A Model for Responses of Vertebral Numbers in Fish to Environmental Influences During Development

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Abstract
A model is proposed in which the number of vertebrae formed in an embryo is determined by two independent processes each building up with time. The processes may possibly but not necessarily represent growth and differentiation. Final number is fixed by the level that one process has attained when it is suddenly terminated by arrival of the second process at a critical level. Varying the temperature or other environmental conditions during development can differentially affect the time courses of the two processes and hence alter the numerical outcome. The model, termed "atroposic," is shown to encompass a welter of apparently conflicting published data on vertebral responses of many fish species to different constant temperatures or to single or double temperature changes. It suggests how vertebral numbers may respond strongly and in either direction to temperature perturbations, and how the responses may be extralimitary, and how large responses may be produced by quite brief temperature pulses. Concepts of several temperature-sensitive periods and of shock effects are abandoned. The model is shown to be capable of computerized fit to almost all published data on variation in vertebrae, but to only some on variation in fin-ray number. The atroposic model seems to approximate reality, but the present mathematical form may be only a special case of a more general form yet to be developed.Key words: environmental conditions, meristics, models, temperature responses, vertebrae counts, Salmo trutta, Oryzias latipes, Plecoglossus altivelis