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Predicting the evolution of sex on complex fitness landscapes.

Misevic D, Kouyos RD, Bonhoeffer S - PLoS Comput. Biol. (2009)

Bottom Line: Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements.The presence of loci that are not under selection can, however, severely diminish predictor accuracy.Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

View Article: PubMed Central - PubMed

Affiliation: Institute of Integrative Biology, ETH Zürich, Zürich, Switzerland.

ABSTRACT
Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, Delta Var(HD), also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

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Correlations between predictors on different landscapes.We highlight the relationships among ΔVarHD, ΔVaradd, and ΔMeanfit on smooth, random, and NK2 landscapes, in simulations with infinite population size. Each cross mark (+) represents a predictor value for a single simulation. Red (blue) crosses indicate simulations in which the frequency of sexually reproducing individuals increased (decreased) in the competition phase. For clarity of presentation, up to 5 outlier points were eliminated from random and NK2 landscapes. These outliers in predictor values are typically characteristic of a small number of populations that did not reach the equilibrium genotype frequencies by the end of the burn-in phase.
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pcbi-1000510-g002: Correlations between predictors on different landscapes.We highlight the relationships among ΔVarHD, ΔVaradd, and ΔMeanfit on smooth, random, and NK2 landscapes, in simulations with infinite population size. Each cross mark (+) represents a predictor value for a single simulation. Red (blue) crosses indicate simulations in which the frequency of sexually reproducing individuals increased (decreased) in the competition phase. For clarity of presentation, up to 5 outlier points were eliminated from random and NK2 landscapes. These outliers in predictor values are typically characteristic of a small number of populations that did not reach the equilibrium genotype frequencies by the end of the burn-in phase.

Mentions: To test whether combinations of the predictors could increase the accuracy of prediction of the evolution of sex we plot for each landscape the value of the predictors ΔVarHD, ΔVaradd and ΔMeanfit against each other and color code whether the number of sexual individuals increased (red) or decreased (blue) during deterministic competition phase (see Figure 2). If the blue and red points are best separated by a vertical or a horizontal line, then we conclude that little can be gained by combining two predictors. If, however, the points can be separated by a different linear (or more complex) function of the two predictors, then combining these predictors would indeed lead to an improved prediction. Figure 2 shows the corresponding plots for the smooth, the random, and the NK2 landscapes. For the smooth landscapes the criterion ΔVarHD>0 or ΔVaradd>0 are both equally good in separating cases where sex evolved from those where it did not. As already shown in Figure 1, ΔVarHD is generally a more reliable predictor of the evolution of sex than ΔVaradd in the more complex random or NK landscapes. Epistasis-based theories suggest that the selection for sex is related to a detrimental short-term effect (reduction in mean fitness) and a possibly beneficial long-term effect (increase in additive genetic variance) [28]. The plots of ΔVaradd against ΔMeanfit, however, do not indicate that combining them would allow a more reliable prediction of the evolution of sex. Generally, the plots show that blue and red points either tend to overlap (in the more complex landscapes) or can be well separated using horizontal or vertical lines (in the smooth landscapes) such that combining predictors will not allow to substantially increase the accuracy of prediction. This is also the case for all other landscapes and all other pairwise combinations of predictors (data not shown). It is possible that some of the effect described in [28] and expected here are too small to be detected with the level of replication in our study. However, as the level of replication used in this computational study goes way beyond what can be realistically achieved in experimental settings we expect that these effects would also not be detected in experimental studies.


Predicting the evolution of sex on complex fitness landscapes.

Misevic D, Kouyos RD, Bonhoeffer S - PLoS Comput. Biol. (2009)

Correlations between predictors on different landscapes.We highlight the relationships among ΔVarHD, ΔVaradd, and ΔMeanfit on smooth, random, and NK2 landscapes, in simulations with infinite population size. Each cross mark (+) represents a predictor value for a single simulation. Red (blue) crosses indicate simulations in which the frequency of sexually reproducing individuals increased (decreased) in the competition phase. For clarity of presentation, up to 5 outlier points were eliminated from random and NK2 landscapes. These outliers in predictor values are typically characteristic of a small number of populations that did not reach the equilibrium genotype frequencies by the end of the burn-in phase.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2734178&req=5

pcbi-1000510-g002: Correlations between predictors on different landscapes.We highlight the relationships among ΔVarHD, ΔVaradd, and ΔMeanfit on smooth, random, and NK2 landscapes, in simulations with infinite population size. Each cross mark (+) represents a predictor value for a single simulation. Red (blue) crosses indicate simulations in which the frequency of sexually reproducing individuals increased (decreased) in the competition phase. For clarity of presentation, up to 5 outlier points were eliminated from random and NK2 landscapes. These outliers in predictor values are typically characteristic of a small number of populations that did not reach the equilibrium genotype frequencies by the end of the burn-in phase.
Mentions: To test whether combinations of the predictors could increase the accuracy of prediction of the evolution of sex we plot for each landscape the value of the predictors ΔVarHD, ΔVaradd and ΔMeanfit against each other and color code whether the number of sexual individuals increased (red) or decreased (blue) during deterministic competition phase (see Figure 2). If the blue and red points are best separated by a vertical or a horizontal line, then we conclude that little can be gained by combining two predictors. If, however, the points can be separated by a different linear (or more complex) function of the two predictors, then combining these predictors would indeed lead to an improved prediction. Figure 2 shows the corresponding plots for the smooth, the random, and the NK2 landscapes. For the smooth landscapes the criterion ΔVarHD>0 or ΔVaradd>0 are both equally good in separating cases where sex evolved from those where it did not. As already shown in Figure 1, ΔVarHD is generally a more reliable predictor of the evolution of sex than ΔVaradd in the more complex random or NK landscapes. Epistasis-based theories suggest that the selection for sex is related to a detrimental short-term effect (reduction in mean fitness) and a possibly beneficial long-term effect (increase in additive genetic variance) [28]. The plots of ΔVaradd against ΔMeanfit, however, do not indicate that combining them would allow a more reliable prediction of the evolution of sex. Generally, the plots show that blue and red points either tend to overlap (in the more complex landscapes) or can be well separated using horizontal or vertical lines (in the smooth landscapes) such that combining predictors will not allow to substantially increase the accuracy of prediction. This is also the case for all other landscapes and all other pairwise combinations of predictors (data not shown). It is possible that some of the effect described in [28] and expected here are too small to be detected with the level of replication in our study. However, as the level of replication used in this computational study goes way beyond what can be realistically achieved in experimental settings we expect that these effects would also not be detected in experimental studies.

Bottom Line: Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements.The presence of loci that are not under selection can, however, severely diminish predictor accuracy.Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

View Article: PubMed Central - PubMed

Affiliation: Institute of Integrative Biology, ETH Zürich, Zürich, Switzerland.

ABSTRACT
Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, Delta Var(HD), also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. Delta Var(HD) is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction.

Show MeSH