THE USE OF THE ABOAV-WEAIRE LAW TO ESTIMATE A BIOLOGICAL CONSTRAINT

Developmental processes may impose limitations and directionality in the mode of development of a particular structure. The main problem is to determine the nature and the respective effects of physical and biological constraints in the development of organisms. The Aboav-Weaire law is a semi-empirical law developed to explain the topological structure of physical materials. In the present paper, we make a formal analysis of the quantitative relationships between physical and biological constraints in biological structures by using the inflorescence of the Araceae as a case study. The Aboav-Weaire law permits to obtain a quantitative estimate of the biological constraint acting on the inflorescences of this family. In the case of the Araceae, the empirical curve presents a constant deviation with respect to the Aboav-Weaire law. This deviation is due to the presence of a biological constraint as opposed to a physical constraint. The biological constraint tends to decrease the variance of the number of sides while it is the inverse situation for the physical constraint. The results obtained using the Araceae model can be used to study the interrelationships between biological and physical constraints in any organism or biological structure.