  The Lotka-Volterra (LV) model is a simple, robust, and versatile model used
to describe large interacting systems such as food webs or microbiomes. The
model consists of $n$ coupled differential equations linking the abundances of
$n$ different species. We consider a large random interaction matrix with
independent entries and a block variance profile. The $i$th diagonal block
represents the intra-community interaction in community $i$, while the
off-diagonal blocks represent the inter-community interactions. The variance
remains constant within each block, but may vary across blocks.
  We investigate the important case of two communities of interacting species,
study how interactions affect their respective equilibrium. We also describe
equilibrium with feasibility (i.e., whether there exists an equilibrium with
all species at non-zero abundances) and the existence of an attrition
phenomenon (some species may vanish) within each community.
  Information about the general case of $b$ communities ($b> 2$) is provided in
the appendix.
