ABSTRACTAim  Optimal body size theories predict that large clades have a single, optimal, body size that serves as an evolutionary attractor, with the full body size spectrum of a clade resulting from interspecific competition. Because interspecific competition is believed to be reduced on islands, such theories predict that insular animals should be closer to the optimal size than mainland animals. We test the resulting prediction that insular clade members should therefore have narrower body size ranges than their mainland relatives.Location  World‐wide.Methods  We used body sizes and a phylogenetic tree of 4004 mammal species, including more than 200 species that went extinct since the last ice age. We tested, in a phylogenetically explicit framework, whether insular taxa converge on an optimal size and whether insular clades have narrow size ranges.Results  We found no support for any of the predictions of the optimal size theory. No specific size serves as an evolutionary attractor. We did find consistent evidence that large (> 10 kg) mammals grow smaller on islands. Smaller species, however, show no consistent tendency to either dwarf or grow larger on islands. Size ranges of insular taxa are not narrower than expected by chance given the number of species in their clades, nor are they narrower than the size ranges of their mainland sister clades – despite insular clade members showing strong phylogenetic clustering.Main conclusions  The concept of a single optimal body size is not supported by the data that were thought most likely to show it. We reject the notion that inclusive clades evolve towards a body‐plan‐specific optimum.

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