Fig. 1

Hypotheses for the evolution of vertebral complexity in mammals. a Random walk (BM model); b long-term continuous upward trend (BMtrend model); c selection toward a high optimum value in mammals (rooted OU1 model); d constrained evolution in non-mammalian synapsids followed by unconstrained radiation in mammals (RR model); e stepwise evolution toward higher optimum in mammals (OU2 model). f Multistep evolution with multiple optima shifts (e.g., OU3A and OU3B)