Martin_G said:
Indeed, the stingray and the elephant have very similar body plans...
Which is why Haller's rule is based on the ratio of brain weight to body weight.
But the question was about Gould's speculation about the reason for this observed relationship - whether it is connected to the weight of neurons needed to control some amount of body surface. The figures look about right as a rough approximation.
Gould was I think extrapolating in rather direct fashion from the well-known Kleiber's law which relates metabolic rate and body surface area. See -
http://universe-review.ca/R10-35-metabolic.htm
So that seems a reasonable starting point. And its seems likely that a neural volume to area-to-control relation exists. But just as Kleiber's law now stresses the fractal nature of dissipative biological organisation, so brain allometry probably also is more about neural volume to a fractal internal "area-to-control". Which would change the expected slope of the scaling relationship.
However, there is a lot else going on that would confound any kind of simple relationship here.
Social behaviour demands larger brains usually. So this would produce correlations between brain size and lifestyle rather than body plan. Except there are reports from ant studies that argue small ants instead make do with smaller more specialised brains as the social behaviour is emergent and does not have to be held as a whole in each little head.
Another thing going on is the increasing complexity of internal control. So there is a switch between cold blooded and warm blooded that changes the slope of the relationship. Which again is not about surface area to control issues.
But then birds are another story because flight creates strong weight constraints and so they have brains which have "encephalised" by a different route - in simple terms, the striatum is what has grown rather than the cortex.
Yet another speculation is that there has been an evolutionary intelligence arms race so you will see larger brains in more modern branches of the family tree. The "marsupials and insectivores are dumber" line of argument.
(Much of this is dredged up from dim memory from a very comprehensive review on the subject - Brain and Mind, edited by David Oakley - which sits in a box in my garage somewhere
).
Then there are much more recent confounding studies that point both ways on how to think about the issues.
One is the finding that baby spiders have brains that extend into their legs as if neural mass is so critical that it must invade other areas until the body grows. But also a finding that miniature parasitic wasps are nearly isometrically scaled - instead of small species having relatively large brains, the brains shrink in stricter proportion. This could involve a shrinking of the neurons themselves, or a shrinkage in performance - less capacity for memory, etc.
So the point is that Kleiber's law does cover the whole animal kingdom and the causal explanation seems pretty straight forward. It is a simple fractal dissipative relationship. And it explains things like why elephants need big ears. Or why cats curl up in a ball if they are cold.
But when it comes to brain allometry, even Haller's rule does not hold that well across the animal kingdom. The miniature insect brain has become an interesting area of research now because of the contradictions appearing.
And it seems unlikely that one single factor will account for the relationships. However, the encephalisation quotient does draw a straight line average which gives a phyla-level benchmark that may pick out a basic brain mass to body mass "generalised control" relationship. And then animals with more social lifestyles lie above the baseline. And those from more primitive clades lie below.
