PMC

Cascading reinforcement as an outcome of shifting acceptance thresholds. (a,c) A restrictive acceptance threshold evolves in sympatry, generating selection for trait divergence: i.e. reproductive character displacement. (b,d) In allopatry, individuals evolve a permissive threshold, and traits do not shift. (e) When individuals from the allopatric population disperse into a sympatric population, the individuals of the sympatric population will reject some of these individuals (blue shaded area) owing to the restrictive acceptance threshold.

Braincases are aligned on the hypophyseal opening, the position of which is indicated by the horizontal pink line. The path of the major cranial blood vessels is shown in red, with inferred paths represented by dotted lines. Character distributions reject the homology of craniospinal processes in ‘placoderms’ and actinopterygians. Illustrations are redrawn from , -, and .

Flow-loop diagram showing significant (solid arrows) and non-significant (dotted arrows) transitions in the correlated evolution between habit and habitat, as well as cases of contingent evolution (red arrows), where the state of one character has a significant influence on the evolution of the other. Thick black arrows indicate transition rates that have a low posterior probability of being zero (Z-score ≤ 5 %) and for which alternative model tests rejected a hypothesis that the given transition rate has a value of zero in favour of a non-zero value across all examined trees. Thin black arrows highlight transitions that have an intermediate posterior probability of being zero (Z-score 10–80 %) and for which alternative model tests failed to reject a hypothesis that the given transition rate has a value of zero across all examined trees. Dashed arrows indicate transition rates that have a high posterior probability of being zero (Z-score <95 %) and for which alternative model tests failed to reject a hypothesis that a given transition rate has a value of zero across examined trees. Red arrows highlight results of contingency tests, where alternative model tests rejected the hypothesis that the two transition rates of one character are equal, or independent of the second character, in favour of different dependent rates across examined trees. The size of each circle is proportional to the percentage of sampled species that are found in each character state combination.

The distribution of similarity score with the nearest neighbour for seen and unseen categories on HWOBC. The vertical axis means the similarity score, the horizontal axis means the instance number. The red dashed line indicates the upper and lower bound thresholds we use to reject instances of the unseen category.