Data from: A structural approach for understanding multispecies coexistence

Although observations of species-rich communities have long served as a
primary motivation for research on the coexistence of competitors, the
majority of our empirical and theoretical understanding comes from
two-species systems. How much of the coexistence observed in species rich
communities results from indirect effects among competitors that only
emerge in diverse systems remains poorly understood. Resolving this issue
requires simple, scalable, and intuitive metrics for quantifying the
conditions for coexistence in multispecies systems, and how these
conditions differ from those expected based solely on pairwise
interactions. To achieve these aims, we develop a structural approach for
studying the set of parameter values compatible with n-species coexistence
given the geometric constraints imposed by the the matrix of competition
coefficients. We derive novel mathematical metrics analogous to
stabilizing niche differences and fitness differences that measure the
range of conditions compatible with multispecies coexistence,
incorporating the effects of indirect interactions emerging in diverse
systems. We show how our measures can be used to quantify the extent to
which the conditions for coexistence in multispecies systems differ from
those that allow pairwise coexistence, and apply the method to a field
system of annual plants. We conclude by presenting new challenges and
empirical opportunities emerging from our structural metrics of
multispecies coexistence.