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A comparison of single-cell trajectory inference methods


Trajectory inference approaches analyze genome-wide omics data from thousands of single cells and computationally infer the order of these cells along developmental trajectories. Although more than 70 trajectory inference tools have already been developed, it is challenging to compare their performance because the input they require and output models they produce vary substantially. Here, we benchmark 45 of these methods on 110 real and 229 synthetic datasets for cellular ordering, topology, scalability and usability. Our results highlight the complementarity of existing tools, and that the choice of method should depend mostly on the dataset dimensions and trajectory topology. Based on these results, we develop a set of guidelines to help users select the best method for their dataset. Our freely available data and evaluation pipeline ( will aid in the development of improved tools designed to analyze increasingly large and complex single-cell datasets.

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Data availability

The processed real and synthetic datasets used in this study are deposited on Zenodo (

The main analysis repository is available at and is divided into several experiments. Every experiment has its own set of scripts and results, each accompanied by an illustrated readme that can be browsed and explored on the Github website.

Code availability

The analysis scripts call several other R packages, of which an overview is available at These packages include dynwrap, used to wrap the output of methods into the common trajectory model, dyneval, which contains the evaluation metrics, dynguidelines, the guidelines app, and dynplot for plotting trajectories.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


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We would like to thank the original authors of the methods for their feedback and improvements on the method wrappers. This study was supported by the Fonds Wetenschappelijk Onderzoek (R.C., 11Y6218N and W.S., 11Z4518N) and BOF (Ghent University, H.T.). Y.S. is an ISAC Marylou Ingram scholar.

Author information

R.C., W.S., H.T. and Y.S. designed the study. R.C. and W.S. performed the experiments and analyzed the data. W.S., R.C. and H.T. implemented software packages. R.C., W.S., Y.S. and H.T. prepared the manuscript. Y.S. supervised the project.

Competing interests

The authors declare no competing interests.

Correspondence to Yvan Saeys.

Integrated supplementary information

  1. Supplementary Figure 1 A common interface for TI methods.

    (a) The input and output of each TI method is standardized. As input, each TI method receives either raw or normalized counts, several parameters, and a selection of prior information. After its execution, a method uses one of the seven wrapper functions to transform its output to the common trajectory model. This common model then allows to perform common analysis functions on trajectory models produced by any TI method. (b) Illustrations of the specific transformations performed by each of the wrapper functions.

  2. Supplementary Figure 2 Results from the evaluation, for all methods and across all evaluation criteria.

    (a) We characterized the methods according to the wrapper type, their required priors, whether the inferred topology is constrained by the algorithm (fixed) or a parameter (param), and the types of inferable topologies. The methods are grouped vertically based on the most complex trajectory type they can infer. (b) The overall results of the evaluation on four criteria: benchmarking using a reference trajectory on real and synthetic data, scalability with increasing number of cells and features, stability across dataset subsamples, and quality of the implementation. (c) Accuracy of trajectory inference methods across metrics, dataset sources and dataset trajectory types. The performance of a method is generally more stable across dataset sources, but very variable depending on the metric and trajectory type. (d) Predicted execution times and memory usage for varying numbers of cells and features (# cells × # features). Predictions were made by training a regression model after running each method on bootstrapped datasets with varying numbers of cells and features. (e) Stability results by calculating the average pairwise similarity between models inferred across multiple runs of the same method. (f) Usability scores of the tool and corresponding manuscript, grouped per category.

  3. Supplementary Figure 3 Accuracy of trajectory inference methods.

    (a) Overall score for all methods across 339 datasets, colored by the source of the datasets. Black line indicates the mean. (b) Similarity between the overall scores of all dataset sources, compared to real datasets with a gold standard, across all methods (n = 46, after filtering out methods that errored too frequently). Shown in the top left is the Pearson correlation. (c) Bias in the overall score towards trajectory types for all methods across 339 datasets. Black line indicates the mean. (d) Distributions of the difference in size between predicted and reference topologies. A positive difference means that the topology predicted by the method is more complex than the one in the reference.

  4. Supplementary Figure 4 Scalability of trajectory inference methods.

    (a) Three examples of average observed running times across five datasets (left) and the predicted running time (right). (b) Overview of the scalability results of all methods, ordered by their average predicted running time from (a). We predicted execution times and memory usage for each method with increasing number of features or cells, and used these values to classify each method into sublinear, linear, quadratic and superquadratic based on the shape of the curve.

  5. Supplementary Figure 5 Agreement between actual values and predictions for execution times and memory usage.

    We created a predictive model of the running time and memory usage based on a set of scaling datasets (left), and validated this model based on the similarity of the predictions and actual values on all benchmark datasets (right). Shown are the values for each method and dataset (n = 65618 for training, n = 11939 for test). Top left indicates the Pearson correlation coefficient.

  6. Supplementary Figure 6 Usability of trajectory inference methods.

    Shown is the score given for each method on every item from the usability score sheet (Supplementary Table 3). Each aspect of the quality control was part of a category, and each category was weighted so that it contributed equally to the final quality score. Within each category, each aspect also received a weight depending on how often it was mentioned in a set of papers discussing good practices in tool development and evaluation. This is represented in the plot as the height on the y-axis. Top: Average usability score for each method. Right: The average score of each quality control item. Shown into more detail are those items which had an average score lower than 0.5.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–6 and Supplementary Notes 1 and 2

  2. Reporting Summary

  3. Supplementary Table 1

    Overview of available trajectory inference tools, and whether they were included in this study.

  4. Supplementary Table 2

    Overview of the real datasets used in this study.

  5. Supplementary Table 3

    Scoring sheet for assessing usability of trajectory inference methods. Each quality aspect was given a weight based on how many times it was mentioned in a set of articles discussing best practices for tool development.

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About this article

Fig. 1: Overview of several key aspects of the evaluation.
Fig. 2: A characterization of the 45 methods evaluated in this study and their overall evaluation results.
Fig. 3: Detailed results of the four main evaluation criteria: accuracy, scalability, stability and usability.
Fig. 4: Complementarity between different trajectory inference methods.
Fig. 5: Practical guidelines for method users.
Fig. 6: Demonstration of how a common framework for TI methods facilitates broad applicability using some example datasets.
Supplementary Figure 1: A common interface for TI methods.
Supplementary Figure 2: Results from the evaluation, for all methods and across all evaluation criteria.
Supplementary Figure 3: Accuracy of trajectory inference methods.
Supplementary Figure 4: Scalability of trajectory inference methods.
Supplementary Figure 5: Agreement between actual values and predictions for execution times and memory usage.
Supplementary Figure 6: Usability of trajectory inference methods.