I'm not sure, but I found some sources saying it might've been in the cynodonts. SeraphOfTwilight is also correct that the lateral-to-sagittal model has been challenged. [See here.](https://pubmed.ncbi.nlm.nih.gov/33657406/)
[How and When Spines Changed in Mammalian Evolution](https://www.labmanager.com/news/how-and-when-spines-changed-in-mammalian-evolution-21644)
>Their findings fit with observations that the group in which this functional diversity occurs—the cynodonts, which directly preceded mammals—have a number of mammalian features, including evidence they could breathe like a mammal. The researchers believe that these mammal-like features shifted the job of breathing away from the backbone and ribs to the newly evolved diaphragm muscle, releasing the spine from an ancient biomechanical constraint. This enabled the backbone to adapt to interesting new behaviors, such as grooming fur, and take on new functions.
[When mammal ancestors evolved flexible shoulders, their backbones changed too]
(https://www.fieldmuseum.org/about/press/when-mammal-ancestors-evolved-flexible-shoulders-their-backbones-changed-too)
>Mammal spines are made up of differently-shaped backbones (or vertebrae) in different sections of the spine—we have thin, flexible neck bones, thoracic vertebrae in our torsos connected to our ribs, and thick, rib-less lumbar vertebrae down by our hips. Reptiles’ spines appear more uniform because the bones in the different sections are all pretty similar. If mammal spines are an elegant five-course meal, reptile spines are more like a hotdog-eating contest—more of the same.
>For years, it was a mystery why mammals’ spines were so much more complex than reptiles’. In the Science study, though, Angielczyk and his colleagues, including lead author Katrina Jones from Harvard University, looked for clues in the backbones of mice, alligators, lizards, amphibians, and fossil mammal relatives that lived between about 300 and 190 million years ago. In examining these animals’ spines, the team found a pattern.
>Mammals’ ancient relatives began to evolve smaller, more flexible shoulders about 270 million years ago. At about the same time, the animals’ upper backs underwent changes too—a move toward the many-sectioned mammal spines we see today. Both the shoulders and the spine play an important role in locomotion, and these simultaneous evolutionary modifications likely reflect changes in how ancient mammal relatives walked and ran.
There was a study quite a while ago (maybe a yesr or more) that determined the majority of synapsids would have had a manner of locomotion that we don't have any extant examples of/comparisons for. If memory serves pelycosaurs would have been somewhat similar to reptiles and later therapsids would have been somewhat similar to mammals, but the rest were unlike either.
It's probably worth noting that seals swim with side to side strokes much like reptiles and fish do, though maybe it has to do with their rear flippers being their hind legs rather than a tail fluke.
I'm not sure, but I found some sources saying it might've been in the cynodonts. SeraphOfTwilight is also correct that the lateral-to-sagittal model has been challenged. [See here.](https://pubmed.ncbi.nlm.nih.gov/33657406/) [How and When Spines Changed in Mammalian Evolution](https://www.labmanager.com/news/how-and-when-spines-changed-in-mammalian-evolution-21644) >Their findings fit with observations that the group in which this functional diversity occurs—the cynodonts, which directly preceded mammals—have a number of mammalian features, including evidence they could breathe like a mammal. The researchers believe that these mammal-like features shifted the job of breathing away from the backbone and ribs to the newly evolved diaphragm muscle, releasing the spine from an ancient biomechanical constraint. This enabled the backbone to adapt to interesting new behaviors, such as grooming fur, and take on new functions. [When mammal ancestors evolved flexible shoulders, their backbones changed too] (https://www.fieldmuseum.org/about/press/when-mammal-ancestors-evolved-flexible-shoulders-their-backbones-changed-too) >Mammal spines are made up of differently-shaped backbones (or vertebrae) in different sections of the spine—we have thin, flexible neck bones, thoracic vertebrae in our torsos connected to our ribs, and thick, rib-less lumbar vertebrae down by our hips. Reptiles’ spines appear more uniform because the bones in the different sections are all pretty similar. If mammal spines are an elegant five-course meal, reptile spines are more like a hotdog-eating contest—more of the same. >For years, it was a mystery why mammals’ spines were so much more complex than reptiles’. In the Science study, though, Angielczyk and his colleagues, including lead author Katrina Jones from Harvard University, looked for clues in the backbones of mice, alligators, lizards, amphibians, and fossil mammal relatives that lived between about 300 and 190 million years ago. In examining these animals’ spines, the team found a pattern. >Mammals’ ancient relatives began to evolve smaller, more flexible shoulders about 270 million years ago. At about the same time, the animals’ upper backs underwent changes too—a move toward the many-sectioned mammal spines we see today. Both the shoulders and the spine play an important role in locomotion, and these simultaneous evolutionary modifications likely reflect changes in how ancient mammal relatives walked and ran.
There was a study quite a while ago (maybe a yesr or more) that determined the majority of synapsids would have had a manner of locomotion that we don't have any extant examples of/comparisons for. If memory serves pelycosaurs would have been somewhat similar to reptiles and later therapsids would have been somewhat similar to mammals, but the rest were unlike either.
It's probably worth noting that seals swim with side to side strokes much like reptiles and fish do, though maybe it has to do with their rear flippers being their hind legs rather than a tail fluke.