### abstract ###
The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment.
To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known.
While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data.
However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution.
Yet, little is known about the distribution of selection differentials between individual viruses and the impact of single polymorphisms on viral fitness.
Here, we estimate the rate of recombination and the distribution of selection coefficients from time series sequence data tracking the evolution of HIV within single patients.
By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be 1.4 0.6 10 5 recombinations per site and generation.
Furthermore, we provide evidence that the selection coefficients of at least 15 percent of the observed non-synonymous polymorphisms exceed 0.8 percent per generation.
These results provide a basis for a more detailed understanding of the evolution of HIV.
A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations.
With the methods developed here, more precise and more detailed studies will be possible as soon as data with higher time resolution and greater sample sizes are available.
### introduction ###
The human immunodeficiency virus ranks among the most rapidly evolving entities known CITATION, enabling the virus to continually escape the immune system.
After infection with HIV, patients typically enter an asymptomatic period lasting several years during which the virus is present at low to medium levels, typically at a viral load of FORMULA to FORMULA copies per ml plasma.
Nevertheless, the number of virions produced and removed is estimated to be around FORMULA per day with a generation time slightly less than two days CITATION.
Due to this rapid turnover and the high mutation rate of FORMULA per site and generation, the sequence diversity of HIV within a single patient can rise to FORMULA percent within a few years and the divergence from the founder strain increases by FORMULA percent per year CITATION, although this rate is not constant CITATION.
The genotypic diversity is subject to positive selection for novel variants that are not recognized by the host immune system or that reduce the sensitivity to anti-retroviral drugs CITATION CITATION, as well as to purifying selection by functional constraints CITATION.
In addition to high substitution rates and strong selection, genomes of different HIV particles within the same host frequently exchange genetic information.
This form of viral recombination works as follows: Whenever a cell is coinfected by two or more viruses, the daughter virions can contain two RNA strands from different viruses CITATION, CITATION.
In the next round of infection, recombinant genomes are generated by template switching of the reverse transcriptase while producing cDNA.
It has been shown that recombination in HIV contributes significantly to the genetic diversity within a patient CITATION CITATION.
In cases of super-infection with several HIV-1 subtypes, recombination can give rise to novel forms that become part of the global epidemic CITATION .
The observation of recombinant viruses after a change in anti-retroviral drug therapy CITATION suggests that recombination might play an important role in the evolution of drug resistance, as predicted by theoretical models CITATION.
The amount by which recombination speeds up the evolution of drug resistance depends on the parameters governing the population dynamics CITATION, many of which are not known to sufficient accuracy.
In vitro estimates of the recombination rate have shown that the reverse transcriptase switches templates about FORMULA times while transcribing the entire genome, resulting in a recombination rate of FORMULA per site and generation CITATION, CITATION.
However, the bare template switching rate is only of secondary importance, since recombination can generate diversity only if the virion contains two RNA strands that originate from different viruses, which requires coinfection of host cells CITATION.
The effective in vivo recombination rate is therefore a compound quantity, to which the template switching rate and the probability of coinfection of a single host cell contribute.
This effective recombination rate has been estimated with coalescent based methods developed in population genetics CITATION, CITATION.
These methods use a single sample of sequences obtained from the diverse population and estimate the recombination rate from topological incongruencies in the phylogenetic tree of the sequence sample.
Together with an estimate of the mutation rate, this allows to estimate the recombination rate in real time units.
Shriner et al. CITATION report an estimate of FORMULA per site and generation, implying almost ubiquitous coinfection of host cells.
Here, we present a different method to estimate recombination rates from longitudinal sequence data, which has been obtained from 11 patients at approximately 6 month intervals CITATION, CITATION.
By comparing sequence samples from successive time points, we can estimate recombination rates from the distance and time dependence of the probability of cross-over between pairs of polymorphic sites.
We find that the effective rate of recombination is FORMULA per site and generation.
Furthermore, we estimate the strength of selection on nonsynonymous polymorphisms by measuring the rate at which allele frequencies change.
We find that a fraction of about 15 percent of the observed nonsynonymous polymorphisms are selected stronger than FORMULA percent per generation.
