Recent analytical advances have permitted quantitative evaluations of evolutionary mode in populations of fossil organisms by providing tests of the null hypothesis that patterns of stratigraphic character variation do not differ from the expectations of a random walk. If the hypothesis can be rejected, then stasis and anagenesis represent alternative evolutionary modes discernable using values of the Hurst estimate. We used this approach to evaluate evolutionary mode in the bryozoan genus Peronopora across 34 characters in eight unbranched, cladistically defined, evolutionary sequences. Eight monophyletic crown species and eight paraphyletic (phenetically distinct) metaspecies constitute 16 species-rank taxa within the genus.

In seven of 15 species-rank transitions that had adequate sample sizes, significant character state changes—both phyletic gradualism and punctuated equilibrium—coincided with speciation events 11% of the time and were limited to more derived, crownward, ancestor-descendant pairs. Each of the 34 measured characters exhibited instances of transpecific stasis or anagenesis. Anagenesis of some characters persisted across unbranched lineages over 13 species (i.e., across 12 speciation events), whereas character stasis continued through unbranched lineages in up to 16 species (i.e., persisted unchanged across all 15 speciation events). Transpecific stasis and anagenesis were recognizable in over one-half of the data set, with stasis being approximately twice as common as anagenesis.

Across all character state transitions, approximately one-half reflect stasis, 30% anagenesis, and 20% could not be differentiated from a random walk. Similarly, across species and metaspecies characterized by a single intraspecific mode, stasis was twice as common as anagenesis and three times more common than undifferentiated random walks. The remaining instances of multiple intraspecific evolutionary modes occurred more commonly within metaspecies than within species. This difference might reflect the more frequent presence of unrecognized cryptic species or subspecies within metaspecies of Peronopora. Instantaneous rates of evolution can be estimated both within and between species of Peronopora for characters displaying anagenesis, potentially providing quantitative insights into evolutionary changes within the lineage.

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