AN ALLOMETRIC TRIDIMENSIONAL MODEL OF SELF-THINNING FOR A GREGARIOUS TUNICATE

Abstract

A tridimensional allometric model of self-thinning was tested in a tunicate population of Pyura praeputialis in the Antofagasta Bay, northern Chile. The theory tested follows the bidimensional allometric theory of Osawa and Allen for the self-thinning rule proposed for plants, except that in addition to mean individual mass we included three new concepts: the number of layers (an equivalent of the leaf area index, [LAI] used in plants), the effective unit area, and the density per unit effective area. We assumed constant tunicate mass per effective unit area and allometry for mean dimensions of the population. The tridimensional model can be reduced to a bidimensional one if density is expressed as the density per unit effective area, which corresponds to the number of individuals relative to the effective area occupied by individuals when they conform a monolayer. The model allows for random sampling and rules out the selection for samples or stands at maximum crowding. The self-thinning of P. praeputialis through a tridimensional model showed an exponent of −1.518 (95% ci,−1.635 to −1.401) for mean tunicate visceral mass, and an exponent of −1.489 (95% ci, −1.588 to −1.390) for the corrected bidimensional model. The two exponents were identical to those predicted from tridimensional allometric theory. The results of this new approach increase the variance explained in comparison to that of classical bidimensional models.