SPMM: estimating infection duration of multivariant HIV-1 infections

Abstract

Abstract.-The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements. The core of this method is a simple hill-climbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distance-based method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment of the topology and branch lengths, only a few iterations are sufficient to reach an optimum. We used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches. The reduction of computing time is dramatic in comparison with other maximum-likelihood packages, while the likelihood maximization ability tends to be higher. For example, only 12 min were required on a standard personal computer to analyze a data set consisting of 500 rbcL sequences with 1,428 base pairs from plant plastids, thus reaching a speed of the same order as some popular distance-based and parsimony algorithms. This new method is implemented in the PHYML program, which is freely available on our web page:

Estimating the basic reproduction number of a pathogen in a single host when only a single founder successfully infects

“…Given the distributional equality η= d Poission(μA), our observations on Eq (1) therefore suggest that the distributional approximation η� d Poission(μa) pertains, as follows. In the present context (the distribution of η under μ = 0.0551 in the Gamma model), the variation of A contributes little to the variance of η m : effectively, as noted by other authors [1,19,24], A behaves as though it were the constant a m ¼ EA m when contributing to random fluctuations in η m . In effect, the approximation A m � a m treats Eq (1) as an expansion in μ around μ = 0 and drops terms quadratic in μ to retain the approximation s 2 ðZ m Þ � mEA m .…”

“…Each daughter lived an independent random time after her birth. To approximate life-cycle times relevant to HIV [19,29], the random times had a gamma distribution with mean 2 days and standard deviation 0.24 days. The shape and rate parameters of the gamma distribution were therefore (n, λ) = (69.4, 34.7) (to make the mean nλ −1 = 2 and variance nλ −2 � 0.24 2 ).…”

“…For each of the 1000 successful realizations,η yielded lnr for the estimater ðIÞ in Eq (18). The simulation also estimated the corresponding standard deviationsŝð lnrÞ given in Eqs (19). For each r and each M, the simulation calculated a sample mean Eð lnrÞ and sample standard deviation sð lnrÞ from the 1000 successfully sampled values of lnr.…”

“…Let m ¼ P N n¼1 ε n be the expected number of novel mutations per generation in the sequences. Despite its biological importance, the effects of preferential selection on sequence data are practically imperceptible during the first six months of HIV infection (see the first paragraph in the Materials and Methods of [19] and Fig 1 in [24]). Assume therefore that (ε n : n 2 (N)) are all small, and that novel mutations are all independent.…”

“…The viral dosage may vary considerably between the modes of transmission above, and in sexual or mother-to-child transmission of HIV, e.g., the genetic diversity at early stages of infection usually reflects the number of viruses founding the infection [14][15][16]. In fact, however, about 80% of all HIV infections arise from a single founding viral sequence [17][18][19]. Moreover, the design of repeated low-dose challenge animal trials is likely to cause infections with a single founding virus.…”