Copyright 0 1990 by the Genetics Society of America
Statistical Genetics of an Annual Plant,Impatiens capensis.
11. Natural Selection
Thomas Mitchell-Olds* andJoy Bergelson?
*Division of Biological Sciences, University ofMontana, Missoula, Montana 59812; and +Department of Zoology, University of
Washington, Seattle, Washington 98 195
Manuscript received May 2, 1989
Accepted for publication October 10, 1989
ABSTRACT
Measurement of natural selection on correlated charactersprovides valuable information on fitness
surfaces, patterns of directional, stabilizing, or disruptive selection, mechanisms of fitness variation
operating in nature, and possible spatial variation in selective pressures. We examined effects of seed
weight, germination date, plant size, early growth, and late growth on individual fitness. Path analysis
showed that most characters had direct or indirect effects on individual fitness, indicating directional
selection. For most early life-cycle characters, indirect effects via later characters exceed the direct
causal effect on fitness. Selection gradients were uniform across the experimental site. There was no
evidence for stabilizing or disruptive selection.We discuss severaldefinitions of stabilizing and
disruptive selection. Although early events in the life of an individual have important causal effects
onsubsequentcharactersand
fitness, there is nodetectable geneticvariance for most of these
characters, so little or no genetic response to natural selection is expected.
T
0 understand adaptive evolution in natural populations we need information on natural selection, which changes phenotypic distributions, and on
genetic variances and covariances, which constrain
genetic change from one generation to the next.
Even
if little genetic variation exists, measurement of natural selection occurring on phenotypes within generations provides valuable information on fitness surfaces, patterns of directional, stabilizing, or disruptive
selection, possible mechanisms of fitness variation operating in nature, and thescale of spatial variation in
selective pressures. Recent theoretical work provides
a basis forestimating and testing thestrength of
natural selection operating on correlated characters
in wild populations (LANDEand ARNOLD1983; MANLEY 1985; MITCHELL-OLDS
and SHAW1987). Several
authors have found evidence fornatural selection
operating on quantitative characters in natural plant
populations (KALISZ 1986; STEWARTand SCHOEN
1987; SCHEMSKE
and HORVITZ1988; VANDER TOORN
and PONS1988; CAMPBELL
1989).
In a previous study (MITCHELL-OLDS
and BERGELSON 1990) we detected maternal or dominance variance for seed weight and germination date, and additive genetic variance for germination date in one
population. Characters expressed laterin the life-cycle
had little or no genetic variance. In this paper we ask
1) Does natural selection operate on quantitative characters in Impatiens capensis? 2) Is this selection direc-
tional, stabilizing, or disruptive? 3) Is there spatial
heterogeneity in natural selection?
Multiple regression (MANLEY1985; LANDEand ARNOLD 1983; ENDLER1986) and path analysis (WRIGHT
1968; MADDOXand ANTONOVICS1983; MITCHELLOLDS1987; CRESPIand BOOKSTEIN
1988) have been
used to examine the effect of correlated phenotypic
characters on components of fitness. LANDEand ARNOLD (1983) notedthat
regression coefficients between particular characters and fitness can be related
to theoreticalparameters
of quantitative genetics:
when phenotypic characters are (approximately) multivariate normalthen the partial regression coefficients, B = P"s, (approximately) equal the average
gradient of the relative fitness surface, weighted by
the distribution of phenotypes, where P is the q X q
phenotypic variance-covariance matrix, s is the q X 1
vector of selection differentials, and q is the number
of characters. Short term response to selection may
be predicted if heritabilities and genetic correlations
are known (FALCONER198 1; LANDEand ARNOLD
1983). The change in mean populationphenotype
following a single generation of selection is given by
A2 = GB, where G is the q X q matrix of additive
genetic variances and covariances, and A2 is the q X 1
vector of changes in mean phenotype of the characters. Let
y = 1/2(1
+ G,j)P"COV[W,(z - Z)(z - 2)']P",
and
The public;~tioncosts of this article were partly defrayed by the payment
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This article must therefore be hereby marked ''advertisement"
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Genetics 124: 4 1 7-421 ( F e b r ~ ~1990)
y,
w =p
+ Z'B + z'yz +
€
where w = relative fitness, p = the population mean,
418
T. Mitchell-Olds and J. Bergelson
variables measured early in the life-cycle may have causal
effects on later characters, while multiple regression does
not address the reason for intercorrelation among predictor
variables. For example, we use path analysis to ask about
causal effects of early growth rate on late growth rate, and
to quantify the total of direct and indirect causal effects of
early growth rate on fitness, while regression does not
consider these issues.
RESULTS
e3
FIGURE1 .-Path diagram of predictor variables influencing fitness. Path coefficients ( l a b l e 1) quantify causal influences of seed
weight (SW),germination d;tre (GD), June si7,e US), early growth
r;ate (PI;). ;uld late growth rate (LG) on subsequent variables and
relative fitness (w).Only statistically significant paths are shown.
Scc tcxr for discussion.
Path analysisrevealssignificant
directeffectsof
early growth and late growth on
fitness (Table1).
Early life-cycle characters (seed weight, germination
date, and June size) had little direct effect on fitness,
insteadinfluencinglatercharacters,whichsubsequently affect fitness (Table2). Direct effects of early
6, = 1 if i = j and zero otherwise, = the q X q matrix
growth rate onfitness were less important than direct
of stabilizing selection gradients, and
t = error. T h e n ,
effects of late growth rate, but early growth rate had
stabilizing and disruptive selection may be analyzed
larger indirect effect, yielding a larger total causal
a
by examiningthecurvature
of the fitnesssurface
effect
onfitness.Germinationdatehad
a negative
(LANDEand ARNOLD 1983,Equations13and14;
effect
on
fitness,
indicating
that
plants
that
germiMITCHELL-OLDS
and SHAW 1987; SCHLUTER1988).
nated early reached larger final size. All other charEstimates of the best linear fit to the fitness surface
acters
had positive effects on fitness.
can be used to predict changesin the population mean
We
investigated
possible spatial variation in natural
due to selection even if the fitness surface is curved
selection
by
dividing
the field site into four 1 X 3.5
(LANDE and ARNOLD 1983).
m2 quadrats. General linear model tests (not shown)
for a selection gradient-by-quadrat interaction found
MATERIALS AND METHODS
no evidence for spatial heterogeneityof natural selecNatural history of Impatiens capensis and experimental
tion ( F ratios <1.9, d.f. = 3, 420, P > 0.10).
design have been detailed in a companion study (MITCHELLIf a second order polynomial model is assumed to
OLDSand BERGELSON1990). Five characters (seed weight,
explain the relationship between characters and
fitgermination date, June size, early growth, and late growth
were transformed to approximate normality and used to
ness, curvature of thefitness surface can be estimated
predict individual relative fitness (finaladult size/mean adult
and tested (Table 3). Although none of the second
size). Selection was measured in a natural population in
order coefficients, yy, a r e individuallysignificantly
Madison, Wisconsin.
different from zero, F test reveals that some combiRegressioncoefficients and their standard errors were
nation(s) of yv a r e significant ( P < 0.001). Although
obtained by weighted, delete-one jackknife of least squares
estimates (KENNEDYand GENTLE1980; MITCHELL-OLDS this test does not permit identificationwhich
of second
1986;
1989). Jackknife t-tests (WU 1986; MITCHELL-OLDS
order terms are nonzero, they cannotall be excluded
MITCHELL-OLDS
and SHAW 1987)
provide approximate tests
from the model, indicating that the surface is signifiof significance that are robust to heteroscedastic and noncantly curved. Backward stepwise regression can be
normal residuals (WU 1986). This approach permits analysis
used to eliminate some terms from the full quadratic
of directional selection gradients, 8, even if the fitness
model (e.g., DRAPERand SMITH 1981),permitting
surface shows moderate curvature (MITCHELL-OLDS
and
SHAW1987). We assessed curvature of the fitness surface
examinationofreduced,simplermodelsof
fitness
by fitting a l l second order terms. All statistical resampling
variation. Such a reduced model indicates w = 0.134
employed original Pascal programs (MITCHELL-OLDS
1989
- 0.370 * EG - 0.013 * GD * EG 0.369 * EG *
and unpublished results).
LG. However, extreme caution must be used
in interPath analysis is a versatile approach that overlaps broadly
pretationofresultsfrom
stepwise regression,since
with multiple regression, structural equation analysis, and
factor analysis (LI 1975; WRIGHT 1968). In many cases it is
putative significance levels may have little validity as
similar t o multiple regression analysis, focusingparticularly
a consequence of multiple tests, multicollinearity, and
on attempts to determine patterns of causal interaction.
chance
correlations
among
predictor
variables
Path analysis includes a path diagram (Figure 1 ) with direct
(DRAPER
and
SMITH
198
1).
causal pathways whose strengths are indicated by path coefMITCHELL-OLDS
and SHAW (1987) noted that if a
ficients (partial regression coefficients) with arrows indicating the direction of causal connection from predictor (e.g.,
transformation of fitness, wt, can be found that conseed weight) to response (e.g.,J u n e size) variables.In a path
verts wt = p z'p t o linearity then fitness maxima o r
analytical framework, the overall correlation between two
minima could not have occurred at intermediate trait
variables is the sun1 of the causal effects via connecting
values. We found that when relative fitness is transpaths. I n the current example, path analysis and regression
analysis are identical except that path analysis assumes that
formed to log(w 0.5), fitness is a linear function of
+
+
+
419
Impatiens Natural Selection
TABLE 1
Standardized partial regression coefficients,
Predictor Variable
Response variable
Germination
June size
rate
growth
Early growth
Late0.70
0.80***
Fitness -0.08*
SW
GD
-0.01
0.13***
0.05
-0.010.08
0.04
-0.54***
-0.10
0.04
EG
JS
rp
LG
0.00
0.31
0.48
0.63***
-0.02
0.37***
0.71
0.48***
n = 454. Figure 1 shows the significant paths in the path diagram. SW = seed weight, GD = germination date, JS =June size, EG = early
growth rate, LG = late growth rate, and w = relative fitness. * Indicates P < 0.05, ** indicates P < 0.01, and *** indicates P < 0.001,
TABLE 2
TABLE 3
Relationship between characters and fitness
Linear and quadratic effects on fitness
Selection
Indirect
Direct
differential
Character
Seed weight
Germination date
June size
Early growth rate
Late growth rate
0.13
-0.36
0.53
0.73
0.74
Total
causal
causal
causai
0.04
-0.08
-0.02
0.37
0.48
0.10
-0.32
0.52
0.38
0.00
0.14
-0.40
0.50
0.76
0.48
All estimates are given in standardized form corresponding to
predictor variables with 7ero mean and unit variance. T h e standardized selection differential equals the covariance between standardized trait values and relative fitness. T h e direct causal effect of
eachcharacter onfitness is thestandardized partialregression
coefficient, or selection gradient. Indirect causal effects are calculated from all causal pathsfrom a variable via eachsubsequent
variable. Total causal influence sunu all direct and indirect pathways.
the charactersmeasured(generallinear
hypothesis
test of second order terms, F = 1.412, d.f. = 15, 433,
P > 0.10). Therefore maximum fitness occurs at extreme trait values, and there is no evidence for stabilizing or disruptive selection (MITCHELL-OLDS
and
SHAW1987).
While regression analysis of natural selection is primarily concerned with estimating and testing the direct effect of characters on fitness, it is clearly desirable that our estimated model be at least partially
capable of predicting the fitness of additional individuals. The predictive ability of the model serves as an
indication of whether our estimated selection differentials adequately portray the action of natural selection in the field. Predictive ability can be assessed by
data splitting (cross validation), in which the data are
split into two parts, one used for estimation and the
other fortesting (SNEE1977; MITCHELL-OLDS
and
SHAW1987). We randomly assigned individuals to
two groups of equal size, and compared thecoefficient
of determination when the model from thefirst group
(/' = 79.3%) was applied to individuals in the second
group (? = 72.2%). Clearly, the regression model
obtained has good predictive ability when applied to
additional individuals.
Variable
Coefficient
t
P
Constant
SW
GD
J S 0.927
EG
LG
SW*SW
GD*GD
JS*JS
EG*EG
LG*LG
SW*GD
SW*JS
SW*EG
SW*LG
GD*JS
GD*EG
GD*LG
JS*EG
JS*LG
EG * LG
0.824
0.015
-0.053
0.032
0.404
0.31 1
-0.007
0.001
-0.023
0.044
0.022
-0.022
0.0 10
0.001
-0.020
-0.024
-0.032
0.029
-0.003
0.006
0.05 1
18.965
0.664
-1.819
0.001
0.507
0.070
0.355
0.001
0.001
0.999
0.968
0.254
0.406
0.513
0.092
0.999
0.958
0.313
0.252
0.231
0.225
0.908
0.837
0.175
8.595
6.719
0.000
0.041
-1.143
0.832
0.655
-1.688
0.000
0.053
-1.011
-1.146
-1.199
1.216
-0.116
0.206
1.359
Test ofgeneral linear hypothesis
Ho: No second order effects
Source
ss
d.f.
MS
Hypothesis
Error
19.310
89.855
15
433
6.203
1.287
0.208
F
P
0.001
n = 454, r 2 = 0.763. Abbreviations as in Table 1.
DISCUSSION
Analysis of natural selection shows that characters
expressedlater in the life-cycle (growthrate) have
strong effects on final fitness, while early life-cycle
traits exerttheirinfluence
on fitness primarily via
subsequent characters. In fact, for most characters,
the indirect effects on fitness exceed the direct causal
effect (Table 2). The implications of such indirect
effects for predicting the response to natural selection
have not been previously addressed. For example, the
selection gradient is often interpreted as the direct
effect of a character on fitness, while holding other
charactersconstant. Yet, in these populations it is
inappropriate to consider changes
in early growth rate
in the absence of subsequent changes in late growth
T. Mitchell-Olds and J. Bergelson
420
6 1
I
I
I
I
-2
0
2
4
4 -
3 -
2 -
-4
Late Growth Rate
FIGURE2.-Plot of fitness, w , as a function of late growth rate, 1
Second order polynomial regression indicates w = 0.870 0.6771
O.130l2 (as shown by the line), with a significant quadratic term
and an intermediate fitness minimum. This would be interpreted
asdisruptive selection according to LANDE and ARNOLD (1983).
Alternatively,
exponentially
increasing
fitness,
w = -0.5
exp(0.252 + 0.461 - 0.0031') provides better statistical fit and
demonstrates that fitness is a monotonically increasing function of
late growthrate.Weinterpret
thisasdirectional
selection for
increased growth rate, rather than disruptive selection on growth
rate. See text and MITCHELL-OLDS and SHAW (1987) for further
discussion.
+
+
+
rate,for such changes will cause increases in late
growth rate. Although it is clear that early events in
the life of an individual have important causal effects
onsubsequentcharacters and final fitness, there is
little genetic variation for these characters within populations, so little or no genetic response to natural
selection should be expected.
In spite of the paucity of genetic variation observed
in this study, these populations have diverged significantly from one another for
most characters examined
(MITCHELL-OLDS
1986). Although the present study
suggests severe short-term genetic constraints on the
abilityof
these populations torespond tonatural
selection, over the long runtheir mean genotypic
values have changed significantly. This lack of correspondence between results of short-term quantitative
genetic studies and long-term changes among populations shows the need for cautious interpretation of
quantitative genetic studies.
Although final plant size varied noticeably across
this field site (T. MITCHELL-OLDS,
personal observation), there was no spatial variability in selection gradients. This indicates that natural selection operates
in a uniform manner over the 3 x 7 m area of this
field site. Several studies (KALISZ 1986; STEWART and
SCHOEN 1987)
have found fluctuatinglevels ofnatural
selection on a spatial scale similar to or slightly larger
than this study. This field site, located in the center
of a gap in the forest overstory, was chosen for its
apparentenvironmental
homogeneity. Presumably,
different patterns of selection would have been observed if the study population had straddled the sunshade boundary adjacent to this field site.
Our inability to exclude all second order terms from
the regression analysis indicates that thefitness surface
is significantly curved(Table3).
Maximum fitness
does not occur at intermediate values of these characters, and there is no evidence for the operation of
stabilizing or disruptive selection.
Several definitions of stabilizing and disruptive selection can be found in therecentquantitative
genetics literature. LANDE and ARNOLD
(1 983) state that
stabilizing/disruptive selection is equivalent to curvature of the fitness surface, y # 0. Others use more
strict definitions, and refer to stabilizing selection as
situations in which maximum fitness occurs at some
intermediate point in the phenotype distribution (e.g.,
KIMURA1983; MANLEY1985; ENDLER 1986;
MITCHELL-OLDS
and SHAW 1987;see Figure 2), and disruptive selection as situations in which minimum fitness
is associated with intermediate phenotypes.While the
choice of definitions does not affect the mathematics
of selection theory, the stricter definition implies that
intermediate phenotypes may evolve in response to
stabilizing selection, while LANDEandARNOLD'S
(1983) definition implies that long-term directional
change of population means could be caused by "stabilizing'' selection.
We are grateful toC. DENNISTON,
R. NAKAMURA,
E. THOMPSON,
D. WIERNASZ,
S. VIA, D. WALLER,B. WEIR, and three anonymous
reviewers for comments and discussion. T.M.O. was supported by
National Science Foundation grants BSR-8311817, BSR-8421272,
and U.S. Department of Agriculture
Competitive Grant 88-37 15 13958. J.M.B. was supported by a NationalScience Foundation
predoctoral fellowship and a National Science Foundation dissertation improvement grant. This is contribution number 103 from
the University of Montana Herbarium and Center for PlantDiversity.
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