Table 1. The mean square error (MSE) of the independent estimation of selection intensity is correlated with the proportion of changes that are synonymous in one gene and nonsynonymous in the overlapping gene (SN changes). Proportion of MSE MSE Phase SN changes Independent Simultaneous Orientation Same-Strand Opposite-Strand 0 1 2 1 2 doi:10.1371/journal.pone.0003996.t001 47% 47% 43% 63% 39% 1.83 1.94 0.64 3.23 0.40 0.04 0.05 0.03 0.06 0.04 in inability to detect positive selection in gene 2 for simulated values of v2v2. To compare the magnitude of error in the independent estimation of each overlap type, we set k = 1, t = 0.35, v1~0:2, and v2~1. We calculated the mean square error (MSE) for the independent estimation of v2 (the parameter whose estimation is most biased) in each overlap type. We use MSE because it measures both the bias and the variance. The most biased type is opposite-strand phase 1 followed by both same-strand phase 1 and phase 2, opposite-strand phase 0, and opposite-strand phase 2 (Table 1). As expected, the magnitude of error among overlap types is correlated with the proportion of sites in each overlap type that are synonymous in one gene and nonsynonymous in the overlapping genes (Table 1). Selection in Overlapping Genes Transition/transversion rate ratio and sequence divergence We tested the influence of transition/transversion rate ratio (k), and sequence divergence (t) on the performance of the new method for simultaneous estimation. Focusing on same-strand phase 1, we set v1~0:2, v2~1 and vary k between 1 and 20, and t between 0.1 and 1.1. We calculated the MSE for the estimation of v2. The results of 100 replications suggest that transition/ transversion rate ratio does not affect the accuracy of the method, whereas the accuracy of the method is reduced for t#0.3 (sequence divergence of ,8% or less, Figure 4). We note that although our method performs well in high sequence divergence, the inference of selection can be biased by the reduced quality in alignment of distant sequences. Testing the new estimation method on genes from influenza H5N1 and H9N2 strains We used the new method to estimate selection pressures in two cases of overlapping genes in avian influenza A. We chose PB1-F2 and NS1 genes (which overlap with PB1 and NS2, respectively), because they were previously reported to exhibit values of dN/dS indicative of positive selection [19,20,25,26]. For each gene, we collected all the annotated gene sequences from the two most sequenced subtypes, H5N1 and H9N2 from the NCBI Influenza Virus Resource [43]. Within each subtype set, we aligned the overlapping regions of all gene pairs at the amino acid level using the Needleman-Wunsch algorithm [44]. We used all pairwise alignments with sequence divergence greater than 5% (since estimation is less accurate at low divergence rates) to estimate selection intensities either simultaneously or independently (Table 2). Using higher cutoffs for sequence divergence did not affect the results (data not shown). Pairs in which the independent estimation of dS was zero (leading to infinity value for dN/dS) Figure 4. The influence of transition/transversion rate ratio (k), and sequence divergence (t) on the performance of the new method. The mean square error (MSE) is plotted against t for k = 1, 10, and 20 (blue, red, and green, respectively). doi:10.1371/journal.pone.0003996.g004 PLoS ONE | www.plosone.org 5 December 2008 | Volume 3 | Issue 12 | e3996