Research articlesWhere traditional extinction estimates fall flat: using novel cophylogenetic methods to estimate extinction risk in platyhelminths
Abstract
Today parasites comprise a huge proportion of living biodiversity and play a major role in shaping community structure. Given their ecological significance, parasite extinctions could result in massive cascading effects across ecosystems. It is therefore crucial that we have a way of estimating their extinction risk. Attempts to do this have often relied on information about host extinction risk, without explicitly incorporating information about the parasites. However, assuming an identical risk may be misleading. Here, we apply a novel metric to estimate the cophylogenetic extinction rate, Ec, of parasites with their hosts. This metric incorporates information about the evolutionary history of parasites and hosts that can be estimated using event-based cophylogenetic methods. To explore this metric, we investigated the use of different cophylogenetic methods to inform the Ec rate, based on the analysis of polystome parasites and their anuran hosts. We show using both parsimony- and model-based approaches that different methods can have a large effect on extinction risk estimation. Further, we demonstrate that model-based approaches offer greater potential to provide insights into cophylogenetic history and extinction risk.
1. Introduction
Parasites comprise a huge proportion of living biodiversity, representing approximately 40% of all species described [1]. The ubiquity of parasitism throughout all ecosystems demonstrates their success and why their role in shaping community structure should not be overlooked [2]. Parasites have been shown to affect trophic interactions [3], competition [4], biodiversity and food webs [5], as a result of the impacts they have on their host species (see [2] for more information on these interactions). The control parasites exert on their community is substantial and if severe parasite extinctions were to occur there could be massive cascading effects across ecosystems [6]. Despite this, much of parasite evolutionary history and ecology is not well understood [7,8]. This is in large part due to insufficient data for both extant and fossil parasites—they tend to be small, soft-bodied organisms that reside in their hosts [9,10], making their discovery and identification difficult [7,8]. Due to gaps in our knowledge, estimating parasite extinction events can be difficult. For many non-parasitic taxa, we can take advantage of census or range data from the recent [11] or look to the fossil record [12,13].
Given this lack of data, parasite extinction risk is often based on the extinction probabilities of their hosts, without incorporating information about the potential for parasites to survive host extinction events [6,14]. Recently, Doña & Johnson [15] proposed the use of cophylogenetic methods to inform extinction risk among parasites through the cophylogenetic extinction rate (Ec) statistic. Cophylogenetic studies estimate parasite evolutionary histories in relation to their hosts [16]. The advantage of this approach is that it explicitly incorporates information about the phylogenetic history of the group—extinctions, duplications, cospeciations or host switching—which would have implications for survival probability during future extinction events [15,17]. This promising approach to estimating extinction risk among parasites therefore hinges on our ability to reconstruct cophylogenetic history.
Cophylogenetic methods can be separated into distance- or event-based [18,19]. Distance-based methods estimate the overall congruence between host and parasite phylogenies [20], while event-based methods aim to infer the events that have occurred between the two groups by reconciling the host and parasite phylogenetic trees. [18]. In this context, reconciliation refers to mapping each node of the parasite tree onto a node or branch of the host tree [21]. Four evolutionary processes (events) are used to explain observed patterns between two trees: cospeciation, duplication, extinction and host switching [22] (figure 1). Cospeciation occurs when a parasite speciates following a host speciation event [23]. Duplication refers to parasite speciation that is independent of the host phylogeny. In this case, a parasite speciates into two daughter lineages, both of which then act on the same host as the parent species. Extinction refers to the extinction of parasite lineages. Host switching occurs when a parasite moves from its ancestral host species and colonizes another host. This typically occurs when the new host is either phylogenetically or ecologically similar to the original host, although host switching can also occur across relatively large evolutionary distances [20,22,23].
Figure 1. Example of a host–parasite association. (a) Illustration of extant relationships. (b) Pink circles show the four common evolutionary events estimated using cophylogenetic methods (cospeciation, host switching, parasite extinction and parasite duplication), and the orange circle shows coextinction, which cannot be inferred using cophylogenetic methods directly [15] (see 'Methods' for more details).
Cophylogenetic studies use information from extant host–parasite interactions (figure 1a) in order to infer ancestral interactions (figure 1b). This is not straightforward, as myriad combinations of events can be used to explain the same set of extant relationships, resulting in hundreds of putative explanations (i.e. evolutionary histories), especially as more taxa are added to each tree [24,25]. To limit the number of possible solutions many cophylogenetic methods rely on a parsimony framework [26,27], i.e. they assume that the simplest explanation is the most likely. This is achieved by assigning fixed costs to each event type. Typically, cospeciation is the null explanation and assigned a cost of zero. Duplication and extinction events are assigned a cost of 1, while host switching is assigned the highest cost, greater than 1. Evolutionary histories with the highest number of cospeciation events, relative to the other event types, will typically have the lowest cost and therefore be preferred [18].
These methods were developed initially under the assumption that cospeciation is the main driver of coevolution [28]. However, recent studies have shown that host switching might be much more frequent than was understood previously [29,30]. This brings into question the rationale behind parsimony-based cophylogenetic methods. Assigning fixed costs to each event with no objective justification has the potential to bias results and infer erroneous phylogenetic histories. A new generation of model-based methods relaxes the assumption that cospeciation is the main driver of coevolution and estimate relative rates of different processes directly from the data, overcoming the biases associated with parsimony-based methods [31].
Here, we apply a model-based cophylogenetic approach to estimate the coevolutionary history of platyhelminth flatworms and their anuran hosts. Platyhelminths have been proposed to be a model group for parsimony-based methods, because levels of host switching are assumed to be minimal [32]. Within the phylum Platyhelminths, the family Polystomatidae are of particular interest. Polystomatidae are thought to be a very host-specific group, acting exclusively on aquatic to semi-aquatic tetrapods, with the exception of the Australian lungfish [33–36]. A high degree of cospeciation has been suggested with their anuran hosts [37]. These parasites are found in the bladder of the host, attaching themselves to the gills of the frogs as larvae before migrating to the bladder to mature [32]. Polystomatidae have been the focus of several other studies, all of which used parsimony-based approaches to analyse their cophylogenetic history [37,38]. We use a model-based approach in the program ALE, following the approach of [31], to reanalyse these relationships and compare the results to eMPress v1.0 [39], a parsimony-based approach. We demonstrate how ALE provides more intuitive results and allows us to better understand the history between the two phylogenies. We also highlight the impact different cophylogenetic methods have on the Ec estimation. While the Ec statistic presents a unique opportunity to estimate parasite extinction rate, we show how it is sensitive to the cophylogenetic methods used.
2. Methods
(a) Data
Our analyses require an ultrametric phylogeny for both the anuran host and polystomatid parasite species, as well as information about host–parasite associations. We used published molecular sequence alignments taken from [38] to estimate the trees. Each dataset contains 17 species. The parasite alignment consists of two nuclear genes, complete 18S and partial 28S genes. The host alignment consists of two mitochondrial genes, 12S and 16S. Two host species have not been sequenced for both genes. Instead, the missing genes were taken from phylogenetically closely related species, as per the classification proposed by [40]. Previous analysis showed that the replacement of these genes does not impact the phylogenetic position of taxa in this dataset [38].
The species affected were Bufo regularis and Hyperolius marmoratus (figure 2).
Figure 2. Tanglegram showing the relationship between polystome parasites and their anuran hosts using the Bayesian MCC trees generated from our analysis. (Online version in colour.)
(b) Phylogenetic analysis
To estimate ultrametric trees, we took a Bayesian approach to account for uncertainty in topology and relative branch lengths. All phylogenetic reconstructions were carried out using RevBayes v.1.1.0 [41]. A birth–death model was used for both reconstructions. The host tree was calibrated using a uniform prior on the root U(66, 148.1), based on the fossil age constraints of the Neobatrachia suborder [42], although our goal is not to focus on the absolute age of any speciation event. The age of the polystome tree was fixed to 100. An uncorrelated lognormal relaxed clock model was assumed to estimate branch rates for both trees, along with a GTR+Γ substitution model. Further description of model parameters and priors can be found in the electronic supplementary material.
(c) Parsimony-based approach
We first analysed the coevolutionary relationship between polystomes and anurans using eMPress v1.0 [39], a parsimony event-based method (successor of the Jane [43] reconciliation tool). eMPress reconciles host and parasite trees under the DuplicationTransfer-Loss (DTL) model. The input for eMPress is a summary tree for both the host and parasites (we used the Bayesian maximum clade credibility (MCC) trees) and information about the tip associations. As with other parsimony event-based methods, it relies on costs to produce the maximum-parsimony reconciliations (MPRs). Within eMPress, cospeciation is fixed to zero and loss is set to 1.0 by default. A costscape is provided as an overview of the solution space for the reconciliation [44]. It splits up a range of potential costs into equivalence classes, wherein all the combination of costs in a particular space will produce the same set of MPRs. For our dataset, the costscape estimated six equivalence classes, (electronic supplementary material, figure S3 the x- and y-axis show the duplication and host-switching costs, respectively). We chose a cost for duplication and host switching from each equivalence class when carrying out tree reconciliation. Using eMPress, we produced one median MPR for each reconciliation [45] (electronic supplementary material, figure S4) and calculated the significance of the relationships estimated (i.e. was the cost less than expected by chance?). This significance was calculated by randomizing the tips of the branches and then re-calculating the cost to reconcile the phylogenies. It is then possible to determine whether the original cost was less than expected by chance, (p < 0.05).
(d) Model-based approach
We then used ALE v0.4 (https://github.com/ssolo/ALE) to re-evaluate the phylogenetic history between the polystome and anurans. ALE uses a DTL model, similar to eMPress; however, this time in a probabilistic framework. Originally used to understand gene family evolution [46], this implementation of the DTL model uses different evolutionary events to explain the difference between gene trees and species trees. This version of the DTL model does not require costs to be set a priori as in parsimony-based approaches. Using a probabilistic approach, it estimates the maximum-likelihood rates for each event type that best explains the difference between the two phylogenies, be it gene species trees or host parasite trees [47,48]. The use of ALE for cophylogenetic studies has been implemented in [31,49].
For our analysis, we used the undated version of the DTL model in ALE. This approach does not take into account the branch length of the phylogenies. Instead it uses only the topology and node order [50,51]. This version was more appropriate for our phylogenies given uncertainty in divergence times. By ignoring the branch lengths, the absolute timing of speciation events was not taken into account [50]. We treated the anuran host trees as the ‘species tree’ and the polystome parasite trees as the ‘gene family tree’. The input here was the entire posterior distribution of trees for both the parasites and hosts, accounting for phylogenetic uncertainty [31].
We applied this model to our dataset to obtain maximum-likelihood estimates for relative rates of parasite speciation, host switching and parasite extinction. The inferred rates were then used to reconcile the parasite and host phylogenies using the different events. A sample of 1000 reconciled trees was taken to calculate the average number of each event. By default, ALE also estimates the number of cospeciation events, i.e. where none of the other DTL events took place. As such, ALE can estimate the relative number of all event types proposed to explain the coevolution of hosts and parasites.
Based on the estimates we obtain for the number of events, we then assessed the significance of these results. That is, did any of the events occur more frequently than expected by chance? To test this, datasets were simulated with no explicit assumptions of codiversification [27], following the approach described in [31]. Parasite trees were simulated using the R package TreeSim [52]. One thousand trees matching the parasite tree properties, in terms of tip number, were generated under a birth–death model, with λ = 1.0 and µ = 0.9. Each of these trees was then analysed using ALE, while keeping the host tree constant [31].
Finally, we used model selection to assess the role of different cophylogenetic processes. Within the ALE program, all three DTL model parameters are estimated by default. Any of these variables can be fixed to zero before running the analysis. This allows us to ‘turn off’ different processes. By setting any of the DTL events to zero, they are removed from the model and cannot be used when reconciling the host and parasite trees. In this way, if you assign host switching to zero, only parasite duplication and parasite extinction can be used to explain the observed data. The full list of models tested is shown in table 1. The Akaike information criterion [53] and model probabilities [54] were calculated to assess how well the different models performed.
| model | K | logL | AIC | Δi | Wn |
|---|---|---|---|---|---|
| TL | 2 | −44.23 | 92.47 | 0 | 0.67 |
| DTL | 3 | −44.24 | 94.48 | 2.00 | 0.24 |
| T | 1 | −47.67 | 97.34 | 40.87 | 0.05 |
| DT | 2 | −47.74 | 99.49 | 7.02 | 0.02 |
| DL | 2 | −68.6 | 141.13 | 48.65 | 1,83 × 10−11 |
| L | 1 | −11352.20 | 22706.40 | 22613.92 | 0 |
| cosp | 0 | −11354.90 | 22709.80 | 22617.32 | 0 |
| D | 1 | −11354.92 | 22711.84 | 22619.36 | 0 |
This enabled us to determine which parameters are important for describing the coevolution of the polystome-anuran system.
(e) Estimating cophylogenetic extinction rate
Here we are interested in estimating the cophylogenetic extinction rate for parasites with their hosts. This is different from the rate of parasite extinction estimated in the previous section. The cophylogenetic methods described above calculate primary parasite extinction events—that is, extinction events among parasites that occurred independently of their hosts [55]. An alternative metric is needed to calculate host-driven extinction risk. Studies have shown that the biggest potential risk to parasites is the extinction of their host populations [6,55,56]. Extinction of host species can result in either both host and parasite going extinct (secondary parasite extinction) [55] (figure 1) or the parasite switching hosts. Since typically we lack direct evidence of either event, Doña & Johnson [15] recently proposed a novel approach to estimating cophylogenetic extinction rate (Ec). By including information about the phylogenetic history of the group, it is possible to approximate how parasites will respond to host extinction events. Ec is calculated as where L is the number of losses, E is the number of events other than host switching (i.e. the number of cospeications, duplications and extinctions) and S is the number of host switches. The risk of extinction increases as the number of primary parasite extinctions increases and decreases as the number of host switches, cospeciations and/or parasite speciations increases. The number of host switches is doubled as the authors reasoned that the ability to switch hosts will be crucial to survival given host extinction [15]. We calculated the Ec rate using the number of events estimated in eMPress, (only when the relationship was found to be significant) and in ALE under the full DTL model for all 1000 tree reconciliations. We also calculated the Ec rate using output from the analysis of Badets et al. [38], where they used TreeMap v2.02ß [57], an older parsimony event-based method. This allowed us to investigate how different methods used to infer cophylogenetic history impact estimates of extinction risk.
3. Results
(a) Parsimony-based approach
eMPress produced a costscape with six equivalent classes. These classes had a different number of events and different numbers of MPRs associated with them. Table 2 shows the combination of events estimated for each of the classes. Out of the six classes, four were found to produce a cost lower than expected by chance for reconciliation. eMPress allows the user to output median MPRs as a way to summarize the solution space. We found that between the different costs, the median MPRs produced quite different patterns based on the event costs set. The use of median MPRs and the clustering methods (not discussed here, but see [21]) help the user to explore the solutions output by eMPress, however, deciding which of the different classes (i.e. which costs to set) remains challenging.
| cosp | D | T | L | no. MPRs |
|---|---|---|---|---|
| 9 | 0 | 7 | 3 | 6* |
| 8 | 0 | 8 | 1 | 48* |
| 9 | 1 | 6 | 7 | 4* |
| 9 | 4 | 3 | 20 | 2* |
| 9 | 5 | 2 | 27 | 1 |
| 8 | 8 | 0 | 45 | 1 |
(b) Model-based approach
The implementation of the DTL model within the program ALE calculated the maximum-likelihood rates of parasite duplication, host switching and parasite extinction [31,46]. For our analysis, these rates were estimated to be 0.0 for duplication, 0.21 for host switches and 0.17 for extinction. Given these relative rates, the average number of each event estimated was 0 for parasite duplication, 6.55 for host-switching events, 4 for parasite extinction and 13.4 cospeciation events. The estimated number of host switches could then be mapped along the branches of the host tree, shown in figure 3. This allowed us to identify regions of the host tree where host switching was most prevalent and the host taxa that were potentially involved.
Figure 3. Average number of host-switching events. The estimated number of events is represented along the branches of the host MCC tree.
The results of the simulations to test for significance are shown in figure 4. The number of estimated cospeciation events was found to be significantly more frequent than expected by random chance, while host switching occurred significantly less than expected. The results are consistent with current understanding of the relationships of this group [58].
Figure 4. (a) Average number of events estimated to have occurred between anuran and polystome lineages using the top four models: T, TL, DT and DTL. (b–d) Estimates of events from simulated datasets. Black vertical line indicates the number from the empirical analysis for comparison. Note: Estimates for parasite duplication not shown as no duplication events were estimated using the simulated datasets. (Online version in colour.)
The results of the model selection were determined using AIC and model probabilities. Table 1 shows the results of these tests in descending order. Four models accounted for majority of the model probabilities. The model with the highest support was one in which host switching, parasite extinction and cospeciation were all allowed (probability = 0.67). In addition, all of the top four models contain host switching. This highlights the importance of host switching in the shared history of these two groups. Any model that did not allow for host switching received no support. The pure cospeciation model also received no support. Overall the results of the DTL model suggest that while host-switching events and parasite extinction have happened less frequently than cospeciation, both have played an important role in the coevolutionary history.
(c) Estimating cophylogenetic extinction rate
Estimates of cophylogenetic extinction rate (Ec) show that the results can be strongly impacted by the cophylogenetic method used. The results from eMPress produce a wide range of rates depending on the cost set a priori. The highest parasite extinction rate estimated was a result of the analysis that has the highest cost for host switching. This causes less host switches to occur resulting in the Ec rate increasing. On average, ALE estimated the lowest parasite extinction rate, with TreeMap estimating a relatively high rate.
4. Discussion
Understanding the mechanisms by which parasites have evolved and diversified has the potential to provide valuable information for assessing their extinction risk [15]. Current approaches to estimating parasite extinction often rely on host extinction probability [55,59]. Alternatively, by incorporating information about how parasites have coevolved with their hosts, better-informed estimates of parasite extinction risk can be obtained [15]. It is therefore critical that cophylogenetic methods accurately capture the shared history of parasites and their hosts. In this study, we re-analysed the coevolutionary history of polystome parasites and their anuran hosts. Using both a parsimony-based (eMPress) [39] and a model-based (ALE) [48] approach, we investigated the output of these different methods and the implications for predicting parasite extinction risk.
Polystomes have been considered a model group for studying cophylogenetics because they are highly host specific [37,58]. Previous studies have suggested that these two lineages have coevolved predominantly via cospeciation [37]. This is a result of both field observations based on extant taxa and phylogenetic analysis of molecular data [32,37,38]. Today polystomes have a global distribution, with species found in Africa, Madagascar, Europe, as well as North and South America [38]. Their direct life cycle requires freshwater to lay eggs, for larval development and to infect hosts. This makes dispersal of polystomes only possible once they have infected the host [34,36]. In addition, based on the current distribution of the parasites, vicariance-driven speciation has been linked to that of their anuran hosts. These observations suggest a long-standing association between the two lineages and advocates for at least a moderate level of cospeciation to have occurred [60].
For our dataset, eMPress provided a costscape which had six equivalence classes. The costscape algorithm implemented in eMPress is a helpful tool when trying to select costs. It allows the user to systematically go through a range of costs for the events without choosing costs arbitrarily. What remains difficult is choosing which equivalence class, or which reconciliation is optimal. If the user had ‘expert knowledge’ of the empirical group or, had some information about costs unsed previous studies, they could use the cost space to see how alternative costs effects the reconciliations. Without this prior knowledge, however, it may be difficult to choose which class to use. While eMPress does offer many advantages over other parsimony-based methods,—notably over its predecessor Jane where summarizing the solution space was not possible—choosing the costs a priori still has a major impact on the results. Based on our analysis, different reconciliations can have a demonstrably large effect on downstream analysis (such as the Ec calculation used here). This approach also set cospeciation to zero and the user is unable to edit this. Another potential issue with eMPress is that it does not account for topological uncertainty. The input used here is two summary trees, both of which are assumed to be correct. For our analysis, both of the summary trees (electronic supplementary material, figures S1 and S2) contain nodes that have low support. Assuming these trees are correct in this way, could therefore produce inaccurate results.
Estimating cophylogenetic history using a probabilistic DTL model offers several advantages over parsimony-based methods. It removes the need to assign costs to the events and allows them to be freely estimated in a probabilistic framework [31,48]. It can also use the full posterior distribution of trees for both the hosts and parasites, thus incorporating topological uncertainty. The output of this approach is demonstrably more informative than that of eMPress. In addition to estimates of cophylogenetic events, figure 4a, ALE allowed us to further investigate their relative importance between polystomes and anurans. Simulations revealed that cospeciation has occurred more frequently than expected, suggesting an evolutionary tendency towards cospeciation. This finding fits well with past studies of the group, but has not previously been demonstrated using a probabilistic approach that makes no prior assumptions about the relative contribution of each cophylogenetic process. Further, model testing showed the importance of host switching and parasite extinction in the group's history.
An added benefit of using ALE is that the output can be mapped back onto the host tree (figure 3). This could be informative when using host fossil calibrations to estimate the divergence times of parasites. Due to their poor fossil record, host fossils are often be used to calibrate parasite phylogenies [9,38,61]. Such approaches can, however, result in a certain degree of circular reasoning. That is, using the host fossils to date the parasite tree and then using those dates to make statements about their evolutionary relationships [9,61]. As such, using host fossils to date parasite phylogenies should be done with caution. Having a way to predict which taxa have experienced less host switching could provide justification for using host fossils in this way. Based on our results, for example, using host fossils from the genus Hyla could be more reliable than using fossils of Rana, which have experienced comparatively more host switching.
In addition, our results demonstrate how cophylogenetic methods can impact estimates of host-dependent extinction risk among parasites. We used a new metric, cophylogenetic extinction risk (Ec) that uses the output of event-based cophylogenetics [15]. The advantage of this approach is that it allows us to estimate extinction risk, in the absence of any direct evidence about the number of coextinction events through time, which are rarely, if ever, directly observable (figure 1). It is difficult to interpret the output from eMPress in this context. The parasite extinction risk ranges from 0.04 to 0.51 depending in the costs set for the analysis figure 5. These results illustrate how the Ec metric provides an intuitive summary of extinction risk taking into account cophylogenetic history. For example, lower estimates of parasite extinction risk are associated with higher estimates of host switching. The results also highlight how estimates of parasite extinction risk will be sensitive to the estimated cophylogenetic history and using parsimony-based methods will in turn be sensitive to the costs assigned to each event. Only the probabilistic DTL model places no prior assumptions on the relative contributions of different cophylogenetic processes, as well as reflecting uncertainty in the tree topologies, thus we advocate using this approach in combination with the Ec metric.
Figure 5. Parasite extinction Ec rate estimates. The histogram shows the range of estimates calculated using 1000 tree reconciliations from ALE under the full DTL model. All vertical lines are added here as a comparison and represent a single parsimony-based estimate associated with different event costs. Purple lines represent the parasite extinction risk estimated from eMPress output and the green from Badets et al. [38].
The approach used here is an improvement on previous attempts to estimate parasite extinction risk, as it does not solely rely on host extinction risk. Further extensions could benefit from incorporating additional information. For example, the addition of a scaling factor to account for phylogenetic distance in host-switching events. The Ec calculation currently takes all host switches as equal. Some parasites can, however, switch hosts across large phylogenetic distances. Taking platyhelminths, the group used in this study, as an example, one parasite lineage has successfully dispersed to a species of African hippopotamus [38]. Although host-switching events across this distance are rare among platyhelminths, including information about the phylogenetic distance of host-switching events would be valuable for assessing coextinction risk, especially among less host-specific groups. It would also be useful to account for changes in host population size. Current approaches to estimating cophylogenetic history or extinction risk, assume that the potential for host switching has remained constant through time. Given that the possibility for parasites to switch hosts is dependent on the availability, as well as suitability, of potential host species, changes in current and potential host population size will also play a key role in parasite extinction risk.
Improving estimates of parasite movements is important, not only for parasite conservation, but also for predicting potential threats from parasites. Invasive parasites species can have detrimental effects on ecosystems [62,63]. As such, identifying the parasites that are most likely to survive their host extinction events and disperse to new hosts or areas could provide valuable information for conservation efforts.
5. Conclusion
Parasite extinctions threaten the stability of many ecosystems. Whether they go extinct with their hosts through coextinction events or survive through subsequent host-switching events has important implications for their surrounding communities. Here we investigated the use of a new cophylogenetic extinction rate metric using polystome parasites and anuran hosts as a case study. We found parasite extinction risk was highly sensitive to the method used to estimate cophylogenetic events. Thus, to fully use this metric, we need to be confident about the approach used to reconstruct coevolutionary history. The probabilistic DTL model in ALE used here provided the most intuitive results, while also removing biases associated with parsimony-based methods and allowing for the inclusion of more information. Model-based approaches offer the current best way to advance our understanding of cophylogenetic history and extinction risk among parasites.
Data accessibility
All data and code used for the analysis are available on github: https://github.com/laumul/Cophylo.
See also the electronic supplementary material [64].
Authors' contributions
L.P.A.M.: conceptualization, data curation, formal analysis, investigation, methodology, writing—original draft and writing—review and editing; R.C.M.W.: conceptualization, methodology, supervision, writing—original draft and writing—review and editing; K.D.B.: conceptualization, methodology, supervision, writing—original draft and writing—review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.
Conflict of interest declaration
We declare we have no competing interests.
Funding
K.D.B. was supported by I.3.4 Action of the Excellence Initiative—Research University Program at the University of Warsaw.
Acknowledgements
We thank Adam Kocsis for technical support, as well as Jordan Satler, Michael Landis and Mariana Braga for advice on model-based approaches. We also thank the two reviewers for their positive and constructive comments.
