  In the analysis of complex ecosystems it is common to use random interaction
coefficients, often assumed to be such that all species are statistically
equivalent. In this work we relax this assumption by choosing interactions
according to the cascade model, which we incorporate into a generalised
Lotka-Volterra dynamical system. These interactions impose a hierarchy in the
community. Species benefit more, on average, from interactions with species
further below them in the hierarchy than from interactions with those above.
Using dynamic mean-field theory, we demonstrate that a strong hierarchical
structure is stabilising, but that it reduces the number of species in the
surviving community, as well as their abundances. Additionally, we show that
increased heterogeneity in the variances of the interaction coefficients across
positions in the hierarchy is destabilising. We also comment on the structure
of the surviving community and demonstrate that the abundance and probability
of survival of a species is dependent on its position in the hierarchy.
