# Drosophila Wing Integration and Modularity: A Multi-Level Approach to Understand the History of Morphological Structures

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples and Shape Analyses

#### 2.2. Measurement Error

#### 2.3. Comparative Analysis

#### 2.4. Multi-Levels Approach

- Static Level: This is basically the level of variation among individuals in a consistent sample, where all individuals belong to the same species and ontogenetic phase [4]. For this level, integration and modularity patterns were studied by examining the variation patterns derived from the pooled within species and sex covariance matrix of wing shape.
- Developmental Level: This level arises from the interactions between developmental processes that generate different traits, and hence produce covariation between them [4]. Covariation arises as result of the processes that generated the morphological structures under study, and it is therefore possible, within certain boundaries, to use morphological covariation to infer how the traits interact developmentally. The study of FA is an effective manner to remove genetic and environmental variation among individuals [3], as the left and right sides of an structure share the same genome and almost the same environmental circumstances, hence the differences between the sides can be assumed to be derived from random fluctuations during the developmental process [3,32,37,38]. Therefore, we used the covariance matrix of fluctuating asymmetry to analyse developmental level integration (i.e., this will allow us to study directly the intrinsic, developmental component of integration and modularity). It is important to keep in mind that the calculation of the FA is provided by the ANOVAs for shape considering individual and side effects, and the interaction between them. The MS related to the individual effect was used as an estimator of individual variation, and the MS related to the interaction (individual x side) as an estimator of FA.
- Evolutionary Level: Covariation among evolutionary changes in different features, arise from several processes including drift, mutation, selection and gene flow [4]. To study evolutionary integration and modularity a comparative approach is required to consider the phylogenetic structure of the data. Consequently, morphological integration and modularity across Drosophila species can be assessed by studying the relations between shape features and the evolutionary changes along the branches of the phylogeny.

#### 2.5. Integration

#### 2.6. Modularity

#### 2.7. Allometry

#### 2.8. Comparison within Levels

## 3. Results

#### 3.1. Static Level

#### 3.2. Developmental Level

#### 3.3. Evolutionary Level

#### 3.4. Comparison within Levels

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dorsal view of Drosophila wing morphology showing the 15 landmarks used to characterize its shape. The dotted line indicates the boundary between the anterior (red) and posterior (blue) compartments.

**Figure 3.**Percentages of total shape variation and overall structure integration by principal component (PCA) using covariance matrices (CM) of: (

**A**) CM pooled within-species (

**B**) CM of fluctuating asymmetry, (

**C**) CM of shape independent contrasts.

**Figure 4.**Modularity hypotheses at different integration levels comparing the covariation between anterior and posterior compartments of the wing. (

**A**) Static RV coefficient, (

**B**) Developmental RV coefficient, (

**C**) Evolutionary RV coefficient, (

**D**) Static CR coefficient, (

**E**) Developmental CR coefficient (

**F**) Evolutionary CR coefficient. The arrows indicate the RV and CR coefficient between the anterior and posterior compartments, and the histograms represent the distribution of coefficients for the alternative landmark partitions.

**Figure 5.**Patterns of wing shape variation associated with the PCs at different levels: (

**A**) Static Integration by the covariance matrix of shape pooled by species, (

**B**) Developmental integration using the covariance matrix of fluctuating asymmetry and (

**C**) Evolutionary integration using the covariance matrix of the independent contrasts of shape. PC1 and PC2 are shown and the figures to the left and right correspond to the shape for each PC score with a magnitude of −0.1 and +0.1, respectively.

**Figure 6.**Patterns of wing shape covariation between anterior and posterior compartment associated with the PLS axis at different levels. (

**A**) Static Integration by the covariance matrix of shape pooled by species, (

**B**) Developmental integration using the covariance matrix of fluctuating asymmetry and (

**C**) Evolutionary integration using the covariance matrix of the independent contrasts of shape. PLS1 and PLS2 are shown and the figures to the left and right show the shape for a PLS score with a magnitude of −0.1 and +0.1, respectively.

**Table 1.**Measurement error Procrustes ANOVA for both Drosophila’s wing centroid size and shape, characterised by matching symmetry.

Centroid Size | |||||||
---|---|---|---|---|---|---|---|

Effect | SS | MS | df | F | p | Pillai tr. | p (param) |

Individual | 11.478684 | 0.604141 | 19 | 1466.1 | <0.0001 | ||

Side | 0.001664 | 0.001664 | 1 | 4.04 | 0.0589 | ||

Ind × Side | 0.007829 | 0.000412 | 19 | 3.07 | 0.0014 | ||

Error 1 | 0.005366 | 0.000134 | 40 | ||||

Shape | |||||||

Effect | |||||||

Individual | 0.1654094 | 3.35 × 10^{−4} | 494 | 52.68 | <0.0001 | ||

Side | 0.0001051 | 4.04 × 10^{−6} | 26 | 0.64 | 0.919 | ||

Ind × Side | 0.0031397 | 6.36 × 10^{−6} | 494 | 9.67 | <0.0001 | 13.14 | <0.0001 |

Error 1 | 0.0006835 | 6.57 × 10^{−7} | 1040 |

**Table 2.**Principal component analysis between three levels of variation: Static (pooled by species), fluctuating asymmetry, and evolutionary, with their corresponding values after allometry correction (A). The table values are the eigenvalues and percentages of total variance for the first three PCs accounts.

Eigenvalues | % Total Variance | ||||||
---|---|---|---|---|---|---|---|

Level of Integation | PC1 | PC2 | PC3 | PC1 | PC2 | PC3 | Cumulative |

Static | 0.00004798 | 0.00003807 | 0.00002962 | 21.103 | 16.744 | 13.025 | 50.872 |

Developmental | 0.00002477 | 0.00001866 | 0.00001616 | 15.019 | 11.312 | 9.801 | 36.132 |

Evolutionary | 0.00023655 | 0.00010357 | 0.00006316 | 41.987 | 18.383 | 11.21 | 71.58 |

Static (A) | 0.00003817 | 0.00003626 | 0.00002842 | 17.94 | 17.043 | 13.356 | 48.339 |

Developmental (A) | 0.00002467 | 0.00001808 | 0.00001603 | 15.09 | 11.055 | 9.808 | 35.953 |

Evolutionary (A) | 0.00020041 | 0.00009249 | 0.00005925 | 39.558 | 18.256 | 11.695 | 69.509 |

**Table 3.**Angular comparison between the vectors of first three PC’S and PLS’s between different levels of variation.

Static Integration | Angular Value |
---|---|

PC1-PLS1 | 16.675° |

PC2-PLS2 | 29.974° |

PC3-PLS3 | 28.923° |

Developmental Integration | |

PC1-PLS1 | 19.868° |

PC2-PLS2 | 61.799° |

PC3-PLS3 | 66.981° |

Evolutionary Integration | |

PC1-PLS1 | 7.297° |

PC2-PLS2 | 17.697° |

PC3-PLS3 | 27.616° |

**Table 4.**Matrix correlation between the different covariance matrices at different levels of variation: A: Static Integration by the covariance matrix of shape pooled by species, B: Developmental integration using the covariance matrix of fluctuating asymmetry and C: Evolutionary integration using the covariance matrix of the independent contrast of shape.

Matrix Correlation/p-Value | Developmental Integration | Evolutionary Integration |
---|---|---|

Static Integration | 0.95038357 | 0.85631863 |

Developmental Integration | - | 0.74279388 |

Matrix Correlation/p-Value | Developmental Integration | Evolutionary Integration |

Static Integration | <0.0001 | <0.0001 |

Developmental Integration | - | <0.0001 |

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Benítez, H.A.; Püschel, T.A.; Suazo, M.J. *Drosophila* Wing Integration and Modularity: A Multi-Level Approach to Understand the History of Morphological Structures. *Biology* **2022**, *11*, 567.
https://doi.org/10.3390/biology11040567

**AMA Style**

Benítez HA, Püschel TA, Suazo MJ. *Drosophila* Wing Integration and Modularity: A Multi-Level Approach to Understand the History of Morphological Structures. *Biology*. 2022; 11(4):567.
https://doi.org/10.3390/biology11040567

**Chicago/Turabian Style**

Benítez, Hugo A., Thomas A. Püschel, and Manuel J. Suazo. 2022. "*Drosophila* Wing Integration and Modularity: A Multi-Level Approach to Understand the History of Morphological Structures" *Biology* 11, no. 4: 567.
https://doi.org/10.3390/biology11040567