Estimation of the SNP Mutation Rate in Two Vegetatively Propagating Species of Duckweed

Discussion

Using whole genome sequencing on 46 MA lines, we report a low per base pair, per generation SNP mutation rate in two species of duckweeds under two growth conditions. An important result in our study is that de novo mutations appear to have considerably reference biased genomic coverage in both duckweed species. We believe that this pattern is not indicative of sequencing or genome assembly errors but rather is a by-product of vegetative reproduction for several reasons. First, upon our inspection of the data in an independent study of mutation rates in S. polyrhiza by Xu et al.; we noticed similar levels of reference bias in Illumina short-read sequencing data at validated de novo mutations. Second, our own validation with Sanger sequencing showed that mutations with a higher reference bias in the Illumina dataset tended to have higher reference base peaks in their Sanger sequencing chromatograms and vice versa. Moreover, after filtering, most ancestral heterozygous sites that were shared by all lines in the three clonal genotypes were not reference biased in such a manner and those that were, were found in regions highly enriched for non-reference base calls. None of our putative de novo mutations are found in such regions; due to the low genetic diversity in duckweed, de novo mutations were generally the only heterozygous variants present in the immediate genomic area. This means that mapping bias due to divergence from the reference is unlikely to cause the strong allelic coverage bias we observed. Finally, a study of mutations in a vegetatively growing fairy-ring mushroom also reported patterns of reference bias with an average allelic coverage of 44% across 111 de novo mutations (Hiltunen et al. 2019). Therefore, the reference bias in our mutations is most likely a signature of the segregation of multiple cell lines from generation to generation in our duckweed MA experiment. Given that vegetative reproduction through clonal budding is the main form of reproduction in duckweed (Landolt 1986), it seems reasonable that duckweed might not undergo a single cell phase for prolonged periods of time.

Simple models can be helpful in clarifying how multi-cell descent during vegetative reproduction may affect mutation rates and our estimation of them. Assume that clonal reproduction occurs by n parental cells forming a diploid offspring (generation 1). If a mutation occurs in one of these n cells, because of multi-cell descent, the offspring will be a genetic mosaic (i.e., not all cells will be genetically identical). The mutation begins at a frequency of 1/2n in the offspring. With conventional single-cell descent, where n = 1, a new mutation is expected to be at 50% frequency, but the frequency will be lower than 50% whenever n > 1. The n cells multiply in some (unknown) growth pattern to produce the mature offspring, which then itself reproduces. In the absence of detailed knowledge of developmental growth trajectories, we do not know what the representation of the original n cell lineages will be in the subsequent generation.

We can consider two simple scenarios: If only one of these original cell lineages gives rise to the next set of n cells used to produce the next generation (generation 2), then the mutation will either be completely lost from the lineage (if it was not in the chosen cell lineage) or it will be present in heterozygous state in all cells of future generations (if it was present in the chosen cell lineage). In this first scenario, the genetic mosaicism resulting from multi-cell descent persists only a single generation. Thus, in an experiment such as ours, only mutations occurring in the very last generation will be affected by this issue (i.e., multi-cell descent is a trivial issue in this case). A second scenario is that all cell lineages grow at equal rates and, each generation, n cells are chosen at random to form the next daughter. This is conceptually similar to the process of coalescence in a population (of cells here rather than individuals) of size n. Thinking backward in time, all cells must eventually trace their coalescent history to a single cellular ancestor, but it may take many generations for this to happen (i.e., 2n generations, on average, but with variance proportional to n²). Thinking forward in time, a mutation occurring in one of the n cells forming the generation 1 offspring may be present for many future generations, possibly becoming quite common within individuals, before eventually being present in all future cells (with chance 1/n) or none of them (with chance (n - 1)/n). With even modest values of n (e.g., 8 < n < 80), genetic mosaicism can persist for many generations. Mutations that will eventually be present in all lineages—as well as those that will eventually be eliminated—will thus be found below the 50% frequency expected in a “traditional” (i.e., non-mosaic) heterozygote. Although this second scenario as formulated here is unrealistically simple (e.g., random and independent choice of n cells for each generation), it illustrates how multi-cell descent can have consequences across multiple generations. Though developmental growth trajectories in duckweed are insufficient to formulate a more realistic model, we suspect that multiple cell lineages persist across multiple generations in duckweed and is responsible for the clear bias toward mutant SNPs being less than 50%. Recent work on segregating mutations in a single Zostera marina seagrass clone has made similar arguments to this model (Yu et al. 2020). In their study, Yu et al. uncovered a large class of reference biased SNPs that were present in some but not all sampled Z. marina ramets. By reconstructing the genealogical relationship of the sampled ramets, the authors demonstrated that such SNPs changed in frequency during vegetative growth, with some reaching heterozygous fixation in specific ramets. The authors argued that this data were well explained by a model of “somatic drift” whereby de novo mutations arise at low frequency within a single cell lineage before ultimately either reaching fixation or being lost.

Calculating mutation rates in organisms with multiple segregating cell lineages poses a technical challenge due to the difficulty of assessing power when mutations are present in only a subset of the cells of an individual. We implemented a method that takes into account the fraction of reads we expect to support a de novo mutation by using observed mapping patterns of putatively de novo mutations, similar to the approach used by Hiltunen et al. (2019). This method considers the fact that we have reduced power to detect recently arisen mutations that are at low frequency within their MA lines, giving a more accurate estimate of the SNP mutation rate. This approach is an admittedly crude attempt to address the problem. Rather than assuming the expected frequency of the mutant allele is 50%, we simply choose a lower value based on the observed coverage at putative de novo mutations. In reality, this lower value is unknown and will differ among mutations depending upon when each mutation arose, i.e., there is an unknown distribution of mutation frequencies at the end of the MA experiment. Nonetheless, our approach is an improvement over completely ignoring the issue. Moreover, the variation in mutation rate estimates inferred using different values for the assumed expected mutant frequency provides some sense of the sensitivity of these estimates to this assumption. However, the issue of the unknown distribution of mutation frequencies adds a caveat to the between-species comparison. Because of the moderate difference in coverage between species, which affects the power to detect mutations segregating at different true frequencies, the estimates for the two species may be somewhat differentially affected by any bias introduced by our method.

A natural consequence of the lack of a single cell phase is that from a population genetics perspective, the mutation rate becomes a harder parameter to interpret. On one hand, we may be interested in calculating the mutation rate that captures every new mutation that has arisen in a clonal bud. Alternatively, from an evolutionary perspective, we might be only be interested in mutations that will not only arise in a clonal bud but also persist in a future clonal descendant such that they contribute to population level genetic diversity. Aside from random inter-cell lineage “drift”, cell lineage selection may bias which de novo mutations are eventually lost in a clonal lineage (Otto and Orive 1995), although this process likely has a minimal effect on mutation rate estimates in most mutation accumulation studies. In principle, we might be able to calculate an “evolutionarily relevant” mutation rate by performing long term mutation accumulation experiments allowing the majority of de novo mutations to either be lost or to have fixed within a clonal lineage such that all cells in any clone will be either fully homozygous (in the case of loss) or heterozygous (in the case of fixation). However, from a practical standpoint, it is hard to know a priori how many generations will be necessary for this process to occur. In practice, we could attempt to estimate the frequency of de novo mutations that have become sufficiently common such that they are likely to not be lost before fixation leading to an estimate of an evolutionarily relevant mutation rate. For example, we could assume that mutations found in at least 50% of cells (i.e., at a frequency of at least 25% in a clonal bud) are more likely than not to eventually fix in their clonal lineage, being found in 100% of cells in some future generation. In reality, some of these mutations are still likely to be lost before they have a chance to fix while simultaneously some mutations that are below 50% frequency might still reach fixation in the future. More generally, the lower the frequency cut-off we use for mutations that are “likely” to fix, the better the chance that we capture all of the mutations that will reach fixation with the caveat that we will also be capturing more mutations that will eventually be lost. In our study we opted to use a read number cut-off rather than a frequency cut-off as we were primarily concerned about differentiating true de novo mutations from false positives, a task that is particularly challenging in organisms with low mutation rates. In practice, our filtering criteria results in us mostly identifying mutations with an allelic frequency of at least 20% (61/71 de novo mutation reported in our study). As mentioned above however, some of these mutations may still be lost prior to fixation within an organism meaning that the mutation rate we report here is likely inflated compared to a true “evolutionarily relevant” rate. To some extent, this upward bias is counter-balanced by mutations that could eventually go to fixation but are at too low frequency at the time of sequencing to be either observed or even inferred by our power calculation that is based on some threshold frequency (10–50%; Tables S2-5).

Our estimate of the mutation rate in S. polyrhiza (8.39E-11 per bp per gen.) is similar to the estimates reported by Xu et al. (7.92E-11 per bp per gen.), however there are two important differences between our studies. First, our MA experiment was conducted only in the lab, while Xu et al. placed MA lines both in the lab and in the field, observing no mutations in the lab setting, likely due to the smaller number of MA generations in their study. Second, Xu et al. used ancestral heterozygous sites to estimate their power to detect de novo mutations which are not strongly reference biased in a similar manner. This suggests that the estimate from Xu et al., while conducted in a more naturally realistic environment, may be an underestimate of the mutation rate in the field.

The estimates of the per generation, per base pair mutation rate in S. polyrhiza and L. minor are among the lowest so far for multicellular eukaryotes (Figure 5, Supplemental Table 6). One potential explanation for why duckweeds have lower mutation rates than other plants is the smaller number of cell divisions they likely go through compared to their larger, long-lived relatives. Mutation rate studies in trees have indeed shown that while per generation tree mutation rates are high (on the order of 1E-08 mutations per bp), mutation rates per unit growth (a proxy for number of cell divisions), must be several orders of magnitude lower (Xie et al. 2016; Hanlon et al. 2019; Orr et al. 2020). However, duckweeds do appear to exhibit a low mutation rate compared to animals which have limited cell divisions between meiotic events due to a segregated germline. Moreover, our per generation duckweed mutation rate estimates fall on the lower end of values seen in green algae and other unicellular eukaryotes, organisms which unlike duckweed only go through a single cell division per generation (Figure 5). Overall, these patterns fit with previous work that has suggested that number of cell divisions per generation alone is not enough to fully explain variation in mutation rates (Lynch 2010).

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Figure 5

Comparison of per base pair, per generation mutation rates between duckweed and other eukaryotic species. Duckweed estimate highlighted by red box. References: (Ossowski et al. 2010; Lynch 2010; Denver et al. 2012; Schrider et al. 2013; Weller et al. 2014; Zhu et al. 2014; Venn et al. 2014; Keightley et al. 2015; Uchimura et al. 2015; Yang et al. 2015; Farlow et al. 2015; Ness et al. 2015; Smeds et al. 2016; Xie et al. 2016; Besenbacher et al. 2016 p.; Feng et al. 2017; Liu et al. 2017; Oppold and Pfenninger 2017; Flynn et al. 2017; Krasovec et al. 2017, 2018, 2019; Hanlon et al. 2019; Orr et al. 2020).

The low mutation rate observed in our study is consistent with efficient selection against mutator alleles in highly asexual organisms such as duckweed, bacteria and unicellular eukaryotes (Kimura 1967; Leigh 1970). This explanation would also predict that the mutation rate should be higher in L. minor than in S. polyrhiza as genomic analyses and field observations suggest that L. minor outcrosses more frequently than S. polyrhiza (Vasseur et al. 1993; Ho 2018; Xu et al. 2019; Ho et al. 2019). However, we did not observe a significant difference in mutation rate between species in our study. This could either be because we did not have the power to differentiate between such overall low mutation rates, because the difference in rates of sexual reproduction is not large enough between duckweed species, because a difference in rates of sex has arisen in recent history, or because factors other than reproductive mode play a larger role in shaping mutation rate evolution. The overall low mutation rate in both species is in contrast to the theoretical prediction that strong linkage in asexual genomes can allow mutators to fix in asexual populations if they hitchhike to fixation with beneficial mutations they produce (André and Godelle 2006). Population genomic analyses in duckweed have shown that selection on protein coding genes is weak as evidenced by elevated measures of π_N/π_S (Ho 2018; Xu et al. 2019; Ho et al. 2019)_. This suggests that strongly beneficial mutations might be too rare to allow mutators to be selected for in duckweed.

Xu et al. inferred a global N_e for S. polyrhiza of ∼1x10E-06 so it might also be possible that the large effective population sizes of these species allow selection to be efficient enough to lower the mutation rate more than in most multicellular eukaryotes (Sung et al. 2012; Lynch et al. 2016). This explanation, however, is also inconsistent with the fact that measures for the efficacy of selection suggest that selection is weak in duckweed, likely due to the predominance of asexual reproduction (Xu et al. 2019; Ho et al. 2019).

In conclusion, we report a very low SNP mutation rate in two species of duckweed consistent with previous results in this group. We found that de novo mutations appear at low frequencies within MA lines suggesting the presence of multiple segregating cell lineages. We then used an approach that allows us to estimate the mutation rate when multiple cell lineages are transmitted across generations. The low mutation rate of these duckweeds is consistent with the idea that a higher degree of asexual reproduction leads to strong selection for low mutation rates.