# The asexual genome of Drosophila

Stephan Schiffels1,∗, Ville Mustonen2 and Michael Lässig3,∗

(1 Department for Archaeogenetics, Max-Planck-Institut for the Science of
Human History, Kahlaische Str. 10, 07749 Jena, Germany
2 Department of Biosciences, Department of Computer Science, Institute of
Biotechnology, University of Helsinki, PO Box 65, 00014 Helsinki, Finland
3 Institut für Theoretische Physik, Universität zu Köln, Zülpicherstr.
77,50937, Köln, Germany
∗ Corresponding Author )

## Abstract

The rate of recombination affects the mode of molecular evolution. In high-
recombining sequence, the targets of selection are individual genetic loci;
under low recombination, selection collectively acts on large, genetically
linked genomic segments. Selection under linkage can induce clonal
interference, a specific mode of evolution by competition of genetic clades
within a population. This mode is well known in asexually evolving microbes,
but has not been traced systematically in an obligate sexual organism. Here we
show that the _Drosophila_ genome is partitioned into two modes of evolution:
a _local interference_ regime with limited effects of genetic linkage, and an
_interference condensate_ with clonal competition. We map these modes by
differences in mutation frequency spectra, and we show that the transition
between them occurs at a threshold recombination rate that is predictable from
genomic summary statistics. We find the interference condensate in segments of
low-recombining sequence that are located primarily in chromosomal regions
flanking the centromeres and cover about 20% of the _Drosophila_ genome.
Condensate regions have characteristics of asexual evolution that impact gene
function: the efficacy of selection and the speed of evolution are lower and
the genetic load is higher than in regions of local interference. Our results
suggest that multicellular eukaryotes can harbor heterogeneous modes and tempi
of evolution within one genome. We argue that this variation generates
selection on genome architecture.

## Author Summary

The _Drosophila_ genome is an ideal system to study how the rate of
recombination affects molecular evolution. It harbors a wide range of local
recombination rates, and its high-recombining parts show broad signatures of
adaptive evolution. The low-recombining parts, however, have remained dark
genomic matter that has been omitted from most studies on the inference of
selection. Here we show that these genomic regions evolve in a different way,
which involves clonal competition and is akin to the evolution of asexual
systems. This regime shows a lower efficacy of selection, a lower speed of
evolution, and a higher genetic load than high-recombining regions. We argue
these evolutionary differences have functional consequences: protein stability
and protein expression are gene traits likely to be partially compromised by
low recombination rates.

## Introduction

Genetic linkage affects molecular evolution by coupling the selective effects
of mutations at different loci. This coupling, which is often called
interference selection, generates two basic evolutionary processes: a strongly
beneficial mutation can drive linked neutral and deleterious mutations to high
frequency; conversely, a strongly deleterious mutation can impede the
establishment of a linked neutral or beneficial mutation. The first process is
an instance of hitchhiking or genetic draft [1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12], the second is known as background selection [13, 14, 15, 16, 17, 18,
19, 20, 21]. In both cases, interference selection has the same consequence:
by spreading the effect of selected mutations onto neighbouring genomic sites,
it reduces speed and degree of adaptation.

In an evolving population, interference links between genomic loci are
established by new mutations, reinforced by selection on these mutants, and
reduced by recombination. Hence, strength and genomic range of interference
are set by all three of these evolutionary forces. In sexually reproducing
organisms with a sufficiently high recombination rate, interference has
limited effects because it remains local; that is, it acts only on mutations
at proximal genomic positions but is randomized by recombination at larger
distances. Without recombination, however, interference becomes global: it
couples the evolution of mutations across an entire chromosome. Under strong
selection pressures, chromosome-wide genetic linkage generates a specific mode
of evolution in which populations harbour competing clades of closely related
individuals, each clade containing a distinct set of beneficial and
deleterious mutations. This evolutionary mode, which is commonly called clonal
interference [22], is well known in asexually evolving microbial [23] and
viral populations [24, 25]. Theoretical models suggest that a similar mode of
evolution, in which selection acts on extended segments of genetically linked
sequence, arises in sexual populations at low recombination rates [26, 27].
However, finding evidence for this mode of evolution in the eukaryotic genome
of an obligate sexual organism has remained elusive so far.

_Drosophila_ is an ideal system to map differential effects of interference in
one genome. Fruit flies show overall high rates of adaptive genetic mutations
[28, 29, 30], at least in high-recombining parts of the genome (low-
recombining parts have been excluded from most previous studies). At the same
time, local recombination rates vary by orders of magnitude within the
_Drosophila_ genome. In particular, extended segments of low-recombining
sequence are located in genomic regions flanking the centromeres and, to a
lesser extent, the telomeres [31]. In this paper, we present a systematic
analysis of linkage effects across the _Drosophila_ genome. For two
populations of _D. melanogaster_ , we map the frequency statistics of
mutations and the divergence from the neighboring species _D. simulans_ in
their dependence on the local recombination rate. Consistently in both
populations, we find two clearly distinct regimes: a _local interference_
regime in high-recombining regions and an _interference condensate_ regime in
extended low-recombing regions, which cover about 20% of the autosomes. We
delineate these two regimes by the statistics of synonymous mutations. In the
local interference regime, the amount of synonymous mutations decreases with
recombination rate and the frequency spectrum follows an almost perfect
inverse-frequency power law, as predicted by classic theory [32]. This
indicates that the establishment of synonymous mutations is constrained by
background selection [14, 15, 13, 16, 18], but established mutations evolve
predominantly under genetic drift. In contrast, the frequency spectrum of the
interference condensate regime shows a specific depletion of intermediate- and
high-frequency variants, which is consistent with genetic draft over extended
genomic distances [6, 7].

To corroborate this scenario, we develop a scaling theory of evolution under
positive and negative selection and limited recombination, building on recent
models of asexual and sexual evolution [22, 11, 27, 33, 34, 35, 20, 36]. This
theory provides a unified framework for background selection and genetic
draft. It describes how amount and frequency-dependence of mutations depend on
the recombination rate, and it predicts the transition point from local
interference to the interference condensate. Over a wide range of evolutionary
parameters, the transition occurs at a threshold recombination rate that is
close to the sum of the rates of deleterious mutations and of beneficial
substitutions per unit sequence; these rates can be inferred from genomic
summary statistics. In the _Drosophila_ genome, the predicted threshold
recombination rate is numerically close to the point mutation rate, in perfect
agreement with the transition point observed in mutation frequency spectra.

Our scaling theory also provides the tools to infer key evolutionary features
of the condensate regime from genomic data. We use this inference to quantify
similarities of the _Drosophila_ interference condensate to asexual evolution,
and to understand the likely biological impact of the condensate mode of
evolution. Specifically, we show that genes in condensate regions are less
evolvable in response to positive selection and have a higher genetic load
than genes in the local interference regime. We discuss how these evolutionary
differences can impact gene functions in the condensate and generate selective
pressure on genome architecture.

## Results

### Evolutionary modes in recombining genomes

Why there are two distinct evolutionary regimes in recombining genomes can be
understood from a remarkably simple scaling theory. We consider genome
evolution under deleterious mutations with rate $u_{d}$, beneficial mutations
generating substitutions with rate $v_{b}$, and recombination with rate
$\rho$; all of these rates are measured per base pair unit of haploid sequence
and per generation. In terms of these rates, we estimate the probability that
a given selected mutation evolves autonomously —i.e., free of background
selection and genetic draft—, generalizing a previous argument by Weissman and
Barton for evolution solely under beneficial mutations [26]. We first compute
the average amount of interference generated by the substitution of a
beneficial mutation with selection coefficient $s$ at a given focal site in
the genome. This mutation takes an average time of order $\tau_{s}\sim 1/s$
from establishment to high frequency and generates a linkage correlation
interval of size $\xi_{s}=1/(\rho\tau_{s})\sim s/\rho$ around the focal site.
Other mutations at a distance $r\lesssim\xi_{s}$ are likely to retain their
genetic linkage to one of the alleles at the focal site and are subject to
strong interference; more distant mutations are likely to randomize their
genetic linkage to the alleles at focal site by recombination within the time
span $\tau_{s}$. Hence, each beneficial substitution generates an
_interference domain_ with an area $\tau_{s}\times\xi_{s}\sim 1/\rho$ around
its focal point in genomic space-time [26]. By exactly the same argument, each
deleterious mutation creates background selection in an interference domain
with area $\tau_{s}\times\xi_{s}=1/\rho$ around its focal point. In this case,
$\tau_{s}\sim 1/s$ is the expected time between origination and loss of the
deleterious allele. While genetic draft acts on all other mutations in the
genomic neighborhood of the driver mutation, background selection strongly
affects only mutations on the genetic background of the deleterious allele,
but this difference does not affect the scaling of interference domains. To
estimate the joint effects of beneficial and deleterious mutations, we combine
both kinds of interference interactions into a single _interference density_
parameter

$\omega=\frac{u_{d}+v_{b}}{\rho}.$ (1)

This parameter delineates two universal evolutionary modes of recombining
genomes:

Figure 1: Evolutionary modes in recombining genomes (schematic). The
interference density $\omega$, defined in equation (1), delineates two regimes
that differ in strength and genomic range of interference selection. (a) Local
interference ($\omega\lesssim 1$). This regime has a dilute pattern of
interference domains generated by deleterious mutations (blue) and beneficial
substitutions (red). These domains have space-time densities $u_{b}$ and
$v_{b}$, respectively; each domain covers a space-time area $1/\rho$.
Interference selection occurs only within interference domains; mutations
under selection evolve in a largely independent way. (b) Interference
condensate ($\omega\gtrsim 1$). In this regime, interference domains generate
a densely packed pattern. Interference domains have characteristic sizes
$\xi=\tilde{\sigma}/\rho$ and $\tau=1/\tilde{\sigma}$ in space and time, as
detailed in equation (5). Mutations are subject to strong interference
selection, which curbs the speed of evolution.

The _local interference_ mode ($\omega\ll 1$) has a dilute pattern of
interference domains: the domains of beneficial substitutions and of
deleterious mutations are randomly distributed with probabilities $u_{b}$ and
$v_{b}$ per unit sequence and per unit time (Fig. 1a). The space-time shape of
a domain, which is given by the scales $\xi_{s}$ and $\tau_{s}$, depends on
the selection coefficient of its focal mutation, but its area $1/\rho$ is
universal. Because the interference domains are, on average, well-separated in
the local intereference mode, different mutations under selection are
statistically independent. Hence, the rate of beneficial substitutions with
selection coefficient $s$ is related to the underlying mutation rate $u_{b}$
and the haploid effective population size $N$ by Haldane’s classic formula for
individual sites, $v_{b}=2Nsu_{b}$ [37]. A given (beneficial or deleterious)
mutation evolves autonomously if its own interference domain has negligible
overlap with any of the other interference domains, which happens with
probability $p_{0}={\rm e}^{-\omega}$. Two target mutations on different
genetic backgrounds see the same red domains but different blue domains;
however, the no-interference probability $p_{0}$ is independent of background.

The _interference condensate_ mode ($\omega\gg 1$) has densely packed and
overlapping interference domains. This indicates strong interference over
extended genomic segments: genomic space-time is jammed by mutations under
selection (Fig. 1b). By the definition of $\omega$, the condensate is a broad
evolutionary regime: it is generated by a sufficiently large supply of
substantially beneficial or deleterious mutations, or a combination of both,
but it does not depend on details of their effect distribution. Remarkably,
the condensate domains have not only a universal area but also a typical shape
that is given by universal scales $\tau$ and $\xi=1/(\rho\tau)$. Below, we
will infer these scales from genomic data in _Drosophila_.

A key evolutionary quantity to map these evolutionary modes is the average
fitness variance in a population, $\Sigma$, which measures the efficacy of
selection: by Fisher’s fundamental theorem, $\Sigma$ equals the rate of
fitness increase by frequency gains of fitter genetic variants in the
population. As detailed in Methods, our scaling theory captures the dependence
of $\Sigma$ on the evolutionary parameters in both interference modes. In the
local interference regime, $\Sigma$ depends linearly on the rates $u_{d}$ and
$u_{b}$, which reflects the statistical independence of mutation events. In
the interference condensate, $\Sigma$ is curbed to a sublinear function of
$u_{d}$ and $u_{b}$, which signals a reduced efficacy of selection caused by
the jamming of genomic space-time (Fig. 1b). To test these results of our
scaling theory, we performed simulations of evolving populations (see Methods
for simulation details). In Fig. 2a, the average fitness variance per unit
sequence, $\varsigma^{2}$, is plotted against $\omega$ (with a suitable
rescaling factor, as explained in Methods). In the regime $\omega\ll 1$, the
rescaled fitness variance data obtained for a wide range of parameters
$u_{d}$, $u_{b}$, $\rho$ collapse onto a uni-valued, linear function of
$\omega$. In the interference condensate ($\omega\gtrsim\omega^{*}$), the
fitness variance is seen to be curbed, and the rescaled data for different
evolutionary parameters show some spread. Here we evaluate $\omega$ in terms
of the mutation rates and the average selection coefficient of beneficial
mutations, $\omega=(u_{d}+2N\bar{s}u_{b})/\rho$, which maps the same regimes
as equation (1) because $v_{b}\simeq 2N\bar{s}u_{b}$ for $\omega\lesssim 1$.

Figure 2: Genomic markers of interference. Simulations of evolution with
beneficial mutations (rate $u_{b}$ per bp, selection coefficient $s$),
deleterious mutations (rate $u_{d}$ per bp, selection coefficient $-s$), and
recombination (rate $\rho$ per bp) in haploid populations of size $N$. (a)
Scaled fitness variance per site, $\varsigma^{2}/(s\rho)$, plotted against the
interference density $\omega=(u_{d}+v_{b})/\rho$ with $v_{b}=2Nsu_{b}$.
Simulation data for different values of $u_{d}$ and $u_{b}$ (marked by the
color of points) are shown together with theoretical predictions for the local
interference regime ($\omega\lesssim 1$, black line) and the interference
condensate ($\omega\gtrsim 1$, green line). See equations (9) and (8). (b)
Frequency spectrum of neutral mutations. Simulation results for parameters in
the local interference regime (blue dots) and in the interference condensate
(orange dots) are shown together with fits to the spectral functions
$Q_{0}(x;\nu\\!=\\!0)$ (blue line) and $Q_{0}(x;\nu\\!=\\!2.7)$ (orange line).
The shape distortion at intermediate frequencies is a universal characteristic
of the condensate regime. The secondary branch at high frequencies is a
feature of outgroup-directed spectra, which are appropriate for our data
analysis; see text below and equations (19) and (25). (c) Shape parameter
$\nu$, plotted against interference density $\omega$. Site frequency spectra
from simulations are fitted to the spectral function $Q_{0}(x;\nu)$. (d)
Neutral sequence diversity $\pi$ plotted against interference density
$\omega$. Simulation data is shown together with theoretical predictions for
the local interference regime ($\omega\lesssim 1$, black line) and the
interference condensate ($\omega\gtrsim 1$, green line). See equations (11)
and (12). Simulation parameters: $N=2000$, $\rho=10^{-7}-10^{-4}$,
$u_{d}=0-3.0\times 10^{-6}$, $u_{b}=0-2.5\times 10^{-7}$.

The reduction in the efficacy of selection and, in particular, the diminishing
return of beneficial mutations in the interference condensate are hallmarks of
asexual evolution in large populations, which are known from experiments with
microbial populations [38, 23, 39, 40] and from theoretical models [22, 36,
12, 33]. They signal the competition between genetic clades in an evolving
population, which prevents some beneficial mutations to reach substantial
frequencies because they are outrun by other clades. At the same time,
deleterious mutations can reach fixation if they are part of a successful
clade; this effect is often referred to as Muller’s ratchet [41, 42, 43, 44,
45, 46]. We conclude that the condensate regime shares important
characteristics with asexual processes, in accordance with previous results in
refs. [26, 27, 11]. Our scaling theory expresses this link mathematically: the
modes of evolution in recombining systems can be mapped onto corresponding
modes of asexual evolution in a specific low-recombination limit (Methods).

In a minimal scaling theory that is based on the interference density, the
local interference regime and the interference condensate are separated by a
smooth transition at a characteristic value $\omega^{*}$ of order 1. The
transition occurs when the interference probability $e^{-\omega}$ becomes of
order 1; the transition point marks the onset of nonlinearity in the fitness
variance. For a broad range of evolutionary parameters, which includes
realistic assumptions for the _Drosophila_ genome, this behavior is confirmed
by our simulations (Fig. 2a) and is consistent with analytical results for
specific cases [26, 27], including the low-recombination limit [33, 20, 12].
In Methods, we detail this minimal scaling theory and discuss extensions that
cover parameter regimes with systematic shifts of the transition point
$\omega^{*}$ above or below 1 (Supplementary Figure S1).

### Genomic signature of interference selection

The fitness variance is a key summary statistics to map evolutionary modes
under interference selection but it depends on the a priori unknown rates
$u_{d}$ and $v_{b}$. The distribution of mutation frequencies $x$ at neutrally
evolving sites, the so-called neutral site frequency spectrum $q(x)$, provides
an alternative test that can be directly evaluated from population-scale
sequencing data. At high recombination rates, the neutral spectrum is
dominated by genetic drift and has the universal Kimura form $q(x)\sim 1/x$
[32] (blue line in Fig. 2b). At low recombination, the spectrum shows a
characteristic depletion of intermediate- and high-frequency mutation counts
(red line in Fig. 2b). This shape distortion is a result of genetic draft,
which generates faster frequency changes and, hence, fewer variants in this
frequency range than genetic drift. This distortion turns out to be a robust
feature that can be read off from genomic data even if the exact form of the
spectrum is hidden by noise and confounding factors.

We can compare the site frequency spectrum inferred from genomic data with
spectra derived from specific evolutionary models. All analytically solvable
models make strong simplifying assumptions on the evolutionary process,
specifically on rate and effect distributions of mutations generating
interference selection. The exact form of the spectral function depends on
these model details, but broad shape features are a universal markers of
interference. An important class of models are so-called travelling fitness
waves, which describe the asymptotic regime of linked genetic variation
generated by multiple coexisting mutations with individually small selection
coefficients [33, 34, 36, 47]. Fitness waves generate a steady turnover of
sequence variation at a characteristic rate $\sigma$. In the asymptotic wave
regime, genetically linked neutral sites have a spectrum depleted at
intermediate frequencies, as given by an inverse-square power law $q(x)\sim
1/x^{2}$ for $x<1/2$ and a minimum near $x=1/2$ [27]. These models underscore
an important general point: genetic draft — i.e., mutation frequency
trajectories shaped by the substitution dynamics of a beneficial allele at a
genetically linked locus — and the associated shape distortion of site
frequency spectra is universally generated by a sufficient supply of
deleterious or by beneficial mutations [45, 46]. In the following, we use a
specific model with spectral shapes depleted at intermediate frequencies that
are tunable to the _Drosophila_ data reported below. The model contains a
focal site that evolves by mutations, selection, and genetic drift; the site
is also subject to background selection and genetic draft with rate $\sigma$.
Draft is generated by linked strongly beneficial alleles, each of which occurs
on a random genetic background and leads to instantaneous fixation or loss of
mutations at the focal site. The resulting spectral function of neutral sites
takes a simple approximate form, $Q_{0}(x;\nu)={\rm e}^{-\nu x}/x$, with a
shape parameter $\nu$ that is proportional to the draft rate $\sigma$ (dashed
lines in Fig. 2b; details on $Q_{0}(x;\nu)$ are given in Methods). In the
following, this model will serve to parametrize the universal shape distortion
of empirical spectra, without pretence to resolve details of the underlying
selective forces.

In Fig. 2cd, we show that mutation frequency data produce two consistent
markers of interference. First, we fit neutral site frequency spectra obtained
from numerical simulations to the form $Q_{0}(x;\nu)$ and plot the inferred
shape parameter $\nu$ against the interference density $\omega$ of the
underlying evolutionary process. Over a wide range of rates $u_{s},u_{b}$, and
$\rho$, we find $\nu\approx 0$ (i.e., neutral spectra of the form $q(x)\sim
1/x$) in the local interference regime ($\omega\lesssim\omega^{*}$) and
$\nu>1$ (i.e., neutral spectra with depletion of intermediate and high
frequencies) in the condensate regime ($\omega\gtrsim\omega^{*}$). Below, we
will link the shape parameter $\nu$ to specific evolutionary characteristics
of the condensate regime. Second, we record the sequence diversity at
synonymous sites as a function of the interference density $\omega$ (Fig. 2d).
This quantity shows a strong dependence on $\rho$ in the local interference
regime ($\omega\lesssim\omega^{*}$) and a weaker dependence in the
interference condensate ($\omega\gtrsim\omega^{*}$), a pattern that is
predicted by our scaling theory and will be described in more detail below.
Hence, both genetic draft on neutral mutations and the depletion of the
diversity pattern set on at the transition point $\omega^{*}$ from local
interference to the interference condensate (Fig. 2cd), the same point that is
marked by the onset of nonlinearity in the fitness variance (Fig. 2a). The
validity range of our inference method is detailed in Methods.

### Interference selection in the _Drosophila_ genome

To obtain a genome-wide map of interference in the _Drosophila melanogaster_
genome, we use sequence data from an American [48] and an African population
[49]. To equalize coverage, we take a random sample of 25 individuals in each
population. At this sampling depth, site frequency spectra are quite
insensitive to low-frequency variants (which would arise, for example, from a
recent population expansion) but are perfectly suitable for studying
intermediate-frequency variants, which are at the center of this study. Based
on a published high-resolution recombination map for the Drosophila genome
[31], we partition genomic sites in the autosomes (i.e., chromosomes 2L, 2R,
3L, 3R) according to the local recombination rate evaluated in windows of
$10^{5}$ base pairs. This partitioning covers a range of rates between
$10^{-10}$ and $10^{-7}$ with an average of $2.4\times 10^{-8}$ per unit
sequence and per generation (often reported in units of $10^{-8}$ per unit
sequence and per generation, called centiMorgans per Megabase).

In each recombination rate bin and in different sequence categories, we record
the outgroup-directed site frequency spectrum, $\hat{q}^{o}(x)$, which is
defined as the number of sites per unit sequence at which a fraction $x=k/n$
of the sampled individuals have a mutant allele and a fraction $1-x$ have the
outgroup allele (with $k=0,1,\dots,25$ and $n=25$; we disregard sites with
more than two alleles). Following common practice, we determine the outgroup
allele by alignment with the reference genome of the neighboring species D.
simulans. These empirical spectra differ in two ways from the model spectra
introduced above. First, the spectra $\hat{q}^{o}(x)$ are evaluated for
discrete frequencies in a small sequence sample, which introduces sampling
corrections compared to model distributions derived for larger populations (we
use a hat to mark this difference; sampling corrections are detailed in
Methods). Second, model spectra are directed from the ancestral allele at the
origination time of the mutation. A substitution between the ingroup and the
outgroup species reverses the role of the ancestral and allele mutant at part
of the sequence sites. In a sequence class with a given density $d$ of
substitutions, the ancestor-directed and the outgroup-directed spectra are
related by a linear map, $q^{o}(x)=(1-d)\,q(x)+d\,q(1-x)$; the same map
relates the sample spectra $\hat{q}^{o}(x)$ and $\hat{q}(x)$. Hence, outgroup-
directed spectra have a primary branch with a maximum at low frequency and a
secondary branch with a maximum at high frequency.

Figure 3: Interference regimes in the _Drosophila_ genome. (a,b) Outgroup-
polarized frequency spectra of synonymous mutations. Sample spectra
$\hat{q}_{s}^{o}(x)$ from two populations of _D. melanogaster_ at three values
of the recombination rate $\rho$, together with model spectra $q_{s}^{o}(x)$
with maximum-likelihood shape parameter $\nu$ as indicated (solid lines). See
equations (2) and (25). (c) Spectral shape of synonymous mutations. Inferred
shape parameters $\nu$ from two populations are plotted against the scaled
recombination rate $\rho/\mu$. (d) Sequence diversity at synonymous sites,
$\pi_{s}$, plotted against the scaled recombination rate $\rho/\mu$ (dots).
Data from two populations is shown together with theoretical predictions for
the local interference regime ($\omega\lesssim 1$, black line) and the
interference condensate ($\omega\gtrsim 1$, green line). See equations (11)
and (12). The data of (c,d) consistently maps the condensation transition to a
threshold value $\rho^{*}/\mu\sim 1$, as predicted by scaling theory.

In Fig. 3ab, we plot the sample spectra of 4-fold synonymous sequence sites,
$\hat{q}_{s}^{o}(x)$, for three representative bins of high, intermediate, and
low recombination rates in the American and the African population. These
spectra have a striking common pattern. Across high and intermediate
recombination rates, they follow almost perfectly the standard Kimura inverse-
frequency form, $q(x)\sim(1-d)/x+d/(1-x)$, which appears as straight lines
over most of the frequency range in the double-logarithmic plots of Fig. 3ab.
This form indicates that the dominant evolutionary force acting on synonymous
genetic mutations at high and intermediate recombination rates is genetic
drift. It shows that the average selection at synonymous sites is weak, making
this class a good approximation of neutrally evolving sequence. It also
excludes strong demographic effects affecting the spectral form at
intermediate frequencies (notwithstanding small differences at low frequencies
between the American and the African population, which reflect differences in
their recent demography [50, 51]). Strong selective sweeps are known to
deplete the density and to distort the spectrum of synonymous mutations in the
local vicinity of the positively selected site [29, 52]; however, the rate of
these sweeps is low enough not to affect the aggregate spectra (Fig. 3ab). In
contrast, the spectra at low recombination rates show a depletion of
intermediate and high frequencies. This depletion signals genetic draft on
synonymous mutations, which we attribute interference selection. The argument
for interference selection will be completed below, where we show that the
onset of the shape distortion occurs at a value $\omega^{*}\sim 1$ predicted
by the interference scaling model and is accompanied by a consistent
$\rho$-dependence of the synonymous sequence diversity.

To map the transition point between local interference and interference
condensate, we calibrate draft model spectra for neutral sites,

$q_{s}(x)\approx\theta_{s}\,Q_{0}(x;\nu),$ (2)

to the empirical frequency spectra $\hat{q}_{s}^{o}(x)$ of synonymous sequence
sites in D. melanogaster. We use a consistent Bayesian inference scheme that
includes sampling effects and the map from outgroup-directed to ancestor-
directed spectra (Methods). This scheme provides maximum-likelihood values and
confidence intervals of the the shape parameter $\nu$ (Fig. 3c) and of the
mutation density $\theta_{s}$ (shown below in Fig. 5a) in each recombination
bin, without additional fit parameters. The synonymous spectral data signal an
onset of interference selection at a threshold recombination rate
$\rho^{*}\approx\mu$, corresponding to a shape parameter or rescaled draft
rate $\nu=1$. Regions with $\rho\gtrsim\rho^{*}$ are inferred to be in the
local interference regime, regions with $\rho\lesssim\rho^{*}$ are in the
interference condensate. This regime is characterized by moderate interference
with values of the shape parameter in the range $\nu\lesssim 2$. To obtain
some insight on the selective effects causing interference, we infer
“corrected”, ancestor-directed sample spectra $\hat{q}_{s}(x)$ by an inverse
linear map (Methods). The low-recombination spectra $\hat{q}_{s}(x)$ are
monotonic and well approximated by the spectral functions $Q_{0}(x;\nu)$ of
the draft model, but they do not show the minimum at $x=1/2$ characteristic of
the travelling-wave model (Supplementary Figure S2). This suggests the
underlying interference selection includes drivers under substantial selection
and is at some distance from the travelling-wave regime of multiple mutations
with individually small effects.

Figure 4: Frequency spectra of nonsynonymous mutations. (a,b) Outgroup-
polarized sample spectra $\hat{q}_{a}^{o}(x)$ from two populations of _D.
melanogaster_ , together with maximum-likelihood spectra $q_{a}^{o}(x)$ of the
two-component model (solid lines: full spectrum, dashed lines: neutral
component). See equations (3) and (27). Our inference uses the shape parameter
$\nu$ inferred from synonymous mutations (Fig. 3c); other inferred model
parameters are reported in Supplementary Table S2.

The partitioning of the _Drosophila_ genome in local interference regions and
interference condensate regions can be consistently traced in all sequence
categories (Fig. 4, Supplementary Figure S3). At low recombination rates, all
of these site frequency spectra show qualitatively the same depletion of
intermediate and high frequencies that is characteristic of the condensate
regime. Specifically for nonsynonymous mutations, we calibrate a two-component
model

$q_{a}(x)\approx\theta_{a}\,Q_{0}(x;\nu)+\theta^{\prime}_{a}\,Q(x;\zeta_{a},\nu)$
(3)

to the empirical spectra $\hat{q}_{a}(x)$. Here $Q(x;\zeta,\nu)$ is a spectral
function for sequence sites with mean selection coefficient $s_{a}$ that are
subject to genetic draft with rate $\sigma$. This function contains branches
$Q_{\pm}(x;\zeta_{a},\nu)={\rm e}^{(\pm\zeta-\nu)x}$ that correspond to
beneficial and deleterious mutations, respectively, and depend on the rescaled
selection coefficient $\zeta$ (Methods). We obtain maximum-likelihood model
parameters $\theta_{a},\theta^{\prime}_{a},\zeta_{a}$ in each recombination
bin, using an extended Bayesian inference scheme. This scheme includes a model
for cross-species evolution under selection and the resulting, more complex
linear map between ancestor-directed and outgroup-directed spectra (Methods).
Remarkably, the spectra for nonsynymous mutations (Fig. 4) can be explained
across all recombination classes by the two-component model (3) with the same
shape parameter as inferred for synonymous sites (Fig. 3c) and, hence, with
the same threshold rate $\rho^{*}$. The maximum-likelihood model includes
near-neutral sites with spectral shape $Q_{0}(x,\nu)$, which is of Kimura form
for $\rho>\rho^{*}$, as well as moderately selected sites with spectrum
$Q(x;\zeta_{a},\nu)$ and mean effect of order $\zeta_{a}\sim 20$, which
produce excess frequency counts in the range $x\lesssim 0.1$ (see dashed vs.
solid lines in Fig. 4). These excess counts cannot be explained by demographic
factors, because they are common to both populations and no comparable excess
is observed at synonymous sites. Across all recombination rates, the inferred
mutation densities $\theta_{a}$ and $\theta_{a}^{\prime}$ are much lower than
the density $\theta_{s}$ at synonymous sites (Fig. 5a), indicating that a
large fraction of amino acid changes is under strong selection and hence,
suppressed in the frequency range of our spectra. The inferred selective
effects of amino acid changes that do appear in our spectra are consistent
with the expected fitness landscape of proteins. Important molecular
phenotypes of proteins, such as fold stability or enzymatic activity, are
quantitative traits encoded by multiple sequence sites. Such traits
generically contain weakly and moderately selected constitutive sites, even if
the trait itself is under strong stabilizing selection [53]. The maximum-
likelihood selection coefficients $\zeta_{a}$ (Supplementary Table S2) are
just one order of magnitude higher than the scaled draft rate $\nu$ in the
lowest recombination classes. This suggests that a fraction of nonsynonymous
sites is affected by genetic draft in the condensate regime; this point is
discussed further below.

### Predicting the condensation transition in _Drosophila_

The threshold recombination rate marking the onset of interference selection
is numerically close to the point mutation rate in the _Drosophila_ genome,
$\mu=2.8\times 10^{-9}$ per generation and per unit sequence [54] (see Fig.
3b). In light of our scaling theory, this is hardly surprising: the
interference density $\omega$, which determines the transition between local
interference and interference condensate, is determined by a balance between
the rates of local mutations and recombination. We now combine the scaling
theory, our evolutionary model, and our Bayesian inference scheme to
independently predict the transition point $\rho^{*}$, as well as the behavior
of the sequence diversity in both interference regimes, solely from genomic
data in the high-recombination regime. This serves as a stringent consistency
test for the scaling theory and provides additional evidence for our inference
of interference selection in the _Drosophila_ genome.

Figure 5: Interference density and condensation transition. (a) Mutation
densities of synonymous mutations, $\theta_{s}$, and of nonsynonymous
mutations, $\theta_{a}$ and $\theta^{\prime}_{a}$, inferred from spectral data
of the African population and plotted against the scaled recombination rate
$\rho/\mu$. (b) Synonymous divergence, $d_{s}$, and nonsynonymous sequence
divergence, $d_{a}$, to the outgroup species D. simulans. (c) Fraction of
deleterious nonsynonymous mutations, $\alpha_{d}$, as given by equation (33).
(d) Fraction of adaptive amino acid substitutions, $\alpha_{b}$, as given by
equation (34). (e) Interference density, $\omega$, as given by equation (4).
The condensation transition $(\omega^{*}\sim 1)$ is mapped to a threshold
value $\rho^{*}/\mu\sim 1$ (dashed line).

First, we estimate the rate of deleterious mutations in protein-coding
sequence from the reduction in mutation density of amino acid changes compared
to synonymous changes, $u_{d}/\mu=\alpha_{d}$, where
$\alpha_{d}=1-(\theta_{a}/\theta_{s})$ is the fraction of amino acid mutations
that are deleterious. Moderately deleterious and strongly deleterious amino
acid changes contribute partial fractions $\theta^{\prime}_{a}/\theta_{s}$ and
$(\theta_{s}-\theta_{a}-\theta_{a}^{\prime})/\theta_{s}$, respectively.
Second, we estimate the rate of beneficial substitutions in a similar way from
the excess of amino acid substitutions compared to the number expected in the
near-neutral component, $v_{b}/\mu=\alpha_{b}\,(d_{a}/d_{s})$, where
$\alpha_{b}=1-(d_{s}/d_{a})(\theta_{a}/\theta_{s})$ is the fraction of amino
acid substitutions that are beneficial. In Methods, we derive these
expressions from our evolutionary model and show how they can consistently be
extrapolated into the condensate regime. The expression for $\alpha_{b}$
resembles a McDonald-Kreitman test [55, 56], but our mixed model (3) affords
an improved estimate of the mutation density $\theta_{a}$ by discounting
moderately deleterious mutations. Equation (1) then gives a simple estimate of
the interference density from genomic summary data,

$\omega=\frac{\mu}{\rho}\left(\alpha_{d}+\alpha_{b}\frac{d_{a}}{d_{s}}\right)=\frac{\mu}{\rho}\left(1+\frac{d_{a}}{d_{s}}-2\frac{\theta_{a}}{\theta_{s}}\right).$
(4)

In Fig. 5ab, we collect the relevant data of the Drosophila genome in all
recombination classes: the maximum-likelihood mutation densities $\theta_{s}$
and $\theta_{a}$ inferred from spectral data, and the corresponding sequence
divergence levels $d_{s}$ and $d_{a}$, defined as the number of substitutions
between each D. melanogaster population and the D. simulans reference genome.
From these data, we infer $\rho$-dependent fractions $\alpha_{d}$ and
$\alpha_{b}$ (Fig. 5cd) and the resulting interference density $\omega$ (Fig.
5e).

For $\rho>\rho^{*}$, we consistently find a deleterious mutation rate
$u_{d}\approx 0.9\mu$ and a beneficial substitution rate $v_{b}\approx 0.1\mu$
that are approximately independent of $\rho$ (Fig. 5cd). Hence, the local
interference regime has an approximately constant density of interference
domains and an interference density that is inversely proportional to the
recombination rate, $\omega\sim 1.0\,\mu/\rho$. As inferred above, the
Drosophila genome includes a sizeable fraction of moderately selected sites
and genome-wide positive selection is not dominated solely by strong selective
sweeps; these characteristics suggest the minimal scaling theory in terms of
the interference density is applicable. This theory makes three quantitative
predictions:

  1. (a)

In the local interference regime, the mutation densities $\theta_{s}$ and
$\theta_{a}$, as well as the sequence diversity are proportional to the
probability of no interference, $p_{0}={\rm e}^{-\omega}\approx{\rm
e}^{-\mu/\rho}$. This formula generalizes the standard model of background
selection, which predicts the size of the error-free sequence class to depend
exponentially on the rate of deleterious mutations [14]. Indeed, the observed
$\rho$-dependence of the sequence diversity at synonymous sites is in good
agreement with this theory in the local interference regime, $\pi_{s}\sim{\rm
e}^{-\mu/\rho}$ (Fig. 3d, see definition in Methods), in broad agreement with
previous observations [57, 48].

  2. (b)

The transition to the interference condensate occurs at a threshold
interference density $\omega^{*}$ of order 1. This determines the threshold
recombination rate $\rho^{*}\sim\mu$ (Fig. 5e), in agreement with the observed
onset of interference selection (Fig. 3c).

  3. (c)

In the interference condensate, the sequence diversity depends only weakly on
the recombination rate. This dependence can be derived from a simple scaling
argument based on extremal value statistics: an expected number
$\omega/\omega^{*}$ of beneficial mutations with average selection coefficient
$\bar{s}$ originate in each interference domain, but only the fittest of these
mutants reaches fixation. This determines the draft rate
$\sigma\approx\bar{s}(1+\log(\omega/\omega^{*}))$, which sets the sequence
diversity $\pi_{s}\simeq 2\mu/\sigma$ [6, 19, 27]. With condensate
interference densities bounded in the range $\omega\approx(0.85-1.0)\mu/\rho$
(Fig. 5e), we obtain the leading $\rho$-dependence
$\pi_{s}\sim(1+\log(\rho^{*}/\rho))^{-1}$, which is in agreement with the
observed pattern (Fig. 3d). Our scaling argument is consistent with the
scaling of $\sigma$ in the numerical simulations (Fig. 2c) and with previous
results for evolution solely under beneficial mutations [26]. In a state of
stationary fitness, however, beneficial substitutions are a generic feature of
the condensate regime. Even in the absence of adaptation, they compensate the
fixation of deleterious mutations fixed by interference selection [44, 58].
Below, we will discuss the likely loci of these dynamics in the _Drosophila_
genome.

Taken together, genetic variation in _Drosophila_ is in remarkable quantitive
agreement with our interference scaling theory over two decades of
recombination rates. Fig. 6 charts the local interference density $\omega$ in
the autosomes of _D. melanogaster_ , the high-resolution recombination map of
ref. [31] and our genomic inference. Extended condensate regions, shown in
orange, are located primarily adjacent to the centromere regions and, to a
lesser extent, to the telomeres. The major part of condensate sequence
maintains a residual level of recombination, corresponding to interference
densities in the range $1<\omega\leq 4$. The remaining 9% of the autosomal
genome consists of 38 contiguous segments with no recorded recombination
($\omega>4$); these segments have an average length of 0.2 Mb and a maximum
length of 0.9Mb. We now turn to inferring key genomic and evolutionary
features of the interference condensate.

Figure 6: Map of evolutionary modes in the _Drosophila_ genome. Position-
dependent local interference density $\omega$ in the four autosomes, inferred
from the recombination rate $\rho$ in windows of 100kb (see text and Fig. 5e).
Condensate segments ($\omega>1$) cover about 20% of the genome and are located
primarily in chromosomal regions flanking the centromeres (orange: segments
with $1<\omega<4$; violet: segments with no recorded recombination,
$\omega>4$). We use the map of local recombination rates from ref. [31].

### Linkage correlations in the condensate

Although the condensate is a complicated regime of strongly correlated
mutations, it has remarkably simple emergent scaling properties. Because
interference domains in the condensate are densely packed, the draft rate
$\sigma$ becomes similar to the neutral coalescence rate, $\tilde{\sigma}$,
which is also the scale of fitness differences between competing clades. The
emergence of a characteristic scale of genetic turnover is a common feature of
models of asexual evolution [12, 59]. Under finite recombination, the rate
$\tilde{\sigma}$ sets the genomic correlation length
$\xi=\tilde{\sigma}/\rho$; coexisting mutations at a distance $r\lesssim\xi$
are likely to retain their genetic linkage over a mean coalescence time
interval $\tau=1/\tilde{\sigma}$ (Fig. 1b). We can estimate the coalescence
rate from the inferred values of draft rate and synonymous mutation density
[12], $\tilde{\sigma}=\sigma+2\mu/\theta_{s}$, or equivalently from the
neutral sequence diversity $\pi=2\mu/\tilde{\sigma}$ (Methods). Together, we
obtain the simple estimates

$\tilde{\sigma}=\frac{2\mu}{\pi},\qquad\xi=\frac{2\mu}{\rho\pi},$ (5)

which determine the universal shape of interference domains in the condensate
regime (Fig. 1b). In coalescent models under selection, the same scaling
$\tilde{\sigma}\sim\mu/\pi$ links the coalescence rate to the neutral sequence
diversity, in some cases with logarithmic corrections [19, 27]. In the
condensate regime, we find coalescence times $\tau$ about an order of
magnitude lower than at high recombination rates (Fig. 7a) and genomic
correlations up to $\xi\lesssim 10^{4}$ base pairs (Fig. 7b), signalling that
neighboring genes are often in common interference domains.

Figure 7: Interference domains and speed of evolution in the condensate. (a)
Coalescence time, $\tau=1/\tilde{\sigma}$, and (b) linkage correlation length,
$\xi$, plotted against the scaled recombination rate $\rho/\mu$. In the
condensate regime, these scales determine the characteristic shape of
interference domains (Fig. 1b). See equations (5) and (21). (c) Fitness
variance per site, as given by equation (6). This quantity displays a
drastically reduced efficacy of selection in the condensate, consistent with
the reduced fraction of adaptive substitutions (Fig. 5d).

### Speed and cost of evolution in the condensate

The most important asexual feature of the interference condensate is the
drastically reduced efficacy of selection. In the _Drosophila_ genome, we can
quantify this effect in two ways. First, the fraction of beneficial
substitutions, $\alpha_{b}$, which takes stable values of about $50\%$ in the
local interference regime, sharply drops in the condensate to below $10\%$ in
the lowest recombination class (Fig. 5d). Second, the fitness variance per
unit sequence of the condensate is related to the neutral sequence diversity,

$\varsigma^{2}=\frac{2\rho\mu}{\pi}$ (6)

(Methods). The $\rho$-dependent values of $\varsigma^{2}$ inferred from the
synonymous sequence diversity $\pi_{s}$ (Fig. 7c) show a sharp drop in the
efficacy of selection within the condensate regime; the fitness variance in
the lowest recombination class is by a factor 10 lower than at the transition
point $\rho^{*}$. The strong dependence of the fitness variance on the
recombination rate is in tune with the simulation results (Fig. 2a). We
conclude that interference selection curbs rate and selective effects of
adaptive evolution in the condensate regions of the _Drosophila_ genome.

The reduced efficacy of selection has an immediate consequence for genome
functionality in the condensate regime: interference selection generates
_emergent neutrality_ of sequence sites with selection coefficients
$s\lesssim\sigma$; these sites become disfunctional because their alleles are
randomized by interference selection [12]. We can estimate the resulting
fitness cost (or genetic load) for a protein, $\Delta
F=(\ell/2)\int_{0}^{\sigma}s\,f(s)\,ds$, where $f(s)$ is the distribution of
selection coefficients and $\ell$ is the length of the protein. This cost
increases with decreasing $\rho$, because $\sigma$ as inferred through the
shape parameter increases (Fig. 3c). Emergent neutrality says that the genetic
load in the two modes differs not only in magnitude, but qualitatively. In the
local interference regime, a genetic locus under moderate selection ($s>1/2N$)
incurs classical mutational load, where the beneficial allele is always
prevalent and only a small minority fraction of the population, of average
$\mu/s$, carries the deleterious allele. In the condensate, deleterious and
compensatory beneficial substitutions generate a new equilibrium in which the
deleterious allele becomes dominant in the population with probability
$1/(1+{\rm e}^{s/\sigma})$ [12]. Hence, the functional impact of moderately
deleterious alleles ($s<\sigma$) becomes important. Emergent neutrality likely
affects part of the nonsynonymous sites in the moderate selection class (Fig.
4), as well as intron, UTR, and synonymous sites under selection for codon
usage. Assuming that just a few percent of these sites become effectively
neutral, the above estimate predicts a substantial scaled fitness cost
$2N\Delta F\sim 10-100$ per gene, even if the effect of each individual site
is weak. This fitness cost is specific to genes in the condensate regime; its
likely consequences for genome architecture are discussed below.

## Discussion

The main method development of this paper is a unified scaling theory of
genetic draft and background selection. This theory identifies a dominant
scaling variable, the interference density $\omega=(u_{d}+v_{b})/\rho$, to
discriminate between two evolutionary modes: the local interference regime
($\omega\lesssim\omega^{*}$) and the interference condensate
($\omega\gtrsim\omega^{*}$). In the local interference mode, mutations evolve
in an approximately independent way by selection and genetic drift; in the
condensate, they are locked into clades of genetically linked sequence
segments and many are governed by linkage. This mode requires a sufficiently
high supply of mutations under substantial (beneficial or deleterious)
selection but is insensitive to details of the evolutionary process – in
particular, to the rate of adaptation. Over a broad range of evolutionary
parameters, the transition point $\omega^{*}$ between local interference and
condensate is of order 1. The frequency spectrum of neutral mutations can be
used as a marker of the evolutionary mode: the “convective” frequency
evolution in the condensate regime is signalled by a characteristic depletion
of intermediate and high frequencies.

In the _Drosophila_ genome, we build a case for the joint presence of these
evolutionary modes from a number of mutually consistent observations from
sequence data. We infer the rates of deleterious amino acid changes, $u_{d}$,
and the rate of beneficial substitutions, $v_{b}$, in protein coding sequence.
Given these selective building blocks of the interference density $\omega$,
our scaling theory predicts how genetic variation depends on recombination:
the sequence diversity varies strongly in the local interference regime,
$\pi\sim{\rm e}^{-\omega}$, and weakly in the condensate,
$\pi\sim(1+\log(\omega/\omega^{*}))^{-1}$; the transition point between these
regimes, $\omega^{*}\sim 1$, marks the onset of genetic draft. Together,
amplitude and shape of mutational spectra change in a concerted way. These
predictions are in agreement with direct genomic data of synonymous mutations.
While any single characteristic of genetic variation could be explained by
alternative evolutionary scenarios, the consistent joint pattern of diversity
and spectral shape over the entire range of recombination rates provides
strong evidence for an interference condensate in the _Drosophila_ genome
(Fig. 3cd).

Our results suggest that the established rationale of a strong evolutionary
advantage of sex applies to about 80% of the Drosophila genes, which are in
the local interference regime. The other 20%, some 3000 genes in the
interference condensate, show evolutionary similarities with asexual systems.
In the condensate regions, we infer a significantly lower fitness variance per
unit sequence, indicating reduced evolvability in response to adaptive
pressure. This may signal that condensate genes respond less efficiently to
existing positive selection for change or that they are subject to less
selection for change in the first place. We also infer a significantly
increased fitness cost (genetic load) concentrated in weakly and moderately
selected sequence sites, whose alleles are randomized by emergent neutrality
[12]. This finding suggests that the evolutionary partitioning of the
_Drosophila_ genome is also a functional partitioning. We hypothesize that
condensate genes have systematically lower intrinsic fold stability than other
genes. They should also have reduced codon usage bias, which may affect speed
and efficiency of translation and, hence, increase the cost of protein
expression. These hypotheses on the functional impact of interference
selection can be tested by experiment and by targeted sequence analysis.

A salient feature of _Drosophila_ is that both evolutionary modes coexist in
one genome. This implies that functional and fitness differences between
condensate genes and other genes play out in the same individual, the same
environment, and the same population. Over macro-evolutionary time scales,
these differences can generate feedback effects on genome architecture. First,
we expect selection against too long recombination coldspots. This is
qualitatively in line with observations: in 91% of the autosomes, the
_Drosophila_ genome maintains a residual level of recombination, keeping
interference selection capped to a moderate level ($\omega\leq 4$); the
remaining zero-recombination sequence is fragmented into short contiguous
segments (Fig. 6). Second, a given gene incurs a fitness cost that depends on
its target function and on the interference regime it is placed in. Therefore,
genes with high requirements on protein stability or translation efficiency
should be suppressed in the condensate. Whether there are differences in gene
content and gene functions between the local interference regime and the
condensate that can be explained as a consequence of differences in
interference selection is an interesting question for future research.

### Methods

#### Scaling theory

The heuristic scaling approach used in this paper is based on three main
ingredients: (i) In the local interference regime, the behavior of an
evolutionary observable can be calculated approximately from single-site
population genetics. (ii) The crossover to the interference condensate regime
can be described by a scaling function that depends only on the variable
$\omega$ given by equation (1). Here and in the following, crossover is used
as a technical term of scaling theory that is not to be confused with the
genetics term. (iii) In the condensate, evolutionary observables follow broad
heuristic constraints, and there is a matching condition between both scaling
regimes at the crossover point $\omega^{*}$. We consider long genomic segments
that evolve under limited recombination; individual sequence sites have a
distribution of selection coefficients with $2N\bar{s}\gg 1$, where $\bar{s}$
is the average selection coefficient and $N$ is the effective population size.
For simplicity, we neglect prefactors of order 1 and corrections to scaling,
which often depend on more specific model assumptions. Our analysis in the
main text builds on a minimal model with the following scaling relations:

  1. (a)

The average fitness variance per unit sequence, $\varsigma^{2}$, takes the
form

$\varsigma^{2}\simeq\left\\{\begin{array}[]{ll}(u_{d}+v_{b})\bar{s}&(\omega\lesssim
1,\mbox{local interference})\\\ \\\ \rho\sigma&(\omega\gtrsim
1,\mbox{interference condensate}),\end{array}\right.$ (7)

where $\sigma$ is a characteristic selection strength in the condensate
regime. The local interference expression
$\varsigma^{2}\simeq(u_{d}+v_{b})\bar{s}$ follows from direct calculation by
single-site population genetics, assuming statistical independence of selected
alleles at different sites. The leading condensate asymptotics
$\varsigma^{2}\simeq\rho\sigma$ is then already determined by the scaling
properties (ii) and (iii). Specifically, we evaluate the matching condition
$\sigma(\omega^{*})=\bar{s}$ at the crossover point $\omega^{*}\sim 1$ of the
minimal scaling theory with the requirement that $\varsigma^{2}$ depends only
weakly on $u_{d}$ and $v_{b}$ in the condensate. This is expected from the
jamming of genomic space-time shown in Fig. 1b and implies that the
recombination rate becomes a limiting factor of $\varsigma^{2}$ in the
condensate. The scaling argument given in the main text suggests a specific
functional form in the condensate, which is given by

$\sigma\simeq\bar{s}\,(1+\log(\omega/\omega^{*}));$ (8)

see also ref. [26]. Equation (7) can be rescaled to a dimensionless form,

$\frac{\varsigma^{2}}{\rho
s}\simeq\left\\{\begin{array}[]{ll}\omega&(\omega\lesssim 1,\mbox{local
interference})\\\ \\\ \dfrac{\sigma}{s}&(\omega\gtrsim 1,\mbox{interference
condensate}),\end{array}\right.$ (9)

which is confirmed by our simulation results (Fig. 1c). Equations (7) and (9)
and, in particular, the minimal crossover scaling $\omega^{*}\sim 1$ are
consistent with previous results for evolution under beneficial mutations [26]
and under background selection including moderate effects ($\log(2Ns)\sim 1$)
[17, 60]. Strong heterogeneities in the effect distribution or background
selection by strongly deleterious mutations generate systematic shifts of the
crossover point $\omega^{*}$; the corresponding extensions of scaling theory
are discussed below.

  2. (b)

As explained in the main text, $\sigma$ determines the characteristic scales
of time and genomic distance in the condensate[26],

$\tau\simeq\frac{1}{\sigma},\qquad\xi\simeq\frac{\sigma}{\rho}\qquad(\omega\gtrsim
1,\mbox{ interference condensate}).$ (10)

  3. (c)

The neutral sequence diversity, $\pi=2\int_{0}^{1}x(1-x)\,q(x)\,dx$, can be
estimated by the form

$\pi\simeq\left\\{\begin{array}[]{ll}2\mu N{\rm e}^{-\omega}&(\omega\lesssim
1,\mbox{ local interference})\\\ \\\ \dfrac{2\mu}{\sigma}&(\omega\gtrsim
1,\mbox{ interference condensate}).\end{array}\right.$ (11)

Using again the matching criterion $\sigma(\omega^{*})=\bar{s}$ at the
crossover point $\omega^{*}$, equation (11) interpolates between background
selection in the local interference regime and neutral evolution under genetic
draft with rate $\sigma$ in the condensate regime [17, 60, 20, 27]. In the
local interference regime, $\pi$ is proportional to $N$, which implies that
established neutral mutations evolve predominantly under genetic drift and
their spectrum is of Kimura form. Hence, the genetic draft of neutral
mutations and the resulting depletion of intermediate and high frequencies is
a marker of the condensate regime, which sets on at the crossover point
$\omega^{*}$. Equation (8) then predicts the form of the diversity in the
condensate regime,

$\pi\simeq\frac{2\mu}{\bar{s}(1+\log(\omega/\omega^{*}))}.$ (12)

Equations (7) – (11) show that $\pi$ measures key characteristics of the
condensate regime, the spacetime scaling (equation (5)) and the fitness
variance per unit sequence (equation (6)). In the main text, we use the sample
sequence diversity at synonymous sites,
$\pi_{s}=2\sum_{k=0}^{n}(k/n)(1-k/n)\,\hat{q}^{o}_{s}(k/n)$ to infer these
characteristics in the Drosophila genome. As discussed in the main text, the
Drosophila genome has a distribution of selective effects that includes sites
with weak and moderate selection, for which the minimal scaling theory with
$\omega^{*}\sim 1$ should be applicable. We find clear evidence that $\pi_{s}$
follows the scaling behavior predicted by equations (11) and (12); see Fig.
3d.

#### Extensions of scaling theory

Evolution by beneficial and deleterious mutations is a complex process whose
details depend on their rates and effect distribution. The minimal scaling
theory is a coarse approximation of this process. It provides useful
approximations of genomic statistics over a wide range of evolutionary
parameters, which includes settings appropriate for _Drosophila_. Here we
discuss two extensions that serve to link our scaling theory to existing
evolutionary models and to delineate the range of validity of the minimal
model.

  1. (a)

Background selection with strong effects. Equation (11) predicts the onset of
interference selection for sites of selection coeffcient $s$ at a
characteristic value

$\omega^{*}=\log(Ns).$ (13)

This expression is consistent with known results of background selection
theory [15, 20, 27, 43]. If background selection involves only strongly
selected sites ($2Ns\gg 1$), we obtain a shift of the crossover point
$\omega^{*}$ observed in aggregate data to values above 1 (Supplementary
Figure S1a). The crossover point is still marked by the onset of interference
selection on neutral sites and the resulting spectral shape distortion. This
regime is not relevant for _Drosophila_ , where we observe $\omega^{*}\sim 1$
and consistently, genomic sites under weak and moderate selection.

  2. (b)

Selective sweeps. An adaptive process driven by strongly beneficial mutations
with rate $v_{b}$ and average selection coefficient $s_{b}$ generates a
fitness flux $\phi=v_{b}s$, which measures the speed of adaptation per unit
sequence [30]. Under this process, a genomic focal site is subject to linked
sweeps at a rate $\sigma_{\rm
sweep}=v_{b}\xi_{s}=v_{b}s_{b}/\rho=2N\phi/\rho$. Focal sites of selection
coefficient $s<s_{b}$ are strongly affected by interference for $\sigma_{\rm
sweep}>s$, which sets the crossover point to interference selection,

$\omega^{*}=\frac{s}{s_{b}}\leq 1.$ (14)

In the special case of equal selection coefficients at all sites ($s=s_{b}$),
the crossover point is again $\omega^{*}=1$, independently of $s_{b}$ [26, 61]
(Supplementary Figure S1b). The onset of interference on neutral sites and the
resulting spectral shape distortion occur at a value
$\omega_{0}=1/(2Ns_{b})=\omega^{*}/(2Ns)$, which is smaller than $\omega^{*}$.
This regime is not observed in _Drosophila_ ; strong sweeps are too rare to
distort neutral spectra for $\omega<1$.

#### Link to asexual evolution

An explicit expression for $\sigma$ can be obtained if we identify the total
fitness variance per correlation interval, $\xi\varsigma^{2}=\sigma^{2}$, with
the corresponding quantity in models of asexual populations with a genome of
length $\xi$ [26]. In the intermediate fluctuation regime of travelling waves,
this identification yields the analytic expression
$\sigma=\bar{s}\log(\dots)$, where $\log(\dots)$ stands for a weak and model-
specific dependence on the parameters $u_{b}$, $\bar{s}$, $N$ and the system
size $\xi$; see equation (15) of ref. [61]. This form has a leading
large-$\xi$ asymptotics consistent with our scaling argument given in the main
text, $\sigma\simeq\bar{s}\log\xi\simeq\bar{s}\log(\rho^{*}/\rho)$. In ref.
[27], an analogous identification is discussed for evolutionary processes
dominated by weakly selected alleles.

The theoretical limit of strictly asexual evolution, which is reached at very
low recombination rates $\rho\ll\sigma/L$ in a genome of length $L$, can be
described in terms of our scaling theory by substituting $L$ for the
correlation length $\xi=\sigma/\rho$ resp. $\xi_{s}=s/\rho$. In this limit,
the interference density (1) for mutations of effect $s$ takes the form

$\omega=\frac{L(u_{d}+v_{b})}{s}=\frac{U_{d}+V_{b}}{s},$ (15)

which depends on the genome-wide rates $U_{d}=Lu_{d}$ and $V_{b}=Lv_{b}$. For
$V_{b}=0$, the identity (13) for $\omega^{*}$ becomes the well-known criterion
for the onset of Muller’s ratchet in asexual populations,
$U_{d}/s\sim\log(Ns)$ [42, 62, 43, 45].

#### Evolutionary model: mutation frequency distributions

As explained in the main text, we use a specific model of interference
selection to parametrize site frequency spectra: individual sites evolve under
mutations (with rate $\mu$), selection (with site selection coefficient
$s>0$), genetic drift (in a population of effective size $N$), and
periodically recurrent genetic draft (with rate $\sigma$). The draft model
generates site frequency spectra that can be estimated analytically by a
saddle-point approximation to the path integral of mutation frequency paths
[63]. For beneficial mutations (of selection coefficient $s$) and deleterious
mutations (of selection coefficient $-s$) at two-allelic sites, we obtain the
frequency distributions

$\displaystyle q_{\pm}(x)$ $\displaystyle=$
$\displaystyle\frac{1}{Z_{\pm}(\theta,\zeta,\nu)}\,q_{0}(x)\,\int
p(\tau(\tilde{s},x),\sigma)\,\exp\left[-\frac{\theta_{0}}{4N\theta}\int_{0}^{\tau(\tilde{s},x)}\frac{\big{(}\dot{x}(t;\tilde{s})\mp
sg(x(t;\tilde{s}))\big{)}^{2}}{g(x(t;\tilde{s}))}\,{\rm
d}t\right]\,d\tilde{s}$ (17) $\displaystyle\simeq$
$\displaystyle\theta\,Q_{\pm}(x;\zeta,\nu)\qquad\Big{(}\frac{1}{N}\leq x\leq
1-\frac{1}{N}{\Big{)}},$

respectively; these distributions depend on the mutation density
$\theta=\theta_{0}{\rm e}^{-\omega}=\mu N{\rm e}^{-\omega}\ll 1$, the scaled
draft rate $\nu=2N\sigma\theta/\theta_{0}$, and the scaled site selection
coefficient $\zeta=2Ns\theta/\theta_{0}$. The function
$q_{0}(x)=x^{-1+\theta}(1-x)^{-1+\theta}$ denotes the neutral spectrum under
genetic drift. The no-sweep probability $p(\tau,\sigma)$ over a time interval
$\tau$ is assumed to be strongly suppressed for $\tau\gtrsim 1/\sigma$. The
exponential weight involves the maximum-likelihood frequency path with
effective selection coefficient $\tilde{s}$, which is denoted by
$x(t,\tilde{s})$. This path follows the equation of motion
$\dot{x}(t,\tilde{s})=\tilde{s}g(x(t,\tilde{s}))$ with $g(x)=x(1-x)$ and has a
sojourn time $\tau(\tilde{s},x)$ up to frequency $x$. The prefactor
$Z_{\pm}(\theta,\zeta,\nu)$ ensures the normalization
$\int_{0}^{1}q(x)\,dx=1$. An approximate evaluation of the integral in
equation (LABEL:qsel1) results in the remarkably simple spectral function

$Q_{\pm}(x;\zeta,\nu)=\frac{{\rm e}^{(\pm\zeta-\nu)x}}{x}.$ (18)

This function consistently interpolates between the asymptotic regimes of
effectively neutral mutations ($\zeta\ll\nu$, i.e., $\tilde{s}\simeq\sigma$),
which are dominated by genetic draft ($Q\simeq{\rm e}^{-\nu x}/x$), and
strongly selected mutations ($\zeta\gg\nu$, i.e., $\tilde{s}\simeq s$), which
evolve in an autonomous way ($Q\simeq{\rm e}^{\pm\zeta x}/x$). For the
spectral function of neutral sites, we use the shorthand

$Q_{0}(x;\nu)=\frac{{\rm e}^{-\nu x}}{x}.$ (19)

The family of spectral functions (18) provides a good parametrization of the
spectral data in our simulations (Fig. 1d), as well as in all sequence classes
and recombination rate classes of Drosophila (Fig. 3ab, Fig. 4, and
Supplementary Figure S3). Frequency distributions of the form (17) serve as
building blocks for our genomic inference; see equations (2) and (3) of the
main text and equations (25) – (27) below.

The spectral functions of the draft model map the crossover from drift-
dominated to draft-dominated evolution in analytical form. The neutral site
frequency spectrum (2) determines the sequence diversity

$\pi\approx\frac{\theta}{1+\nu/2},$ (20)

which is consistent with the scaling behavior (11). In the local interference
regime $\pi\simeq\theta=\mu N{\rm e}^{-\omega}$; i.e., background selection
reduces diversity but does not affect the shape of the frequency spectrum. In
the condensate regime, $\pi\simeq 2\mu/\sigma<\theta$, i.e., diversity and
spectral shape are determined by interference selection [6]. These features
hold for broad classes of interference selection [46], making the spectral
functions a convenient choice for parametrizing the Drosophila site frequency
spectra. Specifically, we use the condition $\nu>1$ on the shape parameter
inferred from the spectrum of synonymous sequence sites as a marker of the
interference condensate regime.

#### Evolutionary model: substitution dynamics and allele occupancy

The draft model also serves to parametrize the sequence evolution between the
ingroup species D. melanogaster and the outgroup species D. simulans. In this
model, allele substitutions at individual sites take place with Kimura-Ohta
rates that depend on the local coalescence rate (or inverse effective
population size)

$\tilde{\sigma}=\frac{2\mu}{\pi}=\sigma+\frac{2\mu}{\theta}\simeq\left\\{\begin{array}[]{ll}\dfrac{{\rm
e}^{\omega}}{2N}&(\omega\lesssim 1,\mbox{ local interference})\\\ \\\
\sigma&(\omega\gtrsim 1,\mbox{ interference condensate}).\end{array}\right.$
(21)

Consistently with equations (11) and (20), the coalescence rate maps again the
crossover between local interference and condensate regime. The beneficial and
deleterious substitution rates

$u_{\pm}(\zeta,\nu)=\mu\,\frac{\zeta/\tilde{\nu}}{1-{\rm
e}^{-\zeta/\tilde{\nu}}},$ (22)

depend on the scaled selection coefficient $\zeta$ and the scaled coalescence
rate $\tilde{\nu}\equiv 2N\tilde{\sigma}\theta/\theta_{0}=\nu+1$. Models of
this form have been shown to provide an excellent approximation to the
equilibrium substitution dynamics in linked genomes under different scenarios
of interference selection [12, 58]. The rates (22) consistently determine the
equilibrium occupancy probabilities of beneficial and deleterious alleles,

$\lambda_{\pm}(\zeta,\nu)=\frac{1}{1+{\rm e}^{\mp\zeta/\tilde{\nu}}},$ (23)

as well as the expected sequence divergence between in- and outgroup species,

$d(\zeta,\nu)=\tau\big{[}\lambda_{-}(\zeta,\nu)u_{+}(\zeta,\nu)+\lambda_{+}(\zeta,\nu)u_{-}(\zeta,\nu)\big{]}=\frac{d_{0}}{(\zeta/\tilde{\nu})\sinh(\zeta/\tilde{\nu})},$
(24)

where $\tau_{d}$ is the divergence time and $d_{0}=\mu\tau_{d}$ the expected
divergence at neutral sites.

#### Ancestor-directed, outgroup-directed, and corrected frequency spectra

As explained in the main text, the evolutionary model specified by equations
(22) – (24) serves to relate the outgroup-directed frequency spectra
$q^{o}(x)$ and the basic frequency distributions of the draft model,
$q_{\pm}(x)$ (equation 17) without additional fitting parameters.
Specifically, the ancestor-directed spectrum $q_{s}(x;\theta,\nu)$ at
synonymous sites, which is of the form (2), determines the outgroup-directed
spectrum

$\displaystyle q^{o}_{s}(x;\theta,\nu)$ $\displaystyle=$
$\displaystyle\theta_{s}\big{[}(1-d_{0})Q_{0}(x;\nu)+d_{0}Q_{0}(1-x;\nu)\big{]}$
(25)

with the spectral function $Q_{0}(x;\nu)$ given by equation (19). In other
sequence classes, we use ancestor-directed spectra of the form (3),

$\displaystyle q(x;\theta,\theta^{\prime},\zeta,\nu)$ $\displaystyle=$
$\displaystyle\theta\,Q_{0}(x;\nu)+\theta^{\prime}\,Q(x;\zeta,\nu)$ (26)
$\displaystyle=$
$\displaystyle\theta\,Q_{0}(x;\nu)+\theta^{\prime}\,\big{[}\lambda_{+}(\zeta,\nu)Q_{-}(x;\zeta,\nu)+\lambda_{-}(\zeta,\nu)Q_{+}(x;\zeta,\nu)\big{]}$

with the spectral functions $Q_{\pm}(x;\zeta,\nu)$ given by equation (18) and
the allele occupancy probabilities $\lambda_{\pm}(\zeta,\nu)$ given by
equation (23). These determine the outgroup-directed counterparts

$\displaystyle q^{o}(x;\theta,\theta^{\prime},\zeta,\nu)$ $\displaystyle=$
$\displaystyle\theta\big{[}(1-d_{0})Q_{0}(x;\nu)+d_{0}Q_{0}(1-x;\nu)\big{]}$
(27)
$\displaystyle+\theta^{\prime}\big{[}\big{(}1-d(\zeta,\nu)\big{)}\big{(}\lambda_{+}(\zeta,\nu)Q_{-}(x;\zeta,\nu)+\lambda_{-}(\zeta,\nu)Q_{+}(x;\zeta,\nu)\big{)}$
$\displaystyle+d(\zeta,\nu)\big{(}\lambda_{+}(\zeta,\nu)Q_{-}(1-x;\zeta,\nu)+\lambda_{-}(\zeta,\nu)Q_{+}(1-x;\zeta,\nu)\big{)}\big{]}.$

We can reconstruct the synonymous spectrum $q_{s}(x)$ from $q_{s}^{o}(x)$ by
inverting the linear map (25),

$q_{s}(x)=\frac{1-d_{0}}{1-2d_{0}}\,q_{s}^{o}(x)-\frac{d_{0}}{1-2d_{0}}\,q^{o}(1-x).$
(28)

Applying this transformation to the outgroup-polarized spectral data of
synonymous mutations, $\hat{q}_{s}^{o}(x)$ (Fig. 3ab), produces the corrected
spectral data $\hat{q}_{s}(x)$ shown in Supplementary Figure S2. These provide
a bona fide improved approximation to the underlying spectrum $q_{s}(x)$.
However, the reconstruction becomes noisy in the limit $x\to 1$, where
$\hat{q}_{s}^{o}(x)$ is dominated by the component $\hat{q}_{s}(1-x)$.

#### Bayesian estimation of model parameters

Consider a sequence class with population frequency spectrum
$q(x;\theta,\theta^{\prime},\zeta,\nu)$ given by a two-component model of the
form (3); the associated outgroup-polarized spectrum
$q^{o}(x;\theta,\theta^{\prime},\zeta,\nu)$ is given by equation (27). In that
class, a sample of $n$ random individuals contains mutations of discrete
outgroup-polarized frequency $x=k/n$ with probability (see also ref. [64])

$\displaystyle\tilde{q}^{o}(k/n;\theta,\theta^{\prime},\zeta,\nu)$
$\displaystyle=$ $\displaystyle\left(\\!\\!\begin{array}[]{c}n\\\
k\end{array}\\!\\!\right)\int_{0}^{1}x^{k}(1-x)^{n-k}q^{o}(x;\theta,\theta^{\prime},\zeta,\nu)\,dx\qquad(k=0,1,\dots,n);$
(31)

this expression yields closed analytical expressions involving hypergeometric
and Gamma functions.

By calibrating the model distributions
$\tilde{q}(k/n;\theta,\theta^{\prime},\zeta,\nu)$ with observed site frequency
spectra $\hat{q}^{o}(k/n)$ and divergence data, we can infer parameters of the
model (25) for synonymous sites and of the mixed model (27) for other sequence
classes. Our inference is based on total log likelihood score of the observed
frequency counts in a given sequence class,

$S(\theta,\theta^{\prime},\zeta,\nu)=L\sum_{k=0}^{n}\hat{q}^{o}(k/n)\log\tilde{q}^{o}(k/n;\theta,\theta^{\prime},\zeta,\nu),$
(32)

where $L$ is the total number of sequence sites in the class. We have
developed a consistent Bayesian inference scheme that takes into account the
allele occupancy (23), the evolutionary dynamics (24), and the sampling
statistics (31). This scheme proceeds in a hierarchical way: we first
determine a posterior distribution of parameters $(\theta_{s},\nu)$ for
synonymous sites, using the single-component model (25). Then we obtain the
posterior distribution of parameters
$(\theta_{a},\theta^{\prime}_{a},\zeta_{a},\nu)$ for amino-acid changes and
the analogous distributions for other sequence classes, using the mixed model
(3) with the same value of $\nu$ as for synonymous sites (this constraint does
not induce a significant drop in likelihood score). Our inference scheme is
implemented in a software called “hfit” https://github.com/stschiff/hfit using
special functions and numerical optimization routines from the Gnu Scientific
Library http://www.gnu.org/software/gsl/, and a custom MCMC algorithm to
obtain Maximum Likelihood estimates and confidence intervals for all
parameters.

The Bayesian inference scheme, together with the substitution model given by
equations (22) – (24), allows a direct estimate of the rates $u_{d},v_{b}$ and
of the interference density $\omega$ from observed frequency spectra and
substitutions at synonymous and non-synonymous sites. First, the rate of
deleterious mutations in a given sequence class is simply
$u_{d}=\mu\lambda_{+}\theta/\theta_{s}$. Equation (27) then determines the
total rate of deleterious nonsynonymous mutations,

$u_{d}=\mu\,\alpha_{d}=\mu\,\left(\frac{\lambda_{+}(\zeta_{a},\nu)\,\theta^{\prime}_{a}}{\theta_{s}}+\frac{\theta_{s}-\theta_{a}-\theta^{\prime}_{a}}{\theta_{s}}\right),$
(33)

which is the sum of contributions from moderately deleterious changes and from
strongly deleterious changes. Second, the rate of adaptive amino acid
substitutions is given by the excess of nonsynonymous divergence compared to
the expectation from the equilibrium model (24),

$v_{b}=\mu\,\frac{d_{a}}{d_{s}}\,\alpha_{b}=\mu\,\frac{d_{a}}{d_{s}}\left(1-d_{s}\frac{\theta_{a}}{\theta_{s}}-d(\zeta_{a},\nu)\frac{\theta^{\prime}_{a}}{\theta_{s}}\right).$
(34)

Here we have treated synonymous mutations as (approximately) neutral. In the
local interference regime, we have $\zeta_{a}\gg 1$ and, hence,
$\lambda_{+}(\zeta_{a},\nu)\approx 1$ and $d(\zeta_{a},\nu)\approx 0$.
Equations (33) and (34) then reduce to the expressions given in the main text,
$u_{d}/\mu=\alpha_{d}$ with $\alpha_{d}=1-(\theta_{a}/\theta_{s})$ and
$v_{b}/\mu=\alpha_{b}\,(d_{a}/d_{s})$ with
$\alpha_{b}=1-(d_{s}/d_{a})(\theta_{a}/\theta_{s})$. These expressions are
evaluated using measured divergence data $d_{s},d_{a}$ and maximum-likelihood
spectral parameters $\theta_{s},\theta_{a}$. They enter equation (4) for the
interference density $\omega$, which serves to estimate the threshold
recombination rate $\rho^{*}$ from the condition $\omega^{*}=1$. To estimate
the fraction of adaptive substitutions, $\alpha_{b}$, in the condensate regime
(Fig. 5d), we use the full expression (34).

#### Genomic data and sequence annotation

We downloaded the complete genome sequences of 168 lines from the _Drosophila
Melanogaster Reference Panel (DGRP)_ from the DGRP website
http://dgrp.gnets.ncsu.edu and of 27 lines sampled from Rwanda from the
_Drosophila Population Genomics Project_ http://dpgp.org as fasta files. We
downloaded the reference sequences from Drosophila simulans and from
_Drosophila yakuba_ , aligned to the reference sequence of _Drosophila
melanogaster_ from the UCSC genome browser (https://genome.ucsc.edu). For both
outgroups, we compute outgroup-directed allele frequencies at all sites at
which (i) there is a valid outgroup allele, and (ii) at least 150 lines of the
DGRP sequences or 25 lines of the DPGP sequences have a called allele. We then
downsample all sites to 25 called alleles, using random sampling without
replacement (hypergeometric sampling).

We downloaded gene annotations from flybase [43]. We define annotation
categories as follows. Intergenic: intergenic regions that are at least 5kb
away from genes, Intron: introns of protein-coding genes, UTR: untranslated
regions in exons, Synonymous: protein-coding sites of the reference genome at
which none of the three possible point mutation changes the encoded amino
acid, Nonsynonymous: protein-coding sites on the reference at which any of the
three possible point mutations changes the encoded amino acid. Most genes have
multiple associated transcripts due to alternative splicing. We choose the
transcript corresponding to the longest encoded protein coding sequence for
each gene and annotated introns, UTRs, synonymous and nonsynonymous sites
according to that transcript. See Supplementary Table S1 for the number of
sites in a given annotation category on the different chromosomes.

Maps of mean recombination rates within 100kb windows were obtained from
Comeron et al. [31] through the website http://www.recombinome.com. We use the
recombination map to annotate every site in the Drosophila genome. We then use
only synonymous sites on the autosomes (2L, 2R, 3L and 3R) and define quantile
boundaries on this set. Specifically, we sort all recombination rate values of
this set of sites and determine recombination rate bins by dividing the data
set into 21 equally large subsets of values. We then use these quantile
boundaries to bin all sites (not just synonymous sites) into bins according to
their local recombination rate. The quantile boundaries used in this study for
autosomal data are (in cM/Mb): 0.0, 0.069, 0.217, 0.415, 0.44, 0.821, 1.055,
1.29, 1.415, 1.592, 1.741, 1.938, 2.169, 2.354, 2.612, 2.838, 3.156, 3.461,
3.796, 4.244, 5.395, Infinity. All binned allele frequency data is given in
Supplementary Table S1.

#### Simulations of evolutionary processes in recombining populations

We use the SLiM simulator [65] to simulate a population of sequences evolving
under mutations, drift, selection, and recombination; the genome of each
individual has $100,000$ sites. To mimic the Drosophila phylogeny, we start
from a single population of size $N=1000$ that evolves for $10,000$
generations, then splits into ingroup and outgroup populations of size
$N=1000$; these evolve in isolation for another $10,000$ generations. Finally,
we sample one individual from the outgroup population and 20 individuals from
the ingroup population.

We consider three classes of mutations: neutral mutations, beneficial
mutations and deleterious mutations, the latter two with fixed selection
coefficient $s_{\mathrm{ad}}=0.01$. The rate of neutral mutations is
$\mu=1.5\times 10^{-6}$, the rate of beneficial mutations varies from
$u_{b}=0$ to $2.5\times 10^{-7}$, and the rate of deleterious mutations from
$u_{d}=0$ to $3\times 10^{-6}$. We also run simulations with only one class of
selected mutations (i.e., $u_{d}=0$ or $u_{b}=0$). The recombination rate
$\rho$ varies in the range $10^{-7}$ to $10^{-4}$.

We use these simulations to display the transition from local interference to
the interference condensate and to corroborate our scaling theory (Fig. 2). In
particular, the simulations demonstrate that the maximum-likelihood shape
parameter $\nu^{*}$ inferred from the spectral data of synonymous sequence
sites can serve as a faithful marker of the interference condensate regime.

## Acknowledgments

We would like to thank P.W. Messer for comments on an earlier version of the
manuscript.

## Legends for Supplementary Tables

Supplementary Table S1: Drosophila site frequency spectra. The table lists the
site frequency spectrum data that we analyse here. The data is separated into
five annotation classes and 21 recombination bins.

Supplementary Table S2: Parameter estimates. The table lists all parameter
estimates obtained from Drosophila data using our draft model.

Figure S1: Extensions of scaling theory. The scaled fitness variance per site,
$\varsigma^{2}/(s\rho)$, is plotted against the interference density $\omega$
for simulated evolution with two complementary distributions of selective
effects. (a) Background selection. Evolution under solely deleterious
mutations with rate $u_{d}=3\times 10^{-6}$ and a single-valued selection
coefficient $(-s)$ (marked by color); other simulation parameters as in Fig.
2. The onset point of interference selection, $\omega^{*}$, increases with
$s$, in qualitative agreement with equation (13) (dashed lines indicate the
predicted value of $\omega^{*}$). (b) Selective sweeps. Evolution under solely
beneficial mutations with rate $u_{d}=2.5\times 10^{-7}$ and a single-valued
selection coefficient $s$ (marked by color); other simulation parameters as in
Fig. 2. The onset point of interference selection, $\omega^{*}\sim 1$, is
independent of $s$, as predicted by equations (1) and (9). Both selection
scenarios have been studied in previous work [17, 60, 26] but are not
realistic assumptions for Drosophila. Figure S2: Corrected frequency spectra
of synonymous mutations. Ancestor-directed empirical spectra $\hat{q}_{s}(x)$
for two populations of D. melanogaster are reconstructed from the outgroup-
directed spectra $\hat{q}_{s}^{o}(x)$ (Fig. 3ab) by the inverse linear map
(28). Figure S3: Frequency spectra of mutations in UTR, introns and intergenic
sequence. Outgroup-polarized sample spectra $\hat{q}^{o}(x)$ from two
populations of _D. melanogaster_ , together with maximum-likelihood spectra
$q^{o}(x)$. We use the shape parameter $\nu$ inferred from synonymous
mutations (Fig. 3c) and a two-component model of the same form as for
nonsynonymous mutations; see equations (3) and (27).

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