River networks' universal fractal structure not only defines their hydrology and connectivity, but has also profound biological consequences, especially regarding stability and persistence of organismal populations. While rivers' scaling features are captured by Optimal Channel Networks, knowledge on adequate network topologies has hitherto been only partially transferred across geo- and biosciences. Consequently, ecologists have often studied riverine populations via random networks not respecting real rivers' scaling character. Here we show that an alleged property of such random networks (branching probability) is a scale-dependent quantity that does not reflect any recognized metric of rivers' fractal character, and hence cannot be a driver of ecological dynamics. Moreover, we show that random networks lead to biased estimates of population stability and persistence, while only Optimal Channel Networks yield estimates comparable to real rivers. We hence advocate Optimal Channel Networks as model landscapes for realistic and generalizable projections of ecohydrological dynamics in riverine networks.