1. The convolutions of the human cortex arose because of neural expansion within a limited (cranial) space. Correct? Or is there more to the story?

From Tim Bunnell (ASEL, AIDuPont/Linguistics/Computer Science)

A subtly different/additional point is that the convolutions maximize the surface area of the cortex rather than its volume. Convolutions would presumably not arise if maximizing the volume of cortical tissue was the main constraint.

yes the folding of the cortex is "designed" to maximize surface area for a given volume.Homo sapiens has by far the most convoluted cortex. A rat brain, by comparison, looks quite smooth. One way to evaluate this to look at brain/body weight ratio. In the mammal group, humans stand out as a real oddity on this measure with a very high ratio.

The need for expansion within a limited skull is the basic story of the convolutions, Bill. The 6-layer sturcture of the cortex was laid out early, and its function has not changed appreciably through the mammalian order. Therefore, the way to make it work better (if you're not going to make it thicker, or change the strategies it uses) is to make more of it, at the expense of subcortical tissue. In humans, 2/3 of the cortex is not visible from the surface. If the sulci were ironed out, human cortical surface area would be about 6 square feet (but still only the thickness of a penny).

2. What is the extent of cortical convolution in non-human brains?

From David P M Northmore (Psychology/Neuroscience)

Convolutions generally absent in most mammals (e.g. rats), and limited in monkeys.

Mammals have cortex. Higher reptiles (crocodilians) have a primitive form in small amounts, but cortex is basically a mammalian phenomenon. All mammals have three basic fissures: the hippocampal fissure that arises from pushing the olfactory bulb so far forward in front of the developing brain (it flexes upward, creating the fissure), the endorhinal fissure that runs axially along piriform cortex (where olfaction is processed), and the rhinal fissure that develops between the paleocortex and neocortex because they're developing in opposite directions. Mammals with only these three are called lissencephalic, or smooth-brained. Rats are at about the top of the list. Those with fissures within the surface of the neocortex are called gyrencephalic. Number of fissures depends on the size of cortex. The size of cortex depends on the size of the mammal and its occupation: in general, herbivores are less well endowed than carnivores. Cats and on up have well-defined sulci throughout the neocortex.