# Morphometric Analysis of Surface Utricles in Halimeda tuna (Bryopsidales, Ulvophyceae) Reveals Variation in Their Size and Symmetry within Individual Segments

^{*}

## Abstract

**:**

_{3}content within segments.

## 1. Introduction

_{3}precipitation.

_{3}tissue content among species [3,4]. It has been observed that taxa with larger primary utricles and longer lateral adhesion layer tend to be less calcified than species with smaller utricles and comparatively short lateral adhesion layer, resulting in a shorter diffusion pathway for dissolved ions between the interutricular spaces and the external environment [4].

## 2. Materials and Methods

#### 2.1. Sampling and Microscopy of Segments

#### 2.2. Morphometric Analysis of Surface Utricles

^{th}-order cyclic symmetry [18,21].

_{n}symmetry group of a single n-gon, with its size normalized to unitary length of the longest distance from any vertex to the center of mass [17], is created by sequential rotation of its vertices around the center of mass of this configuration by an angle corresponding to 2*pi*i/n radians, where i varies from 1 to n (Figure 1d). The points are averaged and unfolded by inverted sequential rotation to a regular n-gon. The CSM is then defined as:

_{i}represents individual vertices of each polygon and a CSM value of 0.0 corresponds to the perfectly regular n-gon; while an increase in polygon asymmetry leads to a corresponding CSM increase, approximating a value of 1.0 in extremely asymmetric configurations [21].

_{n}of each of the analyzed n-gons was carried out using the function procGPA implemented in the package shapes, version 1.2.5 [23], of the R software, version 3.5.1. This widely used procedure transforms the original coordinates of the n-gons which represented the cyclic symmetry group C

_{n}of a single analyzed polygon to an optimal registration using translation, rotation, and scaling to a unitary centroid size. The consensus configuration representing the mean values of n vertices is necessarily a regular polygon with n vertices. The residual distances among individual elements of the symmetry group represent their shape differences. The Procrustes distances (PDs) between the original configurations of the analyzed polygons and the mean shapes produced by the GPA of their cyclic symmetry group were then used as the measure of their shape asymmetry. It should be mentioned that the evaluation of PDs among the configurations formed by the complete cyclic symmetry group is closely related to CSM [24]. Therefore, we expected these measures to yield very similar results.

#### 2.3. Statistical Analysis of Utricle Parameters

#### 2.4. Morphometric Analysis of Segments

## 3. Results

#### 3.1. Correlation among Utricle Parameters

#### 3.2. Utricle Size

#### 3.3. Utricle Symmetry

#### 3.4. Number of Polygon Vertices of Utricle Shapes

#### 3.5. Morphology of Segments and Their Relation to Utricle Size and Symmetry

^{2}= 0.108, p = 0.036). Although the p-value of this relationship proved to be above the Bonferroni-corrected threshold, the area of utricles in the basal position was the single most important explanatory factor with regard to the shape of the analyzed segments (Table S5). The segments with relatively small utricles in their basal parts tended to have more reniform shapes, while these located on the opposite side of this model had relatively narrower and inversely conic shapes (Figure 4c).

## 4. Discussion

_{3}content in their segments [3,4]. Thus, it is conceivable that different parts of H. tuna segments may also reach different calcification levels. Such a hypothesis could be tested by a detailed analysis of CaCO

_{3}gradients within segments; preferably those with relatively large size, as our analyses showed that the within-segment utricle size gradient was considerably more pronounced in relatively large segments. These segments usually have discoid to reniform shapes, which are considered “typical” for Mediterranean H. tuna [1,2,38]. Conversely, the analyses showed that smaller segments with shapes considered deviant from the species-specific template that more often occur in lower portions of Halimeda thalli [7] had a considerably less pronounced gradient in surface utricle area. However, it should be noted that this might have also been related to the fact that the actual spatial distance among the bottom, center, and marginal locations was smaller in these segments, rather than to their shape differences from the considerably larger reniform segments.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Morphology of Mediterranean H. tuna and surface views of the peripheral utricles: (

**a**) a single branch of H. tuna consisting of four mature segments and one developing protosegment in the apical position. Note that only the mature segments were used in subsequent morphometric analyses. Scale bar = 5 mm; (

**b**) segment with five positions selected for the analyses of surface utricles, depicted as: B—bottom, C—centre, T—top, L—left, R—right. Scale bar = 1 mm; (

**c**) microphotograph showing surface views of peripheral utricles. Vertices of a single polygon are depicted. Scale bar = 75 µm; (

**d**) 6th-order cyclic symmetry group of the same polygon depicted in (c). The vertices of this size-normalized hexagon are sequentially rotated around the center of mass of this configuration by 2*pi*i/6 radians, where i varies from 1 to 6. The continuous symmetry measure (CSM) value is the average squared distance between the original vertices and the co-ordinates of the perfectly symmetrical hexagon (depicted by black stars).

**Figure 2.**Microphotographs showing the surface views of peripheral utricles of Mediterranean H. tuna in (

**a**) bottom and (

**b**) top positions of a single segment. Scale bar = 50 µm.

**Figure 3.**Boxplots showing the differences in (

**a**) utricle area and (

**b**) polygon asymmetry among different positions on segments. Significant differences between adjacent positions are depicted as *** indicating the p-value = 0.001. The values of mean differences are included in Table 3.

**Figure 4.**Plots showing the ordination structure of segment shapes: (

**a**) two principal components describing most of the variation in segment outlines. Shapes corresponding to marginal occupied positions on both axes are shown; (

**b**) the ordination plot of PC1 vs. PC2 with the allometric line (which was reconstructed by the multivariate regression model) projected onto the ordination space. The signs “CSmin” and “CSmax” correspond to shapes typical of segments with minimum and maximum centroid size values; and (

**c**) the ordination plot of PC1 vs. PC2. The line representing the multivariate regression of segment shapes on their mean utricle area in the bottom positions projected onto the ordination space. The signs “MbUAmin” and “MbUAmax” correspond to shapes typical for segments with the minimum and maximum areas of utricles in their bottom positions.

**Figure 5.**Linear correlation between the segment size (CS) and the difference in means of utricle parameters sampled: (

**a**) at the bottom and along the lateral margins of individual segments, and (

**b**) at the bottom and in the apical parts of segments. The outline shapes of selected segments along the gradients are shown.

**Table 1.**Results of the linear correlation analyses among the utricle parameters. Pearson’s r values are shown above the diagonal, the coefficients of determination (R

^{2}) below the diagonal. Probabilities (p-values) that individual correlations are not different from zero based on the permutation tests were 0.0001 in all comparisons.

Area | CS | CSM | PDs | No. Vertices | |
---|---|---|---|---|---|

area | --- | 0.978 | 0.123 | 0.131 | 0.479 |

CS | 0.957 | --- | 0.218 | 0.220 | 0.615 |

CSM | 0.015 | 0.047 | --- | 0.971 | 0.132 |

PDs | 0.017 | 0.049 | 0.944 | --- | 0.134 |

no. vertices | 0.229 | 0.378 | 0.017 | 0.018 | --- |

**Table 2.**Results of three separate analysis of variance models evaluating the variation in surface utricle parameters of H. tuna.

Utricle area [mm^{2}] | Df | SS | MS | η^{2} | partial η^{2} | F | Z | p |

Plant | 6 | 0.00018 | 3.057 × 10^{−5} | 0.091 | 0.148 | 4.415 | 1.769 | 0.021 |

Position | 3 | 0.00044 | 1.452 × 10^{−4} | 0.217 | 0.297 | 652.88 | 6.892 | 0.001 |

Segment (plant) | 25 | 0.00017 | 6.925 × 10^{−6} | 0.086 | 0.140 | 3.377 | 3.324 | 0.001 |

Plant:position | 18 | 0.00003 | 1.402 × 10^{−6} | 0.013 | 0.028 | 6.306 | 5.337 | 0.001 |

Position:segment (plant) | 75 | 0.00015 | 2.051 × 10^{−6} | 0.077 | 0.126 | 9.225 | 12.361 | 0.001 |

Residuals | 4672 | 0.00104 | 2.220 × 10^{−7} | 0.517 | ||||

Total | 4799 | 0.00201 | ||||||

CSM | Df | SS | MS | η^{2} | partial η^{2} | F | Z | p |

Plant | 6 | 0.02199 | 0.00367 | 0.025 | 0.028 | 2.987 | 1.749 | 0.029 |

Position | 3 | 0.01034 | 0.00345 | 0.012 | 0.013 | 21.276 | 3.467 | 0.001 |

Segment (plant) | 25 | 0.03068 | 0.00123 | 0.036 | 0.039 | 2.407 | 2.609 | 0.003 |

Plant:position | 18 | 0.00451 | 0.00025 | 0.005 | 0.006 | 1.548 | 1.369 | 0.082 |

Position:segment (plant) | 75 | 0.03824 | 0.00051 | 0.044 | 0.048 | 3.146 | 6.798 | 0.001 |

Residuals | 4672 | 0.75722 | 0.00016 | 0.877 | ||||

Total | 4799 | 0.86300 | ||||||

No. polygon vertices | Df | SS | MS | η^{2} | partial η^{2} | F | Z | p |

Plant | 6 | 2.09 | 0.34894 | 0.001 | 0.001 | 1.886 | 1.098 | 0.129 |

Position | 3 | 2.55 | 0.85163 | 0.001 | 0.001 | 1.983 | 1.087 | 0.131 |

Segment (plant) | 25 | 4.63 | 0.18505 | 0.002 | 0.002 | 0.956 | −0.080 | 0.550 |

Plant:position | 18 | 3.07 | 0.17068 | 0.002 | 0.002 | 0.398 | −2.630 | 0.993 |

Position:segment (plant) | 75 | 14.52 | 0.19364 | 0.007 | 0.007 | 0.451 | −4.496 | 1.000 |

Residuals | 4672 | 2006.1 | 0.42939 | 0.987 | ||||

Total | 4799 | 2032.99 |

**Table 3.**Results of permutation tests evaluating differences in mean values of utricle polygon areas and asymmetry among different positions on segments. The observed differences in mean values are shown above the diagonal and the p-values based on 999 permutations are shown below the diagonal.

Utricle area [mm^{2}] | mean value | bottom | centre | Top | lateral |

bottom | 0.001543 | --- | 0.000458 | 0.000821 | 0.000736 |

centre | 0.002001 | 0.001 | --- | 0.000363 | 0.000278 |

top | 0.002364 | 0.001 | 0.001 | --- | 0.000085 |

lateral | 0.002279 | 0.001 | 0.001 | 0.001 | --- |

CSM | mean value | bottom | centre | top | lateral |

bottom | 0.02028 | --- | 0.00402 | 0.00006 | 0.00098 |

centre | 0.01626 | 0.001 | --- | 0.00395 | 0.00304 |

top | 0.02022 | 0.905 | 0.001 | --- | 0.00091 |

lateral | 0.01930 | 0.109 | 0.001 | 0.138 | --- |

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Neustupa, J.; Nemcova, Y.
Morphometric Analysis of Surface Utricles in *Halimeda tuna* (Bryopsidales, Ulvophyceae) Reveals Variation in Their Size and Symmetry within Individual Segments. *Symmetry* **2020**, *12*, 1271.
https://doi.org/10.3390/sym12081271

**AMA Style**

Neustupa J, Nemcova Y.
Morphometric Analysis of Surface Utricles in *Halimeda tuna* (Bryopsidales, Ulvophyceae) Reveals Variation in Their Size and Symmetry within Individual Segments. *Symmetry*. 2020; 12(8):1271.
https://doi.org/10.3390/sym12081271

**Chicago/Turabian Style**

Neustupa, Jiri, and Yvonne Nemcova.
2020. "Morphometric Analysis of Surface Utricles in *Halimeda tuna* (Bryopsidales, Ulvophyceae) Reveals Variation in Their Size and Symmetry within Individual Segments" *Symmetry* 12, no. 8: 1271.
https://doi.org/10.3390/sym12081271