cooperative behavior is widely spread in microbial populations . 
 an example is the expression of an extracellular protease by the lactic acid bacterium lactococcus lactis , which degrades milk proteins into free utilizable peptides that are essential to allow growth to high cell densities in milk . 
 cheating , protease - negative strains can invade the population and drive the protease - positive strain to extinction . by using multiple experimental approaches , as well as modeling population dynamics 
 , we demonstrate that the persistence of the proteolytic trait is determined by the fraction of the generated peptides that can be captured by the cell before diffusing away from it . 
 the mechanism described is likely to be relevant for the evolutionary stability of many extracellular substrate - degrading enzymes .