Feeding ducks, bacterial chemotaxis, and the Gini index

TL;DR

This paper investigates how bacterial chemotaxis influences resource distribution and inequality among bacteria, using a simple model and the Gini index to quantify effects like chemotactic levelling and its impact on population fitness.

Contribution

It introduces a novel application of the Gini index to quantify resource uptake inequality in chemotactic bacterial populations and explores the redistributive effects of chemotaxis.

Findings

Chemotaxis can reduce inequality in resource uptake among bacteria.

The model demonstrates chemotactic levelling as a redistribution mechanism.

Implications for population fitness and resource allocation are discussed.

Abstract

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.