Jordán, F. 2001. Ecosystem flow networks and community control. In:
Villacampa, Y., Brebbia, C. A. and Usó, J.-L. (eds.), Ecosystems and Sustainable
Development III, WIT Press, Southampton, pp. 771-780.
Ecosystem flow networks and community
control
F. Jordán
Collegium Budapest, Institute for Advanced Study, Hungary
Abstract
It is not easy to construct the food web graph of a community: both points and
links are strongly questionable. Although recently described modern food webs
are finely resoluted (have many points), two serious problems still remain. First,
these are generally binary webs: links give no information on the importance of
interactions (the number of large weighted webs is small). Second, their
properties are very sensitive to methodology (i.e. data collection and aggregation
procedure). Thus, high resolution in itself cannot guarantee reality. It is suggested
that the mostly valuable conclusions on community organisation can be drawn by
comparing weighted webs depicting the same community under different
conditions. In this case, the comparison of similarly described webs may partly
diminish methodical problems.
Seasonal trophic flow networks of the Chesapeake Bay ecosystem are
compared and differences are discussed from the viewpoint of community
control. Changes in the functional importance of trophic links and the structural
importance of trophic components are analysed. The main conclusion is that
trophic control in the Bay community seems to be the strongest during winter.
1 Introduction
Classical food web collections [1, 2] were criticised (e.g. Paine [3]) and recently,
following methodical consensus [4], the number of modern webs is increasing
(see one of the best: Martinez [5]). However, until we understand the problems of
aggregation much better (see Solow and Beet [6]) and can estimate the level of
redundancy in ecological systems more exactly [7], these webs are not trivially
much better. Besides the careful determination of trophic components, two other
problems appear. First, these are generally binary webs but information on the
quality of links (e.g. flux magnitude [8], interaction strength [9]) would be
extremely important for understanding community organisation [8]. Second, even
if both points and links of the food web graph are described with large efforts,
web properties still remain very sensitive to methodology. One possibility to
diminish methodical problems is to compare webs describing the same
community under different conditions. For example, both binary [10] and
weighted [11] webs presenting temporal variation in trophic interactions are
available. If similarly produced (i.e. described and aggregated) webs are
compared, some of the methodical biases and artefacts will surely disappear. It is
the change of food web structure what may shed a new light on community
control. Thus, it is suggested that staring at a set of comparable webs can be more
useful than staring at single, however highly resoluted webs (see Lawton [12]).
The scarcity of data obviously limits statistical analyses of pairs (e.g.
stressed/control, Ulanowicz [13]) or larger sets (e.g. four seasons, Baird and
Ulanowicz [11]) of webs, and this is especially true for quantitatively weighted
trophic networks. Nevertheless, as the number of weighted and well aggregated
modern webs increases, our picture will be improved. In this paper, I present an
analysis of one of the available comparable sets of weighted trophic flow
networks. My aim is to explain the changes of food web structure from the
viewpoint of community control [14].
2 Methods and results
The Chesapeake Bay is one of the best studied coastal regions of North America.
Baird and Ulanowicz [11] published the seasonal carbon flow network diagrams,
based on data on the mesohaline community of the Bay.
29
25
WINTER
28
26
29
30
SPRING
32
28
26
19
23
33
24
9
21
31
17
27
13
18
22
15
16
19
23
9
21
17
13
8
12
18
22
15
16
11
8
12
11
14
14
7
7
6
3
6
3
5
2
5
34
2
1
34
4
1
4
29
30
25
SUMMER
32
28
33
31
27
10
19
23
20
33
31
13
15
FALL
32
28
26
27
17
18
25
24
9
21
22
29
30
26
19
23
9
21
17
13
16
22
18
15
16
8
12
8
12
11
11
14
14
7
7
6
3
6
3
5
5
2
2
34
34
1
4
1
4
Figure 1: Seasonal carbon flow networks of the Bay.
Table 1. Seasonal magnitudes of carbon flows for each source/sink pair (after Baird & Ulanowicz [11]).
from
to
floww
flowsp
flowsu
flowf
from
to
floww
flowsp
flowsu
flowf
from
to
floww
flowsp
flowsu
flowf
1
2
34
5
1
2
6
1
2
7
2
7
8
8
9
1
2
7
1
2
7
1
2
7
3
2
3
5
6
7
7
7
8
8
8
9
9
9
10
10
11
11
11
12
12
12
13
13
13
14
15300
67140
12600
6300
1210
50
2520
5092
4280
1328
525
525
1050
145
95
10
57
37
4
337
220
23
29895
29440
86799
50416
25208
0
0
6067
23920
31665
2162
692
691
1348
174
114
12
680
445
47
1795
1176
124
49545
23920
60536
95680
47840
26956
22724
19320
5667
5667
2834
1265
1265
2530
1159
552
3550
2325
245
1288
844
88
1834
1202
126
50400
43680
74438
18746
9373
3549
0
3731
2460
2460
1231
975
956
1914
330
217
23
250
163
17
449
294
31
31918
3
3
3
4
3
3
11
12
15
16
18
8
8
1
2
8
1
2
8
8
14
15
18
12
14
15
16
17
17
18
19
19
19
19
19
19
20
21
22
22
22
23
23
23
24
25
25
25
26
26
3667
4880
1120
560
3485
75
24
9
20
196
43
4,4
12
14
65
1,8
0
3,2
0,7
0,2
0,1
0
8
7410
16805
12350
6175
4059
270
84
34
68
702
152
17,4
55
63
300
7
41
90
3,9
2
13
9330
28000
17333
8667
3360
940
300
120
160
2560
540
4,9
1,9
117
136
652
8
46
102
1,3
4,5
1,3
0,2
5
25
4800
7980
5366
2684
3252
415
130
52
104
1080
232
2
93
108
517
4
24
53
2
0,6
0
2
13
15
18
14
15
16
22
14
15
22
14
15
18
22
23
27
22
18
22
23
31
19
21
22
23
1
26
26
27
27
27
27
28
28
28
29
29
29
30
30
30
31
32
32
32
32
33
33
33
33
34
2
2
3
8
1
3,8
0,6
1,1
12083
3
3
2
7
24
1,5
68
34
11
75
11
21
0,8
0,7
3
7,4
0,4
6,9
3,7
1
1,1
0,1
7
4,4
18630
6
6
265
76
26
11
0
13
1,6
54
8
15
1
1
4
30
0,4
4,6
3,7
2,8
1,3
0,1
8,1
5
26956
3
3
49
14
5
2
0
9
1
20
3
6
0,9
0,9
3,2
54
0,1
0,8
0,6
0,5
0
0
2,1
1,2
16585
The original diagrams written in energy language [15] are redrawn as
conventional food webs, where consumers are always in higher position (Figure
1). For simplicity, undirected links are shown: arrowheads would always point at
higher points. Detrital cycling links and the original source components "energy
and nutrients" and "exogenous input" are excluded from this analysis (explained
below). Thus, only producers, consumers and storages are considered.
2.1 Flow data and important links
Links are characterised by the magnitude of carbon flux from prey to consumer
(expressed in mg C/m2 per season). Table 1 contains seasonal flow data
(published in [11]; w = winter; sp = springtime; su = summer; f = fall). Seasonal
carbon flows between each pair of prey (so=source) and consumer (si=sink) can
be ranked according to the ratio of that flow in the "carbon menu" of the
consumer in question [16]. For example, sink #25 gets carbon from sources #14,
#15, and #18 in winter. Based on feeding ratios, in the menu of consumer #25,
they are ranked in this order. It will be assumed that the magnitude of fluxes
characterise, in some sense, the importance of trophic links.
Table 2. Components of the trophic flow network (after Baird & Ulanowicz [9]).
1. phytoplankton
2. suspended bacteria
3. sediment bacteria
4. benthic diatoms
5. free bacteria
6. heteromicroflagellatae
7. microzooplankton
8. zooplankton
9. ctenophore
10. sea nettle
11. other suspension feeders
12. Mya
13. oysters
14. other polychaetes
15. Nereis
16. Macoma spp.
17. meiofauna
18. crustacean deposit feeders
19. blue crab
20. fish larvae
21. alewife and blue herring
22. bay anchovy
23. menhaden
24. shad
25. croaker
26. hog choker
27. spot
28. white perch
29. catfish
30. blue fish
31. weak fish
32. summer flounder
33. striped bass
34. dissolved organic carbon
2.2 Keystone indices and important points
The names of the 34 major trophic components of the Bay are given in Table 2.
Points representing these groups can be characterised by their position in the flow
network. A traditional measure of network position is "status" (with
"contrastatus" and "net status", all introduced by Harary [17, 18]). I have slightly
modified these measures and introduced "keystone index" [19], which is
ecologically more reasonable. Considering a simple species deletion model
(similar to Pimm [20]), we may calculate, on purely topological grounds, how
many species will be secondarily extinct, following the removal of the xth species:
extinction is caused by the disconnection of network flows.
Whereas carbon flows are strictly directed in the trophic network, population
dynamical effects spread in both bottom-up and top-down directions [21], and in
both direct and indirect ways [22, 23]: this calls for considering undirected edges
if community control is to be analysed.
Table 3. Seasonal keystone indices of components.
COMP
KW
KSP
KSU
KF
COMP
KW
KSP
KSU
KF
1
23,5
28,5
31,5
28,5
18
1,36
1,23
1,57
1,19
2
14,11
15,36
18,34
15,77
19
6,13
4,71
4,62
4,42
3
8,97
9,14
9,95
9,81
20
-
-
0,3
-
4
0,5
0,5
0,5
0,5
21
0,53
0,67
0,55
0,52
5
3,29
6,5
3,81
4,11
22
1,11
3,43
3,46
3,94
6
3,29
6,5
3,81
4,11
23
0,64
1,51
1,37
1,85
7
5,9
6,5
7,46
6,22
24
-
0,42
0,3
-
8
3,4
5,53
7,27
4,51
25
0,83
-
0,73
0,5
9
1,54
1,38
1,79
1,51
26
0,83
1,88
1,78
1,84
10
-
-
2,59
-
27
-
1,74
1,67
1,72
11
1,29
1,3
1,31
1,26
28
2,32
0,82
0,45
0,49
12
1,29
1,55
1,56
1,51
29
0,83
0,83
0,73
0,79
13
1,12
1,09
1,1
1,09
30
-
3,25
3,11
3,27
14
1,52
1,44
1,44
1,61
31
-
0,53
0,44
0,55
15
1,69
1,65
2,15
2,27
32
-
2,42
2,2
2,48
16
0,36
0,73
0,73
0,69
33
-
7,72
7,44
0,89
17
1,19
1,19
1,19
1,19
34
3,29
6,5
3,81
4,11
Table 4. Seasonal congruency values (C) for non-specialist consumers.
consumer
Cw
Csp
Csu
Cf
7
8
9
10
11
12
13
17
19
22
23
25
26
27
28
29
30
32
33
33 %
100 %
17 %
100 %
100 %
100 %
100 %
53 %
0%
33 %
66 %
75 %
100 %
33 %
-
17 %
66 %
17 %
100 %
100 %
100 %
100 %
33 %
0%
0%
50 %
17 %
0%
33 %
66 %
83 %
66 %
100 %
83 %
17 %
100 %
100 %
100 %
100 %
100 %
47 %
0%
0%
33 %
42 %
33 %
66 %
0%
50 %
66 %
66 %
33 %
83 %
17 %
100 %
100 %
100 %
100 %
33 %
0%
0%
66 %
58 %
33 %
66 %
33 %
17 %
83 %
58 %
average
65 %
50 %
58 %
54%
The bottom-up keystone index (Kb) of species x measures how many species
extinctions will follow the deletion of the xth species, caused by the disconnection
of flows from the bottom up:
K b  c 1
n
1
1

K bc .
dc dc
(1)
Here, n is the number of species x's predators, dc is the number of preys eaten by
its cth predator, and Kbc is the bottom-up keystone index of its cth predator. Kb has
to be calculated first for higher points in the web. The top-down keystone index
(Kt) can be calculated similarly with the web upside down. Thus, this index
measures how many species will go extinct, following the removal of species x,
caused by the disconnection of the flows from the top down. In the simplest case,
K  Kb  Kt .
(2)
The possibility of weighting, according to the relative importance of bottom-up
and top-down forces, is open (e.g. mKb + nKt). The overall keystone index (K)
reflects the positional importance of a point in maintaining any kinds of network
flows. This index, although simple and represents only a certain aspect of
"species importance", can give a quantitative prediction of keystones (which is a
major task in community ecology, see [24, 25]). The seasonal keystone indices of
each component are given in Table 3.
2.3 Congruency analysis
The question is how important points are related to important links. In other
words, if we analyse the prey choice of a non-specialist consumer, how large
carbon intakes do belong to positionally important preys. Because we are
interested in bi-directional effects mediated by trophic interactions, and detrital
links can well be considered as unidirectional (detritus pool affects mostly
detritivores but rarely feeds back directly to higher-level organisms), cycling
links and source components ("energy and nutrients" and "exogenous input")
given in [11] have not been taken into account.
Since being in a key position means both to be a main energy gate [26] and to
have far-reaching top-down effects [27], it is suggested here that if large flows fit
well to positionally important network points, trophic control can be considered
stronger. Large nutrient flows give also a strong top-down control ability to main
gates. The congruency between important flows (Table 1) and important positions
(Table 3) predicts the strength of trophic community control (versus nontrophic
control, i.e. mutualism, interference competition, etc.).
Congruency values calculated by a combinatorial stepwise method and
expressed in percents are shown at Table 4. The method can be illustrated with
the following example. In springtime, component #32 intakes carbon from
components #18, #22, #23, and #31 (see Figure 1). The magnitudes of carbon
flows are 0.4, 6.9, 3.7, and 1, respectively (Table 1). The corresponding prey
ranking is #22 - #23 - #31 - #18. The springtime overall keystone indices (Ksp) are
3.43, 1.51, 0.53, and 1.23, respectively (Table 3). These can be ranked as #22 #23 - #18 - #31. Perfect congruency (100%) with the previous rank would be
identical to that, while the worst congruency (0%) would correspond to the
reversed rank order (#18 - #31 - #23 - #22). These can be transformed into each
other in six or more steps (where each step means the exchange of two
neighbours in the sequence). Thus, each sequence can be characterised by
percentage values according to six steps (0%, 17%, 34%, 50%, 67%, 84%, and
100%; the minimal number of steps, of course, depends on the length of a
sequence). The rank based on positional keystone indices (#22 - #23 - #18 - #31)
corresponds to a 83% level congruency with the rank of flows (#22 - #23 - #31 #18).
Congruency values averaged for each season inform about the dynamics of
prey choice and seasonal variation in the significance of trophic community
control. It has to be emphasised that if a biological system as complex as an
ecosystem is characterised by a single index, much information is lost.
Nevertheless, higher level phenomena may be revealed only by this way [28,29].
3 Discussion
The seasonal dynamics of the Chesapeake Bay ecosystem comprise both
dynamical and structural changes in the trophic flow network of carbon.
Structural changes involve the presence/absence of both trophic components
(component #24 is not present during winter) and trophic links (component #33
eats component #19 only in summer and springtime). Dynamical changes involve
both seasonally different magnitudes of carbon flows (component #7 gains carbon
mainly from component #1 in summer but from component #6 in winter) and
changes in the relative positional importance of network points (component #7 is
in more important position in summer than in other seasons). The relationship
between important links and important points also changes: larger carbon flows
come mainly from positionally more important preys during winter, and from
positionally less important preys, for example, in springtime.
A single macroscopic community index (average congruency) was used to
express the nature of community-level regulation. Seasonal values of this index
inform about community control dynamics during the year. In conclusion, winter
is the season when trophic control is the most powerful.
It is unavoidable to list three main shortcomings of the analysis presented.
First, as a theoretical study, it is sensitive to the quality of data (published in
[11]). Even if this weighted trophic flow network is one of the best available food
webs, the quality of data can always be criticised. Second, material flows were
represented by only a single element (carbon). There are attempts to take other
elements into account [30] but the carbon data base is the richest up to date.
Third, conclusions are not general because results have no statistical value: a
single community was analysed. It is questionable how these results (65% versus
50%) are significant but, as far as I think, statistical analyses could only be
evaluated if we knew much more about constraints and limits on food web
organisation. The same difference tells different stories depending on the
realisable range of a particular community index.
An approach and a method have been suggested to reveal some aspects of
community control. Even if an excellent data base is needed for performing this
kind of analysis, the predictive power of quantitative approaches may be helpful.
As a number of community-level patterns change systematically during
ecosystem development [31], community indices may help in understanding the
properties of, for example, strongly perturbed ecosystems [32]. Ecosystem studies
focusing on the (changing) relationships between functional components and
interactions between them strongly emphasise the necessity and importance of the
network perspective in ecology [33].
Acknowledgements
I thank István Molnár and Professor Gábor Vida for continuous help and
discussions, Professors Robert E. Ulanowicz and Stuart L. Pimm for comments
on earlier work, and Professor Eörs Szathmáry for a fruitful stay in Collegium
Budapest. Viktor Müller is kindly acknowledged for checking English. My work
was supported by a grant of the Hungarian Scientific Research Fund (OTKA F
029800) and the Bolyai Award of the Hungarian Academy of Sciences.
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