The ichnotaxonomy and stratigraphic, geographic and environmental distribution of fish (Undichna) and amphibian (Lunichnium) swimming traces are reviewed. The ichnospecies of Undichna consist of various combinations of sinusoidal waves of differing complexity. Some of the more complex ichnospecies are made up of elements of the simpler forms, and morphological subset relationships between them are presented. Such subset series represent potential taphoseries relationships (i.e. preservational variants that reflect, for example, undertrails), or series of minor behavioural variations. Such a system can be used to highlight that different ichnospecies occurring at a locality may be taphonomic or minor behavioural variants of each other. Caution should, therefore, be exercised before erecting new ichnospecies on the basis of limited material if its morphology is a subset of an existing ichnospecies. However, the naming of such simpler ichnospecies is valid if they represent a recurrent morphology, and it is valid to erect new ichnospecies whose morphology is not a subset of an existing ichnospecies. Specimens that demonstrate intergradation between ichnotaxa can be used to justify their synonomy. Ichnotaxonomic revisions reduce the number of ichnospecies in Undichna from 14 to nine. U. radnicensis, a highly variable ichnospecies, is synonymized with U. britannica on the basis of material from China that demonstrates they can intergrade. U. prava is a partial U. tricosta, which falls within the minimum diagnosis of U. simplicitas. U. gosiutensis is regarded as a subjective junior synonym of U. quina. U. westerbergensis, originally attributed to a ‘crossopterygian’ fish performing a tetrapod-like gait, is reassigned as a distinct ichnospecies within Lunichnium because it demonstrates the same morphology, representing similar behaviour, albeit by a different producer. L. anceps and L. gracile are synonymized with L. rotterodium. New specimens of U. bina and L. rotterodium are also described from the Lower Permian Robledo Mountains Formation of southern New Mexico, USA.

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