weight of living cetaceans, and it's more likely to be preserved and measurable than some other measures that might be used.
This method, combined with CT scans of the insides of the skulls to determine their internal volume, was used in 2004 to provide the first detailed survey of the EQ values of fossil whales and dolphins. This showed that early whales, living during the Eocene epoch over 35 million years ago, did not have particularly high EQs; indeed, they were consistently below 1, meaning that the brains were actually smaller than we'd expect for animals of their size - but consistent with many of the hoofed mammals of the time.
Then, as the Eocene came to a close and the following, Oligocene, epoch dawned, there was a sudden, rapid, increase in brain size among whales. By 28 million years ago, there were some whales with EQ values around 3 on the scale then in use, approximately the same level as a chimpanzee and way above anything outside of the cetaceans and primates today. There is a likely reason why this dramatic change happened when it did, because the leap corresponds with something else that's thought to have arisen in whales at the same time: echolocation.
In this regard, it's worth noting that not all whales have exceptionally large brains. The filter-feeding baleen whales have relatively normal-sized brains for their body size (although, obviously, that's still rather a lot in absolute terms) and, crucially, do not use echolocation.
The study also showed a second, smaller, increase in cetacean relative brain size in the Middle Miocene, around 18 million years ago, when the first delphinoids appeared. This is the group that includes the dolphins, porpoises, and a few moderately sized whales, but excludes, for example, the sperm whales. The change here seems to have been driven by the cetaceans in question becoming smaller overall, while their brains shrank less than would be expected, leaving them proportionately larger. Since then, it appears, there hasn't really been much change; there were delphinoids 15 million years ago with EQs of around 5, which remains the highest it ever gets today (humans score 7 on this particular version of the scale).
However, there is a potential problem here, and it relates to the other part of the calculation - determining how large the brain of a fossil whale would have been. In most mammals, given a reasonably complete skull, this isn't especially hard, since it's possible to use latex moulds or (more commonly these days) CT scans to measure the volume of the inside of the skull, which should match pretty closely to the size of the brain.
But, with cetaceans, that's not necessarily so. Even in other mammals, the brain itself isn't literally the only thing inside the braincase. Some of the relevant nerves are in there too, along with the meninges that surround and protect the brain and line the inside the skull, and a few other features too... but none of these are particularly large or change that much over time. But, in some living cetaceans, there is a quite considerable difference between the size of the skull and the size of the brain inside it.
Much of this is occupied by a complex of blood vessels called the rete mirable, which may help to cool the brain down. Land-dwelling artiodactyls have one of these, too (humans, and most other mammals, do not) but it's exceptionally large in many cetaceans. Indeed, the bowhead whale, a filter-feeder, has a brain that only occupies about 40% of the space inside the skull, with the remainder taken by the rete, the other nerves and protective structures that we'd expect to find there anyway, and quite a lot of fluid cushioning.
Of course, the researchers who performed the 2004 study were aware of this, and took it into account, determining that the proportions of the skull taken up by these extra features hadn't changed too much over the course of evolution so that, even if the exact EQ values were off by a little, the sudden increases in relative brain size still had to be real.
Last year, however, a more complete analysis called some of this into question. This new study used the more modern version of the EQ formula but was also able to add new information to that used to guess the brain and body sizes of incomplete fossils. The researchers examined the brains and skulls of living artiodactyls, both the ground-based hoofed sort, and the aquatic cetaceans, to get a better idea of just how much of the skull is occupied by the brain, where it turns out that the volume of cerebrospinal fluid makes a much larger, and more predictable, contribution than previously thought. (As they pointed out, people studying living animals don't normally do this sort of comparison because there wouldn't be any point - if you want to know how big the brain is, you just weigh it). They were also able to get a better fit of how overall body weight correlates to the skull measurements used to guess it from fossils, since it turns out that this is slightly different for dolphins than it is for most true whales.
When they do all of this, the apparent jump in relative brain size at the dawn of the Oligocene disappears. Instead, what we see is a gradual increase in brain size among the earliest whale fossils that can be studied in this manner, which simply continues once the echolocating whales appear on the scene. The second jump, with the arrival of the delphinoids, does remain, in part because the estimates arrived at for these more modern fossils don't change very much, so that the same processes seem to be valid.
There is no doubt that the brains of cetaceans are even larger than we'd expect given their large body size. A bottlenose dolphin, for example, has a brain larger than a human's despite having a body that's less than twice the size of ours, weight for weight. But this is the culmination of a slow trend towards increasing brain size over millions of years, not, for most whales, the result of a rapid change when they first developed echolocation. This doesn't necessarily mean that echolocation has nothing to do with it, since that too, may have developed more slowly than we thought, and there's still the issue that the dolphins and their close relatives did, indeed, undergo a jump in brain size when they first became distinguishable from their more primitive ancestors.
But the issue may be more complicated than we thought, with a number of different factors operating together to drive the increased brain size, and, plausibly, the overall intelligence, of what are likely the brightest non-primate mammals.
[Photo by "safaritravelplus", available under the CC0 creative commons license.]
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