results
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First of all the results depicted in Fig. \[fig:balanced\] suggest that the impact of the degree of symmetry on metapopulation viability decreases with increasing $L/N$. Already at $L/N>3$ no statistical significant impact of the degree of symmetry, i.e. no systematic differences depending on the degree of symmetry, can be detected on the basis of the scenarios and the statistical evaluation chosen.

At a small number of dispersal connections per patch ($L/N=1,2$) metapopulation viability is significantly reduced for more symmetric dispersal (Fig. \[fig:balanced\], lower panels). The reason for this effect straightforwardly can be understood from considerations concerning the structure of the underlying dispersal patterns: Let us first focus on patterns with $L/N=1$. In this case a metapopulation with a symmetric dispersal pattern necessarily consists of a number of patches only pairwisely connected through dispersal (Figure \[fig:Algorithm-examples\]). The largest closed dispersal cycle (synonymous to the giant component of the dispersal network [@Berchenko09]), hence, involves only two patches. For the particular metapopulation model applied a lower bound for the extinction probability of a pair of patches per time step is $e^2$. On the contrary the mean size of the largest closed dispersal cycle estimated from the $100$ dispersal patterns generated for 