not restricted to cases with regular dispersal only, although the relaxation of regular dispersal is not not sufficient to explain the qualitative differences in the results as shown in the previous section.

The description of the random patterns investigated in [@Vuilleumier06] does not provide all information necessary for an in-depth comparison with our results. In [@Vuilleumier06] the number of dispersal connections was chosen randomly for each of the $2,000$ metapopulations. Additional information provided on two particular patterns suggest that the densities are comparable or higher than the densities we investigated in our study. From our results we therefore do not expect a significant impact of dispersal asymmetry at these density of connections.

The analysis of the results in [@Vuilleumier06] is based on the number of connected patches in contrast to our analysis using the global mean number of connections $L/N$. The statistics of the number of connected patches seems to differ significantly between the asymmetric and the symmetric connectivity matrices investigated, a phenomenon we were not able to reproduce. In particular the example of a symmetric random pattern with more than $85$ connections per patch but only $96$ connected patches raises questions, since the largest cycle of closed dispersal in 