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Inbreeding, male viability, and the remarkable evolutionary stability of the aphid X chromosome

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Fig. 1: Elevated effects of X chromosome-autosome fusion on gene dosage in aphids.
Fig. 2: Minimum F values at which invasion of an X-autosome fusion is prevented, representing the derived equation F > mb/(1 − m/2 − m2b/2).
Fig. 3: Number of generations for invasion of a X-autosomal fusion for various values of m and b, assuming no inbreeding (F = 0).

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Acknowledgements

I thank Sophie Archambeault for help with creating figures, and two anonymous reviewers for thoughtful comments that greatly shaped and improved this work.

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Appendix: A simple model for selection on an X-autosome fusion

Appendix: A simple model for selection on an X-autosome fusion

Let m represent the fraction of offspring that are males. Let b represent resource allocation, that is, the fraction of resources from an inviable offspring that are reallocated to increased fitness of siblings. Assume that the sex ratio of the offspring produced from these reallocated resources is the same as for all offspring (namely, a fraction m males). Let F represent the fraction of sexually produced offspring that are homozygous at a given locus due to inbreeding. Assume equal fitness of inbred and outbred individuals. We can then calculate the brood fitness (that is, the total fitness of all offspring of a given mother) as well as the chromosomal fitness (the brood fitness weighted across offspring by 0.5 for heterozygotes and 1 for homozygotes and male), as shown in Table 1. Note that, as expected, the fitness for the fused chromosome is higher than wildtype (unfused) in heterozygotes (due to reallocation of resources from males lacking the fused chromosome to offspring bearing the fused chromosome), but lower than wildtype in homozygotes (due to overall decrease in offspring production due to male inviability). The fused chromosome is not expected to invade the population when the weighted average chromosomal fitness is lower than that of wildtype, namely:

\(0.5\,{\times}\,\left[ {1 + b/\left( {1 - m/2} \right)} \right]{\times}\left( {1 - F} \right) + 0.25\,{\times}\,(1 + mb)\,{\times}\,F < 0.5\), which simplifies to

$$F > mb/\left( {1 - m/2 - m^2b/2} \right).$$

Cutoff values for F are shown in Fig. 2.

Table 1 Expected values for quantities under the model described.

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Roy, S.W. Inbreeding, male viability, and the remarkable evolutionary stability of the aphid X chromosome. Heredity (2021). https://doi.org/10.1038/s41437-021-00440-x

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