Share This Paper. Figures, Tables, and Topics from this paper. Figures and Tables. Citations Publications citing this paper. A branching process for the early spread of a transposable element in a diploid population John M. Macias , Alyssa J. Confinement of gene drive systems to local populations: a comparative analysis. John M. Marshall , Bruce A. References Publications referenced by this paper. Population genetics of autocidal control and strain replacement.
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D Fraction of homo- ho and heterozygous he cluster insertions at different generations g. E The three phases of TE invasions for different transposition rates u. Fifty replicates are shown. F Number of cluster insertions for the three phases of TE invasions. G Fraction of individuals without cluster insertions i. H Stability of phases measured in standard deviation sd. The shotgun phase sh. Interestingly, we observed that at the onset of the shotgun phase each individual had on the average acquired 3. This result can be explained by the fact that cluster insertions are segregating.
Assume a scenario where a single cluster insertion has a population frequency of 0. The TE will thus be active in the 6. Our data suggest that on the average 3. We noticed that in some replicates TE copy numbers increased abruptly during the shotgun phase fig.
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To quantify the stability of the phases, we computed the standard deviation of the TE abundance population mean during each phase for every replicate separately fig. Our results thus suggest that silencing of TE invasion by segregating cluster insertions is unstable. Solely, fixation of a cluster insertions results in permanent inactivation of the TE and thus in stable TE copy numbers. Next, we asked which factors influence the dynamics of TE invasion under the trap model.
We evaluated the impact of the transposition rate u , the genome size, the size of the piRNA clusters in percent of the genome size , the population size N , and the excision rate v. We assessed the impact of these factors on the following key properties of invasions: the length of the phase, the TE abundance at the beginning of the phase, the abundance of cluster insertions at the beginning of the phase, and the stability of the phase quantified as standard deviation of the TE abundance per phase and replicate.
We found that the transposition rate had a strong influence on the length of the rapid invasion phase but little influence on other properties, including the abundance of TE insertions fig. As expected, the genome size had very little influence on the invasion dynamics fig.
The reason why it had any influence at all may be that we ignored insertions into already occupied sites. Such double insertions are more likely to occur in smaller genomes where fewer TEs will accumulate as a consequence. The size of the piRNA clusters had an enormous influence on the number of TEs accumulating during an invasion, where most TEs were found for small clusters fig.
For small clusters, many more insertions will be necessary until one copy randomly jumps into a piRNA cluster. Interestingly, the population size influenced the length of the shotgun phase, where larger populations have longer shotgun phases fig. Genetic drift is weak in large populations. Hence, fixation of cluster insertions, which marks the end of the shotgun phase, will require more time.
Due to this longer duration of the unstable shotgun phase, more TEs will accumulate in large populations fig. The excision rate only had a small influence on invasion dynamics fig. With our model, excisions from piRNA clusters are not feasible as we assume that TEs are inactive transpositions as well as excisions in individuals with a cluster insertion. Also, the recombination rate only had a weak influence on invasion dynamics supplementary fig. Surprisingly, we found that irrespective of the simulated scenario always about four to six cluster insertions per diploid where necessary to stop the invasions fig.
Influence of different factors on TE invasions. We studied the influence of the transposition rate A , the genome size B , the size of piRNA clusters, in percent of the genome C , the population size D , and the excision rate E. We show the impact of the different factors on the length of the phase in generations , the TE abundance per diploid individual at the start of the phase, the number of cluster insertions per diploid individual at the start of the phase and the stability of phase measured in standard deviation of the TE abundance sd.
The somatic pathway mostly relies on a single cluster, that is flamenco , which is located in low recombining regions of the X-chromosome. We hypothesized that this difference in architecture may have an impact on invasion dynamics. A single cluster in nonrecombining regions resembles the somatic architecture flamenco-model and multiple clusters distributed over five chromosomes resembles the germline architecture germline-model; fig.
For each architecture, we simulated replicates. We found a pronounced difference of TE invasion dynamics between the flamenco- and germline-model fig.
Although the length of the rapid invasion phase is significantly longer in the germline-model, the length of the shotgun phase is significantly longer in the flamenco-model fig. Notably, the number of TE insertions accumulating during an invasion is much lower in the flamenco-model than in the germline-model fig. Also, the number of cluster insertions necessary to stop an invasion is significantly lower with the flamenco-model fig.
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This result raises the question what causes these pronounced differences between the flamenco- and the germline-model. We suggest that recombination, due to the random assortment of cluster insertions located on different chromosomes, is responsible. Recombination among cluster sites will generate individuals with multiple redundant cluster insertions but also individuals with few or no cluster insertions.
The TE will be active in these individuals devoid of cluster insertions. Recombination thus leads to an inefficient silencing where on the average about four cluster insertions per diploid are necessary to furnish the majority of individuals with at least one cluster insertion. This hypothesis is in agreement with our results. Under the germline-model, individuals carry various numbers of cluster insertions, whereas in the flamenco-model the vast majority carries exactly two fig.
The few individuals with three four cluster insertions in the flamenco-model are likely due to multiple simultaneous insertions into the cluster at the same generation. We found that the invasion dynamics of the flamenco-model with recombination are similar to the germline-model fig. We asked whether the absence of recombination in germline clusters has an influence on the invasion dynamics.
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