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Article

Trends in the Use of Proper Methods for Estimating Mutation Rates in Fluctuation Experiments

by
Guillem A. Devin
and
Alejandro Couce
*
Centro de Biotecnología y Genómica de Plantas, Universidad Politécnica de Madrid (UPM), 28223 Madrid, Spain
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(12), 1100; https://doi.org/10.3390/axioms12121100
Submission received: 5 August 2023 / Revised: 30 October 2023 / Accepted: 27 November 2023 / Published: 1 December 2023
(This article belongs to the Special Issue Mathematics, Statistics, and Computation Inspired by the Fluctuation Test: In Celebration of the 80th Anniversary of the Luria-Delbrück Experiment)
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Abstract

:
The accurate quantification of mutation rates holds significance across diverse fields, including evolution, cancer research, and antimicrobial resistance. Eighty years ago, Luria and Delbrück demonstrated that the proper quantification of mutation rates requires one to account for the non-linear relationship between the number of mutations and the final number of mutants in a cell population. An extensive body of literature has since emerged, offering increasingly efficient methods to account for this phenomenon, with different alternatives balancing accuracy and user-friendliness for experimentalists. Nevertheless, statistically inappropriate approaches, such as using arithmetic averages of mutant frequencies as a proxy for the mutation rate, continue to be commonplace. Here, we conducted a comprehensive re-analysis of 140 publications from the last two decades, revealing general trends in the adoption of proper mutation rate estimation methods. Our findings demonstrate an upward trajectory in the utilization of best statistical practices, likely due to the wider availability of off-the-shelf computational tools. However, the usage of inappropriate statistical approaches varies substantially across specific research areas, and it is still present even in journals with the highest impact factors. These findings aim to inspire both experimentalists and theoreticians to find ways to further promote the adoption of best statistical practices for the reliable estimation of mutation rates in all fields.

1. Introduction

The mutation rate, whether spontaneous or induced, is a key biological parameter, and its accurate estimation is consequently of great importance for many biological problems. Examples include efforts to understand DNA damage and repair mechanisms [1] as well as the propensity for unwanted evolution in the context of cancer [2], infectious diseases [3,4,5], and biotechnology [6,7]. The standard method used to estimate mutation rates in bacteria, yeasts, and somatic cells derives from the seminal Luria–Delbrück fluctuation test [8]. Other alternatives exist, but they either require substantial time and resources (i.e., mutation accumulation experiments, which enable genome-wide estimates of mutation rates and spectra but suffer from several sources of uncertainty [9,10]) or are generally impractical due to specific strain and/or equipment requirements [1,11]. Fluctuation tests, in brief, involve cultivating multiple replicate cultures from a single clone, allowing them to accumulate independent mutations for a short period of time, and screening for mutants in a selective environment. The observed distribution of mutants among replications is used to infer the most likely number of mutations per culture (m), which is then translated into the mutation rate via division using an estimate of the total number of viable cells (R) [12]. However, as Luria and Delbrück realized, the growth of mutant clones that arises before the last generation results in a non-linear relationship between the final mutant count and m. As a result, the number of mutants observed across many replicated experiments is expected to exhibit a large degree of variability, and proper statistical methods have to be used to account for this phenomenon. The current study was partly motivated by the recurrent observation that despite early warnings against the use of simple methods (e.g., arithmetic mean) to estimate mutation rates from fluctuation tests [13], inappropriate methods continue to be prevalent in the scientific literature.
The arithmetic mean is well-known to yield very imprecise mutation rate estimates. For instance, in experiments with four replicates and 10 mutations per culture, Couce and Blazquez found accurate estimates (within half or double the true value) using the arithmetic mean in only about 6% of cases, whereas the Ma–Sandri–Sarkar maximum likelihood estimator (MSS-MLE), an advanced method, provided accurate estimates in approximately 98% of cases. Despite this inaccuracy, researchers may still be tempted to use the arithmetic mean when, instead of absolute values, they are interested in relative effects between experimental and control conditions. However, the arithmetic mean also suffers from poor reproducibility, a crucial property for such comparisons. In the previous Couce and Blazquez example, arithmetic-mean-based estimates matched other estimates for the same condition in only about 59% of experiments, whereas MSS-MLE estimates were reproducible in 92% of cases [14].
To account for the phenomenon of fluctuation in mutagenesis experiments, many methods of differing complexity have been proposed over the decades [15]. These methods are based on the model of mutant clone expansion in an exponentially growing cell population proposed by Lea and Coulson [13], extending Luria and Delbrück’s work [8]. Different methods present experimentalists with a different balance between accuracy and ease of use, and in addition, some may be more apt than others for use under particular experimental conditions. For convenience, throughout this text, we will make the distinction between classic, formula-based methods and advanced, generating-function-based methods. The classic methods rely on formulas simple enough to be implemented without the use of specialized computational resources. These methods include the p0 method [8], which is based on the proportion of cultures with no detected mutants; the Lea–Coulson and the Jones median estimators [13,16], which both leverage different properties of the expected median number of mutants; and Drake’s formula [17,18] which is based on the linear increase in the mutant frequency that is expected in sufficiently large populations. The relative advantages and disadvantages of these methods have been reviewed elsewhere [19].
While formula-based methods offer a reasonable accuracy and ease of use, a more efficient approach involves employing probability-generating functions for the Luria–Delbrück distribution. These advanced techniques allow for the comparison of the entire dataset through a fluctuation experiment with numerous generated distributions, enabling researchers to determine the parameters that best fit the data. These more advanced methods require of the use of computers, but compared with the formula-based methods, they offer more robust and accurate estimates (since all observations are used) and are applicable in most experimental situations [12,14]. In the last two decades, the increasing availability of computing resources has contributed to the gradual but steady adoption of these methods. The first advanced method that gained traction among researchers was the MSS-MLE method [20], which could be implemented using spreadsheets but saw a wider adoption when the online tool FALCOR was released in 2009 [21]. Two other advanced methods have recently gained traction. The first one, the empirical probability-generating function (GF) method, became available through the online tool bz-rates in 2015 [22] and through the R package and online tool flan in 2017 [23]. The second method is a more recent refinement of the MSS-MLE based on a Newton–Raphson type iterative algorithm (NR-MLE), being accessible at first through rSalvador, a package within the popular statistical software R, published in 2017 [24], and later through webSalvador, an online tool introduced in 2021 [25]. The advantages and disadvantages of these methods are discussed in depth in a recent work by Łazowski (2023), which also demonstrates through simulations that rSalvador provides the most accurate estimates [26]. The development of these tools has been accompanied by further theoretical research to broaden their applicability beyond the assumptions of the Lea–Coulson model. For instance, methods can now be applied to situations where final population sizes vary among experiments, where mutants grow differently than the wild type and where only a sub-sample of the culture is screened for mutants [22,24,27,28]. Moreover, methods have been developed to deal with specific ecological complications such as growth in colonies and biofilms or in the presence of killing agents [29,30,31]. More details about the major tools are provided in Supplementary Table S1.
The Ames test merits specific mention due to its typical reliance on the arithmetic mean and its considerable volume of annual publications. Introduced in 1973 [32,33], it is an adaptation of the Luria–Delbrück fluctuation test for the swift and standardized assessment of the mutagenic potency of different agents. The Ames test uses a set of Salmonella typhimurium auxotrophic strains to score revertant mutations in the histidine operon; adding potential mutagens to the plates should lead to the formation of more mutant colonies, which can be used as a proxy of the agent’s mutagenic potency. Currently, the Ames test is the most common method for assessing the mutagenic and antimutagenic potential of compounds and conditions. The recommended guidelines (e.g., those of the U.S. Environmental Protection Agency [34], US Food and Drug Administration [35], and the Organization for Economic Cooperation and Development [36]) typically involve employing the arithmetic mean with low-replication experiments (n = 3). While researchers are often more interested in fold changes over the negative control than absolute mutation rates, this setup is susceptible to false positives due to the arithmetic mean’s sensitivity to the large fluctuations in mutant counts expected in these types of experiments. More recent work recommends the use of dose–response relationships, which may, in principle, mitigate the issue of high sensitivity to fluctuation [37].
On the 80th anniversary of the Luria–Delbrück experiment, here, we set out to identify the prevailing trends in the adoption of appropriate methods for estimating mutation rates in bacteria. We anticipated that the increased availability of readily accessible computational methods would lead to a greater use of best statistical practices. Concurrently, we expected inappropriate methods to become more niche-specific, driven, for example, by the prominence of the Ames test in toxicology. Finally, we investigated whether the usage of inappropriate methods correlates with journal visibility and reputation. We considered two opposing possibilities. On the one hand, inappropriate methods might tend to be associated with lower-tier journals; higher-ranked journals may consult more reviewers and editorial board members, which should facilitate the detection of any technical issues during the review process. Furthermore, once published, the higher visibility of the articles in these journals should help to identify any issues that might escape the peer review process. On the other hand, top-tier multidisciplinary journals often feature broader studies, and the reviewers’ expertise may not fully cover, in depth, all the technical details involved. To quantitatively examine these expectations, we conducted a systematic analysis of 140 peer-reviewed articles published in the past 20 years that employed fluctuation methods for bacteria. To gain further insight into the factors influencing the observed trends, we categorized the articles based on the specific analysis method used, the paper’s general topic, and the impact factor (IF) of the publishing journal.

2. Material and Methods

2.1. Literature Search Selection Criteria

We used Google Scholar (https://scholar.google.com/ (accessed on 4 August 2023)) to search for studies that quantified mutation rates using the Luria–Delbrück fluctuation test. We chose this search engine instead of popular alternatives (e.g., Web of Science, Pubmed) because in preliminary tests, we observed that Google Scholar systematically retrieved more relevant hits than the others, presumably because it searches for the desired query terms anywhere in the text of the articles rather than restricting the search to titles, abstracts, or keywords alone. Our preliminary searches on Google Scholar showed a large body of literature (e.g., 1650 results containing the term “Luria Delbrück fluctuation”). To ensure a manageable number of papers for manual curation, we decided to focus on studies with bacteria, and we limited the search to the last 20 years of published literature (articles dated between 2002 and 2022). We began by using the Advanced Search option with the following Boolean terms in the “all of the words” field: “bacteria” AND “mutation rate” AND “fluctuation test”. To exclude articles on other organisms, we added “-mammal-mouse-plant-yeast-algae-viral-phage” to the search. We opted to use “viral” and “phage” instead of “virus” as exclusion terms so as to avoid excluding articles that focused on bacteria but cited the original 1943 Luria–Delbrück publication, which contains “virus” in its title. Furthermore, we realized that many relevant articles known to us used various synonyms instead of the key term “fluctuation test”. For this reason, we conducted the search using the nine most common synonyms for “Luria-Delbrück fluctuation test”, separated with a vertical bar, which acts as the Boolean term “OR” in the Google Scholar search tool. As Google Scholar has a limit of 252 characters per search, we divided our search of 295 characters in two and conducted an additional search using the plural forms of all nine synonym terms. The final search terms are available in Supplementary Table S2.
This search strategy yielded 376 raw results. We manually validated all of them to ensure our bibliographical corpus consisted solely of peer-reviewed publications using the Luria–Delbrück fluctuation test for bacteria. After validation, 240 articles were excluded for various reasons, including being non-peer-reviewed (e.g., book chapters, research theses, preprints), merely mentioning the test without actually using it, or being duplicates, leaving us with a count of 136 articles. Additionally, four relevant articles were added, having been initially excluded due to artifactual issues with our filters. In one instance, the pdf file contained a neighboring article that dealt with mouse platelets [38]. The remaining exclusions involved authors briefly mentioning one of our exclusion terms but using bacteria as the model of study for reporting mutagenesis [39,40,41]. Finally, the curated set comprised 140 articles and they can be found fully referenced in Supplementary Table S3.

2.2. Data Curation

For each study, we extracted into a list the method used to handle mutagenesis data obtained using the Luria–Delbrück fluctuation test, resulting in a total of eight different methods. These methods were grouped into two main categories for convenience. The first group comprised articles that only use the mean or the median to report mutant frequencies, estimators not specifically designed for dealing with the vast fluctuation expected in Luria–Delbrück experiments. Within this category, we created a distinct subcategory for papers that utilized variants of the Ames test, which were kept separate for downstream analyses due to their significance. The second category encompassed proper fluctuation analysis methods of varying degrees of sophistication. Here, we established a subcategory for so-called classic methods, which rely on simple formulae (e.g., the p0 method [8], Jones median [16], or Drake’s method [17,18]). In contrast, we treated the most advanced computational methods individually, as we were interested in tracking their adoption once they became available via off-the-shelf tools (e.g., FALCOR [21], bz-rates [22], rSalvador [24]; the recently published mlemur was not considered because it was published after 2022 [26]).
Finally, we recorded three important aspects that we hypothesized might influence the use of appropriate methods for fluctuation analyses. Firstly, we noted the year of publication to track the evolution of methods over time. Secondly, we retrieved the journal’s impact factor in the year of publication for each article from Clarivate Analytics’ Journal Citation Reports [42], allowing us to explore potential correlations between journal prestige and methodological choices. Lastly, we categorized the articles based on their general research topics. Five major themes emerged: (1) antimicrobial resistance, including articles describing the targets, mechanism of action, and the basis of resistance for both novel and established antimicrobials; (2) evolutionary genetics, encompassing articles focusing on bacterial adaptation to different challenges, such as antibiotic exposure or limited resources, and the role that mutation rates play in adaptive dynamics; (3) DNA repair, including articles exploring mechanisms that either prevent or correct DNA damage; (4) stress-induced mutagenesis (SIM), a topic that could be seen as a subcategory within DNA repair but that we treated separately due to its significance in the literature and its position at the intersection of DNA repair, antimicrobial resistance, and evolutionary genetics; and 5) genotoxicity, encompassing articles investigating the mutational effects of different chemicals and environmental agents.

3. Results and Discussion

3.1. Proper Methods for the Rise Linked to Increased Computational Availability

To understand the trends and factors involved in the use of the Luria–Delbrück fluctuation test, we devised a bibliographic search strategy focused on studies conducted in bacteria over the last 20 years, as described in the Materials and Methods. After applying filters and manually curating the initial 376 hits, we identified a total of 140 articles that met our specific inclusion criteria. To facilitate the interpretation of temporal trends, given the moderate sparsity of the data, we grouped the articles based on the methods they used, and we aggregated the resulting numbers in 4-year intervals. Overall, we observed a consistent increase in the total count of articles that reported conducting the Luria–Delbrück fluctuation test, from 17 articles published between 2003 and 2006 to 38 articles published between 2019 and 2022 (Figure 1), which speaks to the sustained relevance that the measurement of mutation rates holds for many research problems. Reassuringly, the fraction of articles employing appropriate analytical methods increased throughout the studied period (from 58.8% to 71.1%). Moreover, we observed evidence that the release of user-friendly, readily available software preceded a surge in the use of advanced methods in the literature. For instance, the introduction of the online tool FALCOR in 2009 [21] was followed by a notable increase in the utilization of the MSS-MLE method from 2011 to 2018, with this even becoming the most widely used technique overall in the period from 2015 to 2018 (41.7% of the total studied papers). Shortly after, new software tools for mutation rate estimation were released, especially “BZ rates” (2015) [22] and “rSalvador” (2017) [24], which allowed for the implementation of more modern approaches like the generating function and the Newton–Raphson method, respectively. As with FALCOR, right after appropriate computational tools became readily available, we observed a clear rise in the usage of these advanced methods, even to the detriment of the MSS-MLE method.

3.2. Inappropriate Methods Are Still Widespread, but Their Prevalence Varies across Sub-Fields

Next, we asked whether certain sub-fields were more prone to the use of inappropriate methods in the Luria–Delbrück fluctuation test or if this usage remained relatively constant across research areas. Figure 2a shows that, indeed, the use of inappropriate methods can be observed in all five thematic categories identified. However, we observed notable differences among categories. Genotoxicity studies exhibited the highest prevalence of inappropriate methods’ usage (88.9%), largely due to the dominant influence of the Ames test in this field, as we correctly anticipated. Interestingly, only two articles in the genotoxicity category reported the use of appropriate methods, and they are from groups mostly working in the areas of DNA repair and in evolutionary genetics.
The DNA repair category, which had the highest number of articles (43), also showed a significant proportion of articles with inappropriate method usage (53.5%). We confirmed that this mixed behavior did not emerge from an underlying temporal trend, such as old articles being more prone to the use of inappropriate methods compared to more recent ones (frequency of inappropriate methods in 4-year intervals: 0%, 42.9%, 88.9%, 58.3%, and 41.7%). In contrast to these two categories, evolutionary genetics, antimicrobial resistance, and stress-induced mutagenesis exhibited a clearly lower prevalence (albeit still substantial) of inappropriate methods’ usage (20%, 20%, and 28.6%, respectively), potentially indicating greater familiarity and openness to using quantitative and computational methods among researchers in these areas.

3.3. Impact Factor Fails to Predict Inappropriate Method Usage

Lastly, we asked whether the use of inappropriate methods correlates with journal visibility and reputation. Inappropriate methods may be more commonly expected in lower-tier journals, since higher-ranked journals should be exposed to higher levels of scrutiny both during peer review and post-publication. Alternatively, technical details may go unnoticed in the broad, large studies typically published in top-tier multidisciplinary journals. We observed that genotoxicity studies using the Ames test and, thus, non-fluctuation methods, tend to exhibit the lowest impact factors across all the categories considered (Figure 2b, red boxplot). However, when we exclude the Ames test category from the analysis and focus on the remaining studies using arithmetic mean or median methods (Figure 2a, orange boxplot), we find that these inappropriate methods demonstrate no discernible pattern of association with impact factors. Indeed, the results show that inappropriate methods are pervasive across a wide range of impact factors, ranging from 0.4 to 63.8, spanning various topic breadth levels, from niche-specific to multidisciplinary (Figure 2b). Remarkably, we found that inappropriate methods were relatively common in journals with high impact factors (IF > 10), accounting for up to 29.4% of all cases across categories, and we even identified one instance of their use in a top-tier journal (IF > 30). While limited in number, these observations highlight the fact that the increased visibility of these venues may not necessarily prevent the use of subpar statistical tools. Finally, another noteworthy observation is that the use of the most advanced methods was not associated with either lower- or higher-tier journals: the fact that many articles in lower-tier journals use the best-in-field computational methods can be seen as a testament to how readily available and easy to use the new tools have made these methods for experimentalists.

4. Conclusions

Theoreticians have developed numerous methods to estimate mutation rates from the characteristically fluctuating data obtained through the Luria–Delbrück fluctuation test [8]. Over the last two decades, the release of user-friendly computational tools has facilitated the availability of the most advanced methods, promising greater accuracy, efficiency, and adaptability in various scenarios beyond the standard assumptions [21,24]. As a consequence of these advancements, here, we asked whether experimentalists have generally adopted these best-in-field methods or, at the very least, have abandoned the use of long-dismissed, inappropriate methods such as the arithmetic mean. Our analyses of 140 manually curated articles that reported conducting fluctuation tests with bacteria reveals interesting trends and factors in this regard. We observed that the use of inappropriate methods is still commonplace, although certain sub-fields suffer from more prevalence than others (e.g., genotoxicity vs. evolutionary genetics, 88.9% vs. 20%, respectively). Of note, we detected the use of inappropriate methods even in top-tier journals, although, in general, our results suggest that the presumed level of scrutiny, both pre- and post-publication, bears no influence on the quality of the methods used to conduct fluctuation tests for bacteria. Nevertheless, we noticed a clear and promising trend towards the increased adoption of the most advanced methods, likely driven by the accessibility and user-friendliness of computational tools that facilitate the most efficient utilization of fluctuation data. In conclusion, experimentalists are gradually embracing the most accurate, efficient, and versatile methods, although further efforts are needed to promote their widespread usage across research fields.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/axioms12121100/s1, Table S1: Advanced computational tools for mutation rate estimation; Table S2: Google Scholar query inputs and corresponding number of hits per search; Table S3: References [38,39,40,41,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178] are cited in the Supplementary Materials: List of articles used in this work.

Author Contributions

Conceptualization, A.C. and G.A.D.; methodology, G.A.D.; software, G.A.D.; validation, A.C. and G.A.D.; formal analysis, G.A.D.; investigation, G.A.D.; resources, A.C.; data curation, G.A.D.; writing—original draft preparation, G.A.D. and A.C.; writing—review and editing, A.C. and G.D; visualization, G.A.D.; supervision, A.C.; project administration, A.C.; funding acquisition, A.C. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Agencia Estatal de Investigación (Proyectos de I+D+i, PID2019-110992GA-I00; Centros de Excelencia “Severo Ochoa”, SEV-2016-0672), and a Comunidad de Madrid “Talento” Fellowship (2019-T1/BIO-12882).

Data Availability Statement

All data presented in this study are contained within the article or supplementary materials.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Temporal trends in the use of different statistical methods to evaluate the Luria–Delbrück fluctuation test in bacteria. Stacked areas depict the proportion of the selected studies employing specific methods or method families. The Y-axis represents the cumulative number of articles, while the X-axis displays five 4-year time periods. The two lower layers (red colors) indicate non-fluctuation methods, such as the median or the arithmetic mean, which have long been recognized as inappropriate for analyzing fluctuation data. Within this group, the lowest layer denotes articles reporting the use of the Ames test for mutagenesis assessment (dark red). The upper layers (in increasingly darker shades of blue) represent appropriate methods that explicitly address the phenomenon of fluctuation. Among these, in ascending order, we distinguish between classic, formula-based methods and computational-based methods (MSS-MLE: Ma–Sandri–Sarkar maximum likelihood estimator method; NR-MLE: Newton–Raphson maximum likelihood estimator method; GF: generating function method). See text for details on the different methods. The plot was generated using R version 3.6.1 with the “ggplot2” and “dplyr” libraries.
Figure 1. Temporal trends in the use of different statistical methods to evaluate the Luria–Delbrück fluctuation test in bacteria. Stacked areas depict the proportion of the selected studies employing specific methods or method families. The Y-axis represents the cumulative number of articles, while the X-axis displays five 4-year time periods. The two lower layers (red colors) indicate non-fluctuation methods, such as the median or the arithmetic mean, which have long been recognized as inappropriate for analyzing fluctuation data. Within this group, the lowest layer denotes articles reporting the use of the Ames test for mutagenesis assessment (dark red). The upper layers (in increasingly darker shades of blue) represent appropriate methods that explicitly address the phenomenon of fluctuation. Among these, in ascending order, we distinguish between classic, formula-based methods and computational-based methods (MSS-MLE: Ma–Sandri–Sarkar maximum likelihood estimator method; NR-MLE: Newton–Raphson maximum likelihood estimator method; GF: generating function method). See text for details on the different methods. The plot was generated using R version 3.6.1 with the “ggplot2” and “dplyr” libraries.
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Figure 2. Factors influencing the use of different statistical methods to evaluate the Luria–Delbrück fluctuation test for bacteria. (a) The heatmap depicts the abundance of articles based on research topics and the methods used, out of a total of 140 articles. The Y-axis categories represent the five major research topics that emerged from our analyses, while the X-axis categories represent four classes of methods for analyzing fluctuation test data. The color code indicates method appropriateness, with the two leftmost columns representing inappropriate methods (ranging from white to red) and the two rightmost columns representing appropriate methods (ranging from white to blue). Darker shades of red or blue indicate a higher prevalence of articles utilizing inappropriate or appropriate methods, respectively. Plot generated using R version 3.6.1 with the library “ggplot2” and “cowplot”. (b) Boxplots represent the distribution of impact factors (IFs) for 140 analyzed articles grouped based on the methods used. The Y-axis displays IF values, a proxy for article visibility, while the X-axis presents four major method classes for fluctuation test data analysis. Color coding follows the convention of previous plots (i.e., red for inappropriate methods and blue for appropriate methods). The plot was generated using R version 3.6.1 with the library “ggplot2” and “ggthemes”.
Figure 2. Factors influencing the use of different statistical methods to evaluate the Luria–Delbrück fluctuation test for bacteria. (a) The heatmap depicts the abundance of articles based on research topics and the methods used, out of a total of 140 articles. The Y-axis categories represent the five major research topics that emerged from our analyses, while the X-axis categories represent four classes of methods for analyzing fluctuation test data. The color code indicates method appropriateness, with the two leftmost columns representing inappropriate methods (ranging from white to red) and the two rightmost columns representing appropriate methods (ranging from white to blue). Darker shades of red or blue indicate a higher prevalence of articles utilizing inappropriate or appropriate methods, respectively. Plot generated using R version 3.6.1 with the library “ggplot2” and “cowplot”. (b) Boxplots represent the distribution of impact factors (IFs) for 140 analyzed articles grouped based on the methods used. The Y-axis displays IF values, a proxy for article visibility, while the X-axis presents four major method classes for fluctuation test data analysis. Color coding follows the convention of previous plots (i.e., red for inappropriate methods and blue for appropriate methods). The plot was generated using R version 3.6.1 with the library “ggplot2” and “ggthemes”.
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Devin, G.A.; Couce, A. Trends in the Use of Proper Methods for Estimating Mutation Rates in Fluctuation Experiments. Axioms 2023, 12, 1100. https://doi.org/10.3390/axioms12121100

AMA Style

Devin GA, Couce A. Trends in the Use of Proper Methods for Estimating Mutation Rates in Fluctuation Experiments. Axioms. 2023; 12(12):1100. https://doi.org/10.3390/axioms12121100

Chicago/Turabian Style

Devin, Guillem A., and Alejandro Couce. 2023. "Trends in the Use of Proper Methods for Estimating Mutation Rates in Fluctuation Experiments" Axioms 12, no. 12: 1100. https://doi.org/10.3390/axioms12121100

APA Style

Devin, G. A., & Couce, A. (2023). Trends in the Use of Proper Methods for Estimating Mutation Rates in Fluctuation Experiments. Axioms, 12(12), 1100. https://doi.org/10.3390/axioms12121100

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