New Results

Purifying Selection Shapes the Dynamics of P-element Invasion in Drosophila Populations

Anna M. Langmüller, Benjamin C. Haller, Viola Nolte, Christian Schlötterer
doi: https://doi.org/10.1101/2024.12.17.628872

Abstract

Background Transposable elements (TEs) are DNA sequences that can move within a host genome. Many new TE insertions have deleterious ebects on their host and are therefore removed by purifying selection. The genomic distribution of TEs thus reflects a balance between new insertions and purifying selection. However, the inference of purifying selection against deleterious TE insertions from the patterns observed in natural populations is challenged by the confounding ebects of demographic events, such as population bottlenecks and migration.

Results We used Experimental Evolution to study the role of purifying selection during the invasion of the P-element, a highly invasive TE, in replicated Drosophila simulans populations under controlled laboratory conditions. Because the change in P-element copy number over time provides information about the transposition rate and the ebect of purifying selection, we repeatedly sequenced the experimental populations to study the P-element invasion dynamics. Based on these empirical data we used Gaussian Process surrogate models to infer parameter values characterizing the observed P-element invasion trajectory. We found that 73% of P-element copies are under purifying selection with a mean selection coebicient of -0.056, highlighting the central role of selection in shaping P-element invasion dynamics.

Conclusion This study underscores the power of Experimental Evolution as a tool for studying transposable element invasions, and highlights the pivotal role of purifying selection in regulating P-element dynamics.

Background

Transposable Elements (TEs) are DNA sequences that can move and amplify within a host genome [1]. The evolutionary fate of TEs depends not only on their ability to replicate within the genome of their host, but also on the harm their activity might cause to their host [2]. Despite the challenges posed by their potentially disruptive behavior, TEs are ubiquitous in the tree of life [3,4], thriving in countless species, and have fascinated evolutionary biologists since their discovery more than seven decades ago [5].

It is widely accepted that some TEs insertions are harmful for their hosts [2,3,6], but the fraction of new TE insertions that are deleterious, and the distribution of their fitness ebects, remain open questions [7,8]. Because measuring the ebect of individual TE insertions on host fitness is tedious and a large number of independent insertions must be studied to obtain representative patterns, most evidence for purifying selection operating against TEs relies on the low abundance of TE insertions in specific regions of the host genome [9–11]. One limitation of this approach is the assumption of a uniform insertion probability of TEs across the genome. However, TEs can exhibit strong insertion preferences for specific genomic regions [3,12,13], which makes it dibicult to distinguish between insertion bias and purifying selection.

An alternative method for detecting genomic signatures of purifying selection is based on the frequency spectrum of TEs within natural populations [14,15]. As with SNPs, demographic events such as population bottlenecks or admixture events pose a major challenge to the interpretation of TE frequency spectra [6,16]. Furthermore, recent TE activity can cause a shift in the site frequency spectrum that resembles the pattern expected from purifying selection, again making it dibicult to distinguish between insertion bias and purifying selection [14,15,17]. Finally, the low population frequencies of TE insertions — caused by recent TE activity [15] and purifying selection — present a significant obstacle because detecting a specific TE insertion and estimating its frequency reliably requires high sequencing coverage.

Experimental Evolution (EE) [18,19], a powerful approach to study evolution under controlled laboratory conditions, is becoming increasingly popular as an alternative method to study TE invasion dynamics [20–22]. By combining EE with whole-genome sequencing of pooled individuals, an approach called Evolve and Resequence [23–25], researchers can minimize confounding factors that complicate the interpretation of polymorphism patterns in natural populations. Moreover, EE enables the replication of the invasion process, allowing stochastic (random) ebects to be distinguished from deterministic patterns across multiple evolutionary replicates [18,19,24].

The P-element [26,27] — one of the best-studied TEs in eukaryotes [28] — is a DNA transposon with a remarkable invasion record [29–31]. Likely introduced into Drosophila simulans from D. melanogaster in a single horizontal transfer event [32], the P-element spread through D. simulans populations worldwide in less than a decade [31]. Drosophila species curb P-element invasions through the piRNA pathway, a specialized defense mechanism involving small RNAs that target and silence TEs [33,34]. Most piRNAs originate from specific genomic regions known as piRNA clusters, which collectively comprise approximately 3.5% of the Drosophila genome [33]. Current studies suggest that the ebective silencing of P-elements across the genome relies on the presence of at least one P-element insertion within a piRNA cluster, which serves as a template for the production of P-element-specific piRNAs [35,36].

In this study, we used EE to investigate how purifying selection shapes the invasion dynamics of the P-element in experimental D. simulans populations. We followed the increase in P-element copy number in replicated EE studies across time. Using these time-resolved empirical invasion curves together with an individual-based simulation framework matching our experimental setup, we show that only 27% of the P-element copies can be considered as ebectively neutral, while the remaining 73% are subject to purifying selection with an average selection coebicient of -0.056. The genome-wide average selection coebicient for P-element copies outside piRNA clusters is -0.041, highlighting the importance of purifying selection in shaping P-element invasion dynamics.

Results

The P-element rapidly invades experimental populations

To explore the influence of purifying selection on TE invasion dynamics, we analyzed the P-element invasion in replicate D. simulans populations from two EE experiments conducted under identical environmental conditions (Figure 1). These experimental populations were established from about 200 isofemale lines derived from a natural D. simulans population (Tallahassee, Florida). During the collection of the isofemale lines this natural D. simulans population was at the onset of a P-element invasion [32], where 25–44% of these isofemale lines were estimated to be P-element carriers [31]. The 1st wave EE experiment was started shortly after the isofemale line collection, thus all evolutionary replicates had only a small number of P-element copies at generation 0. The 2nd wave experiment on the other hand was established about 4 years after the 1st wave experiment from the same isofemale lines. During this period those isofemale lines that already contained a P-element at the time of collection, acquired additional P-element copies [11]. As a consequence, the 2nd wave experiment started from a higher number of initial P-element copies. Because of the small ebective population size during the maintenance of the isofemale lines, many of the P-element insertions that occurred in the isofemale lines between the setup of the 1st and 2nd wave experiment were deleterious. Purifying selection could only operate once the flies were maintained in large, outbred populations [11]. To track P-element invasion dynamics, we sequenced the replicate populations using the Pool-Seq approach [37] in both EE experiments and estimated P-element copy numbers per haploid genome using DeviaTE [38].

Figure 1.
Figure 1.

Schematic overview of the experimental design. Isofemale lines were established from a natural population of Drosophila simulans, where the P-element has been invading [32]. Isofemale lines carrying an active P-element (indicated by red squares) are expected to accumulate P-element copies until an active defense mechanism is triggered [33,39]. In May 2011, three large replicate populations were established, using 202 isofemale lines. These populations, referred to as the “1st wave” Experimental Evolution (EE) experiment, are maintained with non-overlapping generations under a cycling hot temperature regime and were sequenced every 10th generation to monitor the P-element invasion dynamics [20]. In June 2015, a second EE experiment was initiated using three new replicate populations derived from 191 surviving isofemale lines [11]. These populations, referred to as the “2nd wave” EE experiment, were maintained under the same environmental conditions and were also sequenced over time to track the P-element invasion.

Our data confirmed that, the average initial P-element copy number in the 2nd wave experiment was significantly higher than in the 1st wave experiment (6.92 vs. 0.86, Figure 2). Despite distinct initial dynamics, both EE experiments reached a similar P-element copy number plateau: approximately 15 copies per haploid genome, after around 20 generations (Figure 2). This suggests that the timing and ultimate copy number plateau are consistent across both waves, indicating that these aspects of the P-element invasion are robust to initial conditions.

Figure 2.
Figure 2.

Estimated P-element copy number per haploid genome from the 1st (amber) and 2nd (dark navy blue) wave Experimental Evolution study. Sequenced time points are shown as circles.

Purifying selection shapes P-element invasion dynamics

We estimated similar P-element copy numbers per haploid genome in generations 0 and 10 in the 2nd wave experiment (means: 6.92 vs. 5.91, Figure 2). We previously hypothesized that this pattern arises from the balance between purifying selection, which removes deleterious P-element insertions, and transposition activity, which introduces new P-element copies [11]. Nevertheless, a comprehensive understanding of P-element invasion dynamics necessitates the availability of reliable estimates of the strength of selection operating on new P-element insertions. While genetic editing enables the inference of selection operating on specific TE insertions [40], it is evident that this approach is not feasible to describe the costs associated with insertions throughout the entire genome. Therefore, we used computer simulations to estimate the strength of purifying selection in our EE experiments.

Simulation Framework

To investigate the potential influence of purifying selection on P-element invasion dynamics in the 1st and 2nd wave experiments, we developed an individual-based model for transposon dynamics in SLiM [41]. A comprehensive description of the model can be found in the Materials & Methods section. Figure 3 provides a schematic overview of the individual-based model, and Table 1 gives an overview of all model parameters. In brief, the individual-based model is able to simulate P-element invasions in EE experiments reflecting the empirical setups of the 1st and 2nd wave, respectively. As a host defense mechanism, we implemented a classic “trap model” [35,36,39]: P-elements transpose with a defined probability unless silenced by an insertion in a piRNA cluster [33], which immediately inactivates all P-elements in the genome. Outside piRNA clusters, purifying selection acts on P-elements with a selection coebicient s drawn from a beta distribution and a dominance coebicient h of 0.5 (co-dominance). By modifying the parameters of the beta distribution, it is possible to create a gradual transition between simulation scenarios where the majority of P-elements are ebectively neutral and scenarios where the majority of P-elements are subject to strong purifying selection.

Figure 3.
Figure 3.

Schematic overview of the individual-based simulation model mimicking the P-element invasion dynamics in our Experimental Evolution experiments. (A) Simulation Setup: Ancestral outbred populations are generated by mixing about 200 isofemale lines (five flies each). Each line carries the P-element with probability pcarrier. We modeled diploid individuals with five chromosomes, each with a fixed length of 32.4 Mb and a recombination rate of 4×10⁻⁸ per bp per generation. For the 1st wave, P-element insertions are assumed to be heterozygous. For the 2nd wave, since the experiment started with isofemale lines that had been maintained at small populations sizes for 4.5 years [11], the model assumes that all P-element insertions are homozygous due to increased inbreeding and the likely establishment of a defense mechanism. The parameter fregulatory defines the fraction of each chromosome with P-element-regulatory properties (piRNA clusters; blue rectangles). (B) Trap Model: The P-element remains active (filled rectangle) unless one of its copies transposes into a piRNA cluster (blue rectangles). The probability of transposition for a single P-element per generation is controlled by the transposition rate u. Once a piRNA cluster acquires a single P-element insertion, all P-elements in the genome are immediately inactivated (unfilled rectangles with red borders). (C) Simulated Distribution of Fitness EBects (DFE): The DFE for P-elements is modeled using a beta distribution with parameters α and β. Positive selection is not considered in our model. (D) Simulated Data: The simulation output used in the analyses contains the average P- element copy number per haploid genome across 100 simulation runs, taken at the same time points used in the two Experimental Evolution studies.

View this table:
Table 1.

Model parameters of the individual-based P-element invasion model and their considered ranges. The range for pcarrier was guided by a previous study estimating that 25–44% of the isofemale lines used in the 1st and 2nd wave experiment carried the P-element [31], while the range for fregulatory was based on the estimate that approximately 3.5% of the Drosophila genome consists of piRNA clusters with TE-regulatory properties [33].

By comparing simulated invasion outcomes to empirical data and quantifying the fit, systematic exploration of this model’s parameter space (Table 1) would in principle allow us to determine the level of purifying selection that best fits the observed P-element copy number trajectories from the 1st and 2nd wave experiments. However, exhaustively probing our five-dimensional parameter space in this manner would be very computationally intensive [42], even using an optimized model. To address this challenge, we used Gaussian Process (GP) surrogate modeling [43]. A GP is a statistical model that serves as a surrogate for the individual-based model, allowing rapid prediction of the individual-based model’s behavior based on previously simulated data. The utility of the GP approach lies in its capacity to extrapolate from sparse data, thereby predicting the behavior of a system, such as our individual-based model, at untested parameter combinations. We trained two separate GPs — one for the 1st wave and one for the 2nd wave — using simulation outcomes from the individual-based model as described further in the Materials & Methods section. We then explored the accuracy of our trained GPs with a test dataset of 5,000 additional simulation outcomes spanning a broad range of parameter combinations, for both the 1st and 2nd wave experiments. For this test dataset, the GPs accurately predicted trajectories of P-element copy numbers across generations (Figure 4). Based on these results, we conclude that the GPs provide an ebicient and precise alternative to the individual-based model. This allowed us to use the GPs to find the model parameters that best replicate the experimental data, ultimately allowing us to estimate the level of purifying selection for which our individual-based model best fits the empirical time-series data.

Figure 4.
Figure 4.

Gaussian Process (GP) performance: A test dataset consisting of 5,000 data points was simulated with the individual-based model (x axis) for the (A) 1st wave and (B) 2nd wave and compared to the predictions of the GP (y axis). One data point in this test dataset comprises a specific combination of five model parameters (Table 1) and the corresponding predicted P-element copy numbers for six time points. The observed and predicted P-element copy numbers are shown (gray dots) for each of those six time points (the six panels), with amber lines indicating the identity line (x = y). Normalized root mean square errors (NRMSE) for the time points are shown at the bottom right of the corresponding panels. The analysis shows that the GP can predict the copy number observed in the individual-based model very accurately. Only at extremely high copy numbers — well beyond the empirical estimates (Figure 2) — can a slight underestimation be observed.

Purifying selection as a central mechanism: model fitting results

After validating the performance of the GPs with the simulated test dataset, we used the GPs to predict P-element invasion dynamics — the P-element copy number per haploid genome for six evolved time points corresponding to the sequenced time points of the empirical EE experiments — across 106 model parameter combinations. To ensure that later generations, which tend to have higher copy numbers (Figure 2), did not disproportionately influence the fit, we quantified the fit between the model predictions and the experimental data using the normalized root mean square error (NRMSE; please refer to the M&M section for further details), where a lower NRMSE value indicates a better agreement between the predicted and empirical P-element invasion curves.

By fitting GP predictions from 106 parameter combinations to the 1st wave invasion dynamics, we observed a wide range of NRMSE values, spanning from 0.60 to 39.28. The best fit, characterized by the lowest NRMSE, corresponded to a parameter combination with notable purifying selection outside piRNA clusters (s̄ = −0.045, Figure 5). Although the initial invasion dynamics of the 1st and 2nd wave EE experiments diber considerably, we reasoned that the genome-wide distribution of fitness ebects for P-elements should be constant between the two experiments. Thus, we used the parameters estimated from the 1st wave experiment to predict the invasion trajectory of the 2nd wave experiment. Interestingly, this resulted in a remarkably accurate prediction of the invasion dynamics of the 2nd wave experiment, which has been conducted four years later with an 8-fold higher initial P-element copy number (Figure 5). This result highlights the robustness and predictive power of our parameter estimates even for rather distinct invasion trajectories in the first generations.

Figure 5.
Figure 5.

Gaussian Process (GP) predictions provide a good fit to the empirical data — model parameters estimated only from 1st wave data: (A) 1st wave experiment (B) 2nd wave experiment. Each grey line represents an empirical evolution replicate, with sequenced time points indicated by dots. GP predictions are indicated by amber diamonds. (C) The simulated distribution of fitness eaects (DFE) used for generating predictions in panels (A) and (B). The parameter combination used for the GP prediction is: pcarrier = 0.189, fregulatory = 0.014, u = 0.278, α = 0.484, β = 10.327. Predictions based on parameters inferred from the 1st wave accurately describe the P-element invasion dynamics in the 2nd wave.

After confirming that the parameters inferred from the 1st wave also explain the 2nd wave data, we proceeded to jointly infer parameters using data from both experiments. We reasoned that this could further improve parameter estimates because the estimates will be based on twice the amount of data. The overall fit metric was calculated as the sum of the NRMSEs for the 1st and 2nd wave experiments (NRMSE sum). We observed a considerable degree of variation in the NRMSE sums across the evaluated parameter combinations, with values ranging from 1.340 to 80.365 (Figure S1A). As anticipated, the NRMSE values were strongly correlated between the 1st and the 2nd wave experiment (Spearman’s ρ = 0.87, Figure S1B), consistent with similar evolutionary dynamics driving the P-element invasion in both EE experiments.

In the best-fitting scenario (Table 2), approximately 20% of the isofemale lines were predicted to carry the P-element, which is slightly below the empirical estimate of 25– 44% [31]. Additionally, the estimated piRNA cluster size (fraction of each chromosome with the P-element-regulatory properties) under this scenario is 1.7%, which is approximately half the size as suggested previously [33]. The results of the parameter tuning indicated that a significant amount of purifying selection against single P-element insertions is necessary to account for the observed invasion dynamics. The best-fitting parameter combination, as indicated by the lowest NRMSE sum, Table 2) was obtained for 𝛼 = 0.461 and 𝛽 = 10.743, which yielded to an average genome-wide selection coebicient s of -0.041 for P-element insertions outside the piRNA clusters. This indicates that selection is ebective against P-element insertions in experimental Drosophila populations, which have typically ebective population sizes Ne < 300 [44,45]. Based on the average Ne estimate from the 1st wave experiment [45] and the aforementioned best-fitting parameter combination, our results indicate that only 27% of P-elements are ebectively neutral (i.e., 𝑁e|𝑠| ≤ 1, Table 2) in our experimental populations. Additionally, our findings suggest that strong selection can occur, with the 95th percentile of the selection coebicient (|𝑠|) reaching 0.16 (Table 2).

View this table:
Table 2.

Summary statistics describing the 1 (“best fit”) versus 100 (“top 100”) parameter combination(s) with the lowest NRMSE sum (NRMSE sum = NRMSE 1st wave + NRMSE 2nd wave) from the parameter exploration with the Gaussian Process model, grouped by average expected selection eaicacy (Ne = 221 [45]). Values in square brackets represent the range between the 2.5th and 97.5th percentiles of individual metrics. |s̄| = mean selection coeaicient outside piRNA clusters (Ε(|𝑠|) = 𝛼/(𝛼 + 𝛽)); 95th percentile |𝑠| = 95th percentile of |𝑠| outside piRNA clusters; Neutral fraction = expected fraction of eaectively neutral (|𝑠| ≤ 1/𝑁e) P-element insertions outside of piRNA clusters; |s̄effective| = mean selection coeaicient for P- element insertions outside piRNA clusters where selection is strong enough to overcome genetic drift (|𝑠| > 1/𝑁e); NRMSE = Normalized root mean square error; Results are robust to changes in the eaective population size estimate (Table S1).

We also used the mean Ne estimate from the 1st wave experiment [45] to categorize parameter combinations into two distinct scenarios: those exhibiting ebicient purifying selection against the average P-element insertion, and ebectively neural ones. In the latter case, genetic drift is so strong that the invasion trajectory of an average P-element insertion is indistinguishable from a neutral one, even if the insertion is slightly deleterious. Simulation scenarios classified as ebectively neutral had the best fit to the data when they included larger piRNA clusters and higher P-element activity (Table 2).

Nevertheless, simulations incorporating ebicient purifying selection yielded a better agreement with empirical invasion dynamics. These scenarios accurately reproduced both the rapid increase in P-element copy number that occurred during the 1st wave and the transient plateau that was observed between generations 0 and 10 in the 2nd wave. In contrast, neutral scenarios consistently failed to replicate these patterns (Figure 6). This conclusion holds even when potential biases were considered, such as focusing solely on the parameter combination with the lowest NRMSE sum. The qualitative pattern remains consistent when using average parameter values from the 100 combinations with the lowest NRMSE sums (Figure S2). Moreover, our results remain consistent when the Ne estimate was modified, as this parameter serves as a threshold for neutrality in our approach. Doubling the Ne estimate from 221 to 442 did not result in any qualitative alterations to the outcomes, thereby reinforcing the conclusion that purifying selection plays a pivotal role in shaping the observed P-element invasion dynamics (Table S1).

Figure 6.
Figure 6.

Gaussian Process (GP) predictions provide a good fit to the empirical data — parameters estimated jointly from 1st and 2nd wave data. GP predictions from the parameter combinations with the lowest NRMSE sum when compared against empirical data are shown for scenarios without expected eaective purifying selection (𝛦(|𝑠|/2) ≤ 1/(2𝑁e), steel blue) and scenarios with expected eaective purifying selection (𝛦(|𝑠|/2) > 1/(2𝑁e), orange), Ne = 221 [45]. Each grey line represents an empirical evolution replicate, with sequenced time points indicated by dots. GP predictions are marked by diamonds, while the dashed colored lines represent the average P-element copy number per haploid genome across 100 simulation runs with the individual-based model. The colored ribbons show the range between the 2.5th and 97.5th percentiles of P-element copy number trajectories simulated with the individual-based model. (A) 1st wave experiment. (B) 2nd wave experiment. (C) Simulated distribution of fitness eaects (DFE) used in (A) and (B). Results are robust to averaging parameter values across 100 combinations with the lowest NRMSE sums (Figure S2).

Discussion

The power of Experimental Evolution to study TE dynamics

To evaluate the role of purifying selection in controlling TEs, we investigated the dynamics of P-element invasions in two Drosophila EE experiments. Because low-frequency TE insertions, a hallmark of the early stages of an invasion process, are very dibicult to study empirically, we used the P-element copy number as a summary statistic to describe the invasion dynamics. Through careful model analysis, we estimated the distribution of fitness ebects of P-element insertions in these experiments.

While beneficial fitness ebects have been documented for some TE insertions (e.g., [46–50]), we reasoned that such cases are rare, and thus unlikely to substantially impact the population-level dynamics of a P-element invasion. Furthermore, a previous analysis of the 1st wave experiment found no evidence for positive selection acting on any P-element insertion site in 10 replicate populations over 60 generations [44]. We thus focused our analysis on deleterious ebects of P-element insertions. We fitted an individual-based simulation model to data from the two EE studies to infer the distribution of deleterious fitness ebects, first from the 1st wave alone, and then from both the 1st and 2nd waves combined. Both approaches yielded similar estimates. Remarkably, parameters inferred only from the 1st wave accurately predicted the invasion dynamics observed in the 2nd wave experiment, conducted four years later under diberent initial conditions. Overall, we observed that substantial purifying selection outside of piRNA clusters (s̄ = −0.041, Table 2) was necessary to accurately capture the observed P-element invasion patterns in both experiments. TE invasions are challenging to analyze in natural populations due to their rapid dynamics and confounding demographic factors such as gene flow. Excitingly, this study not only demonstrates that purifying selection is a key evolutionary force shaping P-element invasions, but also highlights the utility of EE, in combination with simulation and modeling-based approaches, for studying TE invasions in the lab.

Alternative Mechanisms of TE Regulation

A key feature of our study is the individual-based modeling framework used to simulate P-element invasion dynamics in experimental Drosophila populations. As with any model, it is based on a number of simplifying assumptions that inevitably omit some aspects of biological realism, and these assumptions might influence the model outcomes. For example, our individual-based simulations are based on the classic trap model, which posits that a single TE insertion in a piRNA cluster silences all TEs of that type. Given that the distribution of TEs in piRNA clusters dibers from predictions under the trap model [51,52] and that the removal of piRNA clusters does not necessarily induce TE activity [53], alternative mechanisms of TE silencing must be considered.

One potential mechanism could be paramutations, whereby insertions outside of piRNA clusters can be converted into piRNA-producing loci in the presence of maternally deposited piRNAs [54–56]. In a recent study, Scarpa et al. (2023) demonstrated with comprehensive computer simulations that this additional layer of defense against TEs can help to resolve some of the discrepancies between observed and predicted TE copy numbers under the classic trap model in natural Drosophila populations [54]. Since this study focused on the overall abundance of TE families in D. melanogaster, it remains unclear to what extent paramutations are shaping TE invasion processes in natural and experimental populations over time. Given the excellent fit between the simulations under the trap model and our empirical data, it is possible that paramutations are not essential to explain the observed P-element dynamics in our two EE experiments. Even more importantly, the transient P-element copy number plateau observed between generations 0 and 10 in the 2nd wave experiment, along with the subsequent increase in copy number in later generations, is more readily explained by purifying selection rather than by paramutations. Further work is required to evaluate the extent to which paramutations influence the invasion dynamics of the P-element and other TEs.

Most TE insertions are deleterious

The ebective population size is a key factor in determining whether a mutation is “seen” by selection or behaves ebectively neutrally [57]. In EE experiments with Drosophila, such as those presented in this work, estimates of ebective population size typically range from 200 to 400 [44,45]. At this ebective population size, purifying selection can only act on mutations with strongly deleterious ebects. In natural Drosophila populations, the ebective population size is several orders of magnitude larger [58,59]. This implies that in natural Drosophila populations, only a small fraction of P-elements is likely to be ebectively neutral — much fewer than the 27% estimated from our empirical data. This idea aligns well with the observation that only a small fraction of the genome shares P-element insertions between D. melanogaster and D. simulans [32]. While this is typically attributed to non-random insertions of actively transposing P-elements [12], we propose that purifying selection in large natural populations might drive independent enrichment of P-element insertions at genomic regions subject to relaxed purifying selection.

Conclusions

Our study highlights the crucial role of purifying selection in shaping TE invasion dynamics, specifically in the context of P-element invasions in D. simulans. Using an individual-based model, we demonstrated that substantial purifying selection is needed to replicate the observed invasion dynamics in two EE studies. This study not only highlights EE as a valuable tool for understanding TE behavior, but also illustrates how computational modeling can complement experimental work to study TE invasions. Future work could expand this modeling framework to include additional regulatory mechanisms such as paramutations, advancing our understanding of TE behavior in diverse environments.

Methods

Experimental Evolution

The details of the 1st wave EE experiment have been previously published [20,45]. Additionally, Pool-Seq data for generations 0 and 10 of the 2nd wave EE experiment are available in Langmüller et al. (2023) [11]. This study adds generation 15–60 of the 2nd wave experiment. This section only provides an overview of the experiments and specific information regarding already published data can be found in those sources. To maintain consistency and facilitate comparison between studies, we used the same replicate identifiers as in the original publications.

Setup & Maintenance of Experimental D. simulans Populations

For the 1st wave [20], replicate populations were established from 202 isofemale lines collected from a natural D. simulans population in Tallahassee, Florida [60], which experienced a P-element invasion at the time point of sampling [32]. For the 2nd wave experiment, three replicate populations were established using the surviving 191 out of 202 isofemale lines that were originally collected [11]. All replicate populations were maintained with non-overlapping generations in a cycling hot environment (12 hours of light at 28°C; 12 hours of darkness at 18°C) and at a constant population size (N = 1,000 for the 1st wave; N = 1,250 for the 2nd wave) for 60 generations.

Genomic Sequencing

All experimental populations were sequenced using the Pool-Seq approach [37] with at least 500 flies per sample. In the 1st wave, populations were sequenced every 10th generation, resulting in 21 samples (7 time points; 3 replicate populations) [20,45]. To more ebectively monitor the rapid invasion of the P-element, we increased the number of sequenced time points at the beginning of the 2nd wave experiment. For this wave, populations were sequenced at generation 0, as well as at generations 10, 15, 20, 25, 30, and 60, also resulting in 21 samples. Genomic DNA for all new samples was extracted from half the number of individuals that had contributed to the next generation (approximately 600 flies). To facilitate comparison across studies, we adopt the Fxx nomenclature for sequencing samples, where ’xx’ represents the generation in our EE experiment. Paired-end libraries for generation F60 were prepared and sequenced along with those for generation F0 using the NEBNext Ultra II DNA Library Prep Kit (New England Biolabs, Ipswich, MA) with an insert size of 300bp. Paired-end libraries for generations F15, F20, F25, and F30 were processed in the same way as those for generation F10, using a protocol with 10% of the reagents provided in the NEBNext Ultra II FS DNA Library Prep Kit (New England Biolabs, Ipswich, MA). Steps for all library preparations are described in more detail in [11]. We sequenced all libraries using a 2 × 150 bp protocol on a HiSeq X Ten.

P-element Copy Number as a Summary Statistic for Invasion Dynamics

Given the rapid spread of the P-element in our experimental populations, most individual P-element insertions are expected to remain at low frequency. This poses a major challenge for accurately estimating empirical P-element insertion frequenies, irrespective of whether pools of individuals or single individuals are being analyzed. Therefore, we used the estimated P-element copy number per haploid genome as a summary statistic for describing the P-element invasion in the experimental populations. We used DeviaTE [38] to estimate P-element copy number per haploid genome in both EE experiments. DeviaTE calculates P-element copy number by comparing the number of reads mapped to the P-element consensus sequence with the number of reads mapped to single copy genes [38,61]. For the 1st wave, P-element copy number estimates were previously published in Kofler et al. 2022 and can be found in the supplemental data (replicates 1, 3, and 5 from the hot environment) [45].

For 2nd the wave, we used ReadTools (v1.5.2.) [62] to demultiplex (–maximumMismatches 3 –maximumN 2) and trim barcoded sequencing files based on sequencing quality (– mottQualityThreshold 15 –disable5pTrim –minReadLength 25). Since DeviaTE does not take paired-end read information into account [38], we merged paired-end read files prior mapping. We mapped reads to a reference genome that included the Drosophila P-element consensus sequence [63] along with three single copy genes (rpl32, traDic jam, rhino), using bwa bwasw (v0.7.17; –M) [64]. Finally, we estimated P-element copy number per haploid genome with DeviaTE (–minID 1) [38].

Our genomic analysis pipeline follows Kofler et al. 2022 with some minor diberences (e.g., we used a more recent version of bwasw) [45]. To verify the consistency between pipelines, we re-analyzed three randomly selected samples from Kofler et al. (2022) using our updated pipeline. The copy number estimates from the two pipelines dibered by less than 5 %, which we considered an acceptable level of consistency (data not shown).

P-element Invasion Models

Individual-based Models

We implemented an individual-based P-element invasion model in SLiM (v4.0.1) [41]. Our individual-based model simulates an obligatory outcrossing population with discrete, non-overlapping generations and a constant census size of 1,000 individuals (flies). Each fly has a diploid genome consisting of five chromosomes, each with a length of 32.4 Mb and a recombination rate of 4×10-8 per bp per generation, mimicking Drosophila simulans [65,66]. At the end of each chromosome, we modeled a piRNA cluster region capable of regulating P-element activity [33,39]. The size of simulated piRNA clusters is regulated by the model parameter fregulatory. The only genomic variants included in the individual-based model are P-element insertion sites (Figure 3A).

The ancestral population (generation 0) is initialized by mixing 200 inbred fly strains (isofemale lines), using five flies per line. Single lines might be P-element carriers, with a user-specified probability pcarrier (Table 1). If a line carries the P-element, the number of initial P-element insertion sites is drawn from a Poisson distribution, where the rate parameter λ is chosen such that, given the value of pcarrier, the average P-element copy number per haploid genome for the simulated EE experiment fits the empirical data (1st wave: 0.86 P-element copies per haploid genome; 2nd wave: 6.92). All flies from the same isofemale line are isogenic, meaning they share the same set of P-element insertion sites. We note that this assumption likely oversimplifies the genetic structure of isofemale lines. Any residual within-line heterogeneity could introduce additional variance in P-element dynamics across simulation runs. However, we averaged individual-based model results across 100 simulation runs for each parameter combination, which would mitigate the ebect of this additional variance, such that our conclusions about the overall invasion dynamics remain robust despite this simplification. For the 1st wave, we modeled heterozygous initial P-element insertions, because the P-element invasion was recent [32]. For the 2nd wave, we modeled homozygous initial P-element insertions, given that the isofemale lines had been maintained at small population sizes for 4.5 years [11], causing increased inbreeding and a likely establishment of defense mechanisms against further P-element proliferation.

To account for a host defense mechanism against the P-element, we incorporated the trap model into our individual-based model [35,36]. Under the trap model, P-element activity is regulated by insertions into piRNA clusters [33]. In our individual-based model, single P-elements transpose with probability u per generation, unless a fly carries at least one P-element insertion in a piRNA cluster. We assumed that P-element proliferation operates exclusively via a copy-and-paste mechanism, with no excision events. This simplification is based on evidence from previous studies that P-elements can increase their copy number through mechanisms such as sister chromatid-mediated gap repair following excision [67] and transposition into unreplicated DNA during cell division, which facilitates copy number increase without significant loss of existing elements [12]. If a single P-element insertion occurs in any piRNA cluster, all P-elements within the genome are rendered inactive immediately and are unable to transpose further (Figure 3B).

We assumed that P-element insertions within piRNA clusters are neutral (selection coebicient s = 0). For all other P-element insertions, the absolute value of s is drawn from a beta distribution with shape parameters α and β (Figure 3C). We considered only purifying selection against P-elements (s <= 0), because no signature of adaptive selection was detected in 10 replicate populations in the 1st wave experiment [44]. We modeled co-dominant fitness ebects (h = 0.5), such that individuals with no P-element insertions at a single locus have a fitness of 1, heterozygous individuals have a fitness of 1 + s/2, and individuals homozygous for the P-element insertion have a fitness of 1 + s, where s is always <= 0. With more than one P-element insertion site, the fitness ebects from each site are combined with the others multiplicatively.

We systematically varied five parameters: the probability that a single line carries the P- element, the fraction of the chromosome capable of triggering a defense against the P- element (piRNA cluster size), the transposition probability, and two parameters governing the distribution of fitness ebects (Table 1). For each parameter combination, simulations were repeated 100 times, and the average P-element copy number per haploid genome was recorded at the same time points used in the empirical EE experiments (Figure 3D). This approach allowed us to directly compare simulation outcomes with observed P- element copy numbers.

Gaussian Process Surrogate Models

Because our individual-based model has five parameters that can be varied (Table 1), exploring the full range of this parameter space with the individual-based model would be a complex and time-intensive task [42]. To streamline this process, we employed statistical emulation, replacing the individual-based model with a surrogate model that can rapidly and accurately predict the individual-based model’s behavior [68]. GP surrogate models [43,69] are particularly well-suited for this task because they are non-parametric models that define distributions over functions. This characteristic allows them to ebiciently extrapolate between sparsely sampled data points. For a detailed introduction to GPs, we defer to Rasmussen and Williams [43].

We implemented our GPs in Python (v3.10.6) using the GpyTorch (v1.11) [70] and PyTorch (v2.0.1) [71] libraries for ebicient GP modeling. We developed two GPs, one for each of the EE experiments (1st and 2nd wave). Specifically, we used a multi-task GP [70,72] to model the relationship between six tasks — the P-element copy number for the evolved generations of the corresponding EE experiment — and five model parameters (Table 1), which serve as predictors across all tasks. Due to time-related dependencies of P- element copy numbers within one experiment, we assumed that tasks are correlated and modeled their relationship using a rank-1 covariance structure. This means that any correlation between single tasks is determined by one single latent factor. The multi-task GP consists of a constant mean function providing a baseline P-element copy number estimate for each task (constant mean = 0 copies), and a covariance function that accounts for both: input-dependent correlation within one task (kinput) and correlations across tasks (ktask): Embedded Image Where 𝑘input(𝑥, 𝑥’) is a radial basis function kernel modeling the covariance between two input data points x and x’ [43], and 𝑘task(𝑡, 𝑡’) models the relationship between tasks t and t’ [70,72]. Using a rank-1 task-kernel simplifies the task covariance matrix 𝐾task to: Embedded Image Where µ is a vector of task weights and 𝜎, represents task-specific, independent noise. During GP training, the task weights µ, 𝑘input hyper-parameters, and task-specific noise are learned by maximizing the log marginal likelihood over observed training data.

We trained GPs on a dataset of 1,000 points using Latin Hypercube Sampling (LHS), a method that ensures evenly distributed exploration of the entire input domain (Table 1), where P-element copy number time series were generated with the experiment-specific individual-based model. We used the Adam optimizer from PyTorch with a learning rate of 0.01 [71] to train each GP over 40 rounds (50 iterations per round). After each round, a snapshot of the GP was saved and evaluated against an independent validation dataset consisting of 5,000 LHS points to determine the optimal training duration and avoid overfitting. We selected the GP snapshot with the lowest root mean square error (RMSE) on the validation dataset for further analysis (snapshot 18 for 1st wave, snapshot 19 for 2nd wave).

To evaluate the GP’s performance, we predicted P-element copy number time series for a test dataset consisting of 5,000 LHS data points. To make GP model performance comparable between the two EE experiments, we report RMSE values normalized by the average observed P-element copy number per time point. This normalization was necessary because the 2nd wave, which has higher absolute P-element copy numbers in the ancestral generation, would otherwise naturally result in higher RMSEs. The trained GP was only challenged when predicting large P-element copy numbers in the test data.

This issue is likely due to our choice of a constant mean of 0 across all tasks (P-element copy number per generation). When data points are sparse, the GP reverts to the prior mean of 0, which tends to downwardly bias the predictions (an alternative approach would be to set the mean to the average observed value in the training data for each respective generation). Another potential source of error lies in the kernel choice. Simulated P-element invasions often involve rapid changes, and the RBF kernel we used might not always fully capture these rapid dynamics. Alternative kernels, such as the Matérn kernel [43,73], might be more ebective at modeling abrupt shifts in behavior, obering a better fit for this type of system. Additionally, the GP’s Bayesian nature obers a way to improve its predictive power. In Bayesian frameworks, predictions are not single values but are accompanied by uncertainty estimates. This uncertainty can guide further sampling in regions where the GP’s predictions are less confident, a technique known as active learning [73]. Because the trained GP predicted P-element copy numbers within the empirical range with high accuracy, we did not explore alternative mean function, kernel choices, and active learning strategies in this study.

Parameter Tuning with Gaussian Process Surrogate Models

We used our trained GPs to comprehensively explore simulated P-element dynamics across the whole input domain (Table 1). For each EE experiment (1st and 2nd wave), we predicted P-element copy number time series for 106 LHS data points. The GPs allowed for rapid predictions: simulating P-element invasion curves for all 106 data points took only 2 seconds on a local machine with an i5-12600K CPU and a GeForce RTX4090 GPU. In comparison, running 108 individual-based simulation runs for the same type of analysis would take several days on a computing cluster, depending on available resources.

To identify the parameter values that best explain the observed P-element invasions, we assessed the fit between the predicted and observed P-element copy number time series. For each evolved generation, we computed the RMSE between the GP prediction and the three replicate experimental populations. Next, we normalized the RMSE by dividing by the average observed P-element copy number at the corresponding generation. Finally, we summed the normalized RMSE across all six evolved generations to generate a single error metric between the simulated and empirical P-element invasion curves for each EE experiment. The fit metric across both EE experiments — NRMSE sum — is simply the sum of the NRMSEs for the 1st and 2nd wave experiments. A lower NRMSE value indicates a better fit between the predicted and observed P-element invasion dynamics.

Declarations

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Availability of data and materials

Information regarding data availability and processing for the 1st wave can be found in Kofler et al. 2018 and Kofler et al. 2022. For the 2nd wave, raw reads of generations 0 and 10 have been previously published (Langmüller et al. 2023) and are available from the European Nucleotide Archive (ENA) under project accession number PRJEB54573 (samples SAMEA110271575 – SAMEA110271580). Raw reads of the remaining generations of the 2nd wave experiment are available from ENA under project accession number PRJEB83416. Time-resolved P-element copy number estimates in the experimental populations, our individual-based P-element invasion models implemented in SLiM [41], simulated data, trained GPs, as well as a Jupyter notebook demonstrating the usage of the GPs are available on GitHub at https://github.com/AnnaMariaL/EE-P_element.

Competing interests

The authors declare that they have no competing interests.

Funding

This research was mainly supported by the European Research Council (ERC, ArchAdapt), and the Austrian Science Funds (FWF, W1225). This research was in part supported by the National Science Foundation (NSF PHY-174958), the Gordon and Betty Moore Foundation (Grant No. 2919.02), and the Aarhus University Research Foundation (AIAS-AUFF).

Author’s contributions

CS designed and supervised the experimental evolution study. AML was responsible for the modeling aspects of the study. VN was responsible for the molecular work. BCH contributed to the design of the individual-based simulation model. AML and CS wrote the initial manuscript draft. All authors revised the manuscript and approved the final version.

Figure S1.
Figure S1.

Normalized root mean square error (NRMSE) for GP predictions using 10⁶ diaerent parameter combinations. (A) Distribution of NRMSE sums, showing variation in the fits between GP predictions and empirical data. While most values are moderate, a few combinations have very low or very high NRMSE values. (B) Comparison of NRMSE for the 1st wave (x axis) versus the 2nd wave (y axis). Each point represents the NRMSEs for one of the 10⁶ data points. The amber line represents the identity line (x = y). Overall, there is strong agreement between the NRMSEs, with a Spearman rank correlation coeaicient of 0.87.

Figure S2.
Figure S2.

Gaussian Process (GP) predictions provide a good fit to the empirical data — parameters estimated jointly from 1st and 2nd wave data (average parameter values from the 100 combinations with the lowest NRMSE sums). GP predictions from the parameter combinations with the lowest NRMSE sum when compared against empirical data are shown for scenarios without expected eaective purifying selection (𝛦(|𝑠|/2) ≤ 1/(2𝑁e), steel blue) and scenarios with expected eaective purifying selection (𝛦(|𝑠|/2) > 1/(2𝑁e), orange), Ne = 221 [45]. Each grey line represents an empirical evolution replicate, with sequenced time points indicated by dots. GP predictions are marked by diamonds, while the dashed colored lines represent the average P-element copy number per haploid genome across 100 simulation runs with the individual-based model. The colored ribbons show the range between the 2.5th and 97.5th percentiles of P- element copy number trajectories simulated with the individual-based model. (A) 1st wave experiment. (B) 2nd wave experiment. (C) Simulated distribution of fitness eaects (DFE) used in (A) and (B).

View this table:
Table S1.

Summary statistics describing the 1 (“best fit”) versus 100 (“top 100”) parameter combination(s) with the lowest NRMSE sum (NRMSE sum = NRMSE 1st wave + NRMSE 2nd wave) from the parameter exploration with the Gaussian Process model, grouped by average expected selection eaicacy (Ne = 442). Values in square brackets represent the range between the 2.5th and 97.5th percentiles of individual metrics. |s̄| = mean selection coeaicient outside piRNA clusters (Ε(|𝑠|) = 𝛼/(𝛼 + 𝛽)); 95th percentile |𝑠| = 95th percentile of |𝑠| outside piRNA clusters; Neutral fraction = expected fraction of eaectively neutral (|𝑠| ≤ 1/𝑁e) P-element insertions outside of piRNA clusters; |s̄effective| = mean selection coeaicient for P-element insertions outside piRNA clusters where selection is strong enough to overcome genetic drift (|𝑠| > 1/𝑁e); NRMSE = Normalized root mean square error

Acknowledgements

We thank all members of the Messer lab for feedback and support. Special thanks to Marlies Dolezal for helpful discussions and to all current and former members of the Institute of Population Genetics, who contributed to the maintenance of the experimental populations over many years.

Footnotes

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Posted December 20, 2024.
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Purifying Selection Shapes the Dynamics of P-element Invasion in Drosophila Populations
Anna M. Langmüller, Benjamin C. Haller, Viola Nolte, Christian Schlötterer
bioRxiv 2024.12.17.628872; doi: https://doi.org/10.1101/2024.12.17.628872
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