ELECTRONIC SUPPLEMENTARY MATERIAL
Estimation of male selection gradients using the Spatially Explicit Mating Model
We considered that each offspring resulted either from self-pollination (with probability s), from
pollen flow from outside the investigated area (with probability m), or from pollen from a
sampled sire (with probability 1-m-s). This allowed us to construct a maximum log-likelihood
function in order to estimate the vector F = (1, 1, 2, 2, …, n, n) containing the selection
gradient coefficients for the n phenotypic traits, along with the parameters (a, b) of the dispersal
kernel (see equation (1)), the selfing rate (s), and the pollen immigration rate (m), as






O


log La, b, F, s, m   log sT g o g jo , g jo  1  s  m  jok a, b, F T g o g jo , g k  mT g o g jo , AF 
o1
kM


(3)
where o was a given offspring, O the total number of offspring, jo the mother of offspring o, k a


given sire, and M the set of all genotyped sires. T g O g jO , X was the Mendelian segregation
probability (e.g. Meagher 1986) of the offspring genotype (go) given the genotype of the mother
( g jO ) and X. X corresponded to the genotype of the mother in case of selfing, to the genotype of
the considered sire (gk) in case of outcrossing with a sampled sire, or to the allelic frequencies in
the pollen cloud external to the neighbourhood (AF) in case of outcrossing with a non-sampled
sire. The external allelic frequencies (AF) were computed from the inferred paternal gametes of
offspring finding no compatible sire within the study site. jk(a, b, F) was the expected
proportion of the pollen of sire k in the local pollen cloud of mother j for a given set of dispersal
parameters (a, b) and levels of selection gradients (F), computed as
 jk (a, b, F) 
 k p jk
 p
l M
l
,
(4)
jl
where pjk corresponded to the probability for a pollen grain to disperse from sire k to mother j
given their relative spatial position, according to the dispersal kernel (with parameters a and b)
described in equation (1), and Φk corresponds to the fecundity of sire k computed from its
phenotypic values (zk1, zk2, …, zkn) for each trait and the values for the selection gradient
coefficients F = (1, 1, 2, 2, …, n, n) as
n
ln(  k )   ln( fi ( zki )) ,
(5)
i 1
where fi(zki) is the multiplicative male fecundity component associated with trait i, as computed
with equation (2).
This method assumed that the father of each offspring was drawn at random according to the
jk’s, i.e. that fertilization events were independent (no joint dispersal of pollen grains). It also
assumed that the pollen of each sampled sire dispersed according to the same dispersal kernel
given by eq. (1). The model was modified from the mating model presented in Oddou-Muratorio
et al. (2005), to allow inclusion of continuous phenotypic values instead of discrete phenotypic
classes.
Table S1. Variation in the phenotypic and reproductive traits measured for 92 plants in the
Petunia axillaris population (except seeds/fruit, which was measured for 39 plants).
Trait
% CV a
max
Plant size
2
309
20 ± 40
204
Floral display size
8
2063
140 ± 312
222
Corolla area (cm2) b
7.31
30.62
20.53 ± 3.94
19.20
Corolla tube length (cm) b
2.77
4.52
3.85 ± 0.34
8.89
1
30
10.36 ± 4.52
43.65
Nectar concentration (% Brix) b
18.14
56.94
35.26 ± 6.27
17.79
Pollen number p/anther (x 103) b
101
249
182 ± 34
19
Pollen size (µm) b
19.5
30.2
26.0 ± 2.7
10.5
36
1313
497 ± 323
65
Seeds/fruit
b
Mean ± sd
min
Nectar volume (µl) b
a
Range
% CV: coefficient of variation.
For traits measured repeatedly within individuals, values were calculated from individual means .
Table S2. Repeatabilities for the phenotypic traits measured in Petunia axillaris for which
several measures were taken in each individual.
Trait
Corolla area b
Corolla tube length b
Nectar volume b
Nectar concentration b
Number of pollen grains per anther
Pollen size b
c
Ra
0.395
0.656
0.181
0.083
0.119
0.240
95 % CI a
0.283 - 0.482
0.568 - 0.727
0.096 - 0.269
0.006 - 0.168
0 - 0.285
0.056 - 0.424
Pa
<0.001
<0.001
<0.001
0.009
0.048
0.001
a
Repeatability (R), 95% confidence intervals (CI), and P-values estimated as described in Nakagawa and Schielzeth
(2010), using the rptR package for R (R Core Team 2014) developed by the same authors.
b
For Gaussian-distributed traits we fitted Linear Mixed-effects Models (LMM) with Restricted Maximum
Likelihood (REML).
c
For count data we calculated repeatability based on Generalized Linear Mixed-effects Models (GLMM), where a
Poisson multiplicative overdispersion model with a square-root link function was fitted by Penalized QuasiLikelihood (PQL).
Fig. S1. Location of the Petunia axillaris population sampled in the South coast of Uruguay (34°
52’ 41.8’’ S, 55° 08’ 28.4’’ W). The population is indicated by a black circle.
Fig. S2. Spatial locations of the individuals in the sampled plot. The plants highlighted with
black filled circles in a) are the potential sires for which phenotypic selection was measured, and
in b) are the maternal plants.
Fig. S3. Procedure used to map Petunia axillaris plants in a two-dimensional coordinates system.
We first constructed a rectangular plot using four woody posts (indicated here as posts 1 to 4).
To ensure that the sides of the rectangular plot were orthogonal, we held one measuring tape
straight in the alignment of post 1, and measured a distance of 10m on each side. We thus
obtained two points (A and B) that were located on a straight line and at the same distance from
the post. We placed the tips (0m and 40m) of a second measuring tape (indicated by a dashed
line) at points A and B to form a triangle, which base was the first measuring tape (bold line).
We tightened the two measuring tapes and placed a post (post 3) where the second measuring
tape indicated a distance of 20m (e.g. half the length of the measuring tape; Figure S3a). We
repeated this procedure to place two more posts in order to form the rectangle (Figure S3a). We
attached two measuring tapes, each to two different posts, to form two parallel graduated lines on
the longer sides of the rectangle (indicated by the bold lines in Figure S3b). We chose the origin
of the first measuring tape as the origin for all the recorded coordinates (indicated in the figure
by a filled circle). We vertically held a level at the centre of a plant and aligned a third measuring
tape to it so that it would cross the two parallel measuring tapes at the same distance from their
origins (Figure S3b). We recorded the x-coordinate of the plant (indicated as an square in Figures
S3b and S3c) as the distance between the first fixed measuring tape and the level (indicated by
the third measuring tape) and the y-coordinate as the distance between the origin of the first fixed
measuring tape and the point where it crossed the third measuring tape (indicated by the first
measuring tape). We could easily and rapidly measure the coordinates of all the plants present in
the plot by repeatedly moving the level to the position of the other plants and aligning the third
measuring tape to it.
Several plants were outside the defined rectangular plot. When these plants were close enough of
the plot, we extended the third measuring tape to reach each plant and proceeded as previously
(Figure S3c). When the plants were too far to proceed in this way, we prolonged one of the sides
of the plot and built another rectangular plot as described previously. We chose a new origin at a
corner of each new built plot and measured its distance to the origin of the first built plot. This
enabled us to calculate the coordinates of each plant according to a unique origin (i.e. the origin
defined in the first plot, indicated here by the filled circle).
Fig. S4. Estimation of corolla area. The picture on the left was obtained by placing the flower in
a “photobox” which kept the angle and distance constant from a digital camera. The area was
estimated from these pictures using image analysis (Abramoff et al. 2004) on binary-transformed
pictures (image on the right).
Fig. S5. Definition of corolla tube length, which is indicated by the white arrow. This
corresponds to distances D1+D2 as defined in Stuurman et al. (2004).
Fig S6. Significant effects of a) floral display size, b) corolla area, c) corolla tube length and d)
nectar concentration on the relative male fecundity of Petunia axillaris individuals as estimated
with equation (2) from Materials and Methods. The curves were drawn using the estimated
significant coefficients (Table 3); the Y axis is in log scale. The dotted lines indicate the mean
population values.
References (for the Electronic Supplementary Material section)
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Meagher TR (1986) Analysis of paternity within a natural population of Chamaelirium luteum. I.
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Oddou-Muratorio S, Klein EK, Austerlitz F (2005) Pollen flow in the wildservice tree, Sorbus
torminalis (L.) Crantz. II. Pollen dispersal and heterogeneity in mating success inferred
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R Core Team (2014) R: A language and environment for statistical computing. R Foundation for
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Stuurman J, Hoballah ME, Broger L, Moore J, Basten C, Kuhlemeier C (2004) Dissection of
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