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Abstract:
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A fundamental question in competition-colonization trade-off is to find subgroups of species according to the similarity of their longitudinal trajectories. In this paper, we propose a novel method named COMPARING for cluster analysis of longitudinal profiles for the species abundances in a biological system. In COMPARING, generalized estimating equation (GEE) is used to account for both the compositional and longitudinal dependence structures, nonparametric B-spline approximation is used to model the longitudinal curves, and a pairwise-distance penalization is used to identify subgroups with similar longitudinal patterns. We further develop and implement the linearized alternating direction method of multipliers (L-ADMM) algorithm for the proposed model and establish its convergence property. Theoretically, we show that the subgroups can be correctly identified with a high probability. Empirically, we illustrate the advantage of COMPARING over its competitors in terms of the accuracy of recovering the underlying clusters. We apply COMPARING to a real dataset to demonstrate how the method detects biologically meaningful subgroups of blood-borne parasites in African buffalo.
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