Development of RecPD

The development of RecPD was inspired by the need to understand the distribution of bacterial gene families, so we will discuss the methods from this context although the method is transferable to any other features of interest (e.g., genetic variants, metabolic capabilities, or taxa). We begin with a phylogeny of strains on which we will map the acquisition, loss, descent, and divergence of a gene family of interest. In most circumstances, this phylogeny will be based on the core genome (i.e., those genes found in all strains of the species) and be constructed from the concatenated sequences of core genes. For simplicity, we will refer to this as the species tree. We also have presence / absence distribution of a gene family of interest that varies among the strains in the study set. The goal of RecPD is to determine the phylogenetic diversity of the gene family by reconstructing its evolutionary history on the species tree, accounting for potential horizontal acquisition events that may have occurred.

Step 1: Assignment of gene family ancestral states on the species phylogenetic tree

To reconstruct the putative lineages where a gene family has arisen during the evolutionary history of a bacterial species, we first begin with ancestral state reconstruction of the gene family. In this case ancestral states considered will be a binary category of gene family presence/absence. To achieve this task, we devised a novel nearest-neighbour (NN) ancestral reconstruction approach (Fig 1A) that begins by identifying which strains in the study set carry the gene family of interest. Based on this, the tips of the species tree are assigned a state of presence or absence for the gene family. Next, each internal/ancestral node is examined and assigned to one of three possible states based on information from the closest-related tips descended from it: 1) ‘present’ if the nearest-neighbour, i.e., closest related, descendant tips of the node both possess the gene family; 2) ‘absent’ if the gene family is absent in the nearest-neighbour descendant tips; 3) ‘split’ if only one nearest-neighbour descendant tip possesses the gene family, which may indicate potential gain/recombination or loss events.

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Fig 1. Outline of the RecPD methodology: Calculating recombination adjusted phylogenetic diversities of feature distributions by employing ancestral state reconstructions.

(A) Tip states are assigned to a given species phylogenetic tree based on presence (teal), or absence (red) of the gene family of interest. (B) Ancestral node states are inferred using one of there ancestral state reconstruction methods and assigned to either presence (teal), absence (red), or split (blue) states, the latter which indicate potential gain/loss events. (C) Branches are assigned to presence states if they join consecutive presence or split nodes/tips (teal), otherwise they are assigned to absence (red). (D) Gene-family lineages are identified, and split state nodes are assigned to gains (teal) or losses (red). Branches descended from the phylogenetic tree root node where no ancestral presence nodes were identified are assigned to absence (grey). RecPD is then calculated as the sum of gene family lineage branch-lengths normalized by the total branch-lengths of the phylogenetic tree.

https://doi.org/10.1371/journal.pcbi.1009899.g001

Our framework also allows for the incorporation of other popular approaches for ancestral state reconstruction, such as most-parsimonious reconstruction (MPR) [11] and maximum-likelihood ancestral character estimation (ACE) [12]. The goal of MPR is to find the overall set of internal node states which results in the fewest number of state changes, e.g., most-parsimonious, between ancestral and descendant nodes. The ACE approach was devised as an improvement on MPR, which incorporates branch-length information and inferred gain and loss rates from which the likelihood of given state for each internal node is determined (i.e., from the likelihoods of the states of its descendants).

As the reconstruction of ancestral states is not a trivial task [13,14]. It is important to emphasize that reconstructed ancestral states can vary depending on the approach used, so it is useful to state the potential strengths and limitations inherent to each. The NN approach may produce spurious evolutionary histories of ancestral gene family loss followed by reacquisition depending on the frequency of gain and loss in different lineages. MPR is less liable under these scenarios but does not incorporate divergence between ancestral and descendant nodes; therefore, it may miss certain internal nodes where a state might be present or could find equally parsimonious scenarios resulting in ambiguous state assignments. In the case of ACE, modelling gains and losses as separate processes may resolve ambiguities in some scenarios, but reliably estimating these rates largely depends on the sampling of the given species phylogeny. State assignments will tend to become more uncertain as the amount of divergence between ancestral nodes increases. A combination of approaches could be used in theory to find consensus assignment, although this method has not yet been developed.

Step 2: Identification of gene family lineages

Ancestral node state assignments made in the previous step are then consolidated to delineate the species lineages and ancestral phylogenetic tree branches where the gene family is likely to have arisen (Fig 1B). This is done by examining all the branches of the species tree and assigning a presence state to branches if their ancestral-descendant node states are also predicted to be present, otherwise a given branch is assigned as an absence state. Some branches may also include nodes where a split/ambiguous state has been assigned as the result of potential gain or loss events occurring in descendant node lineages. In this case, branches are selected for inclusion if the ancestral or descendant node is assigned to the presence state, or both are split states/ambiguous.

After branch-state identification, the final node states are consolidated, with gain and loss event nodes highlighting the particular internal nodes where the gene family appears to have been gained or lost in subsequent descendant lineages respectively (Fig 1C). In addition, the states of tip nodes descended from each gain or loss lineage are updated accordingly.

Step 3: Calculation of RecPD and nRecPD

After the corresponding gain and loss lineages for a given gene family distribution has been determined, its recombination-adjusted phylogenetic diversity, RecPD, is calculated by summing the total branch-lengths of the gain lineages divided by the sum of the total branch-lengths of the species tree (Fig 1D). RecPD values are bounded to have values ranging from (~0 to 1), with the lowest values determined by the tip with the smallest branch length from its most immediate parental node (i.e., when feature prevalence = 1), and reaching a maximum when the feature is present at all tips. In addition, the observed values of RecPD for different gene families of the same prevalence could be used to infer the relative impact of recombination on those families, with high RecPD values corresponding to families less impacted by horizontal transfer and low RecPD values corresponding to families heavily impacted by gene gain and loss. Furthermore, normalizing the RecPD of a gene family by its corresponding Faith’s PD (nRecPD) yields a more accurate measure which indicates the degree of recombination that has given rise to its distribution: where nRecPD ~ 1 indicates vertical inheritance and nRecPD ~ 0 indicates recently occurring horizontal transfer events.

Step 4: RecPD-Derived measures

In addition to RecPD, we can also calculate additional measures based on the ancestral mapping of the gene family onto the species tree (summarized with formal definition in Table 1). These measures can be divided into two classes that either assess the overall topological structuring of gene families within the species tree or summarize the evolutionary events influencing gene family lineages (i.e., those lineages of the species tree where the gene family is predicted to be present) inferred by RecPD. The first class of topology-based measures include: Span, which measures how much of the maximum possible species diversity is realized for the gene family of interest and is akin to the Faith’s PD (S1 Fig); and Clustering, which measures the extent to which the gene family lineages identified by RecPD partition among subclades of the species tree, which may be more or less closely related (S2 Fig). While Span and Clustering are conceptually very similar, the former uses branch lengths, while the latter is a cladistic measure that only considers clade structure. The second class of evolutionary event-based measures include: Longevity, which is the median normalized evolutionary distance since a gene family was initially gained across species lineages (S3 Fig); and Lability, the normalized number of gain, loss, and re-acquisition event nodes occurring across species lineages for a given gene family (S3 Fig).

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Table 1. RecPD and derived measures.

https://doi.org/10.1371/journal.pcbi.1009899.t001

We also developed a comparative measure for directly quantifying the extent of shared ancestry (i.e., correlation) between different gene families, called RecPDcor. For a pair of gene family distributions, RecPDcor is calculated as the sum of the ancestral lineage branch-lengths where they co-occur divided by the sum of branch-lengths from the union of their ancestral lineage reconstructions (S4 Fig). This is in essence the branch-length weighted Jaccard similarity between ancestral gene family lineages.

RecPD accounts for potential recombination events from randomized gene family phylogenetic distributions. As a preliminary exploration of our RecPD method, we present an idealized test-case scenario using a randomly generated species tree of ten tips and assessed the potential impact of recombination inferred from examining all possible gene family presence/absence patterns. We calculated Faith’s PD for each gene family phylogenetic pattern to serve as a baseline evolutionary scenario considering only vertical descent, gene family loss, and no recombination. Fig 2A shows that RecPD was affected by the choice of the ancestral state reconstruction method used (NN, MPR, or ACE). When compared to Faith’s PD, ACE tends to overestimate PD, which is likely due to increasing uncertainty in state assignments for the deepest ancestral nodes the species tree. In contrast, both the NN and MPR methods consistently predict lower PD values than Faith’s, particularly for gene family distributions found in at least half of the species in the tree, with MPR predicting the greatest degree of recombination (Fig 2B and 2C). Therefore, RecPD can serve to identify potential gene family distribution patterns which do not conform to a strictly vertical pattern of inheritance. These results also hold for randomly generated species trees of greater size (S5 Fig).

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Fig 2. RecPD results in lower PD estimates compared to recombination-agnostic Faith’s PD and is affected by ancestral state reconstruction approach employed.

(A) RecPD using three ancestral state reconstruction methods (NN, MPR, and ACE) and Faith’s PD distributions binned by gene family prevalence. Results shown correspond to all 1022 possible randomized gene-family distributions mapped onto a randomly generated example tree topology of ten tips. (B) RecPD normalized by Faith’s PD for three ancestral state reconstruction methods binned by gene-family prevalence. Results shown correspond to all 1022 possible randomized gene-family distributions mapped onto a tree of ten tips. (C) Example gene family distribution of prevalence = 5 illustrating differences in inferred evolutionary events using different methods: Faith’s PD = 5 losses, 0 gains (boxed), RecPD(NN) = 2 losses, 4 gains, RecPD(MPR) = 0 losses, 5 gains, and RecPD(ACE) = 5 losses, 0 gains.

https://doi.org/10.1371/journal.pcbi.1009899.g002

Nearest-neighbours ancestral state reconstruction accurately captures recombination events of simulated gene family evolutionary histories

In the real world, we almost never know the true evolutionary histories of a gene family. Although ancestral reconstruction methods are valuable as a means for reconstructing evolutionary histories, more thorough analyses of genomic data are required for support. Therefore, we simulated gene family histories on randomly generated species trees using a Poisson process to model recombination and loss (Table 2 and S6 Fig). With these ‘known’ gene family histories we evaluated how accurately the different ancestral state reconstruction approaches, NN, MPR, and ACE, perform in identifying recombination events under diverse evolutionary scenarios, e.g., loss-recombination balanced, loss dominant, or recombination dominant.

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Table 2. Gene family evolutionary history simulations: Parameters used.

https://doi.org/10.1371/journal.pcbi.1009899.t002

To determine the accuracy of RecPD and each ancestral reconstruction approach (NN, MPR, and ACE) we calculated the ratio between the calculated RecPD values, and the known PD based on the simulated distribution. As before, Faith’s PD was also calculated as a baseline comparison assuming no recombination. The results of our simulation using a tree of ten tips (Fig 3) show that Faith’s and RecPD using ACE result in similar error rates, largely overestimating the PD of gene families, recapitulating results shown previously (mean error Faith = 0.46 ± 0.68; mean error ACE = 0.57 ± 0.78). Conversely, RecPD using MPR underestimated gene family PD (error MPR = -0.18 ± 0.24). Surprisingly, our newly devised NN method was shown to be the most accurate (mean error = 0.083 ± 0.28) in correctly reconstructing gene family histories evolved under high-recombination scenarios. These results were consistent across different evolutionary scenarios (S7 Fig) and for other simulations using randomly generated species trees of ranging from 50 to 100 tips, with the observed error decreasing with increasing tree size (S8 Fig).

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Fig 3. RecPD with nearest-neighbours (NN) ancestral state reconstruction accurately identifies simulated gene family evolutionary histories, while MPR and ACE over- and under- estimate recombination, respectively.

Summary of simulations of gene family evolution comparing actual phylogenetic diversity to estimated diversity using Faith’s PD and RecPD employing three different ancestral reconstruction methods (NN, MPR, and ACE: see Table 1 for parameters used and number of simulations run). (A) Scatterplots of estimated PD values against actual PD values by method. (B) Corresponding density plot distributions. Results are shown for recombination predominant rate regime on randomly generated trees with 10 tips.

https://doi.org/10.1371/journal.pcbi.1009899.g003

RecPD identifies gene family distributions with shared and unrelated evolutionary histories. We next explored the use of RecPD in the context of identifying gene families with shared evolutionary histories. From the RecPD NN ancestral reconstructions for all randomized gene family distributions generated in our first analysis, we calculated the RecPDcor values of their recombination adjusted evolutionary histories, resulting in 521,731 unique pairwise comparisons (note that identical distributions were excluded). In the case of gene family distributions with identical prevalence, we observed that RecPDcor values can vary considerably (Fig 4), particularly for distributions of lower prevalence, reflective of their greater possibility of having evolved through recombination (see Fig 2). Similarly, RecPDcor values tended to be lower for gene family distributions with greater relative differences in prevalence, which is to be expected as the result of limited overlap in evolutionary histories (S9 Fig).

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Fig 4. Pairwise gene family evolutionary history correlations using RecPDcor differ in comparison to recombination-agnostic and phylogeny-agnostic approaches.

(A) RecPD correlation (RecPDcor) values for randomized gene family distributions vs. prevalence reveals that the majority of low-prevalence trait distributions have distinct evolutionary histories; (B) RecPDcor of trait distributions substantially differs when compared to 1) Faith’s PD based branch-length weighted Jaccard similarity (recombination-agnostic), and 2) tip presence and absence Jaccard similarity (phylogeny-agnostic) measures: 1) Ignoring recombination results in over-estimation of low-prevalence feature evolutionary history correlations (RecPDcor / Faith’s PD < 1); 2) Ignoring evolutionary history results in under-estimation of intermediate-prevalence feature evolutionary history correlations (tip_jacc / RecPDcor > 1).

https://doi.org/10.1371/journal.pcbi.1009899.g004

We also compared RecPDcor against other correlation measures to examine the effect of recombination in determining gene family co-occurrence (Fig 4B). The two measures employed were a Faith’s PD-based (faith_cor) branch-length weighted Jaccard similarity, which ignores recombination and assumes vertical ancestry of gene families, and Jaccard similarity of co-occurrence among species/tips of the tree (tip_jacc), which ignores gene family ancestries. It was observed that the correlations of gene family distributions tended to be overestimated when not accounting for potential recombination, while ignoring their evolutionary history altogether resulted in their underestimation. In the latter case, by comparing the differences between RecPDcor and tip Jaccard similarities, we could identify several instances where tip Jaccard either missed or identified spuriously correlated gene families (Fig 5).

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Fig 5. RecPDcor identifies correlated gene-family distributions missed by tip Jaccard similarity.

Top panels–Distributions of two features (black = present, white = absent) arrayed against a species tree. RecPDcor and tip Jaccard similarities both identify correlated and anti-correlated gene families. Bottom panels–Distributions where RecPDcor reveals correlated gene family distributions where tip Jaccard does not, and where tip Jaccard overestimates correlation of gene families with distinct evolutionary histories. Tree topologies are represented as cladograms with branches of equal length; actual branch-lengths are indicated by branch-thickness as indicated in the legend. Branches are assigned to different categories based on the overlap of their RecPD-inferred gene family lineages: Shared—branches where both traits are present (teal); 2) Unique—branches where only a single trait is present (blue); None–branches where both traits are absent (red).

https://doi.org/10.1371/journal.pcbi.1009899.g005

RecPD characterization of Pseudomonas syringae type III secreted effector families

Pseudomonas syringae is a highly diverse phytopathogenic bacterial species complex that includes over 60 pathogenic varieties that cause many agronomically important crop diseases [15–18]. Decades of research have established P. syringae as an important model for the study of host-pathogen interactions. One factor that makes P. syringae a particularly adept phytopathogen is its use of a type III secretion system and diverse repertoires of type III secreted effector proteins (hereafter effectors), which have evolved to promote disease by disrupting host immunity and cellular homeostasis [19,20]. In turn, plant hosts have evolved a layer of immunity that triggers when receptors recognize the presence or activity of pathogen effectors [19,21–23]. As a result, the outcome of any particular host-pathogen interaction, and pathogen host specificity in general, largely depends on the specific effectors carried by the pathogen and the specific immune receptors carried by the host. These interactions have led to a co-evolutionary arms race and the accumulation of extensive effector and immune diversity. The P. syringae species complex has at least 70 characterized effector families, most of which include numerous diverse alleles that have evolved through both vertical and horizontal evolutionary processes [15]. There is huge diversity in the suites of effectors carried by individual P. syringae strains, with most strains carrying ~30 effectors (±9 stderr) [15].

We applied RecPD to a previously published dataset of 529 representative effector alleles distributed among the 70 effector families identified from a collection of 494 sequenced P. syringe strains [15,24]. P. syringae strains are classified into phylogroups based on their placement in a core genome phylogenetic analysis, with phylogroups varying in overall size and diversity. We mapped effector alleles onto the core genome (i.e., species) tree and found wide variation in the prevalence and distribution of families (Fig 6A) [15]. Relatively few effector families are widely conserved across the P. syringae species complex, and effector families of similar levels of prevalence can be distributed in very different ways across the phylogroups, suggesting the importance of recombination and loss in effector evolution [15,24].

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Fig 6. RecPD reveals significant impact of recombination in the phylogenetic distributions of P. syringae effector families.

(A) Core genome phylogeny of the P. syringae species complex, with internal tree nodes indicating P. syringae phylogroups. The outer ring barplot shows the total number of distinct effector families carried by each strain and coloured according to strain phylogroup designation. (B) Plot of effector family prevalence against RecPD(NN) and Faith PD for all 70 effector families. (C) Effector family RecPD values normalized by Faith’s PD, binned by effector family prevalence. The point size indicates effector family longevity.

https://doi.org/10.1371/journal.pcbi.1009899.g006

We used RecPD to gain a better understanding of effector evolutionary diversity. Not unexpectedly, we find that effector phylogenetic diversity is positively correlated with prevalence, however we note that relying on prevalence alone gives a misleading view of the phylogenetic distribution of effectors as a whole (Fig 6B). Notably, both Faith’s PD and RecPD values were lower on average when compared to effector prevalence, which reflects the impact of shared evolutionary history and the effect of sampling biases inherent in real-world datasets. Furthermore, we also note the importance of considering the effects of recombination when calculating phylogenetic diversity. In the instance of lower-prevalence effector families (found in less than ~ 25% of strains), Faith’s PD values tend to be larger than expected based on the observed prevalence, possibly due to impact of horizontal gene transfer that distributes many of these families across multiple phylogroups (i.e., deeper common evolutionary ancestry including branches with greater evolutionary divergence). The impact of horizontal transfer is much more evident from the RecPD values, which are consistently lower than the corresponding Faith’s PD values. This is made even more clear when we normalize the PD values by calculating the ratio of RecPD to Faith’s PD (nRecPD). Since Faith’s PD assumes strictly vertical ancestry, families with a high ratio (~ 1) can be interpreted as evolving by largely vertical evolutionary processes, while a low ratio supports extensive horizontal transmission. We found that the extent of recombination can vary widely for effector families, even when they have very similar prevalence (Fig 6C). The longevity (median normalized evolutionary distance since an effector family was gained) also appears to be correlated to nRecPD. Taken together, this analysis supports the hypothesis that the majority of effector families have experienced extensive horizontal transfer and have been acquired relatively recently during the evolutionary history of P. syringae.

To concretely illustrate the impact of horizontal transfer and utility of RecPD, we highlight two examples. The first is the effector families HopS and HopAW (Fig 7A), which have nearly identical prevalence, with HopS found in 114 strains and HopAW found in 116 strains, but dramatically different distributions and inferred evolutionary histories. The Faith’s PD values for the two families are 0.152 and 0.198 for HopS and HopAW, respectively. HopS, with a RecPD value of 0.164, appears to largely follow vertical descent from an early acquisition event in the evolutionary history of P. syringae and is highly conserved in phylogroup 1 and 6 strains. In contrast, HopAW, with a RecPD value of 0.048, appears to have been gained and lost at numerous times throughout the P. syringae phylogroups. The second example is the effector families HopH and HopBN (Fig 7B) which have different prevalence (206 vs. 78 strains for HopH and HopBN respectively), but nearly identical RecPD values of ~ 0.16. Their corresponding Faith’s PD values are 0.31 and 0.34, indicating similar overall distribution across the P. syringae species phylogeny despite their difference in prevalence. However, by visually comparing their reconstructed evolutionary histories it can be seen that HopH and HopBN have followed dramatically different evolutionary trajectories. The RecPD derived measures also paint a very different evolutionary picture for each family, as shown in Table 3.

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Fig 7. RecPD gene lineage reconstructions reveal significant differences in evolutionary histories between effector families of similar prevalence and phylogenetic diversity.

Example pairs of effector family distributions mapped onto the P. syringae core-genome phylogeny. (A) Effector families HopS and HopAW show similar prevalence (HopS = 114 and HopAW = 116) but different RecPD values (HopS = 0.399 and HopAW = 0.198). (B) Effector families HopH and HopBN show different prevalence HopH = 206 and HopBN = 78) but similar RecPD values (0.16). Tree topologies are represented in a ‘willow tree’ format, with branches set to equal length, and actual branch-lengths indicated by branch-thickness. Branches are coloured according to overlap between RecPD-inferred gene family lineages.

https://doi.org/10.1371/journal.pcbi.1009899.g007

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Table 3. RecPD and associated measures for selected effector families shown in Fig 7.

https://doi.org/10.1371/journal.pcbi.1009899.t003

Application of RecPD on Pseudomonas spp. growth phenotypes

Pseudomonas is a genus within the Gamma-proteobacteria, which includes hundreds of distinct species isolated from a range of diverse environmental habitats [25]. The genus is known for the remarkable metabolic diversity and the broad range of environmental niches which its members inhabit [26], running the gamut from important opportunistic and emergent pathogens of humans and plants, e.g., P. aeruginosa [27] and P. syringae (as highlighted above) [17,18,28], respectively, to commensal species associated with the plant rhizosphere [29].

Species within the genus Pseudomonas are now typically delineated via multilocus and genomic methods, although historically they were identified using an array of phenotypic and growth assays [30]. While there are many instances where the phenetic assays disagree with the results from molecular typing, these complementary approaches can provide valuable information about the evolutionary processes driving phenotypic diversification. They also provide an excellent opportunity to apply our RecPD methodology.

We examined the relationships among ten representative Pseudomonas species based on the distribution of 18 distinguishing metabolic and phenotypic traits listed in Bergey’s Manual of Systematic Bacteriology [31]. The 18 traits have a mean prevalence of 4.3 +/- 2.7 s.d. and fall into approximately four distinct phenotypic clusters that delimit different Pseudomonas spp. clades (Fig 8). We used 16S rRNA gene sequences to determine the genetic relationships among the ten bacterial species and applied RecPD to examine the phylogenetic diversity of each phenotype/trait across the Pseudomonas species phylogenetic tree. Interestingly, most of phenotype clusters appear to be vertically inherited (nRecPD ~ 1), with only utilization of ketogluconate, L-valine, geraniol, and glucose, and the presence of fluorescent pigments showing signs of horizontal transfer (nRecPD ~ 0.7). These results indicate that most of phenotypes historically used to classify Pseudomonads have been transmitted vertically, explaining why they proved to be robust for species delineation.

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Fig 8. nRecPD indicates largely vertical descent of Pseudomonas spp. growth phenotype distributions, revealing clade specific loss-patterns and between-clade recombination.

A heatmap showing presence / absence profiles of 10 growth phenotypes assayed over 10 representative strains of the genera Pseudomonas. Growth phenotype columns are hierarchically clustered and split into 4 major clusters, while species are arranged according to a 16S rRNA phylogenetic tree. Corresponding nRecPD values calculated for each growth phenotype are indicated by the top horizontal annotation strip, with blue indicating vertical descent (nRecPD = 1) and purple indicating signatures of recombination (nRecPD ~ 0.7).

https://doi.org/10.1371/journal.pcbi.1009899.g008

Definition of RecPD

Given a phylogenetic tree and a list representing feature of interest and its presence/absence state for each tree tip, ancestral state reconstruction is performed (see Methods–Development of RecPD–Step 1) and the ancestral states of internal tree nodes and branches are assigned. Ancestral feature lineages are identified by traversing branches from each feature presence state tip to its deepest ancestral presence state nodes in the tree (i.e. presence state nodes immediately descended from an absent state parental node). RecPD is then calculated by the sum of all unique ancestral presence state branches divided by the total branch length of the phylogenetic tree: Where:

• Br_g- all presence state branch lengths between the deepest ancestral tree presence (g) nodes to directly descendant feature presence tips.
• Br_tree All branch lengths of the phylogenetic tree.

RecPD Development and implementation

All code development, final implementation of RecPD analyses, simulation experiments and figures presented in this work was performed in RStudio (R version 4.0.2) [42]. The ape library [43] was used for basic phylogenetic tree import and processing tasks, generation and visualization of random trees used in methods development section, and ancestral reconstruction using MPR and ACE. Faith’s PD was calculated using the pd() function from the picante library [44]. The ggtree library [45] was used for final phylogenetic tree visualizations. R code for running RecPD can be found in S1 File.

Gene family evolutionary simulation

Simulation gene-family history evolution was performed using a Poisson process to model gene family recombination and loss events onto a provided species tree phylogeny (code supplied in S2 File). The method is motivated by ideas from the modelling of birth-death phylogenetic trees [46], similar approaches used for simulating microbial gene-tree phylogenies [47], and the simulation of bacterial genomes and phenotypic evolution on phylogenetic trees [40]. In essence, it models the evolution of a trait (gene-family, variant, or locus) through loss and recombination occurring along the different lineages of a provided species phylogenetic tree. The tree can be either ultra-metric or non-ultrametric, with branch-lengths representing either time since emergence from a common ancestor, or a molecular evolutionary distance (average expected nucleotide/amino acid substitutions per site).

The model requires two parameters, specifying the rate exponents for each type of event and their values can be scaled according to the maximum root-to-tip death of the phylogenetic tree (in our case this value is scaled to 1):

• Extinction/Death/Loss Rate (Er): losses of a locus/state
• Recombination Rate (Rr: gains of a locus/state from one species lineage to another

These rates can be thought of as a summary of the evolutionary selective pressures acting to maintain a locus/state or its selective advantage helping to propagate it. Note that these rates remain constant throughout the evolutionary history of the species tree, however in reality they are likely to vary under different population bottlenecks or changing environments.

Using these rates the Poisson interarrival time distribution for any event (loss or transfer) can be calculated using the exponential distribution with the rate parameter equal to the sum of the extinction and recombination rates: P(ti) = (Er + Rr) * exp(-(Er + Rr)*ti), where exp is the exponential function and ti is the given inter-arrival time between successive events.

Another important feature of this model is that probabilities of events occurring at a given inter-arrival time:

• Extinction Probability: Er / (Er + Rr)
• Recombination Probability: Rr / (Er + Rr)

In our modelling procedure, first the emergence time of the trait is randomly drawn from a uniform distribution and then randomly assigned to a species lineage existing at that time (trait origination event). Next, the occurrence of events is modelled using a Poisson process by randomly drawing a sequence of interarrival times from the inverse cumulative probability function of the exponential distribution: e_t = -log(1-P(i))/(Er + Rr + Lr)), where i is a random variable sampled from a uniform distribution taking values from [0–1].

The inter-arrival time sequence is cumulatively summed and then added to the emergence time of the first event (cumsum(e_t) + birth_time) which gives a sequence of the the event occurrence times that will then be randomly mapped upon the species tree lineages. Note, only those event occurrence times time of emergence for the locus/state until the time when the species tips are observed (= 1) are considered.

Iterating successively through the event timings, a number between [0–1] is randomly drawn from a uniform distribution (prob_event) and used to determine whether the given event is a loss or recombination:

• Extinction/Loss: if prob_event < = Er / (Er + Rr); otherwise
• Recombination: prob_event > Er / (Er + Rr)

In addition, a locus/state longevity rate (Lr) parameter can be incorporated, which will result in the inter-arrival event distribution of exp(-(L + Er + Rr)), but also add the possibility of no events occurring in the evolution of the trait:

• No Event (Trait State Maintained): if prob_event < = Lr / (Lr + Er + Rr); otherwise
• Extinction/Loss: prob_event < = Er / (Lr + Er + Rr); otherwise
• Recombination: prob_event < = Rr / (Lr + Er + Rr)

If the event is a trait loss, species lineages possessing the locus/state at the given time are extracted and assigned as a loss event, and all descendant lineages occurring after the event time are also assigned as losses. If the event is a recombination, then a species lineage lacking the locus/state at the given time (if it exists) is randomly selected and assigned as a locus gain event, and its descendants are assigned as a locus gain event, in distinction to the initial locus/state origination event. In effect this generates a locus/state distribution presence/absences for the tips of the species tree, as well as the ancestral evolutionary histories of these traits. There may also be tips which never possessed the locus in their evolutionary history (absence). Using this approach, we can examine how frequently locus/state distributions overlap between different evolutionary regimes, e.g. loss dominated vs. recombination dominated.

Pseudomonas syringae type III effector family analysis

Data for P. syringae effectors including NCBI genomic accession numbers for 494 P. syringae strains used for effector identification, associated strain metadata, and classified effector family sequences originates from a previously published study [15]. Genomic assemblies used were generated using the protocol outlined in [15]. Annotation of genome assemblies was performed using prokka (version 1.14.16) [48], pangenome analysis and core-genome nucleotide alignment was produced using PIRATE (version 1.0.4) [49], from which a core-genome phylogenetic tree was generated using IQ-TREE (version 1.6.12) [50]. All software was run in Linux. Generation of effector presence/absence matrices, RecPD analyses, and phylogenetic tree visualization and annotation were performed in R.

Pseudomonas growth phenotype analysis

Growth phenotypic data for Pseudomonas species was extracted from [31] and converted into binary presence / absence format. Corresponding representative species 16S rRNA gene sequences were downloaded from NCBI (including Cellvibrio japonicus as an outgroup according to [25] and aligned using MUSCLE (v3.8.1551) [51]. Phylogenetic tree construction was performed using IQ-TREE (version 1.6.12) [50]. Heatmap visualization was generated using the ComplexHeatmap package in R [52].