Methods for studying polyploid diversification and the dead end hypothesis: a reply to Soltis <i>et al</i> . (2014)

The fate of polyploid lineages has been of long-standing interest to evolutionary biologists. In our previous work (Mayrose et al., 2011a; reviewed in Arrigo & Barker, 2012), we used likelihood methods to estimate the effects of recent polyploidization events on diversification rates (speciation minus extinction). Our goal was to ask whether, across groups, there is a preponderance of evidence for or against the hypothesis that polyploid species diversify at different rates than diploid species. Our results demonstrated that polyploid lineages, when compared with their diploid relatives, tend to form new species more slowly and go extinct more quickly, for a combined effect of lower diversification rates. Soltis et al. (2014) recently called into question our conclusions and raised concerns about our analyses. Some of these concerns reflect open questions and limitations in the available data, but others are based on misinterpretations of the methods used and their implications. In the spirit of furthering the fascinating debate about the macroevolutionary consequences of polyploidization, we offer this response with the hope that it will clarify what has been shown, demonstrate the utility of the methods applied, and inspire future work. Soltis et al. (2014) frame their concerns as a series of arguments, and we follow their framework in responding to the points raised. Before embarking, it is worth reemphasizing what we defined as a ‘polyploid lineage’. Indeed, all angiosperms have one or more polyploidization events in their history if one looks back far enough (Jiao et al., 2011), and thus polyploidy must be defined with respect to a reference time point. Because our focus was on the impacts on diversification of recent polyploidization events, we explicitly defined polyploids ‘as those lineages that underwent a polyploidization event since divergence from their generic ancestor’ (Mayrose et al., 2011a). This definition enabled us to perform a large-scale comparative study using chromosome number changes to infer polyploid transitions in 63 clades of plants. Thus, when asking whether polyploidization impacts subsequent diversification, it must be borne in mind that our analyses were conducted on rather short evolutionary timescales, comparing those taxa that had undergone fairly recent polyploidization (‘neopolyploids’) with those that had not. As we concluded in Mayrose et al. (2011a), it remains an interesting open question whether earlier polyploidy events had different impacts on speciation and extinction, as has been suggested, for example, in the context of mass extinction events (Fawcett et al., 2009; Vanneste et al., 2014). The first criticism leveled is that we overestimated the diversification rates of diploids because ‘increased diversification rates are more likely to arise in large clades than in small ones’ (Soltis et al., 2014). Specifically, Soltis et al. (2014) noted that polyploid lineages, as we defined them, would have to be nested within a larger diploid group, hence the polyploid subclades must be more recent and would thus tend to be smaller. We agree that the polyploid subclades will tend to be younger and, assuming equal diversification rates, polyploid species are expected to be fewer in number, but this should not bias the estimation of diversification rates. The likelihood method that we used (‘binary-state speciation and extinction’, BiSSE; Maddison et al., 2007) estimates instantaneous ‘birth’ (speciation) and ‘death’ (extinction) rates per unit time, not the total number of speciation and extinction events. It thus simultaneously accounts for the amount of time spent in each state and for trait transitions. By analogy, the rate at which a jogger runs may be measured at 10 km h−1, whether they have been running for a long time or a short time. The fact that the polyploid subclades have existed for a shorter amount of time does not bias their inferred diversification rates towards lower values. At an intuitive level, the main phylogenetic information that allows BiSSE to infer trait effects on diversification are the internode distances (see also Ree, 2005). If a trait increases diversification, it should be associated with shorter distances between branching events, compared with the alternative character state, and this association should be seen regardless of the depth of the tree (power issues not withstanding – see the Statistical and analytical arguments section, later). Also at an intuitive level, the main information used to infer extinction rates is the rise near the present in the number of species (Nee et al., 1994). If, compared with diploids, polyploids are found more often on the tips of the tree than expected, then this signal suggests that polyploids have a higher extinction rate: they arise but fail to persist. Indeed, the simulation study by Goldberg & Igic (2008) is highly relevant here: they simulated trees where the ancestor was in one state (diploid in the current case) and only forward transitions were allowed (say, to polyploidy). Although their focus was on the estimation of the transition rate, maximum-likelihood results kindly provided by E. E. Goldberg demonstrate that the extinction rates, speciation rates and diversification rates inferred by BiSSE had point estimates near their true values (Fig. 1). Thus, even though polyploids had less time to diversify, the rate at which they did so is well estimated from simulated data (the age of the clade did not bias the rate estimates). It is worth clarifying a related misconception: Soltis et al. (2014) claim that ‘older genera have more time to spawn polyploids than very young lineages; hence including ‘young’ genera while excluding ‘older’ genera will bias the outcome’. Because BiSSE accounts for the transition time between diploidy and polyploidy, younger clades will have fewer transitions and less time to accumulate species, but this is reflected in broader confidence intervals, not in lower estimated rates of diversification. As suggested by Soltis et al. (2014), an alternative to the probabilistic framework is to restrict comparisons to clades of equal age (sister-clade comparisons). Doing so, however, drops a great deal of information from phylogenetic trees (i.e. dropping all branches not part of a contrast), reducing power. This is particularly true for traits, like polyploidy, which tend to appear on terminal branches of a phylogeny (Mayrose et al., 2011a; Escudero et al., 2014). Moreover, it is often not straightforward to identify sister clades with confidence and without subsequent transitions (Maddison, 2006). In addition, such sister-clade comparisons have been shown recently to be inherently biased in cases where one character state is more often the derived one. In these cases, there must be a transition from the ancestral to the derived state on the branch subtending the derived-state clade. The ancestral-state clade, however, gets a head start by already being in that state. So the time available for diversification of the derived state is less, causing it to artificially appear in clades with lower species richness (Kafer & Mousset, 2014). The second philosophical criticism leveled is that reticulate evolution is common among polyploid lineages – indeed, it defines allopolyploids – and that this reticulation raises questions about the legitimacy of diversification analyses based on bifurcating trees. Notably, this criticism extends beyond our analyses; it applies to most applications of comparative methods using phylogenies that contain taxa that have evolved via reticulation at some point in their histories. The effects of reticulation on comparative analyses in general, and on BiSSE-like analyses in particular, have not been well established. These biases may be particularly pronounced when polyploidy is involved as the effect on the topology and inferred branch lengths is still unexplored. To get some sense of the potential impacts of reticulation on our results, we subdivided our data into those genera whose phylogenies were based solely on chloroplast loci and those that were not. As the chloroplast is uniparentally inherited, the true phylogeny is expected to be bifurcating in the former groups, even in the face of hybridization. The results are shown in Fig. 2: the inferred diversification differences between diploids and polyploids are not significantly different between the cpDNA-based trees and the remaining trees (P > 0.05, two-tailed t-test). While further research is needed to explore the effect of reticulation on cpDNA-based phylogenies, this comparison suggests that hybridization did not strongly bias our results. Regardless, we agree with Soltis et al. (2014) that care should be taken when interpreting results based on models that ignore reticulation. We encourage future method development that accounts for hybridization and allows for its influence on diversification rate estimates to be considered. Soltis et al. (2014) caution that extinction rates are difficult to estimate and claim that our conclusion that ‘polyploids diversify at a lower rate is based on higher inferred extinction rates in polyploids’. We agree that extinction rate estimates should be interpreted cautiously. While simulation studies demonstrate that BiSSE-like methods can estimate extinction rates accurately when the model assumptions hold (Maddison et al., 2007), extinction rates are particularly sensitive to sampling biases and departures from the assumed model (Rabosky, 2010). That said, the primary focus of our work was not to estimate extinction rates, but rather to estimate the net diversification rate (r = speciation rate minus extinction rate) of diploids vs polyploids (rD vs rP). Typically, there are ridges on the likelihood surface, where the same diversification rate can be obtained by different combinations of speciation and extinction rates, all with similar likelihoods of explaining the data. Thus, comparative analyses have more power to measure the net diversification rate than to tease apart whether differences in diversification are due to speciation or extinction (Nee, 2006). Our main result that diploids diversify at a higher rate than polyploids (Fig. 1a of Mayrose et al., 2011a) does not rely on a precise estimate of the extinction rate and accounts for correlations between speciation and extinction. These results led us to conclude that polyploidy is ‘most often an evolutionary dead end’. We realize, however, that some readers may interpret the term ‘evolutionary dead end’ to imply that polyploid lineages will always go extinct before speciating. This was not our intention. Rather, we use the term to indicate that neopolyploids, on average, have lower – frequently negative – rates of diversification relative to congeneric diploids. Consequently, many polyploid lineages are ephemeral and contribute little to the diversity of plants, relative to their diploid relatives. That does not preclude the possibility that occasionally a polyploid lineage will radiate into a successful lineage, as stated in Mayrose et al. (2011a). We believe this nuanced view to be in keeping with that of G. L. Stebbins Jr (e.g. ‘The long-continued evolution needed to differentiate genera, families, orders, and phyla appears to have taken place chiefly on the diploid level…Nevertheless, there is some evidence that many genera and even subfamilies or families of seed plants have had a polyploid origin’. Stebbins, 1950, p. 359). Another statistical argument leveled in Soltis et al. (2014) revolves around the issue of power. In particular, they noted that the clades we examined were smaller than they should be to have sufficient power to infer diversification rate differences. Our approach was not, however, based on characterizing with confidence the diversification rates in individual clades. Instead, we performed a meta-analysis to assess the preponderance of evidence across dozens of clades. If polyploids and diploids diversified at equal rates, then we would expect to see higher polyploid diversification in roughly half of the clades. To assess this, we counted the fraction of Markov chain Monte Carlo (MCMC) steps in which rD > rP, treating this fraction for a clade as a single datum. As shown in Fig. 1(a) of Mayrose et al. (2011a), the majority of clades – 55 out of 63 – exhibited higher diversification for diploids, not polyploids (P = 10–9 exact binomial test of obtaining an outcome as extreme as 55 or more out of 63 trials; P = 10−12 one-sample t-test following a probit transformation testing whether the average fraction of MCMC steps differed from 0.5). By analogy, if one flips a coin once and gets a head, it would indeed be inappropriate to claim support for the coin being biased towards heads. However, observing 55 heads out of 63 coin flips is strong evidence that the coin is biased. Furthermore, there was no significant trend in the percent of MCMC steps showing rD > rP and tree height (from Supporting Information Table S3 of Mayrose et al., 2011a). We argue that approaches like ours that consider the preponderance of evidence across multiple clades is the best way to assess whether a trait, like polyploidy, affects diversification in a repeatable way. This multiclade approach is particularly important given recent concerns raised by Maddison & FitzJohn (2015), argue that single clades is to if there have been transitions in the trait of and by L. & E. E. Goldberg that BiSSE can have a rate when diversification Thus, significant results from a single clade must be interpreted with However, across many trait each by with is likely to support or diversification of the trait polyploidy). Because we multiple clades in Mayrose et al. (2011a), we that in one clade did not our Although our approach is as in Mayrose et al. (2011a), our result should be in many of the analyses of individual clade with which Soltis et al. (2014) concluded was not the the were interpreted in Soltis et al. (2014) because they an in Table of Mayrose et al. (2011a). In that we the which should > > and > with Fig. of Mayrose et al. (2011a). Soltis et al. (2014) that there was a but assumed that it was only in the and then interpreted this as of > were not about the and have a on the we the results from the individual using the The results are with our In clades exhibited significantly higher rates of diversification among diploids than among polyploids (i.e. > of the MCMC steps exhibited rD > using a two-tailed test to an of of the 63 clades a significantly higher rate of diversification for While we caution against conclusions about the of polyploidization in one clade the fact that the majority of MCMC steps rD > rP in one of the clades that the signal for higher diploid diversification is strong and to be This trend was in the extinction rate with clades significantly higher extinction rates in compared with that exhibited significantly higher diploid extinction rates. speciation rates differed less by with clades showing significantly higher speciation rates in polyploids and showing significantly higher speciation rates in diploids. results were obtained using the less suggested by Soltis et al. (2014) of and to an of with diploids significantly more in clades for more in clades for and a significantly higher extinction rate polyploids extinct significantly more often in The of concerns raised in Soltis et al. (2014) to the in our analyses and our of The first is that recent polyploidization events may be because many use a species that within species. species indeed, a particularly so for with In our Mayrose et al. we in level, the chromosome number as the for the species, and did not to identify species. Doing however, would have the speciation rate of diploids (from which these new polyploids and the extinction rate of polyploids many more polyploid tips on the tree would have very recently and would appear to be As out in Soltis et al. (2014), ‘most new polyploids go extinct at the before they are even By these highly ephemeral our was including is expected to an even signal that diploids diversify at higher rates than polyploids – to what was in Soltis et al. Indeed, recent analyses found this Arrigo et al., see in Supporting Information each diploid species with a polyploid and the polyploid was to species by a the terminal branch to that diploid for the genera and As expected, of these polyploid terminal taxa polyploid diversification rates and diploid diversification rates 1). of branch lengths were to the terminal taxa in Fig. net diversification rates for polyploids were lower than diploids in each of these genera and were still further by the into the This study that excluding polyploid is with respect to the conclusions of Mayrose et al. (2011a). The second raised was that we only a fraction of the genera to be The We our analyses are only a As more phylogenies are and with data, a will That said, subsequent analyses with different have similar polyploid lineages tend to diversify more In particular, Escudero et al. (2014) found that polyploid transitions towards the tips of the phylogeny and that polyploid changes less time than changes in single chromosome related criticism raised by Soltis et al. (2014) is that Mayrose et al. did not many of the most genera of plants. analyses Arrigo et al., have examined many of these genera and results with Mayrose et al. (2011a). example, analyses of and – genera noted by Soltis et al. (2014) as from our previous analyses – lower net diversification rates for polyploids than diploids 1). The of lower polyploid diversification rates is with studies using different methods The first was a of conducted in Mayrose et al. to ask whether the number of events inferred from recent analyses can be even if polyploidization does not diversification. These were with a single diploid ancestor and the number of lineages the total number of species. At each of the a species was to or go with extinction with and speciation We assumed that extinction as often as speciation = as estimated by across a of At each speciation the species was with (i.e. polyploidization evolved by with only at with to a of values from et al., to (Mayrose et al., 2011a). to the simulation results (Fig. in Mayrose et al., if polyploids and diploids diversify at equal rates, the average number of events in the evolutionary history of a single lineage is expected to be for from to These estimates are higher than the number of polyploidization events in the history of most angiosperms (Jiao et al., Thus, not only is there no to higher diversification rates for polyploid taxa in to for the number of polyploid events, but such higher rates would be with our current of the of that these is available at The second study was based on the model of & These out that the of polyploidy can be even when polyploidy is due to the of polyploid with to the diploid state. et al. (2014) the model to for diversification and polyploidization rates to on the of a then used to estimate the model for genera are with the Mayrose et al., based on of chromosome number data. the number of species at each within a as data, the study a similar diploids diversify at higher rates than polyploid due to a higher speciation rate from the diploid state via The of the using different data and the view that polyploidization does not species diversification, at related raised by Soltis et al. (2014), which we is that sampling biases may about diversification rates. In particular, if sampling polyploid species when trees or clades with polyploid groups, then diversification rates be biased. In addition, if higher such as genera, are biased with respect to polyploidy (e.g. if polyploid clades into multiple estimated diversification rates of polyploids be biases can be if but the of these biases is We to the best use of the data available at the time and to these conclusions with new data. great are the issues raised in Soltis et al. (2014) about between the data in Mayrose et al. and the As the data that we used are with the and follow the methods in Mayrose et al. The first raised about data involved chromosome in Soltis et al. (2014) that we had to polyploid taxa based on their chromosome = = the in Soltis et al., E. and = Our of chromosome (see in Mayrose et al., and these diploid of = for and as by more recent chromosome & & Because all species have diploid chromosome of = we did not of these species as polyploid to ephemeral (see Soltis et al. (2014) then their Table in which they that taxa were from Mayrose et al. (2011a). We the of these (see in as In the first of their Table Soltis et al. (2014) that we only used out of species and out of of the species of However, the analyses in Mayrose et al. were based on the number of species (see data in Mayrose et al., These from a in the used by Soltis et al. (2014) to view the tree E. Because we diversification at the species level, the of would bias the results towards a higher diversification rate for those species with Thus, we and as in the methods of Mayrose et al. (see also in Supporting while Soltis et al. (2014) did not As stated in the information of Mayrose et al. (2011a), the taxa were used only to the tree and were before our and BiSSE analyses. As in FitzJohn et al. taxa must be in to because they are not well and their diversification would not reflect that of the the estimated diversification rates of the We thus as stated in Mayrose et al. Specifically, the for and did not the in the and were for species of These were thus not used in Mayrose et al. (2011a). As in Mayrose et al. (2011a), we to species that data for one or more of the in a rather than including all species with amount of data. We further stated to be of In cases where all loci in a of many species we our to of loci that the number of species These were in the Supporting Information of Mayrose et al. (2011a). While we agree that alternative have been for example, to use all loci regardless of we this a without clade. Thus, these should not bias the relative diversification rates of diploids and polyploids In we and as In we the for (see later). Soltis et al. (2014) then clades. In the Mayrose et al. of taxa by et al. were because they were not for the of and As the taxa a number of polyploids out of Soltis et al., their have biased our results. Indeed, based on the Soltis et al. (2014) the in diversification rate was of MCMC steps with rD > in Mayrose et al., 2011a; using the vs in Soltis et al., due to a in speciation the in extinction rates was fairly of MCMC steps with > in Mayrose et al., 2011a; vs in Soltis et al., 2014). (Soltis et al., this as the of MCMC steps with but this is with their Fig. by E. Thus, a potential where a bias against polyploids led to their in our However, because the used to the Soltis et al. (2014) phylogeny and were by et al. to be and, for difficult to conclusions about must a more and In the second example, we had the chromosome for As by Soltis et al. (2014), the ancestral chromosome is by including Doing so, Soltis et al. (2014) found that support for higher diploid diversification in this clade from to of MCMC steps with rD > rP). In their example, Soltis et al. (2014) the chromosome number for the clade of by including = as an not only to the phylogeny on et al., but also to infer using (Mayrose et al., 2010). Doing so Soltis et al. (2014) to infer that a of which there were no chromosome in the were similar in chromosome number to the = and to these as diploids in Fig. in Soltis et al. and however, = chromosome for and the study that this is the chromosome number for the subsequent polyploidization in and These data are thus with the same chromosome as the the ancestral chromosome for the of the once the is would be as in our also that in the diversification of Soltis et al. (2014), the tree used multiple of polyploid species which also artificially the inferred diversification rates of polyploid lineages in Soltis et al. even if we use the as by Soltis et al. (2014), the preponderance of evidence across the 63 to support higher diversification rates for diploids out of 63 P = exact binomial Soltis et al. (2014) also differences between the of our trees and those in the they noted that most of these differences were The or trees. Because a of BiSSE is that branch lengths be to time rates be trees had to be for each from the data. To so, we a that likelihood methods to infer trees with branch lengths to time for each of the This further our data across the dozens of which we believe is a when such large-scale analyses. in our analyses we also for phylogenetic topology and relative branch by the diversification across a of trees rather than on estimates from a single inferred We no claim of for these only that they can be used for analyses that for branch was that more trees by including the sister have the if one were to study then earlier polyploid events would be and these well (e.g. all of as an would to the that the clade is with a of and higher If one were to BiSSE using these one would be the on diversification of earlier polyploid events. We such but they would not our that polyploidy events which have in the recent the for most of our tend to lower diversification rates. It is to the possibility that earlier polyploidization events may a different example, loci may have provided of and have been highly earlier of polyploidization in but no this analyses of trees. raised in Soltis et al. (2014) is that we assumed that all genera are equal in This is not, however, an of our If one to the diversification rate within one (e.g. rD of to the diversification rate within (e.g. rD of then it would indeed be that diversification rates were measured in the same of time. In our however, we compared the relative diversification rates of polyploids and diploids within a clade (e.g. rD to rP within of time are needed and the can be of age when for example, the of MCMC steps where rD > The that was used for the diversification in Mayrose et al. is available at The majority of the statistical and analytical arguments in Soltis et al. (2014) from misinterpretations of our an our and differences of about to polyploids in a comparative However, we agree with the broader point that our should not be the of the that more data are needed from a of groups, that more clades would of the and that analyses at phylogenetic evolutionary for polyploidization events earlier in evolution as phylogenetic analyses out in did not lower polyploid et al., 2014). We forward to as more data are and whether the we inferred from the 63 genera in Mayrose et al. are or are not of the fate of polyploid plants more we believe that many character state transitions a meta-analysis as in Mayrose et al., or on a single clade with many is the best available approach for the effects on diversification of traits, like polyploidy, in of its power and its relative to the data and results, we by our conclusion based on the 63 clades examined (Mayrose et al., results indicate that polyploidy is most often an evolutionary dead but the possibility remains that the potential of those polyploids that evolutionary we the is a between polyploids are always evolutionary dead and polyploids are most often evolutionary dead Because polyploidization so often & and because polyploids are with that their we should not that evolution has been by most our of the evidence to is that polyploidization is at the & and the (Mayrose et al., 2011a; Arrigo & Barker, That most are does not preclude the whether by a in or a in indeed, evolution on such We Goldberg for on the and for simulation results and the for This study was by the the and of and by a and of are not for the or of information by the than should be to the Fig. polyploid to species of clades 1). of in Table of Soltis et al. The is not for the or of information by the than should be to the for the

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