[mariuskempe]

That's an interesting point. In fact, the expectation of the random walk is always the same as its starting value, because, although most of the walks go to 0 like you observed, there are very occasionally walks that drift upward to astronomical values.

As for the usefulness of this kind of walk: the process we're modelling is an evolutionary one, where the rate of change is fixed (in this case within the species) and we'd like to detect 'random' (non-selected) evolutionary paths by comparing simulations to historical data.