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Abstract: Here, we evaluate the so‐called Thorson's rule, which posits that direct‐development and larger eggs are favored toward the poles in marine organisms and whose validity been the subject of considerable debate in the literature, combining an expanded phenotypic dataset encompassing 60 species of benthic octopuses with a new molecular phylogeny. Phylogenetic reconstruction shows two clades: clade 1 including species of the families Eledonidae, Megaleledonidae, Bathypolypodidae, and Enteroctopodidae, and clade 2 including species of Octopodidae. Egg size, development mode, and all environmental variables exhibited phylogenetic signal, partly due to differences between the two clades: whereas most species in clade 1 inhabit cold and deep waters, exhibit large eggs and hatchling with holobenthic development, species from clade 2 inhabit tropical‐temperate and shallow waters, evolved small eggs, and generally exhibit merobenthic development. Phylogenetic regressions show that egg size exhibits a conspicuous latitudinal cline, and that both egg size and development mode vary with water temperature. Additionally, analyses suggest that egg size is constrained by body size in lineages with holobenthic development. Taken together, results suggest that the variation in egg size and development mode across benthic octopuses is adaptive and associated with water temperature, supporting Thorson's rule in these organisms. [ABSTRACT FROM AUTHOR]

Algorithms are presented to simultaneously estimate probabilities of speciation and extinction, rates of anagenetic and cladogenetic phenotypic evolution, as well as ancestral character states, from a complete ultrametric species-level phylogeny with dates assigned to all bifurcations and one or more phenotypes in three or more extant species, using Metropolis–Hastings Markov Chain Monte Carlo sampling. The algorithms also estimate missing phenotypes of extant species and numbers of speciation events that occurred on all branches of the phylogeny. The algorithms are discussed and their performance is evaluated using simulated data. That evaluation shows that precise estimation of rates of evolution of one or a few phenotypes requires large phylogenies. Estimation accuracy improves with the number of species on the phylogeny. [ABSTRACT FROM AUTHOR]

Maximum likelihood is a potentially powerful approach for investigating the tempo of diversification using molecular phylogenetic data. Likelihood methods distinguish between rate-constant and rate-variable models of diversification by fitting birth-death models to phylogenetic data. Because model selection in this context is a test of the null hypothesis that diversification rates have been constant over time. strategies for selecting best-fit models must minimize Type 1 error rates while retaining power to detect rate variation when it is present. Here I examine model selection, parameter estimation, and power to reject the null hypothesis using likelihood models based on the birth-death process. The Akaike information criterion (AIC) has often been used to select among diversification models; however. I find that selecting models based on the lowest AIC score leads to a dramatic inflation of the Type 1 error rate. When appropriately corrected to reduce Type 1 error rates, the birth-death likelihood approach performs as well or better than the widely used gamma statistic, at least when diversification rates have shifted abruptly over time. Analyses of datasets simulated under a range of rate-variable diversification scenarios indicate that the birth-death likelihood method has much greater power to detect variation in diversification rates when extinction is present. Furthermore, this method appears to be the only approach available that can distinguish between a temporal increase in diversification rates and a rate-constant model with nonzero extinction. I illustrate use of the method by analyzing a published phylogeny for Australian agamid lizards. [ABSTRACT FROM AUTHOR]