Jan 27, 2026
Version 2
Systematic Method for Identifying Kinematic Sperm Subpopulations V.2
- Cindy Rivas Arzaluz1,
- María Elena Ayala Escobar2,
- Andrés Aragón Martínez3
- 1Instituto de Biotecnología, UNAM;
- 2FES Zaragoza, UNAM;
- 3FES Iztacala, UNAM
- Andrés Aragón Martínez: Correspondence [email protected];
- Laboratory of Gametes and Technological Development
External link: https://doi.org/10.1371/journal.pone.0338399
Protocol Citation: Cindy Rivas Arzaluz, María Elena Ayala Escobar, Andrés Aragón Martínez 2026. Systematic Method for Identifying Kinematic Sperm Subpopulations. protocols.io https://dx.doi.org/10.17504/protocols.io.6qpvr9e6zvmk/v2Version created by Cindy Rivas
Manuscript citation:
Juárez-Contreras NA, Rivas-Arzaluz CU, Pérez OG, Ayala ME, Aragón-Martínez A (2025) Development of an open-hardware semen homogenizer and application to serotonin effects on sperm motility. PLOS One 20(12). doi: 10.1371/journal.pone.0338399
License: This is an open access protocol distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Protocol status: Working
We use this protocol and it's working
Created: January 27, 2026
Last Modified: January 27, 2026
Protocol Integer ID: 241663
Keywords: CASA system, kinematic sperm subpopulations, dataset, identifying kinematic sperm subpopulation, kinematic sperm subpopulations the identification, assisted sperm analysis, kinematic sperm subpopulation, kinematic sperm subpopulations in boar sperm data, processing of motility parameter dataset, boar sperm data, sperm within each subpopulation, motility parameter dataset, sperm, motility parameter, sperm cell, kinematic subpopulation, using principal component analysis, principal component analysis, number of motility parameter, motility parameter value, amplitude of lateral head displacement, principal component, pca, lateral head displacement, various statistical approach, identification process, curvilinear velocity
Funders Acknowledgements:
UNAM-PAPIIT
Grant ID: IN224925
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Abstract
The identification of kinematic sperm subpopulations typically relies on motility parameter values obtained using a Computer-Assisted Sperm Analysis (CASA) system. These parameters are calculated individually for each sperm cell. The number of motility parameters provided depends on the specific CASA system manufacturer. However, commonly evaluated parameters include curvilinear velocity (VCL), average path velocity (VAP), straight-line velocity (VSL), linearity (LIN), straightness (STR), beat cross-frequency (BCF), wobble (WOB), and amplitude of lateral head displacement (ALH).
Various statistical approaches utilize the motility parameter values generated by a CASA system to identify kinematic sperm subpopulations (Martínez-Pastor et al., 2011; Ramón and Martínez-Pastor, 2018). This identification process is typically carried out in two stages. In the first stage, the dataset’s dimensionality is reduced using principal component analysis (PCA). In PCA, components with eigenvalues greater than 1 are retained. In the second stage, these principal components are used as input for clustering algorithms, such as K-means or hierarchical agglomerative clustering.
When employing hierarchical agglomerative clustering, the objective is to group data points based on their proximity to one another while maximizing the separation between groups. This is typically achieved using various distance metrics, with Euclidean distance being the most commonly applied. Selecting the appropriate number of clusters is critical and often involves the use of an objective criterion, such as inertia gain. Graphical analysis of inertia gain can be particularly helpful in this context.
In this document, we present the strategy and procedure for identifying kinematic sperm subpopulations in boar sperm data subjected to different pH conditions (Rivas et al., 2022). The proposed workflow enables the processing of motility parameter datasets obtained via a CASA system to identify kinematic subpopulations in two systematic steps. The final output is a dataset containing the original input data alongside an additional column indicating the cluster assignment for each data point. This resulting dataset facilitates the determination of the proportion of sperm within each subpopulation and allows for assessing the effects of different treatments on these subpopulations.
Guidelines
The dataset used in this workflow is a dataframe consisting of 11,620 rows of data. The file is called motility_results_ph.csv and will be stored in an object named mr. However, for the purposes of this document, a sample of 500 rows will be used.
Object mr:
- Object Type: Data frame
- Number of Rows: 11,620
- Number of Variables: 11
- Description of Variables:
1. ID1 (Factor with 75 levels): A unique identifier that represents date and number of video. Examples of values include "220219-1", "220219-10", etc.
2. ID2 (Factor with 5 levels): Each level is a value of pH ("pH.70", "pH.74", etc.)
3. ID3 (Factor with 6 levels): Each level is the name of a semental ("balder", "berthrand", etc.)
4. VCL (num): Curvilinear Velocity, a measure of velocity along a curved path.
5. VAP (num): Average Path Velocity, the velocity calculated along a smoothed path.
6. VSL (num): Straight Line Velocity, velocity between two points in a straight line.
7. LIN (num): Linearity of movement, calculated as VSL/VCL. It is a value between 0 and 1.
8. STR (num): Straightness of movement, calculated as VSL/VAP. Also a value between 0 and 1.
9. WOB (num): Wobble, a measure of the oscillation of the movement, calculated as VAP/VCL.
10. BeatCross (num): Beat Cross Frequency, the frequency with which the trajectory crosses the midpoint reference.
11. ALH (num): Amplitude of Lateral Head displacement, a measure of lateral movement of head.
Before start
Libraries:
To replicate the procedure presented in this document, ensure that the FactoMineR and dplyr libraries are installed. These can be downloaded and installed directly in R if not already available: https://cran.r-project.org/
Data:
Download the dataset 230819_pluginnuevo3.tab and save it to your working directory. The dataset is available at https://dataverse.harvard.edu (https://doi.org/10.7910/DVN/CRVVSI) (Rivas et al., 2022).
Next steps:
Download the following file directly from R:
Command
new command name
Create an object named mr and store the contents of the downloaded dataset in it
Command
new command name
The file motility_results_ph.csv contain 11,620 lines of data, but for the purpose of this document, a sample of 500 lines of data will be used.
Command
new command name
Stage 1. Acquisition and creation of objects
The dataset used in this workflow is a dataframe that contains 11,620 lines of data, for the purpose of this document, a sample of 500 lines of data will be used.
We can access it and create the working object in two ways:
Option 1
The dataset used in this workflow can be downloaded from our account on the Harvard Dataverse site at https://doi.org/10.7910/DVN/CRVVSI
Save the dataset in your working directory and create an object to work with a sample of the dataset (500 rows). Review the 'Before Start' section.
Option 2
In the R software, download the dataset using the following code
Command
new command name
Create an object named mr and use the read.csv function to read the previously downloaded file
Command
new command name
Load the dplyr library in the R software using the following code
Command
new command name
Expected result
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
Take a sample of 500 rows from the dataset and store them in a new object named mr_sample
Command
new command name
Convert the mr_sample object into a dataframe and verify its structure
Command
new command name
Expected result
## 'data.frame': 500 obs. of 11 variables:
## $ ID1 : Factor w/ 75 levels "220219-1","220219-10",..: 69 28 58 46 70 6 7 28 69 58 ...
## $ ID2 : Factor w/ 5 levels "pH.70","pH.74",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ ID3 : Factor w/ 6 levels "","balder","berthrand",..: 2 3 2 4 2 6 6 3 2 2 ...
## $ VCL : num 265.6 47.2 356.8 239.3 94.3 ...
## $ VAP : num 108.6 36.6 143.3 86 65.6 ...
## $ VSL : num 68.9 28 57 55.4 41.3 ...
## $ LIN : num 0.259 0.592 0.16 0.232 0.438 ...
## $ STR : num 0.635 0.764 0.398 0.644 0.631 ...
## $ WOB : num 0.409 0.775 0.402 0.359 0.695 ...
## $ BeatCross: num 30.8 38.7 28.2 38.1 29 ...
## $ ALH : num 8.62 1.96 12.42 6.7 4.69 ...
The mr_sample object has 500 rows and 11 columns. Column 1 (ID1) represents the identifier of the capture routine video. Column 2 (ID2) corresponds to the treatment, indicating different pH values. Column 3 (ID3) represents the identifier of the donor male.
Stage 2: Principal Component Analysis (PCA)
Load the required libraries
Command
new command name
Create a new object named mr_sample2 that contains only the selected variables (columns)
Command
new command name
Create a new object named res.pca to store the results of the Principal Component Analysis (PCA) function. Specify the following arguments in the PCA function: scale the data, calculate three principal components, include a qualitative variable with no weight in the results, and generate a plot of the results.
Command
new command name
The PCA function generates two plots:
- PCA Graph of Individuals: This plot displays the values of the first and second principal components for each individual, with the corresponding labels observed next to each point.
- PCA Graph of Variables: This plot presents a correlation circle, where each arrow represents the magnitude and direction (positive or negative) of the correlation of a variable with the first and second principal components. For instance, the variable VCL shows a strong positive correlation with the first principal component and a weak correlation with the second principal component
Type res.pca in the console to displays the list of contained objects, followed by their description.
Note
The res.pca object is of the list type, and its contents can be accessed using the $ operator.
Command
new command name
Expected result
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 500 individuals, described by 9 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$quali.sup" "results for the supplementary categorical variables"
## 12 "$quali.sup$coord" "coord. for the supplementary categories"
## 13 "$quali.sup$v.test" "v-test of the supplementary categories"
## 14 "$call" "summary statistics"
## 15 "$call$centre" "mean of the variables"
## 16 "$call$ecart.type" "standard error of the variables"
## 17 "$call$row.w" "weights for the individuals"
## 18 "$call$col.w" "weights for the variables"
The eigenvalues and cumulative variance values reported in Rivas et al. (2022) can be found in the res.pca$eig object
Command
new command name
Expected result
## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 3.96582357 49.5727946 49.57279
## comp 2 2.39521837 29.9402297 79.51302
## comp 3 0.99221034 12.4026292 91.91565
## comp 4 0.42550528 5.3188160 97.23447
## comp 5 0.12786974 1.5983717 98.83284
## comp 6 0.04754866 0.5943582 99.42720
## comp 7 0.03306028 0.4132535 99.84045
## comp 8 0.01276377 0.1595471 100.00000
According to the Kaiser criterion, select the principal components with eigenvalues greater than 1.
Save the coordinate values of each principal component to generate clean and customized graphics
Command
new command name
Expected result
## [1] "Dim.1" "Dim.2" "Dim.3"
Append these columns to the mr_sample_2 object. For example:
Command
new command name
Expected result
## mr_sample_2$ID2 Dim.1 Dim.2 Dim.3
## 1 pH.70 1.155339564 0.06880405 0.8731306
## 2 pH.70 -2.785419405 2.61534418 -1.2313661
## 3 pH.70 2.671369221 -1.14843568 0.2633520
## 4 pH.70 -0.006226783 -0.46870882 1.4537604
## 5 pH.70 -0.884580976 1.51072808 -1.5240606
## 6 pH.70 0.112930932 1.56553832 -0.4460328
Convert the tab2 object into a dataframe using as.data.frame(). After conversion, verify the column names, and preview the first few rows of the dataset. Rename the first column to pH and confirm the updated column names again.
Command
new command name
Expected result
## [1] "mr_sample_2$ID2" "Dim.1" "Dim.2" "Dim.3"
Command
new command name
Expected result
## mr_sample_2$ID2 Dim.1 Dim.2 Dim.3
## 1 pH.70 1.155339564 0.06880405 0.8731306
## 2 pH.70 -2.785419405 2.61534418 -1.2313661
## 3 pH.70 2.671369221 -1.14843568 0.2633520
## 4 pH.70 -0.006226783 -0.46870882 1.4537604
## 5 pH.70 -0.884580976 1.51072808 -1.5240606
## 6 pH.70 0.112930932 1.56553832 -0.4460328
Command
new command name
Expected result
## [1] "pH" "Dim.1" "Dim.2" "Dim.3"
Construct the graph using the prepared tab2 object, ensuring all relevant variables are correctly represented for visualization
Command
new command name
Stage 3: Hierarchical clustering on principal components
After performing the principal component analysis, use the res.pca object as input for the HCPC function.
Create a new object named res.hcpc to store the results of the HCPC function
Command
new command name
The HCPC function generates three plots:
- Hierarchical Clustering Plot: This plot features a dendrogram with a horizontal line suggesting the cutoff point for group formation. The plot also includes an inset with a bar chart indicating the inertia gain. By clicking on the bar or another level of the graph, two additional plots are generated. For this document, the nb.clust argument was set to -1 for automatic cutoff determination, but setting it to 0 allows the user to select the cutoff height manually.
- Hierarchical Clustering on the Factor Map: This plot provides a three-dimensional representation, with the first and second principal components on the x and y axes, respectively, and the hierarchical dendrogram projected in two dimensions along the z axis.
- Factor Map Plot: This graph displays the values of the first and second principal components, with points colored according to the formed groups or clusters. These clusters represent the kinematic subpopulations.
Type res.hcpc in the console to display the list of contained objects, followed by their descriptions. Access the contents of the res.hcpc object using the $ operator.
Note
The res.hcpc object is of the list type, and its contents can be accessed using the $ operator.
Command
new command name
Expected result
## **Results for the Hierarchical Clustering on Principal Components**
## name
## 1 "$data.clust"
## 2 "$desc.var"
## 3 "$desc.var$quanti.var"
## 4 "$desc.var$quanti"
## 5 "$desc.var$test.chi2"
## 6 "$desc.axes$category"
## 7 "$desc.axes"
## 8 "$desc.axes$quanti.var"
## 9 "$desc.axes$quanti"
## 10 "$desc.ind"
## 11 "$desc.ind$para"
## 12 "$desc.ind$dist"
## 13 "$call"
## 14 "$call$t"
## description
## 1 "dataset with the cluster of the individuals"
## 2 "description of the clusters by the variables"
## 3 "description of the cluster var. by the continuous var."
## 4 "description of the clusters by the continuous var."
## 5 "description of the cluster var. by the categorical var."
## 6 "description of the clusters by the categories."
## 7 "description of the clusters by the dimensions"
## 8 "description of the cluster var. by the axes"
## 9 "description of the clusters by the axes"
## 10 "description of the clusters by the individuals"
## 11 "parangons of each clusters"
## 12 "specific individuals"
## 13 "summary statistics"
## 14 "description of the tree"
The res.hcpc$data.clust object contains the data from mr_sample_2, and includes a column named clust at the end, which indicates the cluster to which each data line belongs.
Command
new command name
Expected result
## ID2 VCL VAP VSL LIN STR WOB BeatCross
## 1 pH.70 265.64667 108.57502 68.93514 0.259499 0.634908 0.408720 30.79646
## 2 pH.70 47.19655 36.58363 27.96065 0.592430 0.764294 0.775134 38.72727
## 3 pH.70 356.77786 143.29716 56.96533 0.159666 0.397533 0.401643 28.17391
## 4 pH.70 239.27805 86.00893 55.40223 0.231539 0.644145 0.359452 38.08696
## 5 pH.70 94.31265 65.55947 41.34975 0.438433 0.630721 0.695129 28.96552
## 6 pH.70 165.31839 97.35522 67.48124 0.408190 0.693145 0.588895 28.44828
## ALH clust
## 1 8.619123 3
## 2 1.959340 1
## 3 12.417836 3
## 4 6.697638 3
## 5 4.690355 3
## 6 5.007826 3
This object is crucial as it allows for the analysis of the dataset based on treatments and clusters.
Store the contents of res.hcpc$data.clust in a new object for subsequent analysis.
Command
new command name
The res.hcpc$desc.axes object contains the values for each cluster based on quantitative variables (motility parameters).
Stage 4: Subpopulations in the dataset
One of the objectives of identifying kinematic sperm subpopulations is to describe the effect of experimental treatments on the structure of these subpopulations, starting by analyzing the proportion of sperm from each treatment within each subpopulation. Similarly, it is important to describe the effect of each treatment on each cluster. This aspect is addressed in another protocol (https://dx.doi.org/10.17504/protocols.io.14egn6p4ql5d/v1).
Protocol
CREATED BY
Cindy Rivas
Conclusions
With the proposed workflow in this document, you can process a file of motility parameters obtained from a CASA system to identify kinematic subpopulations in two steps. The outcome is an object that contains the original input data along with an additional column indicating the cluster to which each data line belongs. Analyzing the resulting object allows for identifying the proportion of sperm in each subpopulation and assessing the effect of each treatment on each subpopulation.
Protocol references
Martínez-Pastor F, Tizado EJ, Garde JJ, Anel L and Paz P de (2011) Statistical Series: Opportunities and challenges of sperm motility subpopulation analysis. Theriogenology 75 783–795.
Ramón M and Martínez-Pastor F (2018) Implementation of novel statistical procedures and other advanced approaches to improve analysis of CASA data. Reproduction, Fertility, and Development 30 860–866.
Rivas AC, Ayala EME and Aragon MA (2022) Effect of various pH levels on the sperm kinematic parameters of boars. South African Journal of Animal Science 52 693–704.
Acknowledgements
This work was supported by UNAM-PAPIIT IN224925.
This work was supported by the Programa de Becas Posdoctorales de la Dirección General de Asuntos del Personal Académico (DGAPA), UNAM to the postdoctoral fellow Cindy Ursula Rivas Arzaluz.