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Electronic Supplementary Material
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Seed dispersal patterns in a temperate forest during a mast event: performance of alternative
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dispersal kernels
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Isabel Martínez1, Fernando González-Taboada2
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1
UFZ Helmholtz Centre for Environmental Research - UFZ, Department of Ecological Modelling, D-04318 Leipzig,
Germany
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Área de Ecología, Departamento de Biología de Organismos y Sistemas, Universidad de Oviedo, C/ Catedrático Rodrigo
Uría s/n, ES-33071 Spain
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Author for correspondence
E-mail: isamcano@gmail.com
Telephone: +49 341235 1723
Fax: + 49 341235 3500
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Table S1 (next pages) Estimated parameters for the five models (see Table 1) fitted to the seed
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dispersed densities of each species during the non-mast and beech mast years. Values for each species
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are presented in separate tables. For each parameter, 90% Credible Intervals are presented along with
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the median value. γ is the allometric exponent, βi is the fecundity parameter for year i, and σ and τ are
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the variance parameters on residuals and in random effects in fecundity, respectively. Si and Li are the
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shape and scale parameters of the dispersal kernel estimated for each year i. For the mixture kernel, Si
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and Li refer to the parameters of the Weibull component, while Lexp,i is the estimated parameter of the
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exponential, and pi represents the contribution of the Weibull. r is the Pearson correlation coefficient
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obtained from the correlation between observed and predicted seed density values. dm indicates the
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median seed displacement distance in meters. Finally, the mean deviance (Dmean), the deviance on
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mean parameters (D (θmean)), the effective number of parameters (pD), and the Deviance Information
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Criterion (DIC) to detail the model selection procedures; lower DIC values indicate that a model
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provides a more parsimonious explanation of the data. Differences in DIC of around 10 between
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models indicate clear evidence to reject the alternative model (that with a greater value).
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Table S1 (Corylus)
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Corylus
Kernel
4
5
2Dt
Exponential
Lognormal
Mixture
Weibull
α1
1.90
(1.12,2.94)
-3.68
(-4.89,-2.15)
1.08
(-1.40,3.45)
4.19
(2.32,5.79)
-1.09
(-3.01,0.10)
α2
-1.17
(-1.73,-0.53)
-5.14
(-6.31,-3.67)
17.8
(14.3,20.5)
2.54
(0.48,4.42)
-1.51
(-3.70,-0.47)
γ
2.03
(1.82,2.23)
3.10
(2.41,3.61)
0.77
(-0.27,1.83)
1.80
(1.07,2.46)
2.49
(2.00,3.45)
L1
1.032
(0.580,3.109)
1.687
(1.491,2.838)
0.796
(0.535,1.472)
597.0
(329.6,889.2)
0.393
(0.065,0.753)
L2
1018.7
(102.1,1823.4)
9.51
(0.87,29.67)
1872.7
(1527.9,1987.7)
22.55
(2.46,372.64)
3.20 (0.46,26.31)
S1
0.0233
(0.0103,0.0306)
0.6069
(0.2928,1.1389)
5.2935
(1.3978,9.5289)
0.3760
(0.2656,0.5702)
S2
6.4549
(2.0391,9.6355)
0.5760
(0.5260,0.6075)
2.4496
(0.2695,9.2068)
0.4862
(0.4302,0.5768)
p1
0.977
(0.974,0.988)
Lexp,1
0.281
(0.070,0.971)
p2
2.04
(1.37,2.74)
Lexp, 2
179.9
(2.6,892.5)
σ
0.0018
(0.0015,0.0021)
0.0024
(0.0021,0.0028)
0.0006
(0.0005,0.0007)
0.0012
(0.0010,0.0014)
0.0019
(0.0016,0.0024)
τ
0.0386
(0.0134,0.1781)
0.0581
(0.0203,0.2808)
0.0106
(0.0037,0.0517)
0.0243
(0.0086,0.1116)
0.0431
(0.0148,0.2024)
r
0.51
(0.39,0.65)
0.53
(0.39,0.62)
0.16
(0.01,0.45)
0.44
(0.31,0.61)
0.41
(0.06,0.59)
Dmean
781.9
827.6
971.3
771.8
790.3
D(θmean)
772.1
817.4
965.1
841.7
831.4
pD
9.8
10.2
6.2
-70.0
-41.1
DIC
791.7
837.8
977.5
701.9
749.2
d1
348.2
(190.7,414.7)
3.6
(1.6,6.8)
1.0
(0.0,3.1)
420.4
(220.4,724.1)
13.5
(5.1,1105.2)
d2
11.9 (5.3,19.7)
19.3345
(1.6403,60.3884)
2194.2
(1766.0,2355.2)
312.0
(177.2,1290.3)
101.6
(10.8,481.2)
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Table S1 (Crataegus)
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Crataegus
Kernel
4
5
6
2Dt
Exponential
Lognormal
Mixture
Weibull
α1
-7.15
(-9.15,-5.26)
-7.71
(-8.77,-6.58)
-10.2
(-11.3,-9.0)
-7.35
(-8.44,-4.47)
-5.39
(-6.36,-4.31)
α2
-8.10
(-10.0,-6.68)
-8.01
(-9.39,-6.93)
-12.00
(-13.18,-10.75)
-8.17
(-9.17,-5.21)
-5.80
(-6.68,-4.88)
γ
5.88
(5.35,6.49)
5.87
(5.42,6.28)
6.58
(6.15,7.01)
5.79
(4.82,6.16)
5.12
(4.73,5.41)
L1
1792.8
(1259.8,1984.4)
42.48
(34.09,52.19)
48.31
(40.45,54.85)
68.97
(63.03,74.58)
68.24
(61.05,74.36)
L2
1847.2
(1201.7,1988.0)
39.93
(30.04,52.96)
18.81
(18.43,19.30)
64.61
(55.45,72.34)
65.16
(54.98,72.45)
S1
0.1899
(0.0895,0.4105)
0.5925
(0.5428,0.6471)
4.3608
(2.9764,6.0745)
4.4188
(2.9504,6.4362)
S2
0.4989
(0.1856,0.8470)
0.1133
(0.1006,0.1290)
4.5511
(2.7615,7.1102)
4.2916
(2.7334,6.6622)
p1
0.847
(0.543,0.996)
Lexp,1
0.962
(0.936,0.986)
p2
436.7
(54.8,943.9)
Lexp, 2
0.14
(0.12,0.30)
σ
0.0073
(0.0057,0.0093)
0.0074
(0.0059,0.0094)
0.0078
(0.0063,0.0098)
0.0074
(0.0059,0.0095)
0.0073
(0.0058,0.0093)
τ
0.1076
(0.0373,0.5071)
0.1131
(0.0383,0.5374)
0.1206
(0.0419,0.5656)
0.1149
(0.0388,0.5595)
0.1083
(0.0376,0.5170)
r
0.52
(0.50,0.53)
0.51
(0.50,0.52)
0.60
(0.57,0.61)
0.53
(0.48,0.57)
0.54
(0.52,0.54)
Dmean
2005.5
2007.6
1918.4
1883.6
1952.0
D(θmean)
2011.3
1996.0
1908.4
1886.5
1946.4
pD
-5.7
11.6
10.0
-2.9
5.5
DIC
1999.8
2019.2
1928.4
1880.7
1957.4
d1
775.2
(321.7,879.1)
84.6
(66.0,107.3)
57.3
(44.5,70.0)
133.7
(46.5,581.4)
46.5
(36.0,58.0)
d2
222.2
(85.9,769.6)
79.6
(58.3,107.8)
18.5
(8.1,31.5)
42.6
(31.7,54.4)
44.6
(33.7,57.2)
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Table S1 (Fagus)
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Fagus
Kernel
4
5
6
2Dt
Exponential
Lognormal
Mixture
Weibull
α1
3.85
(2.44,4.71)
6.00
(3.85,8.55)
4.05
(2.62,5.75)
6.86
(3.04,9.24)
2.27
(0.91,4.54)
α2
9.26
(7.60,10.46)
8.06
(5.04,9.65)
8.56 (6.65,9.94)
9.15
(6.89,11.00)
7.90
(6.43,9.96)
γ
0.10
(-0.25,0.62)
0.46
(-0.07,1.30)
0.30
(-0.15,0.89)
0.16
(-0.42,0.81)
0.54
(-0.14,0.96)
L1
50.38
(4.17,932.62)
78.56
(32.88,149.07)
8.76
(3.82,22.19)
203.8
(20.7,1749.9)
2.26
(1.23,6.10)
L2
2.26
(1.72,3.03)
1.61
(1.30,2.04)
2.76
(2.06,3.36)
19.89
(9.29,21.72)
0.208
(0.120,0.292)
S1
6.3340
(1.1548,9.6688)
1.4344
(0.3665,2.0068)
5.4211
(0.95649,9.5334)
2.2310
(0.9350,8.8848)
S2
0.4772
(0.4014,0.5840)
0.9717
(0.8277,1.0957)
9.6116
(1.6243,9.9691)
0.4833
(0.4390,0.5201)
p1
0.668
(0.058,0.972)
Lexp,1
0.540
(0.452,0.618)
p2
84.5
(9.8,847.6)
Lexp, 2
0.79
(0.68,0.95)
σ
0.0051
(0.0041,0.0064)
0.0045
(0.0035,0.0057)
0.0050
(0.0040,0.0063)
0.0045
(0.0035,0.0059)
0.0051
(0.0041,0.0064)
τ
0.0679
(0.0237,0.3191)
0.0594
(0.0209,0.2766)
0.0664
(0.0228,0.3270)
0.0603
(0.0207,0.3049)
0.0679
(0.0237,0.3213)
r
0.75
(0.71,0.79)
0.72
(0.65,0.77)
0.75
(0.70,0.78)
0.74
(0.67,0.78)
0.73
(0.67,0.78)
Dmean
6829.5
7476.2
7009.3
6780.7
7051.1
D(θmean)
6672.9
7262.9
6843.0
6689.0
6918.8
pD
156.6
213.4
166.3
91.7
132.2
DIC
6986.1
7689.6
7175.5
6872.5
7183.3
d1
3.2
(0.6,12.2)
155.8
(64.2,301.8)
23.7
(7.4,99.0)
169.1
(24.9,742.1)
2.1
(0.2,5.7)
d2
15.4
(7.1,29.0)
3.1
(1.4,5.4)
4.3
(2.3,6.8)
6.7
(3.0,11.0)
4.8
(2.9,7.0)
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Table S1 (Ilex)
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Ilex
Kernel
2Dt
Exponential
Lognormal
Mixture
Weibull
α1
3.56
(2.38,4.65)
3.14
(2.25,4.26)
3.11
(2.25,4.47)
3.97
(2.73,5.04)
3.05
(2.07,4.18)
α2
6.27
(4.83,7.50)
4.92
(4.12,6.06)
4.95
(3.82,5.95)
5.45
(4.46,6.79)
4.70
(3.65,5.82)
γ
1.79
(1.37,2.28)
1.86
(1.46,2.21)
1.87
(1.48,2.26)
1.66
(1.20,2.07)
1.95
(1.55,2.34)
L1
5.73
(3.70,9.97)
3.85
(2.02,5.75)
11.70
(7.32,34.14)
19.63
(11.76,160.34)
0.054
(0.019,0.133)
L2
2.66
(1.42,5.36)
3.61
(2.87,4.28)
8.78
(7.16,10.20)
2.04
(1.80,2.56)
0.506
(0.175,0.875)
S1
0.2430
(0.1337,0.4128)
1.4670
(1.2445,1.8627)
6.4894
(1.1604,9.6007)
0.3279
(0.2815,0.3666)
S2
0.0424
(0.0170,0.2407)
1.2364
(1.1520,1.3326)
5.2724
(2.4370,9.5476)
0.4766
(0.3900,0.5530)
p1
0.788
(0.590,0.866)
Lexp,1
0.165
(0.116,0.239)
1.20
(0.81,2.38)
p2
7.0
(6.0,8.0)
Lexp, 2
4
5
6
σ
0.0038
(0.0030,0.0051)
0.0041
(0.0032,0.0053)
0.0041
(0.0032,0.0053)
0.0040
(0.0032,0.0053)
0.0041
(0.0032,0.0053)
τ
0.0518
(0.0182,0.2525)
0.0576
(0.0197,0.2708)
0.0571
(0.0197,0.2645)
0.0559
(0.0195,0.2611)
0.0574
(0.0201,0.2727)
r
0.51
(0.49,0.54)
0.51
(0.49,0.53)
0.51
(0.49,0.53)
0.52
(0.50,0.55)
0.51
(0.49,0.53)
Dmean
13509.4
13943.4
13615.0
13380.0
13648.0
D(θmean)
13428.3
13777.1
13463.7
13189.5
13472.9
pD
81.1
166.3
151.3
190.5
175.0
DIC
13590.5
14109.7
13766.4
13570.5
13823.0
d1
167.5
(38.7,435.7)
7.4
(3.4,12.5)
32.2
(16.1,172.1)
13.1
(6.8,94.0)
25.6
(12.9,46.8)
d2
433.2
(169.0,523.3)
7.0
(4.2,10.5)
18.6
(13.2,24.4)
11.8
(8.4,15.9)
13.3
(8.8,18.5)
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Table S1 (Taxus)
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Taxus
Kernel
2Dt
Exponential
Lognormal
Mixture
Weibull
α1
11.58
(9.68,13.63)
10.04
(8.16,12.41)
9.72
(7.49,12.26)
9.66
(7.41,12.34)
9.71
(7.66,12.15)
α2
14.06
(11.67,16.30)
9.51
(7.61,11.97)
10.49
(8.17,12.82)
9.38
(7.39,12.15)
8.91
(6.74,11.48)
γ
-0.22
(-0.84,0.33)
-0.12
(-0.84,0.44)
0.14
(-0.57,0.81)
0.06
(-0.81,0.69)
0.12
(-0.61,0.72)
L1
7.57
(5.03,11.59)
4.86
(3.70,7.22)
57.96
(22.07,135.04)
0.067
(0.044,0.438)
0.012
(0.006,0.021)
L2
4.99
(3.20,9.56)
4.81
(3.69,6.68)
1279.3
(157.9,1966.1)
0.0064
(0.0015,0.0202)
1.28
(0.86,1.68)
S1
0.0623
(0.0191,0.1409)
1.8303
(1.4757,2.1042)
0.3108
(0.2948,0.4196)
0.2593
(0.2492,0.2686)
S2
0.0022
(0.0007,0.0057)
2.6481
(2.1694,2.8651)
0.2385
(0.2114,0.2722)
2.2589
(1.5227,9.2869)
p1
0.718
(0.287,0.970)
Lexp,1
0.04013
(0.029,0.070)
p2
64.8
(12.1,819.6)
14.0
(8.5,44.2)
Lexp, 2
4
5
6
σ
0.0278
(0.0186,0.0431)
0.0305
(0.0207,0.0462)
0.0290
(0.0196,0.0445)
0.0301
(0.0203,0.0460)
0.0299
(0.0202,0.0456)
τ
0.1811
(0.0598,0.8675)
0.2102
(0.0691,1.0319)
0.1967
(0.0654,0.9328)
0.2064
(0.0685,1.0041)
0.2032
(0.0677,0.9837)
r
0.62
(0.52,0.70)
0.57
(0.47,0.64)
0.61
(0.52,0.69)
0.60
(0.50,0.68)
0.61
(0.52,0.69)
Dmean
2897.3
3164.3
2839.8
2877.6
2840.6
D(θmean)
2771.8
3028.2
2808.8
2795.4
2770.2
pD
125.5
136.1
31.0
82.3
70.4
DIC
3022.7
3300.5
2870.8
2960.0
2911.0
d1
518.1
(314.6,563.4)
9.7
(5.8,15.5)
264.0
(66.8,593.7)
41.1
(19.7,63.9)
73.7
(34.5,422.0)
d2
47.7
(15.2,115.4)
9.7
(5.9,15.0)
1370.1
(689.6,1510.4)
92.7
(36.4,198.0)
27.1
(15.8,87.7)
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Fig. S1 Histograms showing the distance distribution between the seed quadrats and the adult trees of
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each tree species within the study stand. Note the different y-axis scale among tree species.
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5
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