Appendix S1
Fitness reduction for uncooperative fig wasps
through reduced offspring size: A third component
of host sanctions
Jande´r, K.C., Dafoe, A., Herre, E.A.
May 6, 2016
1
1 Additional Methods and Results
1.1 Length measurements correlate with wasp weight
To confirm that the measurements we use correlate with wasp weight we
measured the length of the front femur, head and thorax to the nearest
0.01mm on 36 female wasps from F. popenoei, each having recently emerged
from a different fig to ensure independence, then dried the wasps in 50C for
48 hours and weighed them to the nearest microgram. The length measure-
ments for each individual were significantly correlated with wasp dry weight
(Pearson correlations on log transformed data; weight vs thorax length: n
= 36, r = 0.70, p = 2.0E-6; weight vs head length: n = 36, r = 0.77, p =
2.7E-8; weight vs femur length: n = 36, r = 0.81, p = 2.4E-9; Fig S1).
Wasp dry weight (mg)
.10.09.08.07.06.05.04
Le
ng
th
 (m
m
)
.80
.70
.60
.50
.40
.30
Thorax
Head
Front femur
Page 1
Figure S1. The dry weight of female pollinator wasps of F. popenoei was
significantly correlated with front femur length, head length, and thorax
length.
2
To be able to predict wasp head length from wasp dry weight outside the
normal range for each species (a result of the P- treatment) we collected head
length and dry weight for 20 to 37 wasp individuals from each of five species
that vary in size (wasps from F. citrifolia, F. nymphaeifolia, F. obtusifolia,
F. popenoei and F. perforata; the latter included because its tiny wasps well
represent the range of size-reduced wasps for F. citrifolia). Together these
species covered the entire range of wasp sizes produced in the experiments.
There was a strong positive relationship between wasp dry weight and head
length: (linear regression on logged data: Log head length (mm) = 0.40(Log
dry weight (mg)) + 0.093; r2 = 0.93, t134 = 42.43, p = 3.5E-79.
1.2 The P- treatment does not affect foundress size
Another assumption important for this study is that producing foundresses
for the pollen-free treatment (opening the fig fruit before females have
emerged in order to remove the pollen) does not affect foundress size. To test
this we measured wasp front femur length, head length and thorax length
on 38 P- and 36 P+ wasps from F. popenoei, each having emerged from a
different fig fruit to ensure independence, then dried the wasps in 50C for 48
hours and measured their dry weight. There were no significant differences
in the dry weight or length measurements between P- and P+ experimental
wasps (t-tests; dry weight: t72 = 0.104, p = 0.92; front femur length t72 =
0.439, p = 0.66; head length: t72 = 1.33, p = 0.19; thorax length: t72 =
1.48, p = 0.14).
3

	



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a)# b)#
Figure S2. Diagram of the experimental setups A and B. Wasps were
subjected to either the pollen-free (P-) or pollen-carrying (P+) treatment
and transferred to vials. In experiment A, one foundress was introduced into
each experimental fig. In experiment B, two foundresses were introduced
into each experimental fig. The resulting offspring were collected when figs
had matured.
4
Table S1. Predictions of offspring size based on the four hypotheses
regarding the precision of sanctions. For example, under hypothesis 1A, the
mean offspring size in P-P+ figs would, averaged over many figs, not differ
between the P- and P+ lineages. Under the same hypothesis, P- offspring
in P-P+ figs would on average be larger than those in P-P- figs. Likewise,
P+ offspring in P-P+ figs would not differ in size from those in P+P+ figs.
Hypothesis Within P-P+ P- in P-P+ P+ in P-P+
1A Fig level; 1P+ sufficient P− = P+ > P − P− = P + P+
1B Fig level; pollen-dependent P− = P+ > P − P− < P + P+
2A Flower & nearby level P− < P+ > P − P− < P + P+
2B Flower level only P− < P+ = P − P− = P + P+
Table S2. Wasp mean dry weights (mg) from P+/P- experiments on
five different fig species; n denotes the number of figs. From each experi-
mental fig 10 wasp offspring (where available) were dried and weighed, and
the mean used in the t-tests.
Species; tree P+ weight (sem) n P- weight (sem) n t (df) p
F. cit; BCI17 0.0475 (0.00488) 10 0.0233 (0.00362) 3 -7.13 (11) < 0.001
F. max; BS1 0.0723 (0.00212) 7 0.0651 (0.00163) 5 -2.5 (10) 0.031
F. nym; BN67 0.0878 (0.00284) 15 0.0638 (0.00193) 23 -7.24 (36) < 0.001
F. nym; BS1 0.107 (0.00279) 15 0.0863 (0.00222) 11 -5.55 (24) < 0.001
F. obt; BN64 0.145 (0.00400) 10 0.114 (0.0125) 4 -3.14 (12) 0.008
F. obt; MIL 0.122 (0.00378) 19 0.0984 (0.00229) 32 -5.60 (49) < 0.001
F. pop; BV11 0.0468 (0.00154) 12 0.0462 (0.00113) 32 -0.29 (42) 0.77
F. pop; JG1 0.0409 (0.00530) 2 0.0375 (0.00146) 4 -0.87 (4) 0.43
Table S3. Details regarding the field-collected samples of wasp head
length.
Species crops (n) foundresses (n) emerging (n)
F. citrifolia 3 111 553
F. nymphaeifolia 2 121 605
F. obtusifolia 17 1178 5884
F. popenoei 3 179 894
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1.3 Additional information on how we link the size of female
offspring to fitness
1.3.1 Estimating P (F |hl)
We want to estimate the probability of a wasp of a given head length be-
coming a foundress. Denote this P (F |hl), where hl denotes the head length
of the wasp and F denotes that the wasp becomes a foundress. We have
field-collected data on the head length for emerging wasps, allowing us to
estimate the probability of an emerging wasp having a given head length
P (hl) (Fig. S3). We have data on the head length for wasps that become
foundresses, allowing us to estimate the probability of a foundress having a
given head length P (hl|F ) (Fig. S3). We have data on the baseline proba-
bility of a wasp becoming a foundress for each species P (F ). From this we
can use Bayes’ rule to calculate the desired quantity:
P (F |hl) = P (hl|F )P (F )
P (hl)
To implement this, we first estimate the probability densities P (hl|F )
and P (hl) using a kernel density estimator. Because the data was measured
in intervals of 0.01, we would prefer a density estimator appropriate to this
binning; we do not want our density estimator to fit the absence of data be-
tween measurement intervals. We considered using the estimator described
by Blower and Kelsall (2002). This density estimator is implemented in
the R package bda as the “smkde” estimator type in the bde function,
however the density estimate seemed to depend excessively on the random
seed that we used. Instead we used the generic function density in R,
with a bandwidth of 0.01 and the Gaussian kernel. We tried a variety of
other bandwidths and bandwidth selection methods; the results appeared
robust to them though the densities became much less smooth with smaller
bandwidths in a manner suggestive of them fitting noise more than signal.
After estimating the densities we then calculated P (F |hl).
To produce confidence intervals for P (F |hl) we employed a nonpara-
metric bootstrap: we repeatedly resampled from the data to produce boot-
strapped samples. Specifically we resampled a foundress sample from the
original foundress sample, of the same size as the original foundress sample;
we resampled an emerging sample from the original emerging sample, of the
same size as the original emerging sample. We then reestimated the densi-
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pop
0
10
20
0.25 0.30 0.35 0.40
obt
0
5
10
0.4 0.5 0.6
nym
0
10
20
30
40
0.35 0.40 0.45
b) 
c) 
a) 
Head%length%(mm)%
Pe
rc
en
t%o
f%w
as
ps
%in
%e
ac
h%
siz
e%
ca
te
go
ry
%
0
10
20
0.25 0.30 0.35 0.40
hl
de
ns
ity Wasp typeEmerging
Foundress
cit
0
10
20
30
0.20 0.25 0.30 0.35 0.40
d) 
Figure S3. Distribution of head lengths of field-collected foundresses and
emerging pollinator wasps associated with four fig species.
ties and P (F |hl) for each bootstrapped sample. We then plotted the lower
2.5% and upper 97.5% quantile of the estimates of P (F |hl) for each value
of head length (hl) (Fig. 3).
1.3.2 Calculating average P (F |hl) for P+ and P- offspring
We want to estimate the relative probability of becoming a foundress for P-
offspring compared to P+ offspring. Denote hl−i as the counterfactual head
length for any particular wasp i, if its mother had been a P- foundress instead
of a P+ foundress. We construct this counterfactual using the ratio of the
headlengths for the offspring emerging from unpollinated figs versus polli-
nated figs. For any particular wasp i, then, the relative probability of becom-
ing a foundress can be expressed as a function: g(P (F |hl−i ), P (F |hl+i )). We
use the ratio, so we define the relative fitness ( FRi as: P (F |hl−i )/P (F |hl+i ).
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We then want to calculate the average relative fitness FRi , averaged
across the distribution of head lengths observed for that species. To do so,
we impute a counterfactual head length for a wasp if its mother is a P-
foundress, hli, by multiplying its observed head length hl
+
i by the exper-
imentally estimated ratio of head lengths for the daughters of P- and P+
wasps. Often this imputed head length hli was outside the lower range of
the original data. Estimating P (F |hl) for values of hl outside of the range
of the original data is problematic since it would depend on how our density
estimators extrapolate. In some cases, such as in F. citrifolia the coun-
terfactual head length is far outside the lower range of the data. Rather
than rely on parametric extrapolation, we conservatively opted to estimate
a lower bound of the effect of being a daughter of a P- by rounding all
imputed hl−i up to the minimum head length observed in the P+ data,
where P (F |hl) is non-parametrically identified. Denote this conservative
imputed head length as hl−∗i . For each emerging wasp we then calculate
FRi = P (F |hl−∗i )/P (F |hl+i ). We then average this ratio across the sam-
ple of emerging wasps: FR =
∑
i FRi/N . Thus, we report a conservative
estimate of the average relative probability of becoming a foundress for P-
offspring compared to P+ offspring, assuming that the P- head lengths are
shifted by the experimentally estimated ratio for the P- offspring. In order
to estimate a confidence interval for FR we redo the above procedure using
each bootstrapped estimate of P (F |hl).
1.3.3 Hypothesis test of equal probability of becoming foundresses
of P- and P+ offspring
Finally, we formalize our comparison by conducting a hypothesis test of
the sharp null that P- offspring have the same probability of becoming
foundresses as P+ offspring because P- offspring have the same head length
distributions as P+ offspring. To conduct this we perform the above, taking
as our test statistic the above quantity: FR. We bootstrap observations
for both the emerging and foundress data from the combined emerging and
foundress head length data, which are assumed under the null to be from
the same distribution. Our alternative hypothesis is that P- offspring have a
lower probability of becoming foundresses than P+ offspring (i.e. FR < 1).
Our p-value is then estimated by the proportion of bootstrapped samples
that reveal an average ratio equal to or smaller than the observed ratio.
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2 References
Blower, G., & Kelsall, J. E. (2002). Nonlinear kernel density estimation for
binned data: convergence in entropy. Bernoulli. http://doi.org/10.2307/3318847.
Jande´r, K. C. and E. A. Herre (2010). Host sanctions and pollinator cheating
in the fig tree - fig wasp mutualism. Proceedings of the Royal Society of
London, B series 277: 1481-1488.
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