Electronic Supplementary Materials
Methods
Outlier Detection
Graphical exploration of the raw morph frequency data revealed a clear outlier.
Specifically, the bush to which the low-density treatment was applied in Block 1 had a
much higher frequency of the green morph (0.6) at the end of the experiment than other
bushes (Fig S1). This frequency would indicate selection against the striped morph,
which discords with decades of research in T. cristinae (1). Furthermore, the magnitude
of difference between the high and low treatments in this block was nearly 3 times
larger the maximum difference in all other blocks, and in the opposite direction to the
other blocks (Fig. S1). In response, we performed inter-experimental outlier detection
analysis, comparing the low-density bush in Block 1 to eighteen similarly constructed
blocks from four selection experiments conducted from 2004 to 2012 (1–3), but not
including Blocks 2-5 from the present study. A one-sample t-test, comparing the
average strength of selection against the green morph on A. fasciculatum to a value of 0.10 demonstrated that the low-density bush in Block 1 was an outlier to the past ten
years of data on selection in T. cristinae. Experimental error or unprecedented genetic
drift are the most likely explanations.
Statistical Model Selection and Validation
For the analysis of morph frequencies, we used a linear mixed-effects model (LMM) on
raw, untransformed morph frequency data. Block was included as a random factor.
Because data of this form often do not conform to the assumptions of linear models, we
performed model validation to assess whether our model were appropriate. To
determine whether our data and model errors were normally distributed, we visually
examined quantile-quantile plots, and performed Shapiro-Wilks tests. We concluded
that both the raw data and residuals of the LMM were normally distributed based on QQ
plots (Figures S2 and S3), and Shapiro-Wilks tests corroborate our visual assessment
(raw data: W = 0.992, p = 0.999; residuals: W = 0.930, p = 0.516). We furthermore
provide QQ plots for simulated data drawn from a normal distribution to allow easier
evaluation of error distribution.
To evaluate the assumption of homoscedasticity, we simply show numerically equal
variance (= 5.8 x10-4) across treatments (Fig S4a). There is no heteroscedasticity in the
residuals. Furthermore, while the arcsine-square root transformation is often applied to
frequency data (4), models using transformed data conformed worse to the
assumptions of linear models, showing an increased disparity in variance across
treatments relative to the models using raw data (Fig S5b).
Linear mixed-effects models were implemented in R using the lmm function (nlme
package, 5), and Poisson mixed-effects models were implemented using the glmer
function (lme4 package, 6).
Analyses of morph frequencies including Block 1
We performed analysis identical to the one in the main text, but included data from
Block 1. The inclusion of Block 1 did not qualitatively influence the finding that there
exists selection against the green morph across all treatments (t9 = 5.13, p < 0.001),
even though the outlier bush appeared to experience selection for the green morph,
opposite to all other bushes. The inclusion of Block 1 did, however, affect the analysis of
density-dependent selection, leading to a non-significant effect (t4 = 0.01, p = 0.990). We
do not find the discrepancy between this analysis and the analysis excluding Block 1
surprising, given that the effect of density in Block 1 is extreme in magnitude and
opposite in direction relative to the other four blocks (Fig S1). There were furthermore
no significant differences between treatments on the proportional mortality of striped
(t4 = -0.61, p = 0.573) or green T. cristinae (t4 = -0.16, p = 0.875).
1
Raw Data
2
Table S1. Raw data. Treatment: H = high density, L = low density. All remaining fields are counts for insects collected at end of
3
experiments. Green and Striped: green and striped T. cristinae. Cat 1 – 3: Caterpillar Morphospecies 1, 2 and 3. Cat A – C: Extra,
4
unidentified caterpillar morphospecies. Cat 1 – 3 ostensibly correspond to a single, unidentified (i.e., no species name) caterpillar. Cat A
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– C are distinguishable from one another only within a bush. For example, caterpillars A, B, and C on bush 3H are different species from
6
one another, but Cat A on bush 3H may be a different species from Cat A on bush 2H (or they maybe the same).
7
Block
Treatment Green
Striped
Cat 1
Cat 2
Cat 3
Cat A
Cat B
Cat C
1
H
1
5
2
2
0
1
0
0
2
H
1
9
5
0
0
1
0
0
3
H
3
11
8
3
1
1
1
1
4
H
4
7
8
0
0
1
0
0
5
H
4
9
7
3
2
0
0
0
1
L
3
2
9
3
0
2
3
0
2
L
0
3
4
1
0
0
0
0
3
L
1
5
6
4
1
1
0
0
4
L
1
3
6
1
0
0
0
0
5
L
1
6
10
1
0
1
0
0
8
Figure S1. Green frequency at end of experiment for each block across density
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treatments.
10
11
12
13
14
15
16
17
18
19
20
21
Figure S2: Quantile-quantile plot of raw green frequency data (top-left) and QQ plots 8
22
simulations with data drawn from normal distribution with standard deviation to that
23
of raw data. Dashed line is 1:1.
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25
26
27
28
29
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Figure S2: Quantile-quantile plot of residuals from linear mixed model explaining green
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frequency by treatment with block as random factor (top-left), and QQ plots for 8
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simulations with data drawn from normal distribution with standard deviation to that
34
of residuals. Dashed line is 1:1.
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36
37
38
39
40
Figure S4. Top: mean ± 1SEM for raw frequency data. Bottom: same for asin-sqrt
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transformed data. Note reduced variance on HD treatment for asin-sqrt transformed
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data.
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46
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