Rearranging Eq. (D2) yields (D5) Inserting Eq. (D5 into Eq. (D4) yields: (D6) Inserting Kleiber’s Law, Eq. (2), into Eq. (D6) gives (D7) By defining the taxon-specific parameters a and b as (D8) Eq. (D7 simplifies to (D9) Growth ceases when the derivative in Eq. (D9) equals 0. This occurs when m M, the mass at maturity, implying that (D10) Eq. (D9) thus becomes (D11) Separating variables yields (D12) Defining (D13) 1 1 3 4 4 1 m m dm a dt M − − − = transforms Eq. (D12) into (D14) Integrating and applying the boundary condition that ( = 0) = 0 yields the sigmoid mass-versus-age growth curve: (D15) The age at maturity can be approximated by setting = (1 −ε M, where ε ≪ : (D16) Since 0 ≪ M our expression for simplifies further to (D17) which implies that (D18) This result is consistent with numerous observations (Lindstedt 1981, Calder 1984, Schmidt-Nielsen 1986) that biological timescales (such as lifespan, blood circulation time, etc.) are generally proportional to M1− 4. Hence the WBE ontogenetic theory may provide a theoretical link to empirical observations that greater ages at maturity are positively correlated with longer lifespans and adult body masses, and a more fully-developed theory might help explain the great longevity of the pre-Flood patriarchs. THE AUTHOR Leo (Jake) Hebert, III earned a B.S. from Lamar University, an M.S. from Texas A&M University, and a Ph.D. (all in physics) from the University of Texas at Dallas. His Ph.D. work examined the possible link between solar activity, cosmic rays, and weather and climate. He has been passionate about creation research since his teenage years. He is a research scientist at the Institute for Creation Research in Dallas, TX, where he has been employed since 2011. 1 4 1 1 4 4 0 4 1 1 aM t m m e M M − − = − − HEBERT Allometric and metabolic scaling 2023 ICC 227
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