Abstract
Background
Demographic bottlenecks can severely reduce the genetic variation of a population or a species. Establishing whether low genetic variation is caused by a bottleneck or a constantly low effective number of individuals is important to understand a species’ ecology and evolution, and it has implications for conservation management. Recent studies have evaluated the power of several statistical methods developed to identify bottlenecks. However, the false positive rate, i.e. the rate with which a bottleneck signal is misidentified in demographically stable populations, has received little attention. We analyse this type of error (type I) in forward computer simulations of stable populations having greater than Poisson variance in reproductive success (i.e., variance in family sizes). The assumption of Poisson variance underlies bottleneck tests, yet it is commonly violated in species with high fecundity.
Results
With large variance in reproductive success (V_{k} ≥ 40, corresponding to a ratio between effective and census size smaller than 0.1), tests based on allele frequencies, allelic sizes, and DNA sequence polymorphisms (heterozygosity excess, Mratio, and Tajima’s D test) tend to show erroneous signals of a bottleneck. Similarly, strong evidence of population decline is erroneously detected when ancestral and current population sizes are estimated with the model based method MSVAR.
Conclusions
Our results suggest caution when interpreting the results of bottleneck tests in species showing high variance in reproductive success. Particularly in species with high fecundity, computer simulations are recommended to confirm the occurrence of a population bottleneck.
Keywords:
Conservation; Heterozygosity excess; Mratio; MSVAR; FPR; Sweepstakes reproduction; Type I error; Variance in reproductive successBackground
Demographic fluctuations, including changes in population size and growth rate, are common events in natural populations. Severe population size declines (bottlenecks), however, may have detrimental consequences including increased inbreeding, decreased adaptive potential, increased disease susceptibility, lowered fecundity, and disruption in expression of quantitative traits [13]. As bottlenecks often affect longterm fitness and population viability, or change the balance of drift and selection, they are key events in a species' evolutionary history, and a principal concern for endangered species [4].
Bottlenecks may leave a population genetic signature, such as decreases in number of alleles and heterozygosity, and loss of rare alleles [5,6]. These signatures can be easily detected when temporal samples are available (e.g. museum specimens or fossil remains), so that contemporary genetic variation can be compared to historic levels. A bottleneck, however, may also leave specific signatures in current genetic variation, distinct from those in populations having a history of small and constant size. Indeed, several methods for detecting genetic bottlenecks in the absence of information about historical sizes and in absence of prebottleneck genetic samples exist [710]. Genetic methods for bottleneck detection are useful because: (1) historical (and current) census sizes are rarely known; (2) even when census size (N_{c}) is known, cryptic bottlenecks (change in effective size, N_{e}, without change in N_{c}) may occur; and (3) bottleneck outcomes are highly stochastic, meaning that genetic diversity following the bottleneck is somewhat unpredictable even when the demographic history is known [11,12]. It is therefore important to evaluate the statistical performance of these methods, especially as these tests are key components of many evolutionary, molecular ecology, and conservation genetic studies [1316].
Previous investigations have demonstrated that the statistical power of these tests is highest when the bottleneck is severe or prolonged, and when many loci are used. In addition, factors such as the mutation model and the rate of postbottleneck recovery may also play an important role [9,13,1618]. Also, the methods do not always show similar power. For example, the heterozygosity excess test [9] has low power after rapid recovery [17] whereas the Mratio test [10] remains effective, and the heterozygosityexcess test is weak unless the population is reduced to some tens of individuals [19]. Bottleneck signals are also weakened if the bottleneck occurred gradually, or if the population recovered to its prebottleneck population size [16]. Numerous empirical studies have failed to detect a genetic signal even when a moderate or strong demographic bottleneck is known to have occurred [4,11,20], showing empirically that the power of such tests can be limited.
A lack of statistical power in bottleneck tests may result in an underestimation of the extinction risk. On the other hand, identifying bottleneck signatures when they have not occurred may represent a complementary risk [18,21], yet this remains an often overlooked aspect of studies employing these methods. Controlling type I error rate (FPR, False Positive Rate) is important, particularly given that resources towards conservation tend to be limited [22]. Type I error could result in incorrect population protection status or unwarranted, ineffective, or even detrimental insitu management interventions (e.g., translocations, augmentations). Therefore, an understanding of type I error in realistic situations is essential to properly use and interpret results from these methods.
Investigations of type I error of bottleneck detection methods are few, and have mostly concerned mutation models in microsatellite markers. For example, the probability of type I error can be substantial or extreme (from 40 to 100%) when the wrong mutation model is assumed or when multistep mutations occur [21]. Also, assuming the wrong populationmutation parameter theta (θ = 4N_{e}μ, where μ is the mutation rate) in the Mratio test may result in either type I or type II errors, depending on whether the assumed θ is larger or smaller than the actual value [23]. Remarkably, in spite of frequent use of bottleneck tests, and the conservation decisions that are based on them, little is known about their type I error rates when assumptions of the biological model are violated. For example, the influence of mating patterns [13], age structure [14], and reproductive success [21,22] is rarely known.
Here we focus on type I error rates that may arise in bottleneck tests when the variance of reproductive success (hereafter V_{k}) is larger than the Poisson variance assumed by simple models underlying the bottleneck detection methods. Larger than Poisson V_{k} could cause strong intergenerational genetic drift, because it introduces additional stochasticity (e.g. unaccounted loss of alleles) when only few parents contribute to the next generation [24]. When extreme, this process has been referred to as Sweepstakes Reproductive Success (SRS), in which many individuals “lose” and produce zero or very few offspring, while one or a few individuals "win" and produce many offspring [25,26]. Such extreme reproductive variance can be caused by complete or nearcomplete dominance of one pair, or positively correlated sibling survival, in which all offspring of a particular brood survive or perish [24,25]. Variance can also be extreme when only one male contributes offspring [12]. Large V_{k} reduces the N_{e}/N_{c} ratio, which may explain N_{e}/N_{c} in the order of 10^{2}  10^{3} observed in many amphibians, fish, marine invertebrates, and plants. Even more extreme N_{e}/N_{c} ratios, as low as 10^{3} to 10^{5}, have been reported for lobster, cod, red drum, and oyster [27]. “Chaotic” genetic differences at small geographic scale and at different time intervals often observed in marine organisms has been explained as relating to high V_{k}[26].
Theoretically, the relationship between V_{k} and the N_{e}/N_{c} ratio has been derived under different models [25,28,29], and hence, an increase in V_{k} can be converted into a predictable reduction in N_{e}. However, the effect of V_{k} on the shape of a coalescent tree and on the relationship between different genetic diversity measures (which are the basis for bottleneck testing) have not been investigated [27]. In particular, it remains to be elucidated whether analysis of genetic data from species with large V_{k} will show signature of small but constant size, or whether large V_{k} results in a false signal of a genetic bottleneck. Here we investigate this question for different combinations of N_{e} and V_{k} values, using simulated data to estimate type I errors in two tests commonly applied to microsatellite data to detect bottlenecks, the Mratio [10] and the heterozygosity test [9], and when ancestral and current population size are estimated to infer bottlenecks with the MSVAR method [7]. We also consider the effects of V_{k} on the Tajima’s D test [30], which is used to detect selection as well as deviations from demographic stability in DNA sequence polymorphisms. All these tests assume stable populations with Poissondistributed family sizes, i.e. V_{k} = 2.
Methods
Genetic variation data were generated by simulating demographically stable populations with different effective size (N_{e}) and different variance in reproductive success (V_{k}). For each combination of parameters, 100 replicates were generated. Each data set, consisting of 15 microsatellite markers, was analysed with the Mratio and the heterozygosity excess tests, and with the MSVAR method. The fraction of replicates significantly supporting a bottleneck can be considered as an estimate of the FPR (false positive rate), i.e., the type I error rate. Then a smaller set of simulations was used to analyse two additional markers (microsatellite loci with constrained allelic range and DNA sequence polymorphisms).
Generating the primary set of synthetic data
The software simuPOP [31] was used to generate the virtual data. simuPOP is an individualbased, forwardintime simulator that uses the flexible scripting language Python to allow operators that control sex ratio, number of offspring produced etc., and is one of few simulators to allow such options [32]. Random mating of individuals and family sizes with different distributions (i.e., V_{k}) can be simulated straightforwardly. We analysed 16 combinations of N_{e} (50, 500, 2500 and 5000) and V_{k} (2, 40, 400, and 2000). Population size was assumed to be constant, and the mean number of offspring per mating was always equal to two. In order to obtain the same N_{e} for different V_{k} values, the census sizes required in the simulations were computed using the approximate relationship N_{e}/N_{c} = 4/(V_{k} +2) [25,33]. When V_{k} =2, family sizes were Poisson distributed (as assumed by most population genetics models) and the ratio N_{e}/N_{c} =1. For larger V_{k}, we used a modified gamma distribution of family sizes with decimal values rounded down to the nearest integer (resulting in a discrete distribution approximating a negative binomial, Figure 1). This choice allowed us to maintain the average number of offspring per mating equal to two while producing a long right tail in the distribution. The V_{k} values of 40, 400, and 2000 correspond approximately to N_{e}/N_{c} equal to 0.1, and 0.01, 0.002, respectively.
Figure 1. An example of the distribution of offspring per parent in the simulations. The three panels correspond to the distributions obtained in simulations with V_{k} =2 (top), V_{k} = 40 (middle), and V_{k} = 400 (bottom).
Fifteen neutral, independent microsatellites evolving under a strict stepwise mutation model with mutation rate μ=5×10^{4} were considered. Mutationdrift equilibrium was obtained by running simulations for N_{e} generations, starting from individuals with a Dirichelet distribution of allele frequencies. After verifying that the population had reached a stable equilibrium confirmed by the convergence of the number of alleles (K), the expected heterozygosity (H_{e}), and the inbreeding coefficient F_{is}, 50 individuals were randomly sampled and analysed using ARLEQUIN v3.5 [34] for the summary statistics noted above, the Mratio and the Tajima’s D tests, and using BOTTLENECK v.1.2.1 [9] for the heterozygote excess test, and MSVAR v. 1.3 for the estimation of current vs. ancestral population sizes [7].
Additional simulations
Some specific situations were investigated using additional simulations. First we simulated microsatellite markers where the maximum number of alleles is limited to five, to represent expressed (EST) microsatellites which tend to have a limited allelic range; a restricted allele range may affect the Mratio. Second we simulated DNA sequences of 500 base pairs evolving under an infinite site mutation model with mutation rate μ=10^{7} per site per generation. These simulations were conducted to understand whether the spurious signal of a bottleneck produced by V_{k} > 2 is specific to microsatellites markers, or whether a similar signal would be found when Single Nucleotide Polymorphisms (SNPs) are considered.
Bottleneck tests
Microsatellite data was analysed first with the commonly used Mratio test [10] and heterozygosity excess test [9]. The Mratio test is based on the frequency distribution of allelic sizes, which is expected to have gaps after a bottleneck due to stochastic loss of rare alleles. The Mratio is computed in each data set as simply the ratio of the number of occupied allelic states divided by the number of possible allelic states (e.g. the range). Evidence of deviation from the null hypothesis of demographic stability can be concluded in one of two ways: if the observed value is lower than a simple threshold criteria (Mratio < 0.68 [10], which is widely used as a “rule of thumb” in conservation genetics) or if the observed value is lower than a critical value, determined by reconstructing the null distribution of M using 1000 coalescent simulations. The coalescent simulations used to generate this null distribution assume by definition V_{k} = 2. Also we set the parameters N_{e} and μ to the values used in producing the corresponding data sets. Throughout the paper, we will call Mratio_{ft} test the approach based on the fixed threshold, and Mratio_{sim} test the approach that uses simulations to compute the critical value. The heterozygosity excess test is based on a relationship between heterozygosity and number of alleles, which is predicted to deviate from theoretical expectations after a bottleneck because the former decreases more slowly than the latter. Statistical significance for this test is computed using the Wilcoxon’s signed rank test to compare the expected heterozygosity calculated from the data (H_{e}) to an expected heterozygosity based on the number of alleles present (H_{a}) [9], where H_{a} is computed by simulation using the program BOTTLENECK [35].
We performed also a more sophisticated analysis which is frequently used to detect changes in population size [7]. This analysis uses a fulllikelihood modelbased approach called MSVAR to infer current and past population sizes as well as other parameters. The method can be used to infer a bottleneck if the ratio of past to current population size is significantly greater than unity. From each MSVAR analysis, the posterior distribution of the ratio between ancient and current population sizes was estimated, and the data set was considered to support the bottleneck hypothesis if less than 5% of this distribution was smaller than 1. For each data set (1600 in total), we recorded the MCMC (Monte Carlo Markov Chain) output 40,000 times every 10,000 steps. The first 10% of steps were discarded as burn in. Means and variances for priors and hyperpriors are reported in the legend of Table 1. In some cases this approach has been shown to be more powerful than the simpler statistics explained above [11], but it also relies on more assumptions (a particular demographic model).
Table 1. Simulation results for a population with constant size and standard microsatellite mutations
DNA sequences were analysed with the Tajima’s D test [30], which is based on the comparison between the average pairwise difference (π) and the number of polymorphic sites (S). If equilibrium is not reached after a demographic event, negative D values are expected under population expansion and positive D values are expected under population decline [30]. Tajima’s D is commonly used also to detect deviation from neutrality, i.e. the impact of selection on DNA sequences. Statistical significance is computed by simulations, as implemented in Arlequin [34].
Results
Primary set of simulations
As expected, the average level of genetic variation (expected heterozygosity, H_{e}, and number of alleles, K) increased with increasing N_{e}. The average H_{e} observed for V_{k}=2 is similar to theoretical predictions [36] which are 0.09, 0.42 and 0.78 for N_{e} values 50, 500, and 5000. The number of alleles does not have a simple expectation under the singlestep mutation model, but the observed values are compatible with other results [37]. When V_{k} increases, we observe a trend of decreased genetic variation within each set of simulations with the same N_{e}, and this effect is stronger for K than for H_{e}. For V_{k} > 2, populations also appear to deviate from the HardyWeinberg equilibrium, with larger observed than expected heterozygosity and consequent negative values of the estimated inbreeding coefficient.
The false positives rate (FPR) clearly increases with V_{k}. With V_{k}=2, FPR for the Mratio_{ft} test is either 1% or 0% (indicating probably that this criteria is too conservative) and it varies between 2% and 9% using the Mratio_{sim} test. For the heterozygosity excess test, the FPR with V_{k}=2 is around the nominal 5% or less, and varies between 0% and 14% for the MSVAR analysis (this analysis being more permissive with large values of genetic variation). Very different results are obtained for V_{k} > 2 (Table 1 and Figure 2), especially for N_{e} equal or larger than 500 (i.e., when level of polymorphisms is not too low). All or almost all replicates analysed with the Mratio_{sim} test or with the MSVAR analysis support a bottleneck when V_{k} ≥ 400 and N_{e} ≥ 500. When the more conservative Mratio_{ft} test or the heterozygosity excess test are applied, the FPR decreases, but never below 21%. For V_{k}=40, i.e., when the ratio between effective and census size is equal to 0.1, FPR can reach values as high as 93% or 97% in the Mratio_{sim} test and the MSVAR analysis, respectively. Furthermore, we observe a general trend of FPR to increase with N_{e} (Table 1 and Figure 3). This pattern, likely related to the overall level of genetic variation available for the tests and to the ratio between the sample size and N_{e} (which is decreasing when N_{e} increases), deserves further investigation. In summary, with high variation in reproductive variance, the Mratio and heterozygosity excess tests produce many false positives, and the probability to detect a spurious bottleneck signal tends to increase with increasing effective population size. MSVAR results are in general similar to those obtained with the Mratio_{sim} test.
Figure 2. The false positive rate (FPR) as a function of the ratio N_{e}/ N_{c}under different statistical approaches. FPR refers to simulations with N_{e} = 2500.
Figure 3. The false positive rate (FPR) as a function of the effective population size N_{e}under different statistical approaches. FPR refers to simulation with V_{k} =40.
Additional simulations
Constrained allelic size – Simulations with Ne=500 and V_{k}=2 or 400. When microsatellite alleles exhibit strong size restrictions (only 5 alleles with adjacent number of repeats are possible), the fraction of false positives for the heterozygote excess test increased from 1% to 47% when V_{k} was increased from 2 to 400. This increase in FPR is similar to that observed in the simulations with sizeunconstrained loci. However, none of the replicates with high V_{k} with constrained loci produced small and significant Mratios. The likely explanation is that a reduced allelic range prevents the opening of gaps in the allelic size distribution. In other words, the Mratio test does not tend to suggest a false signal of a bottleneck when analyzing sizeconstrained EST microsatellites.
DNA sequence polymorphism  Simulations with N_{e}= 500 and V_{k}= 400. The Tajima’s D distribution, centered around 0 for V_{k} = 2 in case of constant population size and absence of natural selection, is shifted towards positive values, with a mean of 1.24. The FPR, i.e. the fraction of values significantly larger than 0, is 37%. Thus, the Tajima’s D statistics is similarly affected by an increased variance in reproductive success, and would frequently support a population decline or balancing selection when V_{k} >> 2.
Discussion
In many organisms with high fecundity, the contribution of each individual or pair to the next generation can be highly skewed, with few “winners” (i.e. those who produce many offspring) and many “losers” who do not contribute to the gene pool of the next generation. Under this scenario of Sweepstakes Reproductive Success (SRS) [38], the variance in reproductive success (V_{k}) is larger than assumed by the WrightFisher model. Population genetics theory predicts that the ratio of N_{e} (the effective population size) over N_{c} (the census population size) rapidly decreases from one as V_{k} increases. The SRS model is thus considered a likely explanation for the empirical observation that many marine organisms have much lower genetic variation (and therefore N_{e}) than predicted by their very large N_{c}[39].
While the negative relationship between genetic variation and V_{k} is well known, the effect of V_{k} on the gene genealogy shape reconstructed from a sample of DNA fragments is yet unclear. It is possible that large V_{k} values may introduce distortions in this genealogy, in turn distorting the relationships between genetic variation measures. This is relevant as many statistical analyses for identifying deviations from neutrality and demographic stability assume V_{k}=2 and are based on the relationships between genetic variation measures.
We addressed this question by comparing simulated datasets of single populations with different V_{k} values. Specifically we estimated the impact of large V_{k} on the results from four statistical tests commonly used to detect population size variation: the Mratio test, the heterozygote excess test, a test derived from a Bayesian estimate of ancient and current population sizes, and the Tajima’s D test. Conceptually, when these tests are applied to neutral markers, the null hypothesis includes demographic stability, no migration and V_{k}=2. Rejection of this hypothesis may be interpreted as population decline, but may be also due to large V_{k} in isolated, demographically stable populations. This is relevant in conservation genetics as violation of the assumption of low V_{k} made by these tests can produce incorrect inference, and may suggest incorrect management interventions.
Our simulations show that high V_{k} can strongly increase the rate of false positives (FPR = type I error = incorrect inference of population decline) for all the tests. Further, the larger V_{k}, the larger the rate. FPR is also dependent, to some extent, on N_{e} (and thus the level of genetic variation), but this relationship appears testspecific. Based on our results, it appears that the MSVAR method is most prone to errors, followed by the Mratio with the critical threshold computed by simulations (Mratio_{sim}). The heterozygote excess and Mratio with the traditional threshold are less prone to false positives when V_{k} is large and may be preferred for use, if the goal is to reduce type I errors when evidence of large V_{k} is available. The results we obtained show also that high V_{k} could cause wrong conclusions when the aim of the analysis is to identify signatures of selection. In particular, the negative F_{is} values and positive Tajima’s D produced in our simulations of neutral markers with large V_{k} could be misinterpreted as signals of balancing selection.
When V_{k} is large, a large fraction of siblings is observed every generation. In coalescent terms, several lineages merge in one generation going back in time, producing many short external branches in the gene genealogy and therefore a deviation from the standard Kingman coalescent [27,28]. Allele sharing among individuals will be high and alleles present in one (singletons) or few (rare alleles) individuals will be very low. Considering that bottleneck tests assume the standard Kingman coalescent, or the WrightFisher model it approximates, we propose that the excess of short external branches and corresponding deficit of rare alleles could explain the large FPR. In fact, this situation is expected to result in (a) higher heterozygosity than expected based on number of alleles (and thus positive heterozygote excess test and an overall signal of population decline detected by MSVAR), (b) gaps in the microsatellite allele size distribution (and significant Mratio test) and (c) loss of segregating sites but not substantial reduction in the average pairwise difference (and positive Tajima’s D). We also note that the fraction of siblings and the rate of multiple coalescent events rapidly decreases going back in time (since few lineages survive, additional simulation results not shown); thus, one generation of large V_{k} can generate large FPR. We also note that the constant population size scenario we simulated appears similar, in its effects, to a scenario of a recent and extreme bottleneck in an additional way, with a small recent effective size producing negative Fis values compatible with a population of few individuals [40].
Due to different parameterization of the model of the biological system, our results are not directly comparable with the genetic prediction of recent theoretical models of populations with skewed offspring number and overlapping generations [27,4145]. These models, which allow for simultaneous multiple coalescent events e.g. [42], suggest that in a “many losers, few winners” situation (high V_{k}), the chances to obtain starlike genealogies and excess of rare alleles, i.e., signatures of population expansion, is increased compared to the V_{k} =2 case; this is opposite the result obtained in our study. A possible explanation for the discrepancy is the fact that our simulations considered nonoverlapping generations, and overlap in generations may provide a buffer against the effects of drift and consequent high allele sharing caused by high V_{k}. Additional efforts should be dedicated to make the results produced by theoretical models with multiple merger and those obtained in our study comparable.
Practical applications
Certainly, our results suggest that the genetic signature of a bottlenecks should be interpreted with caution when found in species known to have moderate to large variance in offspring number (as for example in the killer whale, [46]), or where large variance in offspring number is suspected (as for example in many marine species, [26]). In the killer whale example, large variance in offspring number was estimated based on parentage analysis and a demographic bottleneck was inferred from genetic data using the statistical approaches we examined in our study; the authors report that it is unclear whether a bottleneck actually occurred. This work, and our simulations, emphasize that robust, widely applicable, powerful alternative methods of detect a bottleneck are still needed.
An alternative to using the standard bottleneck tests for species with large V_{k} is using computer simulations [16,32]. Summary statistics from observed data can be compared to a distribution of expected values from simulated data created with forward simulations, in simuPOP, spip [47], Nemo [48], cdpop [49] or other software [32]. The distribution of reproductive success and other aspects of the species’ reproductive system can be taken into account in the simulations, allowing the investigator to observe V_{k} effects on the population genetic signal and, more specifically, generating speciesspecific null distributions of the bottleneck tests (as the Mratio statistic) more appropriate for V_{k} larger than 2. Simulating stable populations, and populations with different intensities of demographic decline, can allow statistical comparison to the observed data (with or without formal approaches like Approximate Bayesian Computation, [50]).
The high FPR we uncover may not present a problem for studies that detect a bottleneck by comparing temporal samples, as comparing a modern sample to museum or ancient samples [23], or comparing to a nonbottlenecked but otherwise similar population [17]. Type I error due to V_{k} should not be expected to arise because large V_{k} should affect diversity in both samples. However, this assumes that V_{k} is constant through time. If census size decreases, V_{k} may change through time [12], with unknown effects on our ability to detect a bottleneck by comparing ancient and modern genetic variation levels. The increasing use of ancient DNA and prevalence of studies that infer bottlenecks from temporal samples [51], suggests that it will be important to evaluate the effects of high V_{k} on temporal comparisons.
Finally, considering that our simulations assumed nonoverlapping generations, and also considering that effect of drift decreases proportionally to the number of generations that overlap [25,52], we emphasize that our findings should be considered applicable particularly to organisms with nonoverlapping generations or short generation times (e.g., annual plants, insects, some fish).
Conclusions
We have shown that high reproductive variance increases the rate of false positives in four widely used bottleneck detection tests. Failing to detect a genuine bottleneck is widely acknowledged as harmful in conservation. However, given the limited resources and myriad of necessary conservation actions that are required to protect vulnerable species and populations [53], accurate tests are required to identify population bottlenecks with low false positive rates so that resources can be applied where they are needed most. The current study highlights the high type I error rate of bottleneck tests and emphasizes the need for more sophisticated analysis to evaluate conservation status of species with high reproductive variance.
Competing interests
The authors declare no competing interests.
Authors’ contributions
MM, CVO, and GB conceived and designed the study, MM and AB performed simulations and data analysis, SH drafted the manuscript and GB and OEG worked on it. All authors examined data, discussed results, contributed to manuscript revision and approved the final draft.
Authors’ information
All authors are interested in the demographic and genetic dynamics of small or isolated populations, and in the development and testing of statistical approaches to infer population processes from genetic variation data.
Acknowledgements
Funding was provided by the University of Ferrara, Italy. CvO was funded by the Earth and Life Systems Alliance (ELSA), Norwich Research Park, UK. We thank Lorenzo Zane and Richard Nichols for helpful discussions. GB thanks Camila Mazzoni and Simone Sommer for their hospitality at the at the Berlin Center for Genomics in Biodiversity Research during the revision of this paper.
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