Analysing the information contributions and anatomical arrangement of neurons in population codes
Yarrow, Stuart James
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Population coding—the transmission of information by the combined activity of many neurons—is a feature of many neural systems. Identifying the role played by individual neurons within a population code is vital for the understanding of neural codes. In this thesis I examine which stimuli are best encoded by a given neuron within a population and how this depends on the informational measure used, on commonly-measured neuronal properties, and on the population size and the spacing between stimuli. I also show how correlative measures of topography can be used to test for significant topography in the anatomical arrangement of arbitrary neuronal properties. The neurons involved in a population code are generally clustered together in one region of the brain, and moreover their response selectivity is often reflected in their anatomical arrangement within that region. Although such topographic maps are an often-encountered feature in the brains of many species, there are no standard, objective procedures for quantifying topography. Topography in neural maps is typically identified and described subjectively, but in cases where the scale of the map is close to the resolution limit of the measurement technique, identifying the presence of a topographic map can be a challenging subjective task. In such cases, an objective statistical test for detecting topography would be advantageous. To address these issues, I assess seven measures by quantifying topography in simulated neural maps, and show that all but one of these are effective at detecting statistically significant topography even in weakly topographic maps. The precision of the neural code is commonly investigated using two different families of statistical measures: (i) Shannon mutual information and derived quantities when investigating very small populations of neurons and (ii) Fisher information when studying large populations. The Fisher information always predicts that neurons convey most information about stimuli coinciding with the steepest regions of the tuning curve, but it is known that information theoretic measures can give very different predictions. Using a Monte Carlo approach to compute a stimulus-specific decomposition of the mutual information (the stimulus-specific information, or SSI) for populations up to hundreds of neurons in size, I address the following questions: (i) Under what conditions can Fisher information accurately predict the information transmitted by a neuron within a population code? (ii) What are the effects of level of trial-to-trial variability (noise), correlations in the noise, and population size on the best-encoded stimulus? (iii) How does the type of task in a behavioural experiment (i.e. fine and coarse discrimination, classification) affect the best-encoded stimulus? I show that, for both unimodal and monotonic tuning curves, the shape of the SSI is dependent upon trial-to-trial variability, population size and stimulus spacing, in addition to the shape of the tuning curve. It is therefore important to take these factors into account when assessing which stimuli a neuron is informative about; just knowing the tuning curve may not be sufficient.