patterns are in agreement with our observations, that the degree of symmetry of dispersal matrices has no significant impact on metapopulation viability at intermediate density of dispersal connections [cp. @Vuilleumier10 p. 213, Fig. 6, difference between the plots in the right column].

\[sec:conclusions\]Conclusions
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We investigated the consequences of the symmetry of dispersal patterns on the viability of metapopulations. Our analyses are based on simulations of a stochastic patch occupancy model.

First we define the degree of dispersal symmetry, $\gamma$, which is based on the symmetry of the connectivity matrix (Equation \[eq:def-deg-asymm\]). In order to be able to minimise possibly confounding effects we restrict our main analysis to regular dispersal patterns, where asymmetry does neither affect the homogeneity of dispersal nor the local balances of incoming and outgoing dispersal connections. For these patterns we do not see any negative effect of dispersal asymmetry. For the more general case of non-regular dispersal patterns minor negative effects of asymmetric dispersal on metapopulation viability are confirmed, but only at rather weak densities of dispersal (cp. Section \[sec:discussion:regul\]). At these densities differences in dispersal symmetry generally are accompanied by other hierarchical differences of the dispersal network. This e.g. becomes evident from a neat example 