# Gene flow as a simple cause for an excess of high-frequency-derived alleles

Nina Marchi, Laurent Excoffier

► To cite this version:

Nina Marchi, Laurent Excoffier. Gene flow as a simple cause for an excess of high-frequency-derived alleles. Evolutionary Applications, 2020, 13, pp.2254 - 2263. 10.1111/eva.12998. hal-04719546

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# Gene flow as a simple cause for an excess of high-frequency-derived alleles

Nina Marchi<fnref n="1" />,<fnref n="2" /> ID | Laurent Excoffier<fnref n="1" />,<fnref n="2" /> ID

## Correspondence

Nina Marchi, CMPG, Institute of Ecology and Evolution, University of Berne, 3012 Berne, Switzerland.

Email: nina.marchi@iee.unibe.ch

## Funding information

Swiss National Science Foundation, Grant/ Award Number: 310030B_166605; University of Berne: SELF2018_04

## Abstract

Most human populations exhibit an excess of high-frequency variants, leading to a U-shaped site-frequency spectrum (uSFS). This pattern has been generally interpreted as a signature of ongoing episodes of positive selection, or as evidence for a mis-assignment of ancestral/derived allelic states, but uSFS has also been observed in populations receiving gene flow from a ghost population, in structured populations, or after range expansions. In order to better explain the prevalence of high-frequency variants in humans and other populations, we describe here which patterns of gene flow and population demography can lead to uSFS by using extensive coalescent simulations. We find that uSFS can often be observed in a population if gene flow brings a few ancestral alleles from a well-differentiated population. Gene flow can either consist in single pulses of admixture or continuous immigration, but different demographic conditions are necessary to observe uSFS in these two scenarios. Indeed, an extremely low and recent gene flow is required in the case of single admixture events, while with continuous immigration, uSFS occurs only if gene flow started recently at a high rate or if it lasted for a long time at a low rate. Overall, we find that a neutral uSFS occurs under more restrictive conditions in populations having received single pulses of gene flow than in populations exposed to continuous gene flow. We also show that the uSFS observed in human populations from the 1000 Genomes Project can easily be explained by gene flow from surrounding populations without requiring past episodes of positive selection. These results imply that uSFS should be common in non-isolated populations, such as most wild or domesticated plants and animals.

## KEYWORDS

computer simulation, demographic analysis, gene flow, human genetics, human genome, natural selection, neutral evolution

<footnote n="1">¹CMPG, Institute of Ecology and Evolution, University of Berne, Berne, Switzerland</footnote>

<footnote n="2">²Swiss Institute of Bioinformatics, Lausanne, Switzerland</footnote>
# 1 | INTRODUCTION

Allele frequency changes are driven by the combined action of different evolutionary forces such as mutation, selection, genetic drift and migration (Wright, 1931), but most of the variant frequencies are expected to be rare (Ewens, 1972), leading to a L-shaped site-frequency spectrum (SFS) (Fu, 1995). However, an unexpectedly large proportion of high-frequency-derived alleles, resulting in U-shaped SFS (uSFS), has been documented in multiple species, including wild and domesticated plants (Liu, Zhou, Morrell, Gaut, & Ge, 2017; Morton, Dar, & Wright, 2009; Price et al., 2018), animals (Cooper, Burrus, Ji, Hahn, & Montooth, 2015; de Manuel et al., 2016; Murray, Huerta-Sanchez, Casey, & Bradley, 2010) and even human populations (Henn et al., 2015; Pouyet, Aeschbacher, Thiéry, & Excoffier, 2018).

Several explanations for these uSFS have been proposed. This phenomenon has been notably interpreted as a signature of positive selection at several loci (Akashi & Schaeffer, 1997; Bustamante, Wakeley, Sawyer, & Hartl, 2001), as neutral variants hitchhiking with beneficial mutations during selective sweeps would also be observed at high frequencies (Andolfatto & Przeworski, 2001; Fay & Wu, 2000; Kim & Stephan, 2000, 2002; Lapierre, Blin, Lambert, Achaz, & Rocha, 2016; Pavlidis, Jensen, & Stephan, 2010; Stephan, 2016), thus leading to a uSFS (Hahn, 2018; Ronen, Udpa, Halperin, & Bafna, 2013). This phenomenon could even be accentuated by selection fluctuating over time (Huerta-Sanchez, Durrett, & Bustamante, 2008; Przeworski, 2002). Alternatively, low-frequency-derived alleles mistakenly annotated as ancestral would lead to the emergence of high-frequency-derived variants and also create a uSFS (Baudry & Depaulis, 2003; Hernandez, Williamson, & Bustamante, 2007). uSFS can also emerge in multiple-merger coalescent models that have been developed to account for strong selective sweeps or a very large variance in reproductive success among individuals of a population (Eldon, Birkner, Blath, & Freund, 2015; Rice, Novembre, & Desai, 2018; Sargsyan & Wakeley, 2008; Tellier & Lemaire, 2014), which is not well accounted for in the classical Kingman coalescent framework. Finally, uSFS has also been shown to arise in non-isolated populations, for example in range expanding populations (Sousa, Peischl, & Excoffier, 2014), in structured populations analysed as single populations (Cutter, 2019; Lapierre et al., 2016; Wakeley, 2000) or in structured population receiving low levels of gene flow from surrounding demes (Garrigan & Hammer, 2006; Wakeley & Aliacar, 2001).

Even though most animal and plant populations are not completely isolated and receive migrants from surrounding populations, gene flow has been rarely proposed as an explanation for uSFS, and hypotheses of selection or ancestral allele mis-assignment have been preferred (Li et al., 2012; Liu et al., 2017; Qanbari & Simianer, 2014; Sabeti, 2006). However, Pouyet et al. (2018) recently showed that the uSFS observed in human populations could not be recovered under a complex demographic scenario involving an isolated population, but could be perfectly modelled under a scenario involving gene flow from an unspecified source (i.e. a ghost population), and this, in absence of any positive selection or mis-assignment of ancestral alleles. In order to better investigate the conditions leading to uSFS in non-isolated populations, we have used simulations to

explore the impact of gene flow duration, onset and intensity, as well as of population size and divergence time, on the probability of observing a uSFS. Even though more complex scenarios could certainly lead to uSFS, we have simulated here two simple demographic models of isolation with admixture and of isolation with immigration, which are often used as basic population genetic models (Geneva & Garrigan, 2010; Hahn, 2018; Patterson et al., 2012; Sousa & Hey, 2013) and represent the two ends of the gene flow spectrum. We have then compared the likelihoods of these models for ten populations from the 1,000 Genomes panel where uSFS is observed.

# 2 | MATERIAL AND METHODS

## 2.1 | Simulated scenarios

We modelled a population of *n* haploid individuals and effective size *N* that receives gene flow from an unsampled and often referred to as a "ghost" population (Beerli, 2004; Slatkin, 2005), after their divergence *T*<sub>DIV</sub> generations ago (or expressed in 2*N* units as τ<sub>DIV</sub> = *T*<sub>DIV</sub> / (2*N*) the parameters and their ranges are described in Table 1). However, rather than being simply a non-sampled population, this ghost population is introduced here as a convenient way to partition sampled lineages into two structured components between which coalescent events will not immediately occur. This type of partitioning is for instance found in metapopulation models with migration, where coalescent events occur rapidly during a scattering phase and more slowly during the collecting phase (Wakeley, 1999; Wakeley & Aliacar, 2001). For sake of simplicity, we tested two models at the ends of the gene flow spectrum (Figure 1): one of isolation with admixture (IA) and one of isolation with immigration (II). In the IA model, a single admixture event (i.e. a single pulse of gene flow) occurred *T*<sub>ADM</sub> generations ago (τ<sub>ADM</sub> in 2*N* units), with an admixture rate *a*. In the *II* model, continuous gene flow occurring at rate *m* per generation started *T*<sub>GF</sub> generations ago.

## 2.2 | Simulated genetic data

We used the software *fastsimcoal2* (Excoffier, Dupanloup, Huerta-Sánchez, Sousa, & Foll, 2013) to simulate the genomic diversity in 100 Mb of DNA (which roughly corresponds to the neutral portion of the human genome found in Pouyet et al. (2018)) under the scenarios defined in the previous section. The simulated 100 Mb was modelled as 10,000 blocks of 1,000 independent non-recombining regions of 100 bp. Note that the SNPs simulated in this way are essentially independent (unlinked) SNPs, and that it would have been possible to simulate partially linked SNPs but more simulations would have been necessary to get the same expected SFS (Pouyet et al., 2018). However, we have performed a limited set of simulation using partially linked SNPs, to verify that our conclusions would not change if we were explicitly simulating linkage and recombination (Supporting Information 2).
<table><caption>TABLE 1 Parameters description and ranges used for the simulation of different scenarios</caption><thead><tr><th>Parameter description</th><th>IA model</th><th>II model</th></tr></thead><tbody><tr><td>Effective size (haploid number, N<sub>s</sub>)</td><td>{4,000; 40,000}</td><td>{4,000; 40,000}</td></tr><tr><td>Divergence time<br>τ<sub>DIV</sub> = T<sub>DIV</sub> / (2N)</td><td>{0.005; 0.05;<br>0.25; 0.5; 2.5}</td><td>2.5</td></tr><tr><td>Time of single admixture event<br>τ<sub>ADM</sub> = T<sub>ADM</sub> / (2N)</td><td>{0; 0.025; 0.05;<br>0.125; 0.25}</td><td></td></tr><tr><td>Onset of gene flow<br>(T<sub>GF</sub>)</td><td></td><td>T<sub>DIV</sub> / {10,000;<br>1,000; 100; 10; 1}</td></tr><tr><td>Haploid sample size (n)</td><td>{10; 50}</td><td>10</td></tr><tr><td>Admixture rate (a)</td><td>[0:0.5]</td><td></td></tr><tr><td>Immigration rate (Nm)</td><td></td><td>[0.01:10]</td></tr></tbody></table>

Isolation with admixture (IA)

Ancestral population

<figure><img src="image_2.png" /></figure>

Isolation with immigration (II)

Ancestral population

<figure><img src="image_3.png" /><figcaption>FIGURE 1 Scenarios used to elucidate conditions under which gene flow leads to a uSFS. The populations have diverged T<sub>DIV</sub> generations ago from an ancestral population; their population sizes (N) are identical and constant over time. The results shown in the main text were obtained for a sampling size of 10 individuals and population sizes N = 4,000, but similar results were seen for a ten-time larger size (N = 40,000) after appropriate rescaling of divergence time and migration rate (Supporting Information 1)</figcaption></figure>

We then computed the site-frequency spectrum (SFS) for each block independently using the *fastsimcoal2* command./fsc2 -i File. par -n 10,000 -q -c0 -d -s0 -x -l (Supporting Information 3). The mutation rate was set to 1.20 × 10⁻⁸ per bp per generation (de Manuel et al., 2016; Venn et al., 2014), and we assumed an infinite-site model. We then sampled with replacement 10,000 blocks from the original simulated set to generate a given block-bootstrap data set, and we repeated this procedure 1,000 times to generate 1,000 block-bootstrap SFS.

<figure><img src="image_4.png" /><figcaption>FIGURE 2 Schematic SFS shapes, for a sample of haploid size 10 where SFS<sub>i</sub> is the number of sites with a derived frequency i</figcaption></figure>

## 2.3 | Summary statistics

We computed the global unfolded SFS for each simulated and block-bootstrapped data set of 100 Mb, by summing the 10,000 (respectively, observed or randomly sampled) block-SFS. The 95% confidence intervals of the simulated SFS were computed from the 2.5% and 97.5% quantiles of the SFS entries (all SFS is shown in Supporting Information 4).

We classified simulated SFS into three categories according to their shapes: a monotonously decreasing SFS with a mode at singletons corresponding to a L-shape SFS; a U-shape SFS with a second mode at high derived allele frequencies; a W-shape SFS with a second mode at intermediate derived allele frequencies (Figure 2).

We also used a summary statistic called *D-tail* defined as.

$$D-tail = \frac{SFS_{n-1} - SFS_{n-2}}{SFS_{n-2}}, \text{ where } n \text{ is the haploid sample size and } SFS_i \text{ is the number of sites with a derived frequency } i.$$

## 2.4 | Human data sets and likelihood estimations

We computed the SFS and *D-tail* statistic for ten 1,000 Genomes (1000G) populations: Yoruba in Ibadan, Nigeria (YRI); Luhya in Webuye, Kenya (LWK); Iberian Population in Spain (IBS); British in England and Scotland (GBR); Punjabi from Lahore, Pakistan (PJL); Bengali from Bangladesh (BEB); Kinh in Ho Chi Minh City, Vietnam (KHV); Japanese in Tokyo, Japan (JPT); Colombians from Medellin, Colombia (CLM); and Peruvians from Lima, Peru (PEL). We included the 10 individuals with the highest coverage per population (see Supporting table from Pouyet et al. (2018)). In this data set, we focused on the 493,369 sites formerly identified as evolving neutrally in Pouyet et al. (2018) (i.e. biallelic sites, non-CpG sites, mutations neither affected by biased gene conversion nor by background selection). The ancestral state was defined based on the chimpanzee reference genome (panTro4) to prevent mis-assignment of the ancestral/derived states. We used a block-bootstrap approach based on sets of 100 adjacent SNPs along the genome, to generate 1,000 block-bootstrap SFS and *D-tail* statistics.

We estimated with *fastsimcoal2* the likelihood of four demographic scenarios (Supporting Information 5) inspired from Pouyet
et al. (2018): (a) a first simple scenario, where a fully isolated popu-
lation can go through four different epochs with four different sizes
separated by three bottlenecks of arbitrary size and times, (b) same
as the first scenario but allowing for potential ancestral-state mis-as-
signment (option -ASM in *fastsimcoal*), (c) same as the first scenario
but allowing for continuous gene flow from a ghost population and
(d) same as the first scenario but allowing for a single pulse of ad-
mixture from a ghost population. Parameters were estimated for
each model with the *fastsimcoal2* command line options: -t POP.tpl
-e POP.est -n200000 -d -M -L40 -q -0 -C1 -c1 -B1, where POP is the
acronym of each of the ten 1000G populations (generic input files
made available in Supporting Information 6). In order to scale pa-
rameters, we assumed an ancestral human population size of 20,000
diploids, and a constant and uniform mutation rate of 1.25 × 10⁻⁸
per bp per generation (Scally & Durbin, 2012), which is widely used
in demographic inference in humans (Malaspinas et al., 2016; Pagani
et al., 2015; Raghavan et al., 2015; Schiffels & Durbin, 2014; Sikora
et al., 2017, 2019; Spence & Song, 2019; Steinrücken, Kamm, Spence,
& Song, 2019).

3 | RESULTS

3.1 | Isolation with admixture

To evaluate the impact of the divergence time, we have first sim-
ulated an *isolation with admixture* (IA) model where the admixture
event occurred at sampling time (0 generations ago) for varying di-
vergence times (*T*<sub>DIV</sub>) and admixture rates (*a*).

As expected, without admixture (a = 0), the SFS is L-shaped
(Figure 3a and Supporting Information 7) and the D-tail statistics
are negative (Figure 3b). This is also the case when a > 0 for recent
divergence times (τ<sub>DIV</sub> = T<sub>DIV</sub> / (2N) = 0.005 or τ<sub>DIV</sub> = 0.05). However,
for older divergence times, when τ<sub>DIV</sub> > 0.05, the pattern is more

complex: positive *D-tail* statistics and consistent uSFS are only ob-
served for relatively low admixture rates (between 5% and 20%).
Importantly, the admixture rates leading to uSFS depend on the
sample size *n*: for a larger sample size (*n* = 50), we observe uSFS
for reduced admixture rates (0 < *a* ≤ 0.03), while larger admixture
rates lead to W-shaped SFS with not only one but two internal
maxima (Supporting Information 8). In any case, independently of
sample sizes, *D-tail* values increase for older divergence times, in-
dicating that SFS is more strongly U-shaped with larger divergence
times.

These results are best explained by the immigration of a few
ancestral alleles into the sampled population at sites where the de-
rived allele is fixed in the sample before admixture, thus causing a
decrease in the frequency of derived alleles from *n* to *n*-1. For the
same amount of admixture, this phenomenon is more likely if two
populations have fixed different alleles, the probability of which
increases with divergence times, and becomes substantial when
τ<sub>DIV</sub> ≥ 0.5 (Hudson & Coyne, 2002). To substantiate this explana-
tion, we have performed simulations for τ<sub>DIV</sub> = 2.5, where we com-
puted derived allele frequencies after the admixture event at sites
that were fixed-derived before admixture (Figure 3c). For relatively
low admixture rates (a = 0.05), almost 80% of the previously fixed
derived sites are transformed into nearly fixed sites and SFS be-
comes U-shaped. This proportion drops to 60% when a = 0.1. For
larger admixture rates (a ≥ 0.2), SFS becomes W-shaped (Supporting
Information 7), as admixture events will often introduce more than
one ancestral allele at previously fixed sites.

Note that under the IA model, large admixture rates correspond-
ing to partial genetic replacement (0.5 < a < 1) can also lead to uSFS.
Indeed, uSFS is also obtained for admixture rates between 0.8 and
0.95, in a way symmetrical to low a values (0.05 < a < 0.2, Supporting
Information 9A). In this case, the excess of high derived frequencies
is caused by the immigration of a large number of derived alleles at
sites where the ancestral allele was fixed in the sampled population

<figure><img src="image_5.png" /><figcaption>FIGURE 3 Effect of the admixture rate and time of divergence on SFS properties, under an IA scenario for τ<sub>ADM</sub> = 0. (a) SFS, i.e. the number of sites with a derived frequency *i*, from *n* = 10 haploid individuals for τ<sub>DIV</sub> = 2.5 and various admixture rates *a*; (b) *D-tail* statistic for various divergence times τ<sub>DIV</sub>; (c) proportion of loci in the sampled population that were fixed for the derived allele before the admixture event and which show *i* derived alleles afterwards, when τ<sub>DIV</sub> = 2.5. In panes a and b, dots and solid lines were obtained from simulated data sets, and semi-transparent colours define 95% block-bootstrap confidence intervals. Note that these confidence intervals are so small that they are barely visible on these figures. In pane c, dashed lines stand for uSFS and solid lines stand for W-shaped SFS</figcaption></figure>
(Supporting Information 9B), mimicking the action of positive selection (Hahn, 2018).

## 3.2 | Effects of the onset time of instantaneous and continuous gene flow

When gene flow occurred more than one generation ago, its onset time, intensity and duration might also have a drastic effect on the allele frequency distribution, and thus on the shape of the SFS. To investigate the effect of past gene flow, we have run simulations under both an *isolation with admixture* (IA) and an *isolation with immigration* (II) models, where the populations have diverged for $τ_{DIV} = 2.5$ (i.e. 20,000 generations for effective populations size $N = 4,000$), when $τ_{ADM} > 0$ and when $T_{GF} > 0$ for the IA and II models, respectively.

Under the IA model, uSFS and positive *D-tail* values are observed for admixture $τ_{ADM} < 0.25$. SFS becomes less U-shaped, and *D-tail* values are smaller for older admixture times (Figure 4a). However, even though *D-tail* statistics are lower when admixture is old (i.e. $τ_{ADM} = 0.125$), uSFS is observed for larger admixture rates than when it is very recent (i.e. when $τ_{ADM} = 0$). As expected, the SFS can become multimodal for recent divergence times and large admixture rates ($τ_{ADM} ≤ 0.025$ and $a ≥ 0.2$), and the internal mode moves towards more central values for larger admixture rates (Figure 4c).

Under the II model, we observe uSFS and positive *D-tail* statistics for a large range of onset times for gene flow (from $T_{GF} = T_{DIV}$ to $T_{GF} = T_{DIV}/10,000$; Figure 4b and d), but the amount of gene flow

required to produce uSFS is inversely correlated with the age of the onset of gene flow; that is, small immigration rates ($Nm < 0.5$) are necessary when gene flow is ancient ($T_{GF} = T_{DIV}$) and large immigration rates ($Nm > 1$) are necessary when gene flow is very recent ($T_{GF} = T_{DIV}/10,000$) (Figure 4d). We found an exception for $T_{GF} = T_{DIV}/10$, where both low and high rates lead to uSFS, likely due to the introduction of both ancestral and derived alleles in the population, depending on which allele was fixed ancestral or fixed derived in the sampled population. Interestingly, multimodal SFS only occurs for very specific conditions, that is large immigration rates and intermediate duration of gene flow ($T_{GF} = T_{DIV}/100$, Figure 4d), and in those cases, the internal mode is only seen at high derived frequencies.

## 3.3 | Application to human data

All ten 1000G populations show clear uSFS at neutral sites (Figure 5). Among the four demographic scenarios tested on these human data (Supporting Information 5), only the scenario of genetic *isolation* fails to produce uSFS (Supporting Information 10), shows less good fit especially when looking at normalized SFS (Lapierre, Lambert, & Achaz, 2017), and a significantly lower likelihood than that of the three other scenarios (Supporting Information 11). Expected SFS is found very similar to the observed ones, and the estimated maximum likelihood values are found close to the maximum possible value (computed by assuming that the expected SFS entries would

<figure><img src="image_6.png" /></figure>

**FIGURE 4** Effect of rate and age of gene flow on SFS properties, for $τ_{DIV} = 2.5$ and $n = 10$ under an IA model with different admixture times ($τ_{ADM}$) and rates (a) (left panes) or under an II model with different gene flow onset ($T_{GF}$) and number of migrants per generation ($Nm$) (right panes). *D-tail* statistic (panes a and b) with dots and solid lines obtained from simulated data sets, and semi-transparent colours defining the 95% confidence intervals calculated from the block-bootstrap data sets (note that these confidence intervals are so small that they are barely visible on these figures); SFS shapes (panes c and d) with black numbers indicating the derived frequency *i* of the internal mode of W-shaped SFS
<figure><img src="image_7.png" /><figcaption>**FIGURE 5** Neutral SFS (a) and associated *D-tail* statistics (b) observed in ten 1000G human samples. In pane a, SFS<sub>t</sub> is the number of sites with a derived frequency *i*. In pane b, the whiskers indicate limits of 95% block-bootstrap confidence intervals</figcaption></figure>

be equal to the observed SFS entries) for the three other scenarios: *isolation with ASM, admixture and immigration*. Therefore, we cannot distinguish which of these three scenarios is best on the sole basis of their likelihoods. However, we find that an average of 4.38% (2.75% – 7.59%) of ancestral state mis-assignment is necessary for the *isolation with ASM* model to fit the data. This value is one order of magnitude higher than that previously estimated in Yoruba (0.1%–0.3% in Lapierre, 2017) by using sites for which the nucleotide of an out-group species is different from the two nucleotides defining a SNP in a focal population (Baudry & Depaulis, 2003). It suggests that ASM in a context of genetic isolation is not the cause of the uSFS observed from the human neutral data, and that one of the two models involving gene flow is a more plausible explanation. Overall, the best parameters inferred from gene flow scenarios generally point to mild and recent gene flow (mean admixture rate *a* = 0.06 and time T<sub>ADM</sub> = 171 generations ago for *admixture* scenario; on average, 72 migrants per generation for 540 generations for the *immigration* scenario, i.e. postlast glacial maximum for non-African populations).

4 | DISCUSSION

Gene flow is often overlooked as an explanation for the observation
of an excess of high-frequency-derived alleles. Natural populations
showing uSFS are usually considered as isolated but under selection
(Li et al., 2012; Liu et al., 2017; Qanbari & Simianer, 2014; Sabeti
et al., 2006). However, this strong assumption of genetic isolation is
far from being warranted, as gene flow between populations seems
to be the standard in non-human species (Sexton, Hangartner, &
Hoffmann, 2014), sometimes even extending over species bounda-
ries (Shurtliff, 2013; Wang et al., 2019) and persisting despite habitat
fragmentation due to human activity (Corlatti, Hacklaänder, Frey-
Roos, Hackländer, & Frey-Roos, 2009). For humans, numerous oc-
currences of gene flow between populations have been documented
at every epochs and on every continent (Hellenthal et al., 2014).
Human isolates rather seem to be an exception (Heutink, 2002)
and seem to have emerged recently due to geographical and/or
cultural barriers, for example populations living on islands or re-
mote places (Roberts, 1976; Serre, Jakobi, & Babron, 1985), or

being cultural minorities (Bideau, Brunet, Heyer, & Plauchu, 1994; Capocasa et al., 2013; Mourali-Chebil & Heyer, 2006), and usually present health and fitness issues (Charlesworth & Willis, 2009; Keller & Waller, 2002; Spielman, Brook, Briscoe, & Frankham, 2004). In this paper, the ten 1000G populations we study all show uSFS in their neutral fraction of genomes, where selection is supposed to have almost no effect (Pouyet et al., 2018), suggesting that they are not genetically isolated populations. More generally, we show with simulations that gene flow alone (i.e. in the absence of any selection, for two very contrasting models of gene flow) can actually easily produce an excess of high-frequency-derived alleles and uSFS. Interestingly, we find that uSFS can emerge from gene flow both by (a) the introduction of a few ancestral alleles (II and other IA models) and (b) by a massive input of derived alleles (during a partial genetic replacement, i.e. IA model with admixture rates larger than 0.5). This latter result extends previous ones (Wakeley & Aliacar, 2001), as not only mild gene flow can lead to an excess of high-frequency-derived alleles after a single admixture event. Furthermore, for higher rates of gene flow between deeply divergent populations, we manage to simulate W-shaped SFS, a signal that can also be produced by balancing selection (Bitarello et al., 2018; Croze, Živković, Stephan, & Hutter, 2016), associative overdominance (Gilbert, Pouyet, Excoffier, & Peischl, 2020) or in a heterogeneous structure resulting from divergent sources sampled as a single population (González-Martínez, Ridout, & Pannell, 2017).

Our results are in line with the fact that human populations are
not genetically isolated, even though our study did not formally
identify the source of recently incoming lineages. In our models,
we used an unsampled or "ghost" population as the source of gene
flow (Excoffier et al., 2013), which simply models a reservoir for
some divergent lineages now found in the sampled population
(Beerli, 2004; Slatkin, 2005). It can represent a population that
separated a long time ago from the sampled population, as in
the case of a secondary contact after a period of isolation, like
in hybrid zones at the population or species level (Alcala, Jensen,
Telenti, & Vuilleumier, 2016; Alcala & Vuilleumier, 2014; Hvala &
Wood, 2012; Tine et al., 2014). Such hybridization events have
occurred repeatedly in human evolution (e.g. between anatomi-
cally modern and archaic humans (Dannemann & Racimo, 2018)
or after long-distance dispersals between population of distinct
ancestries (Fortes-Lima et al., 2018; Sedghifar, Brandvain, Ralph, &
Coop, 2015; Verdu et al., 2014). Interestingly, if the source popula-
tion is actually sampled, the joint SFS for the source and the target
populations will reveal in the target population an excess of rare or
event quite frequent derived alleles, for small and large immigra-
tion rates, respectively (Supporting Information 12), as previously
reported in population or species having recently reconnected
(Alcala et al., 2016; Alcala & Vuilleumier, 2014; Fraïsse et al., 2018;
Tellier et al., 2011; Tine et al., 2014). Alternatively, as already men-
tioned above, the “ghost” population does not need to correspond
to a real or an existing population, but can rather simply represent
a set of populations surrounding the sampled population, as in
large spatially structured populations, which can be described as a
continent-island model (Excoffier, 2004; Hahn, 2018), for example
like after a spatial expansion.

This last type of ghost (continent) population can be particularly
relevant to model the history of human populations, as we were not
able to identify the source of gene flow within the available 1,000
Genomes populations (Supporting Information 13). A consensus sce-
nario for the worldwide expansion of humans is a serial founder ef-
fect out of Africa with limited archaic hybridization (Ramachandran
et al., 2005; Stringer, 2014). As uSFS has actually been observed in
simulations of range expansions, one could think that gene surfing
having occurred during past human range expansions could explain
the observed uSFS (Sousa et al., 2014). However, during human ex-
pansions, both recurrent founder effects at the front and migration
between neighbouring demes in the wake of the front certainly oc-
curred, such that gene surfing at the front could have promoted the
fixation of different alleles in different sectors and a mixing of these
sectors in the wake of the expansion could have led to uSFS (Peischl,
Dupanloup, Bosshard, & Excoffier, 2016). We have run additional
simulations to investigate the impact of gene flow during range ex-
pansions on the SFS (Supporting Information 14). We find that uSFS
is only observed when gene flow between adjacent populations on
the front is associated with the expansion, showing that gene surfing
alone cannot lead to an excess of high-frequency-derived alleles. In
addition, we find that uSFS can also stem from a Wahlund effect,
that *is* when the SFS is computed from a population with hidden sub-
divisions (Supporting Information 15). Therefore, uSFS can emerge
from naturally occurring gene flow or from artefactual structure re-
sulting from the sampling of divergent lineages, as both will result in
the potential mixing of differentially fixed alleles.

Whereas uSFS is never observed in completely isolated popu-
lations under a classical Kingman coalescent model, they can cer-
tainly exist under multiple-merger coalescent (MMC) models (Eldon
et al., 2015; Pitman, 1999; Sagitov, 1999; Sargsyan & Wakeley, 2008;
Schweinsberg, 2000; Tellier & Lemaire, 2014), which occur under re-
current episodes of selective sweeps or for extremely skewed distri-
butions of offspring numbers (e.g. oyster, cod, bacteria and viruses
(Árnason & Halldórsdóttir, 2015; Sargsyan & Wakeley, 2008; Tellier &
Lemaire, 2014)). Since different parts of the genome can be differen-
tially affected by selection, a mixture of classical and multiple-merger

coalescent models could be used to model whole genomes (Rice
et al., 2018). Contrastingly, gene flow into a population should affect
the whole genome, even though effective migration rates may be
affected by intragenomic selective processes as well (Petry, 1983;
Sousa & Hey, 2013). It would therefore be interesting to include the
effect of gene flow in the context of multiple-merger models as well.
Along the same lines, procedure contrasting the SFS at different po-
sitions of the genome to evidence selection (Fay & Wu, 2000; Kim
& Stephan, 2002; Nielsen et al., 2005; Pavlidis et al., 2010; Zeng,
Fu, Shi, & Wu, 2006) or methods using the SFS to infer the distribu-
tion of fitness effects (Eyre-Walker & Keightley, 2007; Kim, Huber,
& Lohmueller, 2017; Tataru, Mollion, Glémin, & Bataillon, 2017) do
not take gene flow into account and could thus lead to biased infer-
ences. We therefore hope that our study would promote the inclu-
sion of gene flow when studying the effect of selection on genomic
diversity.

ACKNOWLEDGEMENTS

The authors would like to thank Fanny Pouyet who provided us the
1000G neutral SFS; Stephan Peischl, Guillaume Achaz and Daniel
Wegmann for helpful discussions. NM was partially supported by a Swiss
National Science Foundation No 310030B_166605 to LE and by a Seal
of Excellence Fund grant from the University of Berne (SELF2018-04).

CONFLICT OF INTEREST

None declared.

AUTHOR CONTRIBUTIONS

L.E. and N.M. designed the study and wrote the manuscript, L.E.
performed *fastsimcoal2* parameter estimations from 1000Genomes
data, N.M. run the simulations and analysed the results.

DATA AVAILABILITY STATEMENT

SFS from the simulations and for the ten studied 1,000 Genomes
populations is available upon request to the authors. Furthermore,
the input files necessary to repeat the simulations are provided in
the Supplementary Information.

ORCID

Nina Marchi ID https://orcid.org/0000-0001-6624-5922

Laurent Excoffier ID https://orcid.org/0000-0002-7507-6494

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## SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section.

**How to cite this article:** Marchi N, Excoffier L. Gene flow as a simple cause for an excess of high-frequency-derived alleles. *Evol Appl.* 2020;13:2254-2263. https://doi.org/10.1111/eva.12998