Loss and Recovery of Genetic Diversity in Adapting Populations of HIV
Pleuni Pennings, Sergey Kryazhimskiy, John Wakeley
(Submitted on 15 Mar 2013)
A population’s adaptive potential is the likelihood that it will adapt in response to an environmental challenge, e.g., develop resistance in response to drug treatment. The effective population size inferred from genetic diversity at neutral sites has been traditionally taken as a major predictor of adaptive potential. However recent studies demonstrate that such effective population size vastly underestimates the population’s adaptive potential (Karasov 2010).
Here we use data from treated HIV-infected patients (Bacheler2000) to estimate the effective size of HIV populations relevant for adaptation. Our estimate is based on the frequencies of soft and hard selective sweeps of a known resistance mutation K103N. We observe that 41% of HIV populations in this study acquire resistance via at least two functionally equivalent but distinct mutations which sweep to fixation without significantly reducing genetic diversity at neighboring sites (soft selective sweeps). We further estimate that 20% of populations acquire a resistant allele via a single mutation that sweeps to fixation and drastically reduces genetic diversity (hard selective sweeps). We infer that the effective population size that determines the adaptive potential of within-patient HIV populations is approximately 150,000. Our estimate is two orders of magniture higher than a classical estimate based on diversity at synonymous sites.
Three not mutually exclusive reasons can explain this discrepancy:
(1) some synonymous mutations may be under selection;
(2) highly beneficial mutations may be less affected by ongoing linked selection than synonymous mutations; and
(3) synonymous diversity may not be at its expected equilibrium because it recovers slowly from sweeps and bottlenecks.
Haldane's Sieve 
In this paper, the authors use a data set from a study of the anti-HIV drug efavirenz. This drug has a fairly stereotypic resistance profile which in most cases involves a mutation at amino acid 103 of the reverse transcriptase of HIV (K103N). The authors examine sequences from patients after treatment failure (drug resistant virus) and observe that in a large fraction of the cases, the drug resistance mutation K103N is present on multiple genetic backgrounds or in both of the possible codons for asparagine. This suggests frequent soft sweeps, i.e., evolution of drug resistance is not limited by the waiting time for a point mutation.
The observation of frequent soft sweeps allows to put a lower bound on the product of population size and mutation rate. Since the mutation rate is on the order of 1e-5, the lower bound for the population size is around N>1e5. The authors suggest that the fact that not all patients exhibit obvious soft-sweeps can be used to deduce an upper bound of N. However, one has to realize that the patient sample is heterogeneous, that additional drugs are used along with efavirenz, and that most likely additional mutations have swept through the population. Multiple soft-sweeps in rapid succession will look like hard sweeps. The lower bound makes a lot of sense and does away with a long held erroneous belief that the “effective” HIV population within an infected individual is small.
The debate about the size of the HIV population has some interesting history. In the mid 90ies, it was estimated that roughly 1e7 cells are infected by HIV within a chronically infected patient every day. Virologists studying HIV evolution concluded that every point mutations is explored many times every day (see Coffin, Science, 1995, http://www.ncbi.nlm.nih.gov/pubmed/7824947), which was consistent with the frequent failure of mono-therapy, i.e., therapy with only one drug. Around the same time, it was observed that HIV sequences within a patient typically have a common ancestor about 3 years ago, which translates into roughly 500-1000 generations. Population geneticists then started to convince people that this rapid coalescence corresponds to an “effective” population size of the order of a 1000, and that this explains the observed stochasticity of HIV evolution. Not everybody was convinced and some went through great trouble to show that very rare alleles matter and that the population size is large, see for example http://jvi.asm.org/content/86/23/12525. In this paper, failure of efavirenz therapy is studied in monkeys. Despite the fact that the resistance mutations were at frequencies below 1e-5 before treatment, both codons for asparagine at position 103 are observed a few days after treatment. Via as similar argument as in the above paper, the authors conclude that the population size is large.
There is very little reason to believe that coalescence in HIV is driven by short term offspring number fluctuations (drift). Instead, the coalescence is most likely driven by selection in which case the time scale of coalescence depends weakly on the population size (see e.g. http://arxiv.org/abs/1302.1148).
The tendency of population geneticists to map everything to a neutral model has in this case of HIV produced much confusion. This confusion is easily avoided if people were willing to give up the concept of effective population size and simply call the time scale of coalescent what it is.
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