A Reason for Pleomerism

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Abstract
Pleomerism, the increase in vertebral number with maximum recorded length for species within a family, may be explained for fish by hydrodynamic considerations. A model is developed that suggests that the upper limits of the slope of the relation between log vertebral number and log length should be 0.43 in laminar flow and 0.35 in turbulent flow. These slopes are compared with those of previous studies only with difficulty because (1) those values were for predictive rather than functional regressions, (2) the slope will depend on the range in length of various species across temperature zones, and (3) no distinction was made between structural and locomotor vertebrae. Variations in shape also complicate the relation between vertebral count and length, there are latitudinal factors involved, and maximum length is probably only a weak correlate of the length at which natural selection may be concentrated. When these factors are considered, it is to be expected that observations would provide only a rough approximation to theory.The theory underlying the model is also used to derive a formula for the stride length of fish motion that is then compared with empirical results. Key words: vertebrae counts, body size, locomotion, hydrodynamic equations, mathematical model, stride length

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