Concurrent growth of phenotypic features: a phenomenological universalities approach

Different physical features of an organism are often measured concurrently, because their correlations can be used as predictors of longevity, future health, or adaptability to an ecological niche. Since, in general, we do not know a priori if the temporal variations in the measured quantities are causally related, it may be useful to have a method that could help us to identify possible correlations and to obtain parameters that may vary from population to population. In this paper we develop a procedure that may detect underlying relationships. We do this by generalizing the recently introduced concept of phenomenological universalities to the complex field. In this generalization, allometric growth is described by a complex function, whose real and imaginary parts represent two phenotypic traits of the same organism. As particular solutions of the resulting problem, we obtain generalizations of the Gompertz and the von Bertalanffy-West growth equations. We then apply the procedure to two biological systems in order to show how to determine the existence of mutual interference between trait variations.