# Chemical-Mediated Microbial Interactions Can Reduce the Effectiveness of Time-Series-Based Inference of Ecological Interaction Networks

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Models

#### 2.2. Effective Interaction Matrix

#### 2.3. Data Preparation

#### 2.4. Network Inference Methods

#### 2.4.1. Pearson and Spearman Correlation Coefficient

#### 2.4.2. Local Similarity Analysis (LSA)

#### 2.4.3. Convergent Cross Mapping (CCM)

#### 2.4.4. LIMITS

#### 2.5. Evaluation

#### 2.6. Software

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Implementation of CCM for Network Inference

## Appendix B. Basic Characteristics of Communities

**Figure A1.**Basic characteristics of the communities we used for the evaluation. The black line indicates median, the box edges indicate first and third quartile values, and whiskers indicate maximum and minimum values. (

**a**) The number of major species, (

**b**) Simpson’s diversity index, (

**c**) connectance of effective interaction matrix, and (

**d**) coefficient of variation.

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**Figure 2.**Performance of network inference methods for different models (

**left**) and the comparison of the different pairs of model and method (

**right**) for $\tau =1$ and $\sigma =1$. (

**a**,

**b**) ROC-AUC of networks inferred by the statistics and p-values of each method, respectively, and (

**c**,

**d**) precision ($c=0.5$) of networks inferred by the statistics and p-values of each method, respectively. In the box plot, white lines indicate the median, box edges indicate the first and third quartile value, and whiskers indicate maximum and minimum values. The heatmap on the right side of each panel aids in comparison between the different pairs of models/methods. The value of a cell is obtained by subtracting the median of the pair of models/method in a column from the same value of the pair in a row. Black dots indicate that the difference is significant ($p<0.05$) based on Mann–Whitney test. We compared the performance of the different methods applied to the same model, and we compared the performance when the condition of competition was the same but the property of the interaction was different (M and D or M′ and D′) and when the property of the interaction was the same but the condition of competition was different (M and M′ or D and D′).

**Table 1.**Model parameters. Here, ${u}_{p}\left(x,y\right)$ means that the numbers are randomly drawn from a uniform distribution between $x$ and $y$ with probability p, and otherwise zero.

Description | Value | |
---|---|---|

n | Number of microbes | 10 |

m | Number of chemicals | 5 |

$K$ | Carrying capacity | 1 |

$\delta $ | Dilution rate | 0.01 |

${r}_{i}$ | Growth rate | ${u}_{1}\left(0.05,0.5\right)$ |

${\mathsf{\kappa}}_{ik}$ | Half-saturation density | ${u}_{1}\left(0.5,1.5\right)\times {10}^{-3}$ |

${\rho}_{ik}{}^{+}$ | Positive effect of chemicals on microbes | ${u}_{0.2}\left(0.05,0.5\right)$ |

${\rho}_{ik}{}^{-}$ | Negative effect of chemicals on microbes | ${u}_{0.2}\left(0.05,0.5\right)$ |

${\alpha}_{ki}$ | Maximum consumption rate of chemicals | ${u}_{0.2}\left(0.5,1.5\right)$ |

${\beta}_{ki}$ | Production rate of chemicals | ${u}_{0.2}\left(0.05,0.15\right)$ |

$\u03f5$ | Influx of microbes | ${10}^{-7}$ |

Name | Description | Value |
---|---|---|

N | Number of time series in a data set | 288 |

${M}_{p}$ | Number of pairs in each generation | 32 |

${m}_{p}$ | Number of parents for next generation | 4 |

${t}_{max}$ | Length of time series generated by simulation | 10,000 |

${t}_{0}$ | Length of time series discarded as the initial transient | $2000$ |

${T}_{max}$ | Number of iterations of the optimization procedure | 60 (for M and D) 120 (for M′ and D′) |

$\eta $ | Criterion for major species | ${10}^{-2}$ |

$\omega $ | Threshold value for the evaluation function | 5 |

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**MDPI and ACS Style**

Suzuki, K.; Abe, M.S.; Kumakura, D.; Nakaoka, S.; Fujiwara, F.; Miyamoto, H.; Nakaguma, T.; Okada, M.; Sakurai, K.; Shimizu, S.;
et al. Chemical-Mediated Microbial Interactions Can Reduce the Effectiveness of Time-Series-Based Inference of Ecological Interaction Networks. *Int. J. Environ. Res. Public Health* **2022**, *19*, 1228.
https://doi.org/10.3390/ijerph19031228

**AMA Style**

Suzuki K, Abe MS, Kumakura D, Nakaoka S, Fujiwara F, Miyamoto H, Nakaguma T, Okada M, Sakurai K, Shimizu S,
et al. Chemical-Mediated Microbial Interactions Can Reduce the Effectiveness of Time-Series-Based Inference of Ecological Interaction Networks. *International Journal of Environmental Research and Public Health*. 2022; 19(3):1228.
https://doi.org/10.3390/ijerph19031228

**Chicago/Turabian Style**

Suzuki, Kenta, Masato S. Abe, Daiki Kumakura, Shinji Nakaoka, Fuki Fujiwara, Hirokuni Miyamoto, Teruno Nakaguma, Mashiro Okada, Kengo Sakurai, Shohei Shimizu,
and et al. 2022. "Chemical-Mediated Microbial Interactions Can Reduce the Effectiveness of Time-Series-Based Inference of Ecological Interaction Networks" *International Journal of Environmental Research and Public Health* 19, no. 3: 1228.
https://doi.org/10.3390/ijerph19031228