Optimization and variability can coexist

From molecule counting in bacterial chemotaxis to photon counting in human vision, many biological systems function near the physical limits to their performance. Some see this optimality as a natural consequence of evolution, while others emphasize that evolution is not generally guaranteed to find even local optima. More concretely, microscopic parameters of many biological systems -- be it protein copy numbers or spatial locations of retinal photoreceptors, patterns and strengths of synaptic connections, or sensing thresholds in gene regulatory networks -- are highly variable, and this variability seems like prima facie evidence against optimization. Here we show that this intuition is misleading: in problems ranging from transcriptional regulation to neural computation, variability in parameters can coexist with near optimal performance. Abstracting away domain-specific details, we show that this is possible because the parameter spaces of real biological systems are high dimensional. We discuss the implications of these observations for a range of biological and computational examples.