Additional file 1: Table S1. Summary of NDM founder varieties and sequencing coverage. Table S2. Summary of overlap in sites called from wheat breeders’ genotyping array and SNP sites called in founders from sequencing data. Table S3. Summary of evidence for introgressions segregating among NDM founders. Table S4. Summary of trial inputs and conditions in 2016-17 (year 1) and 2017-18 (year 2). Table S5. Description of all phenotype measurement methods and timings. Table S6. Best Linear Unbiased Estimate for all phenotypes in 504 RILs. Table S7. Summary of all genome-wide significant QTL associations found for SNP-based and Haplotype-based mapping. Table S8. Gene-Deletion-Score (GDS) loci with GDS-phenotype associations with logP> 6. Table S9. Summary of crossing scheme.

Additional file 1: Table S1. Summary of NDM founder varieties and sequencing coverage. Table S2. Summary of overlap in sites called from wheat breeders’ genotyping array and SNP sites called in founders from sequencing data. Table S3. Summary of evidence for introgressions segregating among NDM founders. Table S4. Summary of trial inputs and conditions in 2016-17 (year 1) and 2017-18 (year 2). Table S5. Description of all phenotype measurement methods and timings. Table S6. Best Linear Unbiased Estimate for all phenotypes in 504 RILs. Table S7. Summary of all genome-wide significant QTL associations found for SNP-based and Haplotype-based mapping. Table S8. Gene-Deletion-Score (GDS) loci with GDS-phenotype associations with logP> 6. Table S9. Summary of crossing scheme.

File S1 is a Mathematica notebook containing analysis and derivations for the main text, File S2 is a Mathematica notebook for the supplemental information, File S3 is a python script used to simulate data. The Supplemental Information details an alternative form of density dependence.

<b>Abstract</b><br/>Many organisms spend a significant portion of their life cycle as haploids and as diploids (a haploid–diploid life cycle). However, the evolutionary processes that could maintain this sort of life cycle are unclear. Most previous models of ploidy evolution have assumed that the fitness effects of new mutations are equal in haploids and homozygous diploids, however, this equivalency is not supported by empirical data. With different mutational effects, the overall (intrinsic) fitness of a haploid would not be equal to that of a diploid after a series of substitution events. Intrinsic fitness differences between haploids and diploids can also arise directly, for example because diploids tend to have larger cell sizes than haploids. Here, we incorporate intrinsic fitness differences into genetic models for the evolution of time spent in the haploid versus diploid phases, in which ploidy affects whether new mutations are masked. Life-cycle evolution can be affected by intrinsic fitness differences between phases, the masking of mutations, or a combination of both. We find parameter ranges where these two selective forces act and show that the balance between them can favor convergence on a haploid–diploid life cycle, which is not observed in the absence of intrinsic fitness differences.

File S1 is a Mathematica notebook containing analysis and derivations for the main text, File S2 is a Mathematica notebook for the supplemental information, File S3 is a python script used to simulate data. The Supplemental Information details an alternative form of density dependence.

<b>Abstract</b><br/>Diploid organisms manipulate the extent to which their haploid gametes experience selection. Animals typically produce sperm with a diploid complement of most proteins and RNA, limiting selection on the haploid genotype. Plants, however, exhibit extensive expression in pollen, with actively transcribed haploid genomes. Here we analyze models that track the evolution of genes that modify the strength of haploid selection to predict when evolution intensifies and when it dampens the “selective arena” within which male gametes compete for fertilization. Considering deleterious mutations, evolution leads diploid mothers to strengthen selection among haploid sperm/pollen, because this reduces the mutation load inherited by their diploid offspring. If, however, selection acts in opposite directions in haploids and diploids (“ploidally antagonistic selection”), mothers evolve to reduce haploid selection to avoid selectively amplifying alleles harmful to their offspring. Consequently, with maternal control, selection in the haploid phase either is maximized or reaches an intermediate state, depending on the deleterious mutation rate relative to the extent of ploidally antagonistic selection. By contrast, evolution generally leads diploid fathers to mask mutations in their gametes to the maximum extent possible, whenever masking (e.g., through transcript sharing) increases the average fitness of a father’s gametes. We discuss the implications of this maternal–paternal conflict over the extent of haploid selection and describe empirical studies needed to refine our understanding of haploid selection among seemingly diploid organisms.

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