The roles of plasticity versus dominance in maintaining polymorphism in mating strategies

Although natural selection is expected to reduce variability, polymorphism is common in nature even under strong selective regimes. Discrete polymorphisms in mating strategies are widespread and offer a good opportunity to understand the genetic processes that allow the maintenance of polymorphism in relatively simple systems. Here we explored the genetic mechanism underlying the expression of discrete mating strategies in the rock-paper-scissors (RPS) game. Heterozygotes carry the genetic information for two different strategies, yet little attention has been devoted to the mechanisms underpinning heterozygote phenotype and its consequences for allele frequency dynamics. We explored the maintenance of polymorphism under 1) genetic dominance or 2) plasticity, as mechanisms driving the expression of alternative strategies in males. We developed an alternative mating strategy model and analysed allele frequency dynamics using time series analyses. Our results show that both genetic mechanisms can maintain polymorphism depending on population demographic characteristics but that plasticity can enhance the likelihood that polymorphism is maintained relative to dominance. Time series analysis on simulation outcomes show that the RPS game is mostly driven by a single strategy, but the importance of this strategy on long term dynamics is stronger when gene expression shows dominance rather than plasticity.

strategy winning in all cases. However, this decrease may also be explained by the 23 asymmetry of mating systems between polygynous and monogamous strategists 1 . Such 24 asymmetry may accelerate the extinction speed of m allele compared to others.

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Under the genetic dominance hypothesis, the heterozygote cost does not significantly 26 change the probability or time before extinction of alleles (Table S1). Under the plasticity 27 mechanism, the heterozygote cost only influences the extinction speed of the p allele when P 28 plays against S (Table S1). Under this hypothesis, p and m alleles have similar extinction 29 patterns explained by the matting system asymmetry. Indeed, in these cases, ps individuals

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We then perform a wavelet analysis using the "Morlet" wavelet 11 and a multi- 99 Figure A1 shows the wavelet and the multi-resolution signatures of the three functions:  f1: The wavelet power spectrum shows that a high power spectrum (in dark red) is medium frequency oscillations (period ≈ 8 t.u.). The multi-resolution analysis shows that the signal is composed of a single signals at period = 16 t.u. until t = 5000 t.u.

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where it switches to another single signal at period = 8 t.u.

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 f2: The wavelet power spectrum shows that high power of spectrum is carried by two 106 different temporal scales (period ≈ 20 t.u. and period ≈ 8 t.u.) all along the signal. The 107 multi-resolution analysis shows that the signal is composed of a mixture of two 108 signals with at period = 16 t.u. and period = 8 t.u.

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 f3: The wavelet power spectrum shows that a high power spectrum is located around In this section, the main idea is to determine if a signal (S1) influences another signal whereas it is asymmetrical if a causal relationship exists. When the function is asymmetrical,

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if both the signals are in phase, the function is centered on 0, otherwise the function is 123 centered on the phase difference. The direction of the deviation from 0 reflects the direction 124 of the relationship. If 1 is positive and induces a positive response of 2 , the deviation will be 125 also positive. Finally, the cross-correlation function presents at the same time the effect of S1 126 on S2 (x>0) and the feed-back effects of S2 on S1 (x<0) 6 .

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With complex signals, it can be interesting to identify the time scale at which one 128 signal, S1 or its components influences S2 ( Figure S4). We have seen before that multi-129 resolution tools can split the signal into its different components and we are able to perform 130 correlations between S1 or its components and S2's components to detect the time scale of 131 interactions between S1 (or its components) and S2 (or its components). The intensity of 132 these correlations corresponds to the intensity of the transfer of information from S1 to S2 6 .

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Signals are split into time scale specific sub-signals. For readability, only temporal windows 172 between 4000 t.u. and 6000 t.u., temporal components of oscillations between 4 t.u. and 32 t.u. are represented and the multi-resolution analysis have been normalized.