Physical constraints on body size in teleost embryos

All members of the subphylum "Vertebrata" display the characteristics of the vertebrate body plan. These characteristics become apparent during the phylotypic period, in which all vertebrate embryos have a similar body shape and internal organization. Phylogenetic constraints probably limit the morphological variation during the phylotypic period. Physical laws, however, also limit growth and morphogenesis in embryos. We investigated to what extent oxygen availability-as a physical constraint-might limit morphological variation during embryonic development. This paper gives an analysis of time-dependent diffusion into spherical embryos without a circulatory system. Equilibrium appeared to settle in about 1.5 min in running water and in about 10min in stagnant water. Hence, steady-state conditions were assumed and expressions for maximum body size were obtained for spherical, cylindrical and sheet-like embryos in running water and spherical embyros in stagnant water. Predictions of the model based on literature data suggest that in running water-both for spherical, cylindrical and sheet-like embryos-diffusion alone suffices to cover the oxygen needs of a teleost embryo in its phylotypic period. The size of carp (Cyprinus carpio) and African catfish (Clarias gariepinus) embryos is very close to the predicted maximum. This suggests that in these species the development of a functional circulatory system is correlated with the onset of oxygen shortage. Oxygen availability is therefore a potentially important physical constraint on embryonic morphology, though in most species the circulatory system becomes functional well in advance of the onset of oxygen shortage and other demands than oxygen delivery (e.g. nutrient distribution, waste disposal, osmoregulation) might require the development of a circulatory system.