An allometric tridimensional model of self-thinning for a gregarious tunicate

A tridimensional allometric model of self-thinning was tested in a tunicate population of Pyura praeputialis in the Antofagasta Bay. northern Chile. T he theory tested follows the bidimensional allometric theory of Osawa and A llen for the self-thinning rule proposed for plants. except that in additio n to mean individual mass we included three new concepts: the number of lay ers (an equivalent of the leaf area index, [LAI] used in plants). the effec tive unit area, and the density per unit effective area. We assumed constan t tunicate mass per effective unit area and allometry for mean dimensions o f the population. The tridimensional model can be reduced to a bidimensiona l one if density is expressed as the density per unit effective area, which corresponds to the number of individuals relative to the effective area oc cupied by individuals when they conform a monolayer. The model allows for r andom sampling and rules out the selection for samples or stands at maximum crowding. The self-thinning of P. praeputialis through a tridimensional mo del showed an exponent of -1.518 (95% CI, -1.635 to -1.401) for mean tunica te 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 thos e predicted from tridimensional allometric theory. The results of this new approach increase the variance explained in comparison to that of classical bidimensional models.