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Optimizing Microsatellite Marker Panels for Genetic Diversity and Population

Genetic Studies: An Ant Colony Algorithm Approach with Polymorphic
Information Content

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DOI: 10.3390/biology12101280

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 biology
Article
Optimizing Microsatellite Marker Panels for Genetic Diversity
and Population Genetic Studies: An Ant Colony Algorithm
Approach with Polymorphic Information Content
Ryan Rasoarahona 1,2 , Pish Wattanadilokchatkun 1 , Thitipong Panthum 1,3 , Thanyapat Thong 1 ,
Worapong Singchat 1,3 , Syed Farhan Ahmad 1,3 , Aingorn Chaiyes 4 , Kyudong Han 1,5,6 , Ekaphan Kraichak 1,7 ,
Narongrit Muangmai 1,8 , Akihiko Koga 1 , Prateep Duengkae 1,3 , Agostinho Antunes 9,10
and Kornsorn Srikulnath 1,2,3,11, *

1 Animal Genomics and Bioresource Research Unit, Faculty of Science, Kasetsart University,
50 Ngamwongwan, Bangkok 10900, Thailand; rasoarahonarivoniaina.h@ku.th (R.R.); pish.wa@ku.th (P.W.);
thitipong.pa@ku.th (T.P.); thongthanyapat@gmail.com (T.T.); worapong.singc@ku.ac.th (W.S.);
syedfarhan.a@ku.th (S.F.A.); jim97@dankook.ac.kr (K.H.); ekaphan.k@ku.th (E.K.); ffisnrm@ku.ac.th (N.M.);
koga.aki.ku@gmail.com (A.K.); prateep.du@ku.ac.th (P.D.)
2 Sciences for Industry, Faculty of Science, Kasetsart University, 50 Ngamwongwan, Bangkok 10900, Thailand
3 Special Research Unit for Wildlife Genomics, Department of Forest Biology, Faculty of Forestry, Kasetsart
University, 50 Ngamwongwan, Bangkok 10900, Thailand
4 School of Agriculture and Cooperatives, Sukhothai Thammathirat Open University,
Pakkret Nonthaburi 11120, Thailand; chaiyes.stou@gmail.com
5 Department of Microbiology, College of Science & Technology, Dankook University,
Cheonan 31116, Republic of Korea
6 Center for Bio-Medical Engineering Core Facility, Dankook University, Cheonan 31116, Republic of Korea
7 Department of Botany, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
8 Department of Fishery Biology, Faculty of Fisheries, Kasetsart University, Bangkok 10900, Thailand
9 Interdisciplinary Centre of Marine and Environmental Research, University of Porto, Terminal de Cruzeiros
Citation: Rasoarahona, R.;
Wattanadilokchatkun, P.; Panthum, do Porto de Leixões, Av. General Norton de Matos, s/n, 4450-208 Porto, Portugal; aantunes@ciimar.up.pt
10 Department of Biology, Faculty of Sciences, University of Porto, Rua do Campo Alegre, s/n,
T.; Thong, T.; Singchat, W.; Ahmad,
4169-007 Porto, Portugal
S.F.; Chaiyes, A.; Han, K.; Kraichak,
11 Center for Advanced Studies in Tropical Natural Resources, National Research University,
E.; Muangmai, N.; et al. Optimizing
Bangkok 10900, Thailand
Microsatellite Marker Panels for
* Correspondence: kornsorn.s@ku.ac.th
Genetic Diversity and Population
Genetic Studies: An Ant Colony
Simple Summary: Microsatellite markers are widely used molecular markers for genetic studies,
Algorithm Approach with
but choosing the right set involves a challenging trade-off between effectiveness and cost. The
Polymorphic Information Content.
research aims to enhance the widely used ant colony optimization algorithm by integrating marker
Biology 2023, 12, 1280. https://
doi.org/10.3390/biology12101280
effectiveness indicators. By considering the genetic properties of the markers such as the polymor-
phic information content, the study seeks to determine the suitable way to select a reduced set of
Academic Editors: Claudia Greco,
microsatellites. The approach addresses the accuracy–cost trade-off, aiding genetic assessments,
Daniela Pacifico and Irene Pellegrino
breeding, and conservation efforts with cost-effective solutions. This research provides valuable
Received: 19 August 2023 insights into real-world genetic studies, including breeding programs and conservation initiatives.
Revised: 22 September 2023
Accepted: 23 September 2023 Abstract: Microsatellites are polymorphic and cost-effective. Optimizing reduced microsatellite
Published: 25 September 2023 panels using heuristic algorithms eases budget constraints in genetic diversity and population
genetic assessments. Microsatellite marker efficiency is strongly associated with its polymorphism
and is quantified as the polymorphic information content (PIC). Nevertheless, marker selection
cannot rely solely on PIC. In this study, the ant colony optimization (ACO) algorithm, a widely
Copyright: © 2023 by the authors.
recognized optimization method, was adopted to create an enhanced selection scheme for refining
Licensee MDPI, Basel, Switzerland.
microsatellite marker panels, called the PIC–ACO selection scheme. The algorithm was fine-tuned
This article is an open access article
distributed under the terms and
and validated using extensive datasets of chicken (Gallus gallus) and Chinese gorals (Naemorhedus
conditions of the Creative Commons griseus) from our previous studies. In contrast to basic optimization algorithms that stochastically
Attribution (CC BY) license (https:// initialize potential outputs, our selection algorithm utilizes the PIC values of markers to prime the
creativecommons.org/licenses/by/ ACO process. This increases the global solution discovery speed while reducing the likelihood of
4.0/). becoming trapped in local solutions. This process facilitated the acquisition of a cost-efficient and

Biology 2023, 12, 1280. https://doi.org/10.3390/biology12101280 https://www.mdpi.com/journal/biology

Biology 2023, 12, 1280 2 of 16

optimized microsatellite marker panel for studying genetic diversity and population genetic datasets.
The established microsatellite efficiency metrics such as PIC, allele richness, and heterozygosity
were correlated with the actual effectiveness of the microsatellite marker panel. This approach
could substantially reduce budgetary barriers to population genetic assessments, breeding, and
conservation programs.

Keywords: ant colony optimization; microsatellite; marker selection; polymorphic information;

population genetics

1. Introduction
Microsatellite repeats, also known as simple-sequence repeats, are abundant and
highly polymorphic in numerous eukaryotic genomes. They represent a class of DNA
markers with repeat sequences ranging usually from mononucleotides to hexanucleotide
repeats. Perfect repetitions, interrupted repeats, or combinations with other repeat types
are possible occurrences. Biparentally inherited nuclear DNA microsatellites enable di-
verse applications, including population characterization, origin determination, hybrid
identification, and the assessment of inbreeding levels. Consequently, while genome-
wide single-nucleotide polymorphisms (SNPs) are frequently employed in genetic studies
related to populations, forensics, conservation, and evolution, it is worth noting that mi-
crosatellite genotyping may offer a greater degree of informativeness compared to biallelic
SNP genotyping in several species. This heightened informativeness arises from the fact
that microsatellites represent mutational hotspots, characterized by elevated levels of
polymorphism and a larger allelic diversity within diverse populations [1–4]. The high
polymorphism and Mendelian inheritance of microsatellites make them a good choice, with
significant impacts on breeding programs and conservation efforts. The global utilization of
microsatellite markers in local laboratories with low-cost investment is a practical alterna-
tive to SNP genotyping, which requires advanced equipment and technology. However, the
number of suitable microsatellite loci, which ranges from 10 to 30, may vary depending on
the study field and research group. To measure the level of genetic variation and inbreeding
in indigenous chickens, 15–30 loci derived from FAO reference markers were used [5]. An
interpretation bias arises when comparing data on diversity and identification owing to the
utilization of a large, non-optimized marker panel. However, the use of such a panel does
not guarantee accurate results and can lead to a significant waste of human and financial
resources, ultimately resulting in biased outcomes. The precision and accuracy of every
downstream process following genotyping are mainly dependent on the effectiveness of
the microsatellite panel. Admittedly, while a larger number of loci logically provides more
genetic information on a population, researchers must consider a compromise between
result accuracy and cost-effectiveness by accounting for the margin of error and defined
accuracy criteria.
The widely used ant colony optimization (ACO) algorithm is a heuristic, population-
based, and bioinspired optimization method for solving combinatorial problems [6]. This
concept was proposed by Colorni et al. [7]. By leveraging the inherent behaviors observed
in ant colonies, the ACO algorithm aims to determine the optimal solution by considering
a set of constraints or costs [8]. The selection of an optimal microsatellite panel is driven
by the intricate relationship between the utilized loci and the inferred result, leading to
the categorization of the problem as nonlinear programming [9]. Solving these problems
becomes computationally aspirational, even when dealing with a reasonable number of
microsatellite markers, owing to the existence of multiple discrete decision variables [10].
Similar methods have been proposed to address these problems, including the genetic
algorithm [11], particle swarm optimization [12], traveling salesman [13], and ant colony
algorithm [8], which correspond to the ACO algorithm. In each method, the resource
consumption and underlying logic differ; however, they all display remarkable flexibility
Biology 2023, 12, 1280 3 of 16

in resolving optimization problems across various research domains [14]. These algorithms
identified suitable microsatellite marker sets without relying on prior genetic knowledge.
However, owing to the stochastic nature of metaheuristic algorithms, a local solution, char-
acterized by high accuracy, but not necessarily the optimal accuracy among all possibilities,
may be discovered, which could be distant from the global solution [15].
In this study, we aimed to elucidate the critical accuracy/cost trade-off dilemma in
population genetics research projects. Here, rather than using a raw heuristic optimization
algorithm, the effect of incorporating polymorphic information on the algorithm’s perfor-
mance was explored. We hypothesized that integrating a relevant effectiveness indicator of
a marker set into the ACO algorithm can lead to valuable findings such as reduced compu-
tational time and improved accuracy in identifying the optimal solution. When selecting
the optimal microsatellite panel, the accuracy indicator was used as the cost function to be
maximized [16]. Several approaches have considered polymorphic information content
(PIC) [17], matching probability [18], and gene variability [19] as accuracy indicators for
microsatellite panels. Additionally, a genetic distance matrix was used to provide useful
information for population structure estimation using a reduced set of microsatellites [20].
By conducting a comparative analysis, the impact of incorporating PIC as a decision vari-
able in the algorithm was evaluated. Our approach can help address budgetary barriers to
population genetic assessments, breeding, and conservation programs.

2. Materials and Methods

2.1. Refining an Intriguing Algorithm for Microsatellite Marker Selection
The microsatellite marker selection problem is characterized as a combinatorial search
problem, where there is a search space S and a cost function f that must be minimized [10].
The search space S comprises all possible subsets of markers, totaling 2k potential solutions
for k loci. Each subset was represented by a binary vector I = [i1 , i2 , . . ., in ], where i ∈ {0;1}
indicated whether a specific microsatellite was included in the marker panel or not. The
accuracy of a microsatellite marker panel on a given genotype dataset was quantified using
the cost function f. The cost function f was determined by comparing the average genetic
distance (AGD) between the full set of markers and the reduced set [10]. From a biological
perspective, genetic distance is defined as the accumulated differences in alleles at each
locus [20]. This was calculated based on the allelic frequencies observed from a given set
of microsatellite markers using Equation (1). The genetic distance matrix was generated
using the dist function implemented within the adegenet package in R version 4.2.2 [21].
 
m(k)
 ∑vk=1 ∑ j=1 pkaj pkbj 
D ( a, b) = −ln
r  2 r

 2  (1)
m ( k ) m ( k )
∑vk=1 ∑ j=1 pkaj ∑vk=1 ∑ j=1 pkbj

In this study, a marker selection algorithm was developed to effectively decrease the
number of microsatellite markers used in population genetic studies. This was achieved by
enhancing the ACO algorithm for marker selection [22] and utilizing PIC as an informative
marker indicator [17,23]. The PIC for each microsatellite marker was calculated using the
PopGenUtils package in R version 4.2.2 [21]. In the microsatellite selection scheme, loci were
sorted based on their PIC and the highest-ranking microsatellite was integrated into the
selected marker set.

2.2. Ant Colony Optimization Algorithm

The ACO algorithm was used to select an optimal set of microsatellite markers. The
ACO algorithm, inspired by the natural behavior of ants, is a metaheuristic optimization
technique [7]. To facilitate the application of the ACO algorithm, the search space was
represented by a directed graph [24] with 2 × N nodes, where N denotes the total number of
microsatellite loci [8]. The ant pheromones were randomly distributed along the pathways.
During each iteration, the ants independently construct their solutions by probabilistically
Biology 2023, 12, 1280 4 of 16

selecting pathways based on pheromone trails, which serve as indicators of the solution
quality. Once all the ants have constructed their solutions, the pathways are sorted based
on their quality, and the corresponding pheromone trails are updated. The ACO algorithm
was then executed with the appropriate parameters to identify discriminant microsatellite
loci (Table 1). Finally, the initial pheromone values were adjusted based on the PIC of each
microsatellite marker. Microsatellites with high levels of polymorphisms were preferred to
those with low levels. This approach aims to reduce the computational noise, minimize
the number of required iterations, and avoid potential entrapment in local solutions [25].
The described panel optimization algorithms were implemented using a Python version
3.11 [26] script (File S1) and executed on a Linux Ubuntu server version 18.04 [27].

Table 1. Parameter used for the ant colony optimization algorithm [7,8].

Parameter Description Value

ant_n Ant population size 50
E Number of epochs (iterations) 120
α1 Weight factor of the pheromone trail in the decision-making process 0.7
decay 2 Evaporation rate of the pheromone trail 0.9
1A higher value of α increases the significance of the pheromone trail, making the ants more likely to choose
edges with stronger pheromone concentrations. 2 A small value of decay allows the avoidance of becoming stuck
on local minima and the encouragement of ants to explore new pathways.

2.3. Microsatellite Marker Dataset

The microsatellite selection scheme was evaluated using two datasets obtained from
genetic diversity studies: a chicken genotyping dataset and a Chinese goral genotype
dataset. The chicken dataset, from the Siam Chicken Bioresource Consortium Project,
encompassed 652 individuals, was analyzed using 28 marker loci and available from
https://doi.org/10.5061/dryad.hhmgqnkm0 (accessed on 5 July 2023) [28–31]. The geno-
type information of 79 individuals across 11 markers in the Chinese goral dataset was down-
loaded from https://doi.org/10.5061/dryad.wstqjq2hm (accessed on 5 July 2023) [32,33].
The datasets used in this study were formatted using the GenAlEx tool version 6.51 [34]
and were compatible with Microsoft Excel. The number of alleles per locus (Na ), effec-
tive number of alleles (Nea ), observed and expected heterozygosities (Ho and He ), and
allele richness (AR) were evaluated for each microsatellite locus in both datasets. The PIC
was computed using the “PIC” function available in the polysat package within R version
4.2.2 [35].

2.4. Comparative Evaluation of Marker Selection Schemes: ACO Algorithm, PIC, PIC + ACO,
and Random Selection
A microsatellite marker selection model was fitted to minimize the loss of AGD
accuracy. Four marker-sampling methods were used in this study. The first method
employed in this study was the use of the ACO algorithm to select the most accurate
panel without prior information regarding the polymorphisms of each locus. The second
method involved sorting microsatellites based solely on their PIC and selecting the most
informative loci. The third method involves ranking microsatellites based on their PIC and
subsequently optimizing the set using PIC + ACO. A random selection scheme was used
for the control group. Pairwise comparisons between selection schemes were conducted
using the Tukey honest significance test, using the “pairwise_tukeyhsd” function from the
statsmodel package [26]. The performance of each selection scheme was assessed through
statistical pairwise comparisons using Tukey’s honest significance test. This analysis was
conducted using the “pairwise_tukey_hsd” function from the statsmodel package in Python
version 3.11 [26]. The PIC + ACO algorithm was used to progressively reduce the number
of microsatellite markers to N = 2. The accuracy losses of the estimated values for Ho ,
He , and AR were evaluated. The AGD was reported, and graphical illustrations were
generated using the “boxplot” function from the matplotlib package in Python version
3.11 [36]. Statistical regression analysis was conducted using the “OLS” function from the
Biology 2023, 12, 1280 5 of 16

statsmodel package [37]. The estimation accuracy loss of Ho and He was determined by
gradually reducing the number of microsatellite markers using the “plot” function from
the matplotlib package in Python version 3.11 [36].

2.5. Estimation of Genetic Diversity Measurement on a Reduced Set of Microsatellite Markers

The microsatellite marker panel was assessed for each dataset by setting arbitrary
error tolerances to 1%, 5%, and 10%. As a result, three reduced marker panels were
created for chicken: GGA1 (1% error tolerance-reduced marker), GGA5 (5% error), and
GGA10 (10% error), and three marker panels for Chinese goral: NGR1 (1% error), NGR5
(5% error), and NGR10 (10% error). The Na , Nea , AR, and PIC of the given population
were evaluated in all microsatellite datasets, focusing on two statistical aspects: the mean
difference between the measurements on the optimized and full sets, and the significance of
the association of a higher measurement with the optimized set. The mean difference was
used to explain the extent of deviation between the values reported for the full and reduced
sets of microsatellites. The statistical p-value was calculated using an independent t-test
and classified into four levels of significance: not significant (p > 0.05), slightly significant
(0.01 < p < 0.05), moderately significant (0.001 < p < 0.01), and highly significant (p < 0.001).
The statistical test was performed using the “ttest_ind” function from the stats package
in Python version 3.11 [38]. The results were subsequently visualized using the “boxplot”
function from the matplotlib package in Python version 3.11 [37]. The impact of reducing
the number of microsatellites in a marker panel on population structure estimation was
studied using three analytical methods: the Bayesian clustering algorithm [39], phylogenetic
relationship analysis [40], and multidimensional scaling [41]. Population clustering analysis
was conducted using Structure software version 2.3.4 [42]. The appropriate number of
population clusters was determined by selecting the highest value of the Delta-K statistic,
following the guidelines provided in the STRUCTURE software user manual [43]. The
genetic distance between subpopulations was computed for the phylogenetic analysis
using the “hclust” function from the stats package in R version 4.2.2 [35]. The dimensional
scaling analysis was conducted using both principal component analysis (PCA) [44] with
the “cmdscale” function from the stats package in R version 4.2.2 [35] and the discriminant
analysis of principal components (DAPC). The resulting dimensional coordinates were
visualized using the “dapc” function from the adegenet package in R version 4.2.2.

3. Results
3.1. Pairwise Comparison of Marker Selection Schemes on Two Genotype Datasets
The chicken and Chinese goral genotype datasets comprise Na ranging from 5 to
82 alleles (average: 21), Nea spanning from 1.14 to 26.22 (average: 6.40), AR ranging
from 0.01 to 0.16 (average: 0.06), and PIC values ranging from 0.12 to 0.95 (average: 0.70)
(Table S1). A comparison of the three selection methods indicated that the PIC + ACO
selection scheme demonstrated superior accuracy on the chicken dataset for all marker
quantities (N), except for N = 5 and N = 4, which showed statistical significance (p < 0.01).
However, the ACO selection scheme was the most accurate for N = 5, whereas the PIC
selection method showed the highest accuracy for N = 4. By contrast, for the Chinese goral
dataset, the PIC + ACO scheme was the most accurate for marker sets consisting of nine,
seven, and four loci. The highest accuracy was observed for marker sets comprising ten and
eight microsatellites in the ACO scheme. However, for other values of N, higher accuracy
was observed with randomly selected microsatellite markers than with the ACO, PIC, and
PIC + ACO selection schemes (Tables S3 and S4; Figure S1).

3.2. Microsatellite Panel Selection Using Error Margins of 1%, 5%, and 10%
In the chicken dataset, with an error margin of 1%, the PIC + ACO selection method
identified two microsatellites (LEI0094 and MCW0123) that could be excluded. Similarly,
the ACO and PIC selection schemes each identified one microsatellite (MCW0206 and
ADL0278, respectively) that could be excluded. With a permitted AGD estimation accuracy
Biology 2023, 12, 1280 6 of 16

loss of 5%, the PIC + ACO selection scheme indicated the need for
Biology 2023, 12, x
12 marker loci. Based
6 of 17
on the PIC selection policy, 13 markers were considered effective. The ACO selection
algorithm required 13 markers, with 7 markers (MCW0034, MCW0183, LEI0192, MCW0123,
3.2. Microsatellite Panel Selection Using Error Margins of 1%, 5%, and 10%
LEI0234, MCW0069, and MCW0111)
In the chicken dataset, with an errorcommonly
margin of 1%, theselected by allmethod
PIC + ACO selection three methods, including
the ACO, PIC, identified
and PICtwo microsatellites (LEI0094 and MCW0123) that could be excluded. Similarly,
+ ACO selection schemes. Considering
the ACO and PIC selection schemes each identified one microsatellite (MCW0206 and
a threshold of 10% for AGD
measurement, ADL0278,
all three selection
respectively) methods
that could indicated
be excluded. With a permitheed usability
AGD estimation ofaccu-
7 microsatellite markers,
racy loss of 5%, the PIC + ACO selection scheme indicated the need for 12 marker loci.
with 4 markersBased
(LEI0234, MCW0104,
on the PIC selection policy, 13 LEI0192, and MCW0111)
markers were considered commonly
effective. The ACO selec- selected by both
methods. In the Chinese
tion algorithm goral
required dataset,
13 markers, with 7considering
markers (MCW0034, a 1%
MCW0183,
MCW0123, LEI0234, MCW0069, and MCW0111) commonly selected by all three methods,
error allowance,
LEI0192, all selection
methods indicated
includingthat a full
the ACO, PIC,set
and of
PIC 11
+ ACOmarkers was necessary.
selection schemes. By selecting
Considering a threshold of an error margin,
the same set of10% for AGD measurement, all three selection methods indicated the usability of 7 mi-
markers
crosatellite consisting
markers, with 4 markers of 10 microsatellite
(LEI0234, MCW0104, LEI0192, and markers,
MCW0111) com- excluding SY259F, was
reported by both
monlythe PICbyand
selected both ACO
methods.selection
In the Chineseschemes. In total,a 91%microsatellite
goral dataset, considering error al- markers were
lowance, all selection methods indicated that a full set of 11 markers was necessary. By
identified as usable
selecting using the PIC
an error margin, + ACO
the same selection
set of markers consistingmethod, excluding
of 10 microsatellite markers, SY259F and SY128F.
excluding SY259F, was reported by both the PIC and ACO selection schemes. In total, 9
With an error margin of 10%, the ACO selection method determined that 8 microsatellite
microsatellite markers were identified as usable using the PIC + ACO selection method,
markers were adequate, excluding
excluding SY259F and SY128F. WithSY259F, SY76F,
an error margin of 10%, and
the ACOSY449F. By contrast, the same set
selection method
determined that 8 microsatellite markers were adequate, excluding SY259F, SY76F, and
of 6 microsatellite
SY449F.markers
By contrast, the(SY434F,
same set of 6SY14F, SY12BF,
microsatellite SY129F,
markers (SY434F, SY14F,SY449F,
SY12BF, and SY128F) were
SY129F, SY449F, and SY128F) were identified using both the PIC and PIC + ACO selection
identified using both the PIC
schemes (Figure 1; Table 2).
and PIC + ACO selection schemes (Figure 1; Table 2).

Figure 1. Microsatellite set reported by each of the 3 microsatellite markers selection scheme on the
Figure 1. Microsatellite
two datasets. set reported by each of the 3 microsatellite markers selection scheme on the

two datasets.

Table 2. Microsatellite marker panel selected by the 3-selection scheme using different accuracy
loss margins.

Average Genetic Distance Selection Scheme

Dataset Estimation Accuracy Loss PIC + ACO 1 ACO 2 PIC 3
MCW0034, MCW0104,
MCW0104, LEI0234, LEI0166, MCW0034, MCW0104,
LEI0234, MCW0016,
10% MCW0123, MCW0111, LEI0234, MCW0123,
MCW0111, MCW0183,
ADL0268, LEI0192 MCW0111, LEI0094, LEI0192
LEI0192
MCW0034, MCW0078, MCW0034, MCW0104,
MCW0034, MCW0104,
MCW0098, MCW0165, MCW0330, LEI0234,
MCW0165, LEI0234,
LEI0234, MCW0216, MCW0123, MCW0016,
MCW0123, MCW0206,
5% MCW0123, MCW0206, MCW0111, LEI0094,
MCW0111, LEI0094,
MCW0111, MCW0183, MCW0183, MCW0069,
MCW0183, MCW0069,
MCW0069, ADL0268, MCW0295, ADL0268,
LEI0166, LEI0192
LEI0192 LEI0192
Gallus gallus 28 markers MCW0034, MCW0098, MCW0034, MCW0098,
MCW0034, MCW0098,
MCW0081, MCW0330, MCW0081, MCW0330,
MCW0081, MCW0330,
MCW0165, LEI0234, MCW0165, LEI0234,
MCW0165, LEI0234,
MCW0222, MCW0104, MCW0222, MCW0206,
MCW0222, MCW0206,
MCW0078, ADL0112, MCW0104, MCW0078,
MCW0104, MCW0078,
MCW0216, MCW0111, ADL0112, MCW0216,
ADL0112, MCW0216,
MCW0183, MCW0069, MCW0111, MCW0183,
1% MCW0111, MCW0183,
ADL0268, LEI0192, MCW0069, ADL0268,
MCW0069, ADL0268,
MCW0037, MCW0248, LEI0192, MCW0037,
LEI0192, MCW0037,
MCW0014, LEI0094, MCW0248, MCW0014,
MCW0248, MCW0014,
MCW0103, MCW0067, LEI0094, MCW0103,
MCW0103, MCW0067,
MCW0123, MCW0016, MCW0067, MCW0123,
MCW0016, MCW0295,
MCW0295, LEI0166, MCW0016, MCW0295,
LEI0166, ADL0278
ADL0278 LEI0166
Biology 2023, 12, 1280 7 of 16

Table 2. Cont.

Average Genetic Distance Selection Scheme

Dataset Estimation Accuracy Loss PIC + ACO 1 ACO 2 PIC 3
SY434F, SY14F, SY12BF,
SY434F, SY14F, SY12BF, SY434F, SY14F, SY12BF,
10% SY93F, SY129F, SY128F,
SY129F, SY449F, SY128F SY129F, SY449F, SY128F
SY84BF, SY84F
Naemorhedus griseus 11 SY434F, SY14F, SY12BF, SY434F, SY14F, SY12BF, SY434F, SY14F, SY12BF,
markers 5% SY93F, SY129F, SY76F, SY449F, SY93F, SY129F, SY76F, SY449F, SY93F, SY129F, SY76F, SY449F,
SY84BF, SY84F SY128F, SY84BF, SY84F SY128F, SY84BF, SY84F
SY434F, SY14F, SY259F, SY434F, SY14F, SY259F, SY434F, SY14F, SY259F,
SY12BF, SY93F, SY129F, SY12BF, SY93F, SY129F, SY12BF, SY93F, SY129F,
1%
SY76F, SY449F, SY128F, SY76F, SY449F, SY128F, SY76F, SY449F, SY128F,
SY84BF, SY84F SY84BF, SY84F SY84BF, SY84F
1PIC + ACO, selection scheme involving ranking the markers by their polymorphic information content and
subsequently optimizing the set using the PIC + ACO algorithm. 2 ACO, selection scheme using only the ant
colony optimization algorithm without any prior information on the PIC of the markers. 3 PIC, selection scheme
sorting microsatellites on their PIC and selecting the most informative loci.

3.3. Genetic Diversity Expressed by the Reduced Set of Microsatellites Using Error Margins of 1%
(GGA1 and NGR1 ), 5% (GGA5 and NGR5 ), and 10% (GGA10 and NGR10 )
Biased values of genetic diversity were observed between the full and reduced sets
of microsatellites when employing the aforementioned markers, with varying levels of
statistical significance and discrepancy. On the chicken dataset, the highest divergence in
Na was observed on the reduced set of microsatellites, which had an average of 26.88 alleles
(1.02-fold higher than the full set of loci), 37.83 alleles (1.44-fold), and 48.14 alleles (1.83-fold)
with the GGA1 , GGA5 , and GGA10 marker sets, respectively. Higher values of Nea were
observed on the GGA5 and GGA10 marker sets, with 10.97 (1.38-fold) and 12.6 (1.58-fold),
respectively, whereas a negative discrepancy was observed in the GGA1 marker set, with
an average Nea of 7.49 (0.94-fold). Similarly, the GGA1 exhibited negative discrepancy in
Nea , AR, PIC, Ho , and He : the measured AR was 0.04 (0.98-fold), PIC was 0.75 (0.95-fold),
Ho was 0.59 (0.98-fold) and He was 0.82 (0.99-fold). Conversely, the GGA5 and GGA10
yielded relatively high values: their AR values were 0.06 (1.4-fold) and 0.08 (1.79-fold); their
reported PIC 0.86 (1.07-fold) and 0.88 (1.12-fold); the determined Ho 0.66 (1.10-fold) and
0.68 (1.13-fold); and the He 0.88 (1.06-fold) and 0.90 (1.08-fold), respectively.
For the Chinese goral dataset, discrepancy analysis could only be performed for the
NGR5 and NGR10 microsatellite sets because the NGR1 was not a reduced marker panel.
The Na allele exhibited an average of 8.66 alleles (1.01-fold) for NGR5 and 9.33 alleles (1.09-
fold) for NGR10 . The Nea averaged a value of 2.27 (0.94-fold) for NGR5 and 2.86 (1.19-fold)
for NGR10 . The AR averaged a value of 0.11 (1.01-fold) for NGR5 and 0.11 (1.09-fold) for
NGR10 . The PIC yielded an average value of 0.46 (1.01-fold) for NGR5 and 0.52 (1.14-fold)
for NGR10 . Ho averaged a value of 0.16 (0.87-fold) for NGR5 and 0.22 (1.21-fold) for NGR10 .
The He yielded an average value of 0.48 (1.01-fold) for NGR5 and 0.54 (1.13-fold) for NGR10
(Figure 2; Table S2).
Previously described values were used to demonstrate the correlation between mi-
crosatellite panel quality and population genetic measurements at different levels of sig-
nificance. In the GGA5 marker panel, moderately significant associations (p < 0.01) were
observed for Na , Nea , and AR, and low statistical significance (0.01 < p < 0.05) was deter-
mined for PIC, Ho , and He . For GGA10 , Na and AR were determined to have high statistical
significance (p < 0.001), Nea exhibited moderate statistical significance (0.001 < p < 0.01),
PIC and He had low statistical significance (0.01 < p < 0.05), and Ho had no statistical
significance. However, for the chicken GGA1 and Chinese goral datasets (NGR1 , NGR5 ,
and NGR10 ), insufficient data used for the statistical tests hindered the achievement of
statistically significant findings (Table 3).
 9 of 17
Biology 2023, 12, 1280 8 of 16

Figure 2. Measurement of the

Figure number of of
2. Measurement alleles (Na), the
the number number
of alleles (Na ),ofthe
effective
number alleles (Neaalleles
of effective ), the (N
allele
ea ), the allele
richness (AR), the polymorphic
richness (AR),information content
the polymorphic (PIC), the
information observed
content (PIC),(H o), observed
the and the expected
(Ho ), and het-
the expected
erozygosity (He), comparatively
heterozygositycalculated betweencalculated
(He ), comparatively the full between
set of microsatellites and the reduced
the full set of microsatellites and the reduced
set of microsatellite marker.
set of microsatellite marker.

Previously described values were used to demonstrate the correlation between mi-
crosatellite panel quality and population genetic measurements at different levels of sig-
nificance. In the GGA5 marker panel, moderately significant associations (p < 0.01) were
observed for Na, Nea, and AR, and low statistical significance (0.01 < p < 0.05) was deter-
mined for PIC, Ho, and He. For GGA10, Na and AR were determined to have high statistical
significance (p < 0.001), Nea exhibited moderate statistical significance (0.001 < p < 0.01),
PIC and He had low statistical significance (0.01 < p < 0.05), and Ho had no statistical sig-
Biology 2023, 12, 1280 9 of 16

Table 3. Statistical significance of the association of the number of alleles (Na ), the number of effective
alleles (Nea ), the allele richness (AR), the polymorphic information content (PIC), the observed (Ho ),
and the expected heterozygosity (He ) with the reduced microsatellite marker panel.

Dataset Reduced Panel Measurement Mean-Diff t-Stat p-Val Significance

Na 5.115 −0.394 0.697 ns
Nea 6.813 −1.909 0.067 ns
AR 0.008 −0.397 0.695 ns
GGA1 (26 markers)
PIC 0.122 −1.341 0.192 ns
Ho 0.101 1.975 0.108 ns
He 0.099 2.354 0.193 ns
Na 18.521 3.240 0.003 **
Nea 5.246 3.093 0.005 **
Gallus gallus 28 AR 0.030 3.146 0.004 **
GGA5 (12 markers)
markers PIC 0.110 2.515 0.018 *
Ho 0.105 2.422 0.023 *
He 0.086 2.347 0.027 *
Na 27.857 5.081 0.000 ***
Nea 6.175 3.222 0.003 **
AR 0.045 4.866 0.000 ***
GGA10 (7 markers)
PIC 0.129 2.586 0.016 *
Ho 0.101 1.975 0.059 ns
He 0.099 2.354 0.026 *
Na – – – –
Nea – – – –
AR – – – –
NGR1 (11 markers)
PIC – – – –
Ho – – – –
He – – – –
Na 0.667 0.251 0.808 ns
Nea 0.668 −0.595 0.567 ns
Naemorhedus griseus AR 0.008 0.228 0.825 ns
NGR5 (9 markers)
11 markers PIC 0.015 0.087 0.933 ns
Ho 0.130 −0.899 0.392 ns
He 0.026 0.147 0.886 ns
Na 1.733 0.874 0.405 ns
Nea 1.022 1.249 0.243 ns
AR 0.023 0.892 0.396 ns
NGR10 (6 markers)
PIC 0.142 1.135 0.286 ns
Ho 0.087 0.771 0.460 ns
He 0.140 1.081 0.308 ns
ns: No significant association (p > 0.05). *: Weak significance association (0.05 < p < 0.01). **: Medium significance
association (0.01 < p < 0.001). ***: High significance association (p < 0.01).

3.4. Comparison of Population Structure Inference between the Full Set and Reduced Sets of
Microsatellites
The presence of two population clusters (K = 2) was revealed in the downstream analysis of
the chicken population genotype dataset using STRUCTURE software. Regardless of the number
of microsatellite markers used for the population genetics assessment, the same value of K = 2 was
consistently observed (Table S4; Figure S2). Visualization of population genetics and microsatellite
marker panel accuracy can be achieved using STRUCTURE, phylogenetic trees, PCA, and DAPC
plots (Figure 3, Figures S3 and S4). All 31 chicken subpopulations were classified into K = 2 clusters
with statistical significance for the posterior probability (p < 0.01) for the four studied marker
panels (GGA1, GGA5, GGA10, and the full set of 28 chicken microsatellites). For K = 7, 28 of the
31 subpopulations were successfully clustered into 7 groups using the full set of 28 microsatellites
with statistical significance (p < 0.01). With GGA1, the number of clustered subpopulations
remained at 28, whereas GGA5 clustered 29 subpopulations and GGA10 26 subpopulations. For
K = 9, 30 out of 31 subpopulations were assigned to 9 clusters using the full set of 28 markers,
whereas both the GGA1, GGA5, and GGA10 marker panels reported 29 clustered subpopulations
Biology 2023, 12, 1280 10 of 16

(Figure 3; Table S5). However, with the use of a reduced set of microsatellite markers, different
values were reported, and no inferred clusters were revealed in the membership probability
structure, PCA, and DAPC analysis. Because there was only one genetic subpopulation in the
Chinese goral dataset, no statistical comparison of subpopulation clustering could be inferred.

Figure 3. Phylogenetic relationship of the chicken population estimated using the full set of 28 microsatellites
(a), the GGA1 (b), the GGA5 (c), and the GGA10 (d) reduced marker panels.

4. Discussion
Genetic researchers face the challenge of an increasing number of usable microsatellite
panels, prompting the need for smart and efficient selection of markers in the fields of
genetic diversity, population genetics, and breeding programs. A trade-off between cost
and result quality must be made, considering research expenses and time as limiting
factors. In previous studies, various marker selection algorithms have been investigated,
including the k-optimal [45], decision-tree induction algorithm [46], traveling salesman [13],
ant colony algorithm [8], and genetic algorithm [11]. Considering panel selection as an
optimization problem, any of the previously studied algorithms can be used as they offer a
cost function to minimize or maximize [16].

4.1. Challenges in Microsatellite Marker Panel Selection

The informativeness of microsatellite markers is directly related to their degree of
polymorphism [17]. The polymorphism exhibited by each marker (locus) should be consid-
ered when constructing a microsatellite panel [47]. A reduced panel of 9–12 markers was
considered suitable. However, in genetic diversity and population analyses of species such
as chickens, cattle, and dogs, the use of 18–30 markers is common. These species, which are
known for their numerous varieties and breeds, have been studied and improved through
breeding programs using microsatellite standard sets. However, considerable variations
Biology 2023, 12, 1280 11 of 16

have been observed in the effectiveness and accuracy of each available microsatellite marker
panel. The quality of the results is largely dependent on the choice of the marker set, as
not all microsatellite panels are equivalent [48,49]. Usable and convenient microsatellite
markers can be identified by combing through past studies; however, a universal opti-
mized marker panel does not exist because of the varying genetic marker specifications
across different research domains [50,51]. Another method uses the PIC, allele variation
(Na /Ne ), AR and He as informativeness indicators of a particular locus [49,52]. The use of
a well-selected panel could also compensate for certain genotyping errors and estimate
population genetic measurements within an acceptable accuracy loss [10,53].
The PIC has always been regarded as an accurate quality indicator of microsatel-
lite markers; however, the developed selection scheme does not prioritize the highest
PIC microsatellites [17,23]. With the chicken dataset, of the reported 7-microsatellite set,
LEI0094 and MCW0123, despite having high PIC values—0.93 and 0.88—respectively,
were excluded. Instead, our marker selection scheme (PIC + ACO) included MCW0183
and MCW0016, which have PIC values, of 0.83 and 0.87, respectively. Similarly, among
the 14 microsatellite marker sets, MCW0016, MCW0295, MCW0330, and ADL0268 (with
PIC values of 0.87, 0.84, 0.85, and 0.85, respectively) were excluded, whereas LEI0166,
MCW0165, and MCW0206 (with PIC values of 0.74, 0.69, and 0.81, respectively) were se-
lected. This suggests that the accuracy of individual identification is not always guaranteed
by the highest PIC markers, as microsatellite markers can provide redundant information
due to non-random associations between distant loci [54]. However, regardless of the
chosen accuracy loss threshold, all markers with low PIC values are generally excluded
by the PIC + ACO selection scheme, with an allowed accuracy loss of 10%, all markers
with PIC lower than 0.83 are excluded, and a loss tolerance of 5% excludes all markers with
PIC below 0.69. This suggests that PIC provides valuable insights into the efficiency of
molecular markers for genetic studies, as stipulated by Serrote et al. [17]. Publicly available
microsatellite panels for genetic studies and chicken breeding programs are generally
highly polymorphic [5,28–31]. Similarly, in the second dataset, the same set of markers
was reported using the PIC and PIC + ACO selection schemes for margin tolerances of
1% and 10%, respectively. However, with a 5% margin tolerance, PIC + ACO excluded
SY128F, which was among the top two highest PIC microsatellites in the dataset. In ad-
dition, the highest PIC markers were always selected by the PIC + ACO method for 1%
and 10% error tolerances. Referring to the chicken dataset used in this study, an average
genetic distance accuracy loss ranging from 5% (GGA5 ) to 10% (GGA10 ) was observed.
The chicken genotype dataset revealed that the 7 most informative microsatellites were
MCW0111, LEI0234, MCW0034, MCW0016, LEI0192, MCW0183, and MCW0104 markers.
These markers exhibited higher effectiveness (PIC > 0.83, Na > 28, Nea > 6.79, Ho > 0.58,
and He > 0.85), as suggested by previous studies on chicken population genetics [30,55].
Moreover, the clustering of the putative chicken population was accurately displayed by
visual representations of PCA and DAPC using the 7 selected markers mentioned above.
Microsatellite marker set reduction could be further pursued by increasing the accuracy
loss margin by up to 15%, as reported by Xiong et al. [54] for other types of molecular
markers. The relevance of the proposed microsatellite panel size was further supported by
experiments on the Chinese goral dataset, which did not yield any marker combination
with fewer than 9 markers (NGR5 ).
Microsatellite panels with high levels of genetic diversity are widely available for
numerous species, therefore expanding the applicability and scope of this study [28,56].
The algorithm studied was well-suited for refining a large set of microsatellites (more
than 20 microsatellite sets) with sufficient alleles to allow for some accuracy loss in the
genetic measurement estimations. Using this algorithm, significant budgetary savings
can be achieved by excluding a substantial number of microsatellite markers. Moreover,
valuable insights into the efficiency of microsatellites and their individual contributions
to the effectiveness of marker panels can be obtained [47]. However, the heterozygosity
of individuals is not considered by the AGD function used to assess genetic diversity
Biology 2023, 12, 1280 12 of 16

among populations [20], causing the algorithm to disregard valuable information on gene
diversity and inbreeding within populations. Moreover, failures during microsatellite
marker amplification and genotyping processes have been omitted in almost all studies [57],
potentially leading to the exclusion of some usable microsatellite markers for population
genetic investigation [58].

4.2. Using the PIC as a Discriminative Power Indicator of the Marker

The ant colony optimization (ACO) algorithm, which was proposed in the early 90s
as an approach to resolving optimization problems, has garnered interest because of its
simplicity and versatility [7]. It exists in numerous variants, including the ant system (AS),
ant-Q, max-min ant system, rank-based ant system, BWAS, and hypercube AS [59–62].
The ACO algorithm, which belongs to the group of metaheuristic approaches [14], shares
commonalities with trending optimization algorithms, such as the genetic algorithm (GA),
particle swarm (PSO), or seagull optimization algorithm (SOA). It determines the optimal
solution by spreading pheromones on pathways based on the solution quality [8]. Properly
balancing exploration and exploitation in the algorithm parameters is crucial to avoid
infinite loops or becoming stuck in local solutions [7]. Similar to the trial and reward
concept used in reinforcement learning, every possibility of the microsatellite panel was
assessed using the optimization pipeline used in the ant colony optimization algorithm,
and a quality score was assigned to each based on certain criteria [63]. The original
version of the ant colony optimization algorithm formulated by Colorni et al. [7] used
a stochastically generated initial solution that was gradually improved. However, the
discriminative power of markers is closely related to various variables, including Na ,
Nea , AR, and PIC [17,20]. This led to the investigation of a method that includes this
information as an initial variable to be progressively improved by the heuristic algorithm.
For the chicken dataset, a comparative study of the four selection schemes revealed that
the accuracy of the improved algorithm (PIC + ACO scheme) was higher than that of the
original algorithm (ACO). With the optimized chicken microsatellite and 5% accuracy loss,
3 highly polymorphic markers (MCW0104, LEI0094, and LEI0166) were omitted by ACO
but included in the GGA5 panel.

4.3. Implications for Conservation Effort and Breeding Program

The chicken and Chinese goral datasets used in this study were sufficiently large
to facilitate the use of the marker optimization algorithm [28–33]. The availability of a
large genotype dataset allows for a more optimized exploration of the marker efficiency
mechanism. In addition to the widely developed non-invasive sampling methods [64],
the assessment and elucidation of genetic diversity can be significantly enhanced by the
development of molecular markers. Population dynamics and migration in several animals
have been studied using non-invasive fecal sampling [65]. However, the quality of the DNA
stock after extraction is very low, and not all common sets of microsatellite genotyping are
applicable. The competency of the output results in the full set can be effectively predicted
by optimizing the microsatellite marker panel. Conservation and breeding initiatives can
be greatly enhanced by the in silico development of microsatellite markers, enabling a
more optimized fit for the proposed microsatellite panel reduction scheme presented in
this study [66]. Budgetary barriers to numerous conservation and breeding initiatives
would be considerably alleviated by this approach, offering an opportunity for population
monitoring within an acceptable accuracy loss in conservation and breeding programs.
Interestingly, the number of markers that can be amplified in a single reaction significantly
influences both cost and efficiency. This relationship offers opportunities for cost reduction.
Although marker multiplexing effectively manages this trade-off, PCR efficiency is not
closely tied to polymorphism. In our current study, we prioritize polymorphism, leaving
the amplification efficiency of markers as a potential focus for future research.
Biology 2023, 12, 1280 13 of 16

5. Conclusions
This study explored the use of a modified ACO algorithm, PIC + ACO selection scheme,
to determine the most effective microsatellite panel for genetic diversity research with dif-
ferent accuracy loss tolerances. Experiments on both datasets revealed that microsatellite
markers allow for the exclusion of many markers while maintaining acceptable precision in
population genetics assessment. The optimized reduced set of markers exhibited efficiency
related to various metrics. However, the PIC + ACO selection scheme shows that markers
rely on hidden variables beyond simple metrics. The study results show that reducing lab-
oratory costs could promote conservation initiatives and population genetic investigations
in biodiversity conservation and breeding programs for genetic improvement.

Supplementary Materials: The following supporting information can be downloaded at:

https://www.mdpi.com/article/10.3390/biology12101280/s1. File S1: Python implementation
of ant colony optimization algorithm for selection of an optimized microsatellite marker panel;
Figure S1: Accuracy comparison of four microsatellite marker schemes including the ant colony
optimization (ACO), the selection by polymorphic information content (PIC), and hybrid method
consisting by optimizing the most informative set via ACO (PIC + ACO), and a random selection
used as a control group; Figure S2: Population structure estimation of the chicken using the full
set of 28 microsatellite markers (a), the GGA1 (b), the GGA5 (c) and the GGA10 (d) reduced set of
microsatellite; and the Chinese goral using the full set of 11 microsatellite markers (e), the NGR1 (f),
NGR5 (g) and NGR10 (h) optimized marker panel; Figure S3: Principal component analysis (PCA)
plotting of the population structure estimation of the chicken using the full set of 28 microsatellite
markers (a), the GGA1 (b), the GGA5 (c) and the GGA10 (d) reduced set of microsatellites; and
the Chinese goral using the full set of 11 microsatellite markers (e), the NGR1 (f), NGR5 (g) and
NGR10 (h) optimized marker panel; Figure S4: Discriminant analysis of principal component (DAPC)
plotting of the chicken population using full set of 28 microsatellite markers (a), the GGA1 (b), the
GGA5 (c), and the GGA10 (d) reduced set of microsatellites; Table S1: Summary of microsatellite
markers used in this study; Table S2: Summary of microsatellite markers selected by the PIC + ACO
selection scheme according to various margin errors. Data include number of alleles (Na), effective
number of alleles (Nea), allele richness (AR), polymorphic information content (PIC), and observed
(Ho) and expected heterozygosity (He); Table S3: Statistical comparison between the most accurate
selection method and the random microsatellite selection scheme; Table S4: Number of population
cluster estimated by the Structure software (Evanno et al., 2005 [43]); Table S5: Clustering of each
subpopulations using the Bayesian clustering of the Structure software (Evanno et al., 2005 [43]).
Author Contributions: Conceptualization, R.R., W.S. and K.S.; funding acquisition, K.S.; formal
analysis, R.R., P.W., T.P., S.F.A., N.M., A.A. and K.S.; investigation, R.R., P.W., T.P., S.F.A. and K.S.;
methodology, R.R., P.W., T.P., A.A. and K.S.; project administration, T.T. and K.S.; resources, R.R., P.W.
and T.P.; software, R.R., T.P., P.W., E.K. and W.S.; supervision, A.K., P.D. and K.S.; validation, R.R., W.S.
and K.S.; visualization, R.R., T.P. and K.S.; writing—original draft, R.R. and K.S.; writing—review
and editing, R.R., P.W., T.P., T.T., W.S., S.F.A., A.C., K.H., E.K., N.M., A.K., P.D., A.A. and K.S. All
authors have read and agreed to the published version of the manuscript.
Funding: This research was financially supported by grants from the Faculty of Science, Kasetsart
University, Thailand (No. 6501.0901.1/574) awarded to R. R. and K.S.; the High-Quality Research
Graduate Development Cooperation Project between Kasetsart University and the National Science
and Technology Development Agency (NSTDA) (6517400214) and (6417400247) awarded to TP and
KS; the NSTDA funds (NSTDA P-19-52238 and JRA-CO-2564-14003-TH) awarded to WS and KS;
National Research Council of Thailand (NRCT) (N42A650233) awarded to WS, SFA, NM, PD, KS;
National Research Council of Thailand: High-Potential Research Team Grant Program (N42A660605)
awarded to WS, SFA, AC, NM, PD and KS; the NSRF via the Program Management Unit for Human
Resources & Institutional Development, Research and Innovation (25669999123064) awarded to PW,
WS, AC, SFA, NM, PD and KS; the Kasetsart University Research and Development Institute funds
(FF(KU)25.64) awarded to WS, and KS; the Betagro Group (no. 6501.0901.1/68) awarded to KS; the
e-ASIA Joint Research Program (no. P1851131) awarded to WS and KS; the Office of the Ministry of
Higher Education, Science, Research, and Innovation; and the International SciKU Branding (ISB),
Faculty of Science, Kasetsart University awarded to WS and KS. No funding source was involved in
Biology 2023, 12, 1280 14 of 16

the study design; collection, analysis, and interpretation of data; writing of the report; or decision to
submit the article for publication.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The genotype data used in this project are publicly available on
https://doi.org/doi:10.5061/dryad.hhmgqnkm0 (Gallus gallus genotype dataset, accessed on 5 July 2023)
and https://doi.org/10.5061/dryad.wstqjq2hm (Naemorhedus griseus dataset, accessed on 5 July 2023).
Acknowledgments: We thank the Center for Agricultural Biotechnology (CAB) at Kasetsart University,
Kamphaeng Saen Campus, and the NSTDA Supercomputer Center (ThaiSC) for providing computa-
tional resources. We also thank the Faculty of Science for providing supporting research facilities.
Conflicts of Interest: The authors declare that they have no conflict of interest.

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