Int. J. Plant Sci. 159(2):192-198. 1998.
@ 1998 by The University of Chicago. All rights reserved.
1058-5893/98/5902-0003$03.00
THEORETICAL
POPULATION
GENETICS
OF MATING-TYPE
LINKEDHAPLO-LETHAL
ALLELES
Janis Antonovics,' Kara O'Keefe, and Michael E. Hood
Departmentof Botany,Duke University,Durham,North Carolina27708,U.S.A
The anther-smut fungus Ustilago violacea normally produces haploid sporidia of two mating types, and conjugation
between them is thought to be a prerequisite for infection of the host plant Silene alba. However, some natural
populations contain high frequencies of individuals with mating-type bias, from which sporidia of only one mating
type, usually AI, can be isolated. Such populations show no reduction in fungal transmission rate. The bias is most
readily interpreted as caused by the presence of deleterious recessive alleles, "haplo-lethals," that are linked to mating
type. Haplo-lethals may persist in a heterozygous state if, during teliospore germination, there is premature conjugation
among the immediate products of meiosis, i.e., intratetrad selfing, whereby the free-living haploid stage is bypassed.
We develop a theoretical model that shows how such alleles may spread if they provide a compensatory advantage in
the diploid or dikaryotic phase, for example, through increased disease transmission. There is a limited range of
conditions under which such haplo-lethal alleles may be maintained in a stable polymorphism, but if intratetrad selfing
is high and/or they have substantial advantage in the dikaryotic phase, haplo-lethal alleles linked to mating type can
spread to fixation. The occurrence of populations with a hig5 degree of mating-type bias is therefore readily explained.
Haplo-lethal alleles unlinked to mating type are much less likely to spread. In U. violacea, mating type shows firstdivision segregation; under such situations, haplo-lethal alleles may also readily spread if they are linked to another
centromere.
dergoes karyogamy, and differentiates to produce large
numbers of diploid teliospores (Cummins and Day
1977; Batcho and Audran 1980).
As part ~f a study of metapopulation dynamics of
the S. alba-V. violacea plant-pathogen system (Antonovics et al. 1994; Thrall and Antonovics 1995), we
found many populations of the anther-smut U. violacea with high frequencies of fungal individuals with
mating-type bias from which sporidia of only one mating type could be recovered (Oudemans et al. 1998).
This phenomenon is surprising because, if fusion of
sporidia of opposite mating type is a prerequisite for
dikaryon formation and infectivity in U. violacea, the
absence of one mating type should have severe consequences for fungal fitness. However, our studies
(M. E. Hood, unpublished data) have shown that both
mating types are indeed present immediately after
spore germination and meiosis but that one of the mating types, usually A2, cannot survive in the haploid
stage. Standard techniques for mating-type identification, therefore, recover only the other mating type,
usually AI. Our observations have additionally shown
that, in both biased and unbiased individuals, early
conjugation commonly occurs between adjacent cells
of the promycelium or between the promycelial cells
and sporidial cells produced from the teliospore (Hood
and Antonovics 1998). Genotypes unable to produce
viable free-living sporidia may therefore still contribute to conjugations and thereby produce the dikaryotic
infectious stage. Continued pathogenicity and the presence of sporidia of only one mating type has also been
reported in several species of commercially important
smuts (Fischer 1940; Holton 1951; Grasso 1955; Darlington and Kiesling 1975). Mating-type bias also has
been reported sporadically in U. violacea from a wide
range of host species (Garber et al. 1978) and recently
from S. alba in Switzerland (Kaltz and Shykoff 1997).
Although we have found predominantly Al bias, Garber et al. (1978) noted five cases of Al bias and three
cases of A2 bias in 22 collections of U. violacea.
Introduction
The anther-smut fungus Ustilago violacea (Pers.)
Fuckel (MicrQbotryum violaceum Deml & Oberwinkler) is a heterobasidiomycete in the order Ustilaginales
and an obligate pathogen of many perennial specil-sin
the Caryophyllaceae (Deml and Oberwinkler 1982;
Thrall et al. 1993) including Silene alba (Miller) Krause
(S. latifolia Poiret), a common ruderal plant of eastern
North America. This plant-pathogen system has been
the subject of longstanding studies by ourselves and
collaborators (Alexander et al. 1996), and the fungus
itself h~ been the object of extensive genetic studies
(Caten and Day 1986; Bej and Perlin 1989; Garber
and Ruddat 1994). Following infection, the fungus
spreadsthroughout the plant and causesdevelopmental
changes in the flower that result in sterility and the
production of diseased anthers; plants are much less
affected in terms of vegetative morphology or increased mortality. The diploid teliospores, formed in
the anthers of diseased plants, are usually transmitted
to healthy hosts by insect pollinators (Antonovics and
Alexander 1992; Shykoff and Bucheli 1995; Roche et
al. 1995; Altizer et al. 1998). Once deposited onto
flowers or leaf surfaces, teliospores germinate and concurrently undergo meiosis to produce a germ tube, the
promycelium, usually consisting of three cells; the
fourth cell remains in the teliospore. The promycelium
and spore bud haploid cells, the sporidia, which are of
two mating types, Al and A2. These conjugate and
form infective dikaryotic hyphae that invade and
spread throughout the host plant. Formation of a dikaryon by conjugation between sporidia of opposite
mating type is considered to be a prerequisite for successful infection (Fischer and Holton 1957; Day and
Jones 1968; Garber and Day 1985). In an infected
plant, the fungus colonizes the developing anthers, un'Author for correspondence and reprints; telephone 919-6607332; E-mail [email protected].
1O')
ANTONOVICS
ET Al
.POPULA TION
Our own studies have shown that mating-type
linked haplo-lethals are often at a high frequency in
natural populations of U. violacea on S. alba in Vir-'
ginia (Oudemans et at. 1997), Genetic studies (Oudemans et at. 1997) and observations on early growth
and germination of biased and unbiased fungal genotypes (Hood and Antonovics, unpublished data) have
confirmed that this mating-type bias is consistent with
the "haplo-lethal" hypothesis, Although segregation
distortion systems have been extensively studied from
a theoretical viewpoint (Feldman and Otto 1991), we
do not have a similar basis for understanding the expected dynamics of haplo-lethals. In the context of
segregation distortion, it has been shown that there can
be a protected polymorphism if alleles advantageous
at the gametic stage have a disadvantageous effect in
the diploid phase (Hiraizumi et at. 1960; Feldman and
Otto 1991), but haplo-lethals represent in some ways
the reverse of this case. Moreover, in mating-type
linked haplo-lethals, there will be an unequal frequency of the two mating types in the sporidial stage; the
relative fitness of genotypes through sporidial conjugations may therefore be frequency-dependent.
In the presept study, we develop a theoretical model
for the population genetics of a haplo-lethal allele
when it is completely linked to one mating type, We
consider the conditions for initial increase of a matingtype linked haplo-lethal mutant and the conditions for
a protected polymorphism. We then use these results
to help interpret possible reasons for the wide range
of frequencies of haplo-lethals found in natural populations of U. violacea.
TheModel
We develop recursion equations for the change in
frequency of a haplo-lethal allele linked to mating
type. We first define relevant population parameters
and then develop a model of selection and mating in
the haploid phase. Finally, we introduce selection in
the dikaryotic stage.
Population Parameters
We assume that the population consists of two genotypes: Al +/A2+ at a frequency of U, producing
sporidia of both mating types, and Al +/A2-, at a
frequency of V, producing only Al sporidia as freeliving haploids. The frequency of gametic types in this
population is then (assuming 1: 1 segregation of mating
type)
Al +: a = 0.5,
A2 +: b = 0.5U,
and
A2
-:
c =
O.5V.
Following teliospore germination, the cells produced by the promycelium may either mate directly,
such that they do not have to reach the free-living
sporidia! stage, or they may produce sporidia that subsequently mate.
GENETICS
OF HAPLO-LETHALS
We let <I> be the fraction of "gametes" that undergo
intratetrad selfing, by conjugation among the promycelial cells and sporidia produced during early germination, and thus bypass the free-living sporidial stage.
Correspondingly,let (1 -
<1»
be the fraction of "ga-
metes" that actually contribute to zygotes via the freeliving sporidial mating pool. These fractions represent
the proportions of the two types of "gametes" in a
population without biased individuals. We focus on the
actual contributions to the zygotes (rather than on total
sporidial and promycelial production) in order to sim-
plify the theory and becausethe quantity <I> is a measure of the importance of the promycelial stage to the
life cycle of the fungus in unbiased populations. As
discussed below, the number of free-living sporidia,
and thus the number of zygotes produced via sporidial
conjugation, will decline as the frequency of biased
individuals in the population increases.
Haploid Selection and Mating
With regard to haploid selection, we assume that a
haploid cell has a fitness of one if it does not carry
the haplo-lethal allele, regardless of whether it contributes to dikaryons by intrameiotic selfing or by the
sporidial pool. However, if a cell carries the haplolethal, it is assumed to have a fitness of zero in the
sporidial pool.
With regard to mating, we assume that the gametic
contributions to the zygote via intratetrad selfing are
not influenced by the frequency of the other cell types.
This will be generally true because, during intrapromycelial mating, the alternative mating type is always
present in equal frequency. However, in promycelialsporidial conjugations, sporidia of one mating type
may be rare and limiting, thus reducing the contribution of the promycelial cell with the opposite mating
type. For the sake of simplicity, we ignore this complication.
Sporidia will make gametic contributions to the zygote by matings with other sporidia. In a population
containing some biased individuals (and on the assumption that teliospores are well mixed), the total size
of the sporidial population will be proportional to a +
b = 0.5 + 0.5U, and the frequenciesof the gametic
types in the free-living mating pool will be
Al +: <X= a/(a + b) = 1/(1 + U)
and
A2 +:
~=
b/(a + b)
=
U/(l + U).
We can now calculate the per capita contribution of
the Al + and A2 + sporidia to the zygotes. We can do
this in several ways but focus on two possible models
of sporidial conjugation; the actual dynamics of the
conjugation process in nature are unknown. In the
"random-encounter" model, we assume that the sporidia first associateat random in pairs regardless of mating type, but only pairs of opposite mating type
conjugate. In the "mutual:search" model, we assume
that the sporidia search out each other, for example,
INTERNATIONAL
194
JOURNAL
by pheromones or surface-contact proteins, such that
the minority mating type always achieves matings but
a fraction of the majority mating type remains unmated.
It should be noted that sporidia (and promycelial
cells) are "monogamous," i.e., they do not get multiple opportunities to mate. If there were multiple matings, the random-encounter model would be different.
For example, a rare A2 sporidium would be able to
mate with a large number of Al sporidia and have a
per capita contribution that exceeds one and so have
a greatly enhanced fitness. In reality, a sporidium
mates only once, and its per capita contribution cannot
exceed unity. Our model therefore incorporates the biological reality that as the frequency of the haplo-lethal allele increases, the actual contribution of sporidial conjugations to infection would be expected to
decrease.
OF PLANT
SCIENCES
~ is the frequency of the minority genotype, i.e., A2 + .
The per capita contribution of Al + therefore is
O.5(2~)f<x
= (~f<x) = bfa, and that of A2+ is O.5(2~)f
~ = 1.
The recursions for the frequency of the different gametic types then become
Ta' = acf>+ b(1 - cf»,
Tb' = bcf>+ b(1 - cf»,
and
Tc' = c<\>,
where T = <\>+ 2b(1 - <\».
Since b = O.5Uand c = O.5V,the recursionsfor b
and c become equivalent to recursions for U and V,
namely
U' = U/[<I>+ (1 - <I»U]
and
Random-Encounter Model
In this model, the fraction of sporidia participating
in pairings with the opposite mating type is 2al3, half
of which are Al + and half of which are A2 +. The
per capita contribution of Al + to these matings is
= 13; similarly, the per capita
= a. If there are no biased individuals in the population, then a = 13 = 0.5. How-
therefore O.5(2a~)la
contribution of A2 +
ever, since 1 is defined as the fraction of gametes
actually contributing to zygotes in an unbiased population, we standardize these contributions to 1 by dividing by 0.5 (in a mass-action model without bias,
half the sporidia fail to conjugate).
The recursions for the frequency of the different gametic types then become
Ta' = a<l>+ a(I - <1»213,
<I>
Tb' = b<l>+ b(I - <I»2a,
and
Tc' = c<p,
where a', b', and c' are the frequencies of the gametic
types after haploid selection and mating, and T is the
total of the uncorrected frequencies (or mean fitness)
V' = V<I>/[<I>
+ (1 - <I»U].
Selection in the Diploid Stage
We now introduce selection as follows. We have
assumed aboye that teliospores (and sporidia) were
produced in proportion to the frequency of the parental fungal genotypes. However, if these parental
genotypes contribute differentially to teliospore production, the actual frequencies of spores produced
will be proportional to U(1 - s) and V, where s is
the disadvantage of the unbiased genotype relative
to the biased genotype. Thus, the genotypic fitnesses
are: +/+ = 1 - s, +/= 1, and -/= O. We
assume that the hap1o-lethal is advantageous in the
heterozygote and that s is between 0 and 1. A negative value of s would represent less than full dominance of the wild type for fitness, but under this
scenario the haplo-lethal cannot persist. Correcting
these frequencies for the total gives the actual frequencies of the genotypes after selection of
U* = U(1 - s)/(1 - Us)
= <p +(1
and
and c become equivalent to recursions for U and V:
U' = U{<p+(1 - <p)[2/(U + I)]}
Substituting U* for U and V* for V in the recursion
equations above, we readily obtain the full recursions
that include haploid selection, mating, and diploid selection.
To determine the conditions for equilibrium, we use
the full recursions to estimate the rate of change of U
per generation (U' - U), set this equal to zero, and
solve.
- <p)[4ab/(a+ b)].
Since b = O.5U and c = O.5V,the recursionsfor b
+ [<p + (1
-
<p)[2U/(U + 1)]
and
V'
= V<I>/{<I>+
(1 - <I»[2U/(U+ I)]},
where .U' and V' are the frequencies of the unbiased
and biased genotypes in the next generation, respectively.
Mutual-Search Model
In this model, the fraction of sporidia participating
in pairings with the opposite mating type is 2~, where
V*
= V/(l
- Us).
Results
Random-Encounter Model
Other than the trivial equilibria at U= 0 and U= 1,
a nontrivial equilibrium is possible at
~
ANTONOVICS
ET AL
.POPULA TION GENETICS
0.9
0.8
c
~
~ 0.6
cOJ
;g
"a;
0
Q
c
,Q
-0
OJ
""Qj
UI
195
not possible. The reason is that, because the A2 + are
always in the minority, they can always find an Al +
partner, and their fitness is not a function of the frequency of AI; in contrast, under the random-encounter
model, the chance of an A2 encountering an Al increasesas A2 becomes rare. Setting V to be very small,
we can calculate the conditions for increase of the biased type. For the biased type to invade"when rare, S
must be greater than (1 - <1»;once it invades, it will
go to fixation. The phase diagram for this caseis therefore similar to that for the random-encounter model
(fig. 1), except that there is no region of stable polymorphism.
1.0
0.7
OF HAPLO-LETHALS
0.5
0.4
0.3
Discussion
0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
intra-tetrad selling (I/»
Fig. I Phase diagram showing regions of different equilibrium
frequencies of a haplo-lethal allele linked to mating type under a
random-encounter model (see text) for different degrees of intratetrad selfing and different levels of selection against the homozygous
wild type in the dikaryotic phase. Unshaded area representsthe haplo-lethal unable to invade; hatched area represents the population
polymorphic for haplo-lethal and normal allele; and cross-hatched
area represents the population fixed for haplo-lethal allele.
U
= (2 -
2s -
2<1>+
s<l»
+ s(2 - 2s - <1».
Setting U = 1, we find the upper limit of this equilib-
rium at either s = 1 or s = (1 - <1». Setting U = 0,
the lower limit of the equilibrium is at s = (1 - <1»/(1
- 0.5<1».It follows that for the biased type to invade
and reduce U to less than 1, the amount of intratetrad
selfing, <1>,must exceed 1
- s, the fitness of the un-
biased genotype relative to the biased one. If s is greater than (1 - <1»/(1- 0.5<1»,the biased type will go to
fixation. From the phase diagram showing the different
outcomes for the range of possible values of s and
(fig. 1), it can be seen that at high levels of intratetrad
selfing it is very likely that the bias trait will go to
fixation, whereas at intermediate levels of selfing and
intermediate levels of heterozygote advantage a polymorphism is more likely. In the polymorphic population, when U is close to 1, there will be few biased
genotypes, and the frequency of free-living Al and A2
sporidia will be approximately equal; when U is close
to 0, the population will be highly biased, and the freeliving sporidia will be mostly AI.
We investigated the transient dynamics by computer
simulation of the recursion relationships. Our results
confirmed the stability of the polymorphism and
showed that the approach to equilibrium was generally
asymptotic.
Mutual-Search Model
Under this model. equilibria are possible at only U
= 0 and U = 1. A stable polymorphism is therefore
<I>
Our results confinn the intuition that mating-type
linked haplo-lethal alleles can become established and
spread in a population if there is a high level of intratetrad selfing and if there is a selective advantage of
the haplo-lethal allele in the heterozygous condition.
If the mating among the sporidia is a "random-encounter" process, such spread may lead to the establishment of a stable genetic polymorphism, but the region of polymorphism is small. If the mating among
sporidia is "mutual search," such conditions will lead
to the fixation of the haplo-lethal condition. In the latter situation, the result would be a population in which
only one mating type could be isolated as a free-living
haploid. It is not known whether the random-encounter
or the mutual-search model is more realistic in nature.
We can envisage that, when sporidial densities are low
and encounters rare, the random-encounter model may
be more realistic, because sporidia cannot actively
move to choose the alternative mating type. However,
when sporidial densities are high, it is likely that the
mutual-search model may be more representative, because then sporidia of one mating type are likely to be
in close proximity to sporidia of the other mating type.
In Ustilago violacea, the frequency of the bias trait
can be very variable (Oudemans et al. 1998). In one
local population (2.1c 0.375 OFF R) 55 of 56 fungal
individuals showed mating-type bias. In another site
(6h 0.175-0.375; Oudemans et al. 1997), the overall
frequency of bias was intennediate, but the local distribution of the bias was very patchy, with some patches consisting almost entirely of biased individuals and
others of unbiased individuals (Oudemans et al. 1998;
fig. Ib). This local genetic structure could be consistent with either a stable polymorphism and local dIspersal or with local fixation of either biased or unbiased types and longer distance dispersal among
patches.
The occurrence of mating-type bias is well known
in the smut fungi (e.g., U. nuda; Nielsen 1968) and
other heterobasidiomycetes (e.g., Cryptococcus neoformans; Wickes et al. 1996). Our results show that
extreme bias may be expected from the models of haplo-lethal alleles linked to mating type. Intratetrad selfing is the rule in U. nuda, but little is known about
the sexual cycle of C. neoformans in nature (Ellis and
Pfeiffer 1990).
In terms of the models we have presented, the
spread of hapio-lethals will be determined by the degree of intratetrad selfing as well as the selective advantage of the hapio-lethal alleles in the dikaryotic
state. However, in U. violacea, it is difficult to determine a priori which factor is more important in causing
differences in the frequencies of hapio-lethal alleles
among populations. The degree of intratetrad selfing is
known to be higWy environment-dependent in Ustilago species (Hood and Antonovics 1998), being generally greater under low temperatures and low nutrients. This would lead to the prediction that, all things
being equal, the frequency of mating-type bias should
be greater in cool environments. Determining the relative contribution of intratetrad compared with other
conjugations to subsequent infections in the field may
be possible using markers linked to another centromere and which cosegregate with mating type, on the
assumption of first-division segregation of mating
type. Heterozygotes for such markers would remain
heterozygous in progeny with intratetrad selfing but
would generate homozygotes in the progeny if there
were intertetrad selfing. If only one marker is available, population-wide estimates of intratetrad selfing
are possible, but the inter- or intratetrad origin of a
progeny individual cannot be determined unambiguously if it is heterozygous at that marker. If multiple
markers are present, each at a different centromere,
then, as the number of such markers increases, individuals become identifiable as to their origin with increasing confidence. However, U. violacea is relatively
uniform with regard to allozyme variation (Antonovics
et al. 1996), and consistent RAPD markers have been
difficult to develop (H. M. Alexander and P. V. Oudemans, personal communication). It might be more
feasible to measure the effects of biased and unbiased
fungal genotypes on disease expression and disease
spread. In this case, our model could be used to predict
importance of the free-living haploid stage from the
observed frequency of the hapio-lethal trait and the
selective advantage of the trait in the dikaryotic phase.
Thus, the actual contribution of the sporidial phase
will be given by (1
-
<I>
)[2U/(1 + U)]; then, if the
selective advantage of the hapio-lethal allele in the dikaryotic phase (s) and its equilibrium frequency (U)
are known, the relative importance of intratetrad self-
ing
«I»
can be estimated.
Compensatory influences of hapio-lethal alleles in
smut fungi have been suggested previously. For example, mating-type bias is ubiquitous in U. nuda, a
smut of barley, and Nielsen (1988) suggested that
more rapid infection may result from direct conjugation between cells of the promycelium. Holton and
Dietz (1960) found that individuals of U. avenae and
U. kolleri that were heterozygous for hapio-lethal alleles sporulated on a greater area of host tissue relative
to "wild-type" individuals. Compensatory influences
of mating-type bias have not been demonstrated in U.
violacea. However, the common occurrence of matingtype bias in host races of this species and its high
frequency within populations strongly indicate that
fuese alleles have some advantage in infection or later
stages of disease expression. In U. violacea, although
intrapromycelial conjugation occurs in both biased and
unbiased genotypes, promycelial growth and sporidial
budding is somewhat slower in biased genotypes
(Hood and Antonovics 1998 [in this issueD. There is
therefore a longer time frame during which intrapromycelial conjugation can occur, and this may provide
some advantage to the biased genotype because intrapromycelial conjugation requires less time than do
sporidial budding and conjugation. Given the short florallifespan of, especially, male flowers of S. alba (Alexander 1989; Shykoff et al. 1996), increased intrapromycelial conjugation may result in increased
probability of infection, once spores are deposited on
a flower. In addition, we can also envisage that the
presence of hapio-lethal alleles might select for an increase in the frequency of intrapromycelial conjugation, either through modifiers or as a result of linkage
disequilibrium between alleles for intrapromycelial
conjugation and hapio-lethal alleles. We are currently
investigating tliese possibilities.
Our model is quite general and has therefore made
a number of assumptions that may not hold in particular cases. For example, we have assumed that there
is no inbreeding depression. Moreover, we have assumed that intratetrad selfing (through intrapromycelial conjugation or promycelial-sporidial conjugations)
is independent of the presence of hapio-lethal alleles.
Finally, we have assumed that we are dealing with a
fully mixed population in which biased and unbiased
individuals are equally likely to encounter each other.
However, given population substructuring or limited
mixing on flowers of spore loads from pollinators, the
fitness of the A2 + sporidia from the unbiased type
may only rarely be limited by the availability of Al +
from the biased lines, because the two types meet only
infrequently. This kind of limited mixing would make
the conditions for the spread of hapio-lethal alleles less
stringent.
Hapio-lethal alleles and mating-type loci may show
a wide range of linkage relationships, and in this study
we have explicitly considered only complete linkage
of the hapio-lethal allele to the mating type locus. If
the hapio-lethal allele is unlinked to mating type, then
this is equivalent to the case of a mutant allele that is
disadvantageousin the haploid phase but results in heterozygote advantage and lethality of the double recessive in the dikaryotic stage. Its disadvantage in the
haploid phase would then be inversely proportional to
the degree to which it bypasses the free-living stage
by intratetrad selfing. During intratetrad selfing, an individual heterozygous for a hapio-lethal allele unlinked to mating type, would produce 0.25 +/+, 0.5
+/-, and 0.25 -I-;
the fitness of the hapio-lethal
allele transmitted through !his stage is therefore
halved, i.e., its fitness will be 0.5 <P,where <P(as
ANTONOVICS
ET AL.
-POPULA TION GENETICS
above) is the frequency of intratetrad selfing. The general conditions for a polymorphism when there is opposing selection in the haploid and diploid phaseshave
been derived by Scudo (1967). It can be shown that
an unlinked haplo-1ethal mutant allele can invade if
the difference between the relative fitness of the homozygote wild-type and the heterozygote haplo-lethal
allele in the diploids, s, is greater than the difference
in the relative fitness of the deleterious alleles in the
haploid condition, i.e., 1 - 0.5<1>.
Therefore,the condition for increase of a hap10-1ethalunlinked to mating
type is s > 1 - 0.5<1>.
However, for an allele linked to
mating type, we have shown this condition to be s >
1 - <1>. Therefore, it is substantially easier for a haplolethal mutant to spread if it is linked to mating type.
It also follows that if a haplo-lethal mutant arises unlinked or partly linked to mating type, selection would
favor increased linkage between the haplo-1ethal allele
and the mating-type allele. Haplo-lethal alleles that
segregate independently of mating type have been
found in U. avenae and U. kolleri (Holton and Dietz
1960) and are indicated in U. violacea (Kaltz and Shykoff 1997).
In U. violacea, we ourselves have only detected
haplo-lethal ai1e1esunlinked to mating type in one individual (Hood and Antonovics, unpublished data). In
this individual, the haplo-lethal allele shows first-division segregation. In U. violacea, the mating-type locus also shows first division segregation (Hood and
Antonovics 1998). Matings that result from intratetrad
OF HAPLO-LETHALS
197
selfing are therefore always themselves heterozygous
for a haplo-lethal allele linked to the centromere, and
the allele is always transmitted (Hood and Antonovics
1998). Yet, because the haplo-lethal allele may be associated with either the Al or the A2 mating type,
depending on the direction of independent assortment
in the meiosis of any particular germinating teliospore,
mating-type bias in the sporidial population is evident.
If the haplo-lethal allele is linked to a centromere,
there is no loss of fitness in the haploid phase through
intratetrad selfing. The net fitness of the allele when it
is transmitted by both intratetrad and free-living stages
is thereforesimply <1>, and the condition for its increase
is that s > 1 - <1>. A haplo-lethal that is linked to a
centromere in a system where there is first division
segregation of mating type will therefore be more likely to increase in a population than a centromere unlinked haplo-lethal. First-division segregation of mating type has also been postulated as an important
mechanism for preserving heterozygosity around the
centromeres of nonmating-type chromosomes (Zakharov 1968, 1986; Kirby 1984).
.
Acknowledgments
We wish to thank E. D. Garber for discussions of
the genetics of Ustilago violacea, and for confirming
the mating-type bias during the early stages of this
work. We thank J. Shykoff for helpful comments on
the manuscript.
Literature Cited
Alexander HM 1989 An experimental field study of anther-smut
disease of Silene alba caused by Ustilago violacea: genotypic
variation and disease incidenc~. Evolution 43:835-847.
Alexander HM, PH Thrall, J Antonovics, AM Jarosz, PV Oudemans
1996 Population dynamics and genetics of plant disease: a case
study of the anther-smut disease of Silene alba caused by the
fungus Ustilago violacea. Ecology 74:990-996.
Altizer S, PH Thrall, J Antonovics 1998 Vector behavior and transmission of anther-smut infection in Silene alba. Am Midi Nat (in
press).
Antonovics J, HM Alexander 1992 Epidemiology of anther-smut
infection of Silene alba caused by Ustilago violacea: patterns of
spore deposition in experimental populations. Proc R Soc Lond B
250: 157-163.
Antonovics J, D Stratron, PH Thrall, AM Jarosz 1996 An anthersmut disease (Ustilago violacea) of fire-pink (Silene virginica):
its biology and relationship to the anther-smut disease of white
campion (Silene alba). Am Midi Nat 135:130-143.
Antonovics J, PH Thrall, AM Jarosz, D Stratton 1994 Ecological
genetics of metapopulations: the Silene-Ustilago plant-pathogen
system. Pages 146-170 in L Real, ed. Ecological genetics. Princeton, N.J.: Princeton University Press.
Batcho M,JC Audran 1980 Donnes cytochimiques sur les antheres
de Silene dioica parasitees par Ustilago violacea. Phytopathol Z
99:9-25.
Bej AK, MH Perlin 1989 A high efficiency transformation system
for the basidiomycete Ustilago violacea employing hygromycin
resistance and lithium actetate treatment. Gene 80: 171-176.
Caten CE, AW Day 1977 Diploidy in plant pathogenic fungi. Ann
Rev Phytopathol 15:295-318.
Cummins JE, AW Day 1977 Genetic and cell cycle analysis of a
smut fungus (Ustilago violacea). Methods Cell Bioi 15:445--469.
Darlington LC, RL Kiesling 1975 A compatibility-linked, haplo-
lethal factor in race 1, Ustilago nigra (Tapke). Proc ND Acad Sci
27:116-119.
Day A, JK Jones 1968 The production and characteristics of diploids in Ustilago violacea. Genet Res Camb 11:63-81.
Deml G, F Oberwinkler 1983 Studies in heterobasidiomycetes. Part
31. On the anther smuts of Silene vulgaris (Moench.) Garcke.
Phytopathol Z 108:61-70.
Ellis DH, TJ Pfeiffer 1990 Natural habitat of Cryptococcus neoformans var. gattii. J Clin Microbiol 28:1642-1644.
Feldman MW, SP Otto 1991 A comparative approach to the population-genetic theory of segregation distortion. Am Nat 137:443456.
Fischer GW 1940 Two cases of haplo-lethal deficiency in Ustilago
bullata operative against saprophytism. Mycologia 32:275-289.
Fischer GW, CS Holton 1957 Biology and control of the smut fungi.
Ronald, New York.
Garber ED, ML Baird, LM Weiss 1978 Genetics of Ustilago violacea. II. Polymorphism of color and nutritional requirements of
sporidia from natural populations. Bot Gaz 139:261-265.
",
Garber ED, AW Day 1985 Genetics of a phytopathogenic basidiomycete, Ustilago violacea. Bot Gaz 146:449-459.
Garber ED, M Ruddat 1994 Genetics of Ustilago violacea. XXXII.
Genetic evidence for transposable elements. Theor Appl Genet 89:
838-846.
Grasso V 1955 A haplo-lethal deficiency in Ustilago kolleri. Phytopathology 45:521-522.
Hiraizumi Y, L Sandler, JF Crow 1960 Meiotic drive in natural
populations of Drosophila melanogaster. III. Populational implications of the segregation distorter locus. Evolution 14:433-444.
Holton CS 1951 Methods and results of studies on heterothallism
and hybridization in Tilletia caries and T. foetida. Phytopathol 41:
511-521.
.
Holton CS, SM Dietz 1960 An apparent association of haploid le-
198
INTERNATIONAL
JOURNAL
thai factors with two unique soros types of oat smut. Phytopathology 50:749-751.
Hood ME, J Antonovics 1998 Two-celled promycelia and matingtype segregation in Ustilago violacea (= Microbotryum violaceum). Int J Plant Sci 159:199-205 (in this issue).
Kaltz 0, JA Shykoff 1997 Sporidial mating type ratios of teliospores from natural populations of the anther smut fungus, Microbotryum (=Ustilago) violaceum. Int J Plant Sci 158:575-584.
Kirby GC 1984 Breeding systems and heterozygosity in populations
of tetrad forming fungi. Heredity 52:35-41.
Nielsen J 1968 Isolation and culture of monokaryotic haplonts of
Ustilago nuda, the role of proline in their metabolism, and the
inoculation of barley with resynthesized dikaryons. Can J Bot 46:
1193-1200.
1988 Ustilago spp., smuts. Adv Plant Pathol 6:483-490.
Oudemans PV, J Antonovics, SM Altizer, PH Thrall, L Rose, HM
Alexander 1998 The distribution of mating type bias in natural
populations of the anther smut Ustilago violacea on Silene alba
in Virginia. Mycologia (in press).
Roche B, HM Alexander, A Maltby 1995 Dispersal and disease
gradients of anther-smut (Ustilago violacea) infection of Silene
alba at different life stages. Ecology 76:1863-1871.
OF PLANT
SCIENCES
Scudo PM 1967 Selection on both haplo and diplophase. Genetics
56:693-704.
Shykoff JA, E Bucheli 1995 Pollinator visitation patterns, floral
- rewards and the probability of transmission of Microbotryium violaceum, a venereal disease of plants. J Ecol 83:189-198.
Shykoff JA, E Bucheli, 0 Kaltz 1996 Flower lifespan and disease
risk. Nature 379:779.
Thrall PH, J Antonovics 1995 Theoretical and empirical studies of
metapopulations: population and genetic dynamics of the SileneUstilago system. Can J Bot 73(suppl):1249-1258.
Thrall PH, A Biere, J Antonovics 1993 Plant life-history and disease susceptibility: the occurrence of Ustilago violacea on different species within the Caryophyllaceae. J Ecol 81:489-498.
Wickes BL, ME Mayorga, U Edman, JC Edman 1996 Dimorphism
and haploid fruiting in Cryptococcus neofonnans: association with
the a-mating type. Proc Natl Acad Sci USA 93:7327-7331.
Zakharov IA 1968 Heterozygosity in intratetrad and intraoctad fertilization in fungi. Genetika 4:98-105.
1986 Some principles of the gene localization in eukayotic
chromosomes: formation of the problem and analysis of nonrandom localization of the mating-type loci in some fungi. Genetika
22:2620-2624.