Copyright Ó 2006 by the Genetics Society of America
DOI: 10.1534/genetics.105.051227
Pleiotropic Quantitative Trait Loci Contribute to Population Divergence in
Traits Associated With Life-History Variation in Mimulus guttatus
Megan C. Hall,*,1 Christopher J. Basten† and John H. Willis*
*Department of Biology, Duke University, Durham, North Carolina 27708 and †Syngenta Biotechnology, Research Triangle Park,
North Carolina 27709-2257
Manuscript received September 17, 2005
Accepted for publication November 22, 2005
ABSTRACT
Evolutionary biologists seek to understand the genetic basis for multivariate phenotypic divergence. We
constructed an F2 mapping population (N ¼ 539) between two distinct populations of Mimulus guttatus. We
measured 20 floral, vegetative, and life-history characters on parents and F1 and F2 hybrids in a common
garden experiment. We employed multitrait composite interval mapping to determine the number, effect,
and degree of pleiotropy in quantitative trait loci (QTL) affecting divergence in floral, vegetative, and lifehistory characters. We detected 16 QTL affecting floral traits; 7 affecting vegetative traits; and 5 affecting
selected floral, vegetative, and life-history traits. Floral and vegetative traits are clearly polygenic. We detected
a few major QTL, with all remaining QTL of small effect. Most detected QTL are pleiotropic, implying that
the evolutionary shift between these annual and perennial populations is constrained. We also compared the
genetic architecture controlling floral trait divergence both within (our intraspecific study) and between
species, on the basis of a previously published analysis of M. guttatus and M. nasutus. Eleven of our 16 floral
QTL map to approximately the same location in the interspecific map based on shared, collinear markers, implying that there may be a shared genetic basis for floral divergence within and among species of
Mimulus.
E
VOLUTIONARY biologists have long sought to understand the genetic basis for adaptive divergence
between populations with complex multivariate phenotypes. Adaptation to a novel environment may involve
evolutionary change of multiple genetically correlated
traits as the population approaches a new phenotypic
optimum (Fisher 1930; Orr 2000). If variation in individual traits is governed largely by trait-specific loci,
the selected traits may be able to evolve independently
(unless they are constrained by linkage disequilibrium),
whereas those that are governed by pleiotropic loci are
going to be evolutionarily constrained. The degree of
pleiotropy can have profound effects on the evolutionary
trajectory of particular traits (Lande 1979) and therefore on the nature of divergence of multiple traits between
populations.
An understanding of the degree of pleiotropy affecting multiple traits sheds light on one of the classic
debates in evolutionary biology—whether phenotypic
divergence is the result of fixation of one or two mutations of large effect or due to many mutations of small
effect. Each of these two options could have different
effects on the nature of evolutionary divergence. One
of the earliest views of the genetic basis of adaptation
1
Corresponding author: Department of Genetics, Box 7614, 100 Derieux
Pl., North Carolina State University, Raleigh, NC 27695-7614.
E-mail: [email protected]
Genetics 172: 1829–1844 (March 2006)
was that phenotypic divergence was extremely gradual,
consisting of many genes, each having an infinitesimally
small effect on the trait (Fisher 1930). This view of adaptation had widespread support among early empiricists
(Dobzhansky 1937; Huxley 1942; Muller 1949), although it was later challenged in favor of the alternate
view that adaptations were largely the result of substitutions of single genes with large effects (Gould 1980;
Gottlieb 1984; Turner 1985). The debate continued
(Coyne and Lande 1985; Orr and Coyne 1992) until
more recent evidence based on quantitative trait locus
(QTL) mapping analyses allowed more rigorous testing of this hypothesis. To date, genetic mapping studies
have provided support for both possibilities, some where
few large-effect QTL underlie divergence (Doebley and
Stec 1991; Bradshaw et al. 1995,1998; Sucena and
Stern 2000; Colosimo et al. 2004). Other studies have
demonstrated that divergence can result from many QTL
of small effect (Liu et al. 1996; Laurie et al. 1997; Zeng
et al. 2000; Fishman et al. 2002). However, these patterns
are generally interpreted with respect to individual traits
rather than accounting for correlations among traits. For
example, consider a pair of populations divergent for two
traits, and the difference in each trait is controlled by 5
QTL. Phenotypic divergence in these traits could be explained by as many as 10 QTL (if each QTL were completely independent) or as few as 5 QTL (if all QTL were
pleiotropic). Because phenotypic divergence between
1830
M. C. Hall, C. J. Basten and J. H. Willis
populations generally involves changes in multiple traits
for complex organisms, it is particularly important to account for pleiotropic QTL. Examining traits individually
to uncover the number of QTL controlling phenotypic
divergence could be potentially misleading if pleiotropy
exists.
QTL mapping can serve as a powerful way to understand whether multiple traits have diverged together,
and it can also be used to distinguish the number and
effects of genetic factors controlling divergence in individual traits. Numerous studies have found evidence
for pleiotropy affecting multiple traits (True et al. 1997;
Jiang et al. 1999; Westerbergh and Doebley 2002; Cui
et al. 2004). Of course, fine mapping of pleiotropic QTL
can reveal separate, tightly linked QTL (i.e., Knight
et al. 2001). Most evidence for pleiotropy is based on
overlapping genetic regions detected in separate QTL
mapping analyses for individual traits, rather than accounting for the correlated structure of multiple traits
in a joint QTL mapping analysis. By joint-mapping QTL
affecting multiple divergent traits, we can directly address whether the genetic correlations we see are the
result of broadly pleiotropic QTL vs. unlinked QTL affecting separate traits (Jiang and Zeng 1995).
To understand the genetic basis of complex adaptations, we examine the genetic architecture of phenotypic and life-history divergence between two wild,
primarily outcrossing populations of Mimulus guttatus
(yellow monkeyflower) that differ dramatically in floral,
vegetative, and life-history characters. One of the populations we analyze consists of small annual plants that
produce thin stems and small flowers (Figure 1; Table 1)
and inhabit a high-elevation environment on Iron
Mountain, Oregon (IM). These annuals flower rapidly
and a large proportion of their meristems are reproductive (i.e., they have flowers or floral buds, rather than
leaves). The other population consists of large perennial plants with comparably thicker stems and larger
flowers (Figure 1; Table 1) that live in a coastal, temperate environment in the Oregon Dunes National
Recreation Area (DUN). These plants flower later than
the annuals and a large proportion of their meristems
are vegetative (i.e., they have leaves rather than flowers
or buds). A reciprocal transplant study reveals evidence
for strong local adaptation in each of these two populations (Hall 2005).
The transition between annual and perennial life
histories is common among plants, it is associated with
multiple phenotypic differences, and it is the likely response to different ecological conditions (Stebbins
1974). Do life-history characters such as timing of flowering and proportion of floral vs. vegetative meristem
growth have a genetic basis? Or are these characters affected only by different environmental conditions?
Many life-history characters clearly have a genetic basis
(Paterson et al. 1995; Hu et al. 2003; Westerbergh and
Doebley 2004). In addition, life-history characters can
Figure 1.—Parental representatives of M. guttatus populations grown in a common garden greenhouse. Left, M. guttatus from the Oregon Dunes National Recreation Area (DUN);
right, M. guttatus from Iron Mountain, Oregon (IM).
respond plastically to changing environmental conditions, including the allocation to sexual and vegetative reproduction (Ogden 1974; Schmid and Harper
1985; van Kleunen et al. 2001) and timing of flowering
(Alonso-Blanco et al. 1998; Weinig et al. 2002). One of
the questions we address in this study is whether lifehistory divergence between two populations of M. guttatus
has a genetic basis or is completely environmentally
dependent.
We employ a QTL mapping analysis to understand
the genetic basis of divergence in characteristic floral,
vegetative, and life-history traits between these two populations. Specifically, we address whether the individual
traits differentiating the two populations are affected by
many or few QTL and whether these QTL are of large or
small effect. We also use multitrait composite interval
mapping to clarify whether multiple traits are controlled by pleiotropic (or tightly linked) loci or are controlled by separate genetic loci. Finally, our analysis
offers the opportunity to compare the genetic architecture controlling floral trait divergence both within species (our intraspecific study) and between species, on
the basis of a previously published analysis that examines many of the same floral traits in an interspecific
map of M. guttatus and M. nasutus (Fishman et al. 2002).
Floral traits are excellent candidates for investigating
the genetics underlying divergence. Floral characters
show tremendous variation within and between species,
much of which is heritable (Campbell 1996; Galen
1996; Fishman et al. 2002; Hansen et al. 2003). Variation
in floral morphology is often the result of adaptive divergence (Grant and Grant 1965; Kim and Rieseberg
1999; Fishman et al. 2002). Here we compare the number, effects, and locations of QTL controlling floral
traits and infer whether or not there is a shared genetic
Pleiotropic QTL in M. guttatus
1831
TABLE 1
Phenotypic data for 20 traits measured in M. guttatus on parental lines and hybrids in a common garden
Class
Character
IM62
Corolla width
Corolla length
Corolla tube length
Stamen length
Style length
Stigma–anther distance
Stem thickness
Leaf width
Leaf thickness
Internode length
Days to flower
Above-ground mass
Floral meristems
Vegetative meristems
Total no. meristems
Percentage of reproductive
allocation
Viable pollen grains
Nonviable pollen grains
Total pollen grains
Fraction viable pollen
F1 hybrids
F2 hybrids
MPD/ESD
H2
D/E(F2)
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
5.39
7.47
8.72
9.37
10.58
3.79
7.34
2.37
2.61
1.50
3.03
0.40
1.01
0.84
0.48
2.40
0.34
0.48
0.61
0.65
0.59
0.58
0.46
0.13
0.22
0.24
0.081
0.23
0.031
0.23
0.27
0.48
0.047
0.0062
0.013
0.012
0.0041
0.043
0.08
0.041
0.021
0.023
0.044
0.032
0.031
0.066
0.045
0.05
1.65
3.27
3.13
0.42
0.2
0.34
0.14
0.61
0.09
0.1
0.095
0.037
16.47
20.65
11.39
11.78
13.75
1.96
0.82
12.13
0.27
22.40
30.22
0.98
3.68
2.22
5.78
0.63
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
0.23
0.23
0.13
0.12
0.13
0.083
0.020
0.38
0.0066
0.77
0.40
0.065
0.21
0.17
0.26
0.026
24.61
29.69
16.31
16.90
19.08
2.19
1.97
20.54
0.35
16.63
33.24
0.94
3.26
8.80
11.92
0.30
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
0.19
0.17
0.074
0.068
0.076
0.044
0.032
0.39
0.0039
0.67
0.33
0.044
0.12
0.36
0.38
0.012
131.52
93.53
225.05
0.54
6
6
6
6
10.05
6.06
12.33
0.025
403.12
241.28
644.40
0.62
6
6
6
6
13.80 312.25 6 8.63 434.22 6 27.37
8.92 237.27 6 6.14 480.84 6 28.91
16.62 549.52 6 10.02 915.05 6 30.74
0.011
0.54 6 0.010
0.48 6 0.025
22.94
29.17
16.24
16.64
19.16
2.52
2.00
18.60
0.34
15.78
33.56
1.05
3.15
6.08
9.05
0.39
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
DUN
0.13
0.13
0.066
0.064
0.065
0.038
0.024
0.20
0.0025
0.42
0.19
0.027
0.069
0.18
0.19
0.0090
30.56
37.40
20.09
20.21
24.40
4.19
3.93
24.38
0.40
8.96
43.69
1.21
2.03
6.24
8.27
0.25
0.33
0.33
0.17
0.15
0.17
0.097
0.077
0.50
0.0055
0.52
0.59
0.087
0.17
0.31
0.36
0.0017
Floral and vegetative traits are in millimeters. Mass is in grams. Means and standard errors are given for each class. The mean
populational difference (MPD) for each trait was standardized by its environmental standard deviation (ESD). To test for epistatic
breakdown, we estimated the ratio
D/E(F
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi 2), which indicates the relative magnitude of F2 breakdown (see materials and
methods). The ratio of t ¼ D= VarðDÞtests the null hypothesis that D ¼ 0, which is the expectation under a purely additivedominance model of inheritance (Lynch and Walsh 1998). The values of D/E(F2) in italics are those where we rejected D ¼ 0
(P , 0.05).
basis controlling floral traits between and within
species.
MATERIALS AND METHODS
Study system: The M. guttatus species complex (historically
Scrophulariaceae, order Lamiales) is highly polymorphic and
geographically widespread throughout western North America
(Pennell 1951; Vickery 1978; Sweigart and Willis 2003).
Populations differ in morphology, mating system, life-history
strategy, and habitat type. Although widely studied in ecology
and evolutionary biology, taxonomic classification of the M.
guttatus species complex has been inconsistent. Some authors
have subdivided this taxon into 17 morphologically distinct
species (Pennell 1951), while others designate just a few
subspecies within the complex (Hitchcock and Cronquist
1973). M. guttatus (2n ¼ 28) is the most common and variable
species in the complex.
Populations of M. guttatus can exist as either annuals or
perennials, with perennial populations widespread along the
Pacific coast. Perennial plants can also be found inland along
streams, rivers, and drainage ditches, where there is year-round
moisture. Some authors consider the coastal perennial forms,
M. guttatus var. grandis Greene, to be distinct varieties from the
inland perennials, M. guttatus var. guttatus (Hitchcock and
Cronquist 1973). Annual populations are typically located at
inland sites like seepy hillside meadows, rocky cliff faces, or
road cuts that have abundant soil moisture in the spring and
early summer, but little during the late summer. These small
annuals are called M. guttatus var. depauperatus (Gray) Grant by
some authors (Hitchcock and Cronquist 1973). Plants from
these populations are facultative annuals due to seasonally dry
environmental conditions, and they can be maintained indefinitely in standard greenhouse conditions. Flower size and
vegetative traits differ dramatically between annual and perennial populations, with annuals typically being substantially
smaller than perennials for most size-related traits in the field
(M. Hall, unpublished results) and in common garden experiments (Figure 1; Table 1). Annual plants flower earlier
than perennial plants. Annuals also produce more floral than
vegetative meristems compared to perennial plants, which we
refer to as proportion of reproductive allocation.
For this analysis, we focus on two populations of M. guttatus
that have a high degree of divergence in overall size, habitat,
and life history. The well-studied IM population consists of
small-flowered, diminutive annuals that live on Iron Mountain,
in Oregon’s western Cascades (Willis 1993). These plants
are predominantly outcrossing (Willis 1993; Sweigart et al.
1999) and have a short period of growth and reproduction,
with germination occurring in either the fall or spring,
flowering occurring over a 3- to 5-week period in June through
early July. All plants at this site die by mid-July. The montane
environment experiences fluctuations in temperature and
precipitation ranging from below freezing and .6 m of snow
in the winter to well above 40° with little or no rainfall in the
late summer months (Hall 2005). The DUN population
consists of large-flowered perennial plants with larger, nearly
succulent leaves that inhabit the temperate environment of
1832
M. C. Hall, C. J. Basten and J. H. Willis
Oregon’s coastal sand dunes south of Florence in the Oregon
Dunes National Recreation Area. At this site, temperatures
vary ,20° from summer to winter, and there is continual moisture available to plants from heavy rain (up to 2000 mm in the
winter months) and coastal fog (Hall 2005). DUN plants
typically germinate in the fall and flower from early June
through October or November.
Generation of F2 mapping population: We generated an F2
mapping population from IM and DUN parents to investigate
the genetic basis for quantitative trait differences between
these populations of M. guttatus. The IM parent is a highly
fertile inbred line (IM62) derived from the Iron Mountain
site. This parental line is the same parental line used to construct the previous interspecific map (Fishman et al. 2001).
Two separate wild-collected plants (DUN1 and DUN2) were
used as parents from the DUN perennial population. Each of
the DUN parents was reciprocally crossed to IM62 to produce
four sets of F1 individuals, and one plant from each class was
selected at random to produce the F2 generation. One F1 plant
(IM62 maternal parent, DUN1 paternal parent) was reciprocally crossed to another F1 plant (DUN2 maternal parent,
IM62 paternal parent) to produce two sets of F2 seeds. The
other two F1 plants were also reciprocally crossed to each other
to produce two other sets of F2 seeds, for a grand total of four
sets of F2 seeds. Each F2 individual therefore has a nuclear
genome derived from contributions of three individuals
(IM62, DUN1, and DUN2) and a cytoplasmic genome derived
from either the DUN or the IM population. Note that this
crossing design enforces outbreeding with respect to alleles
derived from the DUN population, but allows for homozygosity of alleles from the highly viable and fertile highly inbred
IM62 line, thereby reducing the potential for transmission
ratio distortion in F2 progeny to be caused by inbreeding
depression. All seeds used in the common garden experiment
described below were the same age: the F1 plants and the
parental plants were recreated by selfing IM62 and reciprocally crossing DUN1 and DUN2 at the same time as the
creation of the F2 lines.
In June 2000, we grew 100 IM62 plants, 50 each of the DUN1 3
DUN2 plants and their reciprocal crosses (see above), and
200 F1 plants along with the F2 mapping population (N ¼ 600
total, with each of the four F2 classes equally represented) in
individual pots in a common garden experiment at the University of Oregon Department of Biology greenhouse. Plants
were grown in 4-in. pots filled with sand over a thin layer of
hemlock bark on the bottom, to prevent sand from escaping
the pot. A thin layer of organic potting mix (Black Gold potting soil; Sun Gro Horticulture, Bellevue, WA) was sprinkled
on top to prevent seed dessication. We planted five seeds of the
same class per pot on June 12, 2000, and pots were placed in
flats in a fully randomized design in the greenhouse during
the long days when flowering begins for each of the native
populations. Plants were watered as needed two to three times
daily and left unfertilized. Germination rates were measured
per pot, and seedlings were thinned to the centermost individual after germination, 2 weeks after planting.
Phenotypic analyses: We measured 20 floral, vegetative, and
life-history traits on all plants that flowered, using an engineering ruler with gradations to the nearest 0.01 inch. All
measurements were converted into millimeters. To estimate
overall plant size (vegetative characters), we measured the
length, width, and thickness of the first two leaves on each
plant at the time of its first flower. At this time, we also measured stem thickness at the base of the plant (between the first
true leaves and the cotyledons) and the internode length
between the first and second set of true leaves. Stem and leaf
thickness were measured with digital calipers to the nearest
0.01 mm. If the vegetative traits continued to grow after
flowering, there could be an association of these traits with
flowering time. However, we chose to measure traits for all
plants at a defined developmental stage. We also recorded the
date of flowering for the first two flowers per plant and used
the average of these 2 days, and for each of these flowers we
measured six floral size traits (corolla width, corolla length,
corolla tube length, style length, stamen length, and distance
separating stigma and nearest anther). For a diagram of these
floral traits, see Fishman et al. (2002).
In addition to date of first flowering, we measured a number
of other life-history traits. After 10 weeks from planting, we
counted the total number of floral and vegetative meristems
on each plant. Floral meristems were scored as any stem
bearing flowers or flower buds, and vegetative meristems were
lacking any flowers or flower buds. The percentage of reproductive allocation was estimated for each plant by dividing
the number of floral meristems by the total number of meristems (floral plus vegetative). After 16 weeks, the soil and sand
were washed from the roots of each plant and the plants were
placed in labeled paper bags. Each bag was placed in a drying
oven for 3 days on lowest heat to remove all of the moisture
from the plants. Dried plants were then weighed on an electronic balance to the nearest 0.1 g with their roots (total mass)
and with the roots removed just below the cotyledons (aboveground mass). The soil granules were nearly impossible to
remove from the roots, particularly for the annual plants;
therefore the total mass was not included in the data set.
We measured male fertility by collecting the anthers from
the first two flowers on each plant and placing them in 60 ml of
lactophenol aniline blue stain (Kearns and Inouye 1993). We
counted the number of viable (darkly stained) and inviable
pollen grains in a 0.8-ml subsample of each collection under a
compound microscope. The aniline blue dye stains intact
(starch-filled) cytoplasm, which may also be present in some
inviable grains; therefore our estimates of pollen fertility may
be slightly relaxed. Total number of pollen grains was also
calculated as a summation of viable and inviable pollen grains.
For each plant, we divided the total number of viable pollen
grains by the total number of pollen grains measured to estimate the percentage of viable pollen per flower.
For each trait measured, we calculated the mean and variance for each class (IM parent, DUN parent, F1, and F2) and
for each of the F2 classes separately. The F1 hybrids are mostly
genetically homogeneous, so the phenotypic variance of this
class reflects just environmental variance, whereas the F2 phenotypic variance reflects both environmental variance and the
segregation of alleles at genetic loci differentiating the parental lines. For the environmental variance (VE), we used the
F1 phenotypic variance. We also estimated the average variance
within F1 classes to account for any differences among classes.
These estimates were very similar to, although slightly smaller
than, on average, the VE calculated from the F1 phenotypic
variance; therefore we simply used the latter. The environmental standard deviation (ESD) for each trait was calculated
as the square root of VE. We calculated the genotypic variance
as VG ¼ Var(F2) VE and then estimated the broad-sense heritability for each trait as H 2 ¼ VG/Var(F2). Genotypic correlations were estimated by calculating covE from the F1 class and
for each pair of traits and then estimating covG ¼ cov[F2] covE. Genetic correlations (rG) among traits were calculated
as covG(i, j )/sisj, where covG(i, j ) is the genetic covariance
between traits i and j and si and sj are the square roots of the
genotypic variances of the two traits, respectively. Genetic correlations were not calculated for traits with negative estimates
of H2. Phenotypic correlations were also calculated among
traits for the F2 hybrids.
We performed a simple statistical test for epistasis (Lynch
and Walsh 1998), using analysis of variance (ANOVA) to
Pleiotropic QTL in M. guttatus
calculate the class means and sampling variances for each trait.
These were used to calculate the test statistic,
zðP1 Þ 1 zðP2 Þ zðF1 Þ
1
;
ð1Þ
D ¼ zðF2 Þ 4
2
where z is the trait mean for each class. In thepabsence
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of
epistasis, D is expected to be zero. The ratio jDj= VarðDÞis a
t-test for epistasis or a rejection of a purely additive-dominance
model. In addition, the ratio of D to the F2 mean expected
under the additive-dominance model (E[F2]) is a relative
measure of the severity of hybrid breakdown.
Linkage map construction: In a previous analysis, we constructed a linkage map for this F2 population (N ¼ 539) at 154
AFLP, microsatellite, and gene-based markers (Hall and
Willis 2005). The linkage map spans 1482 cM Kosambi, includes 14 linkage groups (which presumably correspond to
the 14 pairs of chromosomes in M. guttatus), and has an average interval length of 15 cM. We detected transmission ratio
distortion in nearly half of all markers. Our most distorted
marker, LFY, had a normal percentage of DUN homozygotes,
excess numbers of IM homozygotes (216 observed vs. 119
expected), and fewer than expected heterozygotes (143 observed vs. 238 expected). Although the presence of distorted
markers diminished some of our power to detect QTL, distortion was not so severe as to eliminate entire genotypic
classes; therefore we feel that it had a minimal impact in this
study.
Quantitative trait locus analyses: We mapped QTL for 20
single traits using composite interval mapping (CIM; Zeng
1993, 1994) and for subsets of traits using multitrait composite
interval mapping (MCIM; Jiang and Zeng 1995), using QTL
Cartographer v. 1.17 (Basten et al. 2002) and QTL Cartographer Windows 2.0 (Wang et al. 2005). For each trait, the CIM
procedure tested the hypothesis that a test site in an interval
between adjacent markers had a QTL affecting the trait, while
accounting for genetic background by using multiple regression on additional markers as cofactors. The cofactors
included in each CIM model were determined by forward–
backward stepwise regression, with the critical P-values set at
0.05. Tests were performed at 2-cM intervals with a flanking
window size of 10 cM. The likelihood-ratio (LR) test statistic is
2 ln(L0/L1), where L0/L1 is the ratio of the likelihood under
the null hypothesis (there is no QTL at the test site) to the
alternative hypothesis (there is a QTL at the test site). Experimentwise significant levels (a ¼ 0.05) were determined by
permuting the phenotypes against the genotypes 1000 times
for each trait (Churchill and Doerge 1994).
Because many of the traits (particularly the floral and
vegetative characters) were highly correlated and the singletrait CIM analyses identified QTL for multiple traits mapping
to the same interval, MCIM was used to jointly map QTL affecting (a) six floral traits (corolla width, corolla length,
corolla tube length, stamen length, and style length), (b) four
vegetative traits (stem thickness, leaf width, internode length,
and leaf thickness), and (c) six general traits [including representative floral (corolla width, corolla tube length), vegetative
(stem thickness, leaf width), and life-history traits (days to
flower, percentage of reproductive allocation)]. These traits
were chosen on the basis of their relatively high heritabilities
and genetic correlations. The MCIM procedure is similar to
single-trait CIM, but the LR test statistic is 2 ln(L0/La), where
La is the likelihood under the alternative hypothesis that the
test site is a QTL affecting any of the included traits. MCIM
provides additional power and accuracy for mapping QTL by
taking into account the correlational structure of the phenotypic data ( Jiang and Zeng 1995). Experimentwise significance levels (a ¼ 0.05) were determined by permuting the
1833
phenotypes against the genotypes 1000 times so that the correlations between traits were maintained (Churchill and
Doerge 1994).
To determine if QTL detected by MCIM had pleiotropic effects on the traits in each analysis, individual MCIM likelihoodratio test values were examined for each position where joint
mapping indicated the presence of a QTL ( Jiang and Zeng
1995). Pleiotropy was indicated by the rejection of the null
hypothesis of no more than one trait having a LR test value
greater than a significance threshold value of 5.99 (x20:05;2 ) at a
particular QTL position as determined by the model parameters estimated jointly by MCIM. This test does not require
corrections for multiple tests along the genome because
each position is fixed prior to the test, which increases the
power to detect QTL effects on multiple traits ( Jiang and
Zeng 1995).
RESULTS
Phenotypic analyses: Plants from the two M. guttatus
populations grown in a common garden were highly
divergent for many of the traits measured, indicating
that these differences have a genetic basis (Table 1). For
floral characters, the parental lines differed by 4–11
ESDs, and the mean of the DUN plants was greater than
that of the IM line. The parental lines differed by 2–7
ESDs for vegetative traits. The DUN plants were larger
for all vegetative characters, with the exception of internode distance. All of the floral and vegetative traits
appeared to be additive, with the F1 and F2 means nearly
intermediate between the two parental means. Broadsense heritabilities (H2) were small to moderate for the
floral and vegetative characters (0.22–0.65; Table 1).
The variance of the DUN parents was typically larger
than that of either the IM parents or the two hybrid
classes, consistent with the variance scaling with the
mean.
Life-history and male fertility traits showed less difference compared with floral and vegetative traits between
parental lines (0.4–3 ESDs) and had primarily low
heritabilities (0.031–0.61; Table 1). The IM plants
flowered earlier, produced many floral meristems and
few vegetative meristems, had reduced mass, and produced less total pollen on average than the DUN parental lines. The life-history and fertility traits do not
appear to be entirely additive. For example, for flowering date, both F1 and F2 hybrid classes flowered early like
the IM parent, which is consistent with partial dominance toward the IM parent. However, this trait also
deviated significantly from the predictions of an additivedominance model of inheritance (Table 1), suggesting
some level of epistasis controlling flowering time. All
of the meristem traits show partial dominance in the
hybrids toward the parent with more meristems (IM for
floral meristems and DUN for vegetative meristems).
For male fertility traits, the DUN plants made more
pollen grains (both viable and inviable) than the IM
parents (Table 1), although the fraction of viable pollen
1834
M. C. Hall, C. J. Basten and J. H. Willis
produced did not markedly differ between the parents
or the hybrid classes. The F1 hybrids produced more
viable and less inviable pollen than expected under a
strictly additive model, while the F2 hybrids had the
opposite pattern—they made less viable pollen grains,
more inviable pollen grains, and less total pollen than
expected. All of the pollen grain measures (with the
exception of fraction of viable pollen) were inconsistent
with the additive-dominance model (Table 1), which
implies that epistatic interactions are involved in control
of pollen production.
Genetic and phenotypic correlations: All of the floral
size traits, with the exception of stigma–anther separation (SA), were strongly and positively correlated with
each other, both genetically and phenotypically (Table
2). The total number of pollen grains produced (TP)
was also highly positively correlated both genetically and
phenotypically with the floral size traits. The vegetative
traits had weak to moderate positive genetic correlations with each other, although internode length was
negatively correlated with other vegetative traits. Phenotypic correlations between vegetative traits were moderate to high, with the exception of internode length.
Life-history traits were not strongly genetically correlated
with each other, although flowering date and percentage of reproductive allocation had modest negative genetic and phenotypic correlations with each other, and
they represent important indicators differentiating our
annual and perennial populations. Flowering time had
a strong positive genetic correlation with both corolla
width and stem thickness, and floral and vegetative traits
were highly correlated (both genetically and phenotypically) in a positive direction. Due to the nature of the
genetic correlations, we chose to group our traits in three
sets for further investigation of the cause of genetic correlations among multiple traits. First, we grouped six
floral traits; then we grouped four vegetative traits; and
finally we grouped six representative floral, vegetative,
and life-history traits to determine the extent of pleiotropic QTL affecting multiple traits.
Quantitative trait locus analyses: Floral QTL: We
identified 16 putative QTL affecting one or more floral
traits on the basis of the LR statistic profile of the joint
MCIM model (Figure 2A). Twelve LR peaks exceeded
the threshold of 43.52 (estimated by permutations, a ¼
0.05), although we accepted 5 lower peaks that all had
highly significant LR profiles for one or more floral
traits on the basis of the single-trait analysis produced
by CIM and MCIM (data not shown). These peaks are
located on linkage group (LG)4, LG6, LG8, LG11, and
LG12. One significant peak on LG1 did not affect any of
the six floral traits and was therefore not included.
All of the individual floral traits were polygenic (mean
number of detected QTL per trait ¼ 8.7, range ¼ 5–12).
The direction of allelic effects was consistent, in general,
with the phenotypic differences between parents (i.e.,
the larger-flowered DUN carried the ‘‘plus’’ allele). All 7
QTL affecting stamen length were positive, and most
other floral traits had the majority of QTL in the positive
direction with just a few negative QTL (i.e., 8 of 12 QTL
affecting corolla width were positive). Many of the QTL
showed partial dominance of one parental allele, but
there was no overall pattern of directional dominance
(Table 3A). One QTL (QTL10f) appeared to be overdominant and another QTL (QTL11f) appeared to be
underdominant. These results could reflect true overdominance or underdominance, but they could also
result from a low density of markers (particularly codominant markers) in these regions that makes it difficult to detect QTL tightly linked in repulsion.
We used two different methods to estimate the magnitude of effects of individual QTL on each trait. One
biologically relevant measure of QTL size is to scale the
effect of substituting a single QTL by the difference
between populations. Here, we standardized 2a by the
difference in the parental means (Table 3B). Using this
method, the floral QTL we detected had a range of
individual effects from very small (QTL 11f, ,1% of the
parents’ difference in corolla tube length) to large
(Table 3B, QTL 5f, 24% of the populational difference
in stamen length). Each floral trait had at least one QTL
that explained .17% of the species difference, but the
remaining QTL were small. QTL 5f on LG8 had a consistently large effect on multiple traits (Table 3B). We
also estimated the magnitude of QTL effects relative to
the ESD (Table 3B). This method reveals that most QTL
have small effects, although several have larger effects.
In 45 of 52 of the QTL/trait combinations, the substitution of one parental genotype for the other caused a
change in phenotype equivalent ,1 ESD. The remaining 7 QTL caused a change of .1 ESD for individual
traits, most of which is attributed to the effect of QTL 5f,
which affected all six floral traits, four of which had
homozygous affects .1 ESD.
We used Jiang and Zeng’s (1995) test for pleiotropy
to determine which traits each floral QTL affected.
Nearly all of the floral QTL (14 of the 16) identified by
MCIM had significant effects on multiple traits (Table
3). One of the exceptions identified only affected style
length (QTL 12f), and the other affected only total
pollen production (QTL 1f).
Vegetative QTL: We identified seven putative QTL
affecting one or more vegetative traits on the basis of
the LR statistic profile of the joint MCIM model (Figure
2B). Four LR peaks exceeded the threshold of 40.18
(estimated by 1000 permutations), although we also accepted three marginally significant peaks (on LG6, LG7,
and LG11) on the basis of single-trait LR profiles produced by CIM and MCIM (data not shown). As with the
floral traits, the direction of QTL effects on vegetative
traits was consistent with the phenotypic differences
between parents. No overall pattern of directional dominance was obvious, nor was there evidence for overdominance (Table 4A). We detected fewer QTL for
WW
FL
TL
AL
SL
SA
ST
LW
LT
IL
FT
AM
FM
VM
TM
RA
VI
NV
TP
PV
Corolla width (WW)
0.59 0.533 0.567 0.671 0.152 0.487
0.03 0.16 0.628 0.02 0.95
0.1
0.027 0.307 0.32 0.14
Corolla length (FL)
0.75
0.812 0.751 0.816 0.072 0.591
0.203 0.26 0.309 0.014 0.127
0.05 0.26 0.383 0.631 0.06
Corolla tube length
0.632 0.839
0.808 0.802 0.06 0.45
0.221 0.12 0.02 0.013 0.12
0.1
0.331 0.279 0.605 0.02
(TL)
Stamen length (AL)
0.641 0.768 0.812
0.814 0.29 0.565
0.257 0.21 0.146 0.01 0.52
0.22 0.436 0.254 0.689 0.105
Style length (SL)
0.708 0.825 0.818 0.834
0.247 0.569
0.085 0.26 0.299 0.16 0.46
0.07 0.299 0.291 0.583 0.031
Stigma-anther
0.147 0.136 0.048 0.25 0.331
0.03
0.32 0.09 0.26 0.27 0.126
0.264 0.26 0.051 0.22 0.14
distance (SA)
Stem thickness (ST)
0.461 0.506 0.452 0.461 0.466 0.03
0.307 0.27 0.642 0.39 0.17
0.2 0.18 0.429 0.226 0.24
Leaf width (LW)
0.344 0.293 0.266 0.202 0.26 0.111 0.376
Leaf thickness (LT)
0.228 0.269 0.257 0.191 0.21 0.042 0.442 0.545
0.09 0.901 0.37 1.548
0.021 0.007 0.201 0.199 0.14
Internode length (IL)
0.065 0.007 0.036 0.04 0
0.061 0.14 0.455 0.025
0.609 0.3
0.413
0.07 0.24 0.67 0.39 0.341
Days to flower (FT)
0.02 0.01 0.09 0
0.04 0.06 0.34 0.03 0.169 0.32
0.23 1.611
0.32 1.08 0.927 0.23 0.82
Above-ground mass
0.026 0.007 0
0.044 0.01 0.09 0.05 0.04 0.08 0.016 0.02
2.73
0.37 0.22 0.02 0.25 0.07
(AM)
Floral meristems (FM)
0.189 0.218 0.202 0.125 0.181 0.103 0.202 0.343 0.223 0.117 0.28 0.09
0.668 1.12 0.037 1.12 0.45
Vegetative meristems
0.033 0.072 0.097 0.146 0.059 0.15 0.191 0.15 0.041 0.13 0.213 0.002 0.1
(VM)
Total number
0.1
0.149 0.167 0.187 0.123 0.1
0.258 0.02 0.12 0.08 0.106 0.03 0.264 0.933
meristems (TM)
Percent reproductive
0.121 0.101 0.063 0.01 0.088 0.17 0.019 0.294 0.077 0.159 0.32 0.05 0.598 0.69 0.45
0.25 0.047 0.21 0.1
allocation (RA)
Viable pollen grains (VI) 0.138 0.153 0.133 0.265 0.179 0.14 0.039 0.103 0.062 0.031 0.1
0.057 0.07 0.02 0.01 0.033
0.69 0.768 1.259
Nonviable pollen grains 0.241 0.229 0.202 0.202 0.245 0.084 0.276 0.068 0.159 0.12 0.01 0.03 0.177 0
0.062 0.1 0.14
0.138 0.63
(NV)
Total pollen grains (TP) 0.27 0.276 0.241 0.358 0.308 0.07 0.204 0.133 0.152 0.05 0.1
0.03 0.171 0.02 0.046 0.09 0.792 0.493
0.694
Fraction viable pollen
0.07 0.04 0.04 0.08 0.01 0.15 0.15 0.025 0.07 0.103 0.11 0.057 0.07 0.01 0.03 0.04 0.75 0.62 0.276
(PV)
Trait
Genotypic (above diagonal) and phenotypic (below diagonal) correlations in intraspecific F2 hybrids
TABLE 2
Pleiotropic QTL in M. guttatus
1835
1836
M. C. Hall, C. J. Basten and J. H. Willis
Figure 2.—Likelihood-ratio (LR) test statistic
profile from multitrait composite interval mapping of: (A) six floral traits; (B) four vegetative
traits; and (C) six representative floral, vegetative,
and life-history traits in the intraspecific F2 individuals of M. guttatus. The solid line indicates
the LR significance threshold for joint mapping
generated by permutation analyses (a ¼ 0.05, experimentwide). LR thresholds are 43.52, 40.18,
and 55.97 for floral, vegetative, and multipletraits analyses, respectively. All linkage groups are
along the x-axis, with vertical double lines separating them. The positions of mapped markers (D)
are shown along each linkage group. QTL detected were labeled numerically and with a subscript ( f loral, vegetative, or multiple traits) for
each separate analysis (see text for explanation
of individual peaks).
vegetative traits than for floral traits (mean number of
detected QTL per trait ¼ 4.3, range ¼ 3–5; Table 4A).
Our two methods of estimating QTL effect on vegetative traits produced similar results to those of the floral
traits analysis. Using the method where we standardized
the additive effect of a QTL by the difference in parental
means, we detected QTL with a broad range of effects
from very small (QTL 1v, 7.7% of the parental difference
in stem thickness) to very large (Table 4B, QTL 7v,
91.2% of the parental difference in internode length).
This same very large QTL also had a pronounced effect
when we analyzed the difference with respect to the
ESD, with a substitution of one parental genotype for
the other causing a phenotypic change equivalent to 1.4
ESDs. Although the extent of the effect is difficult to
define, in both cases this QTL appears to be sizeable.
Overall, when the additive effect of a QTL is scaled
relative the ESD, we found that 6 of 17 vegetative QTL
had effects .1 ESD, while the remaining QTL had small
effects.
Six of the seven vegetative QTL detected affected
multiple traits using Jiang and Zeng’s (1995) test for
pleiotropy (Table 4). One exception affected only leaf
thickness (QTL 3v).
Pleiotropic QTL in M. guttatus
1837
TABLE 3
QTL for floral traits from LR profile (Figure 2)
WW
QTL
a
Position
a
TL
d
a
d
A. Additive (a) and dominant (d) effects
1f
3, 4, 55
0.53
2f
4, 7, 89
0.80 0.33
3f
6, 1, 0
0.60
0.17
0.22
4f
8, 1, 0
5f
8, 3, 75
1.08
0.51
1.05
6f
8, 9, 155
1.20 0.41
7f
10, 3, 20
0.71 0.34
0.28
8f
11, 1, 14 1.05
1.08
9f
11, 4, 38 0.43
0.71
10f
11, 6, 100 1.11
1.82
11f
12, 1, 10 0.71 2.88 0.00002
12f
12, 8, 158
0.33
13f
13, 1, 10
14f
13, 3, 49
0.51
0.43
15f
13, 5, 169 1.08 0.54
16f
14, 7, 42
0.36 0.84
0.21
WW
QTL
a
Position 2a/diff 2a/ESD
FL
a
d
0.0072
a
0.13
0.44
0.094 0.036
0.21
1.84
0.33
0.31
0.57
1.06
0.60
0.93
0.22
0.62
0.49
1.42
0.76
1.82
3.01
0.57
1.22
0.36
0.51
0.76
0.55
1.03
0.33
0.17
0.10
0.38
FL
SL
d
a
0.36
0.38
0.53
TP
d
a
d
0.50
0.88
0.045
0.45 82.28 126.36
7.98
53.33
0.77
0.18 36.16
33.04
0.46
0.18
0.031
0.24
0.79
0.43
1.01
0.048
1.18
0.34
0.58
0.42
0.44
0.23
0.68
0.18
0.25
0.27
0.26
TL
2a/diff
AL
0.37
0.13
0.095
0.28
AL
6.48
128.04
44.73
48.50
SL
TP
2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD
B. Homozygous effect (2a) of each QTL standardized by the difference
1f
3, 4, 55
0.12
1.06
2f
4, 7, 89
0.11
0.61
3f
6, 1, 0
0.085
0.46
0.051
0.44
0.059 0.44
4f
8, 1, 0
5f
8, 3, 75
0.15
0.82
0.24
2.10
0.22
1.64
6f
8, 9, 155
0.17
0.92
7f
10, 3, 20
0.10
0.54
0.064
0.56
0.068 0.51
8f
11, 1, 14 0.15 0.80
0.13 0.95
9f
11, 4, 38 0.061 0.33
0.072 0.54
10f
11, 6, 100 0.16 0.85
0.11 0.83
11f
12, 1, 10 0.10 0.54 0.000005 0.00004 0.026 0.20
12f
12, 8, 158
0.076
0.66
0.074 0.55
13f
13, 1, 10
14f
13, 3, 49
0.072
0.39
15f
13, 5, 169 0.15
0.82
16f
14, 7, 42
0.051
0.27
0.048
0.42
0.091 0.68
(diff) in the parental means and by the ESD
0.062
0.58
0.071
0.75
0.10
1.05
0.24
0.0085
0.080
0.023
0.094 0.99
0.24
2.29
0.17
1.74
0.10
0.078
0.73
0.040
0.38
0.086
0.91
0.034 0.36 0.019
0.0058 0.061
0.024
0.090
0.22
0.84
0.75
0.072
0.33
0.059
0.0090 0.095
0.11
0.079
0.083
0.043
1.15
0.83
0.87
0.46
0.13
0.41
Position: LG, marker, centimorgans. QTL effects are shown only in the single-trait LR at a QTL located by joint mapping
(MCIM) that exceeded the significance threshold of 5.99. IM homozygous genotypes were scaled to zero and DUN homozygotes
to 2a, so negative values of a indicate that IM carries the minus allele. WW, corolla width; TL, corolla tube length; FL, corolla
length; AL, stamen length; SL, style length; TP, total pollen grains.
a
Each QTL is numbered and labeled with a subscript corresponding to each of the three analyses ( f loral traits analysis).
Multiple-trait QTL: Five QTL were identified that affected one or more of our six representative floral, vegetative, and life-history traits on the basis of the LR statistic
profile of the joint MCIM model (Figure 2C). These five
LR peaks exceeded the permutation threshold of 55.97.
We found that relatively few QTL explained the trait
differences between parents (mean number of detected
QTL per trait ¼ 2.5, range ¼ 2–4). The direction of QTL
effects was generally consistent with the phenotypic
differences between parents (Table 5A), and there was
no pattern of directional dominance. By scaling the
additive effect of a QTL by the difference in parental
means, we detected QTL with a broad range of effects
from very small (QTL 5m, ,1.0% of the parental difference in corolla tube length) to large (Figure 3, Table 5B,
QTL 5m, 36.1% of the parental difference in leaf width).
Most of these individual QTL effects were moderate,
explaining between 10 and 20% of the phenotypic differences between parents. Alternatively, when scaling
each QTL’s individual additive effect by the ESD, 5 of 15
QTL had homozygous effects .1 ESD, which we consider to be moderate to large QTL.
1838
M. C. Hall, C. J. Basten and J. H. Willis
TABLE 4
QTL for vegetative traits from LR profile (Figure 2)
ST
a
QTL
Position
a
IL
d
A. Additive (a) and dominant (d) effects
1v
4, 2, 17
0.12
0.065
2v
4, 5, 58
0.23
0.22
3v
6, 3, 42
4v
7, 1, 0
0.26
0.25
5v
8, 5, 79
0.24
0.059
6v
8, 9, 163
0.32
0.28
7v
11, 5, 86
a
QTL
Position
2a/diff
d
2.98
5.07
1.91
0.85
1.34
2.91
6.11
5.46
ST
a
LW
a
2a/diff
d
0.47
1.60
0.81
0.89
0.90
2.29
1.67
0.23
1.13
0.91
IL
2a/ESD
LT
LW
2a/ESD
2a/diff
a
d
0.011
0.010
0.018
0.014
0.011
0.023
LT
2a/ESD
2a/diff
2a/ESD
B. Homozygous effect (2a) of each QTL standardized by the difference (diff) in the parental means and by the ESD
1v
4, 2, 17
0.077
0.57
0.44
0.66
0.077
0.18
0.16
0.42
2v
4, 5, 58
0.15
1.10
0.76
1.13
3v
6, 3, 42
0.26
0.69
4v
7, 1, 0
0.17
1.24
0.13
0.31
0.21
0.54
5v
8, 5, 79
0.15
1.14
0.20
0.30
0.15
0.34
6v
8, 9, 163
0.21
1.52
0.15
0.35
7v
11, 5, 86
0.91
1.37
0.37
0.89
Position: LG, marker, centimorgans. QTL effects are shown only in the single-trait LR at a QTL located by joint mapping
(MCIM) that exceeded the significance threshold of 5.99. IM homozygous genotypes were scaled to zero and DUN homozygotes
to 2a, so negative values of a indicate that IM carries the minus allele. ST, stem thickness; IL, internode length; LW, leaf width; LT,
leaf thickness.
a
Each QTL is numbered and labeled with a subscript corresponding to each of the three analyses (vegetative traits analysis).
All five QTL affected multiple traits ( Jiang and Zeng
1995, Table 5). This analysis confirmed that two of the
major QTL detected separately in the floral and vegetative traits analyses (both on LG8) affect both floral and
vegetative traits. These two QTL also affect life-history
traits (QTL 3m affects the percentage of reproductive
allocation, QTL 4m affects days to flowering).
DISCUSSION
The two populations of M. guttatus studied in this
common garden experiment differed markedly in many
phenotypic traits associated with life history and morphology, indicating a genetic basis for the divergence.
As expected from observations of the phenotypes in nature, the annual plants from Iron Mountain in Oregon’s
western Cascades (IM) had smaller flowers and vegetative traits, flowered earlier, and produced more floral
meristems relative to vegetative meristems on average
than the perennial plants from the coastal Oregon sand
dunes (DUN). Our investigation of the genetic basis for
floral, vegetative, and life-history divergence revealed substantial numbers of pleiotropic quantitative trait loci
governing complex phenotypic divergence and also indicated that these classes of traits have different genetic
architectures. Overall, all of the traits were controlled by at
least two QTL, and we detected several large-effect QTL.
Number of quantitative trait loci: The divergence in
floral and vegetative traits between populations of M.
guttatus is controlled by many QTL. Despite the large
number of QTL detected, the sum of QTL effects for
each floral and vegetative trait is ,75% of the difference
between parents. The remaining unexplained difference suggests that there are many QTL that were not
detected in our study. If true, then the divergence
involves a much larger number of genes controlling
phenotypic divergence. Alternatively, epistatic interactions among detected QTL may be responsible for the
unexplained difference. Because each QTL may contain multiple linked genes, and methods of estimating
gene number are inherently biased toward underdetection of QTL and overestimation of QTL effect (Beavis
1994; Zeng 1994), the 16 floral QTL and 7 vegetative
QTL detected in this study are minimum estimates of
gene number. In addition, each gene could contain
multiple substitutions that affect different traits.
When we combined a subset of the floral and vegetative traits with two life-history traits in a multitrait
analysis, we detected fewer QTL overall and fewer affecting each trait. This contradicts our previous results
for four of the six traits. For example, we detected only 3
QTL affecting corolla width using multiple-trait analysis, compared to 12 QTL in the floral traits analysis,
where we concluded that this is likely to be a minimum
Pleiotropic QTL in M. guttatus
1839
TABLE 5
QTL for multiple traits from LR profile (Figure 2)
ST
QTL
a
Position
a
LW
d
a
A. Additive (a) and dominant (d) effects
1m
3, 2, 52
2m
3, 5, 59
3m
8, 3, 77
0.26
0.0022 0.84
4m
8, 9, 165
0.30 0.22
5m
11, 6, 106
2.21
ST
QTL
a
Position
WW
d
0.29
0.77
a
1.18
1.38
0.64
LW
TL
d
0.31
0.31
0.94
WW
a
0.52
0.24
1.07
0.016
RA
d
a
FT
d
a
d
0.16
0.93 0.029
0.58
0.045 0.15
0.059 0.039 0.0039
2.04 2.19
0.65
TL
RA
FT
2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD 2a/diff 2a/ESD
B. Homozygous effect (2a) of each QTL standardized by the difference (diff) in the parental means and by the ESD
1m
3, 2, 52
0.12
1.04
0.14 0.42
2m
3, 5, 59
0.055
0.48 0.24
0.56
3m
8, 3, 77
0.17
1.24
0.14 0.32
0.17
0.90
0.25
2.14
0.21 0.49
4m
8, 9, 165
0.19
1.43
0.20
1.05
0.30
0.92
5m
11, 6, 106
0.36
0.85 0.091 0.49 0.0037 0.032
Position: LG, marker, centimorgans. QTL effects are shown only in the single-trait LR at a QTL located by joint mapping
(MCIM) that exceeded the significance threshold of 5.99. IM homozygous genotypes were scaled to zero and DUN homozygotes
to 2a, so negative values of a indicate that IM carries the minus allele. ST, stem thickness; LW, leaf width; WW, corolla width; TL,
corolla tube length; RA, percent reproductive allocation; FT, days to flower.
a
Each QTL is numbered and labeled with a subscript corresponding to each of the three analyses (multiple-traits analysis).
estimate of gene number. In this third multitrait analysis, the lower genetic correlations among traits (particularly the life-history traits) may inhibit our power to
detect QTL of smaller individual effect on certain traits.
While we are certain that floral and vegetative traits are
governed by many loci, the number of QTL controlling
life-history traits is less clear, although our results suggest the number is small.
Our results of mostly polygenic trait divergence
between populations are consistent with other studies
among different accessions of Arabidopsis, where floral,
vegetative, and life-history traits are mostly polygenic,
with 2–15 QTL detected per trait (Mitchell-Olds
1996; Alonso-Blanco et al. 1998; Juenger et al. 2000;
Perez-Perez et al. 2002; Ungerer et al. 2002). Unfortunately, no consistent patterns emerge to explain why
certain traits are more or less polygenic. One possibility
is that different traits may have experienced different
patterns of selection, which could affect the numbers of
QTL responsible for trait divergence. In a review of the
literature where selection differentials were measured,
Kingsolver et al. (2001) found that the strength of directional selection differed between morphological and
life-history traits, where selection was generally stronger
on morphology. We need more studies that investigate
both the genetic basis controlling trait divergence and
the ecological significance of particular traits in the wild
to better understand how different patterns of selection might affect the total number of genes controlling
adaptive trait divergence.
Comparative mapping of floral QTL within and
between Mimulus species: To what extent is the genetic
architecture controlling floral divergence shared within
and between species? Comparative mapping of the same
traits can reveal whether there are shared QTL locations
and numbers within and beween species. In this interpopulational study we measured five of the same
floral traits as those studied in an interspecific QTL
mapping study of M. guttatus and closely related selffertilizing M. nasutus (Fishman et al. 2002). These two
studies have 27 markers in common (Hall and Willis
2005). To understand the extent to which there were
shared QTL affecting floral divergence between and
within species of Mimulus, we made two comparisons.
First, we compared the total number of QTL detected in
each study. We found a total of 16 floral QTL compared to
the 24 detected interspecific floral QTL, lending support
for the hypothesis that QTL number is positively correlated with genetic divergence (Kim and Rieseberg
1999). However, the smaller number of QTL detected
in this study may also be caused by slightly reduced statistical power due to the smaller number of codominant
markers.
Unfortunately, there are very few existing systems
where QTL analyses have examined divergence between
both populations and species, particularly for comparable traits. QTL affecting grain weight were mapped in
both intraspecific (Yu et al. 1997; Xing et al. 2002) and
interspecific crosses (Moncada et al. 2001; Li et al. 2004)
of rice, where more QTL for grain weight were detected
1840
M. C. Hall, C. J. Basten and J. H. Willis
in the intraspecific crosses relative to the number detected between species. However, it is difficult to directly
compare patterns of phenotypic divergence between
any pair of studies (including Mimulus), as they were
not conducted in the same environment. Furthermore,
domesticated and wild systems have experienced very
different evolutionary histories; therefore direct comparisons between the two may be limited. Clearly, we
need more studies that compare the genetic basis for
phenotypic divergence both at the intra- and at the interspecific level to understand whether a pattern exists
between the degree of genetic divergence and QTL
number.
Second, when we compared the locations of floral
QTL between both maps, we found that 10–11 QTL
map to approximately the same locations (Figure 4).
These shared QTL suggest the possibility that some of
the same underlying genes could be responsible for
divergence in floral traits between and within species
of Mimulus. One shared QTL involves QTL 5f and the
interspecific QTL 13, both tightly linked to marker
CYCB on LG8. Interestingly, these floral QTL actually
affect different sets of traits in the two studies. If these
QTL are caused by the same genes, then they seem to
have very different effects on floral traits within vs. between species of Mimulus. Of course, each QTL spans a
fairly broad genomic region that may contain hundreds
of genes, and the colocalization of the QTL may simply
be due to chance. Fine-scale mapping with additional
markers and ultimately, positional cloning, may help
distinguish whether some of these ‘‘shared’’ QTL affecting floral divergence are truly controlled by the same
underlying genes. However, some QTL clearly mapped
to different locations in the two maps, indicating that
floral divergence may be evolutionarily labile with multiple alternative genetic changes involved in different
lineages.
In rice, there is evidence for shared QTL affecting
grain weight in either intra- or interspecific crosses (Yu
et al. 1997; Moncada et al. 2001; Xing et al. 2002; Li et al.
2004). In one interspecific study, fine-scale mapping
demonstrated that one of the potentially shared QTL
regions affecting grain weight in rice contained 14
genes (Li et al. 2004). There are currently no similar
studies in intraspecific rice that determine whether any
of these genes are actually shared between and within
species. Clearly, this is an important avenue for further
research.
Effects of quantitative trait loci: There is much interest in understanding whether adaptive divergence is
due to major or minor genes (Orr and Coyne 1992).
Figure 3.—Additive effect and direction of effect of major
QTL (on LG8, marker 3) on: (A) corolla tube length and
stamen length from the floral traits analysis (QTL 5f), (B)
corolla tube length and stem thickness from the multitrait
analysis (QTL 3m), and (C) corolla tube length and leaf width
from the multitrait analysis (QTL 3m). Parental means for
each trait are plotted with bars indicating standard deviation.
QTL additive effect is positioned at the midparent with the
homozygous effect of substitution indicated for each trait.
Pleiotropic QTL in M. guttatus
1841
Figure 4.—Comparative
map of floral QTL within
and between species of M.
guttatus and close relative
M. nasutus. The linkage
group is indicated above
both intraspecific (g 3 g,
M. guttatus 3 M. guttatus)
and interspecific (g 3 n,
M. guttatus 3 M. nasutus;
Fishman et al. 2001) maps.
Hatch
marks
indicate
marker placement. Only terminal markers and common
markers are labeled on each
map, with thin lines connecting markers in common. For more detailed
description of map comparisons, see Hall and Willis
(2005). LGs with single common markers are matched
up arbitrarily; note that
the orientation could be
rotated. Arrows point to
the location of QTL affecting one or more floral traits.
Numbers alongside arrows
correspond to the QTL
number given (see Table 3
for intraspecific numbers
and Fishman et al. 2002
for interspecific numbers).
Shaded solid bars are putative shared floral QTL between the two maps. Shaded
gradient bars (LG14) are alternative putative shared floral QTL, depending on
orientation of LGs.
However, there is no standard criterion for defining
major vs. minor QTL. Furthermore, QTL effect sizes
can differ dramatically depending on how they are
estimated (Lexer et al. 2005). Tanksley (1993) characterized QTL as potentially major if they explained
.10% of the phenotypic variation in the segregating
population, generally referred to as percentage of variance explained (PVE). This is the most typical measure
used to estimate QTL effect, and it may be particularly
appropriate for lab or agricultural systems. However, a
more useful measure for understanding adaptive divergence in the wild may be to estimate QTL effect in
terms of the difference between parental populations or
relative to the phenotypic variation within populations.
For example, True et al. (1997) uses a fairly stringent
criterion by defining a major QTL as one for which the
distributions of alternative homozygotes for a particular QTL show little overlap, so that the probability of
misclassification of phenotype is ,5%, equivalent to
3.28 environmental standard deviations. For this study,
we have represented QTL effects in terms of both the
mean difference between parents and relative to the
ESD, as we are most interested in whether substitution
of alternative QTL alleles generates visible differences
in phenotype relative to the two parents.
In this intraspecific study, we detected several sizeable
QTL, the largest of which is on LG8. This QTL alone was
responsible for divergence in floral, vegetative, and lifehistory traits. Although this and a few other fairly large
QTL do not change the phenotype .3.28 ESDs, we
1842
M. C. Hall, C. J. Basten and J. H. Willis
argue that these QTL are major, particularly because
they affect multiple traits. This QTL has a very large
LOD score and a sharp peak, indicating that the QTL
interval is fairly small, and it is very tightly linked to a
single codominant marker, CYCB. A 2-LOD support
interval around this QTL spans ,10 cM (LG8: from 68
to 77 cM). Fine-scale mapping of this interval, followed
by positional cloning may enable us to uncover the gene
or genes responsible for divergence of multiple traits at
this locus.
Most traits had at least one QTL that explained .10%
of the species difference or that changed the phenotype
.1 ESD, and the remaining QTL were of small effect.
Overall, this is consistent with evolutionary predictions
(Orr 1998) and with a few other empirical examples
(Juenger et al. 2000; Perez-Perez et al. 2002) of the
distribution of QTL effects, where the evolutionary shift
in divergent characters between populations of Mimulus is likely to involve a major genetic change with most
of the remaining divergence due to many minor allelic
changes.
Pleiotropic QTL: The floral, vegetative, and lifehistory traits measured in this study are governed largely
by pleiotropic QTL. We define a pleiotropic QTL as a
genomic region that affects multiple traits. This region
could contain multiple tightly linked trait-specific genes
or single genes that have multiple substitutions affecting
different traits. Of the 28 total QTL we detected in this
study, all but 3 affected multiple traits, pointing to a
pleiotropic basis for the genetic associations that we
observed (Tables 3–5). Fine-scale mapping with additional markers and larger mapping populations are
needed to distinguish truly pleiotropic loci from tightly
linked loci. Other studies have consistently found
evidence suggesting that individual QTL have pleiotropic effects on multiple floral, vegetative, or life-history
characters (Mitchell-Olds 1996; Juenger et al. 2000;
Ungerer et al. 2002; Cui et al. 2004; Westerbergh and
Doebley 2004), although all of these studies rely on
QTL mapping on individual traits, rather than using our
approach of joint mapping. The joint-mapping approach offers the advantage of allowing us to directly
test whether different traits are affected by a particular
QTL at that position and provides greater power to detect pleiotropy ( Jiang and Zeng 1995). For this reason,
previous studies may have underestimated the degree
of pleiotropy.
For example, using joint QTL mapping, we identified
16 QTL underlying divergence in one or more of the six
floral traits. Nearly all (14) of these QTL had significant
effects on more than one floral trait for a total of 52
significant QTL–trait effects. If we had analyzed each
floral trait in separate single-trait CIM analyses instead
of in a joint-trait analysis, we would have detected 12
total floral QTL. Reliance on single-trait analysis has
several limitations, on the basis of our results. First, it
would have led us to overestimate the total number of
QTL, because most of the 12 single-trait QTL would
have mapped to the same genomic regions. Second, it
has substantially less power to detect pleiotropic QTL
than do joint mapping analyses (in our case a four- to
fivefold difference in total QTL–trait effects); so we
would have also grossly underestimated the total number of QTL–trait effects. For highly correlated traits,
joint trait–QTL analysis provides a more comprehensive
view of the genetic architecture underlying multivariate
phenotypic divergence.
To better understand the role that pleiotropic QTL
can have on our view of trait divergence, we examined
the joint effect of the major QTL on LG8. In the floral
traits analysis, this QTL had a large effect on both
corolla tube length and stamen length. The direction
of change at this QTL was almost perfectly correlated
between traits (Figure 3A), demonstrating that substitution of this QTL alone into one parent can shift the
phenotype roughly one-quarter of the way toward the
alternate parent for both of these floral traits. Evolutionary divergence for either of these two floral traits is
highly constrained. One might also expect overall ‘‘size’’
QTL to affect both floral and vegetative traits. We
therefore examined the joint effect of this QTL on
corolla tube length and stem thickness. These two traits
are also positively correlated, although not as strongly as
the two floral traits, and the QTL had a major effect on
both traits (Figure 3B). On the basis of the effect of this
QTL, flower size and plant size are likely to evolve jointly
and in the same direction in Mimulus, which fits with a
common observation that larger plants tend to produce
larger flowers. Not all of the detected QTL affected
traits in the same direction. We plotted the antagonistic
effect of this major QTL on corolla tube length and leaf
width. Increases in both of these traits are likely to be
adaptive in both environments (Hall 2005), although
the evolutionary response to selection operating on either trait will necessarily be constrained.
The large number of pleiotropic QTL detected in this
study sheds light on our understanding of the genetic
basis for multivariate divergence. If we were to examine
each of these traits separately, we would misestimate the
total number of QTL. Furthermore, any one QTL with
modest individual effects on multiple traits can actually
have a fairly large effect on the overall phenotype.
Therefore a few pleiotropic QTL can play an important
role in phenotypic divergence between populations or
species.
The evolution of life-history strategy: The divergence between the annual and perennial forms studied
here is complex, consisting of differences in multiple
floral, vegetative, and life-history characters. The lifehistory traits we measured were controlled by few QTL,
suggesting that the evolution of differences in timing of
flowering and allocation of floral and vegetative meristems would require only one or two genetic changes.
For both life-history characters we measured, we showed
Pleiotropic QTL in M. guttatus
that the genetic control of these individual traits is not
independent of other morphological traits, which can
have important implications for the potential for evolutionary divergence.
In QTL mapping experiments of other plant species,
life-history variation is governed mainly by multiple
genetic loci. In Arabidopsis thaliana, timing to flowering
is controlled by 5–12 QTL (Mitchell-Olds 1996;
Alonso-Blanco et al. 1998; Ungerer et al. 2002), and
the particular QTL detected can differ when plants are
grown in different environments (Weinig et al. 2002). In
crop plants, traits differentiating annual and perennial
forms are mostly polygenic (Paterson et al. 1995; Hu
et al. 2003; Cui et al. 2004; Westerbergh and Doebley
2004). Without further genetic dissection of genomic
regions in Mimulus and comparisons in different environments, it is difficult to determine if our results are
inconsistent with polygenic inheritence of life-history
traits.
In this study, we have begun to understand the genetic
basis of phenotypic traits associated with life-history
divergence. Future studies aimed at understanding how
alleles at each QTL affect fitness in the wild will be
particularly informative. We have developed recombinant inbred lines between these two divergent populations that have been placed into each of the native
environments. Understanding the role of QTL genotype 3 environmental interactions and the particular
QTL affecting fitness in these two diverse sites will further our understanding of the genetic basis of adaptation
in the wild.
The authors thank M. Rausher, W. Morris, P. Manos, R. Vilgalys,
A. Case, A. Sweigart, A. Cooley, Y.-W. Lee, D. Lowry, S. McDaniel, and
J. Kelly for advice on earlier drafts of this manuscript. We also thank
L. Fishman for advice on QTL mapping and for providing updated M.
guttatus x M. nasutus map data. We give abundant thanks to E. Gilliam
and K. Sullivan for assistance with quantitative measurements and to
A. Bissell for graphical assistance. This material is based upon work
supported by the National Science Foundation under grant nos.
9727578, 0075704, 0328636, and 010577; by Sigma Xi Grants-in-Aid-ofResearch; and by the National Institutes of Health grant no. GM045344.
LITERATURE CITED
Alonso-Blanco, C., S. E. D. El-Assal, G. Coupland and M.
Koornneef, 1998 Analysis of natural allelic variation at flowering time loci in the Landsberg erecta and Cape Verde Islands
ecotypes of Arabidopsis thaliana. Genetics 149: 749–764.
Basten, C. J., B. S. Weir and Z-B. Zeng, 2002 QTL Cartographer:
A Reference Manual and Tutorial for QTL Mapping. Department
of Statistics, North Carolina State University, Raleigh, NC.
Beavis, W. D., 1994 The power and deceit of QTL experiments: lessons from comparative QTL studies. Proceedings of the FortyNinth Annual Corn and Sorghum Industry Research Conference,
American Seed Trade Institution, Washington, DC, pp. 250–266.
Bradshaw, H. D., S. M. Wilbert, K. G. Otto and D. W. Schemske,
1995 Genetic mapping of floral traits associated with reproductive isolation in monkeyflowers (Mimulus). Nature 376: 762–765.
Bradshaw, H. D., K. G. Otto, B. E. Frewen, J. K. McKay and D. W.
Schemske, 1998 Quantitative trait loci affecting differences in
floral morphology between two species of monkeyflower (Mimulus). Genetics 149: 367–382.
1843
Campbell, D. R., 1996 Evolution of floral traits in a hermaphroditic
plant: field measurements of heritabilities and genetic correlations. Evolution 50: 1442–1453.
Churchill, G. A., and R. W. Doerge, 1994 Empirical threshold
values for quantitative trait mapping. Genetics 138: 963–971.
Colosimo, P. F., C. L. Pelchel, K. Nereng, B. K. Blackman, M. D.
Shapiro et al., 2004 The genetic architecture of parellel armor
plate reduction in threespine sticklebacks. PLoS Biol. 2: 635–641.
Coyne, J. A., and R. Lande, 1985 The genetic basis of species differences in plants. Am. Nat. 126: 141–145.
Cui, K., S. Peng, Y. Ying, S. Yu and C. Xu, 2004 Molecular dissection
of the relationships among tiller number, plant height and heading date in rice. Plant Prod. Sci. 7: 309–318.
Dobzhansky, T., 1937 Genetics and The Origin of Species. Columbia
University Press, New York.
Doebley, J., and A. Stec, 1991 Genetic analysis of the morphological differences between maize and teosinte. Genetics 129: 285–
295.
Fisher, R. A., 1930 The Genetical Theory of Natural Selection. Oxford
University Press, Oxford.
Fishman, L., A. Kelly, E. Morgan and J. H. Willis, 2001 A genetic
map in the Mimulus guttatus species complex reveals transmission
ratio distortion due to heterospecific interactions. Genetics 159:
1701–1716.
Fishman, L., A. J. Kelly and J. H. Willis, 2002 Minor quantitative
trait loci underlie floral traits associated with mating system divergence in Mimulus. Evolution 56: 2138–2155.
Galen, C., 1996 Rates of floral evolution: adaptation to bumblebee
pollination in an alpine wildflower, Polemonium viscosum. Evolution
50: 120–125.
Gottlieb, L. D., 1984 Genetics and morphological evolution in
plants. Am. Nat. 123: 681–709.
Gould, S. J., 1980 Is a new and general theory of evolution emerging? Paleobiology 6: 119–130.
Grant, K., and V. Grant, 1965 Flower Pollination in the Phlox Family.
Columbia University Press, New York.
Hall, M. C., 2005 The genetics of adaptation in annual and perennial Mimulus guttatus. Ph.D. Dissertation, Duke University,
Durham, NC.
Hall, M. C., and J. H. Willis, 2005 Transmission ratio distortion in
intraspecific hybrids of Mimulus guttatus: implications for genomic divergence. Genetics 170: 375–386.
Hansen, T. F., C. Pelabon, W. S. Armbruster and M. L. Carlson,
2003 Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability.
J. Evol. Biol. 16: 754–766.
Hitchcock, C. L., and A. Cronquist, 1973 Flora of the Pacific Northwest. University of Washington Press, Seattle.
Hu, F. Y., D. Y. Tao, E. Sacks, B. Y. Fu, P. Xu et al., 2003 Convergent
evolution of perenniality in rice and sorghum. Proc. Natl. Acad.
Sci. USA 100: 4050–4054.
Huxley, J., 1942 Evolution, the Modern Synthesis. George Allen &
Unwin, London.
Jiang, C., and Z-B. Zeng, 1995 Multiple trait analysis of genetic
mapping for quantitative trait loci. Genetics 140: 1111–1127.
Jiang, C., G. O. Edmeades, I. Armstead, H. R. Lafitte, M. D.
Hayward et al., 1999 Genetic analysis of adaptation differences
between highland and lowland tropical maize using molecular
markers. Theor. Appl. Genet. 99: 1106–1119.
Juenger, T., M. Purugganan and T. F. C. Mackay, 2000 Quantitative trait loci for floral morphology in Arabidopsis thaliana.
Genetics 156: 1379–1392.
Kearns, C. A., and D. W. Inouye, 1993 Techniques for Pollination
Biologists. University of Colorado Press, Niwot, CO.
Kim, S. Y., and L. H. Rieseberg, 1999 Genetic architecture of species
differences in annual sunflowers: implications for adaptive trait
introgression. Genetics 153: 965–977.
Kingsolver, J. G., H. E. Hoekstra, J. M. Hoekstra, D. Berrigan,
S. N. Vignieri et al., 2001 The strength of phenotypic selection
in natural populations. Am. Nat. 157: 245–261.
Knight, C. G., R. B. R. Azevedo and A. M. Leroi, 2001 Testing lifehistory pleiotropy in Caenorhabditis elegans. Evolution 55: 1795–
1804.
Lande, R., 1979 Quantitative genetic analyses of multivariate evolution, applied to brain: body size allometry. Evolution 33: 402–416.
1844
M. C. Hall, C. J. Basten and J. H. Willis
Laurie, C. C., J. R. True, J. Liu and J. M. Mercer, 1997 An introgression analysis of quantitative trait loci that contribute to
a morphological difference between Drosophila simulans and
D. mauritiana. Genetics 145: 339–348.
Lexer, C., D. M. Rosenthal, O. Raymond, L. A. Donovan and L. H.
Rieseberg, 2005 Genetics of species differences in the wild
annual sunflowers, Helianthus annuas and Helianthus petiolaris.
Genetics 169: 2225–2239.
Li, J., M. Thomson and S. R. McCouch, 2004 Fine mapping of
a grain-weight quantitative trait locus in the pericentromeric
region of rice chromosome 3. Genetics 168: 2187–2195.
Liu, J., J. M. Mercer, L. F. Stam, G. C. Gibson, Z-B. Zeng et al.,
1996 Genetic analysis of morphological shape difference in
the male genitalia of Drosophila simulans and D. mauritiana.
Genetics 142: 1129–1145.
Lynch, M., and B. Walsh, 1998 Genetic Analysis of Quantitative Traits.
Sinauer Associates, Chicago.
Mitchell-Olds, T., 1996 Pleiotropy causes long-term genetic constraints on life-history evolution in Brassica rapa. Evolution 50:
1849–1858.
Moncada, P., C. P. Marinez, J. Borrero, M. Chatel, H. Gauch, Jr.
et al., 2001 Quantitative trait loci for yield and yield components in an Oryza sativa x Oryza rufipogon BC2F2 population
evaluated in an upland environment. Theor. Appl. Genet. 102:
41–52.
Muller, H. J., 1949 The Darwinian and modern conceptions of
natural selection. Proc. Am. Philos. Soc. 93: 459–470.
Ogden, J., 1974 The reproductive strategy of higher plants: II. The
reproductive strategy of Tussilago farfara. J. Ecol. 62: 291–324.
Orr, H. A., 1998 The population genetics of adaptation: the distribution of factors fixed during adaptive evolution. Evolution 52:
935–949.
Orr, H. A., 2000 Adaptation and the cost of complexity. Evolution
54: 13–20.
Orr, H. A., and J. A. Coyne, 1992 The genetics of adaptation: a
reassessment. Am. Nat. 140: 725–742.
Paterson, A. H., K. F. Schertz, Y.-R. Lin, S.-C. Liu and Y.-L. Chang,
1995 The weediness of wild plants: molecular analysis of genes
influencing dispersal and persistence of johnsongrass, Sorghum
halepense (L.). Proc. Natl. Acad. Sci. USA 92: 6127–6131.
Pennell, F. W., 1951 Mimulus, pp. 688–731 in Illustrated Flora of the
Pacific States, edited by L. Abrams. Stanford University Press, Palo
Alto, CA.
Perez-Perez, J. M., J. Serrano-Cartagena and J. L. Micol,
2002 Genetic analysis of natural variations in the architecture of Arabidopsis thaliana vegetative leaves. Genetics 162: 893–
915.
Schmid, B., and L. J. Harper, 1985 Clonal growth in grassland perennials. II. Growth form and fine-scale colonization ability.
J. Ecol. 73: 809–818.
Stebbins, G. L., 1974 Flowering Plants: Evolution Above the Species
Level. Harvard University Press, Cambridge, MA.
Sucena, E., and D. L. Stern, 2000 Divergence of larval morphology
between Drosophila sechellia and its sibling species caused by
cis-regulatory evolution of ovo/shaven-baby. Proc. Natl. Acad.
Sci. USA 97: 4530–4534.
Sweigart, A. L., and J. H. Willis, 2003 Patterns of nucleotide
diversity in two species of Mimulus are affected by mating system
and asymmetric introgression. Evolution 57: 2490–2506.
Sweigart, A. L., K. Karoly, A. Jones and J. H. Willis, 1999 The
distribution of individual inbreeding coefficients and pairwise
relatedness in a population of Mimulus guttatus. Heredity 83:
625–632.
Tanksley, S. D., 1993 Mapping polygenes. Annu. Rev. Genet. 27:
205–233.
True, J. R., J. Liu, L. F. Stam, Z-B. Zeng and C. C. Laurie,
1997 Quantitative genetic analysis of divergence in male secondary sexual traits between Drosophila simulans and Drosophila
mauritiana. Evolution 51: 816–832.
Turner, J. R. G., 1985 Fisher’s evolutionary faith and the challenge
of mimicry. Oxf. Surv. Evol. Biol. 2: 159–196.
Ungerer, M. C., S. S. Halldorsdottir, J. L. Modliszewski, T. F. C.
Mackay and M. D. Purugganan, 2002 Quantitative trait loci
for inflorescence development in Arabidopsis thaliana. Genetics
160: 1133–1151.
Van Kleunen, M., M. Fischer and B. Schmid, 2001 Effects of intraspecific competition on size variation and reproductive allocation in a clonal plant. Oikos 94: 515–524.
Vickery, R. K., 1978 Case studies in the evolution of species complexes in Mimulus. Evol. Biol. 11: 405–507.
Wang, S., C. J. Basten and Z-B. Zeng, 2005 Windows QTL Cartographer 2.0. Department of Statistics, North Carolina State University, Raleigh, NC.
Weinig, C., M. C. Ungerer, L. A. Dorn, N. C. Kane, Y. Toyonaga
et al., 2002 Novel loci control variation in reproductive timing
in Arabidopsis thaliana in natural environments. Genetics 162:
1875–1884.
Westerbergh, A., and J. Doebley, 2002 Morphological traits defining species differences in wild relatives of maize are controlled by
multiple quantitative trait loci. Evolution 56: 273–283.
Westerbergh, A., and J. Doebley, 2004 Quantitative trait loci controlling phenotypes related to the perennial versus annual habit
in wild relatives of maize. Theor. Appl. Genet. 109: 1544–1553.
Willis, J. H., 1993 Effects of different levels of inbreeding on fitness
components in Mimulus guttatus. Evolution 47: 864–876.
Xing, Y. Z., Y. F. Tan, J. P. Hua, X. L. Sun, C. G. Xu et al.,
2002 Characterization of the main effects, epistatic effects
and their environmental interactions of QTLs on the genetic
basis of yield traits in rice. Theor. Appl. Genet. 105: 248–257.
Yu, S. B., J. X. Li, C. G. Xu, Y. F. Tan, Y. J. Gao et al., 1997 Importance
of epistasis as the genetic basis of heterosis in an elite rice hybrid.
Proc. Nat. Acad. Sci. USA 94: 9226–9231.
Zeng, Z-B., 1993 Theoretical basis of separation of multiple linked
gene effects on mapping quantitative trait loci. Proc. Natl. Acad.
Sci. USA 90: 10972–10976.
Zeng, Z-B., 1994 Precision mapping of quantitative trait loci. Genetics
136: 1457–1468.
Zeng, Z-B., J. Liu, L. F. Stam, C.-H. Kao, J. M. Mercer et al.,
2000 Genetic architecture of a morphological shape difference
between two Drosophila species. Genetics 154: 299–310.
Communicating editor: S. W. Schaeffer