Errors drive the evolution of biological signalling to costly codes

Reduction of costs in biological signalling seems an evolutionary advantage, but recent experiments have shown signalling codes shifted to signals of high cost with an underutilization of low-cost signals. Here I derive a theory for efficient signalling that includes both errors and costs as constraints and I show that errors in the efficient translation of biological states into signals can shift codes to higher costs, effectively performing a quality control. The statistical structure of signal usage is predicted to be of a generalized Boltzmann form that penalizes signals that are costly and sensitive to errors. This predicted distribution of signal usage against signal cost has two main features: an exponential tail required for cost efficiency and an underutilization of the low-cost signals required to protect the signalling quality from the errors. These predictions are shown to correspond quantitatively to the experiments in which gathering signal statistics is feasible as in visual cortex neurons.