The tight association between apomixis (asexual seed production) and polyploidy in flowering plants is a long-standing evolutionary puzzle. Muralidhar and Haig (2017) proposed, for Taraxacum officinale — the common dandelion, whose European populations mix diploid sexuals with triploid apomicts — a population-genetic model in which a dominant allele arresting female meiosis creates diploid 'partial apomicts' that produce unreduced, parthenogenetically developing eggs and normal haploid pollen; occasional fertilization of those unreduced eggs by haploid pollen then irreversibly yields triploid apomicts, predicting fixation of triploid apomicts and only ephemeral diploid apomicts. The authors themselves flag unresolved factors the model omits: documented production of viable euploid pollen by triploids (a possible route for apomixis to re-enter sexual populations); fertilizations generating tetraploids and higher ploidies; time-varying fitness of clonal lineages (selection among multilocus genotypes and accumulation of deleterious recessives masked in diploid but exposed in haploid pollen); frequency-dependence of the unreduced-egg fertilization rate; and empirical validation via targeted surveys for the predicted ephemeral diploid apomicts. For the genetic architecture, the authors examined a conceptual two-locus case and argued that the equilibrium states of the model are unchanged if multiple loci form the genetic basis of apomixis, although the spread of apomixis is slowed by recombination and segregation in pollen production — an invariance claim never tested against the realistic, now largely mapped multi-locus architecture. The genetic architecture has since been worked out in detail — diplospory maps to a VPS13-like gene and parthenogenesis to the cloned ToPAR locus, two unlinked dominant factors — but the evolutionary model itself has not been extended or tested: no competing or successor model exists, no diploid apomict has been reported from natural T. officinale populations, and none of the model's parameters has been estimated in natural populations. The question of whether the mechanism survives inclusion of its omitted factors and relaxation of its simplifying assumptions, and whether its parameters and central predictions hold in nature, remains open.

Background

Apomixis is asexual reproduction through seeds: embryos develop as clones of the mother plant without the genetic recombination of sexual reproduction. In the dandelion form of apomixis (gametophytic apomixis), three developmental components replace sexual steps: apomeiosis, in which female meiosis is bypassed so an unreduced embryo sac forms (when the megaspore mother cell skips meiosis entirely this is called diplospory); parthenogenesis, in which the unfertilized egg cell develops into an embryo; and autonomous endosperm formation, in which the seed's nutritive tissue also develops without fertilization. Apomixis in angiosperms is strongly associated with polyploidy (possession of more than two chromosome sets: diploids are 2x, triploids 3x, tetraploids 4x), yet there is no obvious reason polyploidy should directly cause apomixis, so the repeated association of the two remains unexplained.

Taraxacum officinale, the common dandelion, is a model system for this puzzle. In Europe it exists as diploid sexual populations (hermaphroditic, self-incompatible outcrossers) alongside triploid apomictic lineages, which produce clonal triploid seeds and mostly inviable aneuploid pollen (pollen with an unbalanced chromosome number). Triploid apomicts nonetheless produce a small fraction of viable euploid pollen (chromosomally balanced haploid, diploid or triploid pollen; documented in crossing experiments by Tas and van Dijk, 1999), and rare tetraploid plants occur in natural populations, consistent with occasional fertilization of triploid eggs by haploid pollen or of haploid eggs by triploid pollen (Verduijn et al., 2004, who described a sexual–asexual cycle running through tetraploids). Apomicts also show 'geographical parthenogenesis' — asexual lineages occupying wider ranges, especially at high latitudes, than their sexual relatives. Diplospory in dandelions is inherited as a single dominant factor at the Diplosporous (DIP) locus, which genetic fine-mapping indicated to be large and apparently duplicated (Vijverberg et al., 2010); fluorescence in-situ hybridization later placed DIP on a nucleolus-organizer-region chromosome without a large hemizygous region (Vašut et al., 2014).

Muralidhar and Haig (2017) asked how triploid apomicts could evolve from diploid sexuals without triploidy itself causing apomixis. Their model posits a dominant allele A that arrests female meiosis in diploids: Aa 'partial apomicts' produce diploid (unreduced) egg cells that can develop into embryos without fertilization, while still producing normal haploid pollen. A proportion uu of the diploid eggs is instead fertilized by haploid pollen, producing triploid Aaa or AAa apomicts, which reproduce only apomictically and shed almost no functional pollen. With fixed viability disadvantages ss (diploid apomicts), tt (Aaa) and ff (AAa) relative to sexual diploids, iteration of the genotype-frequency recursions showed triploid apomicts fix in almost every regime — for equal disadvantages, unless s=t=f>1/3s=t=f>1/3 — while diploid partial apomicts are only a transient stage. Because conversion to triploidy is irreversible, diploid male-fertile apomicts are evolutionarily short-lived, which explains why they have never been observed in dandelions (though diploid apomicts exist in other genera such as Hieracium and Boechera). Because the A allele spreads through haploid pollen onto many genetic backgrounds before the transition, the newly apomictic population contains multiple clonal lineages, explaining the high clonal diversity of triploid dandelion populations.

The authors discuss what the model omits and what remains to be done: (1) triploid-derived euploid pollen, which could transmit apomixis back into diploid sexual populations and change the equilibrium; (2) fertilizations producing tetraploids and higher ploidies, excluded for simplicity; (3) fixed viability coefficients, whereas real apomictic fitness changes over time because clonal lineages are selected as whole multilocus genotypes (fitness has broad-sense heritability — the heritability of the genotype's total value rather than an allele's average effect) and because deleterious recessive mutations accumulate and would be exposed to selection in haploid pollen but masked in diploid pollen; (4) the genetic architecture — the model assumes a single dominant locus, and the authors examined a conceptual unlinked two-locus (AaBb) case, arguing that multiple loci forming the genetic basis of apomixis would slow the spread of apomixis through recombination and segregation in pollen production but leave the basic dynamics and equilibrium states unchanged; (5) a constant fertilization rate uu, whereas uu should decline as the diploid plants that produce haploid pollen become scarce; and (6) empirical validation of the predicted ephemeral diploid apomicts, for which the authors suggested further investigation into the structure of mixed T. officinale populations in Central Europe. Two further open lines of inquiry follow from the post-2017 literature: testing the item-(4) invariance claim against the realistic multi-locus architecture mapped since 2017, and bounding the model's empirical footing in natural mixed populations from published data, since direct estimates of fertility, viability coefficients, and euploid-pollen production rates are unavailable.

Since 2017 the genetic architecture of dandelion apomixis has been largely worked out: genetic dissection showed diplospory and parthenogenesis segregating as unlinked dominant loci (van Dijk et al., 2020); the DIP gene was identified as a VPS13-like gene (a gene resembling vacuolar protein sorting-associated 13; disclosed in patent WO2017/039452 and reported in van Dijk et al., 2020, with molecular function still under investigation); and the parthenogenesis gene PAR was cloned as ToPAR, a C2H2 zinc-finger/EAR-domain protein (a transcriptional-regulator-type protein) able to induce egg-cell division without fertilization in sexual crops (Underwood et al., 2022). This supplies the realistic architecture against which Muralidhar and Haig's claim — that multiple loci slow the spread of apomixis but leave the equilibrium states unchanged — can now be tested; no one has yet tested it.

Problem Statement

Overarching objective: determine whether the Muralidhar–Haig mechanism — origin of triploid apomicts by occasional fertilization of the unreduced eggs of diploid partial apomicts, followed by irreversible conversion — robustly explains the origin, composition, and maintenance of apomictic Taraxacum officinale populations once the factors its own authors omitted are included and its simplifying assumptions are tested against subsequent findings, and whether its parameter values and central predictions hold in nature. This assessment involves the following lines of inquiry for the sexual–apomictic T. officinale system:

(1) the quantitative consequences of the rare viable euploid pollen that triploid apomicts are documented to produce: how much back-transmission of apomixis into diploid sexual populations it causes, and how it changes the equilibrium composition among sexual diploids, diploid partial apomicts, and triploid apomicts — in particular whether triploid fixation and the ephemerality of diploid apomicts survive; (2) the evolutionary role of fertilizations involving triploid eggs or pollen that generate tetraploids and higher ploidies — whether tetraploid intermediates materially alter the dynamics and equilibrium or constitute a side channel; (3) how the outcome changes when viability selection is not fixed: fitness differences among clonal multilocus genotypes (broad-sense heritability of fitness, with apomict mean fitness rising as elite non-recombining genotypes accumulate) and the accumulation and selective exposure of deleterious recessive mutations in haploid versus diploid pollen; (4) how spread rates and equilibrium states change under the now-mapped genetic architecture — at least two unlinked dominant loci (DIP controlling diplospory and PAR controlling parthenogenesis) plus the autonomous-endosperm factor dissected by van Dijk et al. (2020) — rather than the single dominant locus of the model, including whether the equilibrium invariance the authors claimed for a multi-locus genetic basis holds, and whether segregation of the components alters the predicted ephemerality of diploid partial apomicts; (5) the effect of making the fertilization rate uu of unreduced eggs frequency-dependent (declining as haploid-pollen-producing diploids become scarce) on transient and equilibrium dynamics; (6) the empirical footing of the model: bounds on the frequency of the predicted ephemeral diploid apomicts and on the rates of euploid pollen production that can be obtained from published surveys and crossing data, together with a targeted survey design capable of detecting the predicted ephemeral diploid apomicts; direct field estimates of fertility and viability coefficients are unavailable and are therefore out of scope.

These lines of inquiry are scientifically linked: each evaluates the robustness of the same mechanism in the model dandelion system, whose central prediction is the rapid, irreversible conversion of diploid partial apomicts into triploid apomicts with fixation of triploids. Their joint outcome is whether triploid fixation and the ephemerality of diploid partial apomicts survive. The empirical line (6) is to be answered from published data rather than new field measurement, which is out of scope.

References

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