Formal Relationships between Neuronal Response Properties and Psychophysical Performance

One of the major goals of sensory neuroscience is to understand the relationships between physiology and behaviour. To this end, we derived equations that predict what an observer's psychophysical performance should be from the properties of the neurons carrying the sensory code. Our model neurons were characterized by their tuning function to the stimulus, and the random process that generates spikes. We used a generalized Poisson spiking process that can generate any Fano factor (ratio of variance to mean) ? 1. The tuning function was either a sigmoid (Naka-Rushton) function or a Gaussian function. We predicted psychophysical performance by calculating Fisher information, which is approximately equal to the maximum achievable decoding precision. For a population of neurons with identically shaped tuning functions, distributed with a constant density across a log stimulus axis, the Fisher information is given by a remarkably simple expression. In this case, its value is independent of the stimulus value, and this gives rise to Weber's Law. We also allowed certain neuronal parameter values to increase with stimulus value, which gave a near-miss to Weber's law, as often found in contrast discrimination. Our work has two major benefits. Firstly, we can quickly work out the performance of physiologically plausible population coding models by evaluating simple equations, rather than using slow and laborious Monte Carlo simulations. Secondly, the equations themselves give deep insights into the relationships between physiology and psychophysical performance.