Applying Fuzzy Logic to Identify Heterogeneity of the Allometric Response in Arithmetical Space

Abstract

Customary approaches in allometric examination include linear regression in geometrical space, as well as, nonlinear regression in the original scale of data. These protocols could not produce consistent results in a circumstance in which the allometric response manifest heterogeneity as the covariate changes. The paradigm of log-nonlinear allometry offers a mechanism for the analysis of heterogeneity in geometric space. However, the use of a logarithmic transformation in allometry is controversial. In this contribution, we present a fuzzy approach aimed to examination of allometric heterogeneity in direct arithmetical space. Offered construct relies on a hybrid procedure integrating crisp cluster analysis and a fuzzy inference system of Mamdani type. Calibration aims depended on an extensive data set composing measurements of eelgrass leaf biomass and their corresponding areas. Results on raw data suggest heterogeneity more clearly manifest in the normalization constant than in the allometric exponent. Nevertheless, differences in normalization constant values among clusters are only slight for data remaining after removal of inconsistent replicates. This suggests heterogeneity produced by intrinsic factors of leaf growth.