Can Simpson's paradox explain co-operation in Pseudomonas aeruginosa biofilms?

Co-operative behaviours, such as the production of public goods, are commonly displayed by bacteria in biofilms and can enhance their ability to survive in environmental or clinical settings. Non-co-operative cheats commonly arise and should, theoretically, disrupt co-operative behaviour. Its stability therefore requires explanation, but no mechanisms to suppress cheating within biofilms have yet been demonstrated experimentally. Theoretically, repeated aggregation into groups, interleaved with dispersal and remixing, can increase co-operation via a 'Simpson's paradox'. That is, an increase in the global proportion of co-operators despite a decrease in within-group proportions, via differential growth of groups. We investigate the hypothesis that microcolony formation and dispersal produces a Simpson's paradox that explains bacterial co-operation in biofilms. Using the production of siderophores in Pseudomonas aeruginosa as our model system for co-operation, we use well-documented co-operator and siderophore-deficient cheat strains to measure the frequency of co-operating and cheating individuals, in-situ within-microcolony structures. We detected significant within-type negative density-dependant effects that vary over microcolony development. However, we find no evidence of Simpson's paradox. Instead, we see clear within-microcolony spatial structure (cheats occupying the interior portions of microcolonies) that may violate the assumption required for Simpson's paradox that group members share equally in the public good.