1
SUPPLEMENTARY MATERIAL
2
SUPPLEMENTARY NOTES
3
Supplementary Note 1: ML estimators and likelihood ratio tests.
4
ML estimators of mean proportion and standard error
5
In order to calculate the mean proportion of cystocarpic sires to cystocarps,
6
with its associated standard error, for each shore level, maximum likelihood
7
estimators were used as follows:
8
mi as the number of cystocarpic sires in the i-th family out of ni cystocarps in total
9
and p is the mean proportion of cystocarpic sires to cystocarps across families (i.e.,
10
11
females).
We assumed that the binomial function holds and estimated p using MLE as:
12
13
The variance of p, was then estimated using the inversed Hessian as:
14
15
where p was replaced with
16
variance.
Then, the standard error was calculated from the
17
18
19
20
Likelihood ratio test
Assuming a binomial model, the maximum log-likelihood was computed by
substituting
for p. The likelihood ratio, for each shore height, was computed as:
21
.
22
The likelihood ratio was computed as LR = -2lhigh + 2llow, which is approximately
23
chi-square distributed with k = 1 degrees of freedom.
24
Fitting a beta-binomial model
25
Young-Xu and Chan (2008) describe the beta-binomial model and its
26
application to the combination of binomial event rates across multiple studies as
27
ignoring overdispersion, or the presence of greater variability in a data set than
28
expected, when pooling data that are binomial in nature can lead to the erroneous
29
calculation of probabilities and confidence intervals.
30
overdispersion when pooling the 29 females used in this study, we followed the
31
method described by Roumagnac et al., (2004) and Sparks et al., (2008) using R,
32
ver. 3.03. (R Core Team 2014). For both the shore heights, there was unexplained
33
variation, possibly indicating overdispersion, or extra variation between females.
34
However, by comparing the binomial and beta-binomial models using a likelihood
35
ratio test as described above, there as no difference between the two models in the
36
high shore (χ2 = 0.180, df = 1, p > 0.860) or in the low shore (χ2 = 1.763, df = 1, p >
37
0.124). As the beta-binomial model did not provide a better fit for our data set, we
38
used the standard errors and maximum likelihood estimators assuming a binomial
39
distirubtion.
In order to test for
40
41
REFERENCES
42
R Core Team (2014). R: A language and environment for statistical computing. R
43
Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-
44
project.org/.
45
46
Roumagnac P, Pruvost O, Chiroleu F, Hughes G (2004). Spatial and temporal
47
analyses of bacterial blight of onion caused by Xanthomonas axonopodis pv. allii.
48
Phytopathology 94:138-146.
49
50
Sparks AH, Esker PD, Antony G, et al., (2008). Ecology and Epidemiology in R:
51
Spatial Analysis. The Plant Health Instructor. DOI:10.1094/PHI-A-2008-0129-03.
52
(http://www.apsnet.org/edcenter/advanced/topics/EcologyAndEpidemiologyInR/Spa
53
tialAnalysis/Pages/default.aspx)
54
55
Young-Xu Y, Chan KA (2008). Pooling overdispersed binomial data to estimate
56
event rate. BMC Medical Research Methodology 8:58.
57
58
59
60
61
62
63
64
65
66
Supplementary Note 2: Parentage assignments and indirect estimation of spermatial
67
dispersal in haploid-diploid red seaweeds.
68
Parentage analyses in haploid-diploid organisms do not share the same rich
69
literature and, consequently, multiple programs with which to perform parentage analyses as
70
is possible in diploid-dominant seed plants and animals. Red seaweeds, in particular, are
71
characterized by an alternation of free-living haploid and diploid stages, in which gametes
72
are produced mitotically by the gametophytes. In contrast, spores are produced meiotically
73
by the diploid tetrasporophytes. Thus, fertilization and meiosis are separated both in time
74
and space.
75
gametophytes. Moreover, with polymorphic markers, it is possible to identify the paternal
76
genotype without any ambiguity.
77
organism, such as mosses (see, for example, Szövényi et al., 2009). In contrast, diploid
78
male plants or animals contribute one, but not both alleles at any given locus.
The zygote is an exact genetic copy of both its maternal and paternal
This has also been shown in other haploid-diploid
79
Performing analyses matching genotypes, as we did in this manuscript using the
80
Multi-Locus Matches option as implemented in GenAlEx (Peakall and Smouse, 2006,
81
2012), is the most robust type of parentage assignment for red seaweeds, such as Chondrus
82
crispus. Applying existing programs, such as CERVUS (Kalinowski et al., 2007), would
83
result in uncertainty due to the violation of ploidy levels as well as assumptions one must
84
make at different stages of the analysis as implemented by certain programs. For example,
85
CERVUS requires diploid, codominant data. Simply artificially “diploidizing” haploids
86
would result in all female and male haploid genotypes turning into fixed homozygous
87
diploids. These individuals not only do not represent what is occurring on the shore in
88
natural populations, but also would clearly not be in Hardy-Weinberg Equilibrium.
89
CERVUS is one of the most popular programs for analyzing parentage. However,
90
there are certain assumptions made during simulations that do not fit our study system. The
91
program implements simulations of parentage analyses in order to assess the confidence of
92
real parentage assignments and are displayed as the natural log of the likelihood ratio. First,
93
we do not know the average number of candidate parents per offspring that were present.
94
As discussed in the main text of the manuscript, we sampled a 25 m2 area of the high shore
95
and low shore stand in which a frond was sampled every 25 cm, if present. As we sampled
96
only a single frond, we, thus, sampled only a single genet every 25 cm. As Chondrus
97
crispus forms a dense, almost mono-specific band within the intertidal zone and
98
morphological “holdfasts” can be mosaics of different genotypes and ploidies, we are not
99
currently able to estimate the average number of candidate parents per offspring from our
100
field observations. Indeed, this is one of the first detailed studies incorporating the male
101
component of C. crispus populations. Future studies will incorporate such data, where
102
possible, but understanding the average number of genets in this alga is much more difficult
103
than sampling a small forest of trees in which genets are discrete. Field ID of reproductive
104
state, let alone genets, is difficult to impossible without dislodging the frond. Finally, males
105
are likely reproductive weeks before cystocarps are sufficiently large enough to genotype
106
successfully. Our study is the only study, thus far, in this species addressing these questions
107
and will serve as a spring-board for future work and also how to sampled populations.
108
A second parameter calculated during the simulation of genotypes is the proportion
109
of loci mistyped.
110
genotype with a genotype selected at random under Hardy-Weinberg assumptions. Though
111
it is possible to simulate selfing and/or inbreeding, which is clearly occurring in Chondrus
112
crispus, the fixed homozygous state of each “diploidized” gametophyte would be in clear
113
violation of Hardy-Weinberg equilibrium. This raise the question of whether estimates of
114
error rate using these simulations would provide any realistic information to use in a
115
parentage assignment.
116
CERVUS defines a genotyping error as the replacement of a true
Nevertheless, we artificially diploidized each haploid genotype into a fixed
117
homozygote.
118
number of offspring set to 10,000 (as recommended by the program), the number of
We then performed simulations as implemented by CERVUS with the
119
candidate fathers to 557 (the total number of gametophytes sampled on the shore), the
120
proportion of candidate fathers sampled left to the default of 0.59, the proportion of loci
121
typed was set at 0.84 (this metric was calculated by CERVUS as we used the allele
122
frequency module to generate allele frequency data with our diploidized haploids added to
123
the cystocarpic data set) and the porportion of loci mistyped and error rate in likelihood
124
calculations set at 0.01. We, then, performed paternity analyses in which a male parent was
125
assigned to cystocarp by comparing the observed success of parentage assignment against
126
the success rate predicted by simulations.
127
Error rate analysis revealed estimated error rates of 0 across all loci, assuming all
128
known parent-offspring pairs are equally independent and detection probabilities ranging
129
from 0.72 to 0.93 (Table S2_1).
130
gametophyte C-8-122 in the high shore, as also found in our paternity analyses performed in
131
the main text of the manuscript. Four other putative sires were assigned paternity with
132
relaxed confidence (i.e., 20% false positive rate) in which there was mismatching at two
133
loci. Each putative sire was then checked for reproductive phenology and genotype in
134
comparison to each cystocarp sampled from each female. For the high shore female G-6-
135
306’s cystocarp “e,” a phenotypically male frond, A-10-62, was assigned relaxed paternity,
136
but mismatches occurred at two of the five loci. Similarly, the low shore female A-8-16’s
137
cystocarp “o” mismatched at two of the five loci with D-1-169, a phenotypically male frond.
138
Cystocarp “d” from the high female G-5-283 mismatched at one locus with B-3-90, a
139
vegetative frond. Finally, the low shore female A-9-18’s cystocarp “d” mismatched with a
140
low shore frond, A-9-61, at two loci out of four as this cystocarp was not genotyped at locus
141
Chc_04. First, A-9-61 was a reproductive female frond. Though, it is possible, due to high
142
inbreeding levels, that gametophytes could share the same genotype, the occurrence of
143
monoecious gamteophytes is uncertain, but also unlikely. There could, however, have been
144
a male gametophyte which shared the same MLG as A-9-61, but only 4 MLGs (each
145
repeated twice) were found out of a total sample of 586 gameotphytes sampled at the Port de
Four cystocarps were assigned to the vegetative
146
Bloscon. Second, and most importantly, A-9-61 mismatched at two of four loci. Even if
147
there was an identical male MLG, it could not be the putative sire. Thus, using CERVUS
148
resulted in the same results found using the MultiLocus matches option in GenAlEx.
149
Despite some violations during simulations, we obtained the same results using both
150
approaches.
151
differences between parents and offspring, the MultiLocus matches option is more
152
appropriate accompanied by estimates of genotyping error (such as included Krueger-
153
Hadfield et al., 2013, see in particular the discussion on the use of TANDEM allelic
154
binning as well as Matschiner and Salzburger, 2009).
However, for the present until a program can accommodate ploidy level
155
156
Table S2_1. Error rate analysis computed for the paternity analyses performed by CERVUS
157
for the sampled Chondrus crispus population sampled at the Port de Bloscon. Locus: locus
158
name; N compared: number of samples compared; N mismatching: the number of
159
individuals mismatching at each locus; Detection probability: the detection probability of
160
each locus and Error: the estimated error rate.
161
162
163
Locus
N compared
N mismatching
Detection probability
Error
Chc_04
369
0
0.7164
0
Chc_23
455
0
0.9274
0
Chc_24
455
0
0.8320
0
Chc_35
455
0
0.7912
0
Chc_40
441
0
0.8733
0
164
Part II. Indirect estimates of dispersal using existing software.
165
Existing software, such as KINDIST/TWOGENER analyses as implemented in
166
POLDISP (Robledo-Arnuncio et al., 2007), require diploid, co-dominant data. The only
167
way with which to perform such analyses for a haloid-diploid species would be to substitute
168
a dummy allele for each haploid female gametophyte that was not carried by any of the
169
cystocarps. Though this might not bias the analyses, it does not reflect the true nature of the
170
intertidal haploid-diploid populations. Female and male gametophytes are haploid and
171
tetrasporophytes are diploid. Fitting haploid-diploid data into programs, that require co-
172
dominant diploid data, is akin to fitting a square peg into a round hole.
173
Nevertheless, we estimated the distribution of pollen dispersal distances using
174
KINDSIT, the first procedure of POLDISP, and by artificially placing a dummy allele for
175
each female at each locus in order to “create” diploid female gametophytes. We found no
176
decrease in among-sibship correlated paternity with distance (Figure S2_1). In other words,
177
the spermatial pool spatial genetic structure may have been too weak to enable reliable
178
estimation of a dispersal function. This was unsurprising considering we did not find
179
evidence of strong spatial structure using spatial autocorrelation analyses as implemented in
180
SPAGEDI (Hardy and Vekemans, 2002) in a previous study (Krueger-Hadfield et al.,
181
2013). A future investigation sampling every frond from a given spatial scale (e.g., 10 cm2)
182
would enable the direct calculation of dispersal distances for a majority of sires based on the
183
levels of relatedness among females and cystocarpic sires. This would be the most accurate
184
metric as no programs currently exist to estimate dispersal curves in haploid-diploid
185
organisms.
186
187
188
189
Figure S2_1. A regression of among sib-ship correlated paternity, as calculated by
190
POLDISP (Robledo-Arnuncio et al., 2007), on the separation distance of the female
191
gametophytes. There was no decrease in among-sibship correlated paternity with distance
192
in a) the high shore (F1,34 = 1.31, p > 0.25) or b) the low shore (F1,169 = 0.42, p > 0.51).
193
a)
194
195
b)
196
197
REFERENCES
198
Hardy OJ, Vekemans X (2002). SPAGeDi: a versatile computer program to analyze
199
spatial genetic structure at the individual or population levels. Mol Ecol Notes 2:
200
618-620.
201
202
Kalinowski, ST, Taper, ML & Marshall, TC (2007). Revising how the computer
203
program CERVUS accommodates genotyping error increases success in paternity
204
assignment. Molecular Ecology 16: 1099-1006.
205
206
Krueger-Hadfield SA, Roze D, Mauger S, Valero M. (2013). Intergametophytic
207
sefling and microgeographic genetic structure shape populations of the intertidal red
208
seaweed Chondrus crispus (Rhodophyta). Mol. Ecol. 22: 3242-3260.
209
210
Matschiner, M. and W. Salzburger. 2009. TANDEM: integrating automated allele
211
binning into genetics and genomics workflows. Bioinformatics 25: 1982–1983.
212
213
Peakall R, Smouse PE (2006).
214
Population genetic software for teaching and research. Mol Ecol Notes 6: 288–295.
GENALEX 6.2: genetic analysis in Excel.
215
216
Peakall R, Smouse PE (2012). GenAlEx 6.5: genetic analysis in Excel. Population
217
genetic software for teaching and research-an update. Bioinformatics 28: 2537-2539.
218
219
Robledo-Arnuncio JJ, Austerlitz F, Smouse PE (2007).
220
package for indirect estimation of contemporary pollen dispersal. Mol Ecol Notes 7:
221
763-766.
POLDISP: a software
222
223
Szövényi P, Ricca M, Shaw AJ (2009).
224
inbreeding depression in a dioicous moss species. Heredity 103 : 394-403.
225
226
227
228
229
Multiple paternity and sporophytic
230
Supplementary Note 3: Kinship pair comparisons using permutation tests.
231
Four different types of comparison were analyzed using permutation tests
232
conducted by randomly re-sampling kinship coefficients between each group using
233
R, ver. 3.0.3 (R Core Team 2014). Permutation tests were repeated 10,000 times
234
and an empirical type I error rate was calculated for each of the four different
235
comparisons using Bonferroni correction (Sokal and Rohlf 1995).
236
The first comparison was made in order to investigate whether the reference
237
allele frequency used led to different kinship coefficients between the three kinship
238
pairs. The Ritland (1996) and Loiselle et al., (1995) estimators were calculated
239
using the entire shore (high and low 5 m grids combined) or the 5 m grid within each
240
tidal height as reference allele frequencies. There were no significant differences
241
between the reference allele frequencies used for each shore height (Table S3_1).
242
Second, the Ritland and Loiselle estimators were compared for each kinship
243
pair in order to evaluate the differences, if any, between both estimators. The
244
Ritland estimator gives more weight to rare alleles in the population and may,
245
therefore, yield different kinship coefficients as compared to the Loiselle estimator.
246
However, there were no significant differences between the two estimators for each
247
of the kinship pair comparisons after Bonferroni correction (Table S3_2).
248
Third, comparisons were made between different kinship pairs within each
249
shore level stand in order to investigate levels of relatedness between kinship pairs.
250
Female-male and male-male comparisons were not significantly different, indicating
251
that the two kinship coefficients were similar magnitudes. For both female-male and
252
male-male comparisons to male-maleallpop, there were significant differences in
253
which females were more related to their cystocarpic sires and males were more
254
related to the females that they fertilized than to other males in the population (i.e.,
255
males that fertilized carpogonia on other females; Table S3_3).
256
Finally, fourth, the levels of relatedness between each type of kinship pair
257
were contrasted between shore heights.
258
between the levels of relatedness between each kinship pair (Table S3_4). The
259
female-male and male-male comparisons were hypothesized to be more related to
260
each another than the same kinship pairs low on the shore. However, this was likely
261
due to the variable levels of relatedness found between female-male comparisons,
262
the sample disparity between shore heights (nhigh = 6, nlow = 16) and other
263
topographical factors influencing spermatial dispersal.
264
significantly higher levels of inbreeding in the high shore demonstrated by Krueger-
265
Hadfield et al., (2013), increased sampling accompanied with locating the
266
cystocarpic sires would likely reveal a pattern of increased relatedness with shore
267
height. This would likely be driven by the increased fragmentation of populations
268
with increasing tidal height and tidal induced gamete retention.
269
270
271
272
273
274
However, there were no differences
However, based on the
275
Supplementary Note 3, Table 1. Comparisons between reference allele frequencies
276
for the Ritland and Loiselle estimators. The kinship pair comparison column lists
277
the two kinship pairs compared; the shore height column refers to the high or low
278
shore sampling location; the p-values for each comparison are listed under the
279
columns Ritland_shore vs. Ritland_5m and Loiselle_shore and Loiselle_5m.
280
“Shore” refers to the reference allele frequencies sampled from the high and low
281
shore 5 m grids and “5m” corresponds to the reference allele frequencies used for
282
the respective shore height (i.e., high shore 5 m grid for the high shore comparison).
283
The adjusted significance level following Bonferroni correction was 7.5 x 10-4.
Kinship pair comparison
284
285
286
287
288
289
Shore height
Ritland_shore vs. Ritland_5m
Loiselle_shore vs. Loiselle_5m
Female-male vs. Male-male
High
0.3074
0.4281
Female-male vs. Male-male
Low
0.3624
0.4790
Female-male vs. Male-maleallpop
High
0.3083
0.4035
Female-male vs. Male-maleallpop
Low
0.3473
0.4860
Male-male vs. Male-maleallpop
High
0.0326
0.1008
Male-male vs. Male-maleallpop
Low
0.2178
0.4268
290
Supplementary Note 3, Table 2. Comparisons between the Ritland and Loiselle
291
estimators.
292
compared; the shore height column refers to the high or low shore sampling
293
location; the p-values for each comparison are listed under the columns
294
Ritland_shore vs. Loiselle_shore and Ritland_5m vs. Loiselle_5m. “Shore” refers to
295
the reference allele frequencies sampled from the high and low shore 5 m grids and
296
“5m” corresponds to the reference allele frequencies used for the respective shore
297
height (i.e., high shore 5 m grid for the high shore comparison). The adjusted
298
significance level following Bonferroni correction was 7.5 x 10-4.
The kinship pair comparison column lists the two kinship pairs
Kinship pair comparison
299
300
301
302
303
304
Shore height
Ritland_shore vs. Ritland_5m
Loiselle_shore vs. Loiselle_5m
Female-male vs. Male-male
High
0.4904
0.3381
Female-male vs. Male-male
Low
0.4398
0.2674
Female-male vs. Male-maleallpop
High
0.3440
0.4195
Female-male vs. Male-maleallpop
Low
0.2849
0.1269
Male-male vs. Male-maleallpop
High
0.4651
0.0014
Male-male vs. Male-maleallpop
Low
0.0974
0.0692
305
Supplementary Note 3, Table 3. Comparisons between the levels of relatedness
306
between kinship pairs using a) the Ritland_5m estimator and b) the Loiselle
307
estimator.
308
compared; the p-values for each comparison are listed under the columns high
309
(referring to the pairs compared within the high shore stand) and low (referring to
310
the pairs compared in the low shore stand).
311
following Bonferroni correction was 0.003.
312
a)
The kinship pair comparison column lists the two kinship pairs
Kinship pair comparison
The adjusted significance level
High
Low
0.172
0.029
Female-male vs. Male-maleallpop
< 0.001
< 0.001
Male-male vs. Male-maleallpop
< 0.001
< 0.001
High
Low
Female-male vs. Male-male
0.1046
0.004
Female-male vs. Male-maleallpop
< 0.001
< 0.001
Male-male vs. Male-maleallpop
< 0.001
< 0.001
Female-male vs. Male-male
313
314
b)
Kinship pair comparison
315
316
317
318
Supplementary Note 3, Table 4. Comparisons between the levels of relatedness of
319
the three kinship pairs between tidal heights using a) the Ritland_5m estimator and
320
b) the Loiselle_5m estimator. The kinship pair comparison column lists the kinship
321
pair; the p-values for each comparison are listed under the columns high vs. low.
322
The adjusted significance level following Bonferroni correction was 0.017.
323
a)
Kinship pair comparison
324
High vs. low
Female-male
0.3772
Male-male
0.4775
Male-maleallpop
0.2876
b)
Kinship pair comparison
High vs. low
Female-male
0.4943
Male-male
0.4780
Male-maleallpop
0.4399
325
326
REFERENCES
327
Krueger-Hadfield SA, Roze D, Mauger S, Valero M (2013). Intergametophytic
328
sefling and microgeographic genetic structure shape populations of the intertidal red
329
seaweed Chondrus crispus (Rhodophyta). Mol. Ecol. 22: 3242-3260.
330
331
Loiselle BA, Sork VL, Nason J, Graham C (1995). Spatial genetic structure of a
332
tropical understory shrub, Psychotria officinalis (Rubiaceae). Am J Bot. 82: 1420–
333
1425.
334
335
R Core Team (2014). R: A language and environment for statistical computing. R
336
Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-
337
project.org/.
338
339
Ritland K (1996). Estimators for pairwise relatedness and individual inbreeding
340
coefficients. Genet Res. 67: 175-185.
341
342
Sokal RR, Rohlf FJ (1995). Biometry: the principles and practice of statistics in
343
biological research. 3rd ed. W. H. Freeman and Co., New York.
344
345
346
347
348
349
350
351
SUPPLEMENTARY FIGURE LEGENDS
352
Figure 1. a) The location of the females from which cystocarps were genotyped in
353
order to determine paternity in the high and the low 5 m grids. Next to each female
354
code is the kinship coefficient, if calculated, of Loiselle et al., (1995) as calculated
355
using the allele frequencies from the respective shore height 5 m grids. The only
356
sire that was identified from sampled fronds was located 25 cm from the female that
357
it fertilized. An * denotes the male frond which fertilized the female located 25 cm
358
away, C-9-123. b) The location of the females within the 5 m x 5 m grids in relation
359
to all the other sampled fronds in both the high and low shore stands.
360
361
Figure 2. The line represents the number of unique genotypes over the total number
362
of genotypes for all the samples of tetrasporophytes and gametophytes from the 5 m
363
grids by sequentially adding each locus starting with the most polymorphic one (n =
364
8). Individuals missing data at one or more loci were removed prior to analysis.
365
The most polymorphic loci were Chc_04, Chc_23, Chc_24, Chc_35 and Chc_40 and
366
distinguished all individuals fronds. These five loci were used to genotype the
367
cystocarps.
368
369
370
371
372
373
FIGURES
374
Figure 1.
375
376
377
378
379
380
Figure 2.