  Classic experiments on the distribution of ducks around separated food
sources found consistency with the `ideal free' distribution in which the local
population is proportional to the local supply rate. Motivated by this
experiment and others, we examine the analogous problem in the microbial world:
the distribution of chemotactic bacteria around multiple nearby food sources.
In contrast to the optimization of uptake rate that may hold at the level of a
single cell in a spatially varying nutrient field, nutrient consumption by a
population of chemotactic cells will modify the nutrient field, and the uptake
rate will generally vary throughout the population. Through a simple model we
study the distribution of resource uptake in the presence of chemotaxis,
consumption, and diffusion of both bacteria and nutrients. Borrowing from the
field of theoretical economics, we explore how the Gini index can be used as a
means to quantify the inequalities of uptake. The redistributive effect of
chemotaxis can lead to a phenomenon we term `chemotactic levelling', and the
influence of these results on population fitness are briefly considered.
