Relative Growth by the Elongated Jaws of Gars: A Perspective on Polyphasic Loglinear Allometry

Nonlinear regression was used to fit power functions with different forms for random error to data for length of the upper jaw versus length of the rest of body in two species of gars. Growth by the jaws of these species was reported earlier to conform to a pattern of polyphasic loglinear allometry indicative of relatively rapid growth by the jaw in small individuals (allometric exponent greater than 1) and relatively slow growth by the jaw in larger ones (allometric exponent less than 1). The new analyses revealed, however, that the pattern of relative growth by jaws of these fishes does not change with body size: the jaws grow more slowly than the rest of the body throughout life. The flaw in earlier investigations was the unrealistic assumption that data comprising a single sample in log domain form two (or more) statistically distinct distributions when expressed in arithmetic domain. The paradigm used in the current study provides a simple way to fit and compare different power functions, with different forms for random error, directly to raw data and thereby obviates the use of logarithmic transformations in allometric research.