INVESTIGATION

Unraveling the Hexaploid Sweetpotato Inheritance

Using Ultra-Dense Multilocus Mapping

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Marcelo Mollinari,*,†,1 Bode A. Olukolu,‡ Guilherme da S. Pereira,*,† Awais Khan,§ Dorcus Gemenet,**
G. Craig Yencho,† and Zhao-Bang Zeng*,†
*Bioinformatics Research Center, North Carolina State University, Raleigh, North Carolina, †Department of Horticultural
Science, North Carolina State University, Raleigh, North Carolina, ‡Department of Entomology and Plant Pathology,
University of Tennessee, Knoxville, Tennessee, §Plant Pathology and Plant-Microbe Biology Section, Cornell University,
Geneva, New York, and **International Potato Center, ILRI Campus, Nairobi, Kenya
ORCID IDs: 0000-0002-7001-8498 (M.M.); 0000-0003-4143-8909 (B.A.O.); 0000-0002-7106-8630 (G.d.S.P.); 0000-0003-4901-1694 (D.G.);
0000-0001-6583-0628 (G.C.Y.); 0000-0002-3115-1149 (Z.-B.Z.)

ABSTRACT The hexaploid sweetpotato (Ipomoea batatas (L.) Lam., 2n = 6x = 90) is an important staple KEYWORDS
food crop worldwide and plays a vital role in alleviating famine in developing countries. Due to its high Polyploidy
ploidy level, genetic studies in sweetpotato lag behind major diploid crops significantly. We built an ultra- Genetic Linkage
dense multilocus integrated genetic map and characterized the inheritance system in a sweetpotato full-sib Hexasomic
family using our newly developed software, MAPpoly. The resulting genetic map revealed 96.5% collin- Inheritance
earity between I. batatas and its diploid relative I. trifida. We computed the genotypic probabilities across Haplotyping
the whole genome for all individuals in the mapping population and inferred their complete hexaploid Preferential
haplotypes. We provide evidence that most of the meiotic configurations (73.3%) were resolved in biva- Pairing
lents, although a small portion of multivalent signatures (15.7%), among other inconclusive configurations Multivalent
(11.0%), were also observed. Except for low levels of preferential pairing in linkage group 2, we observed a
hexasomic inheritance mechanism in all linkage groups. We propose that the hexasomic-bivalent inheri-
tance promotes stability to the allelic transmission in sweetpotato.

The cultivated hexaploid sweetpotato (Ipomoea batatas (L.) Lam., 2n = are originated from either different or from the same species, re-
6x = 90) is an important staple food crop worldwide with an annual spectively (Comai 2005). While in diploid organisms the study of
production of
113 million tons (FAO 2017). It plays a vital role in allelic transmission and genetic linkage are relatively simple, these
alleviating famine, especially in developing countries in Africa and studies are considerably complicated in polyploids due to the wide
Southeast Asia (Loebenstein 2009). Despite its undeniable social and range of meiotic configurations these species undergo (Sybenga
economic importance, genetic studies in sweetpotato significantly 1975; Gallais 2003; Zielinski and Scheid 2012). Moreover, current
lag behind major diploid crops due to its complex polyploid ge- linkage analysis methods for complex polyploids (i.e., ploidy level
nome. Polyploids are organisms with more than two complete sets . 4) are mostly based on pairwise (or two-point) marker analyses
of homologous chromosomes. They are grouped into two cate- (Fisher 1941; Ripol et al. 1999; Kriegner et al. 2003; Aitken et al.
gories, allopolyploids or autopolyploids, when these chromosomes 2007; Cervantes-Flores et al. 2008; van Geest et al. 2017). These
methods rely on the assumption that the information in isolated
Copyright © 2020 Mollinari et al. pairs of markers is sufficient to detect recombination events between
doi: https://doi.org/10.1534/g3.119.400620 them accurately. In complex polyploids, however, this is rarely the
Manuscript received August 12, 2019; accepted for publication November 12,
case due to the limited mapping population size and the incomplete
2019; published Early Online November 15, 2019.
This is an open-access article distributed under the terms of the Creative Commons information provided by biallelic markers. Here, we present a fully
Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), informative multilocus genetic map of a full-sib hexaploid sweet-
which permits unrestricted use, distribution, and reproduction in any medium, potato population derived from a cross between the cultivars ‘Beau-
provided the original work is properly cited.
regard’ and ‘Tanzania’ (BT population) scored with more than
Supplemental material available at figshare: https://doi.org/10.25387/g3.10255844.
1
Corresponding author: 368 Ricks Hall, 1 Lampe Drive, Raleigh, NC 27607. E-mail: 30,000 informative single nucleotide polymorphisms (SNPs) using
mmollin@ncsu.edu our newly developed R package called MAPpoly. We also inferred

Volume 10 | January 2020 | 281

the haplotypes of all individuals in the full-sib population, which drought tolerance, and resistance for viruses and nematodes (Cervantes-
provided novel insights into the multivalent formation and prefer- Flores et al. 2008; Gemenet et al. 2019), for further QTL studies.
ential pairing in the sweetpotato genome.
Our multilocus analysis considers multiple SNPs simultaneously and Optimized genotyping-by-sequencing
propagates their information through the linkage group (LG) to over- protocol - GBSpoly
come the typical low informativeness of some two-loci combinations. Next-Generation Sequencing (NGS) library preparation protocol was
This strategy is fundamentally important for complex polyploid genome optimized for polyploids and highly heterozygous genomes to produce
analysis since pairs of biallelic markers carry very little information about uniform coverage across samples and loci, GBSpoly (Wadl et al. 2018)
the recombination process individually (Luo et al. 2004; Mollinari and (details in S1 Extended Material and Methods). The optimizations were
Garcia 2019). Moreover, the signal-to-noise (S/N) ratio in complex based on re-engineered barcoded adapters that ensure accurate demul-
polyploid SNP data sets is considerably lower as compared to that in tiplexing and base calls. The 6-9 bp variable length barcodes were
diploids and tetraploids (Mollinari and Serang 2015), thus making the designed to account for both nucleotide substitution and indel errors
genotype calling more prone to errors. The multilocus approach takes (based on edit/levenshtein distance), to minimize phasing errors and to
into account these errors by using the probability distribution of geno- maintain nucleotide diversity at every position along the reads. We also

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types provided by the genotype calling software (Mollinari and Garcia introduced buffer sequences upstream of the barcodes to ensure that
2019). Therefore, multilocus methods are essential to make appropriate the barcodes lie in high-quality base regions by avoiding the elevated
use of the information of multiple-dose markers and assess complex error rates at the ends of the reads. The adapters were ligated to frag-
polyploid inheritance systems. ments generated by double digests, TseI and CviAII, and then size
Several studies attempted to elucidate the polyploidy nature in selected to minimize PCR bias. By designing barcodes that did not
sweetpotato (allo vs. autopolyploid), including cytological and molec- reconstitute the restriction sites, ligated fragments were subjected
ular marker analyses (Gustafsson and Gadd 1965; Magoon et al. 1970; to a secondary digest to eliminate chimeric fragments. Sequencing
Shiotani and Kawase 1987; Austin 1988; Ukoskit and Thompson 1997; was performed on the Illumina HiSeq 2500. For more details, see S1
Kriegner et al. 2003; Cervantes-Flores et al. 2008; Zhao et al. 2013; Extended Material and Methods.
Monden and Tahara 2017), and more recently sequence-based studies
(Roullier et al. 2013; Yang et al. 2017; Muñoz-Rodríguez et al. 2018). Genotype calling
Two polyploidization scenarios were proposed: the first suggests an
We used the software SuperMASSA (Serang et al. 2012) to perform the
allopolyploid origin involving the hybridization of two sweetpotato
genotype calling of parents and offspring of the full-sib population. For
wild diploid relatives, I. trifida and I. triloba (Austin 1988); the second,
quality control purposes, we eliminated SNPs with read depth , 20
well supported by the literature, suggests an autopolyploid origin with
and estimated ploidy levels different from six. We also filtered out SNPs
I. trifida having a dual role in the polyploidization process (Shiotani and
with more than 25% of missing data and with segregation distortion
Kawase 1987; Roullier et al. 2013; Yang et al. 2017; Muñoz-Rodríguez
(P , 5 · 1024 ). Additionally, we removed four individuals with less than
et al. 2018). Corroborating this scenario, the polysomic inheritance
100 reads on average for the selected SNPs (see S1 Extended Material and
observed in several molecular marker studies rules out the strict al-
Methods). We obtained the physical positions of the selected markers in
lopolyploid sweetpotato origin (Kriegner et al. 2003; Cervantes-Flores
two diploid reference genomes of I. trifida and I. triloba (Wu et al. 2018)
et al. 2008; Zhao et al. 2013; Monden and Tahara 2017).
and classified them into shared between both genomes or private to
Nevertheless, none of these studies presented a comprehensive
a specific genome based on the full-sib population genotype calls.
profile of chromosomal pairing for all homology groups across the
whole genome nor the potential formation of multivalents at a pop-
De novo map construction
ulation level. Solving these missing pieces of information is essential to
unravel the precise mode of inheritance in sweetpotato, and conse- Grouping and SNP ordering: We computed recombination fractions
quently, allow an efficient application of molecular techniques in this for all marker pairs considering all possible linkage phase configurations.
complex polyploid breeding system. The BT population coupled with For each marker pair, we selected the recombination fraction associated
high-coverage sequence genotyping used in this study has two essential with the most likely linkage phase and assembled a recombination
characteristics that enabled high-quality mapping: 1) high and uniform fraction matrix for all marker pairs. Using Unweighted Pair Group
sequence read depth across the genome, which allows for high-quality Method with Arithmetic Mean (UPGMA) hierarchical clustering, we
genotype calling including multidose markers, and 2) sufficiently large generated a dendrogram representing 15 LGs corresponding to the
sample size to allow the detection of recombination events in a hexaploid 15 sweetpotato homology groups. To order the SNPs within each LG,
scenario. Additionally, we considered the uncertainty in the genotype we converted the recombination fractions to genetic distances using
calling by modeling the error during the map construction using a Haldane’s map function and applied the unconstrained Multidimen-
hidden Markov model (HMM) (Mollinari and Garcia 2019). Moreover, sional Scaling (MDS) algorithm with the squared LOD Scores to con-
all methods can be readily used in tetraploid and octoploid full-sib struct the stress criterion (Preedy and Hackett 2016).
populations.
Phasing and multilocus map estimation: The parental linkage phase
MATERIALS AND METHODS configuration was obtained by serially adding markers to the map
sequence and evaluating two-point likelihoods associated with possible
Plant material configurations between the inserted markers and the ones already
The mapping population consists of 315 full-sib individuals originated positioned. If the LOD Score between the two most likely configura-
from a cross between the oranged-flesh cultivar ‘Beauregard’ (CIP440132 tions was less than ten for a subset of configurations, we compared
- male) and the African landrace ‘Tanzania’ (CIP440166 - female). These the multipoint likelihoods of these phase configurations to proceed
two cultivars were selected due to their agronomic importance and to the next marker insertion. When the last marker was inserted, we
contrasting traits, such as beta-carotene and dry matter contents, re-estimated the multipoint recombination fractions between all

282 | M. Mollinari et al.

adjacent markers (Mollinari and Garcia 2019). For more details, 1. Regions with haplotype probabilities greater than 0.8 are assumed
see S1 Extended Material and Methods. to be 1.0, otherwise 0.0, forming a binary profile;
2. SNPs within a continuous segment of homolog or gaps
Reference genome-assisted map improvement flanked by crossing-overs smaller than 10 centimorgans (cM)
Using the I. trifida reference, we detected collinearity blocks within each are removed.
LG by visually inspecting abrupt breakages in the scatter plots conti- 3. If the remaining SNPs represent 20% or more of all SNPs in the
nuity (Supplemental Material, S5 Fig.). For each collinearity block, we analyzed LG, use Equation 1 to re-estimate the 400 genotypes
evaluated the multilocus likelihood associated with the initial MDS- across the whole LG and compute a new homolog probability
based “de novo” order and the order provided by I. trifida reference. We profile using Equation 2. Otherwise, consider the probability
selected the maximum likelihood order for each block, tested several profile inconclusive.
orientations among them (S1 File), and chose the configuration that 4. The crossing-over points are assessed by checking the points of
yielded the highest multilocus likelihood for the complete map. Next, probability transition across the LG. Homologs involved in the
we inserted the remaining private SNPs from I. triloba using the geno- chromosomal exchange can be trivially assessed.
mic position constraints imposed by SNPs shared by both genomes. 5. Exchange points closer than 0.5 cM are considered inconclusive

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We also eliminated SNPs that caused substantial map expansions (see since the haplotypes involved in the exchange could be errone-
S1 Extended Material and Methods). Finally, we re-estimated the map ously assigned due to the lack of resolution in the mapping
by considering the probability distribution of the genotype calling pro- population.
vided by SuperMASSA (Serang et al. 2012). We also computed the We applied this procedure to the 15 LGs of all individuals in the
Genotypic Information Content (GIC) (Bourke et al. 2018) for each population. We also present an interactive version of the heuristic
homolog across the entire genome. algorithm at https://gt4sp-genetic-map.shinyapps.io/offspring_
haplotype_BT_population/.
Probability distribution of the offspring genotypes
The probability distribution for all possible 400 hexaploid genotypes was Preferential pairing profiles
calculated using the HMM framework detailed in S1 Extended Material Considering that all homologs pair during a hexaploid meiosis, there are
and Methods. Briefly, if Gk;j denote the jth genotype, j 2 1; ⋯; 400, of an 15 possible configurations for a chromosomal segment. Let C ¼ fci g,
individual in a hexaploid full-sib population at locus k, the conditional i ¼ 1; . . . ; 15 denote a set containing all 15 possible configurations (see
probability distribution of Gk;j is defined as S1 Extended Material and Methods). The posterior probability distri-
bution of the pairing configurations at any position in the genome can

 a ðjÞbk ðjÞ
Pr Gk;j jO; l ¼ 400 k (1) be computed using
P
ak ðiÞbk ðiÞ
i¼1 1X n X400
 

Prðci jO; lÞk ¼ Pr ci Gk;j ; O; l Pr Gk;j jO; l l (3)
where O ¼ fO1 ; ⋯; Oz g is a sequence of observations of z markers, l n l¼1 j¼1
denotes the map parameters, ak ðjÞ denotes the joint probability of the
partial observation sequence to the left of marker k (including k) and where n is the  number21 of individuals in the population,

genotype Gk;j , given the map parameters l; similarly, bk ðjÞ denotes the Prðci Gk;j ; O; lÞ ¼ m2 ! (m ¼ 6 for hexaploids) if Gk;j is consis-
probability of the partial observation sequence to the right of the po- tent with ci , i.e., if genotype Gk;j can be originated from the
sition given the genotype Gk;j and the map parameters l. The quantities pairing configuration ci , 0 otherwise (Mollinari and Garcia
ak ðjÞ and bk ðjÞ can be obtained using the classical forward-backward 2019). We also assessed the preferential pairing for specific ho-
algorithm (Rabiner 1989; Jiang and Zeng 1997). Their derivation is molog pairs ðh; h9Þ using
presented in (Mollinari and Garcia 2019) and briefly described in S1
Extended Material and Methods. X
15
Prðh; h9jO; lÞk ¼ Ii Prðci jO; lÞk; h 6¼ h9 (4)
Offspring haplotype reconstruction i¼1

The probability that an offspring individual carries a specific parental where Ii ¼ 1 if ðh; h9Þ 2 ci , 0 otherwise. In both situations, to test
homolog at position k can be obtained using whether the observed homolog configurations differ from their
expected frequencies under random pairing, we used x2 test with
X
400
 
 P , 1024 to declare significance. We also used the likelihood as-
PrðHk jO; lÞ ¼ Pr Hk Gk;j ; O; l Pr Gk;j jO; l (2)
j¼1
sociated to recombination fractions of single-dose markers to
assess preferential pairing, as suggested by Wu et al. (1992). Fur-
where, Hk 2 fa; b; c; d; e; f ; g; h; i; j; k; lg is the inherited homolog at ther details of methods are given in the S1 Extended Material and
locus k, PrðHk Gk;j ; O; lÞ ¼ 1 if Hk 2 Gk;j , 0 otherwise. We obtained Methods.
the haplotype probability profile for all 15 homology groups (one curve
for each homologs, from a to l) for all individual in the bi-parental Data availability
population by computing PrðHk jO; lÞ at every marker across the ge- The raw DNA sequences are available on the FTP server of the
nome. For more details, see S1 Extended Material and Methods. SweetPotatoBase (ftp://ftp.sweetpotatobase.org/ncsu/). Raw VCF files
are available from figshare. File S2 contains SNP locations in I. trifida
Heuristic algorithm to detect crossing-over events and I. triloba reference genomes, available in the Sweetpotato Geno-
Given the probabilistic nature of the haplotype profiles, we proposed the mics Resource website (http://sweetpotato.plantbiology.msu.edu). All
following heuristic algorithm to detect crossing-over events: remaining relevant data are within the manuscript and its Supporting

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Figure 1 Example of genotype call of SNP Tf_S1_30010438. (A) Scatter plot of the read counts for the two allelic variants A and G. The axes
represent the read counts of both allelic variants. Squared and triangle dots represent parents ‘Beauregard’ and ‘Tanzania’ respectively, and
regular dots represent the offspring. Dashed lines indicate seven possible dosages in a hexaploid individual. The different colors indicate the
dosages assigned to the individuals by SuperMASSA. The low number of individuals observed between genotypic classes (gray dots, with
genotype probability smaller than 0.8), outlines a data set with low noise, producing a clear classification. The genotypes of both parents were
estimated as three doses of the allelic variant A three doses of G. The genotype calling model also considered the expected Mendelian
segregation ratio, which under random chromosome pairing is 1:18:99:164:99:18:1. (B) Inferred probability distribution of genotypes for each
individual in the offspring. The colored dots correspond to individuals with the same genotypic classes in panel A. Loci where the highest
posterior probability was smaller than 0.8 were assigned as missing data (gray dots).

Information files available from figshare. Supplemental material routines to perform all steps involved in the map construction of
available at figshare: https://doi.org/10.25387/g3.10255844. autopolyploid species using a combination of pairwise recombination
fraction and HMM-based map estimation. First, we obtained the re-
RESULTS combination fractions and associated likelihoods for each possible link-
age phase for all SNP pairs (
749 million pairs). Next, we selected the
Genotype calling recombination fractions associated with the most likely linkage phase
Next-generation sequencing produced several millions of barcoded configuration for each SNP pair and applied the UPGMA hierarchical
reads, resulting in approximately 41 million tags, which were aligned clustering. We formed 15 distinct clusters representing I. batatas ho-
against the genomes of two sweetpotato diploid relatives, I. trifida and mology groups (S3 Fig.). For the 15 groups, 93.4% of the SNPs were
I. triloba (Wu et al. 2018), resulting in 1,217,917 and 1,163,397 SNPs, co-located on the same chromosomes in both references and LGs
respectively. We used the software SuperMASSA (Serang et al. 2012) to (S1 Table). These co-located SNPs were selected to build the initial
call a total of 442,184 SNPs anchored to I. trifida genome and 438,808 map. Since each LG had the majority of their SNPs corresponding to
anchored to I. triloba genome. After filtering out low-quality and redun- a distinct chromosome in both references, LGs were numbered after
dant SNPs (S1 Fig. A), we obtained 38,701 SNPs scored in 311 individuals. the diploid references.
SNPs that did not meet the significance threshold (P , 5 · 1024 ) were To order the SNPs in each LG, we used the MDS algorithm (Preedy
uniformly distributed across both reference genomes (S2 Fig.). They also and Hackett 2016). The reordered recombination fraction matrix is
presented lower read depth compared with SNPs that passed the thresh- shown in S4 Fig. A. With the proposed MDS order, the parental allelic
old, indicating that the distortion observed is rather due to data quality variants were phased using the procedure presented by Mollinari and
than a biological characteristic of sweetpotato. For all SNPs, we obtained Garcia (2019). The algorithm is based on LOD Scores of pairwise
the probability distributions of the dosage calls (exemplified in Figure 1). markers as the first source of information to sequentially position the
From the total SNPs, 55.5% were classified as simplex (single-dose allelic variants in specific homologs. For situations where pairwise anal-
markers present in one parent) or double-simplex (single-dose markers ysis had limited power, the algorithm used the likelihood of multiple
present in both parents) and 44.5% were classified as multiplex (S1 Fig. B). markers in a Markov chain for the map construction (see Materials and
Methods and S1 Extended Material and Methods).
Initial “de novo” map construction The initial “de novo” multilocus map is presented in S4 Fig. B.
To build the genetic map, we implemented the R package MAPpoly The length of the LGs ranges from 723.7 cM in LG 8 to 2,037.0 cM in
(https://mmollina.github.io/MAPpoly/). The software comprises LG 4, with a total map length of 20,201.8 cM and 32,200 SNPs

284 | M. Mollinari et al.

(average inter-locus distance 0.63 cM), with no considerable gaps n■ Table 1 Summary of sweetpotato genetic map
between SNPs. Although the MDS algorithm yielded adequate Number of markers
LG Length Total SNPs/cM
global marker orders for all LGs (S4 Fig. C), the resulting map is
(cM) Sa DSb MDc
considerably large. Two main reasons for this inflation are the mis-
placement of closely linked SNPs and genotyping errors (Cartwright 1 290.9 1216 318 1211 2745 9.4
2 184.6 857 197 673 1727 9.4
et al. 2007; Cheema and Dicks 2009; Bilton et al. 2018; Mollinari and
3 222.1 1085 285 1052 2422 10.9
Garcia 2019), which will be systematically addressed in the next 4 227.1 1374 379 1283 3036 13.4
sections. The alignment of the initial “de novo” map against the 5 157.1 892 194 815 1901 12.1
reference genomes is shown in S5 Fig. Despite several chromosomal 6 189.3 970 266 656 1892 10.0
rearrangements, we observed high levels of collinearity between 7 156.3 1005 234 612 1851 11.8
both reference genomes and the estimated map. The collinearity 8 115.5 712 140 312 1164 10.1
extended in blocks with few megabase pairs (Mb), as in LGs 2 and 9 178.1 1403 261 715 2379 13.4
7, up to the whole chromosome in LGs 5, 9, 10, 11, 12, 14, and 15. In 10 188.7 1106 234 822 2162 11.5
cases where the collinearity extended through the whole chromo- 11 145.6 724 177 729 1630 11.2

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12 181.0 1367 246 1048 2661 14.7
some, we observed sites of suppressed recombination (plateaus in S5
13 180.1 762 174 742 1678 9.3
Fig.), possibly indicating the location of centromeric regions. 14 125.3 667 96 590 1353 10.8
15 166.6 1019 265 799 2083 12.5
Reference genome-assisted map improvement and Total 2708.3 15159 3466 12059 30684 11.3
modeling of genotyping errors a
Simplex markers.
To reduce the effects of the local marker misplacement in map inflation, b
Double-simplex markers.
c
we used I. trifida reference genome to propose alternative SNP orders Multiple-dose markers.
within collinearity blocks and evaluated the likelihood of the result-
ing maps, keeping the one with the higher likelihood (see Material
final maps shows a length reduction of 7.fivefold due to the removal of
and Methods and S1 File). We used I. trifida as the primary refer-
spurious recombination events through the several steps of map im-
ence genome because the quality of the assembly is superior and
provement (S6 Fig.).
more closely related to I. batatas when compared to I. triloba (Wu
The final map contains 30,684 SNPs spanning 2,708.4 cM (average
et al. 2018). After the order improvement, 97.0% of the I. trifida
inter-locus distance of 0.09 cM), with 60.7% simplex and double-simplex
SNPs present in the map were locally reordered assuming the
markers, and 39.3% multiplex (Table 1 and Figure 2). All homologs
I. trifida genomic order, (i.e., the genomic order yielded higher showed allelic variations along the LGs indicating that their inheritance
likelihoods for the majority of the cases, see Material and Methods pattern can be assessed in the full-sib population. However, several LG
and S1 File). From the remaining I. trifida SNPs, 1.3% were kept in segments presented identical composition for a subset of homologs, as
their initial “de novo” order and 1.7% were eliminated since their shown by the Genotypic Information Content (GIC) (Bourke et al.
inclusion caused map inflation higher than 2.00 cM. We then posi- 2018). In our results, 81.9% of all map positions in ‘Beauregard’ and
tioned the SNPs private from I. triloba reference genome into the 77.2% in ‘Tanzania’ had a GIC . 80%, revealing that we can reliably
resulting map using the constraints imposed by both genomes (see trace back the inheritance of the most homologs from the offspring to
Material and Methods). The reference genome-assisted reordering the parents (S10 Fig.). A small number of homologs presented an
resulted in a map with 30,723 SNPs spanning 12,937.3 cM with an identical allelic composition for certain segments, which is the case,
average inter-locus distance of 0.42 cM, representing a reduction of for example, of homologs i and j for the most of LG 2 and l and k across
1.sixfold when compared to the initial “de novo” map (S6 Fig., blue the whole LG 11. The complete map can be interactively browsed at
map). To address the effects of genotyping errors, we re-estimated https://gt4sp-genetic-map.shinyapps.io/bt_map/. For a selected seg-
the map using the probability distribution of the genotype callings ment, the browser provides the name of markers, dosages in the parents
provided by SuperMASSA (Serang et al. 2012) as prior information and the linkage phase configuration of the allelic variants. S2 File shows
in the HMM emission function (Mollinari and Garcia 2019), as more map information, including the linkage phase configuration in both
implemented in MAPpoly (S6 Fig., green map). In this case, the parents. S3 and S4 Tables summarize the results of collinearity blocks
map length was 4,764.1 cM with an average inter-locus distance containing the identical SNP sequences between I. batatas genetic map
of 0.16 cM, representing a map reduction of 2.sevenfold when com- and I. trifida and I. triloba genomes, respectively. Thirty-nine blocks were
pared to the reference genome-assisted map. aligned to 326.5 Mb of I. trifida genome, covering 96.5% of the I. batatas
map (2,614.8 cM), with an average density of one SNP/14.2 kb; 107 blocks
Probability distribution of multiallelic genotypes and were aligned to 258.8 Mb of I. triloba genome, covering 83.1% of the map
final map estimation (2,251.8 cM), with an average density of one SNP/13.4 kb. The averaged
For all individuals in the BT offspring, we obtained the conditional genetic to physical map ratios for these regions were of 124.8 kb per cM
probability distribution of the 400 possible hexaploid genotypes in the for I. trifida and 114.9 kb per cM for I. triloba.
whole genome given the estimated genetic map. We used the Markovian
process to propagate the information throughout each LG. The geno- Haplotype reconstruction and multivalent formation
typic probability distribution at each genome position was assessed by To obtain the haplotype composition of all individuals in the full-sib
using the information of all markers in the LG in all individuals of the population, we assessed the conditional probability distribution of the
full-sib population (S2 Table and S7 Fig.). Next, we removed 13 indi- genotypes and appropriately combined them to build 12 profiles (one for
viduals with inconsistent genotypic profiles (S8 and S9 Figs.) and, each homolog) indicating the probability of inheritance of a particular
keeping the marker order, we re-estimated the final map consider- homolog across the whole chromosomes for all individuals in the BT
ing 298 individuals. A comparison between the initial “de novo” and the population (see Materials and Methods). The results can be accessed

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Figure 2 Sweetpotato genetic map. For each of the 15 LGs, we present the I. batatas genetic map with its SNPs anchored in both diploid
reference genomes. Blue lines connecting the map and reference genomes indicate SNPs shared between I. trifida and I. triloba reference
genomes and red lines indicate private SNPs. Above each map, we present a graphical representation of the parental linkage phase

286 | M. Mollinari et al.

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Figure 3 Example of haplotype reconstruction and distribution of meiotic configurations for individual BT05.320, linkage group 1. A) and B)
Probability profiles for 12 homologs indicating the segments inherited from parents ‘Beauregard’ and ‘Tanzania’, respectively. The red line
indicates the approximated centromeric region obtained using the I. trifida reference genome. The arrows indicate recombination points; C)
Recombination signature table indicating the homolog pairs involved in each crossing-over and their position in the map; D) Possible meiotic
configuration that originated gametes for individual BT05.320 in ‘Beauregard’ and ‘Tanzania’ and resulting gamete. Each chromosome is
represented by one chromatid; E) Representation of the meiotic results as a graph: nodes represent the homologs and the edges represent
recombination events between them.

at https://gt4sp-genetic-map.shinyapps.io/offspring_haplotype_BT_ of parental homologs present in a single homolog of a particular offspring

population/. By evaluating the recombination points and the homologs individual indicates the minimum valency of the meiotic configuration
involved in the chromosomal exchange, we proposed a heuristic algo- involved in its gamete formation (see example in Figure 3).
rithm to obtain chains of homologs linked by recombination events. Thus, recombination chains with two homologs indicate the for-
These chains represent the inference of the meiotic process. The number mation of at least a bivalent, three homologous, at least a trivalent, and so

configuration of the homology groups for parents ‘Beauregard’ and ‘Tanzania’. Black and gray rectangles indicate two allelic variants in each
marker in all 12 parental homologs (6 · in ‘Beauregard’ and 6 · in ‘Tanzania’). The Genotypic Information Content (GIC), is presented below each
homology group.

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Figure 4 Percentage of maximum number of homologs connected in the same recombination chain during metaphase I in ‘Beauregard’ and
‘Tanzania’ for all 15 LGs. LG 11 for ‘Tanzania’ was mostly inconclusive and is not shown.

forth. For each LG, we calculated the percentage of the maximum (2018), suggesting that the diploid genome assemblies could be used
number of homologs involved in the same recombination chain (Fig- as robust references for the hexaploid sweetpotato. We also have
ure 4). Most of the configurations involve recombination of two ho- constructed the hexaploid haplotypes of all individuals in the off-
mologs (73.8% in ‘Beauregard’ and 72.8% in ‘Tanzania’), indicating that spring, estimating the level of preferential pairing and multivalent
there was no evidence of a multivalent formation in the majority of formation during the meiotic process at a population level. We used
gametes formed. We also observed 12.8% of gametes in ‘Beauregard’ two high-quality reference genomes to improve the quality of our
and 15.2% in ‘Tanzania’ with haplotype configurations involving three map. However, it is important to notice that in the absence of a
or four parental homologs in a recombination chain (indicating reference genome, it is possible to obtain good estimates of the in-
trivalent or quadrivalent formation), and less than 2% of the meiotic heritance patterns in the studied population just by using the initial
configurations with five or six homologs (indicating pentavalent or MDS “de novo” order and the probability distribution of the geno-
hexavalent formation; details per LG in S5 Table). We also detected type calls in the map construction.
a significant positive linear correlation (P , 1023 ) between the Haplotype inference is the ultimate attainment in linkage analysis
number of individuals with meiotic configurations originated from since it contains the complete information about genome transmission
multivalent formations and the length of LGs (S11 Fig.). across generations. The challenge of performing such inference both
in parents and offspring, would require new approaches to model the
Preferential pairing multiallelic transmission in a very complex meiotic scenario. Here
In a hexaploid organism, there are 15 possible pairing configurations for we accomplished this by propagating the incomplete information of
a chromosome segment during the prophase I of meiosis. To assess the dosage-based SNPs throughout the LG using a Markov chain. As a
level of preferential pairing among homologs, we calculated the prob- result of the efficient combination of multiple SNPs, several LGs
ability profile for each of the 15 possible meiotic pairing configurations displayed fully informative parental haplotypes in most of their
(S12 Fig.) and 15 possible homolog pairs (Figure 5) across all LGs for length (Figure 2 and S10 Fig.). Nevertheless, LG11 had two homo-
both parents. We did not observe significant preferential pairing logs (k and l) carrying the same allelic variations across its entire
across the whole sweetpotato genome, except LG 2 which showed length, which leads us to speculate that these two homologs were
a low but significant preferential pairing between homologs i and j formed by nondisjunction of sister chromatids in meiosis II in one
in parent ’Tanzania’ (P , 1024 , Figure 5). To further ascertain ho- of Tanzania’s parent resulting in an unreduced gamete transmitted
molog preferential pairing, we evaluated the simplex marker infor- to the next generation (Burnham 1962). Even though in some cases
mation, which confirmed our preferential pairing findings using the where not all homologs could be distinguished, we estimated their
multilocus framework (S13 Fig.). probability distribution, which can be readily used in further ge-
netic studies, such as quantitative trait loci mapping performed for
DISCUSSION the BT population (Pereira et al. 2019). Moreover, our multipoint
We have built the first multilocus integrated genetic map of a hexaploid method mitigates the effect of a possible limited sample size pre-
species, sweetpotato, using our newly developed software MAPpoly. In sented in some studies (Hackett et al. 1998; Ripol et al. 1999;
the map, 90 homologs were densely represented in the 15 homology Doerge and Craig 2000; Luo et al. 2001) by using the propagation
groups of cultivars ‘Beauregard’ and ‘Tanzania’ exhibiting high collin- of the information of multiple markers. In doing so, the estimates
earity to two closely related diploid sweetpotato genomes, I. trifida and of the recombination fractions are obtained considering the struc-
I. triloba. The high collinearity found by using our ultra-dense map ture of the whole homology group, rather pairwise marker combi-
corroborates with the high levels of alignment (. 90%) between the nations. We also investigated how the assembled parental homologs
diploid genomes and the parent ‘Tanzania’ reported by Wu et al. were transmitted to their offspring by assessing the probability

288 | M. Mollinari et al.

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Figure 5 Probability profiles for 15 homolog pairs in parents ‘Beauregard’ and ‘Tanzania’ across 15 LGs. The dashed lines in the probability
3
profiles indicate the pairing probability expected under random pairing (15 ¼ 0:2). The lower panels indicate 2log10 P of a x2 independence test
24
for all possible homolog pairs. Dashed lines indicate P , 10 . Homologs i and j presented a low, but significant preferential pairing in LG 2.

Volume 10 January 2020 | Unraveling Sweetpotato Inheritance | 289

distribution of the multiallelic genotypes across the whole genome with studies based on nuclear and chloroplast phylogenies (Roullier
for all individuals in the mapping population. Based on the inferred et al. 2013; Muñoz-Rodríguez et al. 2018) which demonstrated the
probability distributions, we presented a comprehensive probabilis- autopolyploid origin of sweetpotato.
tic reconstruction of the haplotypes of all individuals in a full-sib A variety of intrachromosomal rearrangements were observed be-
hexaploid population. We found that 15% of the offspring showed tween I. batatas map and I. trifida and I. triloba genomes. Rearrange-
the evidence of multivalent formation, i.e., offspring homologs contain- ments mapped to both diploid references, such as the chromosome
ing more than two parental homologs. This leads to intra-homolog var- inversion at the beginning of LG 6 (Figure 2), represent structural
iation, which could not be due to exclusive bivalent pairing. changes exclusive to I. batatas. While the occurrence of such rearrange-
Multivalent configurations often cause faulty chromosomal segre- ments could cause instability to meiotic process at some point of the
gation leading to aneuploidy (Arana and Nicklas 1992; Hollister 2015). evolutionary history of a polyploid species (Lenormand et al. 2016),
Such a phenomenon could cause unbalanced gametes, and conse- given the high level of bivalent signatures and the stable hexasomic
quently the production of pollen and seeds with low viability, posing segregation observed in our analysis, we concluded that these struc-
a significant hindrance to a stable genomic transmission throughout tural changes became fixed and did not cause major disturbances to
generations in polyploids (Mwathi et al. 2017). Multivalents are the meiotic process in sweetpotato.

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usually observed in high numbers in recently formed polyploids, More than a linear order of genetic markers positioned in LGs, a
as in the case of the synthetic autopolyploid Arabidopsis thaliana genetic map is a statement about the inheritance pattern involved in the
(Santos et al. 2003). Most of the established autopolyploids, how- transmission of the genome from parents and their offspring. A full
ever, show considerably fewer multivalents. In a survey involving characterization of this process can be achieved if the mapping method
93 autopolyploid species, Ramsey and Schemske (2002) showed that allows the estimation of haplotypes in both generations. In diploid
the average frequency of bivalents was 63.7% whereas the average organisms, a hidden Markov model was proposed by Lander and Green
frequency of quadrivalents was 26.8%, which are significantly dif- for linkage analysis of multiple markers (Lander and Green 1987). Later
ferent from the theoretically expected (1 · two bivalents (II + II) to on, several studies paved the way for a linkage map construction
2 · one quadrivalent VI) (Sybenga 1975; Jackson and Casey 1982). and haplotype inference in autotetraploid species (Hackett and
For hexaploids, the theoretical proportion of bivalent to multivalent Broadfoot 2003; Leach et al. 2010; Zheng et al. 2016). However,
configurations is 1 · three bivalents (II + II + II) to 6 · one quadri- for complex polyploids, the map construction was restricted mostly
valent plus one bivalent (IV + II) to 8 · one hexavalent (VI) (Jackson to two-point marker analysis. We present the first integrated multi-
and Casey 1982). However, in our work, the number of multivalent locus genetic map with fully phased haplotypes for both parents and
signatures observed was notably low, whereas the number of bivalents offspring in a complex polyploid and, accompanied with it, the fully
was relatively high (Figure 4). These results corroborate the previous developed statistical methods and computational tool MAPpoly.
cytological study by Magoon and co-authors (Magoon et al. 1970), This opens the door for detailed genetic analysis in complex poly-
who found similar levels of multivalent configurations in sweetpotato ploid species in general.
pachytene cells. Nevertheless, our results provide population-level
evidence to the prevalence of bivalent configurations in sweetpotato ACKNOWLEDGMENTS
meiosis. This research was supported by Bill & Melinda Gates Foundation
In a scenario of scarce multivalent formation, the double reduction [grant number OPP1052983]. Research at the International Potato
(DR) phenomenon becomes a rare event. The DR of a given locus is a Center (CIP) was undertaken as part of the consultative group on
consequence of a series of cytological events: multivalent formation, international agricultural research (CGIAR)-Research Program on
crossing-over between the locus and centromere, and migration of the Roots, Tubers and Bananas (RTB) which is supported by CGIAR
the duplicated segment carrying the locus to the same pole of the cell at Fund Donors (http://www.cgiar.org/about-us/our-funders/). The
anaphases I and II (Mather 1936; Butruille and Boiteux 2000; Stift et al. authors thank the anonymous reviewers for their insightful com-
2008). Thus, multivalent formation is a necessary but not sufficient ments and valuable suggestions. We acknowledge the CIP sweet-
condition for the occurrence of DR. Consequently, the low fre- potato breeding team in Peru for running field experiments.
quency of multivalent formation observed in this work indicates
that the occurrence of DR is a rare phenomenon in the BT pop-
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