Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse.

Abstract

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.

Full text

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Copyright ? 2005 by the Genetics Society of America
DOI: 10.1534/genetics.105.046078
Epistasis for Fitness-Related Quantitative Traits in Arabidopsis thaliana
Grown in the Field and in the Greenhouse
Russell L. Malmberg,*,1Stephanie Held,†Ashleigh Waits†and Rodney Mauricio†
*Department of Plant Biology and†Department of Genetics, University of Georgia, Athens, Georgia 30602
Manuscript received May 24, 2005
Accepted for publication August 29, 2005
ABSTRACT
The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a
long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of
Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of
fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus
epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit
number, wefound seven significant epistatic interactions, but onlytwo additive QTL.For seed germination,
length,andwidth,therewerefromtwotofouradditiveQTLandfromfivetoeightepistaticinteractions.The
epistaticinteractionswerebothpositiveandnegative.Ineachcase,themagnitudeoftheepistaticeffectswas
roughly double that of the effects of the additive QTL, varying from ?41% to 129% for fruit number and
from ?5% to 14% for seed germination, length, and width. A number of the QTL that we describe
participateinmorethanoneepistaticinteraction,andsomelociidentifiedasadditivealsomayparticipatein
an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic
effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and
seed length from plants grown in both the field and the greenhouse. While the total number of significant
additive and epistatic QTL was similar under the two growth conditions, the map locations were largely
different. We found a small number of significant epistatic QTL 3 environment effects when we tested
directly for them. Our results support the idea that epistatic interactions are an important part of natural
geneticvariationandreinforcetheneedforcautionincomparingresultsfromgreenhouse-grownandfield-
grown plants.
T
genetics (Avery and Wasserman1992; Phillips 1998).
Each of the different uses of epistasis has the sense of a
phenotypedependentuponinteractionsbetweenalleles
at different loci. In population, evolutionary, or quan-
titative genetics, epistasis is broadly defined as non-
additive interactions between alleles at different genes.
How much does epistasis for fitness contribute to
local adaptation, population differentiation, and speci-
ation? This question dates back more than 75 years to
the differing views of Fisher and Wright, summarized
in Fisher (1958) and Wright (1984), on the genetic
basis of evolutionary change. Wright viewed epistatic
interactions as an essential component of moving from
oneadaptivepeaktoanother.Ontheotherhand,Fisher
emphasized the additive effects of genes, summarized
in his Fundamental Theorem of Natural Selection as a
population’s response to natural selection being pro-
portional to the additive genetic variance of fitness in
the population (Fisher 1958).
HE term ‘‘epistasis’’ has a number of different, yet
related, meanings in the various subdisciplines of
One way to view the question of the importance of
epistasisisfromtheperspectiveofanewmutantallele.If
epistasis is prevalent, then a new mutant allele will in-
teract with many other loci and alleles in the genetic
background, and its fitness may be based not only upon
its direct effects on the phenotype, but also upon its
effects through the interactions. If additivity among loci
is prevalent, then the fitness of a new mutant allele will
depend more upon its direct effects on the phenotype.
With epistatic interactions, the effect of a gene on a
phenotype isa collectiveproperty of anetwork of genes,
rather than a property of a gene itself (Wade 2002). We
need to know the extent and nature of epistatic inter-
actions to understand the genetic architecture of any
quantitative trait, including fitness.
Recently, there has been a resurgence of interest in
the role of epistasis in evolutionary biology as new
theoretical and experimental approaches have been
developed (Coyne et al. 2000; Goodnight and Wade
2000; Whitlock and Phillips 2000; Wolf et al. 2000).
One example of this is in metapopulation biology. The
existenceofepistasiswithinsmall demespermitsamore
rapid response of the demes to selection than would be
expected solely on the basis of the additive variation
present (Whitlock et al. 1993; Wade and Goodnight
1Correspondingauthor:DepartmentofPlantBiology,2502PlantSciences
Bldg., University of Georgia, Athens, GA 30602-7271.
E-mail: russell@plantbio.uga.edu
Genetics 171: 2013–2027 (December 2005)

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1998; Goodnight 2000); group selection permits
changesthatexploit the epistaticvarianceaswell.There
has also been extensive investigation of the theoretical
basis for the conversion of epistatic variance to additive
variance after a population bottleneck (Goodnight
1995; Cheverud and Routman 1996; Cheverud et al.
1999; Lopez-Fanjul et al. 2000, 2004; Barton and
Turelli 2004). A second example is the continuing
interest in understanding the evolution of recombina-
tion. The extent of epistatic interactions and their evo-
lution are deeply intertwined with our understanding
and theories of the evolution of sex and genetic recom-
bination(Malmberg1977;Barton1995;Kondrashov
and Kondrashov 2001; Otto and Lenormand 2002;
Michalakis and Roze 2004).
Inadditiontoestimatingthetotalamountofepistasis,
we need to understand the variation in epistatic inter-
actions among loci within a genome (Phillips et al.
2000). If epistatic interactions are both synergistic and
antagonistic (greater or less than that expected from
consideration of the effects of the alleles considered
independently), then an experimental measurement
or theoretical treatment of the average level of epis-
tasis underestimates the amount that is really present
(Phillipsetal. 2000).InrecentstudieswithRNAviruses,
Bonhoeffer et al. (2004) found positive (synergistic)
epistasis,whileSanjua ´netal.(2004)foundbothnegative
(antagonistic) and positive epistasis. Thus, we need
experimental measurements of epistasis, and a mecha-
nisticcharacterizationofitsnature,toaddressavarietyof
problems in population and evolutionary genetics.
There are several contemporary experimental ap-
proaches to measuring epistatic effects in an evolution-
ary genetics context. One is to use specific mutations as
a starting point and then measure fitness effects with
combinations of other mutations or genetic back-
grounds. Elena and Lenski (1997) with Escherichia coli
and deVisser et al. (1997) with Aspergillus niger have
provided examples, obtaining evidence for both posi-
tive and negative epistatic interactions. Several groups
have used mutations to study epistasis for viral fit-
ness (Bonhoeffer et al. 2004; Froissart et al. 2004;
Michalakis and Roze 2004; Sanjua ´n et al. 2004).
Bonhoeffer et al. (2004) reported evidence for positive
epistasis in human immunodeficiency virus I, while
Sanjua ´n et al. (2004) found both positive and negative
epistasis in vesicular stomatitis virus, especially noting
the synthetic lethals and the significance of the antag-
onistic epistasis for which they provided evidence. In
Arabidopsis thaliana, epistatic interactions for flowering
time have been uncovered beginning with a single locus
and examining the effects of different genetic back-
grounds: the FRI locus upregulates FLC transcription
(Koornneef et al. 1994; Michaels and Amasino 1999;
Schlappi 2001; Caicedo et al. 2004).
A second approach, which we have used, is to follow
a form of QTL mapping (Weller 1986; Paterson et al.
1988; Jansen and Stam 1994; Lander and Botstein
1994;Zeng1994)tofindepistaticinteractions.Inpartic-
ular, one can identify two-way epistatic interactions by
performingacompletepairwiseanalysisofallthemolec-
ular markers. Standard QTL software packages, such as
QTL Cartographer (Basten et al. 2004), estimate epi-
static interactions among already identified additive
QTL,butwillnotcurrentlyperformacompletepairwise
analysisofmapsegmentswithoutregardtoalreadyiden-
tified additive loci. Four computer programs that do
facilitate all pairwise map segment scanning have been
developed:Epistat(Chaseetal.1997),Epistacy(Holland
1998), Pseudomarker (Sen and Churchill 2001), and
BQTL(Borevitzetal.2002).Thereareseveralexamples
of this epistatic QTL approach. Shook and Johnson
(1999) performed QTL analyses of fitness-related life-
history traits in Caenorhabditis elegans recombinant in-
bred lines; they found seven significant epistatic effects.
Similarly,RoutmanandCheverud(1997)andCheverud
(2000) used an all pairwise comparison approach to
identify .100 candidates for epistatic interactions in
mouse body weight, and Peripato et al. (2004) studied
the genetic basis for mouse litter size, finding two addi-
tiveQTLandeightepistaticQTL.WithA.thaliana,Juenger
et al. (2005) found two epistatic QTL for flowering time
in recombinant inbred lines generated from a cross of
the Landsberg and Cape Verde accessions.
In this article, we report an epistatic QTL study of
natural variation of A. thaliana, grown under field con-
ditions, that measured the fitness-related traits of fruit
number, seed size, and germination rate. Our study dif-
fers from other Arabidopsis QTL studies by our analysis
of fitness under field conditions combined with using
the all pairwise map segment comparison method to
uncover epistasis. We find more epistatic interactions
than additive QTL and also larger effects for the epi-
staticinteractionsthanfortheadditiveloci.Ouranalysis
indicatesthat thereisanetworkofadditiveand epistatic
effects underlying these traits. We also compare the
additive and epistatic genetic architecture underlying
seed size and germination in field-grown and green-
house-grownplants.Wefindthegeneticarchitecturefor
greenhouse-grown and field-grown traits to be largely
different. Our experimental approach of measuring
natural variation for fitness as a QTL under field con-
ditions should make the results directly applicable to
understanding the role of epistasis in population and
evolutionary genetics.
MATERIALS AND METHODS
Plant material and growth conditions: All seeds were
obtained from the Arabidopsis Biological Resource Center
(ABRC; Columbus, OH). We used a mapping population of
100 RI lines (ABRC stock no. CS1899) that had been
generated from a cross between the Columbia (ABRC stock
no.CS-933) andtheLandsbergerecta (ABRCstock no.CS-20)
2014R. L. Malmberg et al.

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accessions of A. thaliana (L.) Heynh. Progeny from the initial
cross were taken through eight generations of selfing via
single-seed descent to produce nearly homozygous lines with
an estimated heterozygosity of 0.42% (Lister and Dean 1993;
Juenger et al. 2000). We constructed a linkage map using a
total of 228 markers (chromosome 1, 54 markers; chromo-
some 2, 33 markers; chromosome 3, 37 markers; chromosome
4, 50 markers; and chromosome 5, 54 markers). The map
position of each marker was estimated from the observed
recombination frequencies using the Kosambi mapping func-
tion as implemented by the software MapMaker 3.0 (Lander
et al. 1987). This analysis provided unique positions for each
marker and a map spanning 592 cM of the A. thaliana genome
(99% of the 597-cM estimated size of the A. thaliana genome
based on both the Arabidopsis Genome Initiative sequence
map and the Lister and Dean RI genetic map; http:/ /www.
Arabidopsis.org/servlets/mapper). The mean intermarker dis-
tance was 2.8 cM. Our map did not differ in marker order from
the published linkage map of A. thaliana.
Plantsusedinthegreenhouseexperimentweregrownfrom
seed sowed singly in an ?150-cm3plastic pot filled with a
soilless mix of peat moss, perlite, pine bark, and vermiculite
(Fafard no. 3B, Agawam, MA). All replicates of each RI line
wererandomlyassignedtoanindividualpotinaflat.Theseeds
were cold stratified at 4? for 3 days and then transferred to a
singlegrowthchamberwithcontrolforbothdaylength(14hr)
and temperature (18?). Five replicate plants were grown for
each of the RI lines and seeds were collected from each plant.
For each line, we pooled seeds from all replicates and ran-
domly selected 25 seeds from each line for analysis.
In October 2002, we planted seeds of each line into plastic
trays filled with Fafard no. 3B soilless mix. The seeds were
cold stratified at 4? for 3 days and then transferred to a single
growth chamber with control for both day length (10 hr) and
temperature (15?) until a week before transplanting when
they were moved outdoors to harden. In November 2002, we
transplanted 2448 young plants (at the four true-leaf stage)
to a field at the University of Georgia’s Plant Sciences Farm
in Oconee County, Georgia, where natural populations of
A. thaliana occur. Plants growing naturally in that field were at
the same phenological stage as the transplants. The field was
plowed just before planting, but natural vegetation was
allowed to regrow during the experiment. Therefore, the
experimental plants experienced levels of competition similar
to those of naturally growing plants. We planted 24 replicates
of each of the 100 RI lines and the two parental genotypes
from which the lines were derived. The plants grew, flowered,
and set fruit at a phenological schedule similar to that of the
natural populations. After all plants had senesced, we col-
lected and counted all the fruits from each replicate. Of the
2448 individuals planted in the field, 1942 survived through
the entire season to produce fruit, representing 79% survival.
Three lines failed to reproduce entirely (ABRC stock nos.
CS1900, CS1982, and CS1999) and were included in the
analysis as producing no fruits. The mean replicate number
within each line was 20 (median value was 21 and mode was
22). The replicates ranged from 3 lines with only 1 replicate
(CS1948, CS1949, and CS1978) to 4 lines in which all 24 repli-
cates reproduced. We examined 25 seeds per replicate (a total
of 48,550 seeds) for seed size measurements and 50 seeds per
replicate (a total of 197,100 seeds) for estimates of germi-
nation rate.
Seeds were placed under a dissecting scope andseed length
and width were measured with a video imaging system
(Optimas Image Analysis Software for Windows, version 6.51,
Media Cybernetics, San Diego). Mean seed length and width
were calculated for each line. Seeds used for the germination
assay were sterilized by exposing dry seeds to ultraviolet light
(254 nm) for 2 hr. Seeds from each line were divided ran-
domly into 10 sets of five seeds and each set was randomly
placed in an individual plate (10 replicate plates) containing
an agar medium (0.8% agar with 1% sucrose, B5 vitamins, and
Murashige and Skoog salts). This design confounds plate with
replicate (the set of five seeds in each plate represents a true
replicate but the five seeds within each plate are pseudorepli-
cates), but wefelt that thenumber of replicate plates provided
a sufficiently large set of independent data. Seed sets from
multiple lines were placed in the same plate to reduce the
number of plates used. Plates were positioned horizontally at
15?for12-hrdays.Foreachseed,weobservedhowmanyhours
elapsed before a radicle emerged. Plates were checked every
6 hr until 100% of seeds had germinated. We report the least
squares mean number of hours for each line (after removing
the effect of plate in an analysis of variance).
Additive QTL analysis: Composite interval mapping was
performed using QTL Cartographer (version 1.17, released
January 28, 2005, and WinQTLCart version 2.5, released
February 15, 2005) (Basten et al. 1994, 2004; Wang et al.
2004). The settings used were a walk speed of 1 cM, model 6
standard, regression method 3 forward and backward, and
probabilities of 0.05. Significance levels were set via the pro-
gram’s permutations function using 2000 permutation times
(Churchill and Doerge 1994; Doerge and Churchill
1996). Joint-trait mapping with QTL Cartographer’s JZmapqtl
program was performed to test for genotype 3 environment
interactions for the traits that were grown in both the field
and the greenhouse. Multiple interval mapping with QTL
Cartographer’s MImapqtl program was performed to test for
epistaticinteractionsamongtheidentifiedadditiveQTLusing
the five-phase analyses described in the QTL Cartographer
manual.
Epistatic QTL analysis: We used the programs Epistat
(Chase etal. 1997) (http:/ /64.226.94.9/epistat.htm) and Epis-
tacy (Holland 1998) (http:/ /www4.ncsu.edu/?jholland/
Epistacy/Epistacy.htm) to analyze the quantitative trait data.
For Epistat, we used an automated search for all-pairwise
interactions, with an initial likelihood-ratio cutoff of 4, a value
less stringent than the cutoff of 6 suggested by the authors.
Subsequently we used the Montecarlo simulation program
associated with Epistat to analyze 1,000,000 resampled sub-
groups, as a means of estimating P-values. We ran Epistasy in
the SAS environment (SAS Institute 2001) with a P-value
filter of 0.01, a value higher than is statistically significant. We
removed all interactions in the Epistat and Epistacy outputs
where the two interacting markers were within 50 cM of each
other to avoid linkage effects. The output of both the Epistat
and the Epistacy program was sorted by P-values to find the
values that were significant; these values, and also P-values in
the genetic map neighborhood of the significant values, are
plotted in Figures 2 and 4. Both Epistat and Epistacy provide
estimates of the genotypic values. Epistacy reports this directly
in the output. Epistat reports the values as normalized values
(i.e., mean of 0 and standard deviations of 1; K. Chase,
personal communication); we transformed back to the orig-
inal values by multiplying by the standard deviation and
adding the mean. The estimated genotypic values provided
by both programs were similar.
We modified the Epistacy SAS script to test for epistasis 3
environment effects comparing quantitative traits from plants
growninthefieldand inthegreenhouse. The quantitative trait
was input as values for a single variable, with an associated
variable to indicate the growth environment. The environment
was then specified as a class and added to the ‘‘Proc GLM’’
routine at the core of Epistacy (class &&gnmk&i &&gnmk&j
envirn;model&trait¼&&gnmk&ij&&gnmk&jjenvirn;lsmeans
&&gnmk&i*&&gnmk&j&&gnmk&i*&&gnmk&j*envirn;).
Epistasis for Fitness in Arabidopsis2015

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RESULTS
Our goal was to determine the genetic basis for
quantitativetraitsrelatedtofitness,focusingonepistatic
interactions, in addition to individual locus additive ef-
fects,inplantsgrownundernaturalfieldconditions.We
compared fruit number, germination rate, and seed size
differences in a standard set of Landsberg 3 Columbia
recombinantinbredlinesofA.thaliana(ListerandDean
1993) grown over winter and early spring in a field in
Georgia.Theuseofthesewell-characterizedlinesallowed
ustomap simple quantitativetrait loci and epistatic inter-
actions between pairs of loci for these traits. The genetic
variation reflectsthe differences betweenthesetwoacces-
sions seen under field conditions. At the same time we
were able to compare the genetic variation for germina-
tion and seed size in the same set of recombinant inbred
lines grown in the greenhouse as well as in the field, thus
testing for correlations in the genetic basis of the same
traits under these two different growth conditions.
Additive QTL analysis: We used QTL Cartographer
(Basten et al. 1994, 2004; Wang et al. 2004) to perform
composite interval mapping to identify additive QTL.
Loci that were significant by permutation analysis are
reported in Table 1.We also list additive loci that were
nearly significant and that mapped close to a locus in-
volved in a significant epistatic interaction, as reported
below. In field-grown plants, there are two additive loci
identified for fruit number, two for germination, four
for seed length, and two for seed width. In greenhouse-
grown plants there is one additive locus for germina-
tion, two for seed length, and one for seed width. One
QTL for seed length in field-grown plants corresponds
toaQTLforseedlengthingreenhouse-grownplants, as
judged by map position; all the other loci vary between
field- and greenhouse-grown plants; these results are
graphed in Figure 1. The absolute values of the additive
effects for the fruit number QTL are in the range of
11–13%andaresmaller fortheothertraits,intherange
0.8–3.2%. We indicate correspondences that exist be-
tween these additive QTL and the epistatic interactions,
discussed below, in the last column of Table 1.
Epistatic QTL analysis: Weusedtheprograms Epistat
(Chase et al. 1997) and Epistacy (Holland 1998) to
analyze the quantitative trait data. Both programs can
TABLE 1
Additive QTL
Trait Growth site
QTL
no.
Chromosome
no.
Position
(cM)
LOD
score Significant?
% additive
effect
Partial
R2
Maps close to
epistatic QTL?
Fruit number
Fruit number
Fruit number
Field
Field
Field
1
2
3
1
2
5
91.6
70.4
85.0
2.60
3.69
2.99
No
Yes
Yes
?11.1
13.0
?11.5
0.09
0.14
0.10
Table 2, group 1
Table 2, group 6
Germination
Germination
Germination
Field
Field
Field
1
2
3
3
4
4
72.6
61.4
96.4
2.25
11.79
4.74
No
Yes
Yes
1.0
2.6
0.05
0.34
0.14
Table 2, group 2
Table 2, group 5
Table 2, group 4
?1.6
Seed length
Seed length
Seed length
Seed length
Seed length
Seed length
Field
Field
Field
Field
Field
Field
1
2
3
4
5
6
1
1
2
3
3
5
40.1
91.6
43.3
19.2
39.5
104.3
5.33
6.68
3.12
2.31
3.72
2.44
Yes
Yes
Yes
No
Yes
No
1.4 0.14
0.18
0.08
0.06
0.08
0.06
?1.7
?1.1
0.9
?1.2
0.9
Table 2, group 5
Table 2, group 1
Table 2, group 3
Table 2, group 4
Table 2, group 5
Seed width
Seed width
Seed width
Field
Field
Field
1
2
3
3
3
5
11.4
41.5
119.3
6.83
2.72
5.64
Yes
No
Yes
?1.3
?0.8
1.1
0.16
0.06
0.15
Table 2, group 3
Table 2, group 4
Table 2, group 5
Germination
Germination
Germination
Greenhouse
Greenhouse
Greenhouse
1
2
3
1
2
5
132.5
25.8
109.2
2.37
2.49
3.10
No
No
Yes
?2.8
?3.0
3.2
0.09
0.09
0.10
Table 3, group 1
Table 3, group 2
Seed length
Seed length
Seed width
Greenhouse
Greenhouse
Greenhouse
1
2
2
1
1
2
3.8
99.8
64.4
3.64
2.95
4.1
Yes
Yes
Yes
?2.0
?2.2
1.5
0.12
0.12
0.16
Table 3, group 2
These data were generated by composite interval mapping by QTL Cartographer with 2000 permutations. Additive QTL are
listed that either were statistically significant on their own or were near-significant and additionally mapped close to a locus that
participates in an epistatic interaction. Significance levels were determined by the 2000 permutations. The additive effect is ex-
pressed as a percentage of the overall average for this trait. The last column indicates a possible relationship between an additive
QTL and one member of an epistatic QTL pair (Table 2, column 2) as deduced by similarity in map position.
2016R. L. Malmberg et al.

Page 5

perform a complete comparison of all-pairwise markers
to test for additive 3 additive epistatic interactions from
recombinant inbred line data, although they do so in
different ways. Epistat uses likelihood ratios to compare
epistatic and additive models. From the Epistat output,
we eliminated all interactions that the program identi-
fied as possibly due to linkage, since the lines cannot be
considered to be at linkage equilibrium. We then used
the associated Montecarlo simulation program to re-
sample subgroups as a means of estimating P-values. Epis-
tacy is a SAS script built around a general linear model
analysis. We removed all interactions in the Epistacy
output in which the two markers were within 50 cM of
each other to avoid linkage effects. The final results of
the two programs were nearly identical. The total num-
ber of pairwise interaction tests that we ran was large;
however,themarkersarenotfullyindependentsincethey
arelinked.WeusedthecorrectionsuggestedbyHolland
(1998)ofdividingthedesiredP-value(0.01)byN(N?1)/
2, where N is the number of chromosomes. Hence our
criterion for statistical significance was P ¼ 0.001.
Figure 2 shows the epistatic interactions mapped for
fruitnumberandgerminationrateinthefield-grownRI
lines. To prepare Figure 2, we converted the A. thaliana
genetic map into a single pseudomap by appending
each chromosome map, one after another, with a 10-cM
spacer between the end of one chromosome and the
beginning of the next. We then placed this lumped
linear genetic map onboth x- and y-axes and plotted the
positions of the epistatic interactions detected. The sig-
nificance level of an interaction is indicated by the
darkness of the point plotted (we refer to this type of
graph as an M&M plot).
Although only the P ¼ 0.001 value is significant,
plotting slightly higher P-values allowed us to visualize
the neighborhood of a given interaction. The epistatic
interactions detected generally occur in clusters of
points with more than one point representing a signif-
icant interaction and numerous points representing
interactions individually slightly less than significant.
These clusters seem likely to be the result of a single
underlying epistatic interaction between two loci. The
diameterofthesecloudsofpointsis10–20cM,similarto
the width of an additive QTL peak near its base.
We used QTL Cartographer’s multiple interval map-
ping program, MImapqtl, to test for interactions among
Figure 1.—Comparison of field and greenhouse QTL LOD
scores. This displays the output of WinQTLCartographer
(Wang et al. 2004) composite interval mapping as QTL
LOD score vs. genetic map position for the traits that were
measured from lines grown in both field and greenhouse en-
vironments. (Top) Seed germination; (middle) seed length;
(bottom) seed width. Field growth is a solid line, while green-
house growth is a dashed line. Horizontal lines represent the
significance levels established by permutations.
Figure 2.—Epistatic QTL for fitness traits
in field-grown Arabidopsis. The programs
Epistat and Epistacy were used to estimate
the probabilities of interactions between
map segments for these quantitative traits;
the results from the two programs were com-
bined in each scatter plot. The axes indicate
the genetic map of A. thaliana with one chro-
mosome following another so that the total
is displayed linearly. The x- and y-axes corre-
spond to marker X and marker Y in Table 2.
The plotted squares indicate the P-value for
an interaction between the map segments:
¼ 0.001,
Note that because of the correction for multi-
ple comparisons, these values correspond to a
10-fold-higher statistical significance probabil-
ity. The data in Table 2 contain the P ¼ 0.001
subset of this graph.
¼ 0.003,
¼ 0.005,
¼ 0.007.
Epistasis for Fitness in Arabidopsis2017