  One of the key challenges in synthetic biology is devising robust signaling
primitives for engineered microbial consortia. In such systems, a fundamental
signal amplification problem is the majority consensus problem: given a system
with two input species with initial difference of $\Delta$ in population sizes,
what is the probability that the system reaches a state in which only the
initial majority species is present?
  In this work, we consider a discrete and stochastic version of competitive
Lotka--Volterra dynamics, a standard model of microbial community dynamics. We
identify new threshold properties for majority consensus under different types
of interference competition:
  - We show that under so-called self-destructive interference competition
between the two input species, majority consensus can be reached with high
probability if the initial difference satisfies $\Delta \in \Omega(\log^2 n)$,
where $n$ is the initial population size. This gives an exponential improvement
compared to the previously known bound of $\Omega(\sqrt{n \log n})$ by Cho et
al. [Distributed Computing, 2021] given for a special case of the competitive
Lotka--Volterra model. In contrast, we show that an initial gap of $\Delta \in
\Omega(\sqrt{\log n})$ is necessary.
  - On the other hand, we prove that under non-self-destructive interference
competition, an initial gap of $\Omega(\sqrt{n})$ is necessary to succeed with
high probability and that a $\Omega(\sqrt{n \log n})$ gap is sufficient.
  This shows a strong qualitative gap between the performance of
self-destructive and non-self-destructive interference competition. Moreover,
we show that if in addition the populations exhibit interference competition
between the individuals of the same species, then majority consensus cannot
always be solved with high probability, no matter what the difference in the
initial population counts.
