Since Robert May's work on random community matrices it has been known that stability tends to decrease with complexity. Recently, it was shown that this is not necessarily true in competitive ecosystems. We investigated the stability of random ecosystems and found that it can largely be predicted by simple matrix statistics such as the mean and the variance of the interaction coefficients. We use this to explain why stability can increase as well as decrease with complexity in ecological communities. We argue that the variance, and to a lesser extent the mean, of the interaction coefficients go a long way in explaining patterns in the stability of ecosystems.
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