1 INTRODUCTION

Hybridization is a major concern in conservation biology (Rhymer & Simberloff, 1996) but also a source of evolutionary innovation (Abbott et al., 2013; Arnold, 2015) and adaptive introgression (the introduction of genes from one evolutionary lineage into the gene pool of another) has been shown to play an important role in the evolution and diversification of different clades (Burgarella et al., 2019; Hamilton & Miller, 2016; Oziolor et al., 2019; Suarez-Gonzalez et al., 2018). Thus, the identification of admixed individuals and the assessment of the levels of introgression are fundamental steps to study the effect of hybridization on populations. However, the detection of these admixed individuals can be problematic when the parental species show limited phenotypic differentiation (Randi, 2008). The ineffectiveness of morphological criteria in differentiating cryptic hybrids or admixed individuals (Oliveira et al., 2008) promoted the use of highly polymorphic genetic markers, such as microsatellites or SNPs. The development of software programs based on the analysis of panels of genetic markers and the implementation of Bayesian clustering models has facilitated the detection of hybrids and the assessment of introgression of genes of one species into the gene pool of another.

One of the most widely used programs for these analyses is STRUCTURE (Pritchard et al., 2000) which allows identification of the origin of the genome of each individual. After choosing a K value, i.e., the number of populations, STRUCTURE subdivides the sample into K different clusters - trying to minimize departures from Hardy-Weinberg equilibrium and linkage disequilibrium - and estimates for each individual the proportion of the genome that could originate from each cluster (Barilani et al., 2007). In this way, STRUCTURE is very efficient at separating populations and identifying admixed individuals. A Scopus search (on 26 June 2019) for articles citing the original paper of Pritchard et al. (2000) and containing the words ‘hybrid*’ or ‘introgression’ in the title, abstract or keywords returned a total of 3,446 articles, highlighting the popularity of the software to detect hybridization and population admixture.

However, the power of STRUCTURE to accurately estimate the amount of introgression has been questioned as it could underestimate the number of admixed individuals (Randi, 2008; Sanchez-Donoso et al., 2014; Sanz et al., 2009). The main limitation seems to be related to the detection of old admixture as opposed to F1 hybrids and first generations backcrosses (Oliveira et al., 2008). It has been suggested that estimates of the amount of introgression could be improved by increasing the number of loci (Pritchard et al., 2000; Randi, 2008; Vähä & Primmer, 2006) and using both linked and unlinked markers (Lecis et al., 2006), as this could enable a better assignment of admixed individuals in separate genotypic classes and the identification of past events of hybridization. The use of high number of loci derived from genome-wide data increases resolution in the detection of varying levels of introgression by identifying regions of the genome of different origin (Gómez-Sánchez et al., 2018). Unfortunately, this is not always feasible due to the lack of a reference genome, or due to a trade-off between costs and number of specimens to analyse. In order to characterize population variability, large numbers of samples may need to be studied, making genomic approaches unaffordable and, despite technical advances, studies with reduced number of loci continue to be frequent in day-to-day studies of hybridization and admixture (for example, see Alacs et al., 2010; Arias et al., 2019; De Barba et al., 2017; Sujii et al., 2019). In addition, large numbers of unmapped markers are not necessarily an advantage for the study of ongoing hybridization because they could yield redundant information if they are in complete linkage.

Another factor affecting the performance of STRUCTURE is the sampling scheme, i.e. whether or not samples of each parental population or species are similar in size, and the phylogenetic relationships between the two species (Neophytou, 2014; Puechmaille, 2016). A previous study using empirical data of populations with known ancestry showed that STRUCTURE outperforms other common approaches in the identification of admixed individuals (Bohling et al., 2013). However, this study emphasizes the importance of including in the analyses a portion of individuals that can be a priori diagnosed as nonadmixed for the two parental classes and this may not always be feasible. In many studies genetic analyses are carried out to identify potentially admixed individuals without previously defining reference samples (for example, see Godinho et al., 2011; Muñoz-Fuentes et al., 2007; Oliveira et al., 2008; Ortego et al., 2017; Trigo et al., 2013). This can be particularly important in cases with high levels of hybridization and persistent introgression throughout the distribution range, or in cases where introgression takes place in geographically structured populations for which reference samples from another population may not be appropriate (for example, see Glover et al., 2017; Lavretsky et al., 2019; Sullivan et al., 2016).

In this study we used simulations to determine the accuracy of STRUCTURE in the estimation of the individual level of introgression when nonadmixed reference individuals were not available. We assessed the importance of the number and polymorphism of the loci used, the divergence between the ancestral populations and different rates of hybridization between them. We also studied how adding appropriate reference samples impacts the reliability of the estimates. Our goal was to identify ways to improve the accuracy of the estimates of the degree of introgression.

2 MATERIALS AND METHODS

We carried out simulations of asymmetric gene flow from one population to another to reduce complexity and to facilitate analyses because the allele frequencies for one of the populations would not change over time. However, this is not an uncommon situation. Some examples of this kind of gene flow are the hybridization between domestic and vulnerable wild species (Godinho et al., 2011), admixture between a rare species and an abundant one (An et al., 2017), restocking of game species with farmed animals of alien origin (Sanchez-Donoso et al., 2014), or directional gene flow as a result of the biology of the species hybridizing (Muñoz-Fuentes et al., 2007).

2.2 Simulation of allele introgression

We wrote a script in Python 2.7 to simulate different hybridization rates and to subsample a random subset of individuals from each population to be analysed with STRUCTURE (see Figure 1 for a schematic representation of the simulations). Population A was where admixture took place due to some individuals arriving from population B. The goal of the analyses was to assess if it was possible to correctly estimate the degree of introgression in individuals sampled from the population A using STRUCTURE. Hybridization rate, that is the proportion of breeders originating from population B that contributed to the offspring of population A every generation, was around 1% (0.01) or 5% (0.05). Although high, rates of hybridization this high have been described for diverse taxa (for example, see Lavretsky et al., 2019; Muñoz-Fuentes et al., 2007; Nussberger et al., 2014). A key factor here is that we assume recurrent hybridization every generation and that admixed individuals do not have a reduced fecundity so that they are able to freely interbreed with other individuals in population A. To initiate the simulations (at generation 0), the program randomly selected 1,000 individuals from populations A and B from one of the 100 initial pairs of populations generated with Easypop for a given combination of F_ST and type of marker.

For 10 generations, the programme generated the same number of individuals (1,000) by selecting two parents from the previous generation. Each parent was randomly selected from population A with a probability of (1 − m), where m was the hybridization rate (0.01 or 0.05); otherwise, the parent was randomly chosen from population B (geneflow was unidirectional from B to A). The genotype of the offspring was obtained by randomly selecting one of the two alleles from each parent at each locus with equal probability; loci were independent. For each individual, we calculated the proportion of the genome belonging to population A (q_real): for individuals originating from population B, this proportion was q_real = 0.0; for individuals from population A at generation 0, this proportion was q_real = 1.0; for subsequent generations, the proportion was the average of the values of the two parents. To confirm that the script was working as expected, we calculated the level of introgression expected after 10 generations in the different scenarios as in Verdu and Rosenberg (2011). Indeed, the value corresponded to the average level of introgression per individual in population A.

At the tenth generation, a random subsample of 100 individual genotypes was taken both from population B and from the introgressed population A to be analysed with STRUCTURE. In these subsamples, the number of loci was reduced to 10, 30 or 100 loci chosen at random. The data were used to generate an input file for STRUCTURE. As a result, 5,400 runs of STRUCTURE were carried out with 200 genotypes each (100 from the admixed population A and 100 from population B): three different values of F_ST (0.05, 0.1 and 0.2) × three kinds of markers (two, five or 10 alleles) × three numbers of loci (10, 30 and 100) × two hybridization rates (1% and 5%) × 100 replicates (100 pairs of populations simulated in Easypop for each set of conditions with regard to F_ST and type and number of loci).

The script for these simulations is available at https://github.com/sararvg/introgression_structure. This script was slightly modified for subsequent analyses.

3 RESULTS

We graphically compared the proportion of the genome coming from population A as estimated by STRUCTURE (q_STRUCTURE) with the real values (q_real, Figure 2). Each plot represents 100 runs of STRUCTURE with 200 genotypes, resulting in 20,000 pairs of values of q_STRUCTURE and q_real. Ideally, if the estimates of q by STRUCTURE precisely corresponded to the real values, all points should fall on the diagonal of the diagrams. As expected, increasing the number of loci and the number of alleles per marker improved precision (reduction in the variance) in the estimates of q_STRUCTURE and, to a lesser degree, it also improved accuracy (similarity between q_STRUCTURE and q_real values). At the same time, comparing cases with the same number of loci and alleles per marker, q_STRUCTURE values showed lower variance as the divergence level between the hybridizing populations increased (e.g., Figures S3a versus S4a). However, the comparison of q_STRUCTURE and q_real revealed systematic biases.

Considering a hybridization rate of 1% (Figure 2a, S3a and S4a), for markers with two alleles, q_STRUCTURE estimates tended to be quite independent from q_real, forming scattered clouds of points (meaning that STRUCTURE provided a poor assessment of the ancestry), except when the number of loci was 100 and the genetic differentiation was strong (Figure S4a). When the number of alleles per locus was 5, estimations using 10 or 30 loci were not reliable either and had a large variance. The consistency of the estimates increased notably with the use of 100 loci when F_ST was 0.1 or 0.2 (Figure 2a and S4a). In the cases of markers with 10 alleles, in general, estimations started to improve from 30 loci for all values of F_ST, with reduced variance in q_STRUCTURE values. However, even in the cases with the lowest variance, q_STRUCTURE tended to be larger than q_real (Figure 2a).

With a hybridization rate of 5% (Figure 2b, S3b and S4b), the entire population A was admixed and no pure individuals were left, i.e., no individuals whose genomes derived solely from the ancestral population; the population had turned into a hybrid swarm. Although q_real values were always smaller than 0.85, q_STRUCTURE values tended to be higher, identifying many admixed individuals as nonadmixed (q_STRUCTURE close to 1) and therefore underestimating the magnitude of the introgression in the population (Figure 2b, S3b and S4b).

The Wilcoxon signed rank test confirmed that q_STRUCTURE values were significantly higher than the corresponding q_real (p < 10^–16) for individuals from population A, except in five cases in which q_STRUCTURE was practically uninformative (Figure 2a: F_ST = 0.1, hybridization rate of 1%, 10 markers with two alleles; Figure S3a: F_ST = 0.05, hybridization rate of 1%, 10 markers with two and five alleles, as well as 30 markers with two alleles; Figure S3b: F_ST = 0.05, hybridization rate of 5%, 10 markers with two alleles). This implies that there was a tendency to overestimate the proportion of the genome from the ancestral population in practically all cases (q_STRUCTURE > q_real). A significant linear relationship between q_real and q_STRUCTURE was found in nine cases, when 100 loci with five alleles (only for a high hybridization rate of 5%) or 10 alleles were used (Figure S5), and in all nine cases the regression line was above the diagonal (intercept significantly higher than 0, p < 10^–16). The fact that in the other cases no relationship could be found between q_STRUCTURE and q_real highlights the limited power of analyses with reduced number of loci and alleles.

We used generalized linear models to assess both the effect of the degree of differentiation between the ancestral populations (F_ST) and the number of alleles per marker on the absolute difference between q_STRUCTURE and q_real (the bias in the inference of q) for the two hybridization rates and considering 100 loci. Both variables proved to have a highly significant effect (p < 10^–16). The increase in genetic differentiation showed the stronger effect in reducing the difference between the two q values (Table 1), therefore improving STRUCTURE estimates, but having markers with more alleles also helped.

The degree of overestimation of q by STRUCTURE can be better appreciated in the distribution of q_STRUCTURE − q_real for population A (Figure 3, S6 and S7). While the overestimation was limited when the hybridization rate was 1%, it dramatically increased when the rate was 5%. We compared the distribution of q_real and q_STRUCTURE for an example case (F_ST = 0.1, 30 markers with 10 alleles) for both hybridization rates (Figure 4). Although the two hybridization rates resulted in very different populations with regard to the level of introgression (see q_real in Figure 4), the results obtained with STRUCTURE were almost identical (see q_STRUCTURE), suggestive of a relatively low introgression, and showing that STRUCTURE was unable to differentiate the two cases.

The allele frequencies estimated by STRUCTURE for population A were progressively diverging from the ancestral as the number of generations of introgression increased (Figure 5). At generation 0, before any admixture, the estimates of allele frequencies for populations A and B were similar to the frequencies calculated from the ancestral populations. The distances in this case were not 0 because the estimates obtained by STRUCTURE were based on subsamples of the populations, resulting in sampling errors. As introgression increased the number of alleles from population B into population A in subsequent generations, STRUCTURE estimates of the allele frequencies in population A diverged more strongly from the ancestral ones, while estimates of the allele frequencies for population B remained unaffected. As estimations of q are associated to the inferred allele frequencies, the inaccuracy in the ancestral allele frequency estimates could lead to the observed overestimations in q_STRUCTURE for individuals originating from population A.

A possible solution to improve accuracy in the estimates of the allele frequencies could be the inclusion of reference individuals from the ancestral population A. Generalized linear models showed that (with a hybridization rate of 5%) the accuracy of q_STRUCTURE estimates improved by increasing the proportion of reference individuals and the number of alleles per marker, as well as activating the POPALPHAS option and marking reference individuals with USEPOPINFO (Table 2; Figure 6 and S8). However, q_real and q_STRUCTURE were still very different (Figure 6). When the hybridization rate was lower (1%) the effect of including reference samples was not obvious, and the generalized linear model could not be fitted because the model assumptions were not fulfilled.

Despite the improvement in the estimates with the inclusion of reference individuals, the biases were still very apparent even in the case when 30% of the individuals from A corresponded to reference samples (Figure 6) and q_STRUCTURE values were still significantly higher than the corresponding q_real (p < 10^–16). This could be due to inherent biases in STRUCTURE or difficulties in the inference of the ancestral frequencies when a large proportion of the samples derived from the admixed population. To investigate which was the case, we compared q_real and q_STRUCTURE obtained when analysing small sets of 5 admixed individuals with 100 samples from A before admixture and 100 samples from B. The results (Figure 7) show that the biases in the estimates of q_STRUCTURE practically disappeared. Variance of q_STRUCTURE estimates was quite large when using 30 markers but centred around the corresponding q_real values (along the diagonal in the figures), but still q_STRUCTURE values were significantly higher than q_real (p < .003). As expected, using 100 markers greatly reduced this variance and with 10 alleles q_STRUCTURE and q_real values were not significantly different (p-value = .510). These results imply that STRUCTURE estimates were not intrinsically biased and including a very large number of reference samples and high number of markers helped to reduce biases in the estimates.

The analysis of a data set from a natural population of common quails that experienced introgression from farm quails showed the same pattern when we added reference samples belonging to the same population but from before most of the restocking campaigns (Figure S9). The q values estimated after adding reference showed more admixture than those estimated without adding a proper reference for the wild population (Wilcoxon signed rank test, p < 10^–6). This result confirmed the pattern observed in the simulations.

Given the biases observed with STRUCTURE, we carried out additional analyses with simulated data corresponding to ancestral populations differing by F_ST = 0.1 and 100 biallelic loci with ADMIXTURE, Ohana and sNMF to assess if the same biases were present in all cases. We graphically compared results from the four programs and STRUCTURE exhibited the worst performance under the set of conditions that we evaluated (Figure S10). The Wilcoxon signed rank test confirmed that q values were not overestimated with ADMIXTURE, Ohana and sNMF when the hybridization rate was 1%.

4 DISCUSSION

Our results show that when appropriate reference samples are not included in the analyses, ancestry estimates provided by STRUCTURE can be very biased. In fact, the results provided by this software can be very similar even when comparing populations with completely different levels of introgression (Figure 4).

When populations experience hybridization and admixture during multiple generations, the proportion of the genome deriving from the ancestral local population tends to be overestimated by STRUCTURE, leading to an underestimation of the real degree of introgression and of the number of admixed individuals. Although the precision of the ancestry estimates provided by STRUCTURE tends to improve with higher number of markers and alleles (as suggested by previous studies; McFarlane & Pemberton, 2019; Vähä & Primmer, 2006), this increase in precision does not correspond to an increase in accuracy and similar biases are observed using a small or a larger number of markers. The overestimate is particularly extreme in scenarios of hybrid swarms, as simulated with a hybridization rate of 5%: while none of the individuals was free of introgression, the estimation offered by the program suggested that purebred individuals were majority in the sample.

The poor performance of STRUCTURE under the simulated scenarios could impact the interpretation of admixture patterns in deeply introgressed populations, affected by various generations of hybridization, as in contact zones (Baldassarre et al., 2014; Johnson et al., 2015; Ortego et al., 2018). Extensive admixture could also occur in other cases, such as in the intercrossing between wild and domestic species, which have been coexisting for centuries or decades, or between different wild species that become in contact after a long time of evolution in isolation (Beaumont et al., 2001; Burgarella et al., 2018; Glover et al., 2017; Mckelvey et al., 2016; Scarcelli et al., 2017). It may seem that a hybridization rate of 5%, as in our models, is unlikely to exist in nature. However, similar values have been reported in the literature based on the identification of F1 hybrids (Lorenzini et al., 2014; Muñoz-Fuentes et al., 2007; Pacheco et al., 2017; Sullivan et al., 2016).

The limitations and the poor performance of STRUCTURE in admixed populations were already in part highlighted in the recommendations of Pritchard et al. (2000) about a proper utilization of the software to obtain reliable ancestry estimates. These authors indicate that, in cases of extensive admixture, STRUCTURE cannot estimate ancestral allele frequencies and it cannot give accurate estimates of q because of the high variance in how many of the individual's alleles derive from one or the other population. Our results confirm this and show that introgression leads to poor estimates of the ancestral allele frequencies, as we observe how the allele frequencies estimated for the ancestral population were increasingly different from the real ancestral frequencies (Figure 5), reflecting the allele frequencies for an already admixed population. The biases in the estimates of ancestry persist even in the cases with 100 loci of high polymorphism (Figure 2), suggesting that the estimation of ancestral allele frequencies may not be corrected just by increasing the number of unlinked loci. After repeated introgression during several generations, STRUCTURE may be unable to reliably reconstruct ancestral allele frequencies. Including purebred reference individuals in the data set resulted in a larger improvement in the estimates of q than just increasing the number of markers. However, even replacing 30% of the individuals from the admixed population A by reference individuals was not enough to completely remove the bias (Figure 6) and the best estimates were obtained when analysing just a few target individuals together with many reference individuals (Figure 7).

In order to develop cost-effective genetic tools for the assessment of introgression, efforts have been concentrating in the identification of the most suitable combination of markers. A reduced number of informative loci with high diagnostic power could be as effective as a high number of less informative loci, indicating that the discriminating power could be more important than their number (Oliveira et al., 2015; Randi et al., 2014). However, it is not completely clear what would be the best strategy to identify the most informative loci without previous data on marker variability across populations. On the other hand, in our simulations we considered all loci to be unlinked. The use of linked markers could also improve the identification of older admixture between populations (Falush et al., 2003; Lecis et al., 2006) because introgression can differently affect regions of the genome (for example, see Anderson et al., 2009), but may be less suitable to study ongoing hybridization and introgression.

Our study highlights the importance of carrying out simulations in each study case to assess the reliability of estimates. The level of introgression can be assessed combining different approaches and simulations trying to properly reflect the functioning of the study system (McFarlane & Pemberton, 2019) should be carried out to test the power of the analysis, determine accuracy and assess possible biases (for example, see Oliveira et al., 2008; Randi et al., 2014; Sanchez-Donoso et al., 2014 Sanz et al., 2009).

The estimates by STRUCTURE show a remarkable increase in accuracy when many nonadmixed reference individuals are included in the analysis (Figure 6). Therefore, we stress the importance of including samples from reference nonadmixed populations (for example, museum specimens dating from before an admixture event; see also Sanchez-Donoso et al., 2014) to increase the reliability of STRUCTURE analyses. The availability of these samples can be limited, and historical DNA extraction and amplification can be costly and effort-demanding, but the accuracy in the analysis improves notably, increasing the reliability of the results. When only a limited number of reference samples is available, it could be useful to carry on multiple STRUCTURE analyses including only a small proportion of those samples whose ancestry is unknown (Figure 7), using USEPOPINFO to define the reference samples and comparing the results obtained with different test sample sets. Also, the use of the option POPALPHAS can improve the analyses when source populations are unequally represented and if there is unbalanced sampling (see Wang, 2017). The use of a small number of markers is also known to influence the results of STRUCTURE (Toyama et al., 2020). Nevertheless, Lawson et al. (2018) have shown that different demographic histories can lead to identical results suggesting admixture in STRUCTURE and emphasize the importance of combining analytical approaches to obtain a more robust analysis of recent demographic history. Our comparison of the results provided by different programs showed that not all of them suffer the same biases or to the same degree. Consequently, we strongly suggest to combine STRUCTURE with other approaches and simulations, and evaluate the consistency in the results, especially when it is not possible to include suitable reference samples in the analyses. This is especially important, for example, in the cases where hybridization and introgression can be relevant in the design of management and conservation plans.

In ecology, conservation and evolutionary biology, it is important to efficiently identify hybrids and admixed individuals, as well as to determine gene flow among different populations. STRUCTURE analyses showed a tendency to classify admixed individuals as nonadmixed when reference samples were not included. The misidentification of the degree of introgression can impact our understanding about the evolutionary history of species or the risks of genetic homogenization and extinction, and therefore its implications for management and conservation plans should be carefully considered.

AUTHOR CONTRIBUTIONS

C.V., and I.S.-D. designed the study, S.R. carried out the project and wrote the scripts, S.R., and I.S.-D. analysed the data, S.R. wrote the first draft of the manuscript and all authors contributed to the text. This study was initiated as part of the Master in Biodiversity and Conservation Biology of S.R. at the University Pablo de Olavide (Seville, Spain).