A Consumer-Resource Description of Public-Goods Production in Microbes

During the last century, microbes were studied as organisms that behave individually.
However, over the recent years they have become an important system to study the
evolution of collective behaviours in biological systems. The production of public goods,
substances that are secreted to the external medium and provide benefit to cells in the
vicinity, is one of these behaviours. The aim of this project is to propose a family of
models that can describe the growth of microbial populations when they produce public
goods. In particular, we will focus our description on those bacteria that use quorum
sensing. Quorum sensing is a cell-to-cell communication mechanism that can regulate
the expression of certain collective behaviours, like the production of public goods, in
response to changes in population density. It is proposed a mean-field description based
on consumer-resource ecological models. Therefore, as the simplest possible description,
our formalism intends to be a first step to develop a more elaborated theory to study the
production of public goods in microbes.