An exclusion principle and the importance of mobility for a class of biofilm models

Much of the earth's microbial biomass resides in sessile, spatially structured communities such as biofilms and microbial mats, systems consisting of large numbers of single-celled organisms living within self-secreted matrices made of polymers and other molecules. As a result of their spatial structure, these communities differ in important ways from well-mixed (and well-studied) microbial systems such as those present in chemostats. Here we consider a widely used class of 1D biofilm models in the context of a description of their basic ecology. It will be shown via an exclusion principle resulting from competition for space that these models lead to restrictions on ecological structure. Mathematically, this result follows from a classification of steady-state solutions based on a 0-stability condition: 0-stable solutions are in some sense determined by competitive balance at the biofilm base, whereas solutions that are not 0-stable, while less dependent on conditions at the biofilm base, are unstable at the base. As a result of the exclusion principle, it is argued that some form of downward mobility, against the favorable substrate gradient direction, is needed at least in models and possibly in actuality.