• Karel Janko

    1. Laboratory of Fish Genetics, Institute of Animal Physiology and Genetics, Academy of Sciences of the Czech Republic, Liběchov, Czech Republic
    2. Life Science Research Centre, Department of Biology and Ecology, Faculty of Natural Sciences, University of Ostrava, Ostrava, Czech Republic
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Phylogenetic studies typically demonstrate lower evolutionary ages of clones, relative to their sexual ancestors. This has often been attributed to heightened extinction risk of asexual organisms. We previously criticized such interpretations and demonstrated that the life span of clones is ultimately limited by neutral drift depending on the rate at which new clones are spawned into an asexual community of a finite size. Therefore, it is important to investigate whether the natural rates of such influxes are sufficiently high to account for the relative ephemerality of clones without assuming their increased extinction rate. I applied the neutral clonal turnover model to phylogenies of polyploid asexual ferns and simulated the coalescent trees over a wide range of demographic structures and sampling schemes. On parameterizing the model with biologically relevant estimates of population sizes and plant polyploidization rates, simulated clonal assemblages appeared younger than their sexual counterparts even in the absence of selection against clones. Therefore, differences observed between the ages of sexual and clonal lineages may be explained by the neutral clonal turnover. Researchers should consider the possibility that natural clones may get lost by neutral drift before their fate could eventually be affected by any long-term constraints of asexuality.

Despite the obvious advantages of clonal reproduction, the lack of recombination in asexual genomes is believed to cause severe short- and long-term disadvantages (e.g., mutational meltdown; Gabriel et al. 1993). Molecular phylogenetics has been used since its dawn to study relationships between asexual organisms and their sexual counterparts and to estimate the ages of clones. Ever since, the phylogenetic evidence for the terminal positions of most asexual lineages on the tree of life (reviewed in ref. Avise 2008) is considered to strongly support the existence of mechanisms causally linked to asexuality, which increase the extinction risk of clones in the long-term (hereafter referred to as “clonal decay”).

However, at least since Corley et al.'s (2001) study of parthenogenetic cockroaches, it has become clear that twiggy phylogenetic distributions of asexuals may not necessarily reflect the increase in extinction rate, which is linked to asexuality per se, but rather indicate constraints in switching to an asexual mode of reproduction (see also Schwander and Crespi (2009) for support of this neutral model through the simulated birth–death process). Hence, traditional phylogenetics may theoretically provide false positive support for the hypothesis of lower evolutionary potential of clones. Recently developed tools devoted to phylogeny-based analyses of macroevolution have been used to compare speciation/extinction rates of sexual and asexual taxa. These methods have provided rather surprising results showing either no differences between sexual and asexual lineages (Liu et al. 2012) or even higher diversification rates of asexual lineages (Johnson et al. 2011), which contrasts traditional view of asexuality as an evolutionary dead-end. Such methods, however, are only applicable at the interspecific level. Despite a lack of general agreement on applicability of species concepts and nomenclature to asexuals (see, e.g., Dubois 2011), it is clear that not all clonal organisms deserve “species-like” status and even monophyletic clusters of clonal lineages may not represent evolutionary analogues of traditionally defined sexual species (Birky and Barraclough 2009). Therefore, inconsistent definition of species-like clusters among sexual and asexual entities may seriously bias macroevolutionary analyses. It is nevertheless interesting that Fontaneto et al. (2012) applied the same DNA taxonomy approach to consistently delineate species-like clusters of sexual and asexual rotifers and found higher net diversification rates in asexual Bdelloid rotifers than in sexual Monogononts.

Different complications appear on the microevolutionary scale when analyzing the phylogeny of clones that occur in the form of so-called “sexual–asexual complexes” where new clones are produced dynamically from extant sexual parental species (or a few hybridizing ones in the case of hybrid initiation of asexuality). Given the low divergence of such clones and their origin from the same sexual species, newly recruited clonal lineages may potentially replace any of the existing ones, thus entering the same evolutionary arena for mutation, selection, and drift. Birky and Barraclough (2009) argued that such clusters of asexual individuals and their divergence from sexual ancestors are not comparable to ecological or sexual species. Therefore, the evaluation of asexuality-linked extinction rates in sexual–asexual complexes should not be based on macroevolutionary phylogenetic models (e.g., the birth–death), but rather on coalescent models (Janko et al. 2011). Indeed, Stadler (2009) demonstrated that both classes of models are not equivalent and have quite different properties in terms of tree topology.

The close relatedness and frequent coexistence of sexual and asexual counterparts makes sexual–asexual complexes attractive models for comparative studies. This paper will focus on the interpretation of phylogenies from such type of asexuals. Unless stated otherwise, the terms “phylogeny” or “phylogenetic” will be used to describe the relationships among alleles or individuals, but not among species.

Phylogenetic analyses of asexual complexes are popular, and evidence for recent origins of many clones has commonly been interpreted to represent and increased extinction rate of asexuals (e.g., Billiard et al. 2012). However, statistically sound comparisons of the evolutionary ages of closely related sexual and asexual lineages are still rather scarce and confined to some taxa only (e.g., they are almost absent in higher plants despite the frequent occurrence of asexuality in this group; Beck et al. 2011). One of the most robust phylogeny-based comparative studies of asexual complexes to date was published on Astrolepis ferns by Beck et al. (2011). The authors used relaxed molecular clock dating to estimate the divergence times of 19 auto- and allopolyploid asexual lineages from their closest sexual relatives (five diploid species in total) and compared those age estimates with the ages of the so-called “crown groups” comprising the entire genetic variability of the respective maternal sexual species (see Fig. 1, for a graphical explanation). On average, asexual lineages were seven times younger than their sexual ancestors’ crown groups, and in fact, no asexual lineage was older than its respective crown group. Although confounding effects of other traits, such as polyploidy, are difficult to distinguish (Beck et al. 2011), findings of this type are commonly interpreted as evidence of the limited evolutionary potential of asexuals and their increased extinction rate, which result from clonal decay (e.g., Beck et al. 2011; Billiard et al. 2012).

Figure 1.

Scheme of the simulation (starting at generation 0) modeling the coalescence of samples in sexual species and its asexual counterpart, both composed of two demes interconnected by migration rate m. This example of simulation starts with six sexual and eight asexual samples. New clones are recruited only from the sexual deme 2 into the asexual deme 1 (an example of clonal recruitment is indicated by arrow). The genealogies occurring in the asexual phase are indicated by solid lines whereas those residing in the sexual phase are marked by dotted lines. Clone membership of asexual samples is indicated above. For each clone, its true age as well as the indirect sympatric and allopatric age estimates are indicated along the left margin.


I do not object the primary utility of abovementioned type of age comparisons. However, it should be realized that any comparison of this type is, by definition, “unfair” to asexuals and is not informative about extinction rate of asexuals. This claim stems from the following logic. Although it is commonly assumed that new clones are more or less often generated from sexual ancestors, the reciprocal process is not possible, or at least very unlikely (Beck et al. 2011, reviewed in Janko et al. 2008, but see Domes et al. 2007). Simultaneously, all populations, including those of asexual taxa, are finite in size and hence, their genetic diversity may have a growth limit that is generally determined by the genetic drift. Janko et al. (2008) demonstrated that under a situation of unidirectional gene flow from sexual to asexual forms, the ages of individual clones are affected by the rate of the generation of new clones into finite populations and the loss of previously established clones through drift. Such a neutral clonal turnover model is, in many respects, similar to population genetic or macroecological models incorporating drift. Just as alleles are prevented from indefinite persistence by the process of neutral genetic drift, individual clones will be prevented from becoming ancient by their neutral loss as newer clones become abundant. Clonal turnover also implies several qualitative predictions about the distribution and diversity of clones: areas where new clones are recruited de novo should harbor higher clonal diversity and relatively younger clones than areas into which the clones only immigrate but may not be formed in situ.

This model has serious implications for age comparisons between clones and their sexual counterparts. Under neutral conditions, the coalescent theory predicts that the age of the most recent common ancestor (MRCA) of contemporary genetic variability in a sexual species is primarily affected by the population size, demographic history, and structure of the species. However, by analogy with the mutation–drift equilibrium model (Kimura and Crow 1964), under neutrality, the expected age distribution of clones in a population should be geometrical, with its mean determined as the reciprocal of the rate of influx of new clones into an asexual community of finite size (Janko et al. 2008). Theoretically, the apparent ephemerality of clones may result due to sufficiently high influxes of new clones into the community, even if the fitness of clones does not decay over time. Therefore, the rejection of a proper null hypothesis is required before any phylogenetic data are eventually used to invoke the long-term decay of clones.

A proposed null model of neutral clonal turnover may appear useless in light of the evidence showing that various mechanisms clearly affect sexual and asexual genomes differently (e.g., Paland and Lynch 2006). Yet, it was no later than the 4th century B.C. that the Chinese sage Chuang Tzu warned against ignoring the putative useless, suggesting that “if we have no appreciation for what has no use, we may not talk about what can be useful” (Waley 1939). This concept of the “usefulness of the useless” (Leigh 2007) has been widely employed by macroecologists and population geneticists by implementing neutral theories as suitable null models. I find it unfortunate that in ignoring such issues, phylogenetic studies of asexual organisms leave the critical question unanswered: are any particular long-term disadvantages of asexuality needed to explain the fact that asexual clones appear to be short-lived compared to their sexual progenitors?

Janko et al. (2008) introduced the clonal turnover model as a theoretical null hypothesis for the distributions of clonal ages but two issues prevented the application of this model to real datasets. First, empirical estimates of clonal recruitment rates are often unavailable making it difficult to parameterize the neutral model. Therefore, it is unclear whether values used derive the theoretical null distribution of clonal ages are biologically relevant. Second, Janko et al. modeled only the distribution of “true ages” of simulated clones (i.e., the ages since the actual switch from sexual to asexual mode of reproduction; see also Fig. 1, for graphical explanation). However, such parameter is not equivalent to indirect estimates of clonal ages derived from phylogenetic data. In reality, clonal ages are estimated indirectly either through the magnitude of sequence variation within the monophyletic clonal lineage (as in, e.g., Janko et al. 2005), or through the divergence between asexuals and their closest sampled sexual relatives (as in, e.g., Paland et al. 2005; Beck et al. 2011). Although the former approach may lead to more or less serious underestimates (Butlin 2002; Avise 2008), the latter one is biased upward. This is because the genealogies of sampled clonal lineages spent only a fraction of their time in an asexual phase (corresponding to the true age of the clone), whereas the remaining part of the genealogies’ time were spent in the sexual phase before coalescing with the closest sexual lineage (see Fig. 1, for a graphical explanation). The distributions of true ages of clones may dramatically differ from indirect estimates depending on demographic history of studied taxa and on sampling effort.

In this article, I correct both shortcomings of our previous study. First, I demonstrate that neutral clonal turnover may be applied also to indirect clonal age estimates by studying their behavior under a range of population structure scenarios and sampling schemes. Second, I apply the neutral model to asexual polyploid ferns (Beck et al's 2011 data), where tight association between asexuality and polyploidy makes it possible to estimate the recruitment rate of clones. Having parameterized the model with effective sizes of Astrolepis populations and reported values of polyploidization rates in plants, I show that the simple neutral model may explain the phylogenetic data of asexual complexes without the need to imply clonal decay.

Materials and Methods


The coalescent simulation extended the model of Janko et al. (2011) and its scheme is given in Figure 1. To evaluate the effects of geographical structure, both sexual and asexual taxa were assumed to be structured into two regions/demes interconnected by a migration rate “m,” each with a population size of N females. Although asexual and sexual demes may or may not geographically overlap, I here modeled each deme as a separate entity. I assumed that population sizes of sexual and asexual components were constant as if there was no competition between both types. This is reasonable simplification given that it greatly narrowed the parameter space of model, although I was not interested in testing any particular mechanisms for sexual–asexual coexistence. Furthermore, Hellriegel and Reyer (2000) showed that even under the competition model, the ratio of sexual and asexual components (and hence, their relative population sizes) may remain stable over wide interval of simulated parameter values. As in Beck et al. (2011), I assumed that sexual individuals may occasionally produce asexual progeny at a rate of “c,” but that sex may not re-evolve from asexuals. To study the effect of geographical structure on clonal age estimation, I further assumed that new clones were recruited only into asexual deme 1, which is hereafter referred to as the source, whereas the asexual deme 2 (sink) was populated only by those clones dispersing from the source deme. Analogously, the sexual deme 2 may be referred to as “sympatric,” because it is only from this deme that new clones are recruited, whereas first sexual deme will be referred to as “allopatric.”

I assumed a fully neutral model with no selection against or among clones, and simulated the coalescent process backward in time, starting with 10 samples (terminal nodes) in each deme. Assuming nonoverlapping generations, any two nodes that simultaneously co-occurred within the same deme could have coalesced with a probability inversely proportional to population size. Looking backward in time, any lineage could have immigrated to its actual deme with a probability m. Furthermore, there was a constant per-generation probability (c) that any existing clonal lineage residing in asexual deme 1 was “born” from deme 2 of the sexual ancestor. When such an event happened, the given asexual genealogical lineage switched its location from asexual deme 1 to sexual deme 2 and it was considered to be a founder of a particular clonal lineage. In that case, all asexual nodes belonging to this genealogical lineage were considered to be members of the same clone (Fig. 1). Clones are thus defined sensu Martens et al. (2009), that is as all descendants of a unique founder derived from sexual ancestor.

The simulation continued until all genealogies coalesced into a single node.


During each simulation run, I recorded the crown age of the entire sexual species sensu (Beck et al. 2011).

To evaluate the effect of upward bias inherent in estimating the age of clone through its divergence from closest sexual sample (Beck et al. 2011), I recorded and compared the following data for each clonal lineage (Fig. 1): (1) the direct record of the true age; (2) the indirect estimate based on divergence from the nearest sexual relative sampled in the geographically adjacent sexual deme. This estimate, referred to as the sympatric age estimate, was defined as the age of the node connecting a given clone to its genetically closest sample from the sexual deme 2. (3) the indirect estimate based on divergence from a closest sexual relative in the allopatric sexual deme, referred to as the allopatric age estimate. The latter measure simulates a situation in which the actual parental population of the sexual species is not sampled.

Results and Discussion

I ran the simulations under varying N, m, and c values with 100 replications for each combination of parameter values. The results of the simulation are intuitive (Fig. 2). The crown age was primarily determined by sexual population size as well as its structure, being proportional to N (Fig. 2A vs. 2B and 2C vs. 2D) and inversely proportional to m (Figures 2A vs. 2C and 2B vs 2.D). However, the true ages of clones depended primarily on c, as shown previously (Janko et al. 2008; Fig. 2A, B). For simplicity, population sizes of sexuals and asexuals were kept equal in the simulation. Note, however, that per-generation number of newly recruited clones is given by the product of sexual population size (Nsex) and c. Hence, if populations are unequal, the influx of new clones into asexual community would correlate with Nsex/Nasex. The average age of clones would thus be inversely correlated to that ratio.

Figure 2.

Distribution of age estimates of simulated clones and sexual crown groups. Upper panel: The distribution of true ages of simulated clones as a function of c when N = 1000 (A) and N = 10,000 (B). For each population size, the distribution of the crown age is indicated in the right. Middle panel: The comparison of true ages of simulated clones to indirect sympatric and allopatric age estimates. N = 1,000 (C) and 10,000 (D), other parameter values are identical. For each population size, the distribution of the crown age is indicated in the right. Lower panel: The distribution age estimators of simulated clones under parameter values putatively applicable to Astrolepis. Nm = 1 (E) and 0.1 (F). The crown age distribution is indicated for each Nm plot. For each age estimator, the percentage of simulations when all clones from given run of simulation appeared younger than the respective crown group is indicated below the box plot.

It is worth noting that under the current parameter settings, the mean age calculated over all clones in both demes was relatively less affected by m (comparing Fig. 2A vs. 2C and 2B vs. 2D). This is because the strong population subdivision (i.e., small m) caused that the sink deme harbored very low number of clones (usually a single clone) whose increased ages were effectively offset by many more recent clones in the source deme.

As expected, the two indirect age estimators were biased upward compared with the true age (Fig. 2C, D). The level of upward bias in sympatric estimate correlated with the population size of the sexual species being small in small populations when asexual genealogies spent a relatively small fraction of time in the sexual phase before coalescing with their genetically closest sexual lineage. The allopatric estimate was subject to even stronger upward bias that correlated with m.

The relationship between clonal age and sexual crown age was determined by an interplay between the above-mentioned processes. When populations were small relative to c (e.g., Fig. 2A, C), the ages of clones predated the coalescence of complete sexual variability. Under such conditions, the entire clone community tended to appear monophyletic relative to sampled sexuals, and naturally, there were no differences between sympatric and allopatric clonal age estimates (Fig. 2C). With higher N and/or c, asexual genealogies became embedded within sexual genetic variability, and hence, the crown group attained higher ages than at least some of the clones (Fig. 2B–F). In such situations, differences between sympatric and allopatric estimates became relevant (Fig. 2D). Under sufficiently large N and/or c (Fig. 2E, F), all types of age estimates of observed clones were significantly lower than the crown ages. Ultimately, the differences between estimated ages of clones and their sexual progenitors may reflect sampling effort as well as the demographic structure and stochastic turnover rates of clones even when there is no selection against clones.


Deciding whether observed age distribution of clones deviates from neutral expectations is difficult because neutral and nonneutral models result in similar qualitative predictions (Janko et al. 2008). Nevertheless, one may parameterize the model using empirical estimates of population sizes and rates of natural clonal formation to test whether neutral models fits observed differences between age estimates of sexual and clonal lineages.

The rate of clonal recruitment is a difficult parameter to evaluate. Phylogeny-based inference was usually used to estimate only the minimum number independent origins of clones, which probably greatly underestimates their actual number and recruitment rates. Indeed, in some taxa, successful establishment of clonal strains are extremely rare or even represent a unique event in the group's evolutionary history (Stöck et al. 2010). However, there are asexual taxa where comprehensive model-based analysis of genetic diversity indicated ongoing formation of clones implying high rate of new clone formation (e.g., Janko et al. 2012); the actual clonal recruitment has even been observed under laboratory conditions in some cases (Schultz 1973; Choleva et al. 2012). To my knowledge, no relevant estimates of the rate of clonal recruitment rate are available for asexual complexes in general. However, focusing on Astrolepis, I take advantage of the tight linkage between asexuality and polyploidy. As a reasonable value, I use the empirically estimated rate of plant polyploid formation, which was calculated by Ramsey and Schemske (1998) based on the rate of formation of unreduced gametes and from the contribution of the triploid block sensu Marks (1966). Ramsey and Schemske (1998) estimated rates of autotetraploid formation via the triploid bridge around 7.14 × 10−5 for selfing and 3.32 × 10−5 for backcrossing. The latter value is more relevant to outcrossing Astrolepis (Beck et al. 2011).

Estimating the population structure and size of sexual species is more straightforward. Because Beck et al. analyzed only few specimens per species, which prevents the detailed phylogeographic analysis, I applied the two-deme model to their data and studied the coalescence patterns over wide range of migration rates. I estimated the population size using the following calculation: since Astrolepis laevis was sampled by Beck et al. (2011) in the highest number of specimens (n = 7), I downloaded their sequences from the GeneBank (FN565519, JF929964–67, JF929973–74) and calculated Watterson's estimate of θ using DNAsp version 5 software (Librado and Rozas 2009); because sequences concerned maternally transmitted plastid DNA, θ = 2Nf × μ, where Nf stands for effective number of females and μ is the mutation rate. Using this estimate, I obtained a θlaevis of 0.00481. To translate θlaevis into absolute numbers, I estimated the actual μ from the mean nucleotide divergence (π) between A. laevis and Astrolepis obscura using the Mega version 4.0 software (Kumar et al. 2004) and divided it by the species’ mean divergence time, 3.9 Mya, provided by Beck et al. (2011). Using the TrN+G model for sequence evolution selected with the jModeltest (Posada 2008), π = 0.0336, which results in μ = 8.6E−09 and Nf = 279,000. Estimating the population size of asexual populations is much more difficult, however. When an asexual population is composed of multiple independent clones, only a portion of its genetic variability has been affected by processes affecting asexuals, while the remaining genetic variation is “frozen” from its sexual ancestor (e.g., note that in Fig. 1, a large part of the genetic differentiation between clones 1–3 is spent in the sexual phase). For simplicity, I assumed that sexual and asexual populations were of equal size and substituted the population size and recruitment rates calculated above into the model.

With c = 3.32 × 10−5 and Nf = 137,000 (summing up to 279,000 sexual individuals in both demes together), I found that all types of age estimates of simulated clonal lineages were significantly lower than their respective sexuals’ crown ages under all simulated migration rates (Wilcoxon–Mann–Whitney test, P ≪ 0.01 in all cases; see Fig. 2E, F). In fact, regardless of the method of age estimation adopted, when Nm = 1, all clones, including those in the sink deme, appeared to be younger than the sexual crown groups in 61% of simulations. There was still about one third of simulations with this result, when populations were connected by as few as 0.1 migrants per generation, which is close to the lower limit for species cohesiveness (Rieseberg and Burke 2001).

Hence, provided the assumptions and parameterization of the present model were realistic for Astrolepis, there is a reasonable chance in observing all five sampled crown groups being older than all their clonal derivatives due to neutral clonal turnover alone and there is no need to invoke the long-term disadvantages of asexuality to explain current observations.


Phylogeny-based analyses of asexual complexes almost obligatorily conclude that the observed short-livedness of clones indicates their decay in the long term. Usually, however, such comparative studies do not consider the bias in unidirectional gene flow between sexual and asexual forms. In fact, the observed patterns often do not deviate from the predictions of simple neutral clonal turnover (Janko et al. 2008): clonal diversities are usually higher in areas where asexuals occur in close vicinity to sexual progenitors (sources), whereas the clonal ages are higher in sink areas; older clones also tend to be more geographically widespread than the more recent clones. This study demonstrates that phylogeny-based comparisons of the ages of sexual and asexual clades should not be automatically considered as a proof of clonal decay. Unless neutral evolution could be rejected, it is desirable to assume the neutral clonal turnover because it incorporates less parameters (i.e., is more parsimonious) than models incorporating the clonal decay. Of course, the ultimate interpretation depends on particular design of the model. Ideally, an appropriate null model may closely match the phylogeographic structure of a studied complex and the patterns of the birth of clones from sexual demes. However, the model should be simple enough to allow analytical tractability. For example, a relatively simple two-population model of isolation with migration was proven to be quite robust against moderate violations of its assumptions (Strasburg and Rieseberg 2010).

Although small sample sizes of Astrolepis prevented formulation of complex phylogeographic hypotheses, a simple two-deme neutral model offered a plausible explanation for differences between sexual and clonal ages, implying an interesting interpretation: the influx of new clones may be strong enough to ensure that the existing clones do not have time to degenerate through mutational meltdown and disappear owing to neutral drift alone. It follows that the life spans of clones (and hence the differences between ages of related clonal and sexual lineages) may be largely independent of any long-term disadvantages of asexuality. This indicates the crucial importance of studying the rates of clonal recruitment to understand the evolution of asexuality.

Janko et al. (2011) showed that discriminating between the neutral and nonneutral alternatives might be made easier by analyzing the mutation frequency spectra on sexual–asexual phylogenies. The authors extended previous coalescent models of clonal organisms (Gordo et al. 2002) and studied the evolution of genetic variability of asexual populations composed of multiple clonal lineages. They proposed a method to reduce the confounding effects of genetic variability that is “frozen” from sexual ancestors and showed that Muller's ratchet predictably distorts the genealogies in such polyclonal populations. Reanalysis of published phylogenies of animal asexual complexes showed that the asexual pedigrees often did not significantly deviate from neutrality but in general, the deviations from neutrality were progressively stronger in asexual taxa with relatively old clonal lineages. This is in contrast to the patterns expected from the available population models, which predict strongest deviations from neutrality in those complexes where intensive mutational decay and/or turnover of clones prevent the clones from becoming ancient. Such a discrepancy further highlights the need to ameliorate the conceptual framework for understanding the dynamics of clonal appearance and loss before making any conclusive interpretations.

In particular, it is important to discern whether the observed clonal ages reflect the equilibrium between origination and extinction (as implied in the clonal turnover model) or whether such an equilibrium had not yet been reached. In the latter case, the clonal ages would provide information about the initial period when the sex was lost in the studied taxon but would not be largely informative about the evolutionary potential and maximum life span of asexual lineages [Janko et al. (2011)]. I would like to encourage researchers to invest their efforts in developing more robust methods in order to identify clonal decay from the observed mutation-frequency spectra, which seems more promising than the qualitative analyses of clonal ages for discriminating between the neutral and nonneutral models.

In any case, this study demonstrates that neutral model of clonal evolution is useful in understanding why clonal lineages appear ephemeral and should be taken into account when analyzing asexual phylogenies.


I am thankful to E. Jankova-Drdova, P. Drozd, and J. Kotusz for inspiring comments on this manuscript. I am also obliged to three anonymous referees as well as both editors of this paper, whose comments lead to considerable improvement of the text. The work was supported by grant no. 13-12580S provided by the Czech Science Foundation (www.gacr.cz). Further support was provided by the Academy of Sciences of the Czech Republic (www.cas.cz) by the grant no. RVO 67985904.