Summary: Ecological vector fields \(\dot x_j= x_if_i(x)\) on the nonnegative cone \(\mathbb{R}^n_+\) on \(\mathbb{R}^n\) are often used to describe the dynamics of \(n\) interacting species. These vector fields are called permanent (or uniformly persistent) if the boundary \(\partial\mathbb{R}^n_+\) of the nonnegative cone is repelling. We construct an open set of ecological vector fields containing a dense subset of permanent vector fields and containing a dense subset of vector fields with attractors on \(\partial\mathbb{R}^n_+\). In particular, this construction implies that robustly permanent vector fields are not dense in the space of permanent vector fields. Hence, verifying robust permanence is important. We illustrate this result with ecological vector fields involving five species that admit a heteroclinic cycle between two equilibria and the Hastings-Powell teacup attractor.