pH feedback and phenotypic diversity within bacterial functional groups of the human gut Helen Kettle a , Ruairi Donnelly a,b,d,n , Harry J. Flint c , Glenn Marion a a Biomathematics and Statistics Scotland, Kings Buildings, Edinburgh EH9 3JZ, UK b Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK c Microbiology Group, Rowett Institute of Nutrition and Health, University of Aberdeen, Greenburn Road, Bucksburn, Aberdeen AB21 9SB, UK d Department of Biology, University of York, York YO10 5YW, UK HIGHLIGHTS  Microbial diversity in the human colon is very high with apparently large redundancy (and hence diversity) within functional groups.  Using computer simulation we propose and analyse a fluctuation dependent mechanism for the promotion of diversity.  pH fluctuations follow from microbial growth and interact with small differences in acid tolerance between strains to promote microbial diversity. article info Article history: Received 27 May 2013 Received in revised form 21 September 2013 Accepted 24 October 2013 Available online 7 November 2013 Keywords: Colon Diversity Fluctuating Microbial Competitive exclusion abstract Microbial diversity in the human colon is very high with apparently large functional redundancy such that within each bacterial functional group there are many coexisting strains. Modelling this mathema- tically is problematic since strains within a functional group are often competing for the same limited number of resources and therefore competitive exclusion theory predicts a loss of diversity over time. Here we investigate, through computer simulation, a fluctuation dependent mechanism for the promotion of diversity. A variable pH environment caused by acidic by-products of bacterial growth on a fluctuating substrate coupled with small differences in acid tolerance between strains promotes diversity under both equilibrium and far-from-equilibrium conditions. Under equilibrium conditions pH fluctuations and relative nonlinearity in pH limitation among strains combine to prevent complete competitive exclusion. Under far-from-equilibrium conditions, loss of diversity through extinctions is made more difficult because pH cycling leads to fluctuations in the competitive ranking of strains, thereby helping to equalise fitness. We assume a trade-off between acid tolerance and maximum growth rate so that our microbial system consists of strains ranging from specialists to generalists. By altering the magnitude of the effect of the system on its pH environment (e.g. the buffering capacity of the colon) and the pattern of incoming resource we explore the conditions that promote diversity. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The attempt to explain the mechanisms behind the abundant bio-diversity seen in many resource competition systems, e.g. Hutchinson's ‘paradox of the plankton’ (Hutchinson, 1961), has generated many years of rich debate. The paradox is that although basic resource competition theory predicts the competitive exclu- sion of competing species by the most successful species, with only the same number of species co-existing as there are distinct resources, observations show that in fact far more species than resources coexist in most ecosystems (Tilman, 1977, 1981; Rothhaupt, 1988; Sommer, 1985). Hutchinson himself believed that the paradox was best explained by the prevention of the system from reaching equilibrium as a result of changing external conditions. However, Huisman and Weissing Huisman and Weissing (1999, 2001, 2002) showed that chaotic dynamics can result purely from species competition for abiotic resources, thus internal mechanisms can also keep the system away from equili- brium, and hence from competitive exclusion. Generally in microbial systems, a few abundant taxa dominate the community but also present is a long tail of low abundance taxa which can flourish under favourable environmental condi- tions (Sogin et al., 2006). The microbial system in the human gut is one of the most diverse and heavily populated in existence (Whitman et al., 1998) with up to 10 12 bacteria for every gram of gut contents (Gibson et al., 2004) and several hundred different Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology 0022-5193/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2013.10.015 n Corresponding author. Tel.: þ44 131 451 4731. E-mail address: rd118@hw.ac.uk (R. Donnelly). Journal of Theoretical Biology 342 (2014) 62–69