Fig. 5

Evolutionary outcomes dominated by different strategies. a Theoretical calculations show \(\gamma /\mu\) dependence of producer fractions as a function of the abundance of ferric ions and the normalized environmental stress, where \(\gamma /\mu\) ranges from selfishness (\(\gamma /\mu\) = 0.1) to loyal cooperation (\(\gamma /\mu\) = 50). b Schematic showing that conditional privatization stabilizes bacterial cooperation in the presence of environmental stresses