Bacteria can be found almost everywhere on earth. Often, multiple species of bacteria live together in communities, which perform vital roles that affect everything from our health to the planet’s ecosystems.

A single species within this community can sometimes be particularly important, for example if it is causing disease in its host or producing a vital nutrient. However, the other species within this community can influence the growth of this focus species, either by inhibiting or promoting it.

It is challenging to predict how a certain species is going to fare within a bacterial community as it remains partly unclear how groups of bacteria affect each other. Some theory suggests that adding up or averaging the influences of all the bacteria in a community would be the best way to predict what will happen.

To study these microorganism interactions, Baichman-Kass, Song and Friedman monitored thousands of bacterial communities, consisting of two to four different species. By using species that express fluorescent proteins, they were able to measure the abundance of the specific bacteria of interest in each of these communities.

Baichman-Kass et al. found that in communities where all the species were only competing with or supporting the bacteria of interest, the individual affecting species with the strongest effect dominated the combined effect. This ‘strongest effect’ model offered accurate predictions for the joint effects of competitive communities, however predicting outcomes in supporting communities proved more difficult. This could indicate that the mechanisms for supporting other species are more intricate than the means of competition.

The study of Baichman-Kass et al. brings us closer to understanding how the abundance of a given bacterium can be influenced through the actions of other bacterial species. Among other uses, it may be important in medicine, where it is desirable to reduce the amount of a bacteria that causes disease, or in agriculture where bacteria that protect plants from diseases and fungi, need to be boosted. Improving our ability to predict the outcome of introducing new species to an environment increases both the effectiveness and possible scope of such applications.

Scarce are the environments on Earth not colonized by bacteria. In addition to naturally playing important roles from driving biogeochemical cycles at the ecosystem level (Cavicchioli et al., 2019; Arrigo, 2005; Falkowski et al., 2008) to supporting host health at the individual level (Berendsen et al., 2012; Manor et al., 2020; Gilbert et al., 2018), bacteria have also been harnessed for countless biotechnological applications across industries such as food preservation (Motarjemi, 2002), plant and animal health (Berendsen et al., 2012; Júnior et al., 2021), biocontrol of pathogens (Köhl et al., 2019), as well as decomposition of toxic compounds, and production of valuable ones (Varjani et al., 2017; Ro et al., 2006; Fang and Smith, 2016; Mainka et al., 2021). In natural environments, bacteria often form rich and complex communities, but understanding how these communities organize has proven difficult (Widder et al., 2016). Elucidating the rules that govern microbial ecology can both offer insight into larger ecological systems and allow us to better manipulate and design microbial communities for the desired functions.

The structure of microbial communities is determined by the interactions between the involved species (Konopka et al., 2015; Barbier et al., 2018; Qian and Akçay, 2020). In recent years, much effort has been put into measuring pairwise interactions of different species from, and in, different environments (Foster and Bell, 2012; Vetsigian et al., 2011; Kehe et al., 2021). But it is still unclear to what extent the joint effects of multiple species on a focal species of interest (e.g., a pathogen) can be inferred from pairwise measurements. Such inference may be challenging due to the presence of indirect interactions: the affecting species may alter each other’s abundances (termed interaction chains) or may modify each other’s effect on the focal species (termed interaction modification, or higher-order interactions) (Sanchez, 2019; Wootton, 2002).

Despite a strong theoretical foundation, empirical studies in recent years have shown conflicting results regarding the importance of higher order interactions and indirect effects (Levine et al., 2017). For some functions, such as degradation of complex molecules (Sanchez-Gorostiaga et al., 2019; Gralka et al., 2020) and antibiotic production (Tyc et al., 2014; Qi et al., 2021; Westhoff et al., 2021), clear evidence of such interactions has been found. Furthermore, in both empirical and theoretical studies, the presence or absence of an additional species has been shown to affect interactions, and even the outcome of invasion and coexistence in some systems (Mickalide and Kuehn, 2019; Chang et al., 2022; Hsu et al., 2019). Additional theoretical work has shown that commonly used ecological models (i.e., generalized Lotka-Voltera) do not properly capture microbial community interactions, partially due to the nature of these interactions (chemically mediated as opposed to predator-prey) (Momeni et al., 2017). However, other studies have shown that both structures of, and interactions within, larger communities can be accurately predicted from pairwise interactions alone using variations of said models (Friedman et al., 2017; Meroz et al., 2021; Guo and Boedicker, 2016; Venturelli et al., 2018). This being the case, how microbial interactions combine into the joint effect of multiple species on a single species of interest is still poorly understood.

In our research, we used high-throughput nanodroplet-based microfluidics to measure over 14,000 bacterial communities composed of subsets of a library of 61 soil and leaf isolates of which six were fluorescently labeled (Figure 1). We quantified the effect of individual species and the joint effects of species pairs and trios on the growth of six focal bacterial species and found that the effects of multiple species are dominated by the strongest single-species effect, and specifically that negative effects combine non-additively.

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We conducted high-throughput assays involving 61 affecting species and 6 different focal species to understand the effects of single species, pairs, and trios on the growth of a given (focal) species. The 61 affecting species included soil and leaf isolates as well as lab strains representing 19 genera from four phyla: Proteobacteria (n = 14), Firmicutes (n = 2), Bacteroidetes (n = 2), and Actinobacteria (n = 1) (full list in Supplementary file 1, Source data 1). The focal species were a subset of six of these species (all proteobacteria) that were transformed to constitutively express a fluorescent protein: (Escherichia coli [EC], Ewingella americana [EA], Raoultella planticola [RP], Buttiauxella izardii [BI], Citrobacter freundii [CF], and Pantoea agglomerans [PA]) (see ‘Materials and methods’). Except for EC, which is a lab strain (E. coli K-12 substr. MG1655), all focals were isolated from soil samples (Kehe et al., 2021). First, we characterized each species phylogenetically by performing Sanger sequencing of their 16S ribosomal RNA gene and phenotypically by growing each species on each of 20 different carbon sources and 11 antibiotics. The species showed large variability in carbon utilization profiles with no species growing well on all carbon sources (Figure 1—figure supplement 3). There was also high variability in growth on antibiotics with 15 species showing little or no growth on any antibiotics, while 16 species showed resistance to at least seven antibiotics (Figure 1—figure supplement 4).

We performed the interaction assays in the kChip microfluidics device (Kulesa et al., 2018; Kehe et al., 2019), allowing for extensive screening in parallel (see ‘Materials and methods,’ Figure 1—figure supplement 1). We measured the effects of 243 single species (18–52 for each of the six focal species), the joint effects of 5357 species pairs (between 153 and 1464 for each of the six focal species), and the joint effects of 3009 species trios (from a subset of 26 affecting species on one focal species). Cultures were normalized and mixed after pre-growth, such that the starting densities in the kChip were approximately 1:1 for all species in wells containing two droplets and two affecting species, but ratios varied in three droplet wells (see ‘Materials and methods,’ Figure 1—figure supplements 1 and 2). Interaction assays were carried out in minimal M9 media with 0.5% [w/v] glucose for 24 hr. The growth of the focal species was measured by fluorescence, and effects were calculated as the log ratio of growth in coculture to growth in monoculture (see ‘Materials and methods,’ Figure 1D). Positive and negative effects are defined as a net increase or decrease in growth compared to the monoculture respectively, while affecting species with no observable effect (see ‘Materials and methods’) were defined as neutral.

Joint effects of species pairs tend to be stronger than those of individual affecting species

We started our interaction assays by measuring the individual effects of single affecting species on each of the focal species (see ‘Materials and methods’). Individual effects covered a wide range (median = −0.15, interquartile range = 0.94) (Figure 2A), and positive effects (the focal species reaching a higher density in the presence of an affecting species than in monoculture) were common overall (32.9%, Figure 2B), in line with previous studies (Kehe et al., 2021). The distribution of effects varied based on the focal species, with E. coli and B. izardii showing the most negative (–2.83) and positive (+0.43) median effects, respectively (Figure 2D). Additionally, we found no affecting species that had strong effects across all focal species (Figure 2—figure supplement 1).

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The measured traits of individual species showed no consistent correlations with their effects on the focal species. In particular, the similarity of metabolic profile, resistance profile, or phylogeny between the focal and affecting species did not correlate strongly with the effect across focal species. Some traits showed little to no correlation for most focals (e.g., antibiotic resistance), while other traits were correlated with effect for a number focal species but not all (e.g., phylogenetic distance). Most of these correlations were not statistically significant (Figure 3—figure supplement 1A).

After characterizing the individual effects of all single species, we assayed each pair of affecting species against the focal species. Overall, negative effects were significantly more prevalent in joint pair effects (77.1%) than in effects of individual species (60.5%) (p=1.3e-9, Fisher’s exact test) (Figure 2B and C). The median effect on each focal was more negative by 0.28 on average, though the difference was not significant in all cases; additionally, focals with mostly positive single-species interactions showed a small increase in median effect (Figure 2D). Despite this, the minimum and maximum effects for each focal species remained similar. As with the single affecting species, pairs’ joint effects did not correlate well with species traits, with similarity between the two affecting species, or with their similarity to the focal species (Figure 3—figure supplement 1B). These results indicate that it may be challenging to connect the effects of single and pairs of species on a focal strain to a specific trait of the involved strains using simple analysis.

Negative effects combine non-additively and joint effects are dominated by the stronger single-species effect

Next, we examined how the effects of individual species relate to their joint effect. In particular, we were interested in finding a model that describes the effects of pairs based on the data from single-species effects. Based on previous studies' success in predicting community structure from pairwise interactions (Friedman et al., 2017; Meroz et al., 2021; Guo and Boedicker, 2016; Venturelli et al., 2018), we posited that predicting how effects combine based solely on the effects of the single species should also be feasible. To do so, we considered three models: an additive effect model, a mean effect model, and a strongest effect model.

The additive effect model proposes that the effects of each species on the focal are the same whether they act individually or jointly. Therefore, the combined effect will be equal to the sum of the effects of each species on their own. This is equivalent to additivity of effects between antibiotics, which is common in the drug combinations field (Bollenbach, 2015). The mean model represents a simple phenomenological model that assumes that the effects of different species will be diluted in the presence of a third species. By contrast, the strongest effect model posits that the species with the strongest effect dominates the effect of other affecting species, leaving the joint effect the maximum single effect, and not the sum or mean of single-species effects.

When measured across all species and interaction types, we found that the model that best agrees with the measured effects is the strongest effect model (Figure 3B).Though supplementing the mean model with additional species information (i.e., carrying capacity) did improve the model accuracy, it was still less accurate than the strongest effect model (Figure 3—figure supplement 2). The accuracy of the models and identity of the best-fitting model varied across interaction types. The strongest effect model was the most accurate overall (nRMSE = 0.46, 0.32, and 0.16 for the additive, mean, and strongest models, correspondingly), and considerably more accurate when both species affected the focal negatively (nRMSE = 0.65, 0.25, and 0.16). The additive model was slightly more accurate when one effect was negative and the other positive (nRMSE = 0.14, 0.43, and 0.16). Overall, predictions when both effects were positive were less accurate, but here too the strongest model gave the most accurate predictions (nRMSE = 0.81, 0.78, and 0.69) (Figure 3C).

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The distribution of errors further supported the strongest effect model (Figure 3B, Figure 3—figure supplement 3B): When both single-species effects were negative, the mean model was prone to underestimating the combined effect due to the reduction of the stronger effect by taking into account the weaker effect; while contrastingly, the additive model overestimated effects due to the addition of the weaker effect to the stronger effect, which was more accurate on its own. We saw the opposite trend when both single-species effects were positive, and no particular trend when there was one positive and negative effect. As with the effects themselves, model accuracy was not strongly correlated with any specific species trait (Figure 3—figure supplement 4).

In regard to negative effects, support for the strongest model is also evident in how the difference in size of effect influences the model accuracy (Figure 3—figure supplement 3A). When effects are close to equal, the mean model is fairly accurate while the additive model does particularly poorly as these effects would be calculated as twice the strongest effect. Contrastly, when one effect is much stronger than the other, the additive model is accurate since the addition of the weak effect is negligible, whereas the mean model underestimates the joint effects by taking into account the weaker effect.

The strongest effect model is also the most accurate for larger communities

With this information in hand, we were interested to see whether the same rules held up for larger communities. To this end, we screened trios of a subset (i.e., 26) of the affecting species against a single focal species (E. coli) and found similar trends to all those seen for pairs of affecting species. Similar to what was observed in the move from single species to pairs, effects were stronger (in this case more negative effects) in trios than in the pairs (Figure 4C). Additionally, as with joint pairs’ effects, the strongest effect model was more accurate than the additive and mean models (nRMSE = 2.65, 1.23, and 0.63 for the additive, mean, and strongest models, correspondingly), which is consistent with the fact that the single-species effects in this subset were predominantly negative. Similar distributions of error were seen as in the pairs’ effects, but further exaggerated with the more extreme under and overestimation of the combined trios’ effects by the mean and additive models, respectively (Figure 4A).

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We further explored the additive, mean, and strongest models in trios by basing the model on effects of the three pairs comprising each trio (i.e., joint effect of AB, AC, BC to predict effect of ABC), as opposed to only using single-effect data (i.e. ,effect of A, B, C on their own) (Figure 4A and B). The effects of single species and pairs were measured again independently in this experiment (see ‘Materials and methods,’ Figure 1—figure supplement 1). The move to pairs-based predictions improved the accuracy for both the mean and strongest model, while further pushing the additive predictions away from the observed effects (Figure 4B). These data suggest that even in the presence of additional species the strongest single-species effect still dominates the combined effect of a community.

By measuring thousands of simplified microbial communities, we quantified the effects of single species, pairs, and trios on multiple focal species. The most accurate model, overall and specifically when both single-species effects were negative, was the strongest effect model. This is in stark contrast to models often used in antibiotic compound combinations, despite most effects being negative, where additivity is often the default model (Bollenbach, 2015). The additive model performed well for mixed effects (i.e., one negative and one positive), but only slightly better than the strongest model, and poorly when both species had effects of the same sign. When both single-species effects were positive, the strongest model was also the best, though the difference was less pronounced and all models performed worse for these interactions. This may be due to the small effect size seen with positive effects, as when we limited negative and mixed effects to a similar range of effects strength, their accuracy dropped to similar values (Figure 3—figure supplement 5). We posit that the difference in accuracy across species is affected mainly by the effect type dominating different focal species’ interactions, rather than by inherent species traits (Figure 3—figure supplement 6).

We phenotypically and genetically profiled all species, but did not find strong correlations between the measured traits, or similarity in traits, to the effect on the focal species. Though positive effects were common, making up about one-third of the single-species effects, they became less common as the number of community members increased, making up only 16% of the effects of species pairs. Furthermore, we found similar trends in the larger communities of four species (three affecting species and one focal), both that effects combined in a non-additive manner, being dominated by the strongest single-species effect, and that effects became stronger in larger communities, which is consistent with previous studies (Cook et al., 2006; van Elsas et al., 2012 ; Jones et al., 2021; Piccardi et al., 2019; Gould et al., 2018; Palmer and Foster, 2022).

The mechanistic basis underlying the joint effects of multiple species is still unclear. The additive model’s accuracy for mixed effects may indicate that negative and positive effects act independently. For negative effects, it is difficult to identify a single biological mechanism that could explain why the strongest effect model agreed best with our experimental data. Intuitively, we assumed this could be explained by resource competition (i.e., an affecting species that consumes resources quickly would negatively affect the focal species, as well as the other affecting species). However, this explanation is not consistent with the fact that the affecting species’ growth rate did not correlate well with their effect on some focal species (Figure 3—figure supplement 1A). Secondly, we thought effects could be saturating (either biologically or with regard to the detection limits in this experimental setup), but this would not explain why the model works for weaker effects. A hierarchical ranking, where each species affects all the species ranked below it could lead to the strongest affecting species affecting both the focal and the other affecting species, thus dominating their joint effects, but this does not coincide with the fact that we observed almost no single species or pairs with a strong effect across all focals (Figure 2—figure supplement 1).

As we did not measure the abundance of all species in each community (only the focal), we cannot disentangle interaction modification (changes in per capita effect of specific species), from interaction chains (affecting the amount of an affecting species, and as such its effect on the focal), and further work is needed in order to pinpoint the exact mechanism(s) leading to the dominance of the strongest model for negative effects in our system. We also note that it is possible that the manner in which effects combine is affected by the mechanism of interaction; For instance, previous studies have shown that interference competition can combine additively, or even synergistically, results not seen in our work (Tyc et al., 2014; Westhoff et al., 2021).

Understanding how microbial communities assemble and how large numbers of species interact is of both utmost importance and difficulty. Harnessing such information would open up a plethora of currently underutilized applications in food, medical, and agricultural industries. Specifically, understanding how the effects of multiple species on a single species combine is important for introduction of new species into a given environment. Our results suggest that when we want to affect a single focal species in a given environment (e.g., for biocontrol of a pathogen), introducing the species with the strongest effect on the focal would be sufficient to obtain the desired effect, as synergies were rare in our dataset. In cases where there are multiple strains of interest (e.g., probiotics), introducing multiple species may be beneficial since different affecting species typically have strong effects on different focals. Introducing combinations of species may allow for a more robust function as the chances that one member of the community will have a strong effect on a resident species of interest is more likely.

Further work is needed in order to deepen our understanding of how multiple species affect each other and to see to what extent our findings continue to hold up in more diverse communities, other taxonomic groups, and more complex environments. Specifically, as we saw a decrease in prediction power from pairs to trios, exploring this model with more diverse communities is of particular interest. Additionally, nearly all of the effects in the four member communities were negative, and it is unclear how mixed and positive effect modeling is affected by higher diversity. Lastly, it is important to note that our focal species are all from the same order (Enterobacterales), which may also limit the purview of our findings. Nonetheless, our results suggest that community effects can be predicted from the strongest effect of a single species, greatly reducing the amount of information required to obtain accurate estimations, which can improve our ability to use a bottom-up approach for biotechnological applications, as well as answering fundamental ecology questions.

Sequencing data are provided in Source data 1, and have been deposited to Genbank under accession codes OP389073-OP389107 and OP412780-OP412788.All data generated or analyzed during this study are available on GitHub, and can be found at https://zenodo.org/badge/latestdoi/534114367.

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Decision letter after peer review:

Thank you for submitting your article "Interactions between culturable bacteria are highly non-additive" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, including Wenying Shou as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Meredith Schuman as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Alvaro Sanchez (Reviewer #2).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1) Revise the text with a softer tone. For example, the generality of the conclusions is unknown since the 6 focal species were from 1 family, and since the conclusion only works for a subset of focal species, etc. Please see specific comments especially from Reviewers 2 and 3 about revising the claims.

2) Provide a more rigorous analysis of the fluorescence assay. Exactly what is this assay measuring? How might the correlation between growth/biomass and fluorescence be affected by death, diauxic shift, or prolonged lag / stationary phases? See comments to the authors from Reviewer 3.

Reviewer #1 (Recommendations for the authors):

My only suggestions are on writing. Certain key aspects of experiments can be outlined in the main text. For example, when pairs were introduced, did the inoculum for each strain get halved? Figure 3A graphic is unclear, and can be made much clearer by plotting mono effects and predicted coeffects under the three models.

Reviewer #2 (Recommendations for the authors):

Figure 3: (A) I think this panel could be made clearer. What does the green bar represent? It is not explicitly clarified in the caption. I think it depicts the growth of the green "test" bacteria? Maybe clarifying this in the caption would help. Also, why not add the equation representing the interaction?

Figure 3: (B). The data points are so tiny it is difficult to see them. Maybe using larger dots (I understand there are a lot of them, though. I wonder if there is a clearer way to plot this data). Also the color choice is not the friendlies to color-challenged readers like this reviewer. I had trouble in particular distinguishing the pairs when one species had a positive while the other one had a negative effect from those that were both negative.

Lines 167-169: The authors introduce the "mean effect model". What is the theoretical justification for including this model in the analysis? I mean, in terms of ecological theory? The additive model is justified e.g. in that it is the typical assumption in Lotka-Volterra (and also considered in the antibiotic combination literature cited in the paper). But how about the mean model? It would help if the authors explained/justified the theoretical basis for this. Otherwise it feels a bit random, they could have taken the median, or the square root of the variance, or…

Lines 221-224: The authors write: "We further explored this model by basing trios' data not on the additive, mean, or strongest values of the effects of individual species, but on those of the joint effects of the three pairs comprising each trio (the effects of single species and pairs were measured independently again in this experiment, see Materials and methods, Figure S1)." I have read this sentence five times and I am still not sure what the authors meant

Lines 296-300. The authors may want to more explicitly bring up in their discussion that the predictive ability of the "Dominance", strongest-species model, is significantly worse when they try to predict the effect of a trio than when they try to predict the effect of a pair. This would suggest some caution in the reach of their conclusions, as it is possible that the predictive power of a single species will get worse and worse as the diversity of the community increases. Which, by the way, would not be surprising I think and should not be held against their findings, but I still think it would be good to qualify their statements about the potential reach of their conclusions for the bottom-up prediction of population-level interactions in complex communities. While they do state that "further work is needed…" to figure out if they results hold in more diverse communities (Lines 294-96) I felt that the limitations of the study could be written in a sharper manner.

Finally: I was curious if the authors have considered a model where one of the species is dominant in a pair, but the one that dominates is not necessarily the one with the strongest effect? For instance, is it possible that when A is grown with either B alone or C alone, the suppression of growth from B is stronger than the suppression of growth from C. Yet, in the presence of both B and C, the suppression of growth is exactly the same as that by C (or just closer to C than B)? Do the authors see this in any of their pairs? If so, how many?

Reviewer #3 (Recommendations for the authors):

The metric of growth for the focal species was fluorescence. This can be a risky measurement, because other species could autofluoresce in the emission spectrum. Additionally, fluorescent proteins can continue to fluoresce after cell death and lysis (we have personally observed this after phage infection and antibiotic treatment). I think the paper could use a test to verify that fluorescence was an unbiased proxy for growth.

I am confused by the densities that the species start at. In the methods, it says the focal and affecting species had starter cultures that were 2-fold different in concentration, yet were mixed 1:1, and ended up with a 1:1 ratio. How is this possible? Supp Figure S1 did not help me understand this.

It was surprising to me that inoculation density had no effects. This makes me wonder whether the interactions observed in this study are dominated by primary metabolic competition, because density effects are very common when allelopathy occurs. If this is true, it restricts the generality of the results, and is worth being discussed. Related to this, antibiotic resistance was measured, but what about potential to secrete antibiotics?

I think the density effects should be measured with nRMSE, or even absolute difference from y=x, because there could be a strong correlation without the actual numbers being the same sign or magnitude. For example, in S11-B, most of the datapoints appear below y=x, until the effects are near zero, suggesting an effect-size-specific effect of density.

More discussion could be given on what a "meaningful" difference in nRMSE is.

More details on how the resampling during the bootstrap procedure was done is warranted.

It isn't clear to me how Figure 1C is supposed to show that different models were used-perhaps drop this and just leave this explanation for Figure 3A, which is very clear.

Suggestion for additional analysis using the trait data: this dataset seems perfect for using something like a random forest or other continuous-response, "open box" machine learning approach to agnostically ask whether the trait measurements can be used to predict effect when all the measurements are used, rather than summaries of the measurements in the distance metrics.

Essential revisions:

1) Revise the text with a softer tone. For example, the generality of the conclusions is unknown since the 6 focal species were from 1 family, and since the conclusion only works for a subset of focal species, etc. Please see specific comments especially from Reviewers 2 and 3 about revising the claims.

We have put much effort into better understanding our findings in a manner which allows for a more generalizable framework, while also clarifying the remaining caveats of our study. In regards to the model working best for a subset of the focal species, we believe this due not to inherent characteristics of the focal species, but rather the types of interactions measured for each species. The strongest model works best for pairs where both interactions are qualitatively similar (i.e. positive-positive or negative-negative). Mixed interactions (i.e. negative-positive) were predicted slightly better by the additive model, and overall the predictions were less accurate for positive interactions. As such, focal species with many positive single species effects incur less accurate results for the model overall, and are not always best predicted by the strongest model. To reflect this, we have made revisions throughout the manuscript, including to the title and abstract of the paper.

Furthermore, we have made extensive changes to the discussion, adding caveats regarding the phylogeny of our focals, shortcomings of our models' predictions, and overall softened the tone as suggested. Detailed descriptions of these changes can be found in our responses below. In addition to multiple changes throughout the manuscript, the final paragraph of the Discussion section summarizes many of these caveats as follows:

"Further work is needed in order to deepen our understanding of how multiple species affect each other and to see to what extent our findings continue to hold up in more diverse communities, other taxonomic groups, and more complex environments. Specifically, as we saw a decrease in prediction power from pairs to trios, exploring this model with more diverse communities is of particular interest. Additionally, nearly all of the effects in the 4 member communities were negative, and it is unclear how mixed and positive effect modeling is affected by higher diversity. Lastly, it is important to note that our focal species are all from the same order (Enterobacterales), which may also limit the purview of our findings. Nonetheless, our results suggest that community effects can be predicted from the strongest effect of a single species, greatly reducing the amount of information required to obtain accurate estimations, which can improve our ability to use a bottom-up approach for biotechnological applications, as well as answering fundamental ecology questions. "

(Lines 359-369)

2) Provide a more rigorous analysis of the fluorescence assay. Exactly what is this assay measuring? How might the correlation between growth/biomass and fluorescence be affected by death, diauxic shift, or prolonged lag / stationary phases? See comments to the authors from Reviewer 3.

This issue is addressed in detail in response to Reviewer 3's comments. In brief, we performed interaction assays in an additional system allowing us to measure effects using both fluorescence and optical density. We saw that the effects were highly correlated, easing some of the aforementioned concerns regarding different physiological effects on the fluorescent signal. Moreover, to address concerns of autofluorescence, we ran an additional experiment in the kChip, which included wells of affecting species monocultures so we could measure their fluorescence. The difference between some affecting and focal species was smaller than anticipated with autofluorescence signals even surpassing some of the focal's signals in a handful of cases. In response to this issue, we filtered the dataset to only include affecting species with an autofluorescence signal at least fivefold lower than that of the focal species. This allows us to measure effects of more than 1.5, while still retaining a large dataset.This led to a significant reduction in the size of our dataset, and affected the different focal species unevenly (those focal species with weaker fluorescent signals were disproportionately affected). This reduced the size of our dataset by nearly half (from ~14,000 to ~8,000) as the removal of a single species exponentially affects the amount of pairs and trios that could be used. Additionally, artifacts in the data caused by autofluorescence would weaken negative effects (most of the effects found in our study), and not push observed effects towards the strongest model. Though we ultimately decided to take a conservative approach regarding which data to include, the qualitative claims of our study did not change from those made when using all the collected data.

The following was added in Appendix 1:

"Additionally, an experiment was carried out in the kChip to measure autofluorescence of affecting species. This setup was identical to the droplet preparation and culturing protocol detailed above, except that cultures were not mixed with the focal species prior to droplet generation. In this setup each droplet contains a single species, and wells contain one or two species (depending on whether the droplets were from the same or different cultures). Isolates were only used with focals whose monocultures were at least five times larger than the isolates autofluorescence signal, allowing to measure effects of at least -1.5. Full datasets without autofluorescence filtering can be seen in Appendix 1, Figure 3." (Appendix 1, Lines 37-44)

Reviewer #1 (Recommendations for the authors):

My only suggestions are on writing. Certain key aspects of experiments can be outlined in the main text. For example, when pairs were introduced, did the inoculum for each strain get halved?

We apologize this was not explained clearly enough in the original manuscript. The affecting species densities are halved when introduced to the well, but as the focal species is present in both droplets, its density is not affected. Depending on the combination of types of droplet in each well, density ratios (of the affecting species to the focal) for pairs could be identical or half of the single species coculture (see Figure 1—figure supplement 1 below). We observed that different starting densities did not affect the interactions significantly, and as such, different starting ratios of the same communities were unified for downstream analysis. We have added the following sentence to main text as well in order to clarify the starting densities:

“Cultures were normalized and mixed after pre-growth, such that the starting densities in the kChip were approximately 1:1 for all species in wells containing two droplets and two affecting species, but ratios varied in three droplet wells (see Materials and methods, Figure 1—figure supplement 1).”

Furthermore, we revised the Materials and methods:

“Each well contained droplets with the same focal species such that with this setup, in a well containing two droplets of different affecting species, the starting OD₆₀₀ of each species is 0.01 (as each affecting species is diluted by the other droplet in which it is not contained, but the focal species is not). In wells with three droplets, the starting ratio of the focal to each affecting species (assuming different species in each droplet) was 3:2. When one of the droplets contains a monoculture of the focal or is empty, or more than one droplet contains the same affecting species, these ratios change (see Figure 1—figure supplement 1).” (Lines 430-436)

Lastly, Figure 1—figure supplement 1: has been modified to better reiterate this point both graphically and the figure caption has been corrected to to match the text in the methods section.

Figure 3A graphic is unclear, and can be made much clearer by plotting mono effects and predicted coeffects under the three models.

We have made multiple changes to Figure 3, including to panel A as suggested here and by reviewer 2. Specifically we have added axes titles and a legend to panel A. This is further detailed and shown below in response to Reviewer #2's comments.

Reviewer #2 (Recommendations for the authors):

Figure 3: (A) I think this panel could be made clearer. What does the green bar represent? It is not explicitly clarified in the caption. I think it depicts the growth of the green "test" bacteria? Maybe clarifying this in the caption would help. Also, why not add the equation representing the interaction?

We have added the equations for each model to the panel, a title to the y-axis, and a legend explaining each category on the x-axis. Additionally, We better clarified this panel in the figure caption (see revised figure below).

Figure 3: (B). The data points are so tiny it is difficult to see them. Maybe using larger dots (I understand there are a lot of them, though. I wonder if there is a clearer way to plot this data). Also the color choice is not the friendlies to color-challenged readers like this reviewer. I had trouble in particular distinguishing the pairs when one species had a positive while the other one had a negative effect from those that were both negative.

We agree that it is difficult to see the individual data points. Unfortunately, we were unable to come up with a better way of plotting the data – we have tried several alternatives and we feel that they reduce the amount of information we are able to convey more than they increase the clarity of the data shown. We have adopted your suggestions to (A) make the dots larger and (B) change the color map (for this and all similar plots in the paper) to improve understanding and accessibility for all readers. Below are the relevant panels from Figure 3:

Lines 167-169: The authors introduce the "mean effect model". What is the theoretical justification for including this model in the analysis? I mean, in terms of ecological theory? The additive model is justified e.g. in that it is the typical assumption in Lotka-Volterra (and also considered in the antibiotic combination literature cited in the paper). But how about the mean model? It would help if the authors explained/justified the theoretical basis for this. Otherwise it feels a bit random, they could have taken the median, or the square root of the variance, or…

The justification for this model is not immediately based in ecological theory, but rather offers an intuitive null model for the reader, as the mean is often applied when combining different functions. This is a simplistic phenomenological model that assumes effects of different species would be diluted in the presence of a third species. We have stated so explicitly in the main text to avoid confusion of future readers:

"The mean model represents a simple phenomenological model which assumes that the effects of different species will be diluted in the presence of a third species". (Lines 188-191)

Lines 221-224: The authors write: "We further explored this model by basing trios' data not on the additive, mean, or strongest values of the effects of individual species, but on those of the joint effects of the three pairs comprising each trio (the effects of single species and pairs were measured independently again in this experiment, see Materials and methods, Figure S1)." I have read this sentence five times and I am still not sure what the authors meant

We changed the above sentence to the following to improve clarity:

"We further explored the additive, mean, and strongest models in trios by basing the model on effects of the three pairs comprising each trio (i.e. joint effect of AB, AC, BC to predict effect of ABC), as opposed to only using single effect data (i.e. effect of A, B, C on their own) (Figure 4A,B). The effects of single species and pairs were measured again independently in this experiment (see Materials and methods, Figure 1—figure supplement 1)." (Lines 262-266)

Lines 296-300. The authors may want to more explicitly bring up in their discussion that the predictive ability of the "Dominance", strongest-species model, is significantly worse when they try to predict the effect of a trio than when they try to predict the effect of a pair. This would suggest some caution in the reach of their conclusions, as it is possible that the predictive power of a single species will get worse and worse as the diversity of the community increases. Which, by the way, would not be surprising I think and should not be held against their findings, but I still think it would be good to qualify their statements about the potential reach of their conclusions for the bottom-up prediction of population-level interactions in complex communities. While they do state that "further work is needed…" to figure out if they results hold in more diverse communities (Lines 294-96) I felt that the limitations of the study could be written in a sharper manner.

We have added the following sentence to the discussion, to bring attention to this concern:

"Specifically, as we saw a decrease in prediction power from pairs to trios, exploring this model with more diverse communities is of particular interest." (Lines 361-363)

Finally: I was curious if the authors have considered a model where one of the species is dominant in a pair, but the one that dominates is not necessarily the one with the strongest effect? For instance, is it possible that when A is grown with either B alone or C alone, the suppression of growth from B is stronger than the suppression of growth from C. Yet, in the presence of both B and C, the suppression of growth is exactly the same as that by C (or just closer to C than B)? Do the authors see this in any of their pairs? If so, how many?

We have considered additional models, but in the end decided to focus our predictions using only the information of single effects, to root our models in easily obtainable information. In Author response image 1 we explore two additional models- a weakest effect model and dominant effect model. The weakest effect model assumes that the species with the weaker effect will dictate the combined effect of both species. As is to be expected, due to the strongest model's accuracy, this model was not particularly accurate- and we saw that the weakest effect was only more accurate than the stronger effect model in 23% of cases. It is also worth noting that the accuracy of the weakest model dropped rapidly as the difference in effect size between species grew. This points to the option that the cases in which it was more accurate could be due to minimal differences between strongest and weakest predictions, where measurement noise could tip the balance. We found only 14 pairs where there were large differences (>1) between the single affecting species and the difference in model accuracy (for weakest and strongest). Of these, all were with EC as the focal species, and of the 14, 9 included a specific specie (i.e. P_rhodesiae2) as the stronger single effect, but less accurate predictor.

The dominant effect model chooses whichever single effect is closer to the combined effect to pick as the predicted effect. Though this generates a more accurate fit, this model is not predictive, as it requires the combined effect as input to choose which single species effect to use as the 'prediction'.

Author response image 1

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Reviewer #3 (Recommendations for the authors):

The metric of growth for the focal species was fluorescence. This can be a risky measurement, because other species could autofluorescence in the emission spectrum. Additionally, fluorescent proteins can continue to fluoresce after cell death and lysis (we have personally observed this after phage infection and antibiotic treatment). I think the paper could use a test to verify that fluorescence was an unbiased proxy for growth.

This point brought up by both reviewers 1 and 3 is of great importance. Experiments to test this matter, on some of the species used in this study, and in this system, have been previously performed by Kehe et al. (See doi:10.1126/sciadv.abi7159, specifically figure S8) and these experiments found a high correlation between fluorescent signal, OD₆₀₀, and CFU counts. Nonetheless, we performed an interaction assay measuring fluorescence and OD₆₀₀ simultaneously, so they could be directly compared. We achieved these simultaneous measurements by utilizing the HTD Equilibrium Dialysis System, which enabled us to measure both fluorescence and. OD₆₀₀ for each of the two interacting species when they are cocultured in the same well. Briefly, this system is similar to a 96 well plate, but each well contains a dialysis membrane splitting the well into two halves (similar to the following protocols: https://doi.org/10.1101/2021.01.07.425753, https://doi.org/10.1371/journal.pone.0182163). Bacteria cannot pass through the membrane, but can interact chemically as dividing membrane has 1 μm pores. In each well there was a focal species and an isolate, on separate sides of the membrane, after 24 hours of coculture the OD₆₀₀ and fluorescence was measured for each species separately. We performed this assay for 6 single species with each focal, in triplicate. The correlation between the effect when measured by fluorescence and OD₆₀₀ was strong (r=0.71, p=1e-6). The correlation between the effect when measured in the kChip and the HTD Equilibrium Dialysis System was weaker (r=0.59, p=0.001), we believe this may be caused by the considerable differences in the physical conditions between these two setups. Overall, these results show that fluorescence is a good proxy for change in biomass in our interactions, acting similarly to OD₆₀₀ measurements.

We have added the following paragraphs and figure to the Materials and methods:

"Focal species were transformed with commercially available plasmid pMRE132 containing GFP2 as described by Kehe et al. 2021. Fluorescences has some caveats as a measurement for biomass, as fluorescent signal is not always directly proportional to biomass, expression levels can vary in different physiological states, and signal stability can differ between strains. Nonetheless, as described in Appendix 1, we show that effect sizes assayed using fluorescence and standard OD600 are well correlated (Appendix 1, Figure 1). (Lines 452-457)

"Additionally, isolates were only used with focals whose monocultures were at least five times larger than the isolates autofluorescence signal, allowing to measure effects of at least -1.5. Full datasets without autofluorescence filtering can be seen in Appendix 1, Figure 3. Importantly, affecting species autofluorescence would weaken measured negative effects, and would not systematically generate artifacts that support the strongest effect model." (Lines 462-467)

In addition, we added the following explanations of the experiments carried out to address these issue as Appendix 1:

"Fluorescence assays

To test the accuracy of using fluorescence to assay interactions, we performed the following experiment correlating effect size as measured by fluorescent signal to effect size as measured by OD600. Bacterial strains were seeded from -80 stock directly into 0.5 ml LB medium in a 96 well plate, and grown overnight at 30°C at 900 RPM (on a Titramax 100). Cells were washed 3 times by centrifugation at 3600 rcf for three minutes, removal of supernatant, and resuspension in M9 minimal media (with the addition of 1% [w/v] glucose). All cultures were normalized to 0.02 OD600. HTD96b plates (HTDialysis, Gales Ferry, CT, USA) with membranes containing 1 μm pores splitting each well were seeded with 150 μl affecting species and focal species cultures on opposite sides of the membrane. After a 24 hour growth period at 30°C, shaking at 600 RPM, 100 μl of culture for each side of each well was transferred to a standard 96-well plate and OD600 and fluorescence were measured (Appendix 1, Figure 1). Each interaction was measured using three technical replicates.

To ensure that model accuracy was not influenced by (fluorescent) measurement limitations, we analyzed the competitive effects of models with predictions limited to the range of minimal observed measurements (as we know the maximal measurements were not near saturation). This affected only the additive model (which was the only model that could predict effects stronger than those observed), and its accuracy was improved, but it was still less accurate than the mean and strongest models (Appendix 1, Figure 2).

Additionally, an experiment was carried out in the kChip to measure autofluorescence of affecting species. This setup was identical to the droplet preparation and culturing protocol detailed above, except that cultures were not mixed with the focal species prior to droplet generation. In this setup each droplet contains a single species, and wells contain one or two species (depending on whether the droplets were from the same or different cultures). Isolates were only used with focals whose monocultures were at least five times larger than the isolates autofluorescence signal, allowing to measure effects of at least -1.5. Full datasets without autofluorescence filtering can be seen in Appendix 1, Figure 3.

I am confused by the densities that the species start at. In the methods, it says the focal and affecting species had starter cultures that were 2-fold different in concentration, yet were mixed 1:1, and ended up with a 1:1 ratio. How is this possible? Supp Figure S1 did not help me understand this.

We addressed this issue in response to Reviewer 1, who also had difficulty with this matter. In retrospect, both our wording and graphical explanations were lacking, but have been thoroughly revised to address the issue in the new version of the manuscript.

It was surprising to me that inoculation density had no effects. This makes me wonder whether the interactions observed in this study are dominated by primary metabolic competition, because density effects are very common when allelopathy occurs. If this is true, it restricts the generality of the results, and is worth being discussed. Related to this, antibiotic resistance was measured, but what about potential to secrete antibiotics?

In our discussion we address the reasons we do not believe that the interactions are dominated by metabolic competition (e.g. no hierarchy, weak correlation between effect and growth rate or carrying capacity). Unfortunately, testing for antibiotic secretion specifically is not possible in our current experimental setup. Though whole genome sequencing could potentially offer insight into this matter, we don't currently have that data for the species in our study. We have altered the following paragraph in the discussion to better address how different kinds mechanisms of competition could affect the manner in which they combine:

"As we did not measure the abundance of all species in each community (only the focal), we cannot disentangle interaction modification (changes in per capita effect of specific species), from interaction chains (affecting the amount of an affecting species, and as such its effect on the focal), and further work is needed in order to pinpoint the exact mechanism(s) leading to the dominance of the strongest model for negative effects in our system. We also note that it is possible that the manner in which effects combine is affected by the mechanism of interaction; For instance, previous studies have shown that interference competition can combine additively, or even synergistically, results not seen in our work (Tyc et al. 2014; Westhoff et al. 2021)."

(Lines 336-344)

I think the density effects should be measured with nRMSE, or even absolute difference from y=x, because there could be a strong correlation without the actual numbers being the same sign or magnitude. For example, in S11-B, most of the datapoints appear below y=x, until the effects are near zero, suggesting an effect-size-specific effect of density.

Values in the figure legend of Figure 1—figure supplement 2 have been changed from r² to nRMSEs as suggested. The values are 0.22, 0.16, and 0.24 for panels A, B, and C respectively, and reflect what we maintain to be quite strong correlations for different starting densities, as well as a good absolute fit to y=x. Though there may be effect size specific behaviors (in panel B- 3:1 by 1:1 starting ratios), there is not enough data to draw significant conclusions about this at present.

More discussion could be given on what a "meaningful" difference in nRMSE is.

Though we do not discuss this explicitly in the manuscript, we agree that there is much to be said on the matter of statistically and biologically relevant differences in nRMSE. In the new version of the manuscript we focus our message around the competitive interactions, where there are large differences in the nRMSEs, and soften our claims regarding other interaction types where nRMSEs are closer to one another, to avoid exaggerated claims based on small nRMSE differences.

More details on how the resampling during the bootstrap procedure was done is warranted.

We have revised the relevant paragraph in the Materials and methods sections to include a more comprehensive explanation:

"Root mean square error measuring the accuracy of each model was normalized to the interquartile range for each dataset. Normalized root mean square error median and interquartile ranges were calculated via bootstrapping. The dataset from each focal was sampled 1000 times with replacement. Sampling was done for individual effect measurements (specific wells), and median effect sizes for species, pairs, and trios were recalculated from these sampled datasets. The sampled datasets from each focal were assembled into 'full' datasets (containing all focals) from which nRMSEs were calculated. The median and interquartile range of the normalized root mean square errors were calculated from the 1000 sampled datasets' values." (Lines 509-517)

It isn't clear to me how Figure 1C is supposed to show that different models were used-perhaps drop this and just leave this explanation for Figure 3A, which is very clear.

We agree that the panel title did not match the graphic well, despite this, we feel the panel is important for the overview of our pipeline. As such, we have changed the panel title to "Single species data were used to predict combined effects".

Suggestion for additional analysis using the trait data: this dataset seems perfect for using something like a random forest or other continuous-response, "open box" machine learning approach to agnostically ask whether the trait measurements can be used to predict effect when all the measurements are used, rather than summaries of the measurements in the distance metrics.

As mentioned earlier in response to the last comment of your (Reviewer 3's) public review, similar studies have been done in our research group, but we feel such analyses are beyond the scope of our current study. We do hope to apply principles learned from the other studies to our dataset in the future.

Author details

1. Amichai Baichman-Kass

   Institute of Environmental Sciences, Hebrew University, Rehovot, Israel

   Contribution

   Conceptualization, Data curation, Formal analysis, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0924-3191

2. Tingting Song

   Institute of Environmental Sciences, Hebrew University, Rehovot, Israel

   Contribution

   Isolated strains used in this study

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6740-2085

3. Jonathan Friedman

   Institute of Environmental Sciences, Hebrew University, Rehovot, Israel

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing - original draft, Writing - review and editing

   For correspondence

   yonatan.friedman@mail.huji.ac.il

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8476-8030

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