# Selection for Plastic, Pathogen-Inducible Recombination in a Red Queen Model with Diploid Antagonists

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## Abstract

**:**

## 1. Introduction

## 2. Model and Methods

#### 2.1. Life Cycles

#### 2.2. Species Interaction

#### 2.3. Recombination Strategies

- prevention strategy—with recombination sensitive to the potential infection risk, so that recombination rate of each host class increases proportionally to the frequency $p$ of the dangerous (exactly for this class) parasite class:$${r}^{\mathrm{h}}={r}_{\mathrm{min}}^{\mathrm{h}}+p\cdot \left({r}_{\mathrm{max}}^{\mathrm{h}}-{r}_{\mathrm{min}}^{\mathrm{h}}\right).$$
- remediation strategy—with recombination sensitive to the actual infection status, so that the infected hosts display an increased recombination rate (${r}_{\mathrm{max}}^{\mathrm{h}}$) compared to their resistant counterparts (${r}_{\mathrm{min}}^{\mathrm{h}}$):$${r}^{\mathrm{h}}=\left\{\begin{array}{cc}{r}_{\mathrm{min}}^{\mathrm{h}}\hfill & \mathrm{resistance}\\ {r}_{\mathrm{max}}^{\mathrm{h}}\hfill & \mathrm{infection}\end{array}\right.$$

#### 2.4. Experimental Design

## 3. Results

#### 3.1. The System’s Dynamics and the Optimal Constant Recombination in the Host

#### 3.2. Selection for Plastic Recombination in the Host

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The effect of recombination rate in the parasite (${r}^{\mathrm{p}}$) on the estimation of the optimal constant recombination rate in the host (${r}_{\mathrm{opt}}^{\mathrm{h}}$). The colored curves show the lower (blue) and the upper (red) estimates. All simulations are conducted for the case of obligate parasitism (=1).

**Figure 2.**The evolutionary advantage of plastic recombination over non-zero optimal constant recombination, under in-phase (

**a**) and anti-phase (

**b**) dominance. The colored markers show regimes where the prevention (yellow) and the remediation (red) strategies are favored, either totally (circles) or partially (triangles).

**Figure 3.**The system’s dynamics under different regimes favoring plastic recombination. The plots show the last 500 out of 10,000 generations of the competition between the optimal constant recombination and plastic recombination; yet, the pattern is qualitatively similar also for other time windows. The colored curves stand for the host (green) and the parasite (orange). A, B and M denote, respectively, the two interaction-mediating loci and the modifier locus while W denotes the population’s mean fitness. All examples stand for anti-phase dominance and prevention strategy: (

**a**) A regime with strong overall selection: ${s}^{\mathrm{h}}\approx 0.88$, ${s}^{\mathrm{p}}\approx 0.91$. The optimal constant recombination in the host is high: ${r}_{\mathrm{opt}}^{\mathrm{h}}\approx 0.25.$ The oscillations are fairly regular. The modifier allele for plastic recombination generally increases in frequency, again with fairly regular oscillations; (

**b**) A regime with extremely strong overall selection: ${s}^{\mathrm{h}}\approx 0.98$, ${s}^{\mathrm{p}}>0.99$. The optimal constant recombination in the host is high: ${r}_{\mathrm{opt}}^{\mathrm{h}}=0.32.$ The oscillations are regular. The modifier allele for plastic recombination generally increases in frequency, again with fairly regular oscillations; (

**c**) A regime with weak overall selection due to weak selection in the host: ${s}^{\mathrm{h}}\approx 0.14$, ${s}^{\mathrm{p}}\approx 0.70$. The optimal constant recombination in the host is very low: ${r}_{\mathrm{opt}}^{\mathrm{h}}<0.01.$ The oscillations are irregular. Although the modifier allele for plastic recombination generally increases in frequency, its oscillations are substantially irregular; (

**d**) A regime with weak overall selection due to weak selection in the parasite: ${s}^{\mathrm{h}}\approx 0.85$, ${s}^{\mathrm{p}}\approx 0.16$. The optimal constant recombination in the host is very low: ${r}_{\mathrm{opt}}^{\mathrm{h}}<0.01.$ The oscillations are irregular. Although the modifier allele for plastic recombination generally increases in frequency, its dynamics are considerably irregular; in certain time windows (like here), the decline of the modifier allele for plastic recombination may even temporally prevail.

**Figure 4.**The evolutionary advantage of plastic recombination over zero optimal constant recombination, under in-phase (

**a**) and anti-phase (

**b**) dominance. The colored markers show regimes where the prevention (yellow) and the remediation (red) strategies are favored, either totally (circles) or partially (triangles).

**Figure 5.**The effect of the magnitude of recombination plasticity on the proportion of regimes favoring plastic recombination. The line styles stand for in-phase (sold) and anti-phase (dashed) dominance, while the marker colors stand for prevention (yellow) and remediation (red) strategies.

**Table 1.**Interaction matrix: the two possible outcomes of the interaction as a function of the antagonists’ genotypes. Red and green cells stand, respectively, for infection (I) and resistance (R).

Parasite Genotype | Host Genotype | ||||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{1}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}$ | ${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{1}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | ${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{1}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | ${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}$ | ${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | ${\mathit{A}}_{1}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | ${\mathit{A}}_{2}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}$ | ${\mathit{A}}_{2}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{1}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | ${\mathit{A}}_{2}^{\mathbf{h}}{\mathit{A}}_{2}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}{\mathit{B}}_{2}^{\mathbf{h}}$ | |

In-Phase Dominance (${A}_{1}^{\mathrm{p}}<{A}_{2}^{\mathrm{p}};{B}_{1}^{\mathrm{p}}<{B}_{2}^{\mathrm{p}};{A}_{1}^{\mathrm{h}}<{A}_{2}^{\mathrm{h}};{B}_{1}^{\mathrm{h}}<{B}_{2}^{\mathrm{h}}$) | |||||||||

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | I | R | R | R | R | R | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | I | I | R | R | R | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | I | I | R | R | R | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | R | R | R | I | R | R | I | R | R |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | I | I | R | I | I |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | I | I | R | I | I |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | R | R | R | I | R | R | I | R | R |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | I | I | R | I | I |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | I | I | R | I | I |

Anti-Phase Dominance (${A}_{1}^{\mathrm{p}}<{A}_{2}^{\mathrm{p}};{B}_{1}^{\mathrm{p}}<{B}_{2}^{\mathrm{p}};{A}_{1}^{\mathrm{h}}>{A}_{2}^{\mathrm{h}};{B}_{1}^{\mathrm{h}}>{B}_{2}^{\mathrm{h}}$) | |||||||||

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | I | I | R | I | I | R | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | I | R | R | I | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | I | R | R | I | R | R | R |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | R | R | R | R | R | R | I | I | R |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | R | R | R | R | I |

${A}_{1}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | R | R | R | R | I |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}$ | R | R | R | R | R | R | I | I | R |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{1}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | R | R | R | R | I |

${A}_{2}^{\mathrm{p}}{A}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}{B}_{2}^{\mathrm{p}}$ | R | R | R | R | R | R | R | R | I |

**Table 2.**The relative effects of the examined parameters (${s}^{\mathrm{h}}$, ${s}^{\mathrm{p}}$, and ${r}^{\mathrm{p}}$) and their combinations on the optimal constant recombination rate in the host (${r}_{\mathrm{opt}}^{\mathrm{h}}$).

Parameters/Combinations | In-Phase Dominance (n = 2856) | Anti-Phase Dominance (n = 3307) | ||||
---|---|---|---|---|---|---|

Model A | Model B | Model C | Model A | Model B | Model C | |

Selection Intensity in the Host (${s}^{\mathrm{h}}$) | 0.787 | - | 0.137 | 0.810 | - | 0.238 |

Selection Intensity in the Parasite (${s}^{\mathrm{p}}$) | 0.425 | - | −0.040 | 0.479 | - | 0.029 |

Recombination Rate in the Parasite (${r}^{\mathrm{p}}$) | 0.023 | 0.022 | 0.037 | 0.032 | 0.040 | 0.049 |

Overall Selection Intensity (${s}^{\mathrm{h}}\cdot {s}^{\mathrm{p}}$) | - | 0.974 | 0.889 | - | 0.970 | 0.775 |

R^{2}-Adjusted | 0.891 | 0.949 | 0.961 | 0.901 | 0.942 | 0.962 |

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**MDPI and ACS Style**

Rybnikov, S.; Frenkel, Z.; Korol, A.B.; Fahima, T. Selection for Plastic, Pathogen-Inducible Recombination in a Red Queen Model with Diploid Antagonists. *Pathogens* **2021**, *10*, 898.
https://doi.org/10.3390/pathogens10070898

**AMA Style**

Rybnikov S, Frenkel Z, Korol AB, Fahima T. Selection for Plastic, Pathogen-Inducible Recombination in a Red Queen Model with Diploid Antagonists. *Pathogens*. 2021; 10(7):898.
https://doi.org/10.3390/pathogens10070898

**Chicago/Turabian Style**

Rybnikov, Sviatoslav, Zeev Frenkel, Abraham B. Korol, and Tzion Fahima. 2021. "Selection for Plastic, Pathogen-Inducible Recombination in a Red Queen Model with Diploid Antagonists" *Pathogens* 10, no. 7: 898.
https://doi.org/10.3390/pathogens10070898