I love pelycosaurs. They're probably the most famous non-dinosaurian prehistoric critters. They're not even reptiles, though--they're basal synapsids. They're more closely related to you and I than to lizards and crocodiles. Pelycosauria used to be a coherent group featuring a variety of Permian forms that all looked fairly similar. So similar, in fact, that in at least one case, one distinct genus was considered the female of another genus! Pelycosaurs were largish, lizard-like critters with large skulls and mean, bladed teeth. There was at least one herbivorous pelycosaur, Edaphosaurus, a small-headed form that lived alongside uber-carnivore Dimetrodon.
Some pelycosaurs developed sails on their backs. In Dimetrodon, the sail was tall and roughly symmetrical from front to back, as its tallest point was in the middle. In Edaphosaurus, though, the sail was much shorter on the neck, and the neural spines were swept back, giving the sail a ramp-like profile. Additionally, the neural spines had cross-pieces of bone along its length. The sail would have looked spikey! But most pelyosaurs were sail-less, including basal form Ophiacodon.
Lately I've been hearing that pelycosaurs are not a coherent group. That is, Dimetrodon is closer to stem mammals than Edaphosaurus is. Instead of forming their own family, it would seem that pelycosaurs form a stepwise progression toward stem-mammals, just like rhamphorhynchoids form a stepwise progression toward pterodactyloids. I'm perfectly willing to accept that, but I'd like to know where this idea came from. Additionally, are there any taxa within the traditional "Pelycosauria" that DO form monophyletic groups? There are such minor groupings among rhamphorhynchoids, after all. So while "Rhamphorhynchoidea" is not a monophyletic group, Anurognathidae IS, and so is Rhamphorhychidae (Rhamphorhynchus, Scaphognathus, a few others). So are there any pelycosaurs that form a monophyletic relationship?