Effects of size and temperature on developmental time


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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Figure 1: The effect of incubation temperature on mass-corrected embryonic development time for amphibians (a), fish (b), multivoltine aquatic insects (c) and zooplankton (d) incubated at different constant temperature.
Figure 2: Plot as Fig. 1 but for marine fishes in the field (see Methods).
Figure 3: Plot as Fig. 1 but for aquatic ectotherms (data from Fig. 1a–d) and birds.
Figure 4: Plot as Fig. 1 but for post-embryonic (hatching to adult) development time for zooplankton (rotifers, copepods and cladocerans) incubated at different constant temperatures ranging from 5 to 30 °C.
Figure 5: The relationship between deviations for the fitted line in Fig. 4 (that is, Tc/(1 + (Tc/273)) versus t/m1/4) and whole-body carbon to phosphorus ratios (C:P) for adults of these species.


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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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Correspondence to James. F. Gillooly.

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