Quantifying microbial fitness in high-throughput experiments
- Center for Advanced Biotechnology and Medicine, Rutgers University, United States
- Institute of Integrative Biology, Department of Environmental Systems Science, ETH Zurich, Switzerland
- Department of Environmental Microbiology, Swiss Federal Institute of Aquatic Science and Technology (Eawag), Switzerland
- Department of Biochemistry and Molecular Biology, Robert Wood Johnson Medical School, Rutgers University, United States
Figures
Figure 1
Overview of the choice of encoding and the choice of time scale for quantifying relative fitness.
(A) Example trajectory of relative abundance (top panel) for a mutant invading and eventually replacing a wild-type population. The same trajectory is plotted under the encoding (middle panel) and the encoding (bottom panel). (B) Flowchart to predict the future relative abundance of a mutant given a relative fitness value for some encoding m. The current relative abundance is transformed into the new variable , then projected into the future through a linear extrapolation using (upper horizontal arrow) and finally converted back into a frequency using the decoding function . (C) Four scenarios for a mutant with the same relative fitness per-cycle but with different underlying population dynamics. For each scenario, we show an example trajectory of absolute abundance (stacked) for the wild-type (dark gray) and mutant population (light gray). Each scenario is mapped as a single-dot onto the fold-change diagram (center plot) and colored areas indicate positive (green area) and negative relative fitness per-cycle (blue area; compare Equation 9). Fitness per-cycle has isoclines that are parallel to the identity in the log fold-change (LFC) diagram. (D) Scenario for rank discrepancy between relative fitness per-cycle and relative fitness per-generation . For a given competition (red dot), rank discrepancy occurs in a bow tie-shaped area of the fold-change space (shaded red). Any competition in the right half of this area (blue dot) will have higher mutant fitness but lower mutant fitness (right inset). As small plots on the left, we show possible population dynamics that generate this fold-change variation. Here, the growth rates of the mutant and wild-type are identical in the two scenarios, but the growth period is different (e.g., from additional resources).
Figure 2
Comparison of mutant fitness rankings with different time scales using empirical trait variation.
(A) Overview of pairwise coculture simulations. For each mutant strain (gray), we simulate a competition growth cycle against a reference wild-type strain (blue) using the estimated traits and laboratory parameters for the initial condition (, glucose, ; Methods and see Appendix 1—figure 4 for the underlying trait distribution). (B) Rank discrepancy between relative fitness per-cycle and per-generation . Higher rank is defined as higher fitness, and the rank difference is defined as the rank in minus the rank in . The blue halo marks the mutant with the greatest rank difference. (C) Covariation between wild-type and mutant fold-change across all simulated competitions for all mutant strains (gray dots). The blue halo marks the same mutant as in panel B, with its red bow tie-shaped area defining the space of log fold-changes (LFCs) that would have a rank discrepancy with it (compare Figure 1D), which includes many other mutant competitions.
Figure 3
Discrepancy between fitness per-generation and per-cycle in epistasis detection and long-term evolutionary trend.
(A) Schematic detection of epistasis for two single mutants (light and dark circle). Epistasis occurs if the corresponding double mutant (two-component circles) deviates from the additive fitness (parallelogram shape in solid lines; Methods). (B) Correlation between epistasis in relative fitness per-cycle and per-generation . Each dot corresponds to a hypothetical double mutant that combines pairs of mutations systematically perturbing each of the three growth traits (Figure 2A) in our minimal model of population dynamics (Methods). (C) Heatmap for epistasis in the per-cycle fitness for all double mutants in our simulated data set; same data as in panel B. The rows and columns correspond to the six single mutations in our model of population dynamics (Methods): an increase or decrease in lag time (, ), an increase or decrease in maximum growth rate (, ), or an increase or decrease in biomass yield (, ). (D) Heatmap for epistasis in the per-generation fitness ; same data as in panel B. All epistasis plots are based on 1:1 competition growth cycles with the wild-type (Appendix 1—figures 9–14). See Appendix 1—figure 15 for epistasis patterns at low mutant relative abundance. (E) Hypothetical scenario for trait evolution in an evolution experiment. An evolving population decreases lag time to zero (orange line), increases growth rate until saturation (blue line), and gradually decreases biomass yield (green line). This trend is similar to initial observations from the Long-Term Evolution Experiment (LTEE) (Vasi et al., 1994). (F) Corresponding long-term trend in relative fitness based on the trait evolution in panel E. We estimate relative fitness per-cycle (gray line) and per-generation (red line) every 250 generations. Dotted vertical lines mark the end of trait evolution in lag time and growth rate in panel E. For the actual fitness trend in the LTEE, see Appendix 1—figure 16.
Figure 4
Rank discrepancies between fitness statistics in Long-Term Evolution Experiment (LTEE) competition data.
(A) Rank difference between relative fitness per-cycle and per-generation as a function of time in the LTEE. For each of the 12 lines in the LTEE, we compute the relative fitness per-cycle and per-generation as a function of time, by averaging the data from the LTEE competition data set (Wiser et al., 2013) across replicate measurements (Appendix 1—section S9). For some lines, the time series is truncated due to measurement difficulties (Wiser et al., 2013). Based on the quantitative fitness values and , we compute fitness rankings between the replicate lines at any given time point (higher rank means higher fitness; compare Figure 2B). The rank difference is defined as the rank in minus the rank in , and we combine the rank differences for all evolving lines to compute the maximum rank difference at each time point. Insets: At three chosen time points (, , generations), we show the correlation between relative fitness per-cycle and relative fitness per-generation (each dot corresponds to one of the 12 lines in the LTEE). We quantify the correlation between and with the Spearman rank correlation (panel title). Colors indicate the time point and correspond to the color bar in panel C. (B) Covariation between relative fitness per-cycle and per-generation for evolved populations of the LTEE. Each line of the LTEE contributes roughly two competitions per time point due to replicate measurements (Appendix 1—section S9) (Wiser et al., 2013). The color of the points indicates evolutionary time point; see panel C for the color bar. We highlight the evolved population with the greatest rank difference (blue halo; same as in Appendix 1—figure 17). (C) Same as panel B but comparing relative fitness under the logit-encoding and under the log-encoding .
Figure 5
The choice of library abundance and reference group in bulk competition experiments.
(A) Overview of a pairwise competition experiment with one mutant (top row) and scenarios for bulk competition experiments with many different mutants (middle and bottom rows). The two bulk competition scenarios differ in their initial fraction of the mutant library (colored ovals) in the inoculum (open box). For each scenario, we show a schematic growth cycle (log absolute abundance) in the inset on the right. (B) Schematic relative abundance trajectories for a mutant compared to two alternative subpopulations. We distinguish between the total relative abundance with respect to the population as a whole (height of teal band in the top box) and the pairwise relative abundance with respect to the wild-type (height of teal band in the bottom box; Equation 20). We indicate the sign of total relative fitness (Equation 24) and pairwise relative fitness (Equation 25) on the right. (C) The absolute error between bulk and pairwise competition experiments. The total relative fitness (dark gray dots; Equation 24) and the pairwise relative fitness (orange dots; Equation 25) for mutants in the minimal population dynamics model (Figure 2A, Methods) parameterized by the yeast knockout data (Appendix 1—figure 4) in bulk competition growth cycle with low mutant library abundance (panel A, case II; Methods). The absolute error is defined as the bulk fitness statistic minus the relative fitness in pairwise competition (Equation S92 in Appendix 1—section S15). In the inset, the absolute error for pairwise relative fitness (Equation 25) for a bulk competition growth cycle with 99.9% library abundance (light gray dots; case III). This still includes a wild-type reference at small percentage to be able to compute a pairwise relative fitness. The x-axis and the orange dots in the inset are identical to the main plot. (D) The relative error in bulk competition experiments as a function of mutant library abundance in the inoculum. Each line corresponds to a knockout mutant in our data set and represents the relative error between the pairwise relative fitness in bulk competition and the relative fitness in pairwise competition (Equation S102 in Appendix 1—section S16). The black vertical lines show the recommended mutant library abundance for our data set based on Equation 11 () and based on the more conservative Equation S118 (, Appendix 1—section S16). Note these bounds are calculated a priori and are not the result of a fitting procedure.
Figure 6
Empirical benchmarks of bulk fitness against pairwise competition experiments.
(A) Fitness measurements as reported by van Opijnen et al., 2009 for knockouts of S. pneumoniae. Pairwise fitness was measured in 1:1 competitions of knockout strains with the wild-type over a single growth cycle using the per-generation statistic (Lenski et al., 1991). Bulk fitness was measured from a single growth cycle using 100% initial abundance of the mutant library and a set of neutral strains as the reference to calculate a per-generation fitness, replacing with the library in Equation 10. Since we were unable to obtain the original data, we extracted these fitness data from Figure 3C in the original publication and subtracted 1 to plot as . See Appendix 1—figure 24 for the absolute and relative error of bulk fitness based on these data. (B) Fitness measurements as reported by Levy et al., 2015 for evolved genotypes of S. cerevisiae after 80 generations of the evolution experiment. Pairwise fitness was measured in 1:1 competitions of knockout strains with a fluorescently labeled wild-type over seven growth cycles using relative fitness per-cycle under the log-encoding , divided by a fixed number of generations inferred from the dilution factor. Bulk fitness was measured from relative abundance data throughout the evolution experiment and using a multi-step algorithm, Bayesian inference, and a set of neutral strains as the reference, leading to a pairwise fitness estimate equivalent to (compare SI Equation 50 in Levy et al., 2015). We extracted the fitness data from the table presented in SI Sec. 8.1 of the original publication. See Appendix 1—figure 25 for the absolute and relative error of bulk fitness based on these data.
Appendix 1—figure 1
Predicting the absolute and relative abundance of microbial populations.
(A) Example time series of absolute abundance for a single microbial population (light gray). The observer (eye symbol) of the time series at time t can ask about the future trend in absolute abundance (arrows). (B) Same as panel A but for two microbial strains, such as a wild-type and a mutant. The absolute abundance of the wild-type strain (light gray) is stacked on top of the absolute abundance of the mutant strain (dark gray). (C) The relative abundance for the mutant strain corresponding to panel B. We sketch the mean relative abundance x over time (green line) inferred from multiple replicate cocultures. An error band (light green) around the time series demonstrates the variation between replicates.
Appendix 1—figure 2
The effect of encodings on a non-logistic relative abundance trajectory.
Example trajectory of relative abundance (top panel) for a mutant invading and eventually replacing a wild-type population, simulated with the Gompertz equation . Below, we show the Gompertz trajectory under the encodings and . Compare to main text Figure 1A for a trajectory simulated with the logistic equation.
Appendix 1—figure 3
The variation of wild-type and mutant log fold-change under resource consumption constraints.
(A) Schematic fold-change variation under a perfect resource consumption constraint between wild-type and mutant. Each dot corresponds to a mutant strain in a 1:1 competition growth cycle with the wild-type strain (Appendix 1—section S5). There is negative covariation between mutant and wild-type LFCs because the resource constraint forces one to decrease if the other increases. For our model of population dynamics, we can calculate this constraint exactly (black line: Equation S36 in Appendix 1—section S5). For two mutants (red points) we highlight the bow tie-shaped areas (red shading; compare to main text Figure 1D) where other competitions must lie to have a rank discrepancy between relative fitness per-cycle and per-generation with those mutants, but they are inevitably empty due to the negative covariance across competitions from the resource constraint. Inset: Correlation of fitness per-cycle and per-generation for these same competitions, showing no rank discrepancy. (B) Same as panel A but schematically showing how a deviation from the resource consumption constraint can allow competitions to fall in each other’s red bow tie-shaped regions (e.g., blue, orange, and green competitions compared to the red one), and thus have a rank discrepancy between relative fitness per-cycle and per-generation (inset).
Appendix 1—figure 4
Empirical trait distribution for single gene-knockouts of yeast.
(A) Overview of the growth curve data set and the estimated growth traits for the knockout library of Saccharomyces cerevisiae (Methods) (Warringer et al., 2003). (B) Covariation between estimated maximum growth rate g and lag time λ across all mutant strains (gray dots; Pearson correlation coefficient , ) as well as wild-type replicates (orange dots; , ). The reference wild-type strain for our pairwise coculture simulations is defined by the median trait values (black cross) of all wild-type replicates. (C) Covariation between measured maximum growth rate g and biomass yield Y across all mutant strains (gray dots; , ) as well as wild-type replicates (orange dots; , ). Histograms on the top and right sides of panels B and C are marginal distributions along each axis, with colors matching the scatter points and the vertical black line marking the median wild-type trait value.
Appendix 1—figure 5
Replicate measurements for growth rate, lag time, and yield in our empirical trait data set.
(A) Covariation of growth rate between replicate measurements of the knockouts (gray dots; Pearson correlation coefficient , ). Each dot represents a mutant genotype from the single-gene knockout collection in Saccharomyces cerevisiae (Warringer et al., 2003). For the vast majority of genotypes in our data set (4163 out of 4492 knockouts) we are able to fit two traits from two independent growth curve measurements (Appendix 1—figure 4A; Methods). (B) Covariation of lag time between replicate measurements of the knockouts (gray dots; , ) (C) Covariation of biomass yield between replicate measurements of the knockouts (gray dots; , ).
Appendix 1—figure 6
The distribution of fitness effects under relative fitness per-cycle and per-generation.
(A) Distribution of relative fitness per-cycle for the single-gene knockouts of yeast (gray) and wild-type replicates (orange) in our data set (Appendix 1—figure 4A, Methods) (Warringer et al., 2003), based on the fitness data from main text Figure 2B. The vertical black line marks zero relative fitness (e.g., the median wild-type). (B) Same as panel A but with relative fitness per-generation . (C) Covariation in fitness ranks between relative fitness per-cycle and per-generation . For each fitness statistic, we calculate the mutant ranking (higher rank means higher fitness and mutants with equal fitness are assigned the lowest rank in the group), based on the rank data from main text Figure 2B.
Appendix 1—figure 7
Exploring alternative conditions for rank discrepancy between fitness statistics in yeast gene-deletion data.
Plots columns A and B have the same format as Appendix 1—figure 4B, C, and columns (C) and (D) match main text Figure 2B, C (in reverse order). Row (A): Low mutant frequency . Row (B): Standard mutant frequency , but where we artificially eliminate variation in lag time to test the effect on the fitness rank discrepancy. Row (C): Same as row B but no variation in growth rate. Row (D): Same as row B but no variation in biomass yield. Row (E): Same as row B, but yields of mutants lower than the median wild-type yield are set to the wild-type value.
Appendix 1—figure 8
Hypothetical case where relative fitness per-cycle and per-generation are anticorrelated across mutants.
(A) Covariation between growth rate and lag time for a synthetically generated set of mutants (gray dots) and a single wild-type (orange dot). The variation here may represent the standing variation in an evolved population with improved growth rate and lag time over the wild-type ancestor. The graphic overlap between points means they appear as a single line. (B) Covariation between growth rate and biomass yield for the mutants (gray dots) and wild-type (orange dot) in this synthetic data set. (C) Covariation between relative fitness per-cycle and per-generation . We simulate pairwise competitions for all mutants against the wild-type with the exact same settings as for the empirical data set (main text Figure 2A; Methods). (D) Covariation between mutant and wild-type fold-change in the competitions. Based on the competition data in panel C (gray dots), we estimate the LFC values for all mutant-to-wild-type competitions (gray dots). We highlight the bow tie-shaped area of rank discrepancy for the mutant with the lowest overall fold-change (red shading; compare Figure 1D). The dashed black line shows the isocline for zero relative fitness per-cycle (main text Equation 9). Distributions of relative fitness per-cycle (E) and per-generation (F) for the mutants in panels A and B. Based on the fitness data from panel C.
Appendix 1—figure 9
Competition growth cycles for double mutants—first column of main text Figure 3C, D.
Each row corresponds to a pair of mutations that perturb growth traits in the minimal model of population dynamics (main text Figure 2A, Methods). This figure shows all combinations where the first mutant increases growth rate (first column of main text Figure 3C, D). Column (A): Perturbations of growth traits for single and double mutants. Column (B): Growth curves of wild-type (gray) and mutant 1 (blue). Column (C): Growth curves of wild-type (gray) and mutant 2 (red). Column (D): Growth curves of wild-type (gray) and double mutant (purple).
Appendix 1—figure 10
Competition growth cycles for double mutants—second column of main text Figure 3C, D.
Same as Appendix 1—figure 9 but for mutant pairs where the first mutant decreases growth rate.
Appendix 1—figure 11
Competition growth cycles for double mutants—third column of main text Figure 3C, D.
Same as Appendix 1—figure 9 but for mutant pairs where the first mutant increases lag time.
Appendix 1—figure 12
Competition growth cycles for double mutants—fourth column of main text Figure 3C, D.
Same as Appendix 1—figure 9 but for mutant pairs where the first mutant decreases lag time.
Appendix 1—figure 13
Competition growth cycles for double mutants—fifth column of main text Figure 3C, D.
Same as Appendix 1—figure 9 but for mutant pairs where the first mutant increases biomass yield.
Appendix 1—figure 14
Competition growth cycles for double mutants—sixth column of main text Figure 3C, D.
Same as Appendix 1—figure 9 but for mutant pairs where the first mutant decreases biomass yield. For the double mutant where the second mutant also decreases yield, we cannot use the additive mutation effects (Methods) because that would result in a negative yield for the double mutant. Here, we have defined the double mutant to have a yield value of . This choice does not affect the fitness or epistasis, since biomass yield is a neutral trait with fitness zero in our model of population dynamics.
Appendix 1—figure 15
Epistasis patterns at low mutant relative abundance.
Same as main text Figure 3B–D but where the mutant starts each competition at low relative abundance (; Appendix 1—section S8), compared to the 1:1 initial conditions in main text Figure 3 ().
Appendix 1—figure 16
Long-term fitness trends in the LTEE under relative fitness per-cycle and per-generation.
(A) Fit of a hyperbolic model (pink line; Equation S56 in Appendix 1—section S9) and a power-law model (cyan line; Equation S57 in Appendix 1—section S9) to a pooled time series of relative fitness per-generation . We pool the fitness per-generation from all 12 lines of the LTEE into a single data set (gray dots) and repeat the fits of Wiser et al., 2013 (Appendix 1—section S9). We compute the fraction of variance explained as a measure for the quality of fit. (B) Same as panel A but using relative fitness per-cycle . (C) Same as panel A but averaging fitness across all 12 lines at each time point. Note that the fraction of variance explained is much higher compared to panel A, because the averaged time series has fewer points (Appendix 1—section S9). (D) Same as panel C but using relative fitness per-cycle . For a comparison between our results and the original fit by Wiser et al., 2013, see Appendix 1—section S9.
Appendix 1—figure 17
Comparison of relative fitness per-generation and per-cycle across the complete LTEE competition data set.
(A) Rank discrepancy between relative fitness per-cycle and per-generation for evolved populations of the LTEE. For each fitness statistic, we calculate a ranking (higher rank means higher fitness and mutants with equal fitness are assigned the lowest rank in the group; compare to main text Figure 2B) across all 12 evolved lines and all time points. The rank difference is defined as the rank in minus the rank in . We highlight the evolved population with the greatest rank difference (blue halo). (B) Covariation between the wild-type and mutant fold-change for the competition data from the LTEE (Wiser et al., 2013). The term ‘mutant’ (y-axis) refers to an evolved population at a given time point from one of the 12 lines of the LTEE. We highlight the evolved population with the greatest rank difference (blue halo; same as in panel A) and draw its corresponding bow tie-shaped area of rank discrepancy between and (red shading; compare to main text Figure 1D). The coloring in both panels refers to the time point at which the evolved population was sampled from the LTEE.
Appendix 1—figure 18
Comparison of log encoding and logit encoding for relative fitness per-cycle in the LTEE competition data set.
(A) Same as Appendix 1—figure 17A but for rank discrepancy between logit-encoded relative fitness per-cycle and log-encoded relative fitness per-cycle for evolved populations of the LTEE. (B) Covariation between the wild-type relative abundance and mutant relative abundance at the start of the competition growth cycle for the competition data from the LTEE (Wiser et al., 2013). The term ‘mutant’ in the axis labels refers to an evolved population at a given time point from one of the 12 lines of the LTEE. The coloring in both panels refers to the time point at which the evolved population was sampled from the LTEE.
Appendix 1—figure 19
Predicting relative fitness with monoculture proxies (fitness potentials) under different scenarios of trait variation.
Plots in columns (A) and (B) show growth trait variation across mutants, with the same format as Appendix 1—figure 4B,C. Plots in column (C) show quality of prediction for different monoculture proxies under the trait distribution in columns A and B. As the ground truth, we estimate the relative fitness per-cycle using a simulated 1:1 competition growth cycle (main text Figure 2A; Methods). For each mutant i, we compute the growth rate difference , the lag time difference , the difference in biomass yield , the difference in log fold-change , and the difference in area under the growth curve from simulated monoculture growth curves (Appendix 1—section S10). We quantify the agreement between the monoculture proxy and the relative fitness per-cycle using the Spearman correlation coefficient . Row (A): Empirical growth trait variation from data on yeast single-gene knockout mutants (identical to Appendix 1—figure 4B,C). Row (B): Same as row A but where we artificially eliminate variation in lag time to test the effect on the monoculture proxies. Row (C): Same as row A but with no variation in growth rate. Row (D): Same as row A but with no variation in biomass yield.
Appendix 1—figure 20
The choice of the cutoff time for evaluating the area under the curve (AUC).
(A) Distribution of saturation times in monoculture for the knockouts (gray bars) and wild-type replicates (orange bars) in our empirical data set (Appendix 1—figure 4). The saturation time is defined as the time when the limiting resource is depleted () and can be estimated numerically from the trait data (Methods). Three vertical lines indicate example choices for the cutoff time of the AUC: the most frequent saturation time ( hr; red line), a saturation time halfway in the decay of the distribution ( hr; black line), and an external time scale ( hr; blue line). Covariation between relative fitness per-cycle and AUC with the cutoff times marked in panel A: 13 hr (B), 16 hr (C), and 24 hr (D). We compute the AUC from simulated monoculture knockouts (gray dots) and wild-type replicates (orange dots). As the ground truth, we take the relative fitness per-cycle from a pairwise competition (main text Figure 2A). The red lines show the best fit from a linear regression of to the AUC.
Appendix 1—figure 21
The error in mutant fitness rankings between bulk and pairwise competition experiments.
(A) Rank difference between total relative fitness and pairwise relative fitness in a bulk competition growth cycle with low mutant library abundance (main text Figure 5A, case II). Based on the fitness data in main text Figure 5C, we calculate a mutant ranking for total relative fitness in bulk (main text Equation 24) and a ranking for pairwise relative fitness in bulk (main text Equation 25) (higher rank means higher fitness and mutants with equal fitness are assigned the lowest rank in the group). The rank difference is defined as the rank in total relative fitness minus the rank in pairwise relative fitness . The ranks exactly match in this case because the mutants are sufficiently rare in case II that the population fitness is almost identical to the wild-type fitness. (B) Based on the pairwise relative fitness at low mutant library abundance in main text Figure 5C (orange dots; case II), we calculate a mutant ranking for pairwise relative fitness in bulk (main text Equation 25) and a mutant ranking for the relative fitness per-cycle in pairwise competition (main text Equation 9). The rank difference (orange dots) is defined as the rank in bulk competition minus the rank in pairwise competition. The rank differences are small because the mutants are sufficiently rare in case II that higher-order effects in the bulk competition are minor. (C) Based on the fitness data in the inset of main text Figure 5C, we estimate a mutant ranking for pairwise relative fitness (main text Equation 25) in the case of a bulk competition growth cycle with high mutant library abundance (gray dots; compare to main text Figure 5A, case III). For each case, the rank difference is defined as the rank in the bulk competition minus the rank in pairwise competition. The rank difference for case II (orange dots) is identical to the data in panel B. All fitness statistics in this figure are based on the logit-encoding; however, since the underlying relative abundances are small (), it is approximately equivalent to the log encoding ().
Appendix 1—figure 22
A decomposition for the error from higher-order interactions in bulk competition experiments.
For a bulk competition growth cycle with low mutant library abundance (main text Figure 5A, case II), we calculate the pairwise relative fitness (main text Equation 25) for the knockouts in our empirical data set (Appendix 1—figure 4A) using a previously established approximation (Manhart and Shakhnovich, 2018) (Appendix 1—section S14). The error from higher-order interactions is defined as the pairwise fitness in bulk minus the fitness in pairwise competition. Based on the approximation for our model of population dynamics (Appendix 1—section S14), we derive a decomposition that separates the absolute error into two terms that we call the fitness-dependent error term (dark orange dots) and the fitness-independent error term (light orange dots). For full details on the decomposition, see Appendix 1—section S15.
Appendix 1—figure 23
The relative error between bulk and pairwise competition experiments.
(A) Same as main text Figure 5C but showing relative rather than absolute error. The relative error of each bulk statistic is defined as the absolute error (main text Figure 5C), divided by the fitness in pairwise competition (Equation S102 in Appendix 1—section S16). A dashed gray line indicates the threshold of 1% relative error. (B) Same as Appendix 1—figure 22 but showing relative rather than absolute error. (C) Same as the inset of main text Figure 5C but showing relative rather than absolute error. On the x-axis, we plot the absolute value of relative fitness per-cycle in the pairwise competition.
Appendix 1—figure 24
The bulk fitness error based on measurements by van Opijnen et al., 2009.
(A) Absolute error between the pairwise fitness measured in bulk competition and the pairwise fitness measured in pairwise competition for the set of single-gene knockouts of S. pneumoniae shown in Figure 3C in the original publication. We calculate the Pearson correlation coefficient r and the p-value for the null hypothesis of zero correlation, and indicate the linear regression between the two variables with a red line. (B) Same as panel A but showing relative rather than absolute error. We define a set of knockouts with non-neutral fitness (blue dots; ) to calculate the geometric mean relative error (blue line). See main text Figure 6A for fitness data and experiment conditions.
Appendix 1—figure 25
The bulk fitness error based on measurements by Levy et al., 2015.
Same as Appendix 1—figure 24 but for the set of evolved genotypes of S. cerevisiae shown in Figure 2D in the original publication. In (A), we calculate the Pearson correlation coefficient and the p-value for the null hypothesis of zero correlation, and indicate the linear regression between the two variables with a red line. In (B), we define a set of knockouts with non-neutral fitness (blue dots; ) to calculate the geometric mean relative error (blue line). See main text Figure 6B for fitness data and experiment conditions.
Tables
Appendix 1—table 1
Parameter settings for Gaussian Process optimization.
| Symbol | Range | Interpretation |
|---|---|---|
| th[0] | [−5, 5] | Amplitude of variation on log scale |
| th[1] | [−5, 5] | Flexibility on log scale |
| th[2] | [−3.83, 0.478] | Measurement error on log scale |
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Quantifying microbial fitness in high-throughput experiments
eLife 13:RP102635.
https://doi.org/10.7554/eLife.102635.4
