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MPL resolves genetic linkage in fitness inference from complex evolutionary histories

DOI:10.1038/s41587-020-0737-3
Authors:
Muhammad Saqib Sohail at The Hong Kong University of Science and Technology
Muhammad Saqib Sohail
Raymond Hall Yip Louie at UNSW Sydney
Raymond Hall Yip Louie
Matthew R. McKay at The Hong Kong University of Science and Technology
Matthew R. McKay
John P Barton at Massachusetts Institute of Technology
John P Barton
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Abstract

Genetic linkage causes the fate of new mutations in a population to be contingent on the genetic background on which they appear. This makes it challenging to identify how individual mutations affect fitness. To overcome this challenge, we developed marginal path likelihood (MPL), a method to infer selection from evolutionary histories that resolves genetic linkage. Validation on real and simulated data sets shows that MPL is fast and accurate, outperforming existing inference approaches. We found that resolving linkage is crucial for accurately quantifying selection in complex evolving populations, which we demonstrate through a quantitative analysis of intrahost HIV-1 evolution using multiple patient data sets. Linkage effects generated by variants that sweep rapidly through the population are particularly strong, extending far across the genome. Taken together, our results argue for the importance of resolving linkage in studies of natural selection.
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Articles
https://doi.org/10.1038/s41587-020-0737-3
1Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China. 2Institute for Advanced Study,
Hong Kong University of Science and Technology, Hong Kong, China. 3The Kirby Institute, University of New South Wales, Sydney, New South Wales,
Australia. 4School of Medical Sciences, University of New South Wales, Sydney, New South Wales, Australia. 5Department of Chemical and Biological
Engineering, Hong Kong University of Science and Technology, Hong Kong, China. 6Department of Physics and Astronomy, University of California,
Riverside, Riverside, CA, USA. 7These authors contributed equally: Muhammad Saqib Sohail, Raymond H. Y. Louie. ✉e-mail: m.mckay@ust.hk;
john.barton@ucr.edu
Evolving populations exhibit complex dynamics. Cancers1–6 and
pathogens, such as HIV-1 (refs. 7–9) and influenza10,11, gener-
ate multiple beneficial mutations that increase fitness or allow
them to escape immunity. Subpopulations with different beneficial
mutations then compete with one another for dominance, referred
to as clonal interference, resulting in the loss of some mutations
that increase fitness12. Neutral or deleterious mutations can also
hitchhike to high frequencies if they occur on advantageous genetic
backgrounds13. Experiments have demonstrated that these features
of genetic linkage are pervasive in nature14–16.
Linkage makes distinguishing the fitness effects of individual
mutations challenging because their dynamics are contingent on the
genetic background on which they appear. Lineage tracking experi-
ments can be used to identify beneficial mutations17, but they can-
not readily be applied to evolution in natural conditions, such as in
cancer or in natural infection by viruses or bacteria. Most existing
computational methods to infer fitness from population dynamics
ignore linkage entirely18–25. Ignoring linkage could lead to errors
when genetic hitchhiking or clonal interference are present, which
frequently occur in nature. A few methods have attempted to incor-
porate linkage information, but these methods are exceptionally
computationally intensive and may scale poorly to populations with
many polymorphic variants26–28.
Here we describe a method to infer selection from evolution-
ary histories, captured by genetic time series data, and demon-
strate its ability to resolve linkage effects. Simulations show that
our approach, which we call marginal path likelihood (MPL)29,30, is
faster and more accurate than current state-of-the-art methods for
selection inference. As an example application, we use our method
to reveal patterns of selection in intrahost HIV-1 evolution using
14 patient data sets. The genetic diversity exhibited in these data
sets makes them exceptionally challenging to analyze using exist-
ing linkage-aware methods. With MPL, we observe strong selection
for escape from CD8+ T cell responses, which is partially masked
by linkage due to extensive clonal interference between competing
escape mutants. We further quantify the influence of linkage on
inferred selection across the viral genome. Our results show that
most variants have negligible effects on inferred selection at other
sites, but a small minority of highly influential variants have dra-
matic and far-reaching effects. These highly influential variants are
often ones that sweep rapidly through the population. We also find
modest selection for escape from antibody responses, even in an
individual who develops broadly neutralizing antibodies (bnAbs).
Collectively, our results argue for the importance of accounting for
genetic linkage when inferring selection, while providing a practical
method for achieving this for large data sets.
Results
Evolutionary model incorporating linkage. The principle idea of
our inference approach is to efficiently quantify the probability of an
evolutionary ‘path,’ defined by the set of all mutant allele frequencies
at each time, using a path integral method derived from statistical
physics (Methods). Path integrals for related evolutionary models
have been derived under different assumptions in past work31–33,
but they have not been widely applied for inference. This method
allows us to disentangle the effects of individual mutations from the
sequence background, that is, genetic linkage, without making the
likelihood function intractable. In fact, the path integral can be ana-
lytically inverted to find the parameters that are most likely to have
generated a path.
To define the path integral, we consider Wright–Fisher (WF)
population dynamics with selection, mutation and recombination,
in the diffusion limit34. Under an additive fitness model, the fitness
of any individual is a sum of selection coefficients, si, which quan-
tify the selective advantage of mutant allele i relative to wild-type
(WT). The probability of an evolutionary path is then a product of
MPL resolves genetic linkage in fitness inference
from complex evolutionary histories
Muhammad Saqib Sohail1,7, Raymond H. Y. Louie1,2,3,4,7, Matthew R. McKay 1,5 ✉ and
John P. Barton 6 ✉
Genetic linkage causes the fate of new mutations in a population to be contingent on the genetic background on which they
appear. This makes it challenging to identify how individual mutations affect fitness. To overcome this challenge, we developed
marginal path likelihood (MPL), a method to infer selection from evolutionary histories that resolves genetic linkage. Validation
on real and simulated data sets shows that MPL is fast and accurate, outperforming existing inference approaches. We found
that resolving linkage is crucial for accurately quantifying selection in complex evolving populations, which we demonstrate
through a quantitative analysis of intrahost HIV-1 evolution using multiple patient data sets. Linkage effects generated by vari-
ants that sweep rapidly through the population are particularly strong, extending far across the genome. Taken together, our
results argue for the importance of resolving linkage in studies of natural selection.
NATURE BIOTECHNOLOGY | VOL 39 | APRIL 2021 | 472–479 | www.nature.com/naturebiotechnology
472
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... This makes it more difficult to accurately estimate model parameters since statistics over the path must be estimated from incomplete information. A workaround used in a previous study 4 for this problem is to use linear interpolation to estimate the state of the system between the observed data points. However, this approximation may fail when gaps in time are large enough such that the behavior of the system is highly nonlinear 13 . ...
... Sohail et al. solved this problem analytically in the limit that the population size N → ∞ while the selection coefficients s i and mutation rate µ scale as 1/N (ref. 4 ). In this case, the maximum a posteriori vector of selection coefficientsŝ = (ŝ i ) L i=1 that best explain the data are given bŷ ...
... The reduction in error for Bézier interpolation is more substantial for off-diagonal terms compared to diagonal ones. Consistent with this observation, Bézier interpolation yields smaller improvements in performance for a simple version of MPL in which the off-diagonal terms of the integrated covariance matrix are ignored (Methods; referred to as the single locus (SL) method in ref. 4 ). ...
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... Most existing methods are based on single-locus models which assume independent evolution of loci (Bollback et al. 2008;Malaspinas et al. 2012;Mathieson and McVean 2013;Feder et al. 2014;Lacerda and Seoighe 2014;Steinrücken et al. 2014;Foll et al. 2015;Topa et al. 2015;Ferrer-Admetlla et al. 2016;Gompert 2016;Schraiber et al. 2016;Iranmehr et al. 2017;Taus et al. 2017;Zinger et al. 2019), thus they are unable to directly account for genetic linkage or epistasis. A few methods (Illingworth and Mustonen 2011;Terhorst et al. 2015;Sohail et al. 2021) have been developed that consider the joint evolution of multiple loci, but these assume additive fitness models. Hence, while they account for genetic linkage, they do not consider epistasis. ...
... Due to its analytical form, our approach is straightforward to implement and computationally efficient for moderate numbers of loci. Our method is based on an extension of the marginal path likelihood (MPL) framework (Sohail et al. 2021) to account for epistasis. We use a path integral method derived from statistical physics (Risken 1989) to efficiently represent the likelihood of an observed trajectory of single and double mutant allele frequencies. ...
... For fitness landscapes with epistasis, any inference model that does not explicitly account for epistasis will ascribe the effect of epistasis terms to individual selection coefficients, thereby over-or under-estimating them. To test this, we ran simulations to compare the performance of the MPL method, which accounts for both linkage and epistasis, with the one we proposed previously, which accounts only for linkage and considers a first-order fitness model with no epistasis (Sohail et al. 2021). Here we term this variant as "MPL (without epistasis)". ...
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... For the Dryvax vaccine, 11 sequences were downloaded from NCBI, with accession IDs JN654976 through JN654986, and their consensus sequence was used in the analysis. Similar to our previous works [32,33], an in-house bioinformatics pipeline was developed to align these nucleotide sequences and then translate them into amino acid residues according to the coding sequence positions provided along the reference sequence for VACV and the location of the gene (whether on the forward or reverse strand). MAFFT software was used to perform all multiple sequence alignments [34]. ...
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Resolving genetic heterogeneity in cancer
Article
To a large extent, cancer conforms to evolutionary rules defined by the rates at which clones mutate, adapt and grow. Next-generation sequencing has provided a snapshot of the genetic landscape of most cancer types, and cancer genomics approaches are driving new insights into cancer evolutionary patterns in time and space. In contrast to species evolution, cancer is a particular case owing to the vast size of tumour cell populations, chromosomal instability and its potential for phenotypic plasticity. Nevertheless, an evolutionary framework is a powerful aid to understand cancer progression and therapy failure. Indeed, such a framework could be applied to predict individual tumour behaviour and support treatment strategies.
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