In this section, we outline the method we used to assign genomes to each species cluster. We also verify the robustness of the species assignment by using three different methods and show that they give identical results.

Comparisons of genomes from bacterial populations often reveal clusters at different length and divergence scales (Jain et al., 2018). But the interpretation of such clusters is controversial (Cohan, 2002; Fraser et al., 2009). There are three main possible interpretations for such patterns. One interpretation is that the clusters represent the bacterial analog of eukaryotic species, which are sexually and ecologically isolated from each other. In practice, a whole-genome divergence cutoff of 5% is frequently used to define bacterial species (Jain et al., 2018). An alternative interpretation is that clusters are the result of clonal expansions of particular strains from a much more diverse and possibly more genetically homogeneous population. The third interpretation is that the clusters are the result of uneven sampling from a larger and more diverse population. The unique combination of having a large collection of genomes, with minimal compositional bias, from a geographically isolated population allows us to test these alternatives. We will mainly aim to distinguish between the first two interpretations and the third one by checking whether there are robust genomic clusters in our sample. More discussion on the evidence concerning the first two hypotheses can be found in Appendices 3 and 5.

We used three different methods to check whether the genomes form robust clusters: the phylogenetic tree of the 16S rRNA sequences, average genome-wide divergence from the two reference genomes OS-A and OS-B’, and patterns of divergences between triplets formed by the SAG and the two reference sequences at different loci. The phylogenetic tree of the 16S is the simplest and still the most commonly used method to characterize the diversity of natural microbial communities (Yarza et al., 2014). Because of its practical importance, we included it for comparison with the other two methods. However, in a highly recombining population like the Yellowstone Synechococcus, it is not clear to what extent the 16S divergence accurately reflects the whole-genome diversity. To address this question, we used the divergences across the entire genome as a comparison. The main limitation of using summary statistics such as the average divergence across the entire genome is that it obscures heterogeneities along the genome that could have important ecological and evolutionary implications. There are different ways to address this concern. Here, we used an extension of a method first used in Rosen et al., 2018, which provides a coarse description of the variation in the diversity patterns across different loci. We present the results from each of these analyses next.

We first constructed the phylogenetic tree of 16S sequences. Predicted 16S rRNA sequences (117 from 331 filtered SAGs) were extracted and aligned using MAFFT (v7.453) (Katoh and Standley, 2013). Two sequences (SAGs MA02M11_3 and MuA02C9) were incomplete and were removed from the analysis. The remaining (115) sequences were hierarchically clustered using the average linkage (UPGMA) method implemented in Scipy. Results are shown in Appendix 2—figure 3, with the colored background showing the species assignment using whole-genome divergences (see below) for comparison. We found perfect agreement between the whole-genome assignment and the largest three clusters in the 16S phylogenetic tree.

The average divergence within the α cluster is approximately half that of β (1⋅10−3\begin{document}$1\cdot 10^{-3}$\end{document} vs 2⋅10−3\begin{document}$2\cdot 10^{-3}$\end{document}). However, a significant fraction of the average divergence within β was due to two outliers (MuA1L16 and MusA1J8). After removing the outliers, the average divergence within β decreased to 1.7⋅10−3\begin{document}$ 1.7\cdot 10^{-3}$\end{document}. Closer investigation of the alignments revealed that both outlier β sequences contained a short segment of three SNPs that were identical to all α sequences and different from all other β sequences, at positions 1067–1072. In addition, MuA1L16 contained a larger segment of almost 200 bp (positions 390–570) containing 10 SNPs and an insertion that were different from all other β and were identical to the consensus α\begin{document}$ \alpha$\end{document}. Apart from these segments, the outlier sequences were typical of the β species. This pattern is similar to the SNP blocks discussed in the main text and in Appendix 6 and therefore is likely the result of hybridization between α and β.

We compared the 16S rRNA clusters to whole-genome divergences from the two reference genomes, OS-A and OS-B’. We aligned all of the predicted genes from each SAG to all of the coding DNA sequences (CDS) from each reference genome using BLAST (v2.13.0+) (Altschul et al., 1990). For each SAG, we calculated the divergence to each reference genome (d=1−pident/100\begin{document}$d=1-\text{pident}/100$\end{document}) and calculated the average over the best hits across all genes. The results for all SAGs with more than 100 hits to both references are shown in Figure 1A. Three clear clusters were observed, which we labeled as α, β, and γ. The species of each SAG was assigned as the label corresponding to the cluster it belonged to in Figure 5A.

The previous two metrics do not reflect possible heterogeneity in the patterns of diversity along the genome. To characterize this variation on a gene-by-gene basis, we extended a method that was previously used to analyze amplicon data from the Mushroom Spring in Rosen et al., 2018. We refer to this method as gene triplet analysis. This analysis exploits the separation of scales between and within species clusters. At most loci and in most cells, we observed previously in order to coarse grain the high-dimensional matrix of pairwise divergences into a small number of discrete patterns. Specifically, we take triplets of sequences from the SAGs, OS-A, OS-B’, at loci where all three are homologous and calculate the divergences between all three pairs of sequences. These divergences typically form a triangle as shown in Appendix 2—figure 1. Note that it is possible to have triplets of divergences that violate the triangle inequality, which cannot be represented as triangles in a two-dimensional space. In our data, such cases were rare, but this may not be generally true, particularly for sequences that are not clearly separated and which are the result of extensive recombination. Note, however, that the classification into distinct patterns given below can still be done even in these cases. To reduce the dimensionality of the data further, we define a main cloud diameter dM=0.1\begin{document}$ d_{M}=0.1$\end{document} for the diversity within species. We then classify the shape of the triangle into the 5 distinct patterns shown in Appendix 2—figure 1, depending on whether each side of the triangle is longer or shorter than dM\begin{document}$ d_{M}$\end{document}. For example, denote the divergence triplet by (dXA,dXB,dAB)\begin{document}$(d_{XA},d_{XB},d_{AB})$\end{document}, representing the divergences between the SAG sequence and OS-A, the SAG sequence and OS-B’, and OS-A and OS-B’, respectively. Then the first pattern in Appendix 2—figure 1A (labeled ‘XA–B’) contains loci where dXA<dM\begin{document}$ d_{XA} \lt d_{M}$\end{document}, dXB≥dM\begin{document}$d_{XB}\geq d_{M}$\end{document}, and dAB<dM\begin{document}$d_{AB} \lt d_{M}$\end{document}, the second pattern (labeled ‘XAB’) contains loci where dXA<dM\begin{document}$d_{XA} \lt d_{M}$\end{document}, dXB<dM\begin{document}$d_{XB} \lt d_{M}$\end{document}, and dAB<dM\begin{document}$d_{AB} \lt d_{M}$\end{document}, and so on. The cutoff of dM=0.1\begin{document}$d_{M}=0.1$\end{document} is the same as the one used in Rosen et al., 2018 and provides a good separation between species at a gene by gene basis. The results of our analysis, however, do not depend on the specific value of dM\begin{document}$d_{M}$\end{document} as discussed at the end.

For each SAG, we assigned all genes that were orthologous to OS-A and OS-B’ to one of the five patterns described above. The three rows in Appendix 2—figure 1 show typical examples of an α (Appendix 2—figure 1A), a β (Appendix 2—figure 1B), and the γ (Appendix 2—figure 1C) SAG. The majority of genes across each row in Appendix 2—figure 1 are found in the XA–B, XB–A, and X–A–B patterns, respectively. This is consistent with the species clusters we saw in the genome-wide average divergences from before. However, we also find a significant minority of genes forming other patterns, most notably XAB, representing genes where all three sequences are within the main cloud (d<dM\begin{document}$d \lt d_{M}$\end{document}). Some of these genes were contained in the divergence troughs discussed in the main text. In the case of the γ SAG, the fact that X–A–B is the dominant pattern rules out the possibility that γ is a hybrid resulting from the mixture of α\begin{document}$ \alpha$\end{document} and β. Such hybrids have been observed after recent clonal expansions in acid mine drainage microbial communities (Tyson et al., 2004; Lo et al., 2007), but do not appear to be present at substantial frequency in the Yellowstone community. Instead, it appears that γ is a distinct species that diverged from the other two around the same time α and β diverged from each other.

Using the pattern described above allows us to compare different SAGs to each other and allows us to test the robustness of the species assignment based on the average genome-wide divergence. Specifically, we assigned to each SAG a gene triple fingerprint f=(fXA−B,fXAB,fX−A−B,fX−AB,fXB−A)\begin{document}$ f=(f_{XA-B},f_{XAB},f_{X-A-B},f_{X-AB},f_{XB-A})$\end{document}, representing the fraction of genes with each pattern (note that ∑ifi=1\begin{document}$ \sum_{i}f_{i}=1$\end{document}). We then compared the fingerprints of each SAG with the species assignment based on the average divergence from OS-A and OS-B’ from Figure 1A. We found that the fingerprints formed three clear patterns that exactly matched the assignments based on the average divergence (Appendix 2—figure 2). We tested this assignment for different values of dM\begin{document}$ d_{M}$\end{document} ranging from 1% to 20% and found that the fingerprint patterns were robust across the entire range (data not shown). These results show that the classification into distinct species is robust and consistent across the three methods described.

To estimate abundances of the three main species α, β, and γ in the Octopus and Mushroom Springs, we recruited metagenomic reads from 34 samples taken from both springs to SAGs from each species. We chose the one γ SAG (OA3L13, ≈70% coverage) along with representative SAGs from α (MA02D15, ≈77% coverage) and β (OcA2H14, ≈96% coverage) as reference genomes. Hybridization on length scales longer than the typical read size (150 bp in our case) can lead to errors in our estimates of species abundances. To minimize these errors, we only used core genes where three distinct species clusters could be identified and there was no evidence of hybridization in the single-cell data (see Appendices 1 and 5). This resulted in a set of ≈400 genes for each reference. We aligned all the metagenomic reads to these target gene sequences using BowTie2 (v2.3.4, default parameters) (Langmead and Salzberg, 2012) and extracted reads aligning to each of the three reference sequences using Samtools (v1.7.0) (Li et al., 2009) and bedtools bamtofastq command (v2.26.0) (Quinlan and Hall, 2010).

We assigned the recruited reads to each species cluster if their divergence from their respective reference was less than the ‘main cloud’ radius dM\begin{document}$d_{M}$\end{document}. We determined dM\begin{document}$ d_{M}$\end{document} self-consistently from the data as follows. For each reference, counted the number of reads that had divergences less than dM\begin{document}$d_{M}$\end{document} from that reference sequence and more than dM\begin{document}$d_{M}$\end{document} from the other two reference sequences, for dM\begin{document}$ d_{M}$\end{document} from 1% to 15%. If the population consists of species clusters with typical diversity π\begin{document}$ \pi$\end{document}, the number of reads within the cloud will increase until dM≈π\begin{document}$d_{M}\approx\pi$\end{document}. As dM\begin{document}$ d_{M}$\end{document} approaches the typical divergence between species d≈15%\begin{document}$ d\approx 15\%$\end{document}, more reads will start to map to multiple reference sequences, so the number of reads uniquely assigned to each species cluster will decrease. Therefore, the number of reads uniquely assigned to each species cluster should have a maximum as a function of dM\begin{document}$ d_{M}$\end{document}. We indeed found this to be the case for all three species (data not shown). Empirically, we found that dM=5%\begin{document}$d_{M}=5\%$\end{document} was close to the maximum for all three species, so we used this value throughout our analysis.

We found that the average depth of recruited reads across genes varied within the same sample. However, the variations across samples were highly correlated, which confirmed that most reads aligning to our chosen genes came from genomes that were part of the same species cluster rather than from genes transferred across species (Appendix 3—figure 3). We found that the genes that recruited the largest numbers of reads had read depths that were much more similar within the same sample compared to other genes. Interestingly, we found much more variation in depth between genes within the γ cluster compared to α and β (Appendix 3—figure 3). One likely explanation for this is that γ contains much more diversity compared to either α or β.

We estimated the abundance of each species cluster by averaging the depth of the 100 genes with the highest average depth across all samples for each cluster. We found that γ was more than an order of magnitude more abundant than our detection threshold given by the metagenomic read depth in 32 out of the 34 metagenome samples (Appendix 3—figure 4). Moreover, its abundance in the two samples for which we had single-cell and metagenome data (MSe4 and OSM3) was close to the detection threshold of the single-cell samples, which was around 2%. This explains why we only obtained a single γ cell from the single-cell samples after our quality controls. Finally, we found that the abundance of γ was highly correlated with α across all samples and was only present at abundances higher than O(1)%\begin{document}$ O(1)\%$\end{document} in the Mushroom Spring sample taken from 65°C. This suggests that γ is, together with α, primarily adapted to growth at higher temperatures.

Are other Synechococcus species present in Mushroom or Octopus Spring apart from α, β, and γ? To answer this question, we again used the 34 samples from which we have high-depth metagenomes. We used BLAST with highly sensitive parameter choices to minimize the number of true Synechococcus reads not captured. For computational efficiency, we focused on the 100 genes with highest coverage depth in the metagenomes across all three references.

To determine how much of the population is in the α–β–γ main cloud, we used the same three SAGs as in the previous subsection as references and recruited reads using BLAST (-task blastn -evalue 1e-3 -word_size 6 -num_threads 32). Using these parameters, we could recruit reads belonging to the dominant Roseiflexus species in our samples, which is in a different phylum from Synechococcus. We were therefore confident that any reads from other potential Synechococcus species would be included in our analysis. To limit the analysis to just Synechococcus species, we removed all reads that were more than 20% diverged from all of our references from subsequent analysis.

Because of the large amount of data in this analysis, we focus on just the Mushroom Spring samples taken from different temperatures (MS temperature series). We recruited a total of 4,522,833 reads with an average depth per gene of 4980. We calculated the minimum divergence from the three reference sequences for each read and found 94% within 5% divergence of one of them (Appendix 3—figure 5A). For comparison, we determined the typical divergences between species by dividing the reference sequences into 150 bp segments (the same size as our reads) and calculating the divergences between all three pairs of species (Appendix 3—figure 5B). The middle 95-percentile of the combined distributions extended down to a divergence of around 5% (eight SNPs), consistent with our cutoff for the intraspecies divergences at these loci. These results are consistent with all of the Synechococcus reads being from one of the three species and set an upper bound on the relative abundance of any other species at below 4%.

To check how sensitive our detection method is to the presence of other species, we used the Mushroom Spring sample from 65 in which γ had a relatively high abundance. To mimic the presence of another species, we compared the previous distributions to the distribution of the minimum divergence from α and β only (dashed red line in Appendix 3—figure 5A). We found a 19% decrease in cumulative number of reads within 5% from the references in this case, which was very close to the 21% abundance of γ\begin{document}$ \gamma$\end{document} we estimated in the previous subsection based on the average depth across loci. This shows that our method is sensitive to the presence of other species and illustrates the benefits of combining single-cell and metagenome analysis for identifying unknown species.

To further verify that no other Synechococcus species were present in our samples, we closely examined the diversity of 16S sequences. We used only single reads in our analysis instead of trying to assemble full sequences to prevent misinference caused by hybridization. Because the diversity along the 16S sequence is highly heterogeneous, variation between read recruitment locations can dominate the variation between species. We controlled for this by limiting the analysis to reads that aligned within a given region of the 16S. For 150 bp reads, we found that using segment sizes of 200 bp provided the best compromise between increasing depth and minimizing variance due to alignment location. To find the most informative region, we calculated the nucleotide diversity at each site Hi=2⟨fi(1−f)⟩\begin{document}$\mathcal{H}_{i}=2\langle f_{i}(1-f)\rangle$\end{document}, where fi\begin{document}$f_{i}$\end{document} is the minor allele frequency at site i\begin{document}$ i$\end{document}, and averaged it over all 200 bp segments along the 16S (Appendix 3—figure 6A). We found the diversity varied by more than a factor of four, consistent with the presence of conserved and variable regions. The diversity was nearly identical when using all three species as reference genomes, suggesting our recruitment captured all sequences within the main cloud. The highest average diversity was close to 400–600 bp segments, which we chose for further analysis.

We calculated the distribution of divergences from the γ allele for all reads recruited from this segment for MS temperature series. We found temperatures of 60°C and below had two distinct peaks close to Appendix 3—figure 6B 4% and 8% divergences. For comparison, we calculated the range of divergences from α and β for all 150 bp subsegments within the 400–600 bp segment and found these matched with the two peaks we observed. At 65°C, we also found only two peaks, one close to zero and another close to 4%, consistent with our previous estimates showing that this sample mainly consisted of α and γ cells.

Do peaks correspond to single-species clusters or are they amalgamations of several distinct species with similar divergences from each other? To answer this question, we constructed a multiple-sequence alignment of all of the 16S reads recruited across the 34 metagenome samples and performed a hierarchical clustering on the pairwise divergence matrix using average linkage. Pairwise divergences were calculated by padding the reads with gaps to ensure all sequences were 200 bp in length and calculating the nucleotide divergence ignoring any gaps. For the MS temperature series, we found 97% of reads were in one of the three clusters associated with α, β, or γ (Appendix 3—figure 7A–D). Consistent with our previous results, samples below 65°C had two main clusters close to OS-A and OS-B’ (Appendix 3—figure 7A–C), while at 65°C they were close to γ and OS-A (Appendix 3—figure 7D). Aggregating across all 34 metagenome samples, we found that α and β were the two dominant clusters, with γ being the next largest (Appendix 3—figure 7E, F). We also observed a large difference in the overall abundances of α and β across the two springs, but the very large heterogeneity across samples we found previously (Appendix 3—figure 4) suggests this is likely due to the particular samples used in this study and may not necessarily be an accurate reflection of the overall abundances in the two springs.

In this section, we summarize our analysis of linkage disequilibrium within α and β. The structure of this section is as follows. We begin by reviewing definitions of two commonly used ways to quantify linkage disequilibrium. We then compare the rate of decay of linkage disequilibrium within and between the two species. We next compare the decrease in linkage in the data to theoretical predictions from the neutral model and show that while the decay is similar to the neutral model prediction, the overall shape of the linkage decay curves cannot be fully explained by the classical neutral model. We then show that within α, there is substantial heterogeneity in the rate of linkage decay in low-diversity regions compared to high-diversity ones. Surprisingly, we find that linkage decreases more rapidly in low-divergence regions, suggesting the absence of a clonal frame for α even on short time scales. The final subsection presents a technical validation of our method for processing alignments showing that our results are robust to filtering for outlier gene alleles.

We used two distinct but related methods for quantifying linkage disequilibrium, σd2\begin{document}$\sigma_{d}^{2}$\end{document} and r2\begin{document}$ r^{2}$\end{document}. Both metrics are related to the correlation coefficient between alleles at two loci but differ in their normalization. For a single pair of loci A and B with alleles A/a and B/b, we can define the correlation coefficient between their respective frequencies as(2)rAB2=(fAB−fAfB)2fA(1−fA)fB(1−fB).\begin{document}$$\displaystyle r_{AB}^2 = \frac{(f_{AB} - f_Af_B)^2}{f_A(1 - f_A)f_B(1 - f_B)}.$$\end{document}

Using this expression, we can define a statistical measure of linkage as a function of distance along the genome by averaging over pairs of loci with a given separation x=|xA−xB|\begin{document}$x=|x_{A}-x_{B}|$\end{document}, where xA\begin{document}$ x_{A}$\end{document} and xB\begin{document}$x_{B}$\end{document} are the positions of the two loci along the genome. The two most common ways to perform the average are(3)σd2(x)=⟨(fAB−fAfB)2⟩|xA−xB|=x⟨fA(1−fA)fB(1−fB)⟩|xA−xB|=x,\begin{document}$$\displaystyle \sigma_d^2(x) = \frac{\left \langle (f_{AB} - f_Af_B)^2 \right \rangle_{|x_A - x_B|=x}}{ \left \langle f_A(1 - f_A)f_B(1 - f_B) \right \rangle_{{|x_A - x_B|=x}}},$$\end{document}

and(4)r2(x)=⟨(fAB−fAfB)2fA(1−fA)fB(1−fB)⟩|xA−xB|=x.\begin{document}$$\displaystyle r^2(x) = \left \langle \frac{(f_{AB} - f_Af_B)^2}{f_A(1 - f_A)f_B(1 - f_B)} \right \rangle_{|x_A - x_B|=x}.$$\end{document}

For a neutral panmitic and well-mixed population, both metrics decrease as σd2(x)∼r2(x)∼1/x\begin{document}$\sigma_{d}^{2}(x)\sim r^{2}(x)\sim 1/x$\end{document}. For σd2\begin{document}$ \sigma_{d}^{2}$\end{document}, there also exists an analytic expression (Ohta and Kimura, 1969):(5)σd2=10+2NR22+26NR+4(NR)2,\begin{document}$$\displaystyle \sigma_d^2 = \frac{10 + 2NR}{22 + 26NR + 4(NR)^2},$$\end{document}

where N\begin{document}$ N$\end{document} is the population size, and R\begin{document}$ R$\end{document} the recombination rate per base pair per generation. When recombination is rare and occurs via crossover R(x)≈R0x\begin{document}$R(x)\approx R_{0}x$\end{document}, and the expression is consistent with the scaling σd2(x)∼1/x\begin{document}$\sigma_{d}^{2}(x)\sim 1/x$\end{document} mentioned previously. While numerical and theoretical studies have shown that r2\begin{document}$ r^{2}$\end{document} is more sensitive to low-frequency alleles compared to σd2\begin{document}$\sigma_{d}^{2}$\end{document} (Hudson, 1985; Song and Song, 2007), our analysis did not reveal significant differences between two metrics. We therefore focus here on σd2\begin{document}$ \sigma_{d}^{2}$\end{document} which is more commonly used and easier to compare to theoretical predictions.

We calculated σd2(x)\begin{document}$\sigma_{d}^{2}(x)$\end{document} and r2(x)\begin{document}$ r^{2}(x)$\end{document} for α and β separately and together. Both procedures are similar, so we focus on the analysis for all α and β sequences. Unless otherwise stated, all analyses were performed on alignments of individual genes and the results were averaged across genes. Using this method, we can easily obtain linkage information over distances of up to around 1 kbp. Over longer distances, the results can be dominated by specific recombination events in a small number of unusually long genes and are therefore less useful for quantifying genome-wide statistical patterns. We thus perform most of our analysis up to distances of around 1 kbp, except when calculating typical genome-wide linkage as discussed below.

Alignments for each orthogroup were first trimmed to remove segments with excess numbers of gaps. We then determined a consensus sequence by taking the most common codon sequence at each location along the reading frame, excluding gaps. Each nucleotide was labeled 0 if it was a gap, 1 if it was the same as the consensus, and 2 if it was different from the consensus. While this does not distinguish between biallelic and multi-allelic sites, the latter are much less common than the former and should not affect our conclusions. Finally, we calculated the two linkage coefficients using Equations 3 and 4. To estimate linkage across distances longer than a single gene, we performed the average across SNPs spanning a pair of genes and then averaged the values across a random sample of 1000 pairs of genes.

The linkage calculations within each species were performed in an analogous way, with the exception of a two-step filtering process of the alignments at the beginning. We describe this procedure in detail at the end of this section.

Our analysis showed that within both α and β, linkage quickly decreased by approximately an order of magnitude over a distance of ∼1 kbp (orange circles and blue squares in Appendix 4—figure 1). However, when considering the population as a whole, we find linkage disequilibrium is maintained across the whole length of the genome (black diamonds in Appendix 4—figure 1). Within β, the linkage at distances of 1 kbp was identical to the genomewide linkage between random pairs of genes. Within α, the decrease was slower, but followed a similar pattern. The value of the genome-wide linkage was slightly higher than at 1 kbp, likely because of the reduced sample size at long genomic distances caused by poor genome coverage. Consistent with this, we found that the genomewide-linkage values in both species were close to completely unlinked controls obtained by randomly permuting each column of the alignments (σd2=0.14\begin{document}$ \sigma_{d}^{2}=0.14$\end{document} vs σd2=0.12\begin{document}$ \sigma_{d}^{2}=0.12$\end{document} in α and σd2=0.06\begin{document}$ \sigma_{d}^{2}=0.06$\end{document} vs σd2=0.04\begin{document}$\sigma_{d}^{2}=0.04$\end{document} in β). Overall, these results suggest that the dynamics leading to the reassortment of alleles are similar in the two species and only differ in the length scale over which alleles become unlinked. We discuss this in more detail in the next section.

The fact that both species have similar levels of genomewide linkage despite the sample size of α being less than half of that of β shows that our estimates for the genomewide linkage are not significantly affected by the sample size effect. We further validated this by taking random samples from the β main cloud equal to the size of the α main cloud at each locus and recalculating the linkage curves. We found the results for the full β main cloud and the subsampled main cloud were almost identical (Appendix 4—figure 2). This shows that the sample size does not have a large effect on our results and cannot explain the differences in linkage decay between the two species.

The rapid decrease in linkage sets important limits on how much information about the diversity in the population is contained in samples of marker genes. To illustrate this, we performed a linear regression between the whole-genome divergences and the 16S rRNA divergence. Consistent with our previous analysis, we found slightly stronger linkage in α compared to β, but in both cases, the correlations were weak and the 16S divergences explained less than 10% of the genome-wide divergences (Appendix 4—figure 1B). These results show that frequent recombination in the population makes marker genes, such as the 16S rRNA, poor predictors of the genome-wide diversity.

To get a more quantitative understanding of the effects of recombination on the genetic diversity in our population, we compared our previous results to theoretical predictions from population genetics.

At short distances, the prediction from Equation 5 is that σd2=5/11\begin{document}$\sigma_{d}^{2}=5/11$\end{document}. However, in our data, the value of σd2\begin{document}$\sigma_{d}^{2}$\end{document} for nearby sites was very close to one. While the Yellowstone Synechococcus have a strong mutational bias toward GC nucleotides (Rosen et al., 2018), Equation 5 is independent of the relative rates of mutations. As a result, we conclude that the neutral model cannot explain the linkage curves we observe.

While the overall level of σd2\begin{document}$\sigma_{d}^{2}$\end{document} in our data is inconsistent with the neutral prediction, we can still ask whether the rate of decay with distance has a similar functional form. To do this, we followed Garud et al., 2019 and fit the linkage curves to the following functional form:(6)σd2(x)=A10+ρx22+13ρx+(ρx)2,\begin{document}$$\displaystyle \sigma_d^2(x) = A\frac{10 + \rho x}{22 + 13\rho x + (\rho x)^2},$$\end{document}

where ρ=2NR\begin{document}$ \rho=2NR$\end{document} is the population recombination rate. We performed the fit by choosing A\begin{document}$ A$\end{document} such that the above expression matched the value of σd2\begin{document}$ \sigma_{d}^{2}$\end{document} in the data for neighboring sites (x=1\begin{document}$x=1$\end{document}). We then fitted the curves by eye by adjusting the value of ρ\begin{document}$ \rho$\end{document}.

We found that this functional form could fit the data very well for both species up to distances of x≈300\begin{document}$ x\approx 300$\end{document} bp (Figure 2 in main text). For longer distances, the linkage decrease was slightly slower than predicted by Equation 6. One possible interpretation of this slowdown is that longer distances have a significant overlap with the distribution of lengths of recombined segments Lr\begin{document}$ L_{r}$\end{document}, beyond which we expect linkage to reach the genomewide level (Garud et al., 2019). This suggests that recombined segments as short as 300 bp might play an important role in the recombination process within the population.

We further validated that the linkage curves have the same functional form by rescaling distances between sites by the recombination rate ρ\begin{document}$ \rho$\end{document} inferred previously. We found a very good collapse of the linkage curves for the two species when plotted against the rescaled distances (Appendix 4—figure 3B). This strongly implies that the dynamics leading to the decay of linkage are the same in both species, with the differences between them being length scale over which sites are effectively linked.

Our analysis so far was limited to either distances up to the length of typical genes (∼1 kbp) or across the entire genome. Extending our analysis over distances in between these two extremes is difficult due to several technical challenges. The first is the fact that typical coverages for our SAGs are around 30%. Together with a typical contig size of ∼10 kbp, this means that our sample size quickly decreases with distance. The second challenge is that at longer distances, gene order might vary across genomes, making it difficult to define a genomic distance at the population level.

We calculated the linkage disequilibrium between multi-SNP features, such as SNP blocks or hybrid alleles, using Equation 2 as in the case of biallelic SNPs. In the case of SNP blocks shown in Figure 7D in the main text, we calculate the frequencies for the four haplotypes within SAGs that are covered at both loci. The unlinked controls (represented by solid lines in Figure 7D) were obtained by a random permutation of the alleles at each locus independently, while keeping the SAGs that are covered at each locus fixed. This procedure preserves any correlations in genome coverage between nearby loci and provides the most accurate estimate of rAB2\begin{document}$r_{AB}^{2}$\end{document} for a completely unlinked genome.

The linkage between hybrid gene alleles was calculated similarly as for the SNP blocks, except for the genotype assignment. At each locus, we labeled the most abundant allele using upper case letters (A,B,…\begin{document}$A, B, \dots$\end{document}) and grouped all of the remaining ones into a single allele labeled by a lower case letter (a,b,…\begin{document}$ a, b,\dots$\end{document}). The linkage matrix rAB2\begin{document}$ r_{AB}^{2}$\end{document} and the unlinked control were calculated the same as previously described. The results for α were ⟨rAB2⟩=0.04±0.15\begin{document}$\langle r_{AB}^{2}\rangle=0.04\pm 0.15$\end{document} compared to ⟨rAB2⟩=0.02±0.11\begin{document}$ \langle r_{AB}^{2}\rangle=0.02\pm 0.11$\end{document} for the unlinked control. For β, the results were ⟨rAB2⟩=0.01±0.09\begin{document}$ \langle r_{AB}^{2}\rangle=0.01\pm 0.09$\end{document} compared to ⟨rAB2⟩=0.009±0.08\begin{document}$ \langle r_{AB}^{2}\rangle=0.009\pm 0.08$\end{document} for the unlinked control. Note that the average linkage disequilibrium was close to the unlinked controls in both species, with α having slightly higher linkage. These agree with those from the analysis of SNP blocks shown in the main text.

For each species, we first selected all of the sequences that belonged to SAGs assigned to that species (see Appendix 2). We then calculated the consensus sequence for this group of sequences, as described above, and removed all sequences with divergences greater than a main cloud cutoff c\begin{document}$ c$\end{document}. This is a simple way to remove sequences that are the result of gene-level hybridization (see Appendix 5 and Rosen et al., 2015 for a similar procedure). We chose the main cloud cutoff for each species by calculating the linkage curves for different values and choosing the largest value for which the curves did not noticeably change (Appendix 4—figure 4). Based on this criterion, we use c=0.05\begin{document}$ c=0.05$\end{document} for α and c=0.1\begin{document}$ c=0.1$\end{document} for β throughout.

This section describes the method we used to quantify hybridization at the gene level. Our method uses a set of simple heuristics to assign labels to the species clusters defined in Appendix A based on the composition of species to which the sequences belonged. We then identified hybridization events by searching for discrepancies between the gene and whole-genome labels as explained below.

We first assigned labels to the species-level clusters constructed as described in Appendix 1. Based on the gene triplet results presented in Appendix 2, we expect most sequences to be contained in two main clusters, close to OS-A and OS-B’, respectively, with at least one sequence forming a separate cluster whenever the orthogroup was covered in the γ SAG. Based on this expectation, we considered all of the clusters from each orthogroup in decreasing order of their sizes and labeled them as described in the main text.

We next determined which orthogroups are part of the core genome. We defined a gene as a core gene if it is likely present in all of the genomes in our sample. The average coverage for each SAG in our sample was approximately 30%, so it is not possible to directly determine whether some genes are always present. Instead, we use a statistical measure of the coverage to assign orthogroups to the core genome. Specifically, we used the rank-coverage plot across all orthogroups and SAGs (equivalent to the complementary cumulative distribution) to determine an appropriate cutoff for the core genome. The rank-coverage plot showed three distinct regions. First, there were around a dozen orthogroups that had unusually high abundances, with the number of sequences in some cases being greater than the number of SAGs in our sample. These are likely multiple-copy genes and IS elements and were excluded from further analysis. Then there was a large plateau comprising over 1000 orthogroups with coverages in the range 100−150, followed by a sharp decrease (on a logarithmic scale) in the coverage. We found that setting a coverage threshold for the presence at 20% of the number of SAGs from each species approximately matched the shoulder between the plateau and the sharp decrease, and so we used this as a criterion for assigning core genes.

The final step in our algorithm is to catalog hybridization events, which we do by simply searching for gene sequences whose labels were different from the whole-genome species assignment. Analysis of these results showed a large number of transfers, mainly from β into α, which came from contigs that did not contain any genes labeled as the host species. One explanation for the presence of such contigs is that they represent larger genomic segments flanked by repetitive regions (such as IS elements) that are transferred and integrated into the host genome. Long repetitive genomic segments can lead to contig breaks during assembly, which would explain the complete absence of genes belonging to the host cluster. Alternatively, such contigs could be the result of contamination with external DNA. However, the contamination hypothesis does not explain why there seem to be more transfers from β into than vice versa. We also did not find any evidence of differences in the number of such transfers between the sample containing only α\begin{document}$ \alpha$\end{document} SAGs (OS2005, see Appendix 10) and samples containing mixtures of and β. While this evidence suggests these transfers are very likely the result of hybridization, we cannot rule out the possibility of contamination. We therefore excluded all hybridization events on contigs that did not contain any genes labeled as the host genome from the analysis. The results of our analysis are summarized in Figure 5A, B in the main text.

In this section, we describe the method we used to discover SNP blocks and the statistical analyses we performed.

In order to identify linkage blocks originating from hybridization, the raw alignments from the pangenome construction were processed as follows. We divided core OGs into distinct species clusters, as explained in Appendices 1 and 5, and removed any sequences from SAGs assigned to a different species than the cluster. This was done to avoid false positive blocks due to the presence of recently transferred whole-gene alleles from different species. For OGs with mixed-species mosaic clusters, all sequences in the cluster were initially included. Alignments were then trimmed and codons that contained a high frequency of gaps were removed. Finally, we defined a main cloud of sequences for α and β comprising sequences within a divergence diameter dM=0.1\begin{document}$d_{M}=0.1$\end{document} from the consensus for each species and removed all sequences outside it.

We used a linkage-based approach to search for evidence of hybridization within genes. Visual inspection of the alignments in the highly diverse α genes and in most β genes revealed segments with high SNP density grouped into two haplotypes in strong linkage disequilibrium. We hypothesized that these SNP blocks were the result of intragenic hybridization, and we developed an algorithm to systematically identify them.

The algorithm can be summarized by the following steps:

The inclusion of step 2c accounts for the possibility of more recent low-frequency SNPs emerging after the initial hybridization took place. Note that typical alignments depths are ∼30 for α and ∼70 for β and are considerably larger than nc\begin{document}$ n_{c}$\end{document}.

We applied the above algorithm to the alignments of all of the core genes and obtained a total of 1000 blocks within α\begin{document}$ \alpha$\end{document} and 1483 blocks within β. Most blocks were short, but those in α\begin{document}$ \alpha$\end{document} were on average more than twice as long as those in β (⟨L⟩=68\begin{document}$ \left\langle L\right\rangle=68$\end{document} in α vs ⟨L⟩=29\begin{document}$ \left\langle L\right\rangle=29$\end{document} in β; Appendix 6—figure 1A). Similarly, α blocks contained more SNPs on average compared to β, although here the difference was less pronounced (⟨l⟩=11.3\begin{document}$ \left\langle l\right\rangle=11.3$\end{document} in α vs ⟨l⟩=7.9\begin{document}$\left\langle l\right\rangle=7.9$\end{document} in β; Appendix 6—figure 1B).

To identify hybrid haplotypes, we first determined the consensus sequences for the two block haplotypes, together with the other two species within the block segment. We then labeled any haplotypes whose sequence was identical to one of the other two species as a hybrid segment with the corresponding species as the donor. These results are shown in Appendix 6—table 1.

To control for other processes that could potentially produce similar patterns of linkage disequilibrium, we compared the distributions of divergences between haplotypes and block lengths for cases where a hybrid haplotype could be identified directly to cases we could not. No obvious difference in the distributions could be seen between the two cases, consistent with our interpretation that the blocks without matches to other species in our sample are also the result of hybridization.

We further verified that the divergences between block haplotypes were consistent with what we would expect from hybridization. We calculated the fraction of nonsynonymous and synonymous nucleotide substitutions, pN\begin{document}$ p_{N}$\end{document} and pS\begin{document}$ p_{S}$\end{document}, respectively, between the consensus sequences of each haplotype (see Appendix 7). We then removed blocks with either pN\begin{document}$ p_{N}$\end{document} or pS\begin{document}$ p_{S}$\end{document} were above a threshold of 0.6. This was done to avoid large errors in estimating the divergence, which we calculated using the Jukes–Cantor correction d=−(3/4)ln⁡(1−4p/3)\begin{document}$ d=-(3/4)\ln(1-4p/3)$\end{document} (Jukes and Cantor, 1969). The overall number of such blocks was small (46 out of 1442 in α and 143 out of 2008 in β) so their removal does not affect our conclusions about the typical blocks. We found that the distributions of both the nonsynonymous and synonymous divergences were similar to those previously reported from comparisons of OS-A and OS-B’ (Rosen et al., 2018), and consistent with our hybridization hypothesis (Appendix 6—figure 3).

In this section, we present our analysis of the genetic diversity within individual genes in α and β. In the first subsection, we define the different metrics we used and present the variations in diversity along the genome of both species. In the next four subsections, we compare the diversity of different genes and use the α backbone to roughly infer the time scales of the evolutionary process. In the last subsection, we present a scenario for the evolution of the population.

We quantified the nucleotide diversity across all genes in both α and β using the following procedure. Alignments were trimmed for excess gaps and sequences were assigned to each species as described in Appendix 1. We then define the nucleotide diversity in the usual way as(7)π=1S(S−1)∑i≠j∈Iπij,\begin{document}$$\displaystyle \pi = \frac{1}{S(S - 1)} \sum_{i \neq j \in I} \pi_{ij},$$\end{document}

where I\begin{document}$ I$\end{document} is an index for sequences in the alignment, S\begin{document}$ S$\end{document} is the sample size, equal to the number of elements in I\begin{document}$ I$\end{document}, and πij\begin{document}$\pi_{ij}$\end{document} is the fraction of nucleotide substitutions between i and j, excluding gaps. To calculate synonymous (πS\begin{document}$ \pi_{S}$\end{document}) and non-synonymous diversities (πN\begin{document}$\pi_{N}$\end{document}) we replace πij\begin{document}$ \pi_{ij}$\end{document} with the fraction of synonymous (πijS\begin{document}$\pi_{ij}^{S}$\end{document}) and non-synonymous substitutions (πijN\begin{document}$ \pi_{ij}^{N}$\end{document}), respectively. We calculated πijS\begin{document}$\pi_{ij}^{S}$\end{document} and πijN\begin{document}$ \pi_{ij}^{N}$\end{document} using two different methods: the fraction of fourfold degenerate (4D) and onefold degenerate (1D) sites, respectively, at which i and j differ and using the Nei–Gojobori method (Nei and Gojobori, 1986). We found that both methods gave similar results and used the one that was most convenient for each analysis.

To calculate the divergence between species, we first determined the proportion of sites that were substituted as follows:(8)p=1SαSβ∑i∈Iα,j∈Iβπij\begin{document}$$\displaystyle p = \frac{1}{S_{\alpha} S_{\beta}} \sum_{i \in I_{\alpha}, j \in I_{\beta}} \pi_{ij}$$\end{document}

where Iα\begin{document}$ I_{\alpha}$\end{document} and Iβ\begin{document}$ I_{\beta}$\end{document} are the indices of sequences from α and β in the alignment, and Sα\begin{document}$ S_{\alpha}$\end{document} and Sβ\begin{document}$ S_{\beta}$\end{document} are number of sequences from each species, respectively. The fraction of pairwise substitutions πij\begin{document}$\pi_{ij}$\end{document} is the same as above. We then use the Jukes–Cantor correction (Jukes and Cantor, 1969) to correct for the effect of multiple substitutions at a single site(9)d=−34ln⁡(1−4p3).\begin{document}$$\displaystyle d = - \frac{3}{4} \ln\left(1 - \frac{4 p}{3} \right).$$\end{document}

The synonymous (dS\begin{document}$d_{S}$\end{document}) and non-synonymous divergences (dN\begin{document}$ d_{N}$\end{document}) were calculated in a similar way by replacing πij\begin{document}$\pi_{ij}$\end{document} with πijS\begin{document}$\pi_{ij}^{S}$\end{document} and πijN\begin{document}$ \pi_{ij}^{N}$\end{document} in Equation 8, respectively. Finally, to calculate the diversity within each species separately, we take the sum in Equation 7 over Iα\begin{document}$ I_{\alpha}$\end{document} or Iβ\begin{document}$ I_{\beta}$\end{document} only.

There are two plausible explanations for the heterogeneity within α found in Figure 3 (main text). The low-diversity genes could be due to local sweeps similar to the ones that formed the divergence troughs shown in Figure 5C in the main text. Under this scenario, the high-diversity genes would represent the typical diversity within α that has accumulated since its common ancestor. Since the high-diversity genes are as diverse as typical β genes, this scenario would imply α and β each had common ancestors at similar times in the past. Alternatively, the low-diversity genes could represent the typical diversity within α, with the high-diversity genes being the result of hybridization with other species.

To distinguish between these two possibilities, we developed a method to separate low diversity from high-diversity genes within α. Specifically, we calculated the fraction flS=PlS/LlS\begin{document}$ f_{l}^{\,S}=P_{l}^{\,S}/L_{l}^{\,S}$\end{document} of 4D sites at locus l that were polymorphic within the α alignment. Here, PlS\begin{document}$ P_{l}^{S}$\end{document} is the number of synonymous polymorphisms and LlS\begin{document}$L_{l}^{S}$\end{document} the number synonymous sites at that gene. By using 4D sites, we naturally control for differences in gene conservation. If mutation rates across loci do not vary too much, we expect the distribution of flS\begin{document}$f_{l}^{\,S}$\end{document} across genes to be given by a Poisson distribution. The mean of this Poisson distribution can be fitted from the fraction of sites that are not polymorphic(10)P(k=0|μ)=e−μ=1−∑lPlS∑lLlS,\begin{document}$$\displaystyle P(k=0 | \mu) = e^{-\mu} = 1 - \frac{\sum_l P_l^S}{\sum_l L_l^S},$$\end{document}

from which we get the following estimate for the mean:(11)μ^=−ln⁡[1−∑lPlS∑lLlS].\begin{document}$$\displaystyle \hat{\mu} = - \ln \left[ 1 - \frac{\sum_l P_l^S}{\sum_l L_l^S} \right].$$\end{document}

When we compared this prediction to the data for α, we found that the Poisson distribution gave an excellent fit for around half of the core genes (675 out of 1448) with flS≲0.05\begin{document}$f_{l}^{\,S}\lesssim 0.05$\end{document}. In the remaining core genes (773 out of 1448), flS\begin{document}$ f_{l}^{\,S}$\end{document} was much larger than predicted from the Poisson (Figure 3B in main text). Note that the agreement in the inset of Figure 3B is based on a single fitting parameter. Based on these results, we chose a threshold of flS≤0.05\begin{document}$ f_{l}^{\,S}\leq 0.05$\end{document} to define the α\begin{document}$ \alpha$\end{document} ancestral backbone, with all other genes labeled as hybrid.

To validate our partition, calculate the synonymous diversity πS\begin{document}$ \pi_{S}$\end{document} within each group. We found that our criterion produced a clear separation in the synonymous diversity, with low-diversity genes having a mean πS≈1.7×10−3\begin{document}$ \pi_{S}\approx 1.7\times 10^{-3}$\end{document}, compared to πS≈3.4×10−2\begin{document}$ \pi_{S}\approx 3.4\times 10^{-2}$\end{document} for the high-diversity genes. As a result, we estimate that more than 95% of the genetic diversity within α\begin{document}$ \alpha$\end{document} is the result of hybridization. This result shows that the molecular clock estimate of the time since the most common ancestor based on TMRCA=πS/(2μτ)\begin{document}$T_{MRCA}=\pi_{S}/(2\mu\tau)$\end{document}, where μ is the mutation rate per division and τ\begin{document}$\tau$\end{document} the generation time, should be interpreted with caution. In the case of α\begin{document}$ \alpha$\end{document} the estimate using the average πS\begin{document}$ \pi_{S}$\end{document} across the whole genome would be around an order of magnitude less than the true value, even without considering how mutation rates might change over such long time scales.

We performed a similar analysis for β but did not find any large peak near flS=0\begin{document}$ f_{l}^{\,S}=0$\end{document} (Figure 3C in main text). Instead, the distribution of flS\begin{document}$ f_{l}^{\,S}$\end{document} was close to unimodal but with significantly fatter tails compared to the Poisson. Given the excellent fit to the Poisson for α in the region where SNPs are purely due to mutations, this suggests that other mechanisms play an important role in generating the diversity within β. The most parsimonious explanation is that the hybridization process we observed in α has covered most of the original β genome by this point. While it is not clear what the distribution of flS\begin{document}$ f_{l}^{\,S}$\end{document} should be in this case, it is plausible that it need not be Poisson (Sakoparnig et al., 2021). Further evidence in favor of this hypothesis is the presence of SNP blocks across a large fraction of β core genes, as discussed in the main text and Appendix 6.

The large number of SNP blocks found throughout the genomes of both α and β shows that hybridization is an important source of genetic diversity for the Synechococcus population. However, because of the requirement for perfect linkage within SNP blocks, the total number of SNPs that are the result of hybridization is likely much higher than the one we infer from our algorithm. To obtain quantitative estimates of the total contribution from hybridization to the diversity, we use α as a control. As shown previously, only ≈5% of the total diversity in the high-diversity loci from α can be attributed to mutations. These loci contained 603,588 sites and 64,462 SNPs, of which 10,391 SNPs were found inside SNP blocks. Thus, only around 17% of the SNPs that are likely the result of hybridization, or hybrid SNPs, are included in the SNP blocks.

Within the β core genome, we have 1,591,476 sites and 146,906 SNPs, of which 14,819 were within SNP blocks. Assuming a similar ratio of hybrid SNPs to SNPs in SNP blocks as in α\begin{document}$ \alpha$\end{document}, we estimate that around 90,000 or approximately 60% of SNPs in β are the result of hybridization. This is consistent with β having evolved over longer time compared to α. However, our knowledge of how multi-locus SNP patterns change over the course of evolution is limited, so the estimates for β should be interpreted with caution. In particular, if larger segments continue to be broken up due to recombination, it is likely that the fraction of hybrid SNPs within blocks would decrease over time for a constant minimum block size lmin\begin{document}$ l_{min}$\end{document} (see Appendix 6). Thus, the overall contribution of hybridization to the β genetic diversity may be even higher.

Combining genetic diversity analysis with evidence from the geological record of the Yellowstone caldera allows us to make inferences about the evolutionary history of the Synechococcus population. If we assume that most of the fixed variants between species are the result of mutation accumulation, then we can use the typical synonymous divergence between species to infer the time since the most recent common ancestor for the whole population. Typical bacterial mutation rates for natural populations are around μ∼10−9.5\begin{document}$ \mu\sim 10^{-9.5}$\end{document} per bp per generation (Chen et al., 2022). Using this rate as a baseline and assuming generation times of τ∼1−10\begin{document}$\tau\sim 1-10$\end{document} days gives an estimate of TMRCA∼106.5−107.5\begin{document}$ T_{MRCA}\sim 10^{6.5}-10^{7.5}$\end{document} years (Rosen et al., 2018).

For our argument, the lower bound is the more important one since it determines whether we can exclude the single-colonizer hypothesis. A TMRCA\begin{document}$ T_{MRCA}$\end{document} below 10^6.5 years would imply a shorter division time or higher mutation rate than our estimates. Our lower bound of 1 day for the division time is around the same as the fastest division rate observed in the laboratory. If the population is in steady state, as it appears to be, the division time sets the maximum generation time, which can be attained if the death rate is equally high. If the death rate is lower than this, other factors would limit cell division and the generation times would be longer. Taken together, we can be fairly confident that a generation time of 1 day is a hard lower bound.

The mutation rate is less certain since we do not have any reliable measurements and experimentally measured mutation rates might not be a good predictor of substitution rates over evolutionary times (Rocha, 2018). We can instead use other bacteria to estimate a range of values. In wild-type E. coli, mutation rates of ≈2⋅10−10\begin{document}$ \approx 2\cdot 10^{-10}$\end{document} per bp per generation have been measured in laboratory conditions (Lee et al., 2012), but mutator strains with rates that are up to 100 times higher are also known (Sniegowski et al., 1997). In natural populations, rates as high as 4⋅10−9\begin{document}$ 4\cdot 10^{-9}$\end{document} have been inferred using longitudinal sequencing (Moran et al., 2009). If we use 10⁻⁸⁵ mutations per bp per generation as an upper bound, we would infer a lower bound of TMRCA∼105.5\begin{document}$ T_{MRCA}\sim 10^{5.5}$\end{document} years, which very narrowly overlaps with the time since the formation of the Yellowstone caldera. Thus, while it is not inconceivable that the three species could have diverged within the caldera, such a scenario would require all the relevant parameters to be at the limit of currently known values. In addition, such a scenario would require additional hypotheses to explain why the strains initially diverged into distinct species, with seemingly little genetic exchange between them (Rosen et al., 2018), and then only much later started to hybridize. Taken together, current evidence suggests the most likely scenario is that α, β, and γ diverged from a common ancestor before the formation of the caldera around 640,000 years ago.

By using the diversity within α\begin{document}$ \alpha$\end{document} as a proxy for time, we can obtain estimates on the time scales of spatial mixing that influences the diversity within the population. To do this, we calculated the pairwise distances in the low-diversity regions of the α\begin{document}$ \alpha$\end{document} genome between pairs of cells in each spring separately and pairs of cells from different springs. We found that all three distributions were similar (Appendix 7—figure 1). The mean of the distribution for cells Mushroom Spring was slightly lower than those from the Octopus spring (πS=8.6⋅10−4\begin{document}$ \pi_{S}=8.6\cdot 10^{-4}$\end{document} vs πS=1.1⋅10−3\begin{document}$ \pi_{S}=1.1\cdot 10^{-3}$\end{document}) and this difference could not be explained by differences in sample sizes between the two springs. However, both values were very close to the mean of cells from different springs (πS=1.0⋅10−3\begin{document}$ \pi_{S}=1.0\cdot 10^{-3}$\end{document}). This suggests that the time scale of spatial processes relevant for the long-term evolution of the population, τm\begin{document}$ \tau_{m}$\end{document} is much shorter time scales than TMRCA\begin{document}$ T_{MRCA}$\end{document} for α. Taking TMRCA∼3⋅103\begin{document}$T_{MRCA}\sim 3\cdot 10^{3}$\end{document} years as a reference point sets an upper bound of τm≪3⋅103\begin{document}$\tau_{m}\ll 3\cdot 10^{3}$\end{document} years.

We propose the following scenario that is consistent with our previous discussion. First, we argued that a small number (3–6, but possibly more) of Synechococcus populations that had been evolving separately for ∼106−107\begin{document}$ \sim 10^{6}-10^{7}$\end{document} years independently colonized the Yellowstone caldera after its formation 640,000 years ago. After colonization, they started to hybridize, leading to a gradual mixing of their genomes (Figure 8). This can be most clearly seen in the α species, where the diversity in core genes that do not show signs of hybridization is more than an order of magnitude less than those that do. Moreover, genes that have undergone hybridization account for the majority of diversity within α. Within β, we do not observe such heterogeneity, but we find SNP blocks are even more prevalent than in α (Appendix 6—table 1). The simplest explanation for this pattern is that β has been undergoing hybridization for longer, and by now, all of its core genome has been mixed with other species. Consistent with this explanation, we find that only a small fraction of SNP blocks within β can be traced back to α (Appendix 6—table 1). Most of the β SNP blocks cannot be traced to either α or γ and are likely the result of a combination of hybridization with species that are not currently within the Lower Geyser Basin, have abundances lower than our detection threshold, or have gone extinct.

There are several important parameters that determine the impact of recombination and hybridization on the evolution of the population. First are the rates of recombination and mutation in the population. We denote the population recombination rate by ρ=2TR\begin{document}$ \rho=2TR$\end{document} and the population mutation rate by θ=2Tμ\begin{document}$ \theta=2T\mu$\end{document}, where T is the average time since the most common ancestor, R\begin{document}$ R$\end{document} is the recombination rate per site, and μ is the mutation rate per site. Note that in the panmitic Wright–Fisher model, T in units of generation time is equal to the population size N\begin{document}$N$\end{document}, but this is not generally true (Neher and Hallatschek, 2013; Weissman and Hallatschek, 2014; Birzu et al., 2018; Birzu et al., 2021). A second important parameter is typical length of recombined segments, which we denote by Lr\begin{document}$L_{r}$\end{document}. Finally, there is the typical divergence of recombined segments. In this Appendix, we use the nucleotide distance p\begin{document}$ p$\end{document} or the synonymous distance pS\begin{document}$p_{S}$\end{document}, as defined in Appendix 7. We estimated these parameters for the hybridization process, which we argued previously is the dominant source of diversity in the population.

Before describing the analysis, it is important to note that while some of the simple statistics discussed here may be captured by simple neutral models, the underlying dynamics may be far more complex. Indeed, the analysis in the main text shows extensive evidence of selective sweeps affecting the genetic diversity across a broad range of genomic length scales, contrary to simple neutral theory. Moreover, while our analysis shows that—over time scales implied by our sequencing depth—the Synechococcus population is effectively well-mixed within the caldera, the actual population is obviously not. Synechococcus cells live in a dense microbial mat spread across thousands of springs separated by distances up to ∼10² km (Ward et al., 1998). As a result, we expect the long-term evolution of the population to be described by effective parameters, which may have little relation to recombination rates and population sizes directly measurable in the field or in the laboratory (Neher and Hallatschek, 2013; Weissman and Hallatschek, 2014; Birzu et al., 2018; Birzu et al., 2021). Understanding the relationship between the measurable parameters describing recombination, selection, and spatial dynamics of individual cells and the effective parameters at the population scale is an important and interesting topic for future work.

Many different methods have been proposed to estimate these or other closely related parameters (Croucher et al., 2015; Didelot and Wilson, 2015; Lin and Kussell, 2019). All of the methods we are aware of are based on models that make various assumptions that may not be valid for any given population, such as ours. In our case, an accurate estimate of these parameters requires a quantitative model of the hybridization process and is beyond the scope of the paper. Here, we instead used the results of our previous analysis to get rough estimates of these parameters and compared them to two other commonly used methods.

We considered each species separately, starting with α. For most evolutionary models, θ can be estimated from the nucleotide diversity π (Neher and Hallatschek, 2013). As in the main text, we used only synonymous sites to control for differences in the strength of purifying selection or the accumulation of non-synonymous mutations during rapid adaptation. Based on our previous analysis, we estimated the population synonymous mutation rate θS≈2⋅10−3\begin{document}$ \theta_{S}\approx 2\cdot 10^{-3}$\end{document} (Appendix 7). Because of the clear distinction between the ancestral backbone and hybrid genes in α, we expect this estimate to be reasonably accurate. A rough estimate of ρ\begin{document}$ \rho$\end{document} can be obtained from the linkage disequilibrium curves (Figure 2 in main text). Our previous analysis showed that ρ≈0.03\begin{document}$\rho\approx 0.03$\end{document} and ρ≈0.12\begin{document}$ \rho\approx 0.12$\end{document} gave good fits for α and β, respectively. Taking the ratio, we found a ratio between recombination and mutations of ρ/θS≈15\begin{document}$ \rho/\theta_{S}\approx 15$\end{document}—much higher than previous estimates.

Estimating the mutation rate in β is more difficult because there are no genes unaffected by hybridization. We instead used the fraction of SNPs found in SNP blocks to estimate the diversity purely due to mutations. In Appendix 7, we estimated that around 40% of SNPs are the result of mutations. Multiplying with the synonymous diversity gave θS≈0.02\begin{document}$ \theta_{S}\approx 0.02$\end{document}. Using this estimate, we found ρ/θS≈6\begin{document}$\rho/\theta_{S}\approx 6$\end{document}, which is lower than in α\begin{document}$ \alpha$\end{document} but still significantly higher than values that have been reported previously.

The other recombination parameters can also be inferred from our analysis. As we showed previously, the typical divergence of hybrid segments is given by the synonymous distance between species pS≈0.4\begin{document}$p_{S}\approx 0.4$\end{document}. We estimated the average size of recombined segments from the linkage curves. The recombination rate between two sites on the genome increases linearly with the separation x for distances shorter Lr\begin{document}$ L_{r}$\end{document}. In the standard neutral model, this leads to the scaling σd2(x)∼1/x\begin{document}$\sigma_{d}^{2}(x)\sim 1/x$\end{document} at intermediate distances (see Appendix 4). For x>Lr\begin{document}$ x \gt L_{r}$\end{document}, the recombination rate saturates to the genomewide recombination rate ∼ρLr\begin{document}$ \sim\rho L_{r}$\end{document}, which results in deviations of the linkage decrease from the predicted σd2(x)∼1/x\begin{document}$ \sigma_{d}^{2}(x)\sim 1/x$\end{document} scaling. In α, we observe a deviation around x∼500\begin{document}$ x\sim 500$\end{document} bp. Note that we verified that this plateau cannot be explained by the smaller finite sample size in α\begin{document}$ \alpha$\end{document}. A similar argument gives a shortened segment length Lr∼300\begin{document}$ L_{r}\sim 300$\end{document} bp in beta. While we cannot directly test that the plateau is not due to sample size, the small effect of subsampling we observed earlier suggests it is an unlikely explanation (Appendix 4—figure 2). Note that in both species, our estimated genomewide recombination rate ρLr\begin{document}$\rho L_{r}$\end{document} is much greater than one, consistent with the genomewide linkage being close to the unlinked control, as discussed in the main text.

We compared our analysis to standard methods. ClonalFrameML and other related software are perhaps the most widely used methods to infer bacterial recombination (Didelot and Wilson, 2015). Such methods assume that recombination rates are rare enough that they can be described by a Poisson process on an asexual tree, similar to mutations. We refer to the assumption as the clonal frame hypothesis. ClonalFrameML uses the inferred phylogenetic tree from pairwise distances to identify discrete recombination events and assign them to branches on the tree. The recombination rate, genetic divergence, and length of recombined segments are then inferred from these events.

Note that the clonal frame hypothesis is inconsistent with the rapid decrease in linkage we observed (Figure 2 in main text). Nevertheless, it is useful to see how the method performs on our data.

We used a subset of high-coverage SAGs to create whole-genome alignments for α and β, which we then analyzed with ClonalFrameML. We first selected SAGs more than 75% complete, which resulted in a dataset of 2 α and 12 β SAGs (Appendix 1—figure 1). For each species, we chose the genes that mapped to OS-A or OS-B’ and created concatenated alignments of the entire genome in the order of the references. Missing genes or sequences were replaced by gaps. We constructed the phylogenetic tree using FastTree and ran ClonalFrameML on the alignments and trees with default parameters.

For both species, ClonalFrameML inferred a ratio of recombination to mutation rates ρ/θ≈1\begin{document}$\rho/\theta\approx 1$\end{document} (R/θ\begin{document}$ R/\theta$\end{document} in Didelot and Wilson, 2015) and a fraction of nucleotide differences for imported segments of p=0.07−0.09\begin{document}$ p=0.07-0.09$\end{document} (ν\begin{document}$ \nu$\end{document} in Didelot and Wilson, 2015). Note that both θ and p\begin{document}$ p$\end{document} reported by ClonalFrameML refer to nucleotide rather than synonymous differences. The values of p\begin{document}$ p$\end{document} are around half of the distance between species p≈0.15\begin{document}$ p\approx 0.15$\end{document} and are inconsistent with our metagenome analysis which showed no genomes present in OS or MS at these divergences. The main difference between the species was in the average length of recombined segments, which was almost 10 times higher in α (Lr=365\begin{document}$ L_{r}=365$\end{document}) compared to β (Lr=45\begin{document}$ L_{r}=45$\end{document}).

A detailed comparison of the results of ClonalFrameML with our analysis is beyond the scope of this paper. Nevertheless, we found several inconsistencies in the assignment of recombined segments by ClonalFrameML. Because of the lack of data in α, we focused this analysis on β. First, we found that the distribution of recombined segment lengths was inconsistent with the exponential distribution assumed by ClonalFrameML and had a mean that was almost double the inferred δ=45\begin{document}$ \delta=45$\end{document} (Appendix 8—figure 1). Second, manual validation of a small sample of randomly chosen recombined segments revealed identical patterns present in other cells that were not assigned to the recombination event (data not shown). We suspect that these misassignments are due to the inconsistency of the observed segments with the asexual tree.

The failure of ClonalFrameML to fit the data should not be surprising. As we showed, the low levels of linkage at whole-genome scales in α and β are inconsistent with the existence of a clonal frame assumed by the model. In addition, manual validation of some of the recombined segments detected revealed spurious segments caused by gaps in coverage due to the incomplete nature of the SAGs. These results caution against the naive application of methods such as ClonalFrameML to SAG datasets in general, but also to other populations for which the clonal frame hypothesis may not hold.

An alternative method for fitting the clonal frame model was proposed recently by Lin and Kussell, 2017; Lin and Kussell, 2019. Instead of identifying recombination events directly, they use the correlations between SNPs to infer the recombination parameters statistically. Specifically, they model a local (sample) population that evolves according to a neutral model with recombination. They assume that the population recombines with a larger and more diverse ‘pool’ that evolves according to the same model but with different parameters. Under this model and assuming the recombination to mutation rate ratios are the same in the sample and pool populations, they show that the conditional probability that two sequences differ at a site given that they differ at a second site l bp away, P(l)\begin{document}$ P(l)$\end{document}, depends only on population mutation rate (θ in our notation), the population recombination rate (ρ\begin{document}$ \rho$\end{document}) and the average length of recombined segments (Lr\begin{document}$ L_{r}$\end{document}). By fitting the analytical expression for P(l)\begin{document}$ P(l)$\end{document} from the model to the data, all of the model parameters can be inferred.