Formalising the law of diminishing returns in metabolic networks using an electrical analogy

Abstract The way biological systems respond to changes in parameter values caused by mutations is a key issue in evolution and quantitative genetics, as it affects fundamental aspects such as adaptation, selective neutrality, robustness, optimality, evolutionary equilibria, etc. We address this question using the enzyme-flux relationship as a model of the genotype-phenotype relationship. Applying an analogy between electrical circuits and metabolic networks, we show that a behaviour of diminishing returns, which is commonly observed at various phenotypic levels, is inevitable, irrespective of the complexity of the system.