Optimization and variability can coexist

TL;DR

This paper demonstrates that biological systems can operate near optimal performance while exhibiting high parameter variability due to 'sloppy' dependencies, reconciling optimization with observed biological diversity.

Contribution

It introduces the concept of 'sloppiness' in parameter dependence, explaining how near-optimal performance coexists with extensive parameter variability in biological systems.

Findings

Performance depends weakly on many parameters near the optimum.

Parameter space entropy can be extensive despite high performance.

Variability in parameters is compatible with near-optimal functionality.

Abstract

Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this intuition is wrong. Near an optimum, functional performance depends on parameters in a "sloppy'' way, with some combinations of parameters being only weakly constrained. Absent any other constraints, this predicts that we should observe widely varying parameters, and we make this precise: the entropy in parameter space can be extensive even if performance on average is very close to optimal. This removes a major objection to optimization as a general principle, and rationalizes the observed variability.