Interspecific transfer of genetic information through polyploid bridges

Abstract

Hybridization blurs species boundaries and leads to intertwined lineages resulting in reticulate evolution. Polyploidy, the outcome of whole genome duplication (WGD), has more recently been implicated in promoting and facilitating hybridization between polyploid species, potentially leading to adaptive introgression. However, because polyploid lineages are usually ephemeral states in the evolutionary history of life it is unclear whether WGD-potentiated hybridization has any appreciable effect on their diploid counterparts. Here, we develop a model of cytotype dynamics within mixed-ploidy populations to demonstrate that polyploidy can in fact serve as a bridge for gene flow between diploid lineages, where introgression is fully or partially hampered by the species barrier. Polyploid bridges emerge in the presence of triploid organisms, which despite critically low levels of fitness, can still allow the transfer of alleles between diploid states of independently evolving mixed-ploidy species. Notably, while marked genetic divergence prevents polyploid-mediated interspecific gene flow, we show that increased recombination rates can offset these evolutionary constraints, allowing a more efficient sorting of alleles at higher-ploidy levels before introgression into diploid gene pools. Additionally, we derive an analytical approximation for the rate of gene flow at the tetraploid level necessary to supersede introgression between diploids with nonzero introgression rates, which is especially relevant for plant species complexes, where interspecific gene flow is ubiquitous. Altogether, our results illustrate the potential impact of polyploid bridges on the (re)distribution of genetic material across ecological communities during evolution, representing a potential force behind reticulation.

Full text

PNAS 2024 Vol. 121 No. 21 e2400018121 https://doi.org/10.1073/pnas.2400018121 1 of 10
Interspecific transfer of genetic information through polyploid
bridges
FelipeKauaia,b,c,1 , QuintenBaforta,b , FrederikMortiera,b,c , MarcVanMontagua,b,1 , DriesBontec,1 , and YvesVandePeera,b,d,e,1
Contributed by Marc Van Montagu; received January 1, 2024; accepted April 15, 2024; reviewed by Kirsten Bomblies, Filip Kolar, and Martin Lascoux
RESEARCH ARTICLE
|
EVOLUTION
Hybridization blurs species boundaries and leads to intertwined lineages resulting in
reticulate evolution. Polyploidy, the outcome of whole genome duplication (WGD),
has more recently been implicated in promoting and facilitating hybridization between
polyploid species, potentially leading to adaptive introgression. However, because poly-
ploid lineages are usually ephemeral states in the evolutionary history of life it is unclear
whether WGD- potentiated hybridization has any appreciable effect on their diploid
counterparts. Here, we develop a model of cytotype dynamics within mixed- ploidy
populations to demonstrate that polyploidy can in fact serve as a bridge for gene flow
between diploid lineages, where introgression is fully or partially hampered by the
species barrier. Polyploid bridges emerge in the presence of triploid organisms, which
despite critically low levels of fitness, can still allow the transfer of alleles between
diploid states of independently evolving mixed- ploidy species. Notably, while marked
genetic divergence prevents polyploid- mediated interspecific gene flow, we show that
increased recombination rates can offset these evolutionary constraints, allowing a more
efficient sorting of alleles at higher- ploidy levels before introgression into diploid gene
pools. Additionally, we derive an analytical approximation for the rate of gene flow at
the tetraploid level necessary to supersede introgression between diploids with nonzero
introgression rates, which is especially relevant for plant species complexes, where inter-
specific gene flow is ubiquitous. Altogether, our results illustrate the potential impact of
polyploid bridges on the (re)distribution of genetic material across ecological commu-
nities during evolution, representing a potential force behind reticulation.
whole- genome duplication | polyploidy | introgression | reticulate evolution
e exchange of genetic information across species barriers leads to complex interconnec-
tions between lineages and promotes reticulated evolutionary histories. is phenomenon
has been well documented in bacteria, where horizontal gene transfer signicantly impacts
the spread of DNA fragments among various lineages, challenging the traditional concept
of bacterial species (1). However, recent ndings from the expanding collection of
sequenced genomes reveal that the transfer of genetic material between dierent species
is common across all forms of life (2–5). ese instances of gene transfer between species
have a signicant impact on how we reconstruct evolutionary relationships (6), inuencing
our understanding of the diversication of life as a whole. Identifying the pathways through
which genetic material moves across species is therefore essential to better understand the
mechanisms underlying the emergence and maintenance of biodiversity.
Polyploidy, the outcome of whole genome duplication (WGD), or the addition of one
or more complete sets of chromosomes to a diploid genome, is widely recognized to have
important implications for the generation of genetic novelty over macroevolutionary scales
(7–11). Interspecic gene ow among polyploids, also referred to as WGD- mediated
introgression, has been more recently implicated in promoting adaptation of polyploid
species to specic intracellular demands and challenging environments (12–21). Transfer
of genetic material between the tetraploid cytotypes of Arabidopsis arenosa and Arabidopsis
lyrata, for instance, was shown to stabilize meiosis among the higher ploidy individuals
of both species (15). Introgression mediated by WGD might also have conferred a selective
advantage to polyploid amphibians in adapting to extreme environments (16) and is likely
to be responsible for the highly reticulate evolutionary history of fungi (4, 22). In fact,
articially induced polyploidy is long known among plant breeders to facilitate hybridi-
zation of otherwise sterile diploid hybrids, allowing the generation of agriculturally useful
species (23, 24). In all respects, these observations support the hypothesis that polyploidy
may indeed break the species barrier (16).
WGD is regarded as an extreme mutational event, and its emergence is often linked to
environmental turmoil (10, 25–29). Ongoing eorts to uncover WGDs in the history of life
(30, 31) reveal that several of such events seem to cluster around periods of environmental
Significance
Polyploidy, which results from
the duplication of an organism’s
entire genome, is a known source
of genetic novelty that promotes
speciation, thus contributing to
the evolution and distribution of
biodiversity. Its ecoevolutionary
interactions with coexisting
diploid relatives are nonetheless
elusive. Here, we have developed
a theoretical model to
understand the temporal
dynamics of mixed- ploidy
populations, revealing that
polyploidy may serve as a bridge
for gene ow across diploid
species boundaries. Due to
exceptional hybridization
potential and the intricate mating
dynamics specic to mixed- ploidy
populations, polyploids may play
an important role in the
emergence of intertwined
lineages. Our ndings provide,
therefore, insights into the
mechanisms that underlie the
distribution of genetic material
within ecosystems, leading to
reticulate evolutionary histories.
Reviewers: K.B., Eidgenossische Technische Hochschule
Zurich; F.K., Univerzita Karlova; and M.L., Uppsala
Universitet.
The authors declare no competing interest.
Copyright © 2024 the Author(s). Published by PNAS.
This article is distributed under Creative Commons
Attribution- NonCommercial- NoDerivatives License 4.0
(CC BY- NC- ND).
1To whom correspondence may be addressed. Email:
felipekauai.pereira@psb.vib- ugent.be, marc.vanmontagu@
ugent.be, dries.bonte@ugent.be, or yves.vandepeer@
psb- vib.ugent.be.
This article contains supporting information online at
https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.
2400018121/- /DCSupplemental.
Published May 15, 2024.
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2 of 10 https://doi.org/10.1073/pnas.2400018121 pnas.org
upheaval (7, 32, 33), such as the mass extinction event at the
Cretaceous–Paleogene (K- Pg) boundary (34, 35), indicating a poten-
tial enhanced capacity of polyploids to adapt and respond to stressful
conditions (27, 36–39). Notwithstanding the presumed adaptive
potential, phylogenetic, and theoretical analyses also suggest that
polyploid lineages exhibit higher extinction rates than diploids
(40–42), or eventually evolve back to the (more) stable diploid state
through the process of rediploidization (33). erefore, due to its
usually ephemeral presence in the history of life, it is unclear whether
polyploidy has an appreciable eect on the evolutionary trajectories
of their diploid counterparts, despite its potential to breach the spe-
cies barrier. As there is no clear route known for gene ow from
higher- ploidy levels back to diploids, WGD- mediated adaptive
introgression is expected to operate uniquely at the (transient) poly-
ploid level (21, 43), e.g., from a diploid to its derived tetraploid
toward the tetraploid of another species.
Current theory neglects the presence, even if temporary, of inter-
mediate odd- ploidy levels. For example, triploid cytotypes, known
to exhibit low overall tness (44), may function as genetic bridges
between tetraploids and their diploid counterparts through the gen-
eration of gametes compatible with both ploidy levels. e discovery
that the genes coding for the
C4
photosynthetic pathway in the
tetraploid Neurachne muelleri and the diploid, tetraploid, and hexa-
ploid cytotypes of Neurachne munroi are not paralogous, but likely
shared through hybridization or lateral gene transfer (18) suggests
that the introgression of alleles through WGD may indeed spread
among cytotypes and profoundly impact the evolutionary history of
the recipient species. Clear signs of admixture at the polyploid level
and intraspecic ploidy variation in other grass lineages, such as
Alloteropsis (45, 46) suggest that lateral gene transfer, mediated by
WGD, does occur (47), and that genetic information can introgress
into the (more) stable diploid levels. If this is the case, the duplication
of the entire genome of an organism may not only promote the
generation of genetic novelty, but also the distribution of extant
genetic material among species, thereby catalyzing reticulation. Since
polyploidy incidence in plants is strikingly common (48, 49), as well
as in several animal clades (38, 50), a systematic understanding of
gene ow and cytotype dynamics within and among mixed- ploidy
systems is paramount.
According to the current view, polyploids primarily emerge by
the union of unreduced gametes, which are formed by a rare event
resulting from the nonsegregation of chromosomes during meiosis
(44, 51, 52). For example, unreduced (diploid) gametes may fuse
within a population of diploid organisms to give rise to a new
tetraploid cytotype, which then is expected to face signicant
challenges to establishment due to negative frequency- dependent
selection (53). at is, polyploid establishment is contingent on
successful mating, which depends on the frequency of other organ-
isms displaying the same ploidy level. However, triploid interme-
diates are hypothesized to relieve the frequency- dependent
disadvantage of the emerging tetraploid cytotype by functioning
as bridges between ploidy levels (44, 54–57). is observation is
supported by a number of experimental eorts, which indicate
that triploids may also promote bidirectional interploidy gene ow
in many systems, despite critically low levels of tness relative to
diploids and tetraploids (43, 44, 57–65).
To understand gene ow within and between mixed- ploidy
populations, here we generalize the theoretical framework for
cytotype dynamics introduced by Felber (66), which models
the emergence of autopolyploids, i.e., polyploid organisms
emerging within a single species. We provide an analytical
account of the model by including triploid cytotypes with var-
iable tness, which allows us to derive the equilibrium cytotype
frequencies and gauge the role of triploids within mixed- ploidy
populations as far as their interactions with tetraploid and dip-
loid cytotypes are concerned. Next, we extend this model to a
broader theoretical framework consisting of two independent
mixed- ploidy populations that are partially connected at the
tetraploid level, i.e., displaying WGD- potentiated hybridiza-
tion, using a stochastic individual- based simulation. We then
set out to explore the conditions and constraints for
WGD- mediated interspecic gene ow between diploid cyto-
types of dierent mixed- ploidy species and quantify how much
gene ow at the tetraploid level is necessary to override signals
of direct introgression between the involved diploid species.
Altogether, our results provide insights into the extent to which
polyploids could contribute to reticulation by WGD- mediated
interspecic gene ow, despite their usually transient existence
in ecological systems.
Results
Model for Cytotype Dynamics in a Single Mixed- ploidy
Population. We assume an initially diploid population
consisting of
N
individuals which reproduce sexually in discrete
nonoverlapping generations. Specically, we assume that in each
generation an eectively innite pool of gametes is formed, of
which a random sample of gametes is obtained to generate the next
generation. Gametes can either be haploid or diploid. When two
haploid (diploid) gametes fuse, a diploid (tetraploid) individual
is produced, whereas the fusion of haploid and diploid gametes
produces a triploid individual. Diploid organisms produce diploid
gametes (unreduced) with probability
𝜐
and haploid gametes with
probability
(1 −𝜐)
. e emerging triploid cytotypes are assumed
to display reduced tness
𝜙
, due to aneuploidy or reduction in
viability, for example. Triploids produce either haploid or diploid
gametes, with equal probability, as studied by previous theoretical
models (54, 55) (see Discussion for an account of triploid gamete
formation). Tetraploids, on the other hand, are allowed to generate
only diploid gametes, as there is no known mechanism of viable
haploid gamete formation by tetraploid cytotypes (43) (but see
refs. 67 and 68 for examples of haploid gametes generated by
tetraploid cytotypes in sh).
We dene such a population, which consists of dierent cyto-
types that emerge through the formation and random fusion of
dierent gamete types as a mixed- ploidy population. Notice that
because only haploid and diploid gametes are allowed in our
model (across all ploidy levels), only three cytotypes can emerge
by construction, namely, diploids, triploids, and tetraploids. e
emergence of new cytotypes in the population is therefore a func-
tion of the random fusion of gamete types and is, as such, condi-
tioned on the cytotypes in the population only. It is instructive to
consider the cytotype frequency dynamics in the limit
N
→
∞
,
as studied by Felber (66), where we can describe the time evolution
of cytotype frequencies within such a mixed- ploidy population
through a set of nonlinear recursive equations. Let
gp
be the fre-
quency of the
p
- ploid gamete in the gamete pool produced, where
p∈{1, 2 }
. en, after one generation of random mating one
can compute the frequencies of each gamete type as follows:
[1]
[2]
To precisely understand the formulation in Eqs. 1 and 2, let
x2
,
x3
, and
x4
represent the frequency of diploid, triploid, and
g
1�=g1
2
(1−𝜐)+𝜙g1g2
g1
2
+2𝜙g1g2+g2
2
,
g
2�=𝜐g1
2
+𝜙g1g2+g2
2
g1
2+
2
𝜙
g1g2
+
g2
2
,
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PNAS 2024 Vol. 121 No. 21 e2400018121 https://doi.org/10.1073/pnas.2400018121 3 of 10
tetraploid cytotypes, respectively. In a mixed- ploidy population
which produces haploid and diploid gametes with frequencies
g1
and
g2
, respectively, the expansion of the binomial
(
g
1
+g
2)2
returns the expected frequency of each cytotype:
x2
=
g12
,
x3=2g1g2
, and
x4
=
g22
. By reducing the contribution of triploids
to the gamete pool by a factor
𝜙
, we arrive at the formulation for
the dynamics of gametes in Eqs. 1 and 2. en, gamete equilib-
rium frequencies can be obtained by setting
g1�
=
g1
and
g2�
=
g2
,
and solving for
g1
(note that
g2=1−g1
). We nd that the equi-
librium gamete frequencies satisfy:
[3]
Eq. 3 tells us that two xed points for
g1
(
+
and
−
) exist for
appropriate values of triploid tness
𝜙
and unreduced gametes fre-
quency
𝜐
, one of which is unstable and the other one stable
(SI Appendix, Text S1). e stable equilibrium frequencies, which
the system always converges to under the assumed initial conditions
(an initial population of diploids), are shown for each cytotype as a
function of
𝜐
and
𝜙
(Fig. 1A). e rate at which unreduced gametes
are produced by diploids has a direct inuence on the frequencies of
each cytotype in the population. When
𝜙=0
, i.e., triploids are com-
pletely unviable, we observe that tetraploids overtake the system
(
x4=1
) for
𝜐=0.171
. is is the maximum limit of unreduced
gametes frequency
𝜐′
numerically shown by Felber (66) to allow
stable coexistence between diploids and tetraploids in the absence of
triploids and external selective pressures. Our formulation of Felber’s
model allowed us to generalize his results to the case where triploids
inhabit the system with any tness (
𝜙<0
), and obtain an explicit
analytical expression for
𝜐′
given any
𝜙
as follows:
[4]
As the probability of unreduced gametes
𝜐
increases, the fre-
quency of triploid and tetraploid cytotypes becomes progressively
higher until a value of
𝜐′
is reached (see SI Appendix, Text S1 for
the proof of the result in Eq. 4), over which tetraploids dominate.
For instance, with triploid tness
𝜙=0.30,
Eq. 4 tells us that
𝜐′
is
12.01%
, and below this threshold cytotypes will coexist, i.e.,
display stable nonzero frequencies. We conrmed this expectation
by numerically iterating Eqs. 1 and 2 and comparing with an
individual- based stochastic simulation of the model with nite
population sizes (Fig. 1B).
e inuence of triploid tness on the stable frequencies of cyto-
types within a population is anticipated by the triploid bridge hypoth-
esis, where triploids may aid the emergence of tetraploids by reducing
the eect of minority cytotype exclusion (55). To understand it in a
qualitative manner, notice the probability that a triploid is formed
within a diploid population is
2(1 −𝜐)𝜐
, whereas the formation
probability of a tetraploid is simply
𝜐2
, with
𝜐≪1
. As we increase
triploid tness, the frequencies of triploid cytotypes converge to
higher magnitudes in the system. By extension, the relative proportion
of diploid gametes increases as they are produced with probability
𝜐
in diploids and probability
0.5
in triploids (Eq. 2). e higher load
of diploid gametes within the population, essentially due to a partial
replacement of diploids by triploids, then facilitates the expansion of
tetraploid cytotypes. erefore, despite reduced tness, triploids can
relieve the frequency- dependent disadvantage of tetraploids, aiding
their establishment by introducing a higher number of diploid gam-
etes in the system, in accordance with previous theory (44, 55). is
observation is further supported by several experimental studies across
many plant families, where intermediate (odd- ploidy) cytotypes are
often found and hypothesized to have a signicant impact on admix-
ture (57). Similar patterns can also be inferred, albeit to a lesser extent,
in animal taxa (see SI Appendix, Text S2 in for a more extensive review
of interploidy admixture in both plants and animal lineages).
Mixed- ploidy Model of Interspecic Gene Flow. To understand
how interspecic gene ow can occur at the diploid level through
polyploidization, we have built a stochastic individual- based model
of two discrete nite panmictic mixed- ploidy populations. Both
populations follow largely independent dynamics, as described
in the previous subsection, but are connected by migration with
rate
𝜅
at the tetraploid level, which represents the degree with
which tetraploids break the species barrier (16, 21). e initial
population consists of a set of identical individuals bearing a
diploid genome represented by two nite chromosomes with
L
biallelic unlinked loci. At each mating event, recombination and
gamete formation take place (Methods), with ospring emerging
from the union of its parents’ gametes. Fig.2 illustrates the logical
structure of the model, whereby two mixed- ploidy species (A
and B) are connected only by migration at the tetraploid level.
In this work, we analyze interspecic gene ow in a system that
g∗
1+,g∗
1−=3𝜙+𝜐−3
4(𝜙−1) ±
√
(3−3𝜙−𝜐)2
16(𝜙−1)2−1
2
,
𝜐
�
=(𝜙−1)(2√2−3),
Fig.1. Dynamics of cytotype frequencies in a single deme. (A) Equilibrium
frequency of diploids (solid red line), triploids (solid green line), and tetraploids
(solid blue line) as a function of the probability of unreduced gametes
in diploids
𝜐
, for triploid tness
𝜙=0
,
𝜙=0.30
, and
𝜙=0.60
. Maximum
frequency of unreduced gametes
𝜐
below which coexistence is veried
corresponds to the vertical lines, where tetraploids overtake the system. (B)
Frequency of each cytotype in the mixed- ploidy population per generation,
with
𝜙=0.30
and
𝜐=0.10
, given by the set of Eqs. 1 and 2 in solid black lines,
and by the individual- based stochastic version of the model (in faintly colored
lled circles) with nite population size
N=1,000
(Methods).
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4 of 10 https://doi.org/10.1073/pnas.2400018121 pnas.org
has triploids in both mixed- ploidy populations, for conceptual
clarity. However, asymmetrical gene ow is also expected, as one
of the populations might lack triploid cytotypes due to restrictively
low tness. Triploid intermediates are not required for gene ow
from diploids to tetraploids but are required for introgression from
tetraploids back to diploids (43, 69). A lack of triploid cytotypes
in one mixed- ploidy population thus allows for the emergence of
incomplete bridges with asymmetrical gene ow only to the diploid
in the population with triploids (SIAppendix, Fig.S1).
Let
GA
and
GB
be haploid sequences that represent the reference
genome of species
A
and
B
, respectively. en, we consider a
hypothetical divergent lineage, where each mixed- ploidy popula-
tion represents one of two species that are genetically or ecologi-
cally (Discussion) isolated with genetic distance
d(
G
A
;G
B)
(see
Fig. 3A and Methods for technical details). We rst assume a neu-
tral environment, i.e., the genotype of each individual has no
bearing on how well it performs within its population nor on the
genetic compatibility between two reproducing organisms. e
process of gene transfer between populations down to diploid
levels is then controlled by two parameters: the degree to which
polyploids from one population enter the gene pool of the next
population, represented by
𝜅
, and triploid tness
𝜙
. e system
is initialized so that in each population diploid individuals are
xed for a dierent allele in each one of the
L
loci (see SI Appendix,
Algorithm S1 for technical details on code implementation).
en, as time unfolds, migration at the tetraploid level carries
genetic information from one mixed- ploidy population to the
next at rate
𝜅
. We then measured the frequency of introgressed
alleles at the diploid state per generation and veried that xation
of nonnative alleles can happen even for critically low values of
𝜅
(Fig. 3B).
Once a nonnative tetraploid enters the new mixed- ploidy pop-
ulation, its genetic information can spread by three dierent non-
exclusive pathways; a
4x×4x
cross, in which case the new genetic
information remains at the tetraploid level, and
4x×3x
or
4x×2x
cross, which may produce either a tetraploid or a triploid individ-
ual. Here, we are primarily concerned with the latter two path-
ways, as a triploid organism can then produce haploid gametes
Fig. 2. Mixed- ploidy model of interspecic gene ow. The intercytotype
gene ow within and between mixed- ploidy populations A and B is depicted,
with diploids (2× red circle), triploids (3× green triangle), and tetraploid (4×
blue square) cytotypes, following largely independent dynamics, except by
migration at the tetraploid level, represented by the dashed lines connecting
the tetraploid cytotypes at the upper part of the picture. Solid lines connecting
cytotypes represent possible intercytotype mating events, with the direction
of the arrow indicating the resulting ploidy level. The unordered set next to
each line represents the gametes involved in the mating trial. For example,
a 2n (diploid) gamete owing from a 4× cytotype and a n (haploid) gamete
owing from a 2× cytotype, i.e., {2n,n}, will result in a 3× cytotype. The solid line
between the 2× cytotypes from populations A and B represents the species
barrier.
Fig.3. Frequency of introgressed alleles at the diploid level per generation. (A) The evolutionary history of a hypothetical lineage splitting into two dierent
species, A and B, is presented with each one displaying WGD events (following ref. 21). Diploids (red circle), triploids (green triangle), and tetraploids (blue square),
with the possible gene ow pathways as studied are highlighted. The genetic distance,
d
(G
A
;G
B)
, represents the nucleotide polymorphisms between the two
species following their evolutionary history (Methods). (B and C) The average frequency of homozygous loci with introgressed alleles per generation is shown,
for dierent values of
𝜅
and
𝜙
, respectively, and
𝜙=0.30
(B) and
𝜅=0.50
(C). Homozygous and heterozygous loci are distinguished to highlight that xation
proceeds iteratively through successive recombination events, until the system converges to a 50% equilibrium point of introduced and native homozygous loci
in each deme (see SIAppendix, Fig.S5 for the evolution of introgressed alleles considering only heterozygous loci). (D and E) The total frequency of introgressed
alleles per generation for dierent selection strength values
s
(with
d(
GA;GB
)
=100
%
) (D) for alternative genetic distances using a selection strength of
s=0.01
(E). Shaded ribbons represent
±1
SD from the average.
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PNAS 2024 Vol. 121 No. 21 e2400018121 https://doi.org/10.1073/pnas.2400018121 5 of 10
and backcross with the diploid state inside the population pro-
ducing a new diploid cytotype. e speed and frequency with
which alleles owing through these pathways enter the diploid
state of the new population will then depend on triploid tness
and random eects produced by drift (see Methods). We found
that the frequency of introgressed alleles per generation as a func-
tion of
𝜙
is qualitatively similar to the eect of
𝜅
. Even for
𝜙=0.01
, the frequency of nonnative alleles grows to an average
of 20.7% after 20,000 generations (Fig. 3C). It should be noted,
however, that this eect is in part a consequence of the lower
frequency of tetraploid cytotypes in both populations, as described
by Eqs. 1 and 2. By decreasing
𝜙
and keeping
𝜐
constant, the
frequency of tetraploid cytotypes will decay. erefore, in
SI Appendix, Text S3 we tested the eect of triploid tness by
normalizing
𝜐
as a function of
𝜙
(Eq. 4), which allowed us to show
the same eect decoupled from tetraploid frequencies. Also, in
SI Appendix, Text S4, we further show the evolution of introgres-
sion using a deterministic model of a single biallelic locus in the
limit
N→∞
, where we verify that in the absence of selective
pressures, xation of a nonnative neutral allele happens in the span
of a few generations.
As each population is xed for a dierent allele symmetrical gene
ow at the tetraploid level will eventually lead to an equilibrium
frequency of 50% of allele types in each population given enough
time. erefore, we were interested in the frequency with which a
single mutant allele—subject to drift (Methods)—arising in say,
population A, gets established in population B. We initialized our
system with both populations xed for a wild- type variant and after
cytotype equilibrium frequencies have been reached, as described
by Eq. 3, we released a mutant neutral allele in population A at the
diploid level and measured the number of times the mutant appears
in the diploid gene pool of population B or gets lost. We found the
probability that the mutant survives and introgresses into the diploid
state of population B to be
∼2.3%
, with the time it takes to cross
the bridge well described by an exponential distribution with an
average of
∼43
generations (SI Appendix, Fig. S2).
To further understand gene ow through polyploid bridges, we
built a tness map that modulates the probability of successful
mating with respect to the genetic distance between individuals
and the population’s optimal genome (Methods and Eq. 16).
Essentially, the probability that an individual successfully repro-
duces depends on how well its genetic background approximates
an optimal sequence (reference) that represents the environment
of its population. We rst tested the eect that selection strength,
represented by
s
, has on the average frequency of introgressed alleles
in each population (Fig. 3D). As expected, the larger the selection
strength is, the lower the frequency of nonnative alleles that can
enter a new gene pool at the diploid level, impeding the system
from achieving equilibrium. When genetic divergence is too high,
hybrids are subject to strong selective pressures, and introgression
of nonnative alleles is blocked (Fig. 3E). In our simulations, intro-
gression at the diploid level under high genetic divergence between
populations is primarily hampered by high selection at the tetra-
ploid state (SI Appendix, Fig. S3). Higher recombination rates can,
however, increase optimal allele sorting between lineages for intro-
gression down to the diploid states (SI Appendix, Fig. S4).
WGD- mediated Adaptive Introgression Compared to Adaptive
Introgression through Diploids. We now turn our attention to
the transfer of genes with adaptive value into a new diploid gene
pool from a dierent mixed- ploidy population. WGD- mediated
adaptive introgression has been argued to play a substantial
role in the adaptation of polyploids for both intracellular and
environmental demands (21), but its relevance may extend to
diploids by means of the mechanisms explored previously. Since
reproductive isolation between diploid species is seldom complete
(70), especially in plants (20), the question remains how much
gene ow is necessary at the tetraploid level
(𝜅)
to supersede
diploid- mediated adaptive introgression. If diploid states exchange
genetic information interspecically, even if at low rates, we ask
how much gene ow at the tetraploid level is required to override
diploid- mediated introgression of an adaptive allele into a new
diploid gene pool. is question arises naturally when one asks
about the relative importance of gene ow between polyploid taxa
given that their diploid counterparts are not completely isolated.
More specically, we are interested in the time it takes for an allele
with adaptive value to introgress into a new diploid gene pool
through polyploid bridges and compare it with interspecic gene
ow at the diploid level (Fig.4).
To measure how introgression of a benecial allele between tetra-
ploids diers from gene ow between diploid states, we built a
mainland- island model with unidirectional gene ow from the main-
land (species A) into the island (species B) (71) for each ploidy-
mediated introgression case. We assumed a single biallelic locus,
where the mainland species is xed for a benecial allele
A
(both
diploids and tetraploids) and the island species is xed for a delete-
rious variant
a
(across all cytotypes). e deleterious allele has a negative
additive tness eect
s
on genotypes, whose tness of the homozygous
states is decreased by a factor
(1 −s)
. Here, we shall derive the
equations that describe adaptive introgression through the route
4
x
(
species A
)
→4x
(
species B
)
→3x
(
species B
)
→2x
(species B)
,
i.e., polyploidy- mediated introgression. For the tetraploid gene pool
in the island there are three possible gametes, which we dene as
D1≜AA
,
D2≜Aa
and
D3≜aa
. Gametes of type
D1
migrate from
the tetraploid gene pool at the mainland at a rate
𝜅
, which will mix
with other diploid gametes produced within the island by tetraploid
and triploid genotypes (as described in previous sections). Let
pt
and
rt
represent the frequency of
A
in the island tetraploid and triploid
gene pools, respectively, at time
t
, and
qt=1−pt
and
wt=1−rt
the frequency of their corresponding deleterious variants. Under
Fig.4. Routes for adaptive introgression in a new diploid gene pool. Two
routes are presented for unidirectional gene ows from species A to species B.
Species A is initially (
t=0
) xed for a benecial allele whose frequency in the
tetraploid (
4x
) and diploid (
2x
) states is given by
pt
and g
t
, respectively. Gene
ow from species A to species B is represented by the transfer of gametes (in
curly brackets) between gene pools as before. Gene ow at the diploid level
occurs with rate
𝛽
and at the tetraploid level with rate
𝜅
. The speed with which
a benecial allele will introgress in the diploid gene pool of species B (lower
left corner) was compared when genetic information ows interspecically
through the route
4x→4x→3x→2x
, with the case where gene ow occurs
through the route
2x→2x
, mediated by
𝛽
.
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6 of 10 https://doi.org/10.1073/pnas.2400018121 pnas.org
random mating and assuming no double reduction during meiosis,
with average triploid tness
𝜙=0.30
(44), we found that the pro-
portions of each diploid gamete type in the island gene pool, following
unidirectional gamete migration from the mainland, can be calculated
as follows:
[5]
[6]
[7]
Likewise, we dened haploid gametes in the island as
H1≜A
and
H2≜a
, which can be produced by triploid and diploid cytotypes,
as in the previous models. en, if
gt
and
zt=1−gt
are the fre-
quencies of
A
and
a
, respectively, among the diploid cytotypes, the
proportion of haploid gamete types, following unidirectional migra-
tion from the mainland diploid species into the island (at rate
𝛽
) and
random mating, can be calculated as follows:
[8]
[9]
Eqs. 5–9 thus dene the proportions of all gamete types produced
by all cytotypes within the island at each time
t
with ongoing gene
ow from the mainland. By computing the gamete types, we can
retrieve the genotypes that make up the island population simply by
the expansion of the polynomial
(D1
+
D2
+
D3
+
H1
+
H2)2
, whose
frequencies will decay according to additive selection on the delete-
rious variant. For example, the resulting tetraploid genotype
D22
will
have its frequency decreased by a factor
(1 −0.5s)
as half of its loci
are
a
. By collecting all terms of the expansion and computing the
frequency of
A
within the diploid gene pool, we nd that the recur-
sive equation that describes the evolution of the benecial mutation
among the diploid cytotypes is written as follows:
[10]
where,
[11]
In SI Appendix, Text S5, we provide a detailed derivation of Eqs.
5–9, prove the result in Eq. 10, and provide the explicit formulas
D
1=pt4+2pt3qt+pt2qt2

1−𝜅−𝜙
2

+𝜅+1
2
𝜙

rt3+rt2wt

,
D
2=2pt3qt+4pt2qt2+2ptqt3

1−𝜅−𝜙
2

+1
2
𝜙

2rt2wt+2rtwt2

,
D
3={pt2qt2+2ptqt3+qt4}
(
1−𝜅−𝜙
2
)
+1
2
𝜙(rtwt2+wt3),
H
1={gt2+gtzt}
(
1−𝛽−𝜙
2
)
+𝛽
+1
2
𝜙(rt3+2rt2wt+rtwt2
),
H
2=
{
gtzt+zt2
}(
1−𝛽−𝜙
2
)
+1
2𝜙(rt2wt+2rtwt2+wt3
),
g
t+1=
1
Ψ{
H12+H1H2(1−0.5s)
},
Ψ=H12+2H1H2(1−0.5s)+H22(1−s),
for
pt+1
and
rt+1
. Notice that when
𝜙=0
, the only source of the
benecial mutation in the diploid gene pool comes from
diploid- mediated introgression at rate
𝛽
(Eqs. 8 and 9). When
𝛽=0
,
benecial mutations only arrive through polyploidy- mediated gene
ow (if
𝜙<0
), and thus
gt+1
is only a function of
𝜅
.
Setting
𝜙=0
and
𝛽=𝜅
, we rst measured how the frequency
of allele
A
unfolds in time for introgression at the tetraploid level
(
4x→4x
,
pt
) and compared it with introgression at the diploid
level (
2x
→
2x,gt
) for dierent values of
s
. at is, for the same
introgression rate between tetraploids and diploids, we ask how intro-
gression unfolds between tetraploid and between diploid popula-
tions. As expected, the speed with which allele
A
reaches xation in
the receiver populations depends on how strong selection is on the
deleterious variant
a
, that is, the higher the selection strength on
a
,
the faster introgression occurs (Fig. 5A). Additionally, for any selec-
tion coecient
s<0
, diploid- mediated introgression is always more
ecient (SI Appendix, Fig. S6). Indeed, population genetics theory
predicts that deleterious mutations may accumulate faster in poly-
ploids relative to diploids due to a masking eect (72), which has
been more recently experimentally conrmed by a number of studies
(29, 73). Essentially, due to the higher number of genome copies in
the polyploid state, deleterious mutations are masked from selection,
and therefore are expected to accumulate in polyploid lineages with
much less friction. Alternatively, our results show that this phenom-
enon decreases the eciency with which the introgression of a ben-
ecial allele occurs in a tetraploid as compared to a diploid gene pool.
To understand how both two routes (
4x→4x→3x→2x
and
2x→2x
) dier for an introgressing benecial allele, we measured
the time with which the benecial mutation gets xed within the
diploid gene pool through diploid- mediated gene ow for low
introgression rates (
𝛽≪1
), and computed the WGD- mediated
introgression rate (
𝜅min
) for which the allele gets xed in the same
diploid pool within the same time interval (see SI Appendix,
Algorithm S2 for a description of the algorithm). We then com-
puted the factor
𝜃=𝜅min∕𝛽
as it more clearly informs us on the
minimum increase in WGD- mediated introgression rate necessary
for introgression through polyploidy to be at least as ecient as
diploid- mediated adaptive introgression. We found that
𝜃
is a
linear function of the selection coecient
s
(Fig. 5B), that is, for
each unit increase in
s
the amount of WGD- mediated gene ow
to override diploid- mediated introgression increases linearly.
However, the degree of the increase (slope) as well as the minimum
increase for a neutral allele (intercept when
s=0
) has a complex
relationship with the introgression rate at the diploid level (
𝛽
).
us, in general, we can write
𝜃
as a function of
𝛽
as follows:
[12]
at is,
𝜃
is a linear function of the selection coecient
s
, where
the slope
𝜆(𝛽)
and intercept
𝜂(𝛽)
are unknown functions of
𝛽
. To
nd these unknown functions, we modeled separately the slope
and intercept with respect to the introgression rate at the diploid
level. Both the slope
𝜆(𝛽)
(Fig. 5C) and intercept
𝜂(𝛽)
(Fig. 5D)
were found to be nontrivial functions of
𝛽
, whose forms we could
only approximate locally (
0.001 ≤𝛽≤0.05
). ese approxima-
tions allowed us to retrieve a general equation to estimate the
minimum amount of gene ow at the tetraploid level necessary
to override adaptive introgression mediated by diploid states.
Realizing
𝜅min =𝜃𝛽
, we write:
𝜃(𝛽)=𝜆(𝛽)s+𝜂(𝛽),
[13]
𝜅
min ≈𝛽

0.37
𝛽
0.91 e−0.14𝛽+0.14ln(𝛽)

s+

−22.95

𝛽e−9.07𝛽+1.06ln(𝛽)+8.36
,
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PNAS 2024 Vol. 121 No. 21 e2400018121 https://doi.org/10.1073/pnas.2400018121 7 of 10
For any
s
, Eq. 13 tells us that any
𝜅<0
is sucient to allow
WGD- mediated introgression when diploids are isolated (
𝛽
→
0
)
consistent with our arguments in the previous sections. e use of
Eq. 13 is subject to two experimental challenges in natural or articial
systems. First, the introgression rate at the diploid level
𝛽
must be
recovered, which can be determined by analyses of gene ow using
molecular markers (74), for example. A second challenge concerns
the determination of the selection coecient
s
that a given allele is
subject to relative to an adaptive variant present in the population
from which gene ow is being measured. However, a rst lower- bound
to gene ow at the tetraploid level necessary to override gene ow at
the diploid level can be achieved by setting
s=0
, which informs the
experimentalist on the amount of gene ow between tetraploids
necessary for polyploid bridges to display a relevant impact on the
distribution of neutral genetic material across species boundaries.
Discussion
Understanding how genetic material ows among species is crucial
for our understanding of reticulate evolution. By generalizing the
well- known model of Felber (66) for cytotype dynamics, we show
that the transfer of genetic information between dierent diploid
species is possible under the current understanding of interploidy
mating dynamics and WGD- potentiated hybridization. A notable
example of introgression, potentially explained by gene ow through
polyploid bridges, pertains to genes encoding the
C4
photosynthetic
pathway in Alloteropsis semialata, which have been laterally acquired
from the polyploid Setaria palmifolia complex, most likely in tropical
Africa, where both species co- occur (46). Most of the non-
C4
indi-
viduals in A. semialata are diploids, with
C4
individuals ranging from
diploid to dodecaploid levels (45, 75). Although triploid hybrids
have not been reported so far for A. semialata, the most plausible
path through which genetic information coding for
C4
biochemistry
could have introgressed into the diploid level of the species would
be through compatible crosses that required the presence of a triploid
intermediate, from which a cross of the type
3x×2x
would allow
the information to spread down to the diploid level. An alternative
hypothesis may relate the presence of
C4
diploid individuals to the
process of diploidization. However, despite the fact that diploidiza-
tion is a slow process measured at macroevolutionary scales (33),
there is direct experimental evidence that crosses between photosyn-
thetic types in diploid A. semialata are viable (75). at is, following
introgression from polyploid S. palmifolia, information coding for
C4
biochemistry had to necessarily travel through the dierent ploidy
levels in A. semialata to reach the diploid level, where
C4
and non-
C4
individuals are then capable of exchanging genetic material.
It should be noted that the extent to which WGD facilitates
interspecic introgression at the polyploid level is not entirely clear
(21), which constrains our ability to unequivocally ascertain the
impact of polyploid bridges on macroevolutionary dynamics. For
instance, in a recent study, Marburger et al. (15) were able to
identify bidirectional introgression of genes controlling meiotic
Fig.5. Adaptive introgression eciency comparison between gene ow mediated by diploids and tetraploids in the mainland- island model. (A) Frequency of the
benecial allele
A
as a function of time (iterations) and selection strength
s
in the island at the diploid level through unidirectional gene ow from the mainland’s
diploid population (
gt
, solid lines), and at the tetraploid level through unidirectional gene ow from the mainland’s tetraploid population (
pt
, dashed lines). Gene
ow rates are the same in both cases:
𝛽
=
𝛼
=10
−3
. Additionally,
𝜙=0
. (B) Minimum increase in WGD- mediated introgression rate
𝜃
to achieve xation of the
benecial allele within the same time interval as achieved by diploid- mediated introgression (
𝜙=0.30
). (C and D) Relationship between the slopes and intercepts
of the linear equations (B) as a function of introgression at the diploid level
𝛽
. Equation coecients were retrieved by the Levenberg–Marquardt algorithm.
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8 of 10 https://doi.org/10.1073/pnas.2400018121 pnas.org
processes between tetraploid cytotypes of A. arenosa and A. lyrata.
ese shared introgressed genes, implicated in mechanisms like
meiotic double strand break formation, were deemed instrumental
for the emergence of stable meiotic processes in both lineages.
Nevertheless, the variability in meiotic stability found in the stud-
ied populations suggests that interspecic gene ow at the poly-
ploid level of both species depends on optimal sorting of
segregating alleles for stable lineages to emerge, which is supported
by signatures of selective sweep across their genomes (15). Here,
we demonstrated that although WGD- mediated interspecic
introgression down to the diploid level is constrained with surging
genetic divergence between mixed- ploidy populations, increased
recombination rates can relieve selection pressures, thereby facil-
itating the inux of new allele variants into a new gene pool by
increased eciency in sorting of alleles at higher- ploidy levels.
Interestingly, polyploidization has also been shown to increase
recombination rates in Arabidopsis (76), yet a clear understanding
of the relationship between genetic divergence and WGD- mediated
gene ow remains elusive.
While genetic incompatibility is one of the mechanisms of repro-
ductive isolation that is potentially circumvented by polyploidy,
WGD- potentiated hybridization may also favor the transfer of
genetic material across diverging populations by evading prezygotic
barriers. Indeed, since Levin (53) postulated the principle of minor-
ity cytotype exclusion, the hypothesis that ecological disparities must
exist between ploidy levels for successful establishment of polyploid
cytotypes has led researchers to identify a number of cases where
niche dierentiation or expansion following WGD occurs (16, 37,
38, 77–79). In particular, niche expansion of polyploid organisms
relative to their diploid ancestors might promote secondary contact
among allopatric populations of a specic taxon, restoring therefore
gene ow and counteracting reproductive isolation (21). Within
this paradigm, the interpretation of the migration coecient used
in our model
(𝜅)
could span both evolutionary and ecological
dimensions. On the one hand, WGD may directly breach species
barriers (16, 80) by overcoming putative postzygotic limitations,
and on the other hand promote intraspecic gene ow through
polyploid bridges among diverging populations, via secondary con-
tact or niche overlaps.
For the purposes of our theoretical investigation, we neglected
the possibility of triploid gamete formation by triploid cytotypes
within the main manuscript. It has been shown that the frequency
of triploid gametes is on average higher than the sum of diploid
and haploid gametes produced by triploids (44). is will lead to
an increased probability of tetraploid formation relative to the
present study and would hence increase gene ow from diploid
to tetraploids relative to gene ow from tetraploids to diploids
(SI Appendix, Text S6). Despite the bias in gene ow due to dif-
ferential production of gametes in triploids, the path for inter-
ploidy bidirectional ux of genetic material should remain open.
is contrasts with Cao et al.’s recent assertion (81) that crosses
involving hybrid triploids invariably yield tetraploids, correlating
with a reproductive barrier thwarting gene ow from tetraploids
back to diploid levels, termed a “triploid block.” In SI Appendix,
Text S6, we show that this eect is a consequence of the proba-
bilities for merging dierent gamete ploidy levels during self-
fertilization in triploid cytotypes. e model presented here is
anchored in our current understanding of interploidy mating
dynamics, and self- fertilization—though potentially important in
the establishment of new cytotypes—is tangential to this study’s
analytical purview. e assumption that triploid cytotypes produce
only diploid or haploid gametes is a simplication that allowed
us to obtain an explicit analytical solution to an (extended) version
of the mathematical problem posed by Felber (66). Asymmetry
in the direction of gene ow due to triploid gamete formation
should be considered carefully when assessing interploidy bidirec-
tional gene ow under laboratory conditions, since it may sub-
stantially increase sampling eorts for detection of interploidy
bidirectional gene ow.
roughout this paper, we also assumed additive tness eects
that are proportional to the ploidy level. However, the hybridiza-
tion of two species leading to polyploidy, or allopolyploidization,
may result in nonadditive gene expression patterns on hybrids
(82), which may inuence tness at the polyploid level and there-
fore impact the eciency with which genetic material diuses
through ploidy levels in the recipient gene pool. e extent to
which the emergence of polyploid bridges inuences adaptation
and disturb allele frequencies in real biological systems is yet to
be determined. e ux of genes among diploid states from dif-
ferent species may depend on the rate at which genes ow among
polyploids, which in turn may be conditioned on the spatial and
temporal sequences with which higher- ploidy species come into
contact. Furthermore, the tness map used in this study imposes
selection in an exogeneous manner, that is, the tness of an organ-
ism depends on the distance of its genome to an external sequence
that represents the optimum of the environment in which the
individual inhabits. Selection on hybrids may as well be based on
disruption of parental gene combinations, emerging therefore as
the product of negative epistatic interactions. For instance,
non- Mendelian segregation patterns on synthetic hybrids between
polyploids from cotton have been attributed to epistatic interac-
tions following the merging of parental genomes, whose coadapted
genes constrain the genomic composition of hybrid ospring (83).
Future experimental work is necessary to elucidate the eects of
allopolyploidy on interspecic introgression patterns through
polyploid bridges.
While polyploidy may be a transient phenomenon, i.e., an evo-
lutionary dead- end (10), its periodic emergence in the evolution-
ary history of life can serve as a bridge to connect diverged taxa
and redistribute genetic information among species. Here, we have
provided a systematic study on the dynamics of mixed- ploidy
populations and showed that, when genetic material is explicitly
accounted for, WGD may promote introgression into the more
(stable) diploid lineages from which polyploid species descend.
Recent surveys of polyploidy and hybridization in the wild largely
support the work presented in this manuscript (57). e mecha-
nisms studied here might therefore represent an important com-
ponent of reticulation during evolution and allow us to build a
more general understanding of how species interactions evolve
and how polyploidy aects biological networks. Further theoret-
ical and experimental investigations on the signicance of poly-
ploid bridges may provide insightful results into the delicate
interactions that weave biological networks throughout evolution-
ary history.
Methods
Our stochastic individual- based simulation contains a population of size
N
, where
each discrete diploid individual is represented by a set of two vectors, called
chromosomes, with
L
elements. Chromosome elements are taken from the set
{0, 1}
, representing biallelic loci. In the standard model, all individuals are iden-
tical, i.e.,
Si,k=Sj,k,∀i,j∈{N}
and
k∈{L}
. Mating is synchronous and is
performed by randomly choosing two individuals, with replacement, from their
corresponding mixed- ploidy population, whose gametes formed (see below) are
then joined to make up the genome of the offspring, until the carrying capac-
ity
N
is restored. Notice that the probability that an individual is not chosen to
reproduce in each generation is
(1−2∕N)N
, which approaches
e−2
in the limit
N→∞
, corresponding to drift. When mating is completed then bidirectional
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PNAS 2024 Vol. 121 No. 21 e2400018121 https://doi.org/10.1073/pnas.2400018121 9 of 10
migration occurs at the tetraploid level where each individual has a probability
𝜅
of entering the next population. Each iteration, or generation, corresponds to
a repetition of this process for a total of 20,000 generations.
A mating event consists of randomly selecting two individuals from the same
population, with each one undergoing meiosis, where recombination among
rL
randomly selected loci (
r≪1
) takes place. In a diploid individual, meiosis pairs
the two chromosomes and recombination occurs. Then, a gamete is one of the
resulting chromosomes chosen with equal probability, or both chromosomes,
i.e., unreduced diploid gametes, with probability
𝜐
. In triploids, recombination
occurs randomly between two of the three available chromosomes mimicking
chromosome pairing during triploid meiosis as shown in previous experimental
studies (84). In triploid meiosis three outcomes are possible: i) the individual
produces no gametes with probability
(1 −𝜙)
owing to differential contribution
to the gene pool due to fitness, in which case the mating event fails, ii) a haploid
gamete, or iii) a diploid gamete is randomly chosen out of the three available
chromosomes. We set outcomes ii) and iii) to happen with equal probability
(see Eqs. 1 and 2 in Results for a mathematical description). Finally, meiosis
in a tetraploid individual results in the random formation of two bivalents out
of the four available chromosomes, with no preferential chromosome pairing,
and a gamete is one of the bivalent pairs chosen with equal probability after
recombination has occurred, following previous work (42). Although chromo-
some pairing in polyploid meiosis can take up different forms depending on
polyploid origin (51), our goal is to isolate the effect of recombination, and
not to provide a comprehensive mechanistic understanding of the possible
results following differential recombination patterns in polyploid meiosis. In
SIAppendix, Fig.S7, the reader will find an illustration detailing the meiosis
procedure used in this work.
To understand the dynamics of the model under a selection regime, we devel-
oped a fitness map, assuming allele codominance, that relates the genomes of
individuals to a sequence that represents the optimum phenotype (a reference
genome randomly defined) in their respective mixed- ploidy populations. Let
d(Gi;GD)
be the total distance between the genome of individual
i
to its respective
population’s genome
D
(a single vector), relative to chromosome length
L
. Then,
for each loci
k
in each chromosome
p
of individual
i
, we define the distance to be
[14]
[15]
where
P
is the ploidy level of individual
i.
For a mating trial to be successful we require that both individuals have a
fitness value larger than a random number generated with uniform distribution
in the interval
(0, 1)
; otherwise, the system will choose another pair of individuals
from the same deme until a successful mating event occurs. The fitness
f
of an
individual is given by an exponentially decaying function of the form:
[16]
where
s
represents the selection strength that the populations shall be subject to.
The genetic distance between demes is assigned upon initialization of the sim-
ulation, where the number of alleles that can differ between demes’ sequences
is randomly selected to match the desired genetic divergence (see SIAppendix,
Algorithm S1 for implementation strategies).
Data, Materials, and Software Availability. All relevant data for this study
are included in the article and/or SIAppendix. Java scripts for Individual- based
simulations can be found at https://github.com/KauaiFe/PolyploidBridges (85).
ACKNOWLEDGMENTS. We thank Arthur Zwaenepoel (Unité Évolution, Écologie,
Paléontologie, Université de Lille 1, Villeneuve d’Ascq, France) for helpful dis-
cussions. This work was supported by the European Research Council under the
European Union’s Horizon 2020 Research and Innovation program (No. 833522)
and from Ghent University (Methusalem funding, BOF.MET.2021.0005.01) (to
Y.V.d.P.).
Author aliations: aDepartment of Plant Biotechnology and Bioinformatics, Ghent
University, Gent 9052, Belgium; bCenter for Plant Systems Biology, Bioinformatics and
Evolutionary Genomics, VIB, Gent 9052, Belgium; cDepartment of Biology, Terrestrial
Ecology Unit, Ghent University, Gent 9000, Belgium; dDepartment of Biochemistry,
Genetics and Microbiology, University of Pretoria, Pretoria 0028, South Africa; and
eCollege of Horticulture, Academy for Advanced Interdisciplinary Studies, Nanjing
Agricultural University, Nanjing 210095, China
Author contributions: F.K., Q.B., F.M., M.V.M., D.B., and Y.V.d.P. designed research; F.K.,
Q.B., and F.M. performed research; F.K., Q.B., F.M., D.B., and Y.V.d.P. analyzed data; and
all authors wrote the paper.
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Gp,k,i;Gk,D
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