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Electronic Supplementary Material (ESM)
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Table S1. Protein (P) and carbohydrate (C) composition of the 24 artificial diets used in our
feeding experiments (Experiment 1 and 2). The total nutrient in each diet is given as the sum
of the percentage P and percentage C, with the remaining percentage consisting of
indigestible crystalline cellulose. The four diets used in our choice experiment (Experiment
3) are highlighted with bold text
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4
5
6
Diet
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
7
8
9
10
11
12
Percentage Composition
P
C
P+C
10
30
50
70
9
27
45
63
6
18
30
42
3
9
15
21
2
6
10
14
1.33
4
6.66
9.33
2
6
10
14
3
9
15
21
6
18
30
42
9
27
45
63
10
30
50
70
10.66
32
53.33
74.66
12
36
60
84
12
36
60
84
12
36
60
84
12
36
60
84
12
36
60
84
12
36
60
84
P:C ratio
5:1
5:1
5:1
5:1
3:1
3:1
3:1
3:1
1:1
1:1
1:1
1:1
1:3
1:3
1:3
1:3
1:5
1:5
1:5
1:5
1:8
1:8
1:8
1:8
2
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Table S2. Multivariate Analysis of Variance (MANOVA) examining the effect of diet pair on
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the intake of P and C in male N. cinerea. Univariate ANOVAs were used to determine
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whether P or C intake (or both) contributed to this overall multivariate effect and Tukey’s
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HSD pairwise contrasts used to determine how the intake of P and C differed across specific
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diet pairs.
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Model term
Diet pair
Diet pair
1 vs. 2
1 vs. 3
1 vs. 4
2 vs. 3
2 vs. 4
3 vs. 4
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20
21
22
23
24
25
26
27
28
Pillai’s Trace
0.98
Nutrient
P
C
Nutrient
P
C
P
C
P
C
P
C
P
C
P
C
MANOVA
F6,112
P
17.84
0.0001
Univariate ANOVA
F3,56
P
9.49
0.0001
66.42
0.0001
F1,28
P
12.38
0.002
59.08
0.0001
4.21
0.043
2.37
0.14
26.55
0.0001
108.40
0.0001
1.94
0.18
91.64
0.0001
2.81
0.11
0.27
0.61
8.96
0.006
189.02
0.0001
3
29
30
31
32
33
34
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Figure S1. The distribution of the 24 artificial diets used in our no choice feeding
experiments (Experiment 1 and 2). The diets are distributed along 6 nutritional rails (solid,
black lines that connects diets with a fixed P:C ratio), with 4 diets per rail that differ in total
nutritional content. On each nutritional rail, the diets connected by the isocaloric lines
(dashed, black lines that connect diets with equal calories) have equal total nutrition. The 4
diets marked with red symbols represent those used in diet pairs in our choice experiment
(Experiment 3).
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1:8
80
37
1:5
1:3
1:1
39
40
41
42
% Carbohydrate
38
60
40
3:1
20
5:1
43
44
0
0
45
46
47
48
49
50
51
52
53
54
55
56
20
40
% Protein
60
80
4
57
58
59
60
61
62
63
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Figure S2. The mean (95% CIs) consumption of diets in each diet pair. White bars represent
the high P diet and grey bars the high C diet in each diet pair. The P:C ratio of the diet is
provided above the bar and the total nutritional content of the diet (%) is provided within
the bar in bold. After Bonferroni correction for multiple comparisons (4 comparisons, a =
0.0125), males consumed significantly more of the high C diet than the high P diet (Diet pair
1: t14 = 7.19, P = 0.0001; Diet pair 2: t14 = 14.87, P = 0.0001; Diet pair 3: t14 = 6.12, P = 0.0001;
Diet pair 4: t14 = 14.00, P = 0.0001) in each diet pair.
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Mean diet consumption (mg)
9.33:74.66
9.33:74.66
150
4:32
4:32
100
50
30:6
70:14
0
36%
36%
1
65
66
67
68
69
70
71
72
73
74
75
70:14
30:6
36%
84%
2
84%
36%
3
Diet Pairs
84%
84%
4
5
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77
78
79
80
81
82
83
84
Text S1. Multivariate response surface approach used to characterize the nutritional
landscapes for our three response variables
We used a multivariate response surface approach to examine the effects of protein (P) and
carbohydrates (C) intake on our response variables (sperm number, sperm viability and
male fertility). This approach is based on the methodologies of Lande & Arnold (1983). Prior
to analysis, we standardized each response variable and nutrient intake to a mean of zero
and standard deviation of one using a Z- transformation to ensure that our regression
gradients were presented in the same scale. First, the following linear multiple regression
model is fitted to estimate the linear gradients for P and C intake on the response variable:
R    P  C  
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where R is the response variable, a is the regression intercept, βs represent the partial
regression gradients and ɛ is the random error component.
To estimate the nonlinear (i.e. quadratic and correlational) gradients for nutrient
intake on the response variables, the following nonlinear multiple regression model was
fitted:


R     P   C  P 2  C 2  PC  
2
2
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(Eq.1)

2
(Eq.2)

2
where P 2 and C 2 represent the quadratic gradients for P and C, respectively and PC
represents the correlational gradient for these two macronutrients. For the quadratic
gradients, a negative term indicates a peak on the nutritional landscape, whereas a positive
term indicates a trough. The linear terms are included but not interpreted from Eq. 2: they
are simply included so that the nonlinear effects can be examined when the linear effects
have been removed.
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Text S2. Sequential model building approach to compare nutritional landscapes for sperm
number and male fertility
We used a sequential model building approach to assess whether the linear and nonlinear
effects of protein and carbohydrate ingestion differed for our response variables (Draper
and John 1988; Chenoweth and Blows 2005). As our different responses variables (sperm
number and offspring number) were measured in different scales, it was necessary to
standardize them for statistical comparison. Prior to comparison, we therefore standardized
each response variable and nutrient intake to a mean of zero and standard deviation of one
using a Z- transformation. We then included a dummy variable, response type (RT), in a
reduced model containing only the standardized linear terms:
n
R     RT    N  
0
0
i i
i 1
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where R is our standardized response variables, Ni refers to the intake of the ith nutrient, n
represents the number of nutrients contained in the model and ε is the unexplained error.
From (1), the unexplained (i.e. residual) sums of squares for this reduced model (SSr) was
compared to the same quantity (SSc) from a second (complete) model that included all of
the terms in (1) with the addition of the terms iNiRT which represents the linear interaction
of RT and the ith nutrient.
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n
n
i 1
i 1
R  0  0RT  i Ni   i Ni RT  
(Eq.2)
A partial F-test(Bowerman and O'Connell 1990) was used to compare SSr and SSc from (Eq.1)
and (Eq.2) respectively:
Fa ,b 
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(Eq.1)
(SSr - SSc ) a
SSc b
(Eq.3)
where a is the number of terms that differ between the reduced and complete model and b
is the error degrees of freedom for SSc.
To test whether the quadratic effect of nutrient intake differed between response
variables, the SSr from the reduced model:
n
n
n
i 1
i 1
i 1
R  0  0RT  i Ni   i Ni RT   i Ni 2  
(Eq.4)
was compared to the SSc of the complete model:
n
n
n
n
i 1
i 1
i 1
i 1
R  0  0RT  i Ni   i Ni RT  i Ni 2   i Ni 2RT  
(Eq.5)
using (Eq.3).
To test whether correlational effects of nutrient intake on response variables
differed, the SSr from the reduced model:
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n
n
n
n
n
i 1
i 1
i 1
i 1
i 1
R   0   0 RT   i Ni    i Ni RT   i Ni 2    i Ni 2RT  
n

j1
ij
Ni N j   (Eq.6)
was compared to the SSc of the complete model:
n
n
n
n
n
i 1
i 1
i 1
i 1
i 1
R  0  0RT  i Ni   i Ni RT   i Ni 2   i Ni 2RT  
n
n
n
i 1
j1
 N N     N N RT  
j1
ij
i
j
ij
i
j
(Eq.7)
using (Eq.3).
In summary, the comparison of model (Eq.1) versus (Eq.2), (Eq.4) versus (Eq.5), and
(Eq.6) versus (Eq.7) provides a test for the overall significance of the interaction between
response type and the linear, quadratic and correlational effects of nutrient intake,
respectively. Therefore, significant differences in these model comparisons (as detected
with a partial F-test) demonstrate that the linear, quadratic and/or correlational effects of
nutrient intake on the response variables differ, respectively. We also inspected the
interaction of individual nutrients with the response variable terms from the full model
(Eq.7) to determine which of the nutrients were responsible for the significance of the
overall partial F-test.
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Text S3. Annotated R code used to estimate the angle (θ), and 95% CIs, between linear
vectors for the effects of nutrients on sperm number and offspring number
library(MCMCglmm)
# read in nutritional data for first male trait (e.g. offspring number)
angle.data1<-read.table("offspring.txt",h=T)
attach(angle.data1)
str(angle.data1)
# str(angle.data) should give 3 columns for data structure (e.g offspring number, P intake
and C intake)
# Bayesian linear regression to estimate beta for each variable, produces posterior
distribution based on 15200 estimates of each parameter:
angle.model.offspring<-MCMCglmm(offspring~P+C-1,data=angle.data1,v = 0.02,
nitt=400000,burnin=20000,thin=25)
summary(angle.model.offspring)
# and again for second male trait (e.g. sperm number):
library(MCMCglmm)
angle.data2<-read.table("sperm.txt",h=T)
attach(angle.data2)
str(angle.data2)
angle.model.sperm<-MCMCglmm(sperm~P+C-1,data=angle.data2, v = 0.02,
nitt=400000,burnin=20000,thin=25)
summary(angle.model.sperm)
angles<-numeric(15200)
# creates an empty vector the same length as the posterior distribution, in which angle
estimates for each row of the posterior distribution will be stored as follows:
for(i in 1:15200){
b.offspring<- angle.model.offspring$Sol[i,1:2]
b.sperm<- angle.model.sperm$Sol[i,1:2]
# creates a vector of beta estimates for each variable for each row of the posterior
distribution (and the loop runs through all rows)
angles[i]<- acos((t(b.sperm) %*% b.sperm) / ((sqrt(t(b.sperm) %*% b.sperm)) *
(sqrt(t(b.offspring) %*% b.offspring)))) * (180/pi) }
# calculates the angles between offspring number and sperm number beta's for each row of
the posterior distribution
summary(angles)
# to examine angle estimates which are now stored in the vector called 'angles'
# provides the mean, median, minimum and maximum angle. The 1st and 3rd Quantiles are
functionally equivalent to the 95% CIs. We use the median and 95% CIs in our manuscript
for theta
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Text S4. Comparing the similarities in methodological procedures between our current
study and the published study by South et al. (2011)
Both our current study and the published work of South et al. (2011) used the oviviparous
cockroach Nauphoeta cinerea as the laboratory model and experimental animals were taken
from the same large cockroach cultures that have been maintained under the same
conditions for the last 20 years. When constructing nutritional landscapes to determine the
effect of protein (P) and carbohydrate (C) intake on response variables (sperm number,
sperm viability and male fertility in our current study and sex pheromone expression, weight
gain, attractiveness and dominance in South et al. (2011)), male cockroaches in the two
studies were provided with the same 24 artificial, holidic diets (see Table S1 and Figure S1),
provided food and diet in the same feeding platforms, were maintained in the same plastic
containers and had their dietary intake measured for the same duration (10 days). Diet was
replaced and weighed every 2 days in South et al. (2011) and every 5 days in our current
study. The mean intake of P and C in both experiments were similar, as evidence by
overlapping 95% Confidence Intervals (mean (95%CI), current study = 18.52 (16.99, 20.26)
mg of P and 33.34 (29.38, 37.56) mg of C; South et al. (2011) = 21.99 (19.43, 24.76) mg of P
and 36.60 (31.71, 41.37) mg of C).
Our two studies differ slightly in how dietary choice was examined. In South et al.
(2011), the diets used in the four diet pairs come from two nutritional rails (P:C 1:1 and 1:8)
and two total nutritional contents were used (36 and 84%). In our current study, we used
the same two total nutritional contents (36 and 84%) but we examined a much wider
nutritional space by using more divergent nutritional rails (5:1 and 1:8). Apart from the
replacement and weighing of diets (as described above), all other aspects were the same in
these two experiments.
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References
Lande R, Arnold SJ (1983) The measurement of selection on correlated characters. Evolution
37: 1210-1226.
South SH, House CM, Moore AJ, Simpson SJ, Hunt J (2011) Male cockroaches prefer a high
carbohydrate diet that makes them more attractive to females: implications for the study of
condition dependence. Evolution 65: 1594-1606.