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\begin{document}

\title{Some complexities in interpreting apparent effects of hitchhiking: a
commentary on Gompert, Feder \& Nosil (2021)}



\author[1]{Brian Charlesworth}%
\author[2]{Jeffrey Jensen}%
\affil[1]{University of Edinburgh}%
\affil[2]{Arizona State University}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\selectlanguage{english}
\begin{abstract}
We write to address recent claims by Gompert et al. (2021) about the
potentially important and underappreciated phenomena of ``indirect
selection'', the observation that neutral regions may be affected by
natural selection. We argue both that this phenomenon -- generally known
as genetic hitchhiking -- is neither new nor poorly studied, and that
the patterns described by the authors have multiple alternative
explanations.%
\end{abstract}%



\sloppy


\textbf{Some complexities in interpreting apparent effects of
hitchhiking: a commentary on Gompert, Feder \& Nosil (2021)}

Brian Charlesworth\textsuperscript{1} and Jeffrey D.
Jensen\textsuperscript{2}

\textsuperscript{1} Institute of Evolutionary Biology, School of
Biological Sciences, University of Edinburgh, Edinburgh, UK

\textsuperscript{2} School of Life Sciences, Arizona State University,
Tempe AZ, USA

\textbf{Corresponding author: Brian Charlesworth}

\textbf{Email:}Brian.Charlesworth@ed.ac.uk

Keywords: epistatic selection, genetic hitchhiking, linkage
disequilibrium, selective sweeps, demography

ABSTRACT

We write to address recent claims by Gompert \emph{et al.} (2021) about
the potentially important and underappreciated phenomena of ''indirect
selection'', the observation that neutral regions may be affected by
natural selection. We argue both that this phenomenon -- generally known
as genetic hitchhiking -- is neither new nor poorly studied, and that
the patterns described by the authors have multiple alternative
explanations.

We wish to express a number of concerns about the recent paper by
Gompert \emph{et al} . (2021), who propose a ''widespread indirect
selection hypothesis'', and assert that ``functionally neutral genetic
regions can be affected indirectly by natural selection, via their
statistical association with genes under direct selection''. They add
that ''the genomic extent of such indirect selection, particularly
across loci not physically linked to those under direct selection,
remains poorly understood''. The authors present analyses of several
datasets; they suggest that this process could be an important
phenomenon over both short and long timescales, and may serve to make
``aspects of evolution more predictable'' given that ''conditional on
patterns of LD, indirect selection is a deterministic process.'' We have
concerns about both their conceptual framework, and their interpretation
of the experimental results.

First, the concept of ``indirect selection'' appears to be equivalent to
genetic hitchhiking, which is only mentioned towards the end of their
paper. The term hitchhiking is most often used in relation to the
effects of the spread of a beneficial mutation on variability at linked
sites (a selective sweep: Maynard Smith \& Haigh 1974), or to the
similar effects of the elimination of deleterious mutations (background
selection: Charlesworth \emph{et al} . 1993; incorrectly attributed by
Gompert \emph{et al} . to Begun \& Aquadro 1992). As noted in the recent
review by Charlesworth \& Jensen (2021), the various forms of
hitchhiking can all be described in general terms by the Price-Robertson
identity, which states that the change in mean of a trait is governed by
the additive covariance between the trait and fitness (Robertson 1968;
Price 1970). In this case, the trait is the allele frequency at the
neutral locus, and the covariance is the product of the coefficient of
linkage disequilibrium, \emph{D} , and the additive fitness effect of
the locus under selection (Santiago \& Caballero 1995; Charlesworth \&
Jensen 2021). We note that variation maintained by long-term balancing
selection or divergent selection between populations can also affect
variability at linked sites, but this does not involve changes in allele
frequencies that are noticeable over the short-timescales considered by
Gompert \emph{et al.} (2021), except in the initial phase of their
establishment (see Zeng \emph{et al} . 2021 for a recent theoretical
analysis).

Thus, in one sense their remark about the deterministic nature of
indirect selection is correct. However, the initial value of \emph{D} is
generated by various forms of chance associations between alleles at the
neutral and selected loci, as is indicated by the title of their paper,
so that there is inherently a stochastic element to hitchhiking.
Furthermore, \emph{D} is reduced by a factor of 1 -- \emph{c} each
generation, where \emph{c} is the frequency of recombination between the
two loci concerned. (Charlesworth \& Charlesworth 2010, p.381). Multiple
theoretical analyses of hitchhiking have shown that significant effects
of selection on linked neutral sites only occur if the ratio of
\emph{c}to the selection coefficient at the selected loci is small, or
the neutral loci are embedded within a large number of loci that are
simultaneously experiencing selection (Charlesworth \& Jensen 2021). A
neutral locus can only be affected by a selective sweep at an unlinked
locus (\emph{c} = \selectlanguage{ngerman}½) if there is extremely strong selection, involving a
much greater than two-fold selective advantage to the beneficial allele.
Similarly, background selection caused by unlinked loci is likely to
have only a minor effect on neutral variability (Charlesworth 2012).
Detectable hitchhiking effects involving unlinked loci are therefore
likely to be very infrequent.

Second, their assertion that widespread hitchhiking effects are
''relatively untested'' seems misplaced. One of the most consistent
patterns to emerge from the study of DNA sequence variation over the
past few decades is the generally positive correlation between neutral
variability and the local rate of recombination (Begun \& Aquadro 1992;
Charlesworth \& Jensen 2021). Genetic hitchhiking has long been
discussed as a major factor in generating this genome-wide correlation,
although in some species the mutagenic effect of recombination may
contribute as well (Pratto \emph{et al} . 2014; Arbeithuber \emph{et al}
. 2015). Indeed, the abundant evidence for pervasive background
selection effects has prompted numerous authors to argue that it should
be an essential component in any evolutionary null model when conducting
population genomic studies (\emph{e.g.,} Comeron 2017; Pouyet \emph{et
al} . 2018; Jensen \emph{et al.} 2019).

Third, the authors suggest that, while hitchhiking effects have been
studied over long periods of time, ``it remains unclear whether indirect
selection is pervasive on shorter time scales, such as generations or
decades''. Although it is not obvious how hitchhiking effects could
operate over long time-scales without also acting at short time-scales,
this remark reflects a more fundamental misunderstanding. As described
above, recombination events between directly selected mutations and
linked variants act to diminish hitchhiking effects, so that the
footprints associated with recent hitchhiking events are naturally
stronger than older ones. In fact, recombination, subsequent mutations,
and genetic drift cause these patterns to decay so rapidly that most
effects of individual selective sweeps are \emph{only} detectable over
relatively brief periods of time since their occurrence (Przeworski
2002; Kim \& Stephan 2002). If there has been strong directional
selection at certain loci in the experimental set-ups that are described
by Gompert \emph{et al.} (2021), the short time-scale involved is
certainly favourable for the detection of their hitchhiking effects
(although the statistical power associated with the relatively small
experimental sample sizes and limited number of generations can be
problematic: Barrett \emph{et al.} 2019).

When considering the evidence for hitchhiking effects in the cases
described by Gompert \emph{et al} . (2021), we focus specifically on
their primary example - the stick insect \emph{Tisema cristinae} .
Previous work has documented the existence of an interesting colour
polymorphism, controlled by a 10 megabase region, the
\emph{Mel-Stripe}locus, which appears to be potentially associated with
a chromosomal inversion (Lindtke \emph{et al.} 2017). Among
approximately 7 million SNPS in their sample, Gompert \emph{et al} .
(2021) found 64 SNPs that had \emph{r} \textsuperscript{2} \selectlanguage{english}[?] 0.1 with
\emph{Mel-Stripe} and were also on different chromosomes, where \emph{r}
is the correlation coefficient between pairs of alleles at two loci
(Charlesworth \& Charlesworth 2010, p.373). The first question is
whether this could be generated by the effect of random sampling of the
492 haploid genomes sequenced in their experimental population. Under
the null hypothesis of no LD, an \emph{r} \textsuperscript{2} of 0.1
corresponds to a 1 d.f.\(\chi^{2}\) of 49.2, for which \emph{p} =
2.31 x 10\textsuperscript{--12}, using the incomplete gamma function
with parameter 0.5, which is equivalent to
\({0.5\chi}^{2}\)(\emph{https://keisan.casio.com/exec/system/1180573447}
). The expected number of SNPS with \emph{r} \textsuperscript{2} \selectlanguage{english}[?] 0.1
is thus approximately 2.31 x 10\textsuperscript{--12} x 7 x
10\textsuperscript{6} = 1.62 x 10\textsuperscript{--5}. Not
surprisingly, therefore, this explanation can be ruled out. Note that
the expected value of \emph{r} \textsuperscript{2} generated by random
sampling in the absence of true LD is 1/492 \selectlanguage{english}[?] 0.002, which is not far
from the mean value of 0.004 for all pairs of unlinked SNPs reported by
Gompert \emph{et al} . (2021).

There appear to be at least six possible explanations for this
unexpectedly large number of unlinked SNPs that are in fairly strong LD
with \emph{Mel-Stripe} :

(1) There exist technical errors that results in spurious cases of LD or
incorrect assignment of the locations of SNPs; for example, so that SNPs
that are actually in the \emph{Mel-Stripe} region are placed on other
chromosomes. The quality control details needed to evaluate this
possibility were not presented by the authors.

(2) LD between neutral SNPs and the \emph{Mel-Stripe} locus has been
created by random genetic drift in a panmictic population over a long
period of time. This seems improbable, as the expected value of\emph{r}
\textsuperscript{2} with no linkage is approximately
1/(2\emph{N\textsubscript{e}} ) (Charlesworth \& Charlesworth 2010,
p.383), and the size of the \emph{T. cristinae} population used in the
experiment is said be of the order of thousands of individuals
(Gompert\emph{et al} . 2021).

(3) There has been very recent admixture from a genetically distinct
population or populations, resulting in patches of LD
with\emph{Mel-Stripe} (Charlesworth \& Charlesworth 2010, p.388). No
structure/admixture modelling needed to evaluate this possibility
appears to have been performed.

(4) There has been a recent and severe bottleneck in population size,
generating random LD of a much higher magnitude than expected under a
constant population size (Charlesworth \& Charlesworth 2010, p.389), As
with point 3, these signatures may be detectable using standard
demographic modeling approaches (reviewed in Beichman \emph{et al} .
2018); again, such analyses appear not to have been performed.

(5) The sample used in the experiment has captured an ongoing sweep
involving very strong directional selection on \emph{Mel-Stripe} ; this
seems implausible, given the evidence that the \emph{Mel-Stripe}variants
represent a long-standing balanced polymorphism (Lindtke\emph{et al.}
2017).

(6) There could be epistatic fitness interactions between the SNP loci
and \emph{Mel-Stripe} . This of course does not constitute ''indirect
selection'' (\emph{i.e} ., genetic hitchhiking) of the type proposed by
Gompert \emph{et al} . (2021), but is perhaps what they have in mind
when they refer to ``polygenic selection''. However, it is stretching
credulity that there could be tens of unlinked loci subject to very
strong epistatic fitness interactions with \emph{Mel-Stripe} , resulting
in significant LD. Theoretical analyses of two-locus balanced
polymorphisms have shown that substantial LD requires the measure of
additive x additive epistasis for fitness to considerably exceed the
recombination frequency (Charlesworth \& Charlesworth 2010, pp.420-425).

For example, in the simple symmetric two-locus fitness model of Lewontin
\& Kojima (1960), LD is maintained at equilibrium with free
recombination only if 2 \selectlanguage{english}[?] \emph{e} , where \emph{e} is the epistatic
fitness parameter (fitnesses are here measured relative to the fitness
of the double heterozygote). In this case, with equilibrium allele
frequencies of 0.5 at both loci, \emph{r} \textsuperscript{2} =
16\emph{D} \textsuperscript{2} = 1 -- 2/\emph{e} . Very few convincing
cases of LD maintained by epistatic selection among unlinked loci have
been described. The classic case is that of the Australian
grasshopper\emph{Keyacris scurra} (formerly \emph{Moraba scurra} ),
involving two inversion polymorphisms that show a consistent pattern of
LD across multiple populations, and substantial deviations from
Hardy-Weinberg frequencies that indicate strong viability selection
(Turner 1972). Even here, the magnitude of \emph{r} \textsuperscript{2}
is small. In the sample that showed the highest value of \emph{D}
(\emph{i.e.,} Royalla B 1958), the data in Table 3 of Turner (1972) give
\emph{D} = 0.00116 and\emph{r} \textsuperscript{2} = 0.00349.

In summary, the observation of many unlinked SNPs with substantial LD
in\emph{T. cristinae} seems to raise more questions than it answers, and
cannot be taken as indicating widespread ''indirect selection'' without
much more evidence, including a proper consideration of baseline
expectations related to both technical (\emph{e.g} ., data quality) and
evolutionary (\emph{e.g} ., population history) factors. Furthermore,
even if these alternatives were to be ruled out by further analyses,
genetic hitchhiking is neither a new nor poorly studied phenomenon.

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