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Differential effects of vertical and horizontal transmission in the fitness of an RNA virus: A reanalysis
Infection, Genetics and Evolution 1 (2002) 307–309
Discussion
Differential effects of vertical and horizontal transmission in the fitness of an RNA virus: A reanalysis Santiago F. Elena∗ , R. Sanjuán, A.V. Border´ıa1 , Paul E. Turner2 Departament de Genètica, Institut Cavanilles de Biodiversitat i Biologia Evolutiva, Universitat de València, Apartat 22085, 46071 Valencia, Spain Received 19 December 2001; received in revised form 16 February 2002; accepted 20 March 2002
We agree with every aspect of the critique offered by Morrison (2002). In our previous paper (Elena et al., 2001), we inappropriately used a mixed model II ANOVA to analyze our experimental data. We attempted to nest fixed factors within random ones, but this is invalid (Sokal and Rohlf, 1995). Thus, SPSS conducted a different analysis by automatically setting all factors to random, but the SPSS output did not indicate to us our original flawed logic. We offer no excuse for our mistake, and the senior author (SFE) accepts the full responsibility. We are indebted to Morrison for detecting the subtle (although very serious) flaw in our analysis that escaped our attention and that of the reviewers. However, we describe later that changing the analysis does not affect many of our original conclusions because these were based on factors that are again shown to be statistically significant. Furthermore, we also demonstrate that our empirical results are consistent across blocks, another potential problem indicated by Morrison. Rather than trivializing our original experiments, the new analysis suggests additional conclusions regarding the influence of transmission mode on the fitness of RNA viruses. In reality, this was one of the motivations for our original experiment (Elena et al., 2001).
1. Results of the appropriate ANOVA model Following the suggestions of Morrison (2002), an appropriate mixed model II ANOVA for our experiment is
∗ Corresponding author. Tel.: +34-963-983-666; fax: +34-963-983-670. E-mail address: [email protected] (S.F. Elena). 1 Present address: Servicio de Virolog´ıa Molecular, Centro Nacional de Microbiolog´ıa, Instituto de Salud Carlos III, Majadahonda, 28220 Madrid, Spain. 2 Present address: Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06520-8106, USA.
represented by Wijklm = µ + Ti + Ij + Bk + (TI)ij + (TB)ik + (IB)jk +(TIB)ijk + Fijkl + ξijklm where a fitness value (W) is defined as the mth fitness measurement for individual host l (l = 1, . . . , 5), at inoculum size j (j: large or small) and transmission mode i (i: horizontal or vertical) in experimental block k (k = 1, . . . , 4). In this model, µ is the overall mean fitness, T the effect of transmission mode, I the effect of inoculum size, B the block effect and F is the effect of an individual host. TI, IB, and TIB represent the interaction among the three orthogonal factors. Finally, represents a random error term. As usual, T, I, B, F, and are assumed to be normally distributed with mean 0 and positive variance (Sokal and Rohlf, 1995). Results of the ANOVA are shown in Table 1. Several features of the new analysis are noteworthy. First, the factors and interactions that were statistically significant in our previous (incorrect) analysis are again found to be significant here. Hence, all of the conclusions that we described for the factors inoculum size, interaction between inoculum size and transmission mode, and genetic variability among individual hosts are now confirmed to be valid. Second, none of the interactions between block and the other orthogonal fixed factors (transmission mode, inoculum size, and their interaction) are statistically significant (P ≥ 0.0735). If any of these three interactions were significant, it would mean that the results of the experiment were quite different among the four experimental blocks, invalidating them. Rather, the results are not different among replicate blocks, indicating that our conclusions are solid. Third, following the earlier statement, the newly found significant effect among blocks (P = 0.0229) is simply the consequence of random differences among blocks rather than different patterns of a relationship between fixed factors. That is, as might be expected for such highly mutable
1567-1348/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 5 6 7 - 1 3 4 8 ( 0 2 ) 0 0 0 3 8 - 2
308
S.F. Elena et al. / Infection, Genetics and Evolution 1 (2002) 307–309
Table 1 The appropriate mixed model II ANOVAa Source of variation
SSb
Block Transmission mode Inoculum size Transmission × size Block × transmission Block × size Block × transmission × size Individual host
33.5304 21.3063 120.2667 15.2735 2.6064 1.3267 0.3776 36.1675 53.1541
Error
d.f.
MS
F
P
3 1 1 1 3 3 3 64
11.1663 21.3063 120.2667 15.2735 0.8688 0.4422 0.5627 0.5651
12.8902 24.5391 272.0354 121.1569 6.9016 3.5130 0.2237 1.7968
0.0229 0.0158 0.0005 0.0016 0.0735 0.1648 0.8796 0.0015
169
0.3145
a
Mode of transmission and inoculum size were treated as fixed factors, whereas, replicate experiments (blocks) and individual hosts (flasks) were treated as random factors. Block, transmission mode, and inoculum size were orthogonal factors, whereas, individual hosts were nested within these three factors. Fitness values were transformed using a Box–Cox power function to normalize data and reduce heteroscedasticity of variances (see Section 3.1 in Elena et al. (2001)). b SS is the type III error sum of squares.
RNA genomes, different runs of the evolution experiment could have resulted in fixation of different mutations in the VSV populations; mutations that featured different fitness benefits but caused similar evolutionary patterns overall. This explanation is further supported by the significant differences between individual flasks (P = 0.0015). Finally, and most important, we observed a significant overall effect of transmission mode (P = 0.0158). We note that this interesting result was not seen in our previous analysis (Elena et al., 2001). This finding indicates that the average fitness of vertically-transmitted viral populations (2.4275 ± 0.3299) is significantly less than that of horizontally transmitted viruses (3.3344 ± 0.3917). However, as we indicated in our previous paper, there is a significant effect of transmission mode on fitness in the presence of bottlenecks (Elena et al., 2001; see Section 3.2 and grey bars in Fig. 2), but not in the absence of bottlenecks (see Section 3.4 and black bars in Fig. 2). Moreover, judging from the significant interaction between transmission mode and inoculum size (P = 0.0016), any general conclusions regarding the effects of transmission mode in our experiment should be made cautiously, since such a conclusion must be made in the context of the number of propagules being transmitted.
2. Additional conclusions: the effect of transmission mode on fitness in VSV Our reanalysis (Table 1) clearly demonstrates that transmission mode (horizontal versus vertical) impacts evolution of fitness in RNA viruses. After 80 generations of evolution involving horizontal transmission, VSV populations achieved fitness that was 37.36% higher than that of their counterparts evolved under vertical transmission alone. This result agrees with the general prediction that greater parasite virulence can evolve under horizontal transmission, whereas, vertical transmission of parasites should exert natural selec-
tion for the parasite to be less harmful to its host (Ewald, 1994; Bergstrom et al., 1999, and others). According to Bergstrom et al. (1999), attenuation of vertically-transmitted viruses results from two different genetic forces acting on virus populations, and not solely due to genetic changes or physiological responses in the host, as suggested by Ewald (1994). These two forces are: (1) processes such as Muller’s ratchet where deleterious mutations tend to accumulate in a virus lineage due to severe transmission bottlenecks, and (2) separation of viral genotypes into distinct lineages where competition is reduced and, hence, the ability for selection to improve fitness is weakened. In contrast, given sufficient availability of uninfected hosts in the environment, horizontal transmission should select for faster replicating viruses that are generally assumed to be more virulent. The interplay between transmission mode and inoculum size was extensively discussed in our previous report and we will not offer further discussion here. In short, our conclusions are relevant to the hypothesis of Bergstrom et al. (1999) because we showed that vertically-transmitted pathogens attenuate only in the presence of severe bottlenecks, where viruses were propagated in the deliberate absence of feedbacks relating to host fitness (i.e. in experiments containing only na¨ıve non-evolving hosts). Future experiments could be used to examine the relative importance in VSV evolution of the contrasting hypotheses described by Ewald (1994) and Bergstrom et al. (1999). Several medically-important viruses (including HTLV-1, HIV-1, human papilloma virus, and hepatitis B and C viruses) can spread through either vertical or horizontal transmission. Lipsitch et al. (1996) modelled the evolution of virulence for this special case and found that greater vertical transmission selects for reduced parasite virulence, whereas, greater horizontal transmission (due to increased contagiousness or rate of infectious contact between hosts) does not necessarily lead to enhanced virulence. The reason is that as horizontal transmission increases, the fraction of the population that becomes infected increases as well; thus,
S.F. Elena et al. / Infection, Genetics and Evolution 1 (2002) 307–309
vertical transmission becomes more important. The relevance of these many hypotheses for RNA virus evolution is still very much in doubt, but several of the predictions can be explored using our experimental system. References Bergstrom, C.T., McElhany, P., Real, L.A., 1999. Transmission bottlenecks as determinants of virulence in rapidly evolving pathogens. Proc. Natl. Acad. Sci. U.S.A. 96, 5095–5100.
309
Elena, S.F., Sanjuán, R., Border´ıa, A.V., Turner, P.E., 2001. Transmisión bottlenecks and the evolution of fitness in rapidly evolving RNA viruses. Infect. Genet. Evol. 1, 41–48. Ewald, P.W., 1994. Evolution of Infectious Diseases. Oxford University Press, New York. Lipsitch, M., Siller, S., Nowak, M.A., 1996. The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution 50, 1729–1741. Morrison, D.A., 2002. Inappropriate application of a model for mixed analysis of variance: some comments on Elena et al. (2002). Infect. Genet. Evol., Vol. 1, Issue 4. Sokal, R.R., Rohlf, F.J., 1995. Biometry, 3rd Edition. Freeman, New York.
Discussion
Differential effects of vertical and horizontal transmission in the fitness of an RNA virus: A reanalysis Santiago F. Elena∗ , R. Sanjuán, A.V. Border´ıa1 , Paul E. Turner2 Departament de Genètica, Institut Cavanilles de Biodiversitat i Biologia Evolutiva, Universitat de València, Apartat 22085, 46071 Valencia, Spain Received 19 December 2001; received in revised form 16 February 2002; accepted 20 March 2002
We agree with every aspect of the critique offered by Morrison (2002). In our previous paper (Elena et al., 2001), we inappropriately used a mixed model II ANOVA to analyze our experimental data. We attempted to nest fixed factors within random ones, but this is invalid (Sokal and Rohlf, 1995). Thus, SPSS conducted a different analysis by automatically setting all factors to random, but the SPSS output did not indicate to us our original flawed logic. We offer no excuse for our mistake, and the senior author (SFE) accepts the full responsibility. We are indebted to Morrison for detecting the subtle (although very serious) flaw in our analysis that escaped our attention and that of the reviewers. However, we describe later that changing the analysis does not affect many of our original conclusions because these were based on factors that are again shown to be statistically significant. Furthermore, we also demonstrate that our empirical results are consistent across blocks, another potential problem indicated by Morrison. Rather than trivializing our original experiments, the new analysis suggests additional conclusions regarding the influence of transmission mode on the fitness of RNA viruses. In reality, this was one of the motivations for our original experiment (Elena et al., 2001).
1. Results of the appropriate ANOVA model Following the suggestions of Morrison (2002), an appropriate mixed model II ANOVA for our experiment is
∗ Corresponding author. Tel.: +34-963-983-666; fax: +34-963-983-670. E-mail address: [email protected] (S.F. Elena). 1 Present address: Servicio de Virolog´ıa Molecular, Centro Nacional de Microbiolog´ıa, Instituto de Salud Carlos III, Majadahonda, 28220 Madrid, Spain. 2 Present address: Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06520-8106, USA.
represented by Wijklm = µ + Ti + Ij + Bk + (TI)ij + (TB)ik + (IB)jk +(TIB)ijk + Fijkl + ξijklm where a fitness value (W) is defined as the mth fitness measurement for individual host l (l = 1, . . . , 5), at inoculum size j (j: large or small) and transmission mode i (i: horizontal or vertical) in experimental block k (k = 1, . . . , 4). In this model, µ is the overall mean fitness, T the effect of transmission mode, I the effect of inoculum size, B the block effect and F is the effect of an individual host. TI, IB, and TIB represent the interaction among the three orthogonal factors. Finally, represents a random error term. As usual, T, I, B, F, and are assumed to be normally distributed with mean 0 and positive variance (Sokal and Rohlf, 1995). Results of the ANOVA are shown in Table 1. Several features of the new analysis are noteworthy. First, the factors and interactions that were statistically significant in our previous (incorrect) analysis are again found to be significant here. Hence, all of the conclusions that we described for the factors inoculum size, interaction between inoculum size and transmission mode, and genetic variability among individual hosts are now confirmed to be valid. Second, none of the interactions between block and the other orthogonal fixed factors (transmission mode, inoculum size, and their interaction) are statistically significant (P ≥ 0.0735). If any of these three interactions were significant, it would mean that the results of the experiment were quite different among the four experimental blocks, invalidating them. Rather, the results are not different among replicate blocks, indicating that our conclusions are solid. Third, following the earlier statement, the newly found significant effect among blocks (P = 0.0229) is simply the consequence of random differences among blocks rather than different patterns of a relationship between fixed factors. That is, as might be expected for such highly mutable
1567-1348/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 5 6 7 - 1 3 4 8 ( 0 2 ) 0 0 0 3 8 - 2
308
S.F. Elena et al. / Infection, Genetics and Evolution 1 (2002) 307–309
Table 1 The appropriate mixed model II ANOVAa Source of variation
SSb
Block Transmission mode Inoculum size Transmission × size Block × transmission Block × size Block × transmission × size Individual host
33.5304 21.3063 120.2667 15.2735 2.6064 1.3267 0.3776 36.1675 53.1541
Error
d.f.
MS
F
P
3 1 1 1 3 3 3 64
11.1663 21.3063 120.2667 15.2735 0.8688 0.4422 0.5627 0.5651
12.8902 24.5391 272.0354 121.1569 6.9016 3.5130 0.2237 1.7968
0.0229 0.0158 0.0005 0.0016 0.0735 0.1648 0.8796 0.0015
169
0.3145
a
Mode of transmission and inoculum size were treated as fixed factors, whereas, replicate experiments (blocks) and individual hosts (flasks) were treated as random factors. Block, transmission mode, and inoculum size were orthogonal factors, whereas, individual hosts were nested within these three factors. Fitness values were transformed using a Box–Cox power function to normalize data and reduce heteroscedasticity of variances (see Section 3.1 in Elena et al. (2001)). b SS is the type III error sum of squares.
RNA genomes, different runs of the evolution experiment could have resulted in fixation of different mutations in the VSV populations; mutations that featured different fitness benefits but caused similar evolutionary patterns overall. This explanation is further supported by the significant differences between individual flasks (P = 0.0015). Finally, and most important, we observed a significant overall effect of transmission mode (P = 0.0158). We note that this interesting result was not seen in our previous analysis (Elena et al., 2001). This finding indicates that the average fitness of vertically-transmitted viral populations (2.4275 ± 0.3299) is significantly less than that of horizontally transmitted viruses (3.3344 ± 0.3917). However, as we indicated in our previous paper, there is a significant effect of transmission mode on fitness in the presence of bottlenecks (Elena et al., 2001; see Section 3.2 and grey bars in Fig. 2), but not in the absence of bottlenecks (see Section 3.4 and black bars in Fig. 2). Moreover, judging from the significant interaction between transmission mode and inoculum size (P = 0.0016), any general conclusions regarding the effects of transmission mode in our experiment should be made cautiously, since such a conclusion must be made in the context of the number of propagules being transmitted.
2. Additional conclusions: the effect of transmission mode on fitness in VSV Our reanalysis (Table 1) clearly demonstrates that transmission mode (horizontal versus vertical) impacts evolution of fitness in RNA viruses. After 80 generations of evolution involving horizontal transmission, VSV populations achieved fitness that was 37.36% higher than that of their counterparts evolved under vertical transmission alone. This result agrees with the general prediction that greater parasite virulence can evolve under horizontal transmission, whereas, vertical transmission of parasites should exert natural selec-
tion for the parasite to be less harmful to its host (Ewald, 1994; Bergstrom et al., 1999, and others). According to Bergstrom et al. (1999), attenuation of vertically-transmitted viruses results from two different genetic forces acting on virus populations, and not solely due to genetic changes or physiological responses in the host, as suggested by Ewald (1994). These two forces are: (1) processes such as Muller’s ratchet where deleterious mutations tend to accumulate in a virus lineage due to severe transmission bottlenecks, and (2) separation of viral genotypes into distinct lineages where competition is reduced and, hence, the ability for selection to improve fitness is weakened. In contrast, given sufficient availability of uninfected hosts in the environment, horizontal transmission should select for faster replicating viruses that are generally assumed to be more virulent. The interplay between transmission mode and inoculum size was extensively discussed in our previous report and we will not offer further discussion here. In short, our conclusions are relevant to the hypothesis of Bergstrom et al. (1999) because we showed that vertically-transmitted pathogens attenuate only in the presence of severe bottlenecks, where viruses were propagated in the deliberate absence of feedbacks relating to host fitness (i.e. in experiments containing only na¨ıve non-evolving hosts). Future experiments could be used to examine the relative importance in VSV evolution of the contrasting hypotheses described by Ewald (1994) and Bergstrom et al. (1999). Several medically-important viruses (including HTLV-1, HIV-1, human papilloma virus, and hepatitis B and C viruses) can spread through either vertical or horizontal transmission. Lipsitch et al. (1996) modelled the evolution of virulence for this special case and found that greater vertical transmission selects for reduced parasite virulence, whereas, greater horizontal transmission (due to increased contagiousness or rate of infectious contact between hosts) does not necessarily lead to enhanced virulence. The reason is that as horizontal transmission increases, the fraction of the population that becomes infected increases as well; thus,
S.F. Elena et al. / Infection, Genetics and Evolution 1 (2002) 307–309
vertical transmission becomes more important. The relevance of these many hypotheses for RNA virus evolution is still very much in doubt, but several of the predictions can be explored using our experimental system. References Bergstrom, C.T., McElhany, P., Real, L.A., 1999. Transmission bottlenecks as determinants of virulence in rapidly evolving pathogens. Proc. Natl. Acad. Sci. U.S.A. 96, 5095–5100.
309
Elena, S.F., Sanjuán, R., Border´ıa, A.V., Turner, P.E., 2001. Transmisión bottlenecks and the evolution of fitness in rapidly evolving RNA viruses. Infect. Genet. Evol. 1, 41–48. Ewald, P.W., 1994. Evolution of Infectious Diseases. Oxford University Press, New York. Lipsitch, M., Siller, S., Nowak, M.A., 1996. The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution 50, 1729–1741. Morrison, D.A., 2002. Inappropriate application of a model for mixed analysis of variance: some comments on Elena et al. (2002). Infect. Genet. Evol., Vol. 1, Issue 4. Sokal, R.R., Rohlf, F.J., 1995. Biometry, 3rd Edition. Freeman, New York.