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

Alexandra S. Penn, Tim C.R. Conibear, Richard A. Watson, Alex R. Kraaijeveld, Jeremy S. Webb
DOI: http://dx.doi.org/10.1111/j.1574-695X.2012.00970.x 226-235 First published online: 1 July 2012


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.

  • Biofilm development
  • Simpson's paradox
  • co-operation
  • siderophore production
  • Pseudomonas aeruginosa


Understanding the evolutionary dynamics within complex microbial populations may offer new opportunities for their control or therapeutic treatment, as well as for the refinement and improvement of theoretical models of evolution. A key problem in evolutionary biology is the evolution of co-operation: how are mutants that exploit the benefits of co-operation without paying the costs (cheats) suppressed within populations (e.g. Hamilton, 1964; Maynard Smith, 1964; Maynard Smith & Szathmary, 1995; Frank, 1998; Okasha, 2006)? In an unstructured population in which cheats and co-operators both require a costly ‘public good’, but only co-operators produce it, a ‘tragedy of the commons’ would be expected (Hardin, 1968; Rankin et al., 2007). That is, cheats would out-compete co-operators, leading ultimately to the disappearance of the resource on which both depend and to a population crash. Co-operating bacteria in biofilms produce numerous public goods such as extra-cellular matrix, siderophores, quorum sensing molecules and surfactants (Crespi, 2001; Ghannoum & O'Toole, 2004; West et al., 2007). However, although non-producer cheats arise commonly in vivo, including within biofilms association with chronic infection (De Vos et al., 2001; Schaber et al., 2004), co-operation is remarkably stable within these systems. This has generated much interest (e.g. Rainey & Rainey, 2003; Griffin et al., 2004; Kreft, 2004; Buckling et al., 2007), but remains to be explained fully or experimentally.

A possible explanation may lie in well-known theory that spatial localization and repeated interactions (or anything that preferentially distributes the benefits of co-operation predominantly to those who exhibit the co-operative trait) usually support the evolution of co-operation (Levin & Kilmer, 1974; Wilson, 1975, 1987; Michod & Sanderson, 1985; Nowak & May 1992, Mitteldorf & Wilson, 2000; Lehmann & Keller, 2006; El Mouden et al. 2010, although see Haurt & Doebeli, 2004 for a counter-example). It is also clear that imposed group structure and appropriate dispersal mechanisms can allow co-operation and synergy to be evolutionarily stable, as demonstrated in numerous artificial selection experiments (Wade, 1976, 1977; Goodnight, 1985, 1990; Craig & Muir, 1995; Muir, 1995; Swenson et al., 2000a, b; Penn, 2006). The ability of repeated random group formation, dispersal and re-formation to provide a mechanism for suppression of cheats has also been demonstrated in well-known models (Wilson, 1975, 1980, 1978). Under these conditions, a ‘Simpson's paradox’ (Simpson, 1951) may arise, in which the global proportion of co-operators can increase even whilst it decreases within any one group. This effect is obtained when cheats always increase in frequency relative to co-operators within any one group, but groups with a higher initial proportion of co-operators grow larger than those with a smaller proportion. More generally, a difference in magnitude, if not sign, between the average local change in proportion and global change in proportion of cheats must occur if group structure is affecting selection pressures on social behaviours. If individuals remain in groups for too long (i.e. when groups are allowed to go to the all-cheat equilibrium), this effect will disappear. However, a process of repeated group formation, development, dispersal and re-formation can maintain the global proportion of co-operators at a higher level than would be predicted from within-group dynamics only.

A Simpson's paradox in concert with an aggregation and dispersal process has recently been proposed as a mechanism by which co-operation may be maintained in bacterial populations. Chuang et al. (2009) have shown that given appropriate population structure, such an effect may increase the population of public-good-producing co-operators relative to non-producer cheats in a synthetic system of two strains of Escherichia coli. However, in that experiment, any natural population structure was removed (the bacteria were maintained in a well-mixed planktonic phase throughout), and artificial population structure was imposed (by means of microtitre plate wells). Thus, the importance of Simpson's paradox in natural bacterial populations remains to be determined. Natural populations (that are neither artificially mixed nor artificially subdivided) do in fact exhibit considerable population structure. The predominant mode of bacterial life in nature is in biofilms, within which cells display numerous seemingly co-operative traits. Moreover, the biofilm state, in particular the formation, dispersal and reformation of microcolonies, has the potential to naturally provide appropriate population structure to facilitate the evolution of co-operation. Although the microcolony is a less well-defined structure than a plate well, simple individual-based models indicate that rigidly imposed group structure is not required to exhibit Simpson's paradox or support co-operation, and that such effects can be meaningfully measured without pre-defined group boundaries (Powers et al., 2011a, b). We are thus motivated to investigate whether a Simpson's paradox effect could provide an explanation for the persistence of co-operation in the natural biofilm state.

Bacteria in biofilms display a naturally grouped structure consisting of distinct individual microcolonies extending from the substratum layer. These colonies undergo a formation, development and dispersal process that bears a striking similarity to the aggregation and dispersal process required for Simpson's paradox. Biofilms form on surfaces via the attachment and subsequent proliferation of previously motile cells. Amongst the cells forming the substratum, certain individuals will become foci for rapid clonal growth and begin to form microcolonies (Conibear et al., 2009). We observe within our mixed-strain experiments that surrounding individuals commonly become incorporated into the colonies, leading to mixed microcolonies consisting of both cheats and co-operators (see Results).

Within colonies, cells proliferate rapidly (leading to the formation of steep resource gradients within the colony; Debeer et al., 1994). After a period of growth within colonies, a process of cell detachment is common, with either individual cells becoming motile once again and leaving the colony or propagules consisting of a small number of cells encased in extracellular matrix breaking off (Hall-Stoodley et al., 2004). Such cells or propagules are able to form new biofilm microcolonies downstream. If growth within microcolonies allows for a Simpson's paradox to be established, then the characteristic biofilm microcolony structure combined with repeated colony dispersal and re-formation could function to suppress cheats in scenarios in which bacterial public goods benefit individual survival.

Pseudomonas aeruginosa is a ubiquitous environmental bacterium and an opportunistic pathogen of both animals and plants. In its biofilm form, it is often implicated in chronic infection, particularly in immunocompromised patients (e.g. in the cystic fibrosis lung). The host's defence, which includes iron withdrawal by binding the element to an apotransferrin, is countered by the production of extracellular siderophores, iron-scavenging molecules, by wild-type P. aeruginosa (Guerinot, 1994; Ratledge & Dover, 2000). These molecules are released by the bacteria in the environment and therefore constitute a public good. They are costly to produce but provide fitness benefits when iron is limiting (Varma & Chincholkar, 2007). Pyoverdin-deficient mutant P. aeruginosa cheats, which occur commonly in vivo and which have been shown to accumulate over time (De Vos et al., 2001), do not produce the siderophores and can hence exploit the co-operative wild-type individuals.

In this study, we present the first experimental investigation of whether the key condition for the maintenance of co-operation via an aggregation and dispersal process, a Simpson's paradox, can occur within developing biofilm microcolonies, using a co-operator/cheat system of clinical relevance that occurs commonly in vivo.

Materials and methods

Bacterial strains and culture media

Pseudomonas aeruginosa PAO1 wild type and a pyoverdine (Pvd) siderophore mutant PvdF-2 (Mutant Library ID no. 1390, P. aeruginosa gene no. PA2396, gene product pyoverdine synthetase F, gene pvdF, genome position 2652992, transposon lSlacZ/hah) were obtained from the P. aeruginosa mutant library at the University of Washington Genome Center, Seattle, WA. Routine subculture of all P. aeruginosa strains was carried out on Luria Bertani (LB) medium or, where indicated, King's B medium containing 10 g L−1 glycerol, 20 g L−1 peptone, 15 g L−1 K2HPO4, 1.7 g L−1 NaHCO3, 15 g L−1 MgSO4·7H2O. The antibiotics ampicillin (100 µg mL−1), carbenicillin (200 µg mL−1) or tetracycline (40 µg mL−1), and the iron chelator Apotransferrin (200 µg mL−1) were added to media where appropriate. For biofilm culture, a Casamino acid (CAA) medium was used (5 g CAAs, 1.118 g K2HPO4·3H2O, 0.25 g MgSO4·7H2O), supplemented with sodium bicarbonate to make a 20-mM solution required for chelator activity (Griffin et al., 2004).

Genetic colour-tagging of P. aeruginosa

Plasmid pMF230 (Nivens et al., 2001) that enables constitutive expression of the green fluorescent protein gene in both E. coli and P. aeruginosa was a gift from Michael Franklin, Montana State University. Electrocompetent P. aeruginosa cells were transformed using a Bio-Rad GenepulserXcell™ with the pulse settings 200 Ω, 2.5 kV and 25 µF. Transformed strains were maintained on LB-agar plates containing 100 µg mL−1 ampicillin. Plates were examined under epifluorescence microscopy for green fluorescence, and colonies with bright and uniform fluorescence were selected for experiments.

Dual-strain biofilm culture and imaging

Biofilms containing P. aeruginosa wild-type and PvdF-2 pMF230 were grown in a polycarbonate three-channel flow cell with individual channel dimensions of 1 × 4 × 40 mm and were maintained under continuous culture using 10% strength CAA medium with 200 µg mL−1 apotransferrin. An apotransferrin concentration of 200 µg mL−1 was used as it was found to be the minimum concentration required to limit the growth of the PVDF-2 strain in monoculture under both planktonic batch culture and flow cell biofilm conditions (data not shown). This provides us with the conditions of iron-stress required to perform evolutionary experiments with co-operator/cheat strains. The technique used for inoculating and culturing biofilms in flow cells is as previously described (Moller et al., 1998; Webb et al., 2003). We used an inoculum containing 106 cells of each of the co-operator and cheat strains in 1 : 1 ratio. Before each imaging session commenced, the flow of medium was halted and 20 µL (concentration 1/100 000) of SYTO59, a vital red fluorescent nucleic acid stain allowing for analysis of living specimens (Zandvoort et al., 2002; Invitrogen), in 1 mL 10% CAA was injected into each channel. The flow cell was then clamped shut for 30 min, after which it was unclamped and medium allowed to flow through for 10 min before imaging commenced.

Confocal laser scanning images of biofilms were obtained using a Leica (TCS SP2 MP FCS) upright microscope. Images were acquired using identical gain, offset and pinhole settings for each data collection point. A single argon laser line was used with excitation wavelength of 488 nm and using an emission filter with a bandpass of 500–600 nm for the imaging of green fluorescent protein-tagged bacteria; for SYTO59-stained cells, the excitation wavelength used was 622 nm with the emission maximum at 645 nm. Microcolonies were initially selected for imaging at low magnification by generating random co-ordinates within each channel (excluding edges) and then choosing the closest colony within the field of view. Colonies were subsequently re-imaged at five equally spaced time points over 9 days. Stack depth was set to extend beyond the visible extent of the colony top and bottom. Three-dimensional rendering was performed on the Leica LCSlite package, and microcolony biomass was calculated using comstat software (Heydorn et al., 2000) on the Matlab platform. Intensity thresholds were chosen for each day such that the substratum and the extremities of the microcolony would both be measured. Threshold variance was necessary to allow for slight differences in the absorption of SYTO59 and was normalized as far as possible by comparing the same colony at a fixed distance from the coverslip on each day. Values are calculated means of data from 17 image stacks (with 5–6 image stacks from each of three different channels). After each microscopy session, the flow cell was attached again to the pump to allow continuation of the biofilm growth.

Assessment of pMF230 GFP plasmid stability

Because the biofilm culture medium used in our experiments did not contain antibiotics for selection maintenance of pMF230 in P. aeruginosa, an assessment of the stability of this plasmid in P. aeruginosa over the course of our biofilm experiments was carried out. Serial dilutions of P. aeruginosa biofilm effluents collected after 1, 5 and 26 days were plated onto P. aeruginosa cetrimide agar with and without 100 µg mL−1 carbenicillin. Fluorescent and non-fluorescent CFUs were counted under epifluorescence microscopy and using a low power ×4 objective. Percentage gfp loss was calculated using the number of fluorescent CFUs as a fraction of total number of P. aeruginosa CFUs. We observed 0%, 6.2% ± 0.3 and 16.6% ± 1.0 plasmid loss on days 1, 5 and 26, respectively. Moreover, epifluorescence microscopic analysis of single-strain P. aeruginosa pMF230 biofilms with flow cell apparatus did not reveal observable GFP fluorescence loss during our experiments. We are therefore confident that biological observations involving mixed-strain biofilms in the present work are not attributed to plasmid and GFP fluorescence loss.

Statistical analysis

We analysed total biomass with a linear regression, and the variation in proportion wild type/cheat (with values arcsine square root transformed before analysis) with a one-way anova. We analysed the proportion of cheats within microcolonies (with values arcsine square root transformed before analysis) with a one-way anova, followed by a post hoc Tukey test. Correlation between local and global proportions of cheats was analysed using Pearson.

To analyse microcolony growth, we used a linear modelling approach in R, a programming language and software environment for statistical computing and graphics. Separate analyses were carried out on total growth, wild-type growth and cheat growth. For each response variable, we performed two sets of analyses, one with total biomass and proportion cheats (again, using arcsine square root transformed values) as explanatory variables, and one with wild-type biomass and cheat biomass as explanatory variables. This was done to avoid interdependence of explanatory variables within the same analysis.

In each analysis, we fitted the full model (main factors plus interaction) first, followed by removal of the interaction (which proved to be non-significant in all analyses). Model simplification then continued by removing non-significant main effects until a minimal model was reached.

The five time points at which we measured microcolony biomass result in four intervals (e.g. interval 1 is between the first two time points; interval 4 between the penultimate and ultimate time point). Preliminary analyses showed that the strongest effects on growth were detected when two adjacent intervals were combined, rather than analysing the growth in the four intervals separately, or analysing growth over the period as a whole (i.e. all four intervals combined). Therefore, full analyses as described above were performed on growth in intervals 1 + 2, in intervals 2 + 3 and in intervals 3 + 4.


We examined the growth of microcolonies within biofilms over a 9-day period and carried out microscopic imaging and analysis at five time points within that period. Figure 1 shows a single representative microcolony (rendered in top-down and side-on views), at each of these five time points. After 24 h of growth, most of the microcolony consists of wild type (red fluorescence), with few cheats (green). As time progresses, the microcolony itself increases in overall biomass, and cheats make up a larger proportion of the microcolony's biomass than at the start. Distinct changes in microcolony structure and the distribution of cell types are also visible.

Figure 1

Representative microcolony imaged at the five different time points (T1–T5): wild-type cells are stained red, cheater cells are tagged green; see text for further details.

We used the imaging techniques described above to determine the biomass of wild-type and cheat cells in 17 microcolonies at five equally spaced time points over a 9-day period. The results of these biomass measurements are shown in Fig. 2. Total biomass steadily increases over time (linear regression, F1,83 = 18.36, P < 10−5), but the composition of the community in terms of relative proportions of wild types and cheats varies (one-way anova, F4,80 = 16.80, P < 10−6).

Figure 2

Total biomass and biomass of wild-type cells and cheater cells separately, of the 17 microcolonies at the five different time points (T1–T5): Bars show average ± SE.

Wild-type biomass increases until time point 4, after which time it declines. In contrast, cheats increase from time point 1 to time point 2, after which they decrease over time points 3 and 4, to then increase again at time point 5.

The changes in relative proportions of wild types and cheats, both at a local and global level, are shown in Fig. 3. Proportion cheats in the microcolonies fluctuate significantly over the five time points (F4,80 = 16.80, P < 10−6) and is much lower at time points 1 and 4 than at time points 2 and 5. Global cheat proportions show virtually the same pattern as local proportions, and there is a very high correlation between the two (r = 0.997, P < 10−4).

Figure 3

Average proportion cheats per microcolony at the five different time points (T1–T5; grey bars, average ± SE) and average global proportion cheats at these time points (black bars).

Next, we analysed how and to what degree growth of the microcolony as a whole, and of the two cell types separately, were correlated to initial biomass and proportion cheats. Figure 4 shows the data for the growth of total biomass, wild-type biomass and cheat biomass, as a function of proportion cheats, as that is our key explanatory variable. Table 1 shows the significance, and direction, of the effects of all explanatory variables.

Figure 4

Total microcolony growth (top row of panels), growth of wild-type cells (middle row of panels) and growth of cheater cells (bottom row of panels) plotted against proportion cheats for each microcolony: Growth is calculated for intervals 1 + 2 (= between time points 1 and 3), for intervals 2 + 3 (= between time points 2 and 4) and for intervals 3 + 4 (= between time points 3 and 5). Regression lines indicate significant correlations.

View this table:
Table 1

Overview of the minimal models in R with different response and explanatory variables when intervals 1 and 2, intervals 2 and 3 and intervals 3 and 4 are combined

Response variableExplanatory variablesIntervals 1 + 2Intervals 2 + 3Intervals 3 + 4
Total growthTotal biomassnsnsns
Proportion cheatsnsnsns
Wild-type biomassnsnsns
Cheat biomassnsnsns
Wild-type growthTotal biomassnsnsns
Proportion cheatsnspos, P = 0.0003pos, P = 0.03
Wild-type biomassnsneg, P = 0.02ns
Cheat biomassnspos, P = 0.006ns
Cheat growthTotal biomassnsnsns
Proportion cheatsneg, P = 0.01neg, P = 0.02ns
Wild-type biomasspos, P = 0.02nsns
Cheat biomassneg, P = 0.005nsns
  • pos, positive effect; neg, negative effect; ns, the explanatory variables did not have a significant effect on the response variable.

  • Significant effects and P-values are indicated in bold. Statistical interactions were not significant in any of the models.

First of all, growth in total biomass is never correlated with proportion cheats (Fig. 4, Table 1), or any of our other explanatory variables (Table 1). However various other significant correlations are observable. Cheat growth is negatively correlated with proportion cheats in intervals 1 + 2 and intervals 2 + 3 (Fig. 4, Table 1). Wild-type growth is positively correlated with proportion cheats in intervals 2 + 3 and intervals 3 + 4 (Fig. 4, Table 1). In intervals 1 + 2, cheat growth is positively correlated with wild-type biomass, and negatively correlated with cheat biomass (Table 1). In intervals 2 + 3, wild-type growth is negatively correlated with wild-type biomass and positively correlated with cheat biomass (Table 1).

The microcolonies also show characteristic changes in structure and spatial distribution of cheat and wild-type cells over the course of the experiment (Figs 1 and 5), with 16 of the 17 colonies imaged demonstrating a similar pattern of development. Typically, our images at T1 show (clonal) microcolonies composed of wild-type cells surrounded by a few individual cheat cells. Cheats at this stage are probably simply randomly distributed as a result of the attachment process; however, they may have begun to move towards wild-type microcolonies via chemotaxis. By T2 however, 48 h later, the structure of the colonies has changed distinctly, and we see numerous cheats surrounded by wild-type cells inside the microcolonies.

Figure 5

Microcolony imaged at the five different time points (T1–T5): Clear spatial structuring and differentiation between strains is visible. Wild-type cells are stained red, cheater cells are tagged green; see text for further details.


This work is the first description of co-operator/cheat dynamics in a continuous culture biofilm system and has allowed us to track changes that occur in real-time during microcolony development. Although we find no Simpson's paradox, a more complex picture has emerged. A Simpson's paradox should be visible within the biofilm if two basic conditions are met: Firstly, that the proportion of cheats increases over time within microcolonies (otherwise the cheat behaviour is not selfishly advantageous); secondly, that microcolonies with higher initial cheat proportions grow more slowly, that is total growth is negatively correlated with proportion of cheats (otherwise co-operation is not collectively advantageous). Neither of these conditions is observed consistently during our experiments. However, our experimental set-up is sufficiently sensitive to measure density-dependent growth effects, operating differently on the WT and cheat strains. For example, we find that the growth of each type is self-limiting at different times (cheat growth is negatively correlated with proportion cheats in intervals 1–3, and in intervals 2 + 3, wild-type growth is negatively correlated with wild-type biomass).

Since Simpson's paradox is observed in the artificial planktonic experiment described by Chuang et al. (2009) but not observed here within biofilms, this implies that assumptions about the behaviour and distribution of cheat and wild-type strains that hold for theoretical and artificial conditions do not necessarily hold true in the real biofilm context. Here, we consider the possibility that the more complex spatial structure, cell behaviour and group ‘membership’ could prevent the paradox from occurring.

In order for a Simpson's paradox to be visible in a set of groups that we observe, the fitness benefit of the public good in question should be evenly distributed over all the members of each group. In our experimental scenario, and in vivo, bacteria form their own group structure unlike Chuang's well-mixed plate wells. Chuang's experiment aimed to emulate microcolony structure and we assumed when imaging a microcolony that these would be appropriate groups to consider. However, the production, diffusion and use of siderophores and the dynamic nature of resource gradients forming within the colony may cause this assumption to be violated. For example, at T1, we see cheats surrounding wild-type colonies, but over the next time interval, the structure has changed to one of cheats surrounded by wild type (Figs 1 and 5). Whilst this structure remains in place and wild-type cells continue to grow over the rest of the experimental period, satellite cheat colonies (perhaps produced by clonal growth) also begin to grow around the principal microcolony. This changing spatial structure could play a significant role in determining which cells are connected via sharing of siderophores and hence constitute a valid group. It is well known that resource gradients within microcolonies can act to inhibit the growth of cells in the interior (Debeer et al., 1994). As a colony becomes larger, we would thus expect that the production and hence concentration of siderophores in the centre will become lower than that external to the colony. In this situation, although cheats surrounding and internal to the microcolony will both be subject to its influence with respect to the siderophores which its members produce, they will be exposed to different concentrations, and their growth may well be affected. Depending on the diffusibility of siderophores and hence the resources available, we might well expect to see cheats within the colony become self-limiting in this situation. This might well lead to the significant, negative density-dependence results that we observe over the first three time intervals. And indeed, the growth of wild-type biomass, if principally on the outside of the colony, might therefore be largely unaffected by these cheats that no longer act to reduce available siderophore concentrations. Instead, we observe a negative correlation of growth with within-type biomass during intervals 2 and 3, again implying resource competition restricted to immediate neighbours. In contrast, cheats in satellite colonies surrounding the co-operators might well still be able to profit from an increased availability of siderophores. We would expect that cheats internal and directly external to the microcolony would follow different growth curves and affect the growth of wild type in different ways as the system develops and the availability of siderophores in different locations changes. The disappearance of the significant cheat self-limiting effect observed in final growth stages may be due to the increased growth of satellite colonies within the boundaries of our image during that time. Given the differential structure within our field of view, it seems unlikely that the assumption of homogenous public good sharing is valid and possible that the scale over which resources are shared varies over time and with the particular structure present.

Another assumption that may be violated is that membership of the group is fixed at the outset and the proportions of cell types changed only by differential growth. This will of course hold within the context of a plate well; however, the situation in a real biofilm may be more dynamic. Cell migration within biofilms has been observed experimentally (Klausen et al., 2003), and the migration of cheats towards regions with higher concentrations of siderophores via chemotaxis may well be occurring here. Between T1 and T2 (Figs 1 and 5), we see the structure of colonies change from clonal wild-type groups surrounded by cheat cells, to larger microcolony structures with a large number of cheats surrounded by wild-type cells (note changing size of scale bars). We cannot determine whether cheats have migrated to the interior of colonies or whether they have been encapsulated by microcolony growth. However, cheat movement within microcolonies cannot be ruled out. Additionally, as each individual microcolony imaged is situated within a biofilm, the possibility of cheat cells from the surrounding substratum migrating towards siderophore-producing microcolonies certainly exists. This could be an additional factor changing the proportion of cheats associated with any given colony and, if cheats tended to move towards more productive colonies, could remove any correlation between proportion of cheats present and colony growth measured. Again, this dynamic behaviour would violate the assumptions of the theoretical or artificial models of the Simpson's paradox.

We used an apotransferrin concentration of 200 µg mL−1 in our experiments. The reference range for serum concentration of transferrin in humans is 2.5–4.3 mg mL−1 (Normansell et al., 1994), but may be much lower at the site of a P. aeruginosa biofilm infection. For example, transferrin levels within human sputum from cystic fibrosis patients, where P. aeruginosa biofilms are known to cause pathogenesis, have been measured as falling into two distinct groups of 23 µg mL−1 ± 15 and 75 µg mL−1 ± 58 (Brogan et al., 1975). Thus, it is possible that concentrations of apotransferrin similar to those used in our experiments may be experienced by P. aeruginosa during infection of the CF respiratory airway. Although we have not measured pyoverdine concentrations directly within our experiments, in the context of P. aeruginosa biofilm infections within cystic fibrosis, these have previously been measured to be at 0.85 µM ± 0.48 within cystic fibrosis sputum, a situation in which P. aeruginosa is iron-stressed (Haas et al., 1991). Whilst we have not attempted to recreate clinical transferrin and pyoverdin concentrations exactly, we have sought to recreate comparable conditions of iron-stress that would be necessary for the co-operator/cheat experiments described.

The population dynamics of pyoverdin-deficient P. aeruginosa cheats and pyoverdine-producing wild types within real microcolony structures have clear potential clinical relevance. Pyoverdine cheats are observed in the cystic fibrosis lung and accumulate over colonization time (De Vos et al., 2001), and the proportion of cheats that reduce overall production of a public good can potentially affect clinical outcomes. The presence of quorum sensing-defective mutants in clinical isolates for example has been shown to reduce the production of virulence factors and lead to the formation of weak biofilms (Schaber et al., 2004). Availability of iron is important for biofilm formation (Singh et al., 2002), and the presence of pyoverdine-deficient mutants in mixed biofilm has been shown to decrease total biofilm mass in vitro on a microplate system (Harrison and Buckling 2009). Ultimately, if cheats came to predominate in the population, the virulence of an infection might be reduced. Understanding the means by which cheats are suppressed or come to predominate within biofilm may suggest new avenues for therapeutic intervention.


The existence of conditions producing a Simpson's paradox has been detected in artificial planktonic bacterial co-operator-cheat systems. This same mechanism has been proposed as a possible explanation for the maintenance of co-operation in bacterial biofilms, the predominant mode of bacterial life in nature. We have examined whether microcolony structure within biofilms produces the conditions required for a Simpson's paradox to occur in a co-operator-cheat system. Firstly, we asked whether the proportion of cheats always increased within microcolonies; secondly, whether microcolonies containing a lower proportion of cheats had an increased overall growth rate. Using an experimental methodology that allows us to track the growth rates of co-operative and cheat strains within individual microcolonies in a developing biofilm over time and which is sensitive enough to detect significant density-dependant effects, we find no evidence of a Simpson's paradox or either of the conditions that should produce it.

We suggest that this is because several complicating effects in real biofilms violate the simple assumptions of the theoretical models or simplified experimental set-ups in which Simpson's paradox occurs. Simple models require equal sharing of public goods within a pre-defined group and that group membership is fixed at the outset, after which group size changes only via differential reproduction of the individuals initially present. We contend that neither of these conditions is satisfied in the real biofilm context. Firstly, the changing microcolony structure that we observe over time, in which cheats and co-operators occupy physically distinct areas of the microcolony which vary as colonies develop, coupled with limited diffusibility of siderophores through the extra-cellular matrix, will produce dynamically changing siderophore gradients. These gradients are both dependant on and affect the physical structure and development of the colony and the distribution of co-operators and cheats within it. The actual ‘group’ over which siderophores, and hence fitness, are shared does not correlate straightforwardly to the microcolony structure and probably varies over time. Secondly, the microcolony itself is not physically separated from the biofilm in which it grows. Over the course of colony development, we see cheats from the surrounding substratum become incorporated or possibly migrate into the colony itself meaning that group membership is not fixed. Individual bacteria are not necessarily passive recipients of a group structure that is imposed on them. Additionally, siderophores produced by individuals within a given microcolony will not be limited in extent to within the colony itself. Individuals in the surrounding substratum may also lie within the influence of the colony giving rise to chemotaxis towards the colony or meaning that they themselves are de facto members of the evolutionary group in question. From an evolutionary perspective, group membership will be defined by which individuals share a particular public good and thus influence each others' fitness. The identity of groups in the natural biofilm context is thus considerably more complex and dynamic than models in which group membership is artificially imposed. On the other hand, although it adds complication, the fact that organisms have dynamic behaviours that influence group structure has very interesting implications for the concurrent evolution of group structure and social behaviour (Penn et al., 2008; Powers et al., 2011a, b). Such factors must be taken into account in attempting to explain the evolution of co-operation in this context.


Thanks to Zoe Bigg, Michelle Collins, Natasa Polak and Simon Powers. This work was partially funded by a Biotechnology and Biological Sciences Research Council (BBSRC) David Phillips Fellowship to J.S.W. A.S.P. was funded by a Life Sciences Interface fellowship.


  • Editor: Thomas Bjarnsholt


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