Kolmogorov vector fields with robustly permanent subsystems

The following results are proven. All subsystems of a dissipative, Kolmogorov vector field x(over dot)(i) = x(i)f(i)(x) are robustly permanent if and only if the external Lyapunov exponents are positive for every ergodic probability measure A with support in the boundary of the nonnegative orthant. If the vector field is also totally competitive, its carrying simplex is C-1. Applying these results to dissipative Lotka-Volterra systems, robust permanence of all subsystems is equivalent to every equilibrium x* satisfying f(i)(x*) > 0 whenever x*(i) = 0. If in addition the Lotka-Volterra system is totally competitive, then its carrying simplex is C-1. (C) 2002 Elsevier Science (USA).