Content uploaded by Richard Frost
All content in this area was uploaded by Richard Frost on Jun 04, 2022
Content may be subject to copyright.
COUPLED ANALYSIS OF PAWPAW (
) GENETIC MARKERS AND ANCESTRY
Frost Concepts, Vista CA, USA
Subsets of 49 RAPD markers for 36 Asimina triloba specimens from U.S. NCGR repository sites are
examined for matches to ancestry records. Several known parent-progeny and sibling relationships are
verified, but a few specimens are also determined mislabeled due to excessive dissimilarities. An insight to
the debate of cultivar Overleese vs NC-1 is also presented.
Cultivar ancestry, Graph theory, RAPD markers
The Pawpaw is a deciduous tree native to eastern North America. It produces a potato-size fruit
which has been cultivated by native peoples since antiquity and more recently in home orchards
and small farms in the U.S. [1, 2]. Through the efforts of USDA agro-economist Neal Peterson
 the use of Pawpaw has increased in the past few decades due to his breeding of advanced
cultivars (see Figure 1) and establishment of USDA satellite repositories for Asimina specimens
. The fruit is also being considered as a crop in other parts of the world .
There have been 4 genomic studies of the specimens assembled by Peterson. The first 3 were by
Hongwen Huang, also known for his studies with chestnuts. Of them, the 1st in 2000 was a
preliminary study to determine appropriate single-loci RAPD markers . The 2nd in 2003
applied 71 of these markers to 37 specimens . One pair of the specimens has synonymous
marker values, thus bringing the usable total to 36. Also, 22 of the markers returned by the lab
contained missing values and unfortunately the measurements could not be repeated. Regardless,
Huang processed the data with the NTSYS-pc biostatistical package and employed two
questionable practices: use of markers with missing values  and dissimilarity measurements
with a pseudo-metric . On a positive note, Huang published all the marker data which provides
an opportunity to revisit the study. A few years later Huang published his 3rd study of the
specimens, this time using AFLP markers . This study also used pseudo-metric analysis and
only published the resulting dissimilarity values. The fourth genomic study of the Pawpaws was
by Pomper et al in 2010 . Only 6 SSR markers were used leading to a grossly underdetermined
data matrix. The data also contains many missing values and is thus of no use for further
The present effort involves rectifying the useable data from Huang’s 2nd study with known
ancestry data (Figure 2). Huang’s original 71 markers are considered a balanced set which were
then arbitrarily reduced to 49. As such, dissimilarity relations among the specimens are examined
using subsets of the markers with the goal of identifying one or more marker groups that are
meaningful with respect to ancestry records at an acceptable genetic distance resolution.
International Journal on Computational Science & Applications vol 12:3 pp.1-8, 2022
Figure 1. Known ancestry of U.S. Pawpaw cultivars currently in circulation [3, 11-13].
Figure 2. Ancestry and origins of specimens in H. Huang's RAPD study [3, 11]. The origin of
Wells-PPF is unknown. BEF = Blandy Experimental Farm.
A candidate group of markers was identified after an exhaustive, automated search of 2,121,017
topological graphs produced by subsets of size 44 through 49 of Huang’s error free markers –
sans 17,393 sets which produced one or more zero distances. A complete distance graph 𝐺
determined by the selected marker set was constructed along with a connected least bridges graph
𝐺𝐿𝐵 . Four known parent-progeny pairs appeared as nearest neighbours in 𝐺𝐿𝐵. The
distribution of mismatches is shown in Figure 3 and minimum and maximum distances are
exhibited in Figure 4. Loci mismatches of ancestry relations are given in Tables 1, 2.
Figure 3. Distribution of loci mismatches in complete graph of selected marker set.
Figure 4. Combined graph of distance extrema shown with solid lines, plus selected
neighbouring specimens for orientation denoted by dotted lines. Black vertices denote members
of known sibling sets a-f while grey vertices are members of suspected sibling sets g and h (see
Table 2). Arrowheads specify parent-progeny relations, otherwise spatial orientation is arbitrary.
Table 1. Known and suspected parent-progeny relations. Distance units are loci mismatches.
1-7-1 ≡ Shenandoah
not nearest neighbour
not nearest neighbour
Table 2. Known and suspected sibling relations.
1-68, 1-7-1 ≡ Shenandoah
1-7-2 ≡ Wabash, 2-10, 8-58 ≡ Rappahannock
14, 15, 11
4-2 ≡ Potomac, 11-5 ≡ Susquehanna, 11-13
8, 10, 10
PA-Golden, SAA-Zimmerman-1 and SAA-Zimmerman-2
From the top of Figure 4, one observes the tight cluster of specimens NC-1, Potomac, Prolific,
Middletown, Shenandoah, and Rappahannock. The cultivars 2-10 and Potomac are close enough
to imply at least a sibling relationship. Off to the right note the long distance to the parent-sibling
group of Sweet Alice and the SAA-Zimmermans, plus the adjacent group containing Sunflower
and Wabash. Two of C. Davis' first cultivars Taylor and Taytwo are found below along with
Wilson - a possibly undocumented offspring of Taylor. The numbered cultivar 11-13 – a sibling
of Potomac appears there at great distance from Taylor indicating the large dissimilarity of these
Davis breeds from the specimens above. Wells and Mitchell are found at the bottom – also
dissimilar from those above and the Davis breeds. The specimen Wells-PPF is displaced by 5
mismatches from Wells, indicating one could be the progeny of the other. Peterson apparently
believes the latter is the original.
The distance from Overleese to its progeny 1-7-1 appears excessive and from Taylor to its
progeny 1-23 even more so. Since both parents have suitable distances between other relations,
this calls into question the validity of the labels on 1-7-1 and 1-23. In the case of 1-7-1, the
problem is further emphasized by its relatively large distance to sibling 1-68. For specimen 1-23,
the discrepancy appeared in all marker subsets during the selection process.
In the long-debated case of Overleese vs its suspected sibling NC-1, a distance of 7 was found
which is in the range of 3-8 found for other parent-progeny relations. However, it is also close to
the range of 8-15 found in sibling relations. Consequently the debate appears unresolved by any
genomic measurements performed to date.
The results of the present study are limited by relevance of the original marker set and the process
of selection by ancestry records. Given the range of dissimilarities produced for known relations,
the measurements here should be considered a coarse approximation to the actual displacements
among specimens. Even so, the high correspondence (75%) between measurements and the
known relations of Tables 1, 2 indicate that H. Huang's markers have merit. Therefore the author
believes a retesting of the specimens using all 71 markers at a lab capable of producing error-free
results would be beneficial.
The data from H. Huang's paper was extracted using Adobe Acrobat® and placed in CSV files.
The markers with missing data values were entirely deleted. Specimens 11-13-KSU and 11-13-
PPF were found to have identical marker values and thus replaced by the single label 11-13. This
vetted set contains 36 specimens with 49 markers each.
A software program was then constructed to iterate through progressively smaller subsets of the
original size L = 49. For each subset, basic statistics such as distances in known relations was
extracted, along with parameters of the least bridges graph  produced by the markers including
the component maximal and a list of component vertices. Marker sets producing one or more zero
distances were discarded for poor resolution. The number of zero producing marker sets increased
from 0.085% at L = 47 to 0.85% at L = 44. Also at this latter size the resulting graphs suffered
from too much cohesion and thus no smaller sizes were pursued. Elapsed execution times for this
software program ranged from 0.2 seconds for L = 49 to 3.6 days for L = 44, including I/O.
A second program was written to rate the results. For each subset, a specimen pair from a known
relation was considered "present" if both members of the pair occurred in the same component of
the least bridges graph limited by δopt. Two vectors were formed from this data: numbers of
known relations and numbers of suspected relations, with each value in the last columns of Tables
1, 2 representing a vector component. The 2-norm of the outer product of these vectors was then
used as a score. From the scores a group of 291 candidates was produced. A high degree of
duplication was noticed among the topological structures. The candidates were examined for
cohesion properties and a best-of-class with L = 45 and δopt = 8 was selected. A connected graph
of the selection is shown in Figure 5.
All computation and visualizations for this study were performed with Mathematica® versions
12 and 13. The hardware platform was a deskside Intel® i9-10900KF PC with 32GB RAM and
1TB SSD running Windows® 11. No compatibility issues were detected within this environment.
Figure 5. Least genetic distances between 36 Pawpaw cultivars tested by Huang et al .
Distances represent # of loci mismatches between a rectified set of 45 markers from Huang's
original error-free set of 49. Orientation of Pawpaws is arbitrary except for solid arrows indicating
parent-progeny relations. Dashed arrow indicates suspected parent-progeny relation. Solid lines
(not arrows) are nearest-neighbour relations and dashed lines are least bridges. Names assigned
upon release of a breed to the nursery industry are specified by “≡”. Labels with superscripts a-f
are sets of known siblings, while g-h are sets of possible siblings.
 R. N. Peterson, "PAWPAW (ASIMINA)," Genetic Resources of Temperate Fruit and Nut Crops
290, pp. 569-602, 1991. [Online]. Available: https://www.actahort.org/books/290/290_13.htm.
 C. Ferrer-Blanco, J. Hormaza, and J. Lora, "Phenological growth stages of “pawpaw”[Asimina
triloba (L.) Dunal, Annonaceae] according to the BBCH scale," Scientia Horticulturae, vol. 295,
p. 110853, 2022, doi: https://doi.org/10.1016/j.scienta.2021.110853.
 R. N. Peterson, "Pawpaw variety development: a history and future prospects," HortTechnology,
vol. 13, no. 3, pp. 449-454, 2003, doi: https://doi.org/10.21273/HORTTECH.13.3.0449.
 "NCGR Corvallis - Asimina Germplasm." USDA ARS. https://www.ars.usda.gov/pacific-west-
 R. G. Brannan and M. N. Coyle, "Worldwide Introduction of North American Pawpaw (Asimina
triloba): Evidence Based on Scientific Reports," Sustainable Agriculture Research, vol. 10, no.
3, pp. 1-19, 2021, doi: https://doi.org/10.5539/sar.v10n3p19.
 H. Huang, D. R. Layne, and T. L. Kubisiak, "RAPD inheritance and diversity in pawpaw
(Asimina triloba)," Journal of the American Society for Horticultural Science, vol. 125, no. 4,
pp. 454-459, 2000, doi: https://doi.org/10.21273/JASHS.125.4.454.
 H. Huang, D. R. Layne, and T. L. Kubisiak, "Molecular characterization of cultivated pawpaw
(Asimina triloba) using RAPD markers," Journal of the American Society for Horticultural
Science, vol. 128, no. 1, pp. 85-93, 2003, doi: https://doi.org/10.21273/JASHS.128.1.0085.
 P. M. Schlueter and S. A. Harris, "Analysis of multilocus fingerprinting data sets containing
missing data," Molecular Ecology Notes, vol. 6, no. 2, pp. 569-572, 2006, doi:
 R. Frost, "Re-evaluation of NCGR Davis Ficus carica and palmata SSR profiles," PLoS ONE,
vol. 17, no. 2, p. e0263715, 2022, doi: https://doi.org/10.1371/journal.pone.0263715.
 Y. Wang, G. L. Reighard, D. R. Layne, A. G. Abbott, and H. Huang, "Inheritance of AFLP
markers and their use for genetic diversity analysis in wild and domesticated pawpaw [Asimina
triloba (L.) Dunal]," Journal of the American Society for Horticultural Science, vol. 130, no. 4,
pp. 561-568, 2005, doi: https://doi.org/10.21273/JASHS.130.4.561.
 K. W. Pomper et al., "Characterization and identification of pawpaw cultivars and advanced
selections by simple sequence repeat markers," Journal of the American Society for
Horticultural Science, vol. 135, no. 2, pp. 143-149, 2010, doi:
 K. W. Pomper, S. B. Crabtree, and J. D. Lowe, "The North American Pawpaw Variety:'KSU-
Atwood (TM)'," Journal of the American Pomological Society, vol. 65, no. 4, pp. 218-221, 2011.
[Online]. Available: https://www.pubhort.org/aps/65/v65_n4_a6.htm.
 K. Gasic, J. E. Preece, and D. Karp, "Register of new fruit and nut cultivars list 50,"
HortScience, vol. 55, no. 7, pp. 1164-1201, 2020, doi:
 R. Frost. "Least Bridges Graphs." https://frostconcepts.org/LeastBridgesGraphs/ (accessed
Richard is an old-school numerical analyst with
academic and vocational experience in applied
mathematics, computer science, and
horticulture. He is currently pursuing research
in the genomics of lesser-studied fruits.