Body size and temperature are the two most important variables affecting nearly all biological rates and times1,2,3,4,5,6,7. The relationship of size and temperature to development is of particular interest, because during ontogeny size changes and temperature often varies8,9,10,11,12. Here we derive a general model, based on first principles of allometry and biochemical kinetics, that predicts the time of ontogenetic development as a function of body mass and temperature. The model fits embryonic development times spanning a wide range of egg sizes and incubation temperatures for birds and aquatic ectotherms (fish, amphibians, aquatic insects and zooplankton). The model also describes nearly 75% of the variation in post-embryonic development among a diverse sample of zooplankton. The remaining variation is partially explained by stoichiometry, specifically the whole-body carbon to phosphorus ratio. Development in other animals at other life stages is also described by this model. These results suggest a general definition of biological time that is approximately invariant and common to all organisms.
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We thank S. Dodson, M. Ernest, C. M. Del Rio, E. Toolson, T. Turner and B. Wolf for comments or discussions that improved this manuscript. J.F.G. thanks J. S. Gillooly for support and encouragement. J.F.G., G.B.W. and J.H.B. are grateful for the support of the Thaw Charitable Trust and a Packard Interdisciplinary Science Grant; V.M.S., G.B.W. and J.H.B. for the support of the National Science Foundation; and E.L.C. for the support received as a MacArthur Fellow. G.B.W. also thanks the Theoretical Physics Department at Oxford Unviersity for its hospitality, and the EPSRC for support.
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