Supporting information for
Linking structure and function in food webs: maximization of different ecological
functions generates distinct food-web structures
Authors: Yen J.D.L., Cabral R.B., Cantor M., Hatton I., Kortsch S., Patrício J. &
Yamamichi M.
Table S1. List of binary food web datasets used to test maximization hypotheses
Ecosystem
Name
Richness
Connectance
Marine
Reference
Benguela
29
0.241
Field et al. (1991),
Yodzis (1998, 2000)
Marine
Barents Sea
244
0.027
Planque et al. (2014)
Marine
Large reef
247
0.054
Optiz (1996)
Marine
Southern Ocean
586
0.012
Raymond et al. (2011)
Marine
Small reef
50
0.222
Opitz (1996)
Freshwater
Akatore A
85
0.031
Thompson & Townsend
(2004)
Freshwater
Akatore B
58
0.035
Thompson & Townsend
(2004)
Freshwater
Berwick
79
0.038
Thompson & Townsend
(2004)
Freshwater
Black Rock
87
0.05
Thompson & Townsend
(2004)
Freshwater
Broad
95
0.063
Thompson & Townsend
(2004)
Freshwater
Canton
109
0.06
Thompson & Townsend
(2004)
Freshwater
Catlins
49
0.046
Thompson & Townsend
(2004)
Freshwater
Coweeta 17
71
0.029
Thompson & Townsend
(2004)
Freshwater
Coweeta 1
58
0.037
Thompson & Townsend
(2004)
Freshwater
Dempsters Au
86
0.056
Thompson & Townsend
(2004)
Freshwater
Dempsters Sp
97
0.057
Thompson & Townsend
(2004)
Freshwater
Dempsters Su
107
0.084
Thompson & Townsend
(2004)
Freshwater
German
86
0.048
Thompson & Townsend
(2004)
Freshwater
Healy
96
0.069
Thompson & Townsend
(2004)
Freshwater
Kyeburn
98
0.065
Thompson & Townsend
(2004)
Freshwater
Little Kyeburn
78
0.062
Thompson & Townsend
(2004)
Freshwater
Martins
105
0.031
Thompson & Townsend
(2004)
Freshwater
Narrowdale
71
0.031
Thompson & Townsend
(2004)
Freshwater
North Col
78
0.04
Thompson & Townsend
(2004)
Freshwater
Powder
78
0.044
Thompson & Townsend
(2004)
Freshwater
Stony
113
0.065
Thompson & Townsend
(2004)
Freshwater
Sutton Au
83
0.049
Thompson & Townsend
(2004)
Freshwater
Sutton Sp
79
0.063
Thompson & Townsend
(2004)
Freshwater
Sutton Su
92
0.05
Thompson & Townsend
(2004)
Freshwater
Troy
78
0.03
Thompson & Townsend
(2004)
Freshwater
Venlaw
69
0.039
Thompson & Townsend
(2004)
Estuary
Ythan estuary
91
0.05
Cohen et al. (2009)
Freshwater
Tuesday lake
51
0.093
Jonsson et al. (2005)
Salt marsh
Carpinteria salt
marsh
83
0.072
Lafferty et al. (2006)
Estuary/salt
marsh
Chesapeake bay
36
0.093
Baird & Ulanowicz
(1989)
Estuary/salt
marsh
St. Mark's
48
0.095
Christian & Luczkovich
(1999)
Estuary/salt
marsh
Mangrove estuary
94
0.152
Heymans et al. (2002)
Freshwater
Alford lake
56
0.07
Havens (1992)
Freshwater
Balsam lake
53
0.065
Havens (1992)
Freshwater
Beaver lake
61
0.088
Havens (1992)
Freshwater
Bridge brook lake
75
0.098
Havens (1992)
Freshwater
Chub pond
65
0.099
Havens (1992)
Freshwater
Connery lake
30
0.067
Havens (1992)
Freshwater
Hoel lake
49
0.106
Havens (1992)
Freshwater
Long lake
65
0.098
Havens (1992)
Freshwater
Stink lake
53
0.1
Havens (1992)
Freshwater
Little rock lake
176
0.065
Havens (1992)
Freshwater
Sierra lakes
37
0.218
Harper-Smith et al.
(2005)
Freshwater
Skipwith pond
35
0.309
Warren (1989)
Marine
Mondego Zostera
meadows
47
0.126
Patricio & Marques
(2006)
Marine
Lough hyne
350
0.042
Jacob (unpublished data)
Marine
Chile food web
106
0.128
Navarette & Wieters
(unpublished data)
Marine
NE US shelf
81
0.226
Link (2002)
Marine
Weddell sea
492
0.067
Brose et al. (2006a,b),
Jacob (2005)
Freshwater
Bere stream
137
0.068
Woodward et al. (2008)
Freshwater
Broadstone
stream
34
0.191
Woodward et al. (2005)
Freshwater
Alamitos creek
162
0.143
Harrison (2003)
Freshwater
Caldero creek
126
0.133
Harrison (2003)
Freshwater
Corde Matre
creek
106
0.156
Harrison (2003)
Freshwater
Coyote
190
0.127
Harrison (2003)
Freshwater
Guadeloupe creek
174
0.154
Harrison (2003)
Freshwater
Guadeloupe river
136
0.134
Harrison (2003)
Freshwater
Los Gatos creek
177
0.143
Harrison (2003)
Freshwater
Los Trancos creek
129
0.147
Harrison (2003)
Freshwater
San Francisquito
creek
140
0.167
Harrison (2003)
Freshwater
Saratoga creek
158
0.15
Harrison (2003)
Freshwater
Steverson creek
170
0.165
Harrison (2003)
Freshwater
Blackrock
82
0.052
Harrison (2003)
Freshwater
Broad 2
34
0.191
Townsend et al. (1998)
Freshwater
Ross
117
0.148
Townsend et al. (1998)
Freshwater
Penetetia creek
170
0.14
Harrison (2003)
Terrestrial
Grand Caricaie CI
C1
166
0.075
Cattin Blandenier (2004)
Terrestrial
Coachella
27
0.313
Polis (1991)
Terrestrial
EcoWeb 59
30
0.072
Cohen (1989)
Terrestrial
EcoWeb 60
33
0.062
Cohen (1989)
Terrestrial
El Verde
156
0.062
Waide & Reagan (1996)
Terrestrial
Grand Caricaie
Sn C2
152
0.066
Cattin Blandenier (2004)
Terrestrial
St Martin
44
0.113
Goldwasser &
Roughgarden (1993)
Terrestrial
Grand Caricaie
Cm C1
202
0.072
Cattin Blandenier (2004)
Terrestrial
Grand Caricaie
Cm M2
118
0.072
Cattin Blandenier (2004)
Terrestrial
Simberloff_E1
48
0.104
Simberloff & Abele
(1975)
Terrestrial
Simberloff_E2
63
0.087
Simberloff & Abele
(1975)
Terrestrial
Simberloff_E3
49
0.101
Simberloff & Abele
(1975)
Terrestrial
Simberloff_E7
52
0.094
Simberloff & Abele
(1975)
Terrestrial
Simberloff_E9
71
0.088
Simberloff & Abele
(1975)
Terrestrial
Simberloff_ST2
63
0.087
Simberloff & Abele
(1975)
Table S2. List of weighted food web datasets used to test maximization hypotheses
Ecosystem
Name
Richness
Connectance
Brackish
river
Reference
Rhode river
20
0.133
Correll
(unpublished)
Brackish
river
St Marks
54
0.122
Baird et al.
(1998)
Coastal
lagoon
Maspalomas
24
0.142
Almunia et al.
(1999)
Estuary
Chesapeake
upper
37
0.15
Hagy (2002)
Estuary
Chesapeake
39
0.116
Baird &
Ulanowicz
(1989)
Estuary
Chesapeake
lower
37
0.121
Hagy (2002)
Estuary
Chesapeake
middle
37
0.148
Hagy (2002)
Estuary
California
estuaries
128
0.053
Hechinger et al.
(2011)
Estuary
Mondego
46
0.189
Baeta et al.
(2011)
Estuary
Narragansett
35
0.18
Monaco &
Ulanowicz
(1997)
Freshwater
lake
Lake Michigan
39
0.145
Krause (2004)
Coastal bay
Florida Bay dry
season
128
0.13
Christian &
Luczkovich
(1999)
Coastal bay
Florida Bay wet
season
128
0.129
Christian &
Luczkovich
(1999)
Freshwater
marsh
Everglades
69
0.192
Ulanowicz et
al. (2000)
Freshwater
marsh
Graminoid dry
69
0.192
Christian &
Luczkovich
(1999)
Freshwater
marsh
Graminoid wet
69
0.192
Christian &
Luczkovich
(1999)
10
Freshwater
swamp
Cypress dry
71
0.127
Christian &
Luczkovich
(1999)
Freshwater
swamp
Cypress wet
71
0.125
Christian &
Luczkovich
(1999)
Mangrove
Mangroves dry
97
0.158
Christian &
Luczkovich
(1999)
Mangrove
Mangroves wet
97
0.159
Christian &
Luczkovich
(1999)
Marsh
creek
Crystal control
24
0.217
Ulanowicz
(1986)
Marsh
creek,
elevated
water
temperature
Crystal
disturbed
24
0.174
Ulanowicz
(1986)
Robustness
1.0
1.0
Robustness
Weighted throughput
Throughput
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
1
5
50
500
1
Iteration
5
50
Iteration
Empirical
food web
Simulated
food webs
Iteration
1
Iteration
10
Iteration
100
Iteration
2000
500
Figure S1. Illustration of food-web development through 2000 iterations of the genetic
algorithm. The real food web is the Coachella terrestrial food web (S = 27; C = 0.31). The
example shows maximum-throughput and maximum-robustness food webs with the same S
and C as the Coachella food web. The ‘fitness’ of the simulated food webs is shown over the
2000 iterations of the genetic algorithm, with fitness values scaled to lie between zero and
one. The vertical height of a node is determined by its trophic level.
Fig. S2. Local (left column) and global (right column) metrics comparing real food webs and
20
food webs simulated with maximum throughput. metric (y-axis) is the difference between
simulated and real food webs for a given metric (real food web is the zero line,  values are
based on an average of 20 food webs). Grey shading is the null model range around the fitted
food web (mean distance of null food-web models from the real food webs – projected
symmetrically). Freshwater (open circles), estuarine (closed squares), marine (closed
triangle), and terrestrial (closed circles) food webs are shown.
Fig. S3. Local (left column) and global (right column) metrics comparing real food webs and
food webs simulated with maximum robustness. metric (y-axis) is the difference between
30
simulated and real food webs for a given metric (real food web is the zero line,  values are
based on an average of 20 food webs). Grey shading is the null model range around the fitted
food web (mean distance of null food-web models from the real food webs – projected
symmetrically). Freshwater (open circles), estuarine (closed squares), marine (closed
triangle), and terrestrial (closed circles) food webs are shown.
Fig S4. Weighted variants of local metrics comparing real weighted food webs to maximumthroughput (left column) and maximum-robustness (right column) food webs. metric (y-axis)
is the difference between simulated and real food webs for a given metric (real food web is
the zero line,  values are based on an average of 20 food webs). Grey shading is the null
40
model range around the fitted food web (mean distance of null food-web models from the real
food webs – projected symmetrically).
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