A game theory model for gut bacterial nutrient utilization strategies during human infancy

Abstract

Despite the fact that infant gut colonization patterns have been extensively studied, we have limited knowledge about the underlying ecological processes. This particularly relates to the ecological choice of nutrient utilization strategies. The aim of the current study was therefore to compare empirically determined nutrient utilization strategies with that expected from a combinatorial game theory model. Observational analyses for 100 mother–child pairs suggested mother–child transmission of specialists with the potential to use few nutrients. Generalists, on the other hand, with the potential to use many nutrients, peaked at three months of age for the children. The level of generalists was gradually replaced with specialists up to 12 months of age. Game theory simulation revealed a competitive advantage of generalists in an expanding population, while more specialized bacteria were favoured with the maturation of the population. This suggests that the observed increase in generalists in the three-month-old children could be due to an immature, expanding gut microbiota population while the increase of specialists at 12 months could be due to population maturation. The simulated and empirical data also correspond with respect to an increased α diversity and a decreased β diversity with the number of simulations and age, respectively. Taken together, game theory simulation of nutrient utilization strategies can therefore provide novel insight into the maturation of the human gut microbiota during infancy.

1. Introduction

Eukaryotes depend on a range of services provided by prokaryotes. These include the production of essential metabolites, pathogen protection and nutrient utilization [1]. The large intestine represents the main site of microbial colonization for animals [2]. A range of host benefits has been documented for microorganisms in the large intestine, ranging from mode modulation to providing energy to gut epithelial cells [3]. Therefore, the gut microbiota has even been considered an organ in itself [4].

Despite the importance, very little is known about the underlying ecology in establishing the gut microbiota in the large intestine of humans with increased α diversity, and reduced β diversity with age [5,6]. This particularly relates to the high species richness and functional redundancy [7], combined with an apparent deterministic colonization pattern [8]. The current explanation models advocate the importance of either host selection of service providers [5] or free competition [9]. In the host selection hypothesis, the host actively selects the service providers, while in the free competition model the service providers are selected indirectly through the survival of the host. Host selection of gut bacteria was already discovered in the 1990s by bacteria-free mouse experiments, where it was shown that early colonizers can induce nutrient production from gut epithelial cells [10]. More recently it has been shown that mother's milk contains a range of complex oligosaccharides that are highly selective for bifidobacteria [11], providing a range of benefits to infants [1]. In support of the free competition model, on the other hand, is the relatively large difference in microbiota composition across individuals, while still showing high similarity in functional capacity [7,9]. However, none of the current models can fully explain the observed colonization patterns of the human infant gut. The positive selection model cannot explain the high diversity and functional redundancy of the gut microbiota since it assumes niche selection, while the free competition model cannot explain the convergence of the gut microbiota taxonomic composition across individuals by age [12]. Although there are stable individual differences in the healthy adult gut microbiota [13], there is recent evidence for extensive strain sharing [14].

In this paper, we explore the possibility that the microbial colonization pattern of the human infant gut can follow patterns explained by game theory under a generalist–specialist model (outlined in figure 1). Conceptually, the model represents an extension of the host selection model in order to explain the high species richness and functional overlap. The game theory represents decisions where the outcome is dependent on the choices of others. Using the game theory concept to explain ecological distribution patterns was an idea conceived of by Maynard Smith back in the 1970s [15]. This theory explains resource-sharing across individuals within a population, and how diversity can be maintained. More recently, game theory has been used to explain species richness distribution for both macro- and microorganisms [16]. A particularly attractive feature of the game theory model is that it can be used to explain the establishment of ecosystems with high species richness despite limited numbers of resources [17]. Furthermore, the model does not have to assume barriers in dispersal, like the neutral theory in ecology [18]. Thus, game theory can also explain high microbial species riches under the classical notion by Baas Becking and Beijerinck, stating that everything is everywhere, but the environment selects [19].

Figure 1.

Model for resource competition. (a) Nutrient utilization pattern where red spheres indicate lack of utilization, while green represents the possibility of nutrient utilization. (b–d) Representation of outcomes of competition for the different models. (Online version in colour.)

Competition for multiple nutrient resources resembles that of combinatorial game theory with a large number of players (bacterial species), where the decision of one player affects the outcome of the other players [20]. The simplest form of game theory for microorganisms is the choice of being a specialist that is highly competitive for a limited number of nutrients, or a generalist with a large nutrient utilization repertoire, but a lower competitiveness for each resource [21]. Despite a relatively limited number of nutrients, the number of generalist–specialist strategies are high (sum of binominal coefficient over the number of nutrients). Competition for nutrients under a game theory model could potentially explain the coexistence of more species than nutrients, representing a new framework for better understanding the colonization of the human gut by microbes.

The aim of the current work was to evaluate whether the observed gut colonization patterns for human infants can be explained by a game theory model in relation to generalist or specialist strategies for multiple nutrient competition. This was done by probabilistic simulation in comparison with empirical observations of α and β diversity, in addition to a novel index for nutrient utilization potential.

2. Material and methods

(a). Empirical observations

We reanalyzed the data from Nilsen et al. [22]. Briefly, the first recruited 100 mother–child pairs were selected from the PreventADALL study [23,24] with faecal samples for at least four of the five time points; maternal sample at approximately 18-week pregnancy, offspring meconium samples from birth, and faecal samples from 3, 6 and 12 months of infant age. The functional assignments for nutrient (carbon source) utilization potential were determined by reduced metagenome sequencing (RMS) [12], by functional matching towards the virtual metabolic human (VMH, www.vmh.life) database [25].

(b). Probabilistic simulation

All simulations were done in Matlab R2019a (MathWorks Inc, Natick, MA). For the probabilistic simulation of the ecological measures we assumed 10 nutrient sources and 1023 different nutrient utilization strategies (representing all possible combinations). We assumed an initial colonization of 10⁵ cells with a random distribution of nutrient utilizations strategies. We then assumed an expansion of the population to 10⁶ cells. Then, we assumed a constant population at 10⁶ cells until 10⁸ competition events. The competitions were done assuming the influx of one random unit of nutrients per competition event. In 95% of the competitions, we used a random selection of two bacteria in the population for the competition. To avoid drift, in 5% of the competitions we included one random bacterium from the simulated population and one random bacterium from a metapopulation where the 1023 nutrition utilization types were equally distributed.

The possible outcomes from the pairwise competitions were either that none of the bacteria could use the nutrient with no formation of new cells, that one bacterium would win the competition with the formation of two new cells of that type, or that the nutrient would be shared between the two competing bacteria with the formation of one cell of each type.

We evaluated three competition models. The main generalist–specialist competition model includes a balance between the benefit and cost of having the capacity of nutrient utilization. Given that two organisms compete for the same nutrient, the organism with the overall lowest nutrient utilization capacity will win. In the second model, we removed the disadvantage of having a high nutrient utilization capacity, while in the third neutral model all species had an equal probability of nutrient utilization. All simulations were repeated 10 times. The three models are schematically outlined in figure 1, with the Matlab code being presented in the electronic supplementary material.

(c). Ecological measures

For both the empirical and the simulated data, we included standard measures of α diversity using Simpson's index, and β diversity measures using the Bray–Curtis index. We also included a nutrient capacity (NC) index where we multiplied the percentage of each species with the number of potential nutrient sources the species can use. The resulting numbers were then summed across all species as illustrated in the formula

$$\text{NC}=\sum _{k=0}^n(a\times x),$$

where a is the number of functions for a given species, x is the percentage of the given species and n represents all the species in a sample.

(d). Statistical testing

We used non-parametric testing for the differences between the age categories for the empirical data. Significances were determined using the Kruskal–Wallis test, with post hoc testing for determining pairwise differences, while Spearman correlations were used for the comparison between the empirical and simulated data. All tests were performed using Matlab R2019a.

3. Results

(a). Empirical functional and taxonomic development

The nutrient utilization capacity showed a median of 24 for the 177 bacterial species identified in this work with known nutrient utilization potential (electronic supplementary material, table S1). Bacteroides thetaiotaomicron showed the highest nutrient utilization potential with 77 nutrients, while Coprococcus catus showed the lowest with three nutrients. Bacteria with the widest nutrient utilization potential showed a peak at three months, while declining until 12 months of age, as revealed by the NC index (figure 2c).

Figure 2.

Comparison of empirical (a–c) and simulated data (d–l). The colour code for the empirical data represents significance with red bars being significantly different from the blue. Error bars represent 95% confidence interval. The simulated graphs are based on mean values for 10 simulations, with the red dots representing the starting points. (Online version in colour.)

The empirical data showed a trend with increasing α diversity and decreasing β diversity with age. The meconium samples, however, showed a relatively low β diversity, resembling that of mothers (figure 2a,b)

(b). Simulated functional and taxonomic development

The generalist–specialist simulations revealed a rapid increase in bacteria with a high NC until about 5 million competitions. Then, there was a gradual decrease in NC until 100 million competitions (figure 2f). For the hard completion model, bacteria showed a gradual increase in NC throughout the whole simulation period, while for the neutral model there was a stable NC (figure 2i,l).

Alpha diversity generally showed the opposite trend of NC (figure 2d,g,j,f,i,l). The most pronounced difference between the models was that the generalist–specialist model showed an increased α diversity from about 5 million competitions (figure 2d), while the hard competition showed a rapid decline (figure 2g). For the β diversity, both the generalist–specialist and the hard competition models showed a decline over time (figure 2e,h), while the neutral model showed an increase (figure 2k).

(c). Comparison of empirical and simulated taxonomic development

To obtain a more direct comparison between empirical and simulated data we assumed that the mother's microbiota reflects the microbiota at the age of 5 years, and that this is reached after simulations for 10⁸ competition events.

General trends in comparing empirical and simulated data were revealed by linear regression analyses. The generalist–specialist model showed the same direction in correlation as for the empirical data for all metrices, while the hard competition model only showed the same direction for Bray–Curtis distances, and the neutral model showed no directional resemblance to that of the empirical data. The p-values, however, were generally quite high (figure 3).

Figure 3.

Correlations between age and index values for (a) 1 − Simpson's D, (b) Bray–Curtis distances and (c) nutrient capacity. The different indexes were mean-standardized, while age was log10 transformed. Regression coefficients and p-values are given for Spearman correlations. (Online version in colour.)

4. Discussion

The generalist–specialist game theory modelling provides a potential explanation for the long-standing controversy of increased α and β diversity of the gut microbiota by age [26], which was also reflected in the empirical data in the current work. Earlier explanations are centred on the neutral theory of ecology [27,28]. The neutral theory of ecology, however, is heavily dependent on assumptions about dispersal, making the theory very complex [18]. Here, we show by game theory modelling that a simple trade-off between having the possibility of utilizing high numbers of nutrients and being competitive for these explain better the empirical data than a neutral model. Furthermore, since our model is based on niche selection, it still follows the classical notion of niche selection in microbial ecology [19].

The early increase in generalists at three months for infants, with a subsequent decrease with age, resembles that observed for the generalist–specialist model simulation in the switch from an expanding population to a population with constant size. This may suggest that the expanding gut microbiota population during infancy promotes generalists. The main generalist colonizers of the human infant gut at three months of age are Bifidobacterium longum and Bacteroides vulgatus [29]. B. longum is adapted to utilizing complex human milk oligosaccharides [30,31], while B. vulgatus is adapted to mucin degradation and dietary polysaccharide utilization [32]. Both are generally considered non-harmful; thus the selection of generalists during infancy may be a mechanism to prevent pathogen colonization [33].

With age, the diversity within individuals increases, while the diversity across individuals decreases [12,27,34]. Most of the adult-associated gut bacteria, however, are likely to be recruited after weaning. These are mainly representatives of the class Clostridia, with the ability to form endospores, representing a likely vector for transmission of strictly anaerobic bacteria [34,35]. The relatively low nutrient utilization potential of the bacteria recruited with age suggests they are specialists. The selection of specialists in the gut with age indicates a more functionally mature gut microbiota, supporting that they provide essential functions [1].

The generalist–specialist model shows the best resemblance to the observed diversity and functional colonization patterns for the models compared, adding an explanation to functional redundancy and decreased β diversity with age for the host selection hypothesis [5]. Furthermore, from the principle of parsimony, there is only one underlying assumption of higher competitive advantage if an organism is adapted to use few rather than many nutrients in the generalist–specialist model. For the alternative neutral model to explain the colonization patterns one would have to assume both dispersal restrictions and speciation to be underlying factors [28]. The hard competition model, although simple in nature, cannot explain the observed diversity and functional redundancy of the gut microbiota since the given composition of nutrients would represent a single niche, and the niche exclusion principle would select a single species [36].

We acknowledge that our simulations represent oversimplifications of the complex interactions in the human gut, but still we believe the simulations have validity in explaining ecological patterns in relation to controversial issues such as increased α diversity and decreased β diversity in the human gut with age, in addition to functional redundancy.

Data accessibility

This article has no data.

Authors' contributions

I.L.A. did database searches and commented on the paper; K.R. wrote the paper and did the simulations.

Competing interests

We declare we have no competing interests.

Funding

This work was financially supported by the Norwegian Research Council through project no. 301364 UnveilMe: ‘Unveiling the role of microbial metabolites in human infant development’.