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Positive selection in the human immunodeficiency virus type 1 (HIV-1) env gene has been demonstrated by comparisons of the abundance of nonsynonymous (dn) and synonymous (ds) pairwise variability in the DNA sequence (Bonhoeffer, Holmes, and Nowak 1995; Seibert et al. 1995; Yamaguchi and Gojobori 1997). An increase in dn above the neutral expectation of dn # ds provides an unambiguous indication of the action of positive selection (Kimura 1983). The observed increase in dn in the V3 loop of the env gene is hypothesized to be caused by immune mediated selection for sequence diversity (Brown and Monaghan 1988; Simmonds et al. 1990; Holmes et al. 1992). According to this hypothesis, cytotoxic T lymphocytes (CTLs) are important in limiting the viral population. Viral variants carrying new CTL epitopes may avoid immune recognition and thereby spread in the viral population. The consequence at the molecular level is a decrease in ds/dn to below one (Bonhoeffer, Holmes, and Nowak 1995; Seibert et al. 1995). The most compelling evidence for positive selection is provided by Bonhoeffer, Holmes, and Nowak (1995), who observed an increase in dn over ds in the V3 loop of the env gene by a factor of 10 for sequences obtained from an infected individual after 3 years of infection. Bonhoeffer, Holmes, and Nowak (1995) also observed an increase in ds/dn among samples taken from the infected individual at different stages of the infection. This result was interpreted as evidence for a decrease in the selection pressure during the course of infection. It was hypothesized that the change in selection pressure was caused by a decline in the CD4 CTL population. Although there has been some discussion regarding the method used to estimate ds and dn (Rodrigo and Mullins 1996; Nielsen 1997), it remains the case that there is a significant increase in the ds/dn ratio between the third year of infection and the subsequent years in the data analyzed by Bonhoeffer, Holmes, and Nowak (1995) (Rodrigo and Mullins 1996; Nielsen 1997; Nielsen and Yang 1998). Previous analyses have assumed that a change in ds/dn is evidence for a change in the selection pressure and is caused by changes in the dynamics of the immune system. However, this article will show that even if dn and ds can be estimated with 100% accuracy, an increase in ds/dn similar to the in-

Changes in ds/dn in the HIV-1 env gene