Neurobiologists recently developed tools to record from large populations of neurons, and early results suggest that neurons interact to encode information jointly. However, traditional statistical analysis techniques are inadequate to elucidate these interactions. This thesis develops two multivariate statistical dependence measures that, unlike traditional measures, encompass all high-order and non-linear interactions. These measures decompose the contributions of distinct subpopulations to the total dependence. Applying the dependence analysis to recordings from the crayfish visual system, I show that neural populations exhibit complex dependencies that vary with the stimulus. Using Fisher information to analyze the effectiveness of population codes, I show that optimal rate coding requires negatively dependent responses. Since positive dependence through overlapping stimulus attributes is an inherent characteristic of many neural systems, such neurons can only achieve the optimal code by cooperating.