Predicting the evolution of Escherichia coli by a data-driven approach

A tantalizing question in evolutionary biology is whether evolution can be predicted from past experiences. To address this question, we created a coherent compendium of more than 15,000 mutation events for the bacterium Escherichia coli under 178 distinct environmental settings. Compendium analysis provides a comprehensive view of the explored environments, mutation hotspots and mutation co-occurrence. While the mutations shared across all replicates decrease with the number of replicates, our results argue that the pairwise overlapping ratio remains the same, regardless of the number of replicates. An ensemble of predictors trained on the mutation compendium and tested in forward validation over 35 evolution replicates achieves a 49.2 ± 5.8% (mean ± std) precision and 34.5 ± 5.7% recall in predicting mutation targets. This work demonstrates how integrated datasets can be harnessed to create predictive models of evolution at a gene level and elucidate the effect of evolutionary processes in well-defined environments.

7. The manuscript should demonstrate in more detail that their ensemble's prediction performance is better than that of a naive approach, such as choosing the top 5 most mutated genetic regions. The current discrepancy in the submitted and claimed results don't allow for this verification by reviewers. The ROC and Precision-Recall curves of figure 5 or S5 only illustrate trends and do not demonstrate performance in a manner that can be validated. Additional supplementary files describing the prediction output that generated the ROC and Precision-Recall are necessary to adequately review the ensemble's performance.
8. Line 119: The claim of "For each mutation event, we recorded its genome position" isn't supported by the results or supplementary data: no genomic nucleotide positions are included with any of the mutation data from the manuscript or mutationdb.com. 9. The result descriptions often refer to "mutations", though the abstract majority of supplemental results report on gene level mutation details. This usage of "mutations" is misleading since readers could interpret the results as being generated using additional mutation details.
10.The claim "Gene ontology enrichment showed that 12 out of the top 20 genes most likely to be hit by a mutation are involved in carbohydrate transport and metabolism, an adaptation to the carbon source where the cells grow" (line 136) isn't represented by any results submitted with the manuscript.
11.The functional analysis of "depletion spots" are given, the genes contained within depletion spots are not given in the manuscript's results or supplementary data. Only those genes with mutations have been reported (supplementary file 3).
12.Line 167 The claim "We observe a higher likelihood to hit DNA-related functions in hypermutators" should be quantified.
13.The genetic mutation target results are in binary form, though the ensemble returns probabilities. The manuscript does not describe a means for transforming the ensemble's probability results into binary results.
14.Line 255 and 256: Are the "shared mutations" described by overlapping genes and mutation type (supplemental file 1) or only genes? 15. Figure 4C includes a data point with 114 replicates and a ~60% pairwise overlap ratio. This data point is uniquely described by the 114 replicates from the Tenaillon 2012 ALE (PMID: 22282810). The paper for this experiment had executed the same analysis, though their mutated gene pairwise overlapping ratio was 20%. The manuscripts results shouldn't differ.
16.The integrity of line 260's claim is affected by this discrepancy: "Interestingly, however, if we examine each pair of replicates together, their overlap ratio fluctuates around 60% across the whole range of replicates per experiment (Fig. 4C)." 17.Describe why an Artificial Neural Network, Support Vector Machine, and a Naive Bayes classifier were specifically chosen for the ensemble. 18.Stratification according to features should be used in the cross-validation of the predictor. The use of leave-one-out cross-validation is not appropriate for this data set since it contains groups of relatively homogenous mutation results, as presented in Figure 4C, and will results in overfitting during validation.
19.The forward validation evolution conditions (duration of evolution, passage volume) and mutation calling toolset should be included, otherwise, the experiment can't be reproduced. 20.Line 324: "80.3%" isn't clearly associated with any result in the manuscript.
Minor Revision 1. Over 50 spelling, grammar, and formatting errors were encountered. The manuscript requires thorough editing to remove such issues that degrade the clarity of the work.
2. Figure 3C should describe the trendline approaches and fit metrics 3. Figure 3D should describe the dendrogram distance units.
4. Line 85-86 "change to be mutation targets" doesn't have a clear context. 5. The abstract should report the recall performance of the ensemble. Precision isn't adequate on its own when describing single value representations of supervised learning performance.
6. The text refers to " Fig. 1A", "Fig. 1B", and "Fig. 1C", though figure 1 doesn't include subpanels identified as A, B, or C. 7. The orange line of figure 2 D and E need to be described.
8. Figure 2's description contains multiple formatting issues and subpanel D doesn't have a description.
9. The claim " One sole mutation in the transcription machinery can allow the change of expression of full metabolic pathways." needs a reference.
10.To be more clear, Figure 2E should include some form of "We used a 5kb sliding window along the E. coli MG1655 genome to find regions that were most or least likely to be hit by a mutation." 11.The statistical approach described by leveraging a Gamma distribution (line 150) isn't clearly associated with any results. Reasons for choosing the Gamma distribution should be included or reference.
12.The term "coldspots" should be removed if only to be used once.
14.The manuscript should state the reason and references for the following choice and claim (line 158) "...hypermutator strains, strains with a mutation rate larger than 0.1 mutations per genome duplication that have been identified as such. Hypermutators are generally expected to follow a different trajectory during evolution" 15.The method for generating p-values in Table 1  18.Line 178: Claim "The only pathway enriched in any of the clusters are the two-component systems, which is present in 9 genes in cluster 1 and 8 in cluster 4." needs to reference the supporting results.
19.Line 183: Claim "Mutation on these genes is a general response of the cells to improve the acquisition of the carbon and to cancel the ability of biofilm formation." needs to reference supporting material.
20.Line 199: The choice of a 10% p-value for DAVID needs to be clarified. 21.Line 199: DAVID needs a reference. 22.Line 239: No explanation is given for the result " These two exceptions fall in one cluster when replicates are merged by counting mutation frequency ( Supplementary Fig. S4).
23.What is the difference between the red and black data points in figure 4A? 24.Line 283: Remove the reference to "biological network inference" since its connection to this work isn't explained or obvious.
25. Figure 5A's workflow does not clearly represent the prediction processes. Does the training data contain 83 different types of each feature or a sum of 83 different types across all features? When is the prediction input introduced? 26. Table 2 contains duplicate entries for sufD and spoT. 27.Line 324: "MG1655 genome harbors 86% of coding regions" needs a reference.
28.The choice of model distributions in the methods section "Evaluating the statistical significance of the hotspot genes" should reference material validating these choices.
30.Line 326: The claim that rpoS is a top mutated gene is incorrect according to Table 1, which doesn't include rpoS. 31.Line 351: "limitation of pathways involved in antibiotic resistance" needs a reference. 32.Line 360: "the ensemble predictor was quite accurate". Accuracy was never used as a metric of prediction performance. 33.Line 375: "four categories of attributes: strain, media, and stress." Only 3 categories given. 34.Line 375: "The duration of each evolutionary experiment was represented by 7 attributes corresponding to 7 time intervals." Nowhere in the mutation data is ALE duration described by 7 time intervals.
Reviewer #2 (Remarks to the Author): This paper describes a meta-study of E.coli evolution experiments, in which mutation data under different conditions of stress and adaptive evolution are harvested for a predictive framework based on machine learning methods. The novelty and strong point of this paper is the combination of data from different experiments into a unifying analytical framework, which drastically increases the information about repeatable mutation patterns and lays the ground for training predictive methods. At the same time, this strategy is what raised most of my questions on the paper, which are on the justification of pooling data for specific inference purposes and on the validity of some results. I think the points below should be carefully addressed in a revision. 2. Repeatability of mutational patterns. The pattern observed in Fig. 4a-c can probably be digested in a more informative probabilistic model giving the likelihood to mutate a given gene in a given condition, such that the enhancement of repeatability over a null model of independent mutations (no repeatability) becomes clear. For example, a simple null model of independent mutations would give a frequency of f = 1/k for a given mutation under k replicate experiments. The pattern of fig. 4a is a bit above that, f ~ 1.5 / k; how does that relate to the pattern of fig. 4b can 4c?
3. Inference of epistasis. The analysis of co-occurrence and epistasis on p.8. appears to have an inconsistency. Epistasis means that the selection on one mutation depends on the genetic background it appears on, so only subsequent mutations in the same evolving population can be counted and the data must not be pooled across populations (cf. Methods, line 403-404). I realise that the data may not be informative enough under this more stringent requirement; the analysis of epistasis is not central to the paper and could also be left out without too much loss.
4. Predictive methods. The discussion of this central point of the paper is too short and too much of a black box. It would be interesting to know the consistency of predictions from the different methods. A naive look at fig. 5b suggests that the other methods do not add much to a naive Bayes prediction, perhaps the main analysis should be limited to that method? What happens if more challenging separations into training and validation data are applied? Can we learn informative and biologically meaningful clusters of features, i.e., of strains, media, and stress conditions? Key features of the prediction methods should be described in Methods and Supporting Information to make the paper reasonably self-contained for a non-specialist readership. This manuscript describes the significant effort undertaken by Wang et al. to survey, compile and curate E. Coli mutation events under different environmental settings. Except for a few minor errors, I found the paper well written with a logical flow and interesting findings. The major contribution of this paper is an "ensemble mutation predictor" that predicts which gene/intergenic regions are going to be mutated under a certain condition. I have a few questions and I think they might help me and the readers understand the method better: 1. The authors mention that there are 83 features and they are shown as binary (T/F) individual features in Fig. 5A. (This pane is a bit confusing and might imply that there are 3 sets of features.) It seems that a couple of these features are categorical (e.g., Strain, Medium and Time) and should be encoded as 1-of-K. That is, only one Strain feature can be True and all other Strain features must be False. Stress seems to be different though, as more than one Stress feature can be True. I think feature encoding should be clearly defined and the number of features be updated (all Strain features count as one). Moreover, feature selection should be done differently on categorical features (all levels must be treated jointly).
2. If I understand correctly, there are 1,990 models for 1,990 gene/intergenic regions and all these models are trained independently, whereas mutations observed are presumably dependent. What would be the rationale for assuming independence and how this assumption can be verified/tested? 3. Since there are 1,990 models and 1,990 sets of performance metrics, reporting metrics must include their statistical variation. For example, in Fig. 5B, the ROC curves are averages over all models. Which one is the best-performing model and which one is the worst-performing model? What is the variation in AUC and AUPRC (median, SD, etc)? (On a side note, the title of Fig. 5C is incorrect). I think boxplots of AUCs and AUPRCs could be informative. Moreover, a statistical test must be performed to show superiority of one model over another. In Fig. 5C, the difference between ANS and all underlying models is huge. What is the explanation? Also, I do not think PRCs can be averaged.

1
We would like to thank the reviewers for careful and thorough reading of our work and for the thoughtful comments and constructive suggestions. We have responded each point brought by the reviewers as follows (Each response follows the corresponding remark by the reviewers; remarks are in italics) 1. The title and introduction describe the primary significance of this work as the given framework for predicting mutations. This implies that the manuscript will present substantial content on predicting evolution events using data provided by current literature. Lines  Response: We agree that a large portion of the manuscript is on analysis of the dataset and trends within and this has been done so by design. We believe understanding the data is paramount to any successful prediction effort, as it is quite easy to be misguided otherwise due to data noise, biases and structure. While our goal is to investigate the degree that evolution is predictable, the road to Ithaca is as important. For example, the way we defined conditions (lines 88-89) is part of feature engineering necessary in the machine learning section of the paper, despite being introduced earlier. The hypothesis that the same targets are hit during independent evolution experiments in the same environments, hence mutations can be used as features in predictors, is supported in the section about evolutionary convergence (lines 185-214). Similarly, we explain the predicted mutations (machine learning validation) in a forward validation experiment only under the light of the dataset presented earlier on. To clarify these points, we modified the manuscript in lines 189-190, 216-217, 251-252.

The impact of predicting genetic mutation targets in adaptive evolution is not made clear by the manuscript. The manuscript's only content on the motivation for its work are brief references to similar applications of machine learning (lines 82-85)
. Lacking a clear impact, the manuscript only describes an exercise in consolidating data, mining for trends, applying supervised learning tools, and validating their performance with experimental results.

Response:
We have now expanded on how predicting evolution can affect our understanding of the interplay between environment and evolutionary processes, as well as lead to better experimental designs for testing hypotheses (lines 65-71).
3. The ensemble can't predict completely novel genetic mutation targets, only those that are present in the training data. Reducing the ensemble's power of novel prediction are the regulatory system mutations that serve as general adaptations across many different stresses and mediums (PMID: 27135538). These regulatory system mutations are found in the ensemble's training data. The manuscript should clarify how and what context this level of prediction power would be impactful.

Response:
We agree with the reviewer, statistical learning methods can only generalize past histories to novel input combinations that share fundamental attributes. If we encounter "regulatory system mutations" that function as general adaptations, those would potentially be present ubiquitously in our database, and in that case a solution would be to filter them out during data preparation. However, this is not the case in Mutation DB, as no mutation is present in all conditions. The most frequent mutation target is rpoB, which encodes the β subunit of bacterial RNA polymerase, mutated in10 out of the 33 stresses. Instead, there are mutations that are specific to media: for instance, mutation in satP, a succinate transporter, is specific to M9 + Glycerol media and has appeared in 12 out of the 178 respective samples. To address this question, we measured the number of stresses and media that each mutation appears, please find the detailed analysis with Supplementary File 11 and the corresponding histogram in Supplementary Figure  10. Mutations that are common in the majority of stresses/media exist, but they are the exception rather than the rule. Indeed, only 1.8% and 21% of the mutation sites appear in more than 10% of the stresses and media, respectively in our database. These mutations, although more general than others, are associated with specific stresses and media and hence have predictive value as long as the input embedding to the machine learning methods allow for such associations to take place. This is the case here and we clarify this point in lines 262 to 271, where we also cite the relevant publications.

Response:
We have added normalization and all the replicates for a given culture condition were merged as a binary mutation profile to normalize the variation in the number of replicates for different conditions. Leave-one-condition-out cross validation was used when testing the performance of the prediction. We have elucidated this in lines 416-418.

We calculated a different precision (ours=50%, theirs=44%) and recall (ours=36%, theirs=33%) for the performance of the ensemble's predictions according to the true and false positives given by in the "ML Forward Mutation Prediction" spreadsheet of supplementary file 9. Authors should ensure that their calculations are correct and that their results and approaches are clear. The prediction performance is a key result in the manuscript's intended contribution; this discrepancy is a critical issue to address before publication.
Response: Indeed, we verify the recall of 36% (discrepancy appeared from one gene appearing twice being re-counted in table 2). We has corrected that in the manuscript and the supplemental material. Among the 9 predicted mutations, 4 were really mutated in the experiments, which gives a precision of 44% (4/9). As another reviewer suggested, we now also use bootstrapping to generate multiple datasets to test the robustness of our ensemble predictor, we have included the mean and standard deviation for precision and recall when reporting the results in the abstract and body of the manuscript (lines 13-15, 246). Table 1) aren't included in supplemental files or the online mutationdb.com data describing the mutated genetic region data used to train the ensemble. The manuscript's ensemble cannot predict the mutation of a genetic region without including its mutation in the training data. The authors need to ensure that the submitted results data accurately reflect the claims made in the manuscript. Table 1 and all the genes listed in Table 1 are included in the database. We searched for "ybcS" across the manuscript and did not find this entry. The gene "proV" was in Table 2 and it corresponds to "proK" in the database, which now is consistent between Table 2 and DB.

The manuscript should demonstrate in more detail that their ensemble's prediction performance is better than that of a naive approach, such as choosing the top 5 most mutated genetic regions. The current discrepancy in the submitted and claimed results don't allow for this verification by reviewers. The ROC and Precision-Recall curves of figure 5 or S5 only illustrate trends and do not demonstrate performance in a manner that can be validated. Additional supplementary files describing the prediction output that generated the ROC and Precision-Recall are necessary to adequately review the ensemble's performance.
Response: ROC and PR curves, along with AUCs are provided in Figure 5, with clear evidence that the Ensemble predictor is a superior technique. We believe that taking the top 5 most mutated regions although reasonable, it would not be a better performance comparison (why 5 and not 10 or 15? Who sets that arbitrary threshold?). However, the prediction output of all individual predictors and the Ensemble predictor is included in Suppl. File 9 and we have now also included a confusion matrix to clarify the calculation of those statistical measures. The baseline we used is the frequency of a mutation across all the culture conditions in the database (lines 420-421), which is the also approach the reviewer suggested.
8. Line 119: The claim of "For each mutation event, we recorded its genome position" isn't supported by the results or supplementary data: no genomic nucleotide positions are included with any of the mutation data from the manuscript or mutationdb.com.

Response:
We have added the location of a mutation when reporting the type of mutation in the Supplementary File 2.xlsx.
9. The result descriptions often refer to "mutations", though the abstract majority of supplemental results report on gene level mutation details. This usage of "mutations" is misleading since readers could interpret the results as being generated using additional mutation details.
Response: All 83 features that have been used for prediction are provided in Suppl. File S8 and the methods section has a detailed explanation on what features were taken into account. In our analysis "mutations" means two or more genome sites have one or more nucleotide change. In the manuscript (abstract and results) we note that the predictions are at "gene level" and we now add it in the introduction too to ensure that predictions are made at gene and not nucleotide level (lines 76-77): "Then we used it to train "evolution" predictors that have the capacity of predict gene mutation targets, at gene (not nucleotide) level, given a novel environmental setting"

10.The claim "Gene ontology enrichment showed that 12 out of the top 20 genes most likely to be hit by a mutation are involved in carbohydrate transport and metabolism, an adaptation to the carbon source where the cells grow" (line 136) isn't represented by any results submitted with the manuscript.
Response: We now have added a graph depicting the gene ontology enrichment for the top 20 genes (Supplementary Material, Fig. S1).

11.The functional analysis of "depletion spots" are given, the genes contained within depletion spots are not given in the manuscript's results or supplementary data. Only those genes with mutations have been reported (supplementary file 3).
Response: A new sheet describing the depletion spots was added to the Supplementary File 3.xlsx (also please see legend in the file). In addition, a Figure summarizing the enrichment results was added to Supplementary Material (Suppl. Fig. 3). We also added clarification about depletion spots in lines 112-114.

12.Line 167 The claim "We observe a higher likelihood to hit DNA-related functions in hypermutators" should be quantified.
Response: Among the 36 hypermutators, 100% have at least one DNA repair related gene mutated. In contrast, the percentage is 51% for non-hypermutator lines. We now have added the following clarification in lines 128-130 and we list the DNA related genes in Supplementary File 4.

13.The genetic mutation target results are in binary form, though the ensemble returns probabilities. The manuscript does not describe a means for transforming the ensemble's probability results into binary results.
Response: We set a threshold to transform the predicted probability into a binary result. As the threshold varied, we got a ROC curve and a precision-recall curve (clarified in lines 418-422).
14.Line 255 and 256: Are the "shared mutations" described by overlapping genes and mutation type (supplemental file 1) or only genes?
Response: Shared mutations are described by overlapping genes only. We have now clarified this point in line 201. Figure 4C includes a data point with 114 replicates and a ~60% pairwise overlap ratio. This data point is uniquely described by the 114 replicates from the Tenaillon 2012 ALE (PMID: 22282810). The paper for this experiment had executed the same analysis, though their mutated gene pairwise overlapping ratio was 20%. The manuscripts results shouldn't differ.

Response:
We would like to thank the reviewer for the detailed review. We rechecked our computation and found that the discrepancy is attributed to the difference in the ways to compute the pairwise overlap ratio. In the original paper, it was observed "Among point mutations, none of the 36 synonymous and 157 of the 634 nonsynonymous mutation were shared among two or more lines". We assume the pairwise overlap ratio the reviewer computed is equal to 23% (157/(36+634)). Instead, the way we compute pairwise overlap for two cell lines is different: the overlap ratio is equal to the number of mutations in one cell line divided by the number of unique mutations in both lines. We would like to illustrate the difference between these two ways of calculation in the following example: In the table below, each row represents a replicate and the presence of a cross mark indicates the gene in a column is mutated. If we compute the overlap ratio as in the Tenaillon paper, we get a ratio of 33% (2/6), while with our calculation, we get an overlap ratio of 50% (2/4). Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Replicate 1 X X X Replicate 2 X X X Replicate 3 X X X Replicate 4 X X X In addition, the Tenaillon paper also mentioned that "In contrast to point mutations, 69% (82/119) of larger deletion were identical between at least two lines." Thus, if both point mutations and deletion mutations are taken together as in our work, the numbers would also be different than the 23%.

16.The integrity of line 260's claim is affected by this discrepancy: "
Interestingly, however, if we examine each pair of replicates together, their overlap ratio fluctuates around 60% across the whole range of replicates per experiment (Fig. 4C)." Response: Addressed as part of response to point 15.
17.Describe why an Artificial Neural Network, Support Vector Machine, and a Naive Bayes classifier were specifically chosen for the ensemble.
Response: For two reasons: First the diversity of the multiple predictors is critical for building an effective ensemble predictor and these three methods vary in complexity. In addition, the ANN and SVMs are 32.Line 360: "the ensemble predictor was quite accurate". Accuracy was never used as a metric of prediction performance.

34.Line 375: "
The duration of each evolutionary experiment was represented by 7 attributes corresponding to 7 time intervals." Nowhere in the mutation data is ALE duration described by 7 time intervals.
Response: Now added under the Methods section (line 431).
We would like to thank the reviewer for their detailed and thorough review!

Response:
We agree with the reviewer; the linear pattern is what is expected to see and in fact this is the actual patterns when hyper-mutators and not taken into account. To clarify this point, we have updated Fig. 3c, by removing the hyper-mutators (which are included in the inset plot for completeness).
In addition, we evaluated the synonymous and non-synonymous substitutions, as suggested, and we observe a similar linear pattern (please see supplementary Fig. 6a and 6b). The same linear pattern is observed for the number of synonymous and non-synonymous substitutions in the intermediate time plots, as well as for deletion and insertion mutations ( Supplementary Fig 6c and d). We have also added this clarification in the manuscript (lines 156-158).
We also investigated if there is any systematic bias due to the experimental settings, so we conducted ANOVA analysis to elucidate this point. We split all the evolution runs into two groups according to one of the following factors: generation, strain, medium and stress. These results are shown in Supplementary  Fig 7 and discussed in lines 174-176. Fig. 4a- fig. 4b can 4c?

Repeatability of mutational patterns. The pattern observed in
Response: To address this comment, we used linear regression to fit the pattern and also converted all plots in Fig. 4 to have the same independent variables, so the readers can compare. Fig. 4a now shows a relationship between the frequency (f) of a mutation within a condition and the reciprocal of the number of replicates (1/k) and the black line drawn corresponds to the linear regression line of f=1.49/k + 0.018 (and the reviewer is spot on f~1.5/k). Similarly, the global overlap ratio (g) shown in Fig. 4b decreases as k increases and here we have g= 1.5/k + 0.015, which is very similar to the relationship between the averaged frequency and the reciprocal of the number of replicates. We include the null model (each mutation present in only one replicate, which leads to f = 1/k, where k is the number replicates) as a dotted line in Fig. 4a, with the size of the difference between the dashed and the black line representing the common mutations shared across replicates under any given condition. We have added this analysis in the manuscript (lines 193-196, 203-209 Response: (a) Although we agree log-log is better in general, but we don't think it is appropriate for Fig.  2c as x-axis is indices. For Fig. 2d, we now include the log-log plot as an inset. (b) We have revised the discussion section to be more representative of the state of predictions and potential improvements (lines 300-323).

Response:
We have now changed Fig 5a to better reflect the grouping of the 83 features together. The reviewer is correct, we are using 1-K embedding for strain and medium, while in the case of strain features, it is still binary encoding with multiple non-zero entries allowed. We have added this clarification in the Method part (line 332).
2. If I understand correctly, there are 1,990 models for 1,990 gene/intergenic regions and all these models are trained independently, whereas mutations observed are presumably dependent. What would be the rationale for assuming independence and how this assumption can be verified/tested?
Response: Correct, we assume independence of mutations in this work, the existence of one mutation does not affect the probability of other mutations being present. This is clearly a simplification and future work should address this. We calculated the chi-square test on the null hypothesis model of independent mutations and report it in Supplementary Fig. 11. Another potential improvement to the model would be to add a time series component to the analysis, i.e. adding the order by which mutations happen, as we believe that some mutations are bound to happen earlier in the evolutionary trajectory, given an environment. We have added these points in the discussion section, lines 335.
3. Since there are 1,990 models and 1,990 sets of performance metrics, reporting metrics must include their statistical variation. For example, in Fig. 5B, the ROC curves are averages over all models. Which one is the best-performing model and which one is the worst-performing model? What is the variation in AUC and AUPRC (median, SD, etc)? (On a side note, the title of Fig. 5C is incorrect). I think boxplots of AUCs and AUPRCs could be informative. Moreover, a statistical test must be performed to show