the upper bound for the expectation value of the number of extinct simulation for cases where all simulations went extinct, $1,000\exp(-6.9\times
    10^{-3} t)$, as derived in the manuscript text. From the figure it becomes evident, that the number of non-extinct simulations after an initial relaxation phase indeed decreases exponentially in time (i.e. linear in this logarithmic plot). The upper bound approaches $1/M$ with $t\to T$, which is a general result for sufficiently large $M$ and $T$ as a Taylor expansion of expression shows. For this reason the boundary line indeed exhibits the border between the cases marked red and yellow in Figure \[fig:balanced\].](E50-itime.eps){width=".6\textwidth"}

How meaningful is the statistical evaluation of the results with respect to the effect of the symmetry of dispersal patterns on expected extinction times of metapopulations? In order to approach this question we aim to derive lower and upper bounds for extinction times in the red and green regions of the figures, which then help to evaluate the graphical presentation of the results in more detail. If we disregard the initial time period of relaxation of the metapopulation to a quasistationary state, we can assume that the statistics of extinction times is exponentially distributed. This exponential distribution 