Chemical Game Theory: Linking Metabolite Diversity, Biosynthetic Architecture, and Realized Payoffs

Plant chemodiversity is generally evaluated through metabolite richness, relative abundance, compositional dissimilarity, and biosynthetic organization. However, these descriptors characterize chemical states without explicitly identifying which metabolites, chemical classes, or biosynthetic pathways gain or lose relative representation during transitions between states. Here, we introduce Chemical Game Theory as an operational analogy inspired by the relative-performance principle of replicator dynamics. Metabolites are treated as elementary chemical strategies, biosynthetic pathways constitute higher-order strategies, and normalized chromatographic abundances define their frequencies within a mixture. A centered log-ratio quantity, termed realized chemical payoff within this framework, retrospectively quantifies whether a component gained or lost proportional representation relative to the abundance-weighted mean log change in the system. It is not inferred from a payoff matrix and does not represent Darwinian fitness, interaction strength, or absolute biosynthetic production. Shannon diversity describes metabolite-level coexistence, whereas the General Biosynthetic Diversity Index, GBDI, characterizes abundance-weighted pathway organization and intrapathway diversification. The framework was applied to previously published GC-MS and GC-FID profiles of essential oils from leaves and four developmental stages of the reproductive organ of Piper mollicomum Kunth, sampled over five months. Leaves had the highest numerical mean Shannon diversity and GBDI, although the Shannon difference was not statistically significant. The reproductive stages followed temporally variable compositional trajectories. Across the five descriptive monthly blocks, the terpenoid route gained relative representation during the Stage I to II and Stage III to IV transitions, whereas the mixed category declined. Chemical dominance, Shannon diversity, GBDI, and realized payoff captured related but non-equivalent dimensions of relative chemical organization. As a proof of concept, Chemical Game Theory provides a quantitative language for retrospective analysis of compositional redistribution. Its proposed use for prioritizing plant material and its transferability to other chromatographic platforms require validation with independent datasets, biological replication, absolute quantification, and bioactivity-guided experiments.