1
Table S1. Response and explanatory variables, statistical models, error distributions and link functions for testing the flowering of Lindera triloba
Question
Response variable
Analytical Statistical
level
model†
Did these parameters differ between sexes in each year?
Min. DBH among flowering
Genet
LM
ramets
No. of flowering ramets
Genet
GLM
No. of inflorescences per genet
Genet
GLM
No. of inflorescences per ramet
Ramet
GLM
Did these parameters differ between years in each sex?
Min. DBH among flowering ramets
Genet
No. of flowering ramets
Genet
No. of inflorescences per genet
Genet
No. of inflorescences per ramet
Ramet
LMM
GLMM
GLMM
GLMM
Explanatory variable
Random
Fixed‡
Error
distribution
Link
function
-
S
Gaussian
identity
-
S
S
S
Poisson
Poisson
Poisson
log
log
log
Year
Year
Year
Year
Gaussian
Poisson
Poisson
Poisson
identity
log
log
log
Genet
Genet
Genet
Genet
Did the flowering patterns differ with increasing genet development, and also affect differently by inter-annual environmental factors?
Min. DBH among flowering ramets
Genet
LMM
Genet
S, N, L and interactions
Gaussian
No. of flowering ramets
Genet
LMM
Genet
S, N, L and interactions
Gaussian
identity
identity
Did the sensitivities of the ramet flowering to extrinsic/intrinsic factors differ between sexes?
Flowering probability
Ramet
GLMM
Genet
No. of inflorescences per ramet
Ramet
GLMM
Genet
S, D, M, C, U and
interactions
S, D, M, C, U and
Binomial
logit
2
Negative-binomial
interactions
†LM; linear model, GLM; generalized linear model, LMM; linear mixed-effect model, GLMM; generalized linear mixed-effect model
log
3
‡Sex (S), focal ramet DBH (D), total number of ramets (N), main ramet DBH (M), crowding index of ramets (C) within genets, crowding index of
4
understorey neighbouring trees (U), hours of sunshine during July-August in the previous year (L); interactions were considered up to second-
5
order.
6
Table S2. Summary of the explanatory variables used in the generalised linear mixed-effect models explaining the flowering probability and the
7
number of inflorescences produced on individual ramets within Lindera triloba genets
All
Mean
Female
SD
Mean
Male
SD
Mean
No. of samples analysed†
Genet
239
78
161
Ramet
2015
594
1421
Explanatory variable
DBH of the focal ramet (D)
DBH of the main ramet within genets (M)
Crowding index of ramets within genets (C)
Crowding index of understorey neighbouring trees
(U)
1.71
4.32
5.59
1.83
1.89
6.86
199.99 122.99
1.59
4.27
5.07
1.71
1.96
6.00
205.20 143.01
1.76
4.38
5.89
SD
t-value P-value‡
1.87
1.84
7.05
1.91
0.41
1.03
0.07
0.68
0.31
195.84 113.19
0.54
0.59
8
9
† Only genets within a distance at least equal to the defined radius (12 m) from the plot edges were analysed, since genets close to the plot edges
10
had uncensused neighbouring trees outside the plot.
11
‡ Differences in the overall averages between sexes were evaluated by t-tests.
12
13
Table S3. Sets of candidate models (generalised linear mixed-effect models) explaining the flowering probability and the number of inflorescences
14
produced on individual ramets within Lindera triloba genets.
Response variable Rank
Flowering
1
probability
2
3
4
5
6
7
8
9
10
11
12
13
14
15
AIC
ΔAIC k
2647.81 0.000 14
2648.17 0.357 13
2648.23 0.422 15
2648.26 0.446 15
2648.40 0.590 14
2648.54 0.729 16
2649.12 1.302 15
2649.39 1.573 13
2649.48 1.664 16
2649.49 1.678 14
2649.53 1.717 15
2649.54 1.726 16
2649.64 1.824 15
2649.74 1.931 16
2649.76
1.944 17
Explanatory variable†
S + D + M + C + U + L + D:C + S:D + S:M + S:C + S:U + S:L
S + D + M + C + U + L + D:C + S:D + S:M + S:U + S:L
S + D + M + C + U + L + D:C + S:D + S:M + S:C + S:U + S:L + S:D:C
S + D + M + C + U + L + D:M + D:C + S:D + S:M + S:C + S:U + S:L
S + D + M + C + U + L + D:M + D:C + S:D + S:M + S:U + S:L
S + D + M + C + U + L + D:M + D:C + S:D + S:M + S:C + S:U + S:L + S:D:C
S + D + M + C + U + L + D:C + D:L + S:D + S:M + S:C + S:U + S:L
S + D + M + C + U + L + D:C + S:D + S:M + S:C + S:L
S + D + M + C + U + L + D:M + D:C + D:L + S:D + S:M + S:C + S:U + S:L
S + D + M + C + U + L + D:C + D:L + S:D + S:M + S:C + S:L
S + D + M + C + U + L + D:C + D:U + S:D + S:M + S:C + S:U + S:L
S + D + M + C + U + L + D:C + D:L + S:D + S:M + S:C + S:U + S:L + S:D:C
S + D + M + C + U + L + D:M + D:C + D:L + S:D + S:M + S:U + S:L
S + D + M + C + U + L + D:C + D:L + S:D + S:M + S:C + S:U + S:L + S:D:L
S + D + M + C + U + L + D:M + D:C + D:L + S:D + S:M + S:C + S:U + S:L +
S:D:L
15
Number of
1
16003.25 0.000 16
S + D + M + C + U + L + D:C + D:L + S:D + S:C + S:U + S:L + S:D:C + S:D:L
inflorescences
2
16004.14 0.883 15
S + D + M + C + U + L + D:C + D:L + S:D + S:C + S:L + S:D:C + S:D:L
The models are ranked by AIC (Akaike's Information Criteria); only models with ΔAIC (the difference in AIC score between the model considered
16
and the best one) ≤ 2 are denoted. The k indicates the numbers of parameters (including both fixed- and random-effect intercepts).
17
†As fixed-effect explanatory variables, sex (S), focal ramet DBH (D), main ramet DBH (M), crowding index of ramets within genets (C), crowding
18
index of understorey neighbouring trees (U), hours of sunshine during July-August in the previous year (L) and their interactions are considered.
Table. S4. Summary of the best models (generalized linear mixed-effect models) explaining
the flowering probability and the number of inflorescences produced on individual ramets
within Lindera triloba genets.
Explanatory
variables†
Flowering probability
χ2
12.42
731.62
2.14
2.37
11.21
12.89
37.07
P-value
< 0.01
< 0.01
0.03
0.15
< 0.01
< 0.01
< 0.01
No. of inflorescences
χ2
147.86
208.04
1596.82
14.74
9.09
2547.70
22.34
88.18
3.84
P-value
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
0.05
S
D
M
C
U
L
D:C
D:L
S:D
19.91
< 0.01
S:M
11.61
< 0.01
S:C
5.68
0.02
0.45
0.50
S:U
3.37
0.07
0.70
0.40
S:L
10.80
< 0.01
2259.58
< 0.01
S:D:C
19.25
< 0.01
S:D:L
20.43
< 0.01
To test the statistical significance of each variable, the changes in deviance when each variable
was removed from the best models were compared to χ2 distributions (d.f. = 1).
†As fixed-effect explanatory variables, sex (S), focal ramet DBH (D), main ramet DBH (M),
crowding index of ramets within genets (C), crowding index of understorey neighbouring trees
(U), hours of sunshine during July-August in the previous year (L) and their interactions (up to
second-order) are considered.