![The maximum amount (A–D) and duration (E–H) of reinforcement
Reinforcement as a function of symmetric selection and migration (A and E) with rAM=rMF = 10⁻⁴, different selection coefficients in reinforcing and non-reinforcing populations’ environments (B and F), with gnon-reinf→reinf = greinf→non-reinf = 0.03 and with rAM=rMF = 10⁻⁴, asymmetric migration rates across numerous selection coefficients (C and G, with rAM=rMF = 10⁻⁴), and recombination rates (D and H) with a symmetric selection coefficient of 0.8 and gnon-reinf→reinf = greinf→non-reinf = 0.03. Complete or nontransient reinforcement is visible on the far right of figures F and H, indicated by the darkest green color, and the ∞ symbol in F. The amount of reinforcement is quantified as (p [z, gen = x]−p [z,gen = 0]) / p [z,gen = 0], where pz equals the probability of being fertilized by nonmigrant sperm/pollen, scaled by the frequency of nonmigrant sperm/pollen. Time in generations is represented by “gen”. The data underlying this figure can be found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.](https://www.researchgate.net/publication/364370652/figure/fig4/AS:11431281276322963@1725632867733/The-maximum-amount-A-D-and-duration-E-H-of-reinforcement-Reinforcement-as-a-function_Q320.jpg)
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RESEARCH ARTICLE
Conflict over fertilization underlies the
transient evolution of reinforcement
Catherine A. Rushworth
1,2,3
, Alison M. Wardlaw
1,4
, Jeffrey Ross-Ibarra
2,5
,
Yaniv BrandvainID
1
*
1Department of Plant and Microbial Biology, University of Minnesota, St. Paul, Minnesota, United States of
America, 2Department of Evolution and Ecology and Center for Population Biology, University of California,
Davis, California, United States of America, 3Department of Biology, Utah State University, Logan, Utah,
United States of America, 4Canada Revenue Agency—Agence du revenu du Canada, Ottawa, Ontario,
Canada, 5Genome Center, University of California, Davis, California, United States of America
*ybrandva@umn.edu
Abstract
When two species meet in secondary contact, the production of low fitness hybrids may be
prevented by the adaptive evolution of increased prezygotic isolation, a process known as
reinforcement. Theoretical challenges to the evolution of reinforcement are generally cast
as a coordination problem, i.e., “how can statistical associations between traits and prefer-
ences be maintained in the face of recombination?” However, the evolution of reinforcement
also poses a potential conflict between mates. For example, the opportunity costs to hybrid-
ization may differ between the sexes or species. This is particularly likely for reinforcement
based on postmating prezygotic (PMPZ) incompatibilities, as the ability to fertilize both con-
specific and heterospecific eggs is beneficial to male gametes, but heterospecific mating
may incur a cost for female gametes. We develop a population genetic model of interspecific
conflict over reinforcement inspired by “gametophytic factors”, which act as PMPZ barriers
among Zea mays subspecies. We demonstrate that this conflict results in the transient evo-
lution of reinforcement—after females adaptively evolve to reject gametes lacking a signal
common in conspecific gametes, this gamete signal adaptively introgresses into the other
population. Ultimately, the male gamete signal fixes in both species, and isolation returns to
pre-reinforcement levels. We interpret geographic patterns of isolation among Z.mays sub-
species considering these findings and suggest when and how this conflict can be resolved.
Our results suggest that sexual conflict over fertilization may pose an understudied obstacle
to the evolution of reinforcement.
Introduction
“Once the pollen grain has arrived at the stigma,it has made an irreversible move.There
should be very intense selection for it to get around whatever barriers the female may erect.”—
Janzen (1977)
Reproductive interactions present “different evolutionary interests of the two sexes” [1]. This
sexual conflict (in the general sense, sensu [2]) stems from sex differences in the fitness
PLOS Biology | https://doi.org/10.1371/journal.pbio.3001814 October 13, 2022 1 / 21
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OPEN ACCESS
Citation: Rushworth CA, Wardlaw AM, Ross-Ibarra
J, Brandvain Y (2022) Conflict over fertilization
underlies the transient evolution of reinforcement.
PLoS Biol 20(10): e3001814. https://doi.org/
10.1371/journal.pbio.3001814
Academic Editor: Michael D. Jennions, The
Australian National University, AUSTRALIA
Received: December 9, 2021
Accepted: September 2, 2022
Published: October 13, 2022
Copyright: ©2022 Rushworth et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All code for our
simulations are available on https://github.com/
carushworth/gameto-theory and data summaries
of simulation results are available on the dryad
submission associated (https://datadryad.org/
stash/dataset/doi:10.5061/dryad.rjdfn2zf8) with
this manuscript.
Funding: This work was funded by a collaborative
National Science Foundation award (#1753632 to
YB, #1754098 to JRI). The funders had no role in
study design, data collection and analysis, decision
to publish, or preparation of the manuscript.
consequences of mating. One sex (often the male) generally benefits from increasing their mat-
ing opportunities, while the other sex benefits from choosing mates and/or limiting mating—
resulting in the evolution of more specific forms of sexual conflict (e.g., harmful mating tactics
and mating evasion; [3]). Because mating and fertilization play a key role in mediating gene
flow between divergent populations, sexual conflict can impact the process of speciation. Spe-
cies boundaries may either be strengthened if sexual conflict poses a barrier to gene flow, or
weakened if populations evolve mating tactics that can overcome heterospecific reproductive
barriers [1,4–6].
The cost of producing low-fitness hybrid offspring can favor the evolution of enhanced
reproductive isolation by a process known as reinforcement [7]. Reinforcement is generally
modeled as the evolution of enhanced prezygotic isolation via female preference and male
trait, or trait matching [8,9]. Such models generally include trade-offs between being attractive
to conspecifics and heterospecifics (i.e., species evolve preferences for different trait values),
and as such both sexes tend to benefit from assorting with conspecifics and avoiding the pro-
duction of low-fitness hybrids. As such, most reinforcement theory aims to address the logisti-
cal challenge of maintaining a genetic association between trait and preference [10], rather
than the strategic challenge posed by misaligned interests between the sexes. This is true even
in models of polygyny (i.e., when females have multiple mates) because males who match a
given female trait/preference are assumed to be less attractive to females with a different trait/
preference [8,11]. However, if the trade-off between conspecific and heterospecific is less
severe, missing conspecific mating opportunities can come at a cost for one sex (usually
males), while for the other sex (usually females) the cost of producing a low-fitness hybrid
often outweighs the marginal benefit of additional matings.
The imbalance between sexes in the opportunity costs of heterospecific mating sets the
stage for sexual selection to impact the evolution of reinforcement. For example, Servedio and
Bu¨rger [12] showed that females with preferences for traits maladapted to their environment
can favor males expressing these maladaptive traits, enabling persistence of such traits and
thus inhibiting the evolution of reinforcement. Similarly, because a male preference results in
more competition for mates than does indiscriminate mating [11], reinforcement by male
mate choice is more constrained than reinforcement by female choice [8]. Likewise, Aubier
and colleagues [9] found that male preference for conspecifics only evolved if potential male
effort toward courting unpreferred females could be reallocated to preferred females. These
differences in models of reinforcement by male and female mate choice suggest a conflict in
the evolutionary interests of the sexes during the evolution of reinforcement; i.e., the benefit of
siring low-fitness hybrids may exceed the opportunity cost for a male but not for a female, pre-
senting an overall benefit only to males.
The sexual conflict over reinforcement described above is likely particularly severe for rein-
forcement of postmating prezygotic (PMPZ) isolation, because reproductive effort cannot be
reallocated to preferred partners after mating has already occurred (Janzen’s “irreversible
move”, above [13]). From the male perspective, gametes transferred to heterospecific females
cannot be redirected, so universally compatible alleles in male gametes will be favored.
Whereas from the female perspective, alleles that discriminate against heterospecific gametes
in favor of conspecific gametes will be favored.
Motivated by the genetic basis of PMPZ isolation between hybridizing subspecies of Zea
mays [14], we develop a population genetic model to evaluate how this sexual conflict over
hybridization can alter the evolution of reinforcement. To clarify this process, we model one
locally adapted “reinforcing” population in which an initially rare female-expressed fertiliza-
tion barrier requires a population-specific male signal expressed in the pollen or sperm for
effective fertilization, and another “non-reinforcing” population, which lacks this male signal
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Competing interests: The authors have declared
that no competing interests exist.
Abbreviations: LD, linkage disequilibrium; PME,
pectin methylesterase; PMEI, PME inhibitor; PMPZ,
postmating prezygotic.
and is adapted to a different environment. This female barrier can increase in frequency in the
reinforcing population, leading to the initial reinforcement of reproductive isolation. However,
the male signal then adaptively introgresses across populations. Fixation of the male compatibil-
ity allele across the metapopulation renders the benefit of discerning female-expressed alleles
neutral, ultimately eroding reinforcement. Notably, we find a similar outcome when two popu-
lations have their own unique incompatibilities (i.e., both species are reinforcing but do so by
distinct male signals and female barriers), suggesting that this result is attributable to asymmet-
ric costs and benefits experienced by the sexes, and not simply asymmetric cross-compatibility.
Results
Biological inspiration
Gametophytic factors—pairs of tightly linked loci expressed in pollen and styles—underlie the
PMPZ barrier [15–19]. Counter to the classic reinforcement prediction that reproductive iso-
lation will be highest in areas of sympatry and reduced in areas of allopatry [20], highland teo-
sinte (Z.m. subsp. mexicana) growing in sympatry with domesticated maize landraces (Z.m.
subsp. mays) shows elevated PMPZ isolation from allopatric maize populations, but no eleva-
tion in PMPZ isolation from sympatric maize [21,22]. Our model is inspired by the function
of gametophytic factors and their puzzling biogeographic distribution.
Despite this inspiration, our model is neither specific nor fully faithful to the maize/teosinte
system. We refer to the reinforcing population/species as reinf and the non-reinforcing popu-
lation/species as non-reinf, which roughly represent Z.m. subsp. mexicana and Z.m. subsp.
mays, respectively. Despite being inspired by a hermaphroditic system, we use the terms
“male” and “female” to refer to male and female function, or sperm/pollen and female repro-
ductive tract function, respectively.
Model overview
We deterministically iterate migration, gamete fusion, and selection, between two populations
in secondary contact. See S1 Text for full description of this iteration, and https://github.com/
carushworth/gameto-theory for the R code.
Population structure, migration, and pollination/mating. We model two demes (i.e., a
two-island model) in two differing selective environments. We refer to these as populations or
species/subspecies, as the populations represent two locally adapted (sub)species in secondary
contact. We refer to the selective environment of each population when appropriate. Every
generation, g
non-reinf!reinf
of sperm/pollen in the reinf environment originates from the non-
reinf population. Similarly, g
reinf!non-reinf
sperm/pollen in the non-reinf environment origi-
nates from the reinf population (Fig 1). Within each environment, sperm/pollen and females
meet at random.
Fertilization. Although mating/pollination within a deme is random, fertilization is con-
trolled by a two-locus PMPZ incompatibility (sensu Lorch and Servedio [23], which is a spe-
cific form of a “preference/trait” model, with complete female choosiness [24]). The female-
expressed locus Fis under diploid control. We assume the incompatibility is dominant—i.e.,
females with one or two Falleles discriminate between sperm/pollen alleles, preferentially
accepting those with the Mallele (Fig 1A) at the male compatibility (M) locus. Fertilization is
random for females homozygous for the compatibility allele, f. This notation differs from that
in the existing literature on gametophytic factors, which refer to gametophytic factors as haplo-
types rather than pairs of genotypes (see S2 Text).
We initially assume no direct fitness cost to either the female incompatibility F(e.g., there is
no preference cost) or the male compatibility M, unless otherwise noted. Finally, we assume
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that females expressing the incompatibility genotypes cannot be fertilized by incompatible
sperm/pollen. Incomplete penetrance of the barrier results in expected quantitative differences
in results but does not change the qualitative outcomes (S2 Fig).
Selection. We model isolation by local adaptation following [25] with extrinsic isolation
driven by nlocal adaptation loci, each denoted as Ai, where the subscript iis an arbitrary
index of loci. Our primary analyses focus on the case of one locally adaptive locus (i.e., n= 1),
an assumption that is relaxed where noted. Selection coefficients are s
non-reinf
and s
reinf
in envi-
ronments of the non-reinforcing and reinforcing populations, respectively. Fitness wis multi-
plicative within and among loci, w= (1−s
env
)
#maladapted alleles
.
Initial allele frequencies. At the female-expressed Flocus, we assume that the incompati-
bility allele, F, is initially rare in reinf (1% frequency) and absent in non-reinf.
At the male-expressed Mlocus, we assume that the male compatibility allele Mis initially
fixed in reinf, and absent in non-reinf, respectively. Variation in the initial frequency of Min
reinf, however, has nearly no effect on the outcome (S1 Fig).
At the locally adaptive Alocus, we assume that populations are initially fixed for the allele
locally adapted to their environment (i.e., allele Ais fixed in reinf and absent in non-reinf, and
allele ais fixed in non-reinf and absent in reinf).
Fig 1. Model dynamics. (A) PMPZ incompatibility based on gametophytic factors. The dominant Fallele at the female-expressed locus Fencodes a
fertilization barrier that can only be overcome by the male-expressed compatibility allele Mat locus M.(B) Male gametes disperse between two populations:
one reinforcing (reinf) and one non-reinforcing (non-reinf), each of which face different selective pressures. Colors denote compatibility haplotypes (mf,Mf,
MF), and shapes signify genotypes at the Alocus, which underlies divergent ecological adaptation (aand A). Initially, non-reinf is fixed for the compatible f
female-expressed allele, the incompatible sperm/pollen-expressed mallele, and a locally adaptive allele (haplotype mfa). reinf is initially fixed for the sperm/
pollen compatibility allele M, and locally adapted allele A, with the female-expressed incompatibility Fat an initially low frequency; i.e., haplotype MfA is
initially common, and MFA is initially rare in reinf.(C) We run the model from the initial generation T
0
until the Fallele reaches its equilibrium. If some
reinforcement evolves by time T
1
(equivalent to the Fallele increasing in frequency in reinf), two further outcomes are possible: The Mallele may introgress
onto the locally adaptive background and fix in both populations, leading to the breakdown of reinforcement (bottom right panel of C); or, the Mallele may fail
to spread in non-reinf while Fcontinues to spread through reinf, completing reinforcement (bottom left panel of C).
https://doi.org/10.1371/journal.pbio.3001814.g001
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Recombination and genome structure. We initially assume a locus order of A1MF ,
with recombination rates rA1Mand rMF . Local adaptation loci A2through Anare unlinked to
one another and to the Mand Floci. After presenting these results, we explore alternative
marker orders.
A second gametophytic factor. To ensure that our results are not due to asymmetry of
variation for female choice in only one population, we then introduce a model with a second
unlinked incompatibility locus: AzMzFz. This barrier acts like the first, detailed above, but
with initial frequencies in each population reversed. As such, each population is reinforcing
and non-reinforcing at a different set of loci.
Sexual conflict leads to transient reinforcement
When reinforcement evolves, it is almost always transient. An example of the rise and fall of
reinforcement is shown in Fig 2 (parameter values in legend). Fig 2A shows that the evolution
of substantial reinforcement (Phase 1; Fig 2A) is ultimately fleeting. Reinforcement begins as
the female incompatibility allele, F, increases in frequency in reinf (Fig 2B), preventing fertili-
zation by locally maladapted immigrant haplotypes. This maintains both the high frequency of
locally adapted (A) and male compatible (M) alleles in the environment of non-reinf (Fig 2C),
and large nonrandom statistical association, a.k.a. linkage disequilibrium (hereafter, LD)
between them (note the large value of r2
AM in Fig 2D and 2F).
Subsequently, however, the male compatibility allele Mintrogresses into non-reinf, eventu-
ally recombining onto the abackground and undermining reinforcement (Phase 2 of Fig 2);
i.e., migration of haplotypes from reinf into non-reinf enables recombination of Monto the
locally adapted background. As the Mfa haplotype sweeps through non-reinf (Fig 2E), LD
between Mand Adecreases in both populations (Fig 2D and 2F).
As Mrises in frequency and eventually fixes across the metapopulation (Fig 2B), migrant
sperm/pollen are no longer rejected, indicated by reinforcement approaching zero in Fig 2B.
At this point, selection against Fin non-reinf weakens until it is completely neutral (see discus-
sion of Fig 3, below). From then on, Fslowly equilibrates across populations (Phase 3 of Fig
2A) as continued migration and recombination between the Aand Floci decreases LD
between them (Fig 2D and 2F).
Allele frequency change across the life cycle
We now show how migration, fertilization, and selection drive changes in allele frequencies
across the life cycle (Fig 3). See S3 Text for exact expressions.
Migration homogenizes allele frequencies. The change in allele frequency by migration
is the difference in allele frequencies between populations weighted by the migration rate
(Eq. S1). This homogenization of allele frequencies (Fig 3A) is seen as the decrease in fre-
quency of all “local alleles” (A,M, and Falways decrease in reinf and increase in non-reinf).
The stylar barrier Ffavors the male compatibility allele Mand indirectly favors alleles
in LD with it. The fertilization advantage of Mdepends on the proportion of incompatible
females in the present generation (either heterozygous or homozygous for F). For a dominant
female incompatibility, this equals 1−p
ff
, where p
ff
, the frequency of females homozygous for
the fallele, differs from p2
fdue to nonrandom fertilization. The increase in frequency of allele
M(derived in Eqs. S2 and S3) from sperm/pollen to paternally derived haplotypes equals
Dpfertilization ¼1pff
p0
Mp0
mc
1cp0
mð1Þ
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where cis the intensity of incompatibility (or choosiness), and the superscript 0indicates that
allele frequencies in sperm/pollen are taken after migration, while female frequencies lack 0
because only sperm/pollen migrate.
Phase 1 Phase 2
Phase 3
P
h
a
s
e 1
s
e
2
P
h
a
s
e
3
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
Reinforcement
AM
FM
F
A
A
M
F
F
A
A
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
Allele freq
B
AMf AMF
Amf
AmF
amf
amF
aMf aMF
Rare haps
AM
f
Am
f
A
m
F
am
f
am
F
aM
f
aM
F
R
are
h
aps
A
M
F
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
Hap freq:
C
AM
AFMF
A
M
M
F
AF
A
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
LD: (r2)
D
amf aMf
aMF
Amf
AmF amF
AMf AMF
Rare haps
am
f
Am
f
A
mF am
F
AM
f
AM
F
R
are
h
aps
aM
f
aM
F
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
Hap freq:
E
AM
AF
MF
A
M
M
F
AF
A
0.00
0.25
0.50
0.75
1.00
100101102103104105
Generation
LD: (r2)
F
Fig 2. The rise and fall of reinforcement in 3 phases. A female barrier allele Fpreventing fertilization by mgametes spreads in the reinforcing
population/species reinf (Phase 1: light blue). The compatible sperm/pollen allele, M, next introgresses into the non-reinforcing population/
species non-reinf and spreads (Phase 2: white). After Mfixes, the barrier allele Fslowly disassociates from the reinforcing background, eventually
equilibrating in both populations (Phase 3: light grey). (A) Reinforcement is transient, building in Phase 1 and breaking down in Phase 2. The
pink line shows 0 reinforcement. (B) Allele frequencies in both populations, with solid and dashed lines showing frequencies in reinf and non-
reinf, respectively. The Fallele increases in reinf followed by the global fixation of Mand subsequent neutrality of F. (C) Haplotype frequencies
and (D) gametic linkage disequilibrium (LD) between all pairs of loci over time in the environment of reinf. (E) Haplotype frequencies and (F)
gametic LD between all pairs of loci over time in the environment of non-reinf. LD is measured as r
2
, and all measures describe populations after
selection and before recombination. This figure illustrates a single set of parameter values with 1 adaptive locus. Selection: s
reinf
=s
non-reinf
= 0.75;
Migration: g
non-reinf!reinf
=g
reinf!non-reinf
= 0.1; Recombination: rAM ¼rMF ¼0:0001; Initial allele frequencies: f
M0,reinf
= 1, f
M0,non-reinf
= 0, f
F0,
reinf
= 0.01, f
F0,non-reinf
= 0. The data underlying this figure can be found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
https://doi.org/10.1371/journal.pbio.3001814.g002
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In line with this result, Fig 3B shows that in both populations, the male compatibility allele,
M, increases in frequency during fertilization until it reaches fixation. In addition to directly
increasing the frequency of the Mallele, selection indirectly favors alleles in LD with it (Eqs. S4
and S5). Because LD among alleles from reinf >0, the Aand Falleles increase in frequency
through a fertilization advantage to Min both populations (Fig 3B). This incompatibility sys-
tem generates a trans association between maternally derived Fand paternally derived M
alleles (Eq. S6; [26]).
Allele frequency change by natural selection follows standard expectations. Selection
increases the frequency of the locally adapted allele at locus Ain each environment (Fig 3C;
Eqs. S7 and S8). Likewise, linked selection on Mand Falleles (Fig 3C) reflects LD with the
locally adapted alleles (Fig 2D and 2F), with alleles in positive LD with Aincreasing in fre-
quency in reinf, and decreasing in non-reinf (Eq. S9).
Selection favors the female incompatibility in the reinforcing population and disfavors
it in the non-reinforcing population. The female incompatibility allele, F, which does not
itself impact fitness, still deterministically changes in frequency due to its LD with alleles at
other loci. This LD is generated by both the causal effect of the allele in mediating nonrandom
fertilization, as well as population structure, historical events, etc. We partitioned the extent to
which the increase in frequency of the female isolating barrier Fis attributable to its causal
effect on creating genotypic LD by imposing assortative fertilization (which we call “selection
for reinforcement”) versus “incidental selection” unrelated to the effect of Fon preferential
gamete fusion (see Materials and methods for details). “Selection for (or against) reinforce-
ment” reflects the increase (or decrease) in frequency of Fattributable to the trans LD it imme-
diately generates with the locally (mal)adapted allele. “Incidental selection” reflects the change
in frequency of Fattributable to its LD (largely in cis) with the locally (mal)adapted allele gen-
erated by previous mating and/or historical population structure.
Finitially rises in frequency in reinf because at the outset it preferentially fuses with sperm/
pollen unlikely to contain a locally maladapted allele (Phase 1; Fig 3D). However, F’s persis-
tence once Mhas reached appreciable frequency in non-reinf is primarily attributable to inci-
dental selection, in that it preferentially exists on locally adapted haplotypes (Fig 3D).
M
MF
F
A
A
−.050
−.025
.000
.025
.050
100101102103104105
Generation
'pmigration
AM
F
A
−.050
−.025
.000
.025
.050
100101102103104105
Generation
'pfertilization
B
M
M
F
F
A
A
−.050
−.025
.000
.025
.050
100101102103104105
Generation
'pselection
C
0.010
0.005
0.000
−0.005
−0.010
100101102103104105
Generation
'pFmaternal
D
pecies Allele AFM
Fig 3. Allele frequency change across the life cycle. The change in frequency of alleles initially unique to reinf (A,M, and F) across the metapopulation. The transparent
thick pink line at 0 denotes no change in allele frequency during this life phase. (A) During migration, alleles decrease in frequency in reinf (solid line, indicated by values
below the 0 line) and increase in non-reinf (dotted line, indicated by values above the 0 line). (B) During fertilization, alleles native to reinf (A,M, and F) increase in both
populations. This effect is strongest in the environment of reinf, due to a direct fertilization advantage of Mand the benefit to alleles in LD with M. (C) Selection in reinf
and non-reinf consistently acts to increase and decrease the frequency of A, respectively. Linkage between Aand Mresults in overlapping lines during Phase 1. The
transition from Phase 1 to Phase 2 is marked by a dip in the frequency of A, caused by near-fixation of Fon the Abackground, as migrant haplotypes from non-reinf are
unable to penetrate reinf at F’s peak frequency. (D) Selection on Fis decomposed into 2 components of allele frequency change. In dark blue, we show “selection for
reinforcement” (the Fallele frequency change attributable to preferential fusion with M), which enables avoidance of the maladapted a allele in reinf. In light blue, we show
the allele frequency change attributable to the incidental gametic phase linkage between Fand A; see Materials and methods for more detail. Parameter values: One local
adaptation locus with Selection: s
reinf
=s
non-reinf
= 0.75; Migration: g
non-reinf!reinf
=g
reinf!non-reinf
= 0.1; Recombination: rAM ¼rMF ¼0:0001; Initial allele frequencies:
f
M0,reinf
= 1, f
M0,non-reinf
= 0, f
F0,reinf
= 0.01, f
F0,non-reinf
= 0. Background shading marks Phase 1 (light blue), Phase 2 (white), and Phase 3 (grey) of transient reinforcement,
as in Fig 2. The data underlying this figure can be found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
https://doi.org/10.1371/journal.pbio.3001814.g003
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In non-reinf,Fis disfavored through both selection against this incompatibility (because F
is preferentially fertilized by A-bearing sperm/pollen) and incidental selection acting on the A
locus (because Fis in gametic phase LD with the locally maladapted Aallele). As recombina-
tion erodes LD between Mand A, selection weakens against the incompatibility Fin non-reinf
due to its effects on nonrandom fertilization. Incidental selection against Fin non-reinf simi-
larly weakens as recombination erodes LD between Fand A(Fig 3D).
Determinants of the strength and duration of reinforcement. We now show how vary-
ing parameter values influence the maximum amount (Fig 4A–4D) and duration (Fig 4E–4H)
of reinforcement in the face of this conflict.
Reinforcement often requires strong selection. As selection on the locally adaptive allele
intensifies, both the maximum extent (Fig 4A) and total duration (Fig 4E) of reinforcement
increase. With symmetric selection and symmetric migration, selection on the local adaptation
locus must be exceptionally strong for any reinforcement to evolve—e.g., even with s= 0.3,
only very subtle reinforcement evolves for a very short time. However, other parameter
choices—such as asymmetric migration or selection—can mediate the strength of selection
required for reinforcement to evolve (see below).
With symmetric migration and asymmetric selection, the strength of selection in non-reinf
(the population without the stylar incompatibility) generally has a greater effect on the extent
and duration of reinforcement than does the strength of selection in reinf (Figs 4B and 4F and
S3). This is because strong selection in non-reinf removes the migrant MA haplotype, minimiz-
ing opportunities for Mto recombine onto the locally adapted abackground.
The extent and symmetry of migration mediates reinforcement. With symmetric
migration, intermediate migration rates always maximize the extent of reinforcement (Figs 4A
and S3A), while the duration of reinforcement decreases with the migration rate (Figs 4E and
S3B), regardless of the selection coefficient.
Fig 4. The maximum amount (A–D) and duration (E–H) of reinforcement. Reinforcement as a function of symmetric selection and migration (Aand E)
with rAM ¼rMF = 10
−4
, different selection coefficients in reinforcing and non-reinforcing populations’ environments (Band F), with g
non-reinf!reinf
=
g
reinf!non-reinf
= 0.03 and with rAM ¼rMF = 10
−4
, asymmetric migration rates across numerous selection coefficients (Cand G, with rAM ¼rMF = 10
−4
), and
recombination rates (Dand H) with a symmetric selection coefficient of 0.8 and g
non-reinf!reinf
=g
reinf!non-reinf
= 0.03. Complete or nontransient
reinforcement is visible on the far right of figures Fand H, indicated by the darkest green color, and the 1symbol in F. The amount of reinforcement is
quantified as (p
[z, gen = x]
−p
[z,gen = 0]
) / p
[z,gen = 0]
, where p
z
equals the probability of being fertilized by nonmigrant sperm/pollen, scaled by the frequency of
nonmigrant sperm/pollen. Time in generations is represented by “gen”. The data underlying this figure can be found in https://datadryad.org/stash/dataset/
doi:10.5061/dryad.rjdfn2zf8.
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The effect of asymmetric migration on the extent of reinforcement highlights how migra-
tion mediates this sexual conflict. Migration from non-reinf to reinf favors reinforcement by
increasing the number of maladapted immigrants available for heterospecific matings (Fig
4C). By contrast, increasing migration from reinf to non-reinf accelerates the introgression of
the Mallele into non-reinf, especially at higher migration rates, rapidly undermining reinforce-
ment (Fig 4G). With unidirectional migration from non-reinf to reinf, substantial reinforce-
ment can persist for prolonged time periods (Fig 4C and 4G).
Linkage between female barrier and male (in)compatibility alleles does not strongly
impact the amount or duration of reinforcement. Contrary to classic results of reinforce-
ment theory [10], linkage between the male and female (in)compatibility alleles, rMF , has only
a modest effect on the evolution of reinforcement. This result is seen across most selection
coefficients and most values of rAM (Fig 4D and 4H; reproduced in S5A and S5D Fig). Reor-
dering the loci in the model does not alter this outcome—i.e., the extent and duration of rein-
forcement is largely insensitive to rMF in models with loci in MF A order (S5B and S5E Fig).
Instead, linkage between the local adaptation locus, A, and either Mor Floci are critical
to the evolution of reinforcement. Marker order MAF highlights the impact of recombination
between the components of the PMPZ incompatibility complex on both the duration and inten-
sity of reinforcement (S5C and S5F Fig). While both rAM and rF A modulate the level of rein-
forcement (S5C Fig), the duration of reinforcement is independent of rF A (S5E Fig), and nearly
completely determined by recombination between the male compatibility Mand local adapta-
tion locus A;rAM. When Aand Mare tightly linked, substantial reinforcement can evolve
and last for some time. The strength and duration of reinforcement drops, initially modestly,
and then quite precipitously, as the recombination rate increases, with nearly no reinforcement
evolving when Aand Mare unlinked (Fig 4D and 4H). Selection modulates this effect of
recombination (S4 Fig); when selection is very strong (e.g., s>0.6) some reinforcement can
evolve, even when Aand Mare separated by up to a centiMorgan (i.e., r
AM
= 0.01).
This result suggests that the rate of recombination between the local adaptation and male
compatibility loci, rAM, underlies the sexual conflict over reinforcement. When rAM is high,
meaning Aand Mare loosely linked, Mcan more easily recombine onto the locally adapted a
background, which facilitates its introgression into non-reinf. By escaping from the Aback-
ground, Mhas greater long-term viability in non-reinf than it would if it remained associated
with this locally maladaptive allele, increasing the male benefit to overcoming the
incompatibility.
The presence of multiple unlinked local adaptation loci allows for (transient) reinforce-
ment. Our results so far suggest that transient reinforcement by PMPZ incompatibilities
requires tight linkage between loci underlying incompatibility and a single locus under diver-
gent selection. However, the genetic architecture of local adaptation is often polygenic [27].
We therefore investigate if weaker selection at more unlinked loci can allow reinforcement
to transiently evolve by setting rA1Mto 0.5 and introducing up to 4 additional unlinked local
adaptation Aloci. Fig 5 shows that reinforcement can evolve when alternate alleles at numerous
unlinked loci experience divergent selection in the 2 populations. This is consistent with recent
work showing that, when numerous loci underlie reproductive isolation, selection on early-gen-
eration hybrids acts not against isolated loci, but on phenotypes underlain by pedigree relation-
ships [28]. While the selection coefficients displayed are still quite large, this suggests that
weaker selection at many loci could likely result in the transient evolution of reinforcement.
An opposing gametophytic factor does not stabilize reinforcement. To explore the pos-
sibility that the collapse of reinforcement could be prevented by the presence of distinct
incompatibilities expressed in each population, we included a model in which both
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populations are “reinforcing” but by an independent set of loci. Although a second comple-
mentary incompatibility allows reinforcement to begin at lower selection intensities and
slightly expands the parameter space for which reinforcement stably evolves (S6A Fig), rein-
forcement usually remains transient (S6B Fig).
A large cost of the male compatibility allele can stabilize reinforcement. We next ask
how a cost to the male compatibility allele impacts the evolution of reinforcement; ignoring
the question of how such a costly allele could have spread in reinf. For illustrative purposes, we
limit our focus to exploration of parameters presented in Fig 2 and described in its legend.
Assigning a cost s
M
to the Mallele can lead to one of three qualitatively different outcomes
(S7 Fig). If its cost is sufficiently small (s
M
<0.01 in our example), Mrapidly and adaptively
Fig 5. Oligogenic ecological selection. The maximum strength (A) and duration (B) of reinforcement with ecological
selection at nloci, where all ecologically selected loci are unlinked to one another and to the gametophytic factor. The
selection coefficient sagainst a maladaptive allele is multiplicative within and among loci—e.g., the fitness of an
individual homozygous for the locally maladaptive allele at all nloci is (1−s)
2n
. Migration rate gis symmetric and
recombination rate rMF ¼104. The data underlying this figure can be found in https://datadryad.org/stash/dataset/
doi:10.5061/dryad.rjdfn2zf8.
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introgresses and undermines reinforcement as shown above. A larger cost to M
(0.01<s
M
<0.08) results in an equilibrium level of reinforcement (i.e., partial reproductive iso-
lation [29]) wherein the cost of Mis balanced by a benefit of heterospecific fertilization to M-
bearing pollen/sperm. An even larger cost to M(s
M
>0.08 in our example) prevents the intro-
gression of this allele altogether, resulting in stable reinforcement. In sum, a sufficiently large
cost to the male compatibility allele can stabilize the evolution of reinforcement, but a small
cost does not.
Discussion
For decades, researchers have presented theoretical and empirical challenges to the process of
reinforcement, starting with a foundational paper by Felsenstein that identified recombination
as a critical challenge to reinforcement [10]. Since then, a large body of theory has investigated
the circumstances that permit or hinder the evolution of reinforcement (reviewed in [30]).
Despite its potential role in hampering speciation [1], however, sexual conflict over hybridiza-
tion has received relatively little attention in the literature. When it is mentioned, sexual con-
flict over hybridization is included only as a brief aside in papers concerning the role of sexual
conflict in speciation more broadly [1,5,6].
Here, we identify the transient dynamics generated by sexual conflict over reinforcement
and the evolutionary traces it leaves behind—namely the adaptive spread of female barriers in
one species/population and the adaptive introgression of male compatibility alleles into the
other. These results provide a rich set of predictions and interpretations of empirical patterns
that were absent from previous game theoretic [1,5] and verbal [31] models.
In our model, sexual selection favors sperm/pollen traits that overcome a heterospecific
female barrier. This poses a conflict: Females are selected to avoid the production of maladapted
hybrids, while sperm (or pollen) that increase their fertilization success will generally be favored.
The breakdown of reproductive isolation is marked by the rapid adaptive introgression of the
male compatibility trait into non-reinf, following recombination onto the locally adapted haplo-
type. Back-migration of this allele into reinf hastens its fixation across populations. The final
step in the model is the slow homogenization of the female barrier allele across demes, as the
male compatibility allele fixes in both, rendering the female choice allele ineffective. Such
homogenization of female preference does not occur when reinforcement is stable, and the
male trait does not spread across both populations. Ultimately, we show that barriers acting at
different stages of hybridization can affect how reinforcement proceeds. Below, we discuss the
relationship of our results to previous theory, implications for the process of reinforcement, and
empirical implications for hybridizing taxa, including Z.mays subspecies.
Theoretical context and predictions for reinforcement
Previous models of reinforcement treated the sexes interchangeably [10] or assumed assorta-
tive mating under female control [32–34] (but see [8,9,35] for models with male choice) either
by “matching” or “preference/trait” mechanisms of assortative mating [24]. Both matching
and preference/trait models induce a trade-off between heterospecific and conspecific mating:
a male with a trait favored by heterospecific females will have limited mating success with con-
specific females.
While numerous studies have addressed the role of introgression in reinforcement (e.g.,
[36–40]), a distinguishing feature of our model is the mechanism of nonrandom fertilization,
which we model as a PMPZ incompatibility functioning as a gametophytic factor in Z.mays
[41] and PMPZ barriers in broadcast spawners (e.g., [42]). In this special class of preference/
trait model, introgression of a male compatibility allele is facilitated by the fact that it does not
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prevent heterospecific mating—i.e., by definition, our model lacks a trade-off between con-
and heterospecific mating (i.e., no reallocation sensu; [9]). As such, (in)compatibility-type mat-
ing interactions can result in the transient evolution of reinforcement, while other matching or
preference/trait models cannot.
Implications for reinforcement by pre- versus postmating barriers
Our model assumes that being attractive to one species does not come at a cost of being attrac-
tive to ones’ own species. How does this assumption likely map onto cases of reinforcement by
pre- and postmating isolation mechanisms?
Postmating prezygotic isolation. To the extent that PMPZ barriers function similarly to
those in our study, our model suggests transient reinforcement by PMPZ barriers. However,
physical and/or biochemical properties of PMPZ interactions may minimize the opportunity
for interspecific sexual conflict by enforcing a trade-off between overcoming a heterospecific
barrier and successfully fertilizing conspecifics. This would allow for the evolutionary stability
of reinforcement, consistent with our results from our model that showed that a sufficiently
large cost to pollen/sperm compatibility could stabilize reinforcement. For example, as How-
ard [43] argued, and Lorch and Servedio [23] showed, a preference for conspecific sperm can
stably evolve to minimize heterospecific fertilization. Thus, conspecific sperm precedence in
competitive fertilization likely allows stable reinforcement by PMPZ isolation (as shown by,
e.g., [44]). Likewise, mechanistic features of noncompetitive fertilization can also induce a
trade-off between inter- and intraspecific crossing success. For example, if pollen must grow
an optimal distance to fertilize an ovule (as observed in interspecific Nicotiana crosses) [45],
success on both hetero- and conspecific styles is impossible.
Premating isolation. In principle, our model could apply to the reinforcement of premat-
ing isolation, as well as postmating isolation, so long as there is no trade-off in attractiveness to
each species. There are numerous examples of premating traits that may increase heterospeci-
fic reproductive success without trading off conspecific attractiveness. For example, divergence
in male competitive ability between two lineages of the common wall lizard (Podarcis muralis)
results in asymmetric hybridization [46,47]. Likewise, loci underlying plumage traits appear to
be asymmetrical and adaptively introgress from one to another subspecies of the red-backed
fairywren, Malurus melanocephalus [48], presumably because this trait confers an advantage in
extra-pair copulation due to sensory bias [49]. In a classic example of this phenomenon, plum-
age of the golden-collared manakin Manacus vitellinus appears to adaptively introgress into
Manacus candei upon secondary contact [50], and this spread is likely mediated by female
choice [51]. However, it does not appear that the female preference in any of these cases ini-
tially arose as a mechanism of reinforcement.
Sexual conflict and sexual selection undermine reinforcement
Our model shows that the common phenomenon of sexual conflict (see [3] for examples),
wherein male and female interests are misaligned, can erode reinforcement by PMPZ incom-
patibilities. This role for sexual conflict in removing species boundaries runs counter to the
conventional role it is thought to play in speciation [1]. Previous theory [52] and experiments
[53], as well as natural patterns of reproductive isolation [54,55] and diversification rates [56]
suggest that independent coevolutionary arms races between male and female traits in two
incipient species can pleiotropically result in behavioral or mechanical isolation. In this man-
ner, intraspecific sexual conflict was thought to be an “engine of speciation” [57]. By contrast,
we show that interspecific conflict between the sexes over fertilization hampers speciation.
This highlights an underappreciated challenge to reinforcement by PMPZ barriers. Broadly,
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our results align with studies suggesting that incompatibilities, especially those with a trans-
mission advantage [58], can adaptively introgress across species boundaries [59].
Servedio and Bu¨rger [12] found that Fisherian sexual selection can undermine reinforce-
ment. Specifically, they found that migration of female preference alleles provides a mating
advantage to otherwise locally maladaptive heterospecific male traits by sexual selection,
undermining reinforcement. In contrast, our model shows that the benefit of siring low fitness
hybrids, when the alternative is missed fertilization opportunities that result in no offspring,
can also undermine the evolution of reinforcement. Counter to Servedio and Bu¨rger, we find
that the female incompatibility remains at low frequency in the non-reinforcing species for a
long time. As such, our models make contrasting predictions: Servedio and Bu¨rger’s model
predicts that alternative female preferences will coexist in both populations early in the evolu-
tionary process, while our model predicts that female preference for the “wrong” species signal
will only become common in both populations very late in the process of genetic exchange.
Our model can be seen as a specific instance of the lek paradox [60], as female preference
ultimately erodes variation for a male trait. Following previously proposed resolutions of the
lek paradox (e.g., [61]), Proulx [62] suggested that a female preference for an indicator of
paternal fitness (e.g., sperm competitiveness) could act as a “one allele” mechanism of rein-
forcement (sensu; [10]). Under our model of sexual conflict, however, the lek paradox is ulti-
mately unresolved. Rather, our model results in a male trait fixed in both species, which does
not ultimately aid in assortative mating but is a mark of the “ghost of reinforcement past”.
Empirical implications, predictions, and interpretation of current
observations
Our model, based on a well-characterized PMPZ incompatibility, shows that reinforcement by
such mechanisms is precarious. As such, to the extent that such barriers do not incur a trade-
off between conspecific and heterospecific fertilization success, we predict that reinforcement
by PMPZ barriers should be rare. Thus, the finding that gametic isolation in broadcast spawn-
ers is not the product of reinforcement [63], as well as meta-analyses showing that PMPZ isola-
tion does not differ between sympatric and allopatric species pairs in Drosophila [64] or across
3 angiosperm genera [65], are consistent with our model. Still, negative evidence is not neces-
sarily evidence for the negative.
As such, the few documented cases in which PMPZ barriers are reinforced allow for better
evaluation of our predictions. Specifically, we predict that reinforcement by PMPZ barriers
should often involve certain characteristics, which are consistent with the empirical literature.
These include the following: (1) recent sympatry, so that the male barrier has not yet increased
in frequency (e.g., [66]); (2) a trade-off between male success in overcoming inter- and intra-
specific postmating barriers, as is found in preference/trait mechanisms (e.g., [44]); (3) unidi-
rectional gene flow (e.g., [67]); and/or (4) exceptionally strong postzygotic isolation, such that
gene flow is very rare, as seen in Drosophila yakuba and Drosophila santomea (e.g., [64]). How-
ever, reinforcement by PMPZ isolation in D.yakuba and D.santomea is difficult to reconcile
with our model, as the pair have a stable hybrid zone, no evidence of conspecific sperm prece-
dence, and bidirectional hybridization [68]. Nonetheless, our model suggests a plausible evolu-
tionary mechanism for existing cases of reinforcement by PMPZ isolation and generates
specific hypotheses to be tested.
Predictions for maize and teosinte
Zea mays subsp. mays and Zea mays subsp. mexicana grow in close sympatry and hybridize
[69,70]. Evidence for genome-wide selection against admixture, despite adaptive introgression
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of some teosinte loci into maize [71], is consistent with the idea that hybrids are often disfa-
vored—perhaps because hybrids are removed from maize fields by anthropogenic weeding,
and maize traits expressed in teosinte environments are likely maladaptive [72,73] (although
clear cases of adaptive introgression and deliberate hybridization by farmers exist).
This system has all the ingredients necessary for reinforcement—the occurrence of gene
flow, the presence of a stylar incompatibility in teosinte sympatric with maize, and the reduced
but nonzero fitness of hybrids. However, the elevated pollen discrimination exhibited by high-
land teosinte sympatric with maize [15–18] is surprisingly ineffective in preventing fertiliza-
tion by sympatric maize landraces [21,22], against whom selection for reinforcement should
be strongest.
Our model explains this observation as the initial evolution of reinforcement (i.e., a stylar
barrier sweeps through teosinte) followed by the adaptive introgression of teosinte pollen com-
patibility alleles into maize. Notably, alternative explanations for this pattern are insufficient.
For example, this pattern is not simply attributable to the loss of isolation upon secondary con-
tact, because allopatric teosinte do not reject maize pollen [21,22]. Nor can this be explained
by complex speciation, in which teosinte sympatric with maize would be more recently
diverged from maize than are allopatric teosinte, as this is incompatible with both genetic evi-
dence and the history of maize domestication [74]. We suggest that in most sympatric popula-
tions, at most gametophytic factors, the stylar fertilization barrier (the Fallele) rapidly swept
through teosinte (Phase 1 in Fig 2), and the pollen compatibility allele (M) adaptively intro-
gressed into sympatric highland maize landraces (Phase 2 in Fig 2).
Caveats
Our model made many simplifications and abstractions for tractability and generality. Most
notably, we assumed only two populations, a single gametophytic factor, and a simple multipli-
cative fitness function across a small number of divergently selected loci. Our results show that
the architecture of adaptive differentiation and the linkage between locally adaptive alleles and
PMPZ incompatibilities modulate the rise and fall of reinforcement. Across taxa, adaptive dif-
ferentiation can be controlled by few [75–77] or many [78] loci, and linkage between locally
adaptive alleles and PMPZ incompatibilities is biologically variable and rarely known. In
maize, evidence is mixed—one gametophytic factor tcb1 is tightly linked to a domestication
locus su1 [79,80], which likely experiences divergent selection. However, two other known
gametophytic factors are far from loci under strong divergent selection.
We further assume that the male compatibility allele is initially common and stylar incom-
patibility is initially rare in reinf, and we do not address the origins of gametophytic factors.
While the initial divergence of these alleles is outside the scope of our model, it could be
explained by pleiotropy, selection to prevent polyspermy (a known risk to embryo viability in
maize) [81], or Fisherian runaway selection (as proposed for gametophytic factors by Jain)
[82]. Pleiotropy may explain the initial evolution of gametophytic factors in Z.mays, as they
are members of the multifunction pectin methylesterase (PME) and PME inhibitor (PMEI)
gene families [15–17,83] and could be favored by mechanisms related to other functions. Nota-
bly, a subclass of PMEs contain both PME and PMEI domains, providing a potential explana-
tion for tight linkage of the Mand Falleles [84].
Conclusions
We find that considering the role of sexual conflict—a mismatch between optimal fertilization
outcomes of each sex—in reinforcement generates novel predictions and may explain numer-
ous patterns in nature. Our results are particularly relevant to potential cases of reinforcement
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by gamete recognition in plants, as well as broadcast spawners (e.g., Lysin/VERL in abalone
[85] or Bindin/EBR1 in sea urchins [86]), and even to cases of internal fertilization in which
premating isolation is inefficient, costly, or otherwise unpreferred [87]. In these situations, we
predict that reinforcement by PMPZ will be rare, transient, or involve a trade-off between het-
erospecific and conspecific fertilization (i.e., some mechanism of reallocation). Finally,
although our model is developed specifically for interactions between haploid male gametes
and diploid females, similar dynamics could arise for premating barriers with a similar genetic
architecture and lacking reallocation of male reproductive effort.
Materials and methods
Quantifying reinforcement and its duration
We summarized our results by quantifying the duration and maximum extent of reinforce-
ment. We quantified the amount of reinforcement at generation gas
ðp½z;gen¼g�p½z;gen¼0�Þ=p½z;gen¼0�. Where p
z
equals the probability of being fertilized by nonmigrant
sperm/pollen, scaled by the frequency of nonmigrant sperm/pollen. We quantified the dura-
tion of reinforcement as the number of generations for which the amount of reinforcement
was greater than 0.05.
Partitioning selection
All selection for or against the female incompatibility allele, F, is indirect, as it does not itself
impact fitness; i.e., selection impacts the frequency of an allele at the Flocus, not because of its
effect on fitness, but because of its genetic background (i.e., linkage disequilibrium between F
and A). Each generation, some of the LD between Fand Ais immediately attributable to either
(a) population structure, historical events, etc. (primarily by cis-LD), which we call “incidental
selection” or (b) to the causal effect of the Fallele in generating genetic associations by the
gametes permitting fertilization (primarily via trans-LD; see subsection The generation of
trans linkage disequilibrium during fertilization in the Mathematical Appendix S3), which we
call “selection for reinforcement”. See [24] for a discussion of how LD in cis and trans contrib-
ute to Fisherian sexual selection. We developed this new terminology because “linked selec-
tion” and “indirect selection” are insufficient in distinguishing these causal forces.
Thus, the change in frequency in Fis attributable to both its circumstance (“incidental
selection”) and its causal effect on generating a nonrandom association (“selection for rein-
forcement"). We aim to partition total selection for (or against) the Fallele into incidental
selection (unrelated to the effect of Fon nonrandom fertilization, Δp
F,Incidental
) and selection
for reinforcement (the causal effect of Fon its selective trajectory, Δp
F,Reinforcement
). In this
exercise, we ignore the change in frequency of paternally derived genotypes (which includes
migration, fertilization, and selection), as none of this change is plausibly attributable to the F
allele. We include the subscript mat with each variable to remind readers we are focused on
the maternally derived Falleles.
We first compute the difference in allele frequency between maternally derived haplotypes
in offspring after versus before selection as Δp
F,mat
directly from our results: Δp
F,mat
=p
F,mat-
derived after sel
−p
F,mom
. We then decompose Δp
F,mat
into components of reinforcing and inciden-
tal selection:
DpF;mat ¼DpF;mat;Reinforcement þDpF;mat;Incidental ð2Þ
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Each generation, we find Δp
F,mat, Incidental
by calculating Δp
F,mat
under the counterfactual
case of random fertilization. We then find the change in frequency of Fby selection for rein-
forcement Δp
F,mat, Reinforcement
by rearranging Eq 2.
Computer code. All code is written in R [88] and is available at https://github.com/
carushworth/gameto-theory. We generated figures with the ggplot2 and cowplot packages
[89,90] and used the dplyr package to process numeric results [91].
Dryad DOI
10.5061/dryad.rjdfn2zf8 [92]
Supporting information
S1 Text. Pseudocode for our iteration. A detailed description of our model.
(DOCX)
S2 Text. Traditional notation for gametophytic factors. Our model is inspired by gameto-
phytic factors in that underlie PMPZ barriers between Zea mays subspecies. We connect our
model to the traditional terminology that describes gametophytic factors.
(DOCX)
S3 Text. Mathematical appendix. We derive key analytical results from our model.
(DOCX)
S1 Fig. The initial frequency of Min the reinforcing species does not influence qualitative
results. The impact of variability in the initial frequency of sperm/pollen compatibility
allele, M, in reinf, on the transient reinforcement of postmating prezygotic isolation. All lines
overlap. Parameter values: Selection — s
reinf
=s
non-reinf
= 0.75. Migration — (g
non-reinf!reinf
=
g
reinf!non-reinf
= 0.1). Recombination — rAM ¼rMF ¼0:0001. Allele frequencies — f
M0,reinf
=
displayed by color, f
M0,non-reinf
= 0, f
F0,reinf
= 0.01, f
F0,non-reinf
= 0. The data underlying this figure
can be found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
(EPS)
S2 Fig. Female choosiness alters strength of reinforcement. We allow for an imperfect bar-
rier (i.e., variation in female choice) by allowing females with fertilization barrier genotypes to
be fertilized by a given haplotype, k, with probability xk¼pkð1dkcÞ
Pxk, where p
k
is the frequency of
haplotype kin pollen after fertilization. δ
k
equals 0 for compatible sperm/pollen grains and 1
for incompatible sperm/pollen grains. c, the efficacy of the barrier, is colored in the plot above.
Parameter values: Selection—s
reinf
=s
non-reinf
= 0.75. Migration—(g
non-reinf!reinf
=g
reinf!non-reinf
=
0.1). Recombination—rAM ¼rMF ¼0:0001. Allele frequencies—f
M0,reinf
= 1, f
M0,non-reinf
= 0,
f
F0,reinf
= 0.01, f
F0,non-reinf
= 0. The data underlying this figure can be found in https://datadryad.
org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
(EPS)
S3 Fig. The impact of asymmetric selection on the extent (A) and duration (B) of reinforce-
ment. Reinforcement strength and duration are estimated over a range of symmetric migra-
tion rates with rAM ¼rMF ¼104. The data underlying this figure can be found in https://
datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
(EPS)
S4 Fig. The impact of linkage on the extent (A) and duration (B) of reinforcement. Rein-
forcement strength and duration are estimated over a range of symmetric selection
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Sexual conflict over fertilization
PLOS Biology | https://doi.org/10.1371/journal.pbio.3001814 October 13, 2022 16 / 21
coefficients. g
non-reinf!reinf
=g
reinf!non-reinf
= 0.03. The data underlying this figure can be
found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.rjdfn2zf8.
(EPS)
S5 Fig. Locus order impacts the amount and duration of reinforcement. Top row (A–C) is
reinforcement amount; bottom row (D–F) is duration, as estimated under different marker
orders. Default marker order is AMF : amount (A); duration (D). Marker order MF A:
amount (B); duration (E). Marker order MAF : amount (C); duration (F). Shown are results
with a symmetric selection coefficient of 0.8 and migration g
non-reinf!reinf
=g
reinf!non-reinf
=
0.01. The data underlying this figure can be found in https://datadryad.org/stash/dataset/
doi:10.5061/dryad.rjdfn2zf8.
(EPS)
S6 Fig. Asymmetrical variation in female preference does not underlie transience of rein-
forcement. Incorporating a second gametophytic factor in the non-reinf does not qualitatively
change the amount (A) or duration of reinforcement (B), although reinforcement begins at
lower intensities of selection and reaches completion across more selection coefficients. The
data underlying this figure can be found in https://datadryad.org/stash/dataset/doi:10.5061/
dryad.rjdfn2zf8.
(EPS)
S7 Fig. Introducing a cost (s
M
) to the male compatibility allele impacts the evolution of
conflict over reinforcement. (A) The frequency of the Mallele in non-reinf over time as a
function of the additive cost of the allele (s
M
noted by color, with several values labeled for clar-
ity). The frequency of the Mallele in non-reinf (B) and the extent of reinforcement (C) after
10,000 generations (taken to be the equilibrium value, as evidenced by S7A Fig). Results are
plotted on a log
10
scale for clarity, though numbers are nontransformed. Dashed grey lines in
(B) and (C) note the values (0.0125 and 0.08) at which we transition from transient reinforce-
ment to a polymorphic equilibrium, and then to complete and stable reinforcement, respec-
tively. All measures describe populations after selection and before recombination. This figure
illustrates a single set of parameter values with 1 adaptive locus. Selection: s
reinf
=s
non-reinf
=
0.75; Migration: g
non-reinf!reinf
=g
reinf!non-reinf
= 0.1; Recombination: rAM ¼rMF ¼0:0001;
Allele frequencies: f
M0,reinf
= 1, f
M0,non-reinf
= 0, f
F0,reinf
= 0.01, f
F0,non-reinf
= 0. The data underly-
ing this figure can be found in https://datadryad.org/stash/dataset/doi:10.5061/dryad.
rjdfn2zf8.
(EPS)
Acknowledgments
We are grateful to Robin Hopkins and Maria Servedio, whose comments greatly improved the
manuscript. We also thank Jerry Kermicle for helpful conversation. We would like to acknowl-
edge Felix Andrews for the smorgasbord of statistical advice, although we did not follow it.
Author Contributions
Conceptualization: Alison M. Wardlaw, Jeffrey Ross-Ibarra, Yaniv Brandvain.
Data curation: Catherine A. Rushworth, Yaniv Brandvain.
Formal analysis: Yaniv Brandvain.
Funding acquisition: Jeffrey Ross-Ibarra, Yaniv Brandvain.
Investigation: Catherine A. Rushworth, Alison M. Wardlaw, Yaniv Brandvain.
PLOS BIOLOGY
Sexual conflict over fertilization
PLOS Biology | https://doi.org/10.1371/journal.pbio.3001814 October 13, 2022 17 / 21
Methodology: Yaniv Brandvain.
Project administration: Yaniv Brandvain.
Supervision: Jeffrey Ross-Ibarra, Yaniv Brandvain.
Visualization: Catherine A. Rushworth, Yaniv Brandvain.
Writing – original draft: Catherine A. Rushworth, Alison M. Wardlaw, Yaniv Brandvain.
Writing – review & editing: Catherine A. Rushworth, Jeffrey Ross-Ibarra, Yaniv Brandvain.
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