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Quartet: Disentangling positive and negative components of microbial interactions [1]

['Aamir Faisal Ansari', 'Department Of Chemical Engineering', 'Indian Institute Of Science', 'Bengaluru', 'Karnataka', 'Gayathri Sambamoorthy', 'Thrisha C. Alexander', 'Unilever R D India Pvt Ltd', 'Yugandhar B. S. Reddy', 'Janhavi Raut']

Date: 2026-09 

Interspecies interactions are characterized conventionally by the net influence, positive or negative, a species exerts on another. Community ecology theories rely on these net interactions to describe the behaviour of multispecies communities. The net interactions in turn comprise positive and negative components, arising typically from cross-feeding metabolites and competition for resources. The components remain challenging to disentangle, compromising descriptions of community behaviour. Here, we devised a method to estimate the components when metabolic interactions predominate. We conceived a theoretical resource partitioning strategy which when applied to data on species growth rates disentangles the components. Consequently, the net influence a species has on another is decomposed into its positive and negative components. The interactions between a pair of species are thus defined by the ‘quartet’ of underlying components, specifically the positive and negative components of the net influence of each species on the other. We applied the method to 28 in silico species pairs from a representative oral microbiome and an experimental auxoptroph pair from the literature. We found that positive and negative components had comparable strengths on average. Interestingly, we found species pairs with similar net interactions but disparate components, highlighting the importance of the quartet. Further, weak net interactions could arise from cancellation of strong components. Estimating the quartet helped better understand the complex transitions in community behaviour observed upon varying resource supply in silico and in vitro. The quartet thus offers a more fundamental characterization of interspecies interactions and may help build more reliable community ecology theories, with implications for understanding and design of microbial communities.

Multispecies microbial communities are important to healthcare, the environment, and biotechnology. Their behaviour depends on the interactions between the species involved. The interactions have been characterized conventionally by the net influence, positive or negative, a species has on another. This conventional view has limitations because the net influence is often made up of positive and negative underlying components, arising, for instance, from cross-feeding metabolites and competition for resources, respectively. Disentangling the components has been challenging. Here, we developed a method for disentangling the components when metabolic interactions predominate. The net interactions between species pairs are then replaced by the more fundamental ‘quartet’ of their components. The quartet explains several confounding experimental observations, facilitating better understanding and engineering of microbial communities.

Copyright: © 2026 Ansari et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Here, we developed a broadly applicable method to estimate the positive and negative components of the interactions between a species pair. It is conceptually distinct from existing approaches. The method employs data on species growth rates, which are more readily obtained, either by measurement or by estimation using computational methods, than the data required by extant methods. It then constructs a theoretical partitioning of resources which enables estimation of the positive components. The negative components follow from knowledge of the net interactions. Thus, each net interaction is decomposed into its positive and negative components. Conventionally, as discussed above, a species pair has been characterized by the pair of their net interactions, yielding the broad categorizations of mutualism, competition, and so on. Here, with the two components of each of the net interactions identified, the species pair is characterized by the ‘quartet’ of the components: the positive and negative components of the net interaction of each species with the other. We demonstrate the utility of the method by applying it to an in silico representative oral microbiome and a published experimental dataset on a 2-species community of auxotrophs.

Overcoming the limitation of the conventional characterization requires ways of estimating the underlying positive and negative components. While net interactions are readily measured for culturable species [ 8 , 10 , 21 , 22 , 24 ], methods to disentangle the components are only beginning to be developed. Genome-scale metabolic models and other computational approaches have often deduced the potential for positive and negative interactions [ 17 , 23 , 25 , 26 ]. For instance, the fraction of exogenous metabolites shared between a species pair was used to define a competition index, whereas the fraction of metabolites used by one species but produced by the other in the pair yielded a complementarity index [ 26 ]. Such empirical measures offer insights into the components but do not quantify them. More recently, a method, termed kinetics-based inference of dynamic variation in microbial interactions (KIDI), has been developed to estimate the components when cross-feeding metabolites and shared limiting nutrients are known along with their kinetic relationships with species growth rates [ 27 ]. This development marks an important advance. Often, however, knowledge of the metabolites involved and their kinetic relationships is not available, limiting the scope of KIDI.

This conventional characterization has a fundamental limitation: It adopts an ‘either-or’ view of positive and negative interactions. A species, in contrast, can simultaneously exert both positive and negative influences on another. In many ecological niches and synthetic communities, for instance, interactions are predominantly metabolic in nature [ 17 – 22 ]. In such scenarios, negative interactions typically arise from competition for resources and positive interactions from cross-feeding metabolites. Both these interactions are frequently known to occur together [ 17 , 21 – 23 ]. Positive and negative interactions are thus not exclusive. The net interactions observed experimentally are the resultants of these underlying competing influences. Indeed, the net interactions between the same species pairs can be either positive or negative depending on environmental conditions [ 11 , 17 , 21 , 22 , 24 ], reiterating the ability of species pairs to engage in both positive and negative interactions simultaneously. Hence, employing the net interactions to characterize communities while ignoring the underlying components can limit our understanding of communities, compromise the predictive power of theories, and preclude robust community design.

Multi-species microbial communities are important to human health [ 1 ], environmental sustainability [ 2 , 3 ], and biotechnology [ 4 , 5 ]. Establishing and maintaining stable microbial communities relies on the knowledge of the interactions between the constituent species [ 6 , 7 ]. The interactions have proven challenging to unravel and understand [ 7 – 13 ]. Conventionally, the interactions between a pair of species have been categorized by the nature, positive or negative, of the effect each species has on the survival and/or growth of the other. When the effects are both positive (+,+), i.e., when the species benefit each other, the species are said to exhibit cooperation, or mutualism. When the effects are both negative (-,-), they exhibit competition. Other combinations are termed exploitation or parasitism (+,-), commensalism (+,0), amensalism (-,0), and neutralism (0,0), where ‘0’ implies no effect. Current community ecology theories, beginning with the seminal work of May [ 14 ], predict the behaviour of communities, including their stability, based on this conventional characterization [ 7 , 9 , 15 , 16 ]. For instance, competitive interactions, particularly exploitative ones like the predator-prey interactions, are predicted to be stabilizing as they introduce negative feedbacks, whereas cooperative interactions may introduce dependencies that may render communities unstable [ 7 , 9 , 15 ].

Results

Method to estimate the positive and negative components of species interactions We consider a two-species community, comprising species ‘1’ and ‘2’, in an environment supplied with nutrients (or resources) at a constant rate, (Fig 1A). The resources may contain ingredients that are exclusive to the individual species (e.g., M 1 and M 3 in Fig 1A) or shared by both (e.g., M 2 in Fig 1A). Further, the species may also exchange, or cross-feed, metabolites they produce (e.g., M 4 and M 5 in Fig 1A). As a result of all these interactions, the species may grow. We denote the steady-state growth rates of the species in the community environment as and , respectively, where ‘c’ refers to the community. In the same environment, we denote the steady-state growth rates of the species when present alone, or in monoculture, as and , respectively. If the species experienced no interactions, the monoculture and community growth rates of the respective species would be identical. A difference between the two rates indicates the presence of net interactions between the species. Following convention [7], we define the net influence of species ‘2’ on species ‘ ’ as: PNG larger image

TIFF original image Download: Fig 1. Method to estimate the positive and negative components of the net interactions between species. (A) A hypothetical two-species community supplied with nutrients, M 1 , M 2 , and M 3 , at constant rates, with the supply rate of the shared limiting resource, M 2 (left). Metabolite M 4 , produced by species 1 (pink) and consumed by species 2 (purple), and metabolite M 5 , with the opposite pattern, are cross-feeding metabolites. The species growth rates in the community are and , respectively. The resource supply rates that support the species individually at their community growth rates are (middle) and (right). (B & C) The growth-resource curves of species 1 (B) and species 2 (C) in monoculture. and are the monoculture growth rates of the species at the resource supply rate . The leftover resources, and , yield the associated growth rates and . The interaction components estimated by our method (see text) are illustrated next to the y-axis. (D) A depiction of the net interactions employed conventionally. (E) A depiction of the quartet of components estimated here. https://doi.org/10.1371/journal.pcbi.1014502.g001 (1) implies an overall positive effect of species 2 on species 1, as the growth rate of species 1 in the community is greater than in monoculture. Accordingly, implies a net negative effect. Similarly, we define the net influence of species ‘1’ on species ‘2’ as (2) This pair of net interactions ( , ) yields the conventional characterization of interspecies interactions summarized above. Our goal is to estimate the positive and negative components of these net interactions. The method we devised is based on the following conceptual arguments. We consider the scenario where negative interactions arise from competition for shared resources. How shared resources are partitioned between species is not typically known [17,22,28], leaving the negative components difficult to quantify. We conceived a theoretical partitioning that would prescribe bounds on the negative components and thereby offer estimates of the positive components. Accordingly, we let species 2 receive all the resources necessary for sustaining its growth at the rate observed in the community. The ‘left-over’ resources would then be available for use by species 1. Using knowledge of how the growth rate of species 1 depends on resource availability, we estimate its growth rate that the left-over resources can sustain. If the latter growth rate is smaller than the observed growth rate of species 1, then it would imply that species 1 is sustained additionally by cross-feeding metabolites from species 2 in the community. Indeed, the difference between the observed growth rate and the growth rate from the left-over resources would be an estimate of the positive component of the influence of species 2 on species 1. In the same way, with another theoretical partitioning where species 1 gets all the resources needed to sustain its growth in the community, one can estimate the positive component of the net influence species 1 has on species 2. The difference between the net influence and the positive component would yield the negative component. Below, we formalize these conceptual arguments into a procedure for estimating the components. We denote the supply rate of the shared limiting resource in the environment as R. Species growth rates are expected to increase monotonically with R. We define the curve depicting the growth rate, , of a species in monoculture as a function of R as the ‘growth-resource curve’ of the species, denoted . For the species 1 and 2, we denote the growth-resource curves as and , respectively. These curves are readily determined using experiments, or using genome-scale metabolic models where available, and are analogous to the classical description of the growth rate dependent on the substrate concentration due to Monod [29]. We recall that we consider an environment supplied with resources at a constant rate, (Fig 1A). At this resource supply rate, the respective monoculture growth rates of the two species would be and (Fig 1B and 1C). Using the growth-resource curve of species 2, we estimate the resource supply rate, , at which the growth rate of species 2 in monoculture would equal its growth rate in the community, (Fig 1C). In other words, we find as the value of R that satisfies . If , it implies that not all of the resources supplied to the community were needed for the maintenance of species 2. The remaining, or left-over, resource supply rate, , denoted , would therefore be available to species 1 (Fig 1C). (Note that if , then we set ; the left-over resource cannot be negative.) We now use the growth-resource curve of species 1 and identify its growth rate in monoculture afforded by the left-over resource supply rate , which we denote as (Fig 1B). Thus, . In other words, would be the growth rate of species 1 that the environment would sustain ‘after’ letting species 2 exist at its community growth rate in the absence of additional interactions between the two species. Clearly, the difference between and the observed growth rate, , must be due to the positive effect of species 2 on species 1. We thus estimate the positive component of the interaction as (3) The difference between the net interaction, estimated above (Eq. 1), and the positive component yields the negative component: (4) In the same way, we estimate the components for the effect of species 1 on species 2: We employ the growth-resource curve of species 1 to obtain the resource supply rate, , at which its monoculture growth rate would equal (Fig 1B); i.e., we identify as that value of R at which . The left-over resource, , would be available to species 2 after letting species 1 grow at its community growth rate, . (Again, note that .) From the growth-resource curve of species 2 (Fig 1C), the growth rate, , of species 2 at the left-over resource supply rate is estimated as . The positive component of the net influence of species 1 on species 2 is then (5) and the negative component, (6) Together, the components , , , and form the quartet of interactions between the two species in the community environment (Fig 1D and 1E). Below, we demonstrate the procedure by applying it to a specific species pair.

The quartet of interactions between Streptococcus mutans and Streptococcus parasanguinis We considered the species Streptococcus mutans (Smu) and Streptococcus parasanguinis (Sp), which are part of the human oral microbiome [30]. The (input) data required to apply our method are the growth-resource curves of the two species, and , and estimates of their growth rates in the two-species community, and , at a given resource supply rate, . This would allow us to estimate the quartet at . The input data could be obtained experimentally (see below). Here, for illustration, we used computational approaches. Using genome-scale metabolic reconstructions of the two species (Methods), we predicted their individual growth-resource curves. We considered resources resembling a Western diet and quantified the resource supply rate, , as the fold-increase in the supply rate of the resources over a basal rate (Methods). The ingredients in the resource, which include sugars, amino acids, minerals and a host of other nutrients, along with their basal uptake rates are listed in S8 Table. Unless specified otherwise, thus represents the fold-increase over the basal rate and hence is dimensionless. Further, values of <1 would imply resource constraints, whereas >1 would imply an enriched medium. Over the range of we examined, the growth-resource curves were linear (Fig 2A and 2B), but with different slopes. The curve for Smu had a higher slope than Sp. Thus, at any , the growth rate of Smu, , was higher than that of Sp, . For instance, at , the rates were: and . PNG larger image

TIFF original image Download: Fig 2. The quartet of interactions between the species Smu and Sp. The growth-resource curves of Smu (A) and Sp (B) and the community, monoculture and left-over growth rates of the two species indicated (see text for meanings of the various symbols). (C) The positive (blue) and negative (red) interaction components, forming the interaction quartet, and the net (white hatched) interactions between the species. https://doi.org/10.1371/journal.pcbi.1014502.g002 We now considered a community environment with a resource supply rate and estimated the monoculture and community growth rates of the species (Methods). The growth rate of Smu in the coculture was , while that of Sp was . The corresponding monoculture growth rates of the species were and . The difference between the community growth rates and the monoculture growth rates is attributed to the interactions between the species, driven both by competition for resources and beneficial exchange of cross-feeding metabolites. The list of shared nutrients is in S8 Table, whereas cross-fed metabolites are listed in S9 Table. From these estimates, we obtained the net interactions as the difference of the growth rates in the coculture and monoculture, so that and (Fig 2C). The pair thus exhibited competition, with each species negatively impacting the growth of the other. With this input data, we could now apply our method and estimate the components of these net interactions. Following the procedure above, we first identified the resource supply rate required for Smu to sustain its community growth rate in the absence of additional interactions. This yielded the resource supply rate (Fig 2A), which ensured that (Fig 2B). was less than . This implied that the remaining resources were left over after sustaining Smu at its community growth rate (Fig 2A). Consequently, the left-over growth rate of Sp, . This growth rate was less than that observed for Sp in the community, implying that Sp experienced a positive influence from Smu. The positive component of the influence of Smu on Sp was thus (Eq. (3)): . The negative component followed as the difference between the net interaction and the positive component: We repeated the above procedure for estimating components of the influence of Sp on Smu. The resource supply rate needed for sustaining the growth rate of Sp, , at its community growth rate, , was (Fig 2B). The resource left over after sustaining Sp at its community growth rate was . We estimated the growth rate of Smu that can be afforded by the latter left-over resource to be (Fig 2B). The positive component of the influence of Sp on Smu was thus . The negative component followed from the net interaction: . Our method thus yielded the quartet for the Smu-Sp pair: (Fig 2C). The example above illustrates the application of our method. We next applied it to estimate the quartets of all species pairs in a representative human oral microbiome.

Implications of the quartet for understanding community behaviour The above predictions were made at a single community resource supply rate ( ). We next examined how the quartet would change as the resource supply rate is varied. We considered the pair of Av and Bf, discussed above. Recall that at , the pair exhibited exploitation. We varied over a wide range, from 2 to 10. At each value of in this range, we applied our procedure above and estimated the net interactions as well as the quartet. The net interactions displayed complex non-monotonic trends, with the pair transitioning from exploitation to mutualism with increase in (Fig 4A). Specifically, Bf exerted a net negative influence on Av, which decreased (became more negative) with until 3.5, after which it increased. Eventually, beyond , the interaction changed sign with Bf exerting a positive influence on Av. Av, on the other hand, exhibited a net positive influence on Bf throughout, although the strength of this interaction increased until and then decreased. Thus, at , the community switched from exploitation to mutualism. How such complex trends emerged with increasing is puzzling. We understood this using the quartet. PNG larger image

TIFF original image Download: Fig 4. Variation of the quartet with resource availability for the Av-Bf pair. The variation of (A) the net interactions and (B) the quartet components of the Av-Bf pair with the resource supply rate. Solid lines indicate the influence of Bf on Av and dashed lines of Av on Bf. Positive components are in blue and negative in red. The vertical dotted line marks the transition from exploitation to mutualism with increasing resource supply. The magnitudes of the negative components are plotted for easy comparison with their positive counterparts. https://doi.org/10.1371/journal.pcbi.1014502.g004 We found, interestingly, that all the components of the quartet varied much less sharply with than the net interactions (Fig 4B). The variation of the components relative to each other, however, was more complex and strongly affected by changes in , which in turn influenced the net interactions, introducing transitions in community behaviour. As increased from 2 to ~3.5, the negative component of the influence of Bf on Av, , increased more than its positive counterpart, . (Note that here and in such comparisons throughout, we refer to the magnitudes of the components, ignoring their signs.) The net influence of Bf on Av thus became increasingly negative (Fig 4A). In contrast, over the same range of , the positive component of the influence of Av on Bf, , was larger and increased more steeply with than its negative counterpart, (Fig 4B). The net influence of Av on Bf thus became increasingly positive (Fig 4A). Consequently, the pair became more strongly exploitative as increased from 2 to ~3.5. This trend reversed beyond . Between and , remained higher than , and the latter increased more steeply with than (Fig 4B). The net influence of Bf on Av thus became increasingly less negative after having peaked at (Fig 4A). However, continued to increase with , while started gently decreasing after (Fig 4B), so that the net influence of Av on Bf began to decrease although the interaction remained positive (Fig 4A). Thus, the overall interaction became less exploitative and approached amensalism. Interestingly, beyond , exceeded , so that the net influence of Bf on Av switched from being negative to positive (Fig 4A). Increasing beyond ~7 increased the extent of the positive interaction. Throughout, the influence of Av on Bf stayed positive ( started decreasing gently while increased monotonically) and decreased its magnitude with . Thus, the overall interaction now switched from exploitation to mutualism upon increasing beyond ~7. In summary, the species pair transitioned from weak to strong exploitation, back to weak exploitation bordering on amensalism, and then to mutualism as increased from 2 to 10. These predictions illustrate how depending on the extent of increase in resources, an increase in either positive or negative interactions and hence the extent of cooperation or mutualism can result between the same species, dictated by the differential variation of the quartet components. Remarkably, the components themselves displayed smooth, gentle variations with the resources. Yet, their differential variation led to these dramatic changes in the overall interactions. This general behaviour was also evident with other species pairs we examined (S3 Fig). We examined next whether the quartet would similarly help better understand the behaviour of communities observed experimentally.

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