  In this work, we consider distributed agreement tasks in microbial
distributed systems under stochastic population dynamics and competitive
interactions. We examine how competitive exclusion can be used to solve
distributed agreement tasks in the microbial setting. To this end, we develop a
new technique for analyzing the time to reach competitive exclusion in systems
with two competing species under biologically realistic population dynamics. We
use this technique to analyze a protocol that exploits competitive interactions
to solve approximate majority consensus efficiently in microbial systems. To
corroborate our analytical results, we use computer simulations to show that
these consensus dynamics occur within practical time scales.
