  We consider a multi-species community modelled as a complex network of
populations, where the links are given by a random asymmetric matrix J, with
fraction 1-C of zero entries, where C reflects the over-all connectivity of the
system. The non-zero elements of J are drawn from a gaussian distribution with
mean 'mu' and standard deviation . The signs of the elements J reflect the
nature of density-dependent interactions, such as predatory-prey, mutualism or
competition, and their magnitudes reflect the strength of the interaction. In
this study we try to uncover the broad features of the interspecies
interactions that determine the global robustness of this network, as indicated
by the average number of active nodes (i.e. non-extinct species) in the
network, and the total population, reflecting the biomass yield. We find that
the network transitions from a completely extinct system to one where all nodes
are active, as the mean interaction strength goes from negative to positive. We
also find that the total population, displays distinct non-monotonic scaling
behaviour with respect to the product 'mu'C, implying that survival is
dependent not merely on the number of links, but rather on the combination of
the sparseness of the connectivity matrix and the net interaction strength.
Moreover, the total population levels are optimal when the network has
intermediate net positive connection strengths. At the local level we observe
marked qualitative changes in dynamical patterns, ranging from anti-phase
clusters of period 2 cycles and chaotic bands, to fixed points, under the
variation of mean 'mu' of the interaction strengths. Lastly, we propose an
effective low dimensional map to capture the behavior of the entire network,
and this provides a broad understanding of the interplay of the local dynamical
patterns and the global robustness trends in the network.
