Journal of Marine Systems 27 Ž2001. 289–300
www.elsevier.nlrlocaterjmarsys
Seasonal changes in the positional importance of components in
the trophic flow network of the Chesapeake Bay
Ferenc Jordan
´ )
Department of Genetics, EotÕos
krt. 4 r A, Budapest H-1088, Hungary
¨ ¨ UniÕersity, Muzeum
´
Received 10 December 1999; accepted 3 August 2000
Abstract
Community-level processes may shape food web structure. In this paper, a graph theoretical study of the weighted trophic
flow network of the Chesapeake Bay ecosystem shows how important are positions in the energy Žcarbon. transport system.
The positional importance of components is compared to the quantity of energy flowing through them. We suggest that the
congruence between important network positions and large flows refers to the larger role of trophic interactions in
community control. A seasonal dynamical analysis of the network has led us to the conclusion that winter is the season when
the importance of predation is the highest. q 2001 Elsevier Science B.V. All rights reserved.
Keywords: keystone species; energy flow network; seasonal community dynamics; Chesapeake Bay
1. Introduction
Although ecologists were always strongly interested in species interactions, it is not yet easy to
analyze whole networks of ecological interactions
quantitatively. This is true also for food webs depicting trophic links, even if the most data are available
here. The identification of points and edges in food
web graphs ŽCohen, 1978; Pimm, 1982; Briand,
1983; Pimm et al., 1991. was always heavily debated
ŽPaine, 1988; Polis, 1991; Cohen et al., 1993.. To
estimate the quality of edges Žimportance, strength,
energy flow. seems to be even much more difficult
)
Tel.: q36-1-266-1296; fax: q36-1-266-2694.
E-mail address: [email protected] ŽF. Jordan
´ ..
ŽPaine, 1980.. However, it would be extremely important ŽPlatt et al., 1981; Ulanowicz, 1986a. for
connecting dynamics to structure. We have only a
few experimental data for interaction strength ŽPaine,
1992., and not too many food webs with links
weighted by energy flows Že.g., Crystal River,
Ulanowicz, 1983; Chesapeake Bay, Baird and
Ulanowicz, 1989..
In this paper, my aims are to analyze seasonal
changes in pattern and process represented in a
weighted carbon flow network, and discuss the possible significance of these changes in community
control. I apply a simple graph theoretical method
ŽHarary, 1961; Jordan
´ et al., 1999; Jordan,
´ 2000. to
analyze the importance of trophic positions in energy
flow networks. Then, I compare the importance of
positions to the magnitude of energy flowing through
0924-7963r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 4 - 7 9 6 3 Ž 0 0 . 0 0 0 7 4 - 9
290
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
them, in each season. Results lead to conclusions
about changes in seasonal community regulation.
This connection of pattern to process may contribute
to understanding community organization ŽPolis and
Winemiller, 1996..
2. Trophic dynamics
Since Lindeman’s seminal paper ŽLindeman,
1942., the trophic–dynamic view of ecosystems was
always one of the few ones being able to help us in
looking at whole ecological systems. Mapping the
routes of energy through trophic components as well
as characterizing sources and sinks in energy flow
networks are macroscopic ecological investigations
ŽUlanowicz, 1986a, 1988, 1989; Ulanowicz and
Wolff, 1991; Odum, 1994.. Macroscopic views may
lead to a novel kind of conclusions, for example,
detecting stressed ecosystems by analyzing their system-level properties ŽUlanowicz, 1986b, 1996.. Here,
a macroscopic approach to the seasonal dynamics in
community control is presented.
3. Methods
3.1. Weighted energy flow networks
Carbon flows between major components of the
mesohaline Chesapeake Bay ecosystem had been
estimated and a weighted energy flow network was
published by Baird and Ulanowicz Ž1989.. The rate
of carbon exchanges was measured for each season
Žin mg Crm2 .. These data provide information about
changes in species composition, changes in the pattern of interactions, and, in general, trophic dynamics of the ecosystem. The cumulative trophic flow
network for the whole year ŽFig. 1., the subweb for
winter ŽFig. 2., spring ŽFig. 3., summer ŽFig. 4., and
fall ŽFig. 5., as well as the list of trophic components
ŽAppendix A. are given. The identification of components corresponds to that given in the paper cited
above.
The seasonal flows characterizing sourcersink
transports are shown in Table 1. Here, flow ratio
means the proportion of a given flow in the whole
menu of the consumer in question Žlike at Levine,
1980.. Thus, the sum of ratios characterizing flows
Fig. 1. The cumulative food web of the Chesapeake Bay ecosystem. Numbered circles represent the 34 major components of the trophic
flow network identified by Baird and Ulanowicz Ž1989.. Numbers are ordered to organisms in the Appendix A. For simplicity, undirected
edges are shown Žhigher AspeciesB feed always on lower ones..
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
291
Fig. 2. The winter subweb of the Bay’s cumulative web ŽFig. 1..
going to the same consumer Žsink. always equals one
Žcarbon flows not shown originally at Baird and
Ulanowicz Ž1989. have been calculated and minor
deviations between annual data and seasonal sums
are corrected, see Appendix B..
The comparison of seasonal webs gives information about changes in species composition Žfor example, sea nettle Žspecies a10. is present only in
summer., changes in interaction pattern Žfor example, striped bass Ža33. eats blue crab Ža19. in
Fig. 3. The spring subweb of the Bay’s cumulative web ŽFig. 1..
292
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
Fig. 4. The summer subweb of the Bay’s cumulative web ŽFig. 1..
summer but does not in fall., changes in trophic
positions Žfor example, menhaden Ža23. is a top
predator only in winter., and trophic dynamics Žfor
example, microzooplankton Ža7. gains energy
mainly from phytoplankton Ža1. in summer, but
mainly from heteromicroflagellates Ža6. in winter..
It must be noted that the unnumbered source components Aenergy and nutrientsB and Aexogenous inputB
were excluded from my analysis. These circles Žas
expressed in energy language symbols, see Odum,
Fig. 5. The fall subweb of the Bay’s cumulative web ŽFig. 1..
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
1994. are crucial components in detrital cycles, however, their effects on community regulation patterns
are mediated through the living producers Žand storages..
3.2. Keystone indices characterizing the importance
of trophic positions
Some species are surprisingly important in the
organization of communities. The large effect of
these AkeystoneB species ŽPaine, 1969. may be ascribed to various causes ŽMills et al., 1993; Bond,
1994; Power et al., 1996.. Earlier, we have presented
a model characterizing the importance of species,
considering their position in the energy flow network
ŽJordan
´ et al., 1999.. Species considered as keystones from this view are in the most important
positions of trophic flow network digraphs. This
model predicts keystones better if trophic effects are
more important. The reason is that only trophic
interactions are considered by the model. ŽBoth predation and indirect interactions mediated by exclusively trophic links, for example, exploitative competition, apparent competition or trophic cascade
ŽAbrams et al., 1996.. Thus, indirect mutualism is
one of the excluded ones, for it needs also a competitive link not shown in energy flow networks Žsee
Ulanowicz and Puccia, 1990.. The model accounts
for both top-down and bottom-up type Žas well as
horizontal. effects. Top-down indirect effects acting
through trophic links may also be very important
Že.g., Abrams and Matsuda, 1993., as indirect effects, in general ŽKareiva, 1994; Wootton, 1994..
Keystone indices measure the importance of positions in energy flow networks in bottom-up Ž K b .,
top-down Ž K t . and both directions Ž K .. The K
keystone indices of the ith species give the number
of species going to secondary extinction following
the removal of the ith species Žbecause sources and
sinks may become disconnected, in both directions..
The bottom-up keystone index Ž K b . of the ith species
can be calculated as
n
Kbs
Ý
cs1
1
1
q
dc
dc
K bc ,
where n is the number of its predators, d c is the
number of preys eaten by its cth predator, and K b c
293
is the bottom-up keystone index of its cth predator.
Thus, K b should be calculated first for higher species
in the web. This method needs the exclusion of
trophic loops Žsee Ulanowicz, 1983; this has no
serious effect on results..
The top-down keystone index Ž K t . can be calculated in the same way, but turning the web upside
down. Beside food supply function, trophic control
comprises various indirect effects, acting in both
bottom-up and top-down directions. Interaction feedbacks are of crucial importance, and sometimes topdown interactions dominate under strong trophic
Žpredation. control ŽPaine, 1969.. Thus, it seems
reasonable to analyze the structure of top-down network flows as well Ževen if these effects are less
obvious than the case when the food source of a
specialist consumer suddenly decreases.. Recent
studies also have strongly supported the importance
of a network perspective in system-level ecology
Žsee Higashi and Burns, 1991..
K is the sum of K b and K t . If the relative
importance of bottom-up and top-down forces can be
estimated, weighing is possible. In this case, K may
equal aK b q bK t . However, this possibility seems to
be primarily of theoretical importance, for it is not
easy to estimate the relative importance of the two
kinds of processes ŽHunter and Price, 1992..
The three keystone indices for each component of
the Chesapeake Bay ecosystem for each season are
shown in Table 2. Values are approximated to the
second decimal. Evidently, the sum of K b values for
basal species equals the number of non-basal species
in the community Žif each producer is removed, each
consumer extincts.. Conversely, the sum of K t values for top species equals the number of intermediate
and basal species in the community Žif all top-down
control ceases, each lower species dies, according to
this simple model.. Higher K b and K t values characterize more important species in bottom-up and
top-down flows Že.g., of energy or of regulative
effects., respectively. High K indices characterize
the species at the most important positions of the
flow network Žnow, equal bottom-up and top-down
forces are assumed.. The last row of Table 2 shows
the average K of the whole web.
Some comments on Table 2. Although K b and
K t of species 5, 6 and 34 change in each season,
their K values always equal each other’s. This is
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
294
Table 1
The magnitude of carbon flows Žmg Crm2 . for each sourcersink link in each season Ždata estimated by Baird and Ulanowicz, 1989.
Source
Sink
Floww
Ratio w
Flowsp
Ratio sp
Flowsu
Ratio su
Flowf
Ratio f
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
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
18
14
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
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
26
26
27
15 300
67 140
12 600
6300
1210
50
2520
5092
4280
1328
525
525
1050
–
–
145
95
10
57
37
4
337
220
23
29 895
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
2
2
–
1
1
1
1
0.32
0.01
0.67
0.48
0.40
0.12
0.25
0.25
0.50
–
–
0.58
0.38
0.04
0.58
0.38
0.04
0.58
0.38
0.04
1
1
1
0.67
0.33
1
0.20
0.07
0.02
0.06
0.53
0.12
–
1
0.13
0.15
0.71
0.36
0
0.64
–
0.70
0.20
0.10
0
0.66
0.17
0.17
–
29 440
86 799
50 416
25 208
0
0
6067
23 920
31 665
2162
692
691
1348
–
–
174
114
12
680
445
47
1795
1176
124
49 545
7410
16 805
12 350
6175
4059
270
84
34
68
702
152
–
17.4
55
63
300
7
41
90
3.9
–
–
–
2
13
3
3
2
1
1
1
1
0
0
1
0.41
0.55
0.04
0.25
0.25
0.50
–
–
0.58
0.38
0.04
0.58
0.38
0.04
0.58
0.38
0.04
1
1
1
0.67
0.33
1
0.21
0.06
0.03
0.05
0.54
0.11
–
1
0.13
0.15
0.71
0.05
0.30
0.65
1
–
–
–
0.09
0.63
0.14
0.14
0.06
23 920
60 536
95 680
47 840
26 956
22 724
19 320
5667
5667
2834
1265
1265
2530
1159
552
3550
2325
245
1288
844
88
1834
1202
126
50 400
9330
28 000
17 333
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
6
6
265
1
1
1
1
0.39
0.33
0.28
0.40
0.40
0.20
0.25
0.25
0.50
0.68
0.32
0.58
0.38
0.04
0.58
0.38
0.04
0.58
0.38
0.04
1
1
1
0.67
0.33
1
0.20
0.06
0.03
0.04
0.55
0.12
1
1
0.13
0.15
0.71
0.06
0.29
0.65
1
0.75
0.22
0.03
0.12
0.60
0.14
0.14
0.70
43 680
74 438
18 746
9373
3549
0
3731
2460
2460
1231
975
956
1914
–
–
330
217
23
250
163
17
449
294
31
31 918
4800
7980
5366
2684
3252
415
130
52
104
1080
232
–
2
93
108
517
4
24
53
–
2
0.6
0
2
13
3
3
49
1
1
1
1
0.49
0
0.51
0.40
0.40
0.20
0.25
0.25
0.50
–
–
0.58
0.38
0.04
0.58
0.38
0.04
0.58
0.38
0.04
1
1
1
0.67
0.33
1
0.21
0.06
0.03
0.05
0.54
0.11
–
1
0.13
0.15
0.71
0.05
0.30
0.65
–
0.77
0.23
0
0.09
0.63
0.14
0.14
0.70
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
295
Table 1 Ž continued .
Source
Sink
Floww
Ratio w
Flowsp
Ratio sp
Flowsu
Ratio su
Flowf
Ratio f
15
16
22
14
15
22
14
15
18
22
23
27
22
18
22
23
31
19
21
22
23
1
27
27
27
28
28
28
29
29
29
30
30
30
31
32
32
32
32
33
33
33
33
34
–
–
–
3
8
1
3.8
0.6
1.1
–
–
–
–
–
–
–
–
–
–
–
–
12 083
–
–
–
0.25
0.67
0.08
0.69
0.11
0.20
–
–
–
–
–
–
–
–
–
–
–
–
1
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
18 630
0.20
0.70
0.04
0.60
0.30
0.10
0.70
0.10
0.20
0.18
0.15
0.67
1
0.03
0.58
0.31
0.08
0.08
0.01
0.56
0.35
1
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
26 956
0.20
0.07
0.03
0
0.89
0.11
0.70
0.10
0.20
0.17
0.17
0.66
1
0.03
0.40
0.33
0.24
0.09
0.01
0.56
0.34
1
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
16 585
0.20
0.07
0.03
0
0.90
0.10
0.69
0.10
0.21
0.18
0.18
0.64
1
0.05
0.40
0.30
0.25
0
0
0.64
0.36
1
Floww , flowsp , flowsu , and flowf correspond to flows in winter, spring, summer and fall, respectively. ARatioB gives the proportion of an
energy flow to the whole menu of the consumer. A –B means that the consumer Žsink. of the link is absent from the web in the given season.
A0B means that the consumer is present but does not feed on the prey.
because from the viewpoint of the network flows,
their positions are perfectly equally important. The
three indices of species 4 are always the same, for
this species’ connections to other members of the
community do not change over the seasons. K b s 0
always marks top predators, while K t s 0 always
refers to producers.
Looking at the K values, one may realize that,
for example, microzooplankton Ža7. is a more important member of the energy flow network in summer Ž K su s 7.46. than in other seasons Ž K w s 5.9,
K sp s 6.5 and K f s 6.22.. Blue crab Ža19. is much
more important in winter than during other seasons.
Conversely, menhaden Ža23. is less important in
winter, but it is more or less equally important in
other seasons.
3.3. Relationship between positions and fluxes
Elsewhere ŽJordan
´ et al., 1999., we have suggested that the congruence of important positions
and large flows may indicate that trophic community
regulation Že.g., predation. is of prime importance. If
it is true, an analysis of prey choice considering the
positional keystone indices of preys may provide
interesting information about community regulation.
This investigation takes into account only non-specialist consumers, of course.
This analysis is presented by following an example. In springtime ŽFig. 3., summer flounder Ža32.
eats bay anchovy Ža22., menhaden Ža23., weak fish
Ža31., and crustacean deposit feeders Ža18.. Carbon
flows from these sources to the flounder are 6.9, 3.7,
1 and 0.4, respectively. The ratios in the flounder’s
menu are 0.58, 0.31, 0.08 and 0.03, respectively. The
springtime keystone indices Ž K sp . of these species
are 3.43, 1.51, 0.53 and 1.23, respectively. Therefore, the perfect congruence of important positions
and large flows would occur if summer flounder
preferred bay anchovy, then menhaden, crustacean
deposit feeders, and finally, weak fish Žsequence
22-23-18-31.. From this best sequence, we can reach
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
296
Table 2
Bottom-up Ž K b ., top-down Ž K t ., and bi-directional Ž K . keystone indices for the 34 major components of the flow network for each season
Ž K w , K sp , K su and K f for the four seasons.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Average
K bw
K tw
Kw
K bsp
K tsp
K sp
K bsu
K tsu
K su
K bf
K tf
Kf
23.5
14
8.83
0.5
2.18
1.18
2.54
2.28
0
–
0.17
0.17
0
1.33
1.5
0.17
0
1.17
0
–
0
0.33
0
–
0
0
–
0
0
–
–
–
–
3.18
0
0.11
0.14
0
1.11
2.11
3.36
1.12
1.54
–
1.12
1.12
1.12
0.19
0.19
0.19
1.19
0.19
6.13
–
0.53
0.78
0.64
–
0.83
0.83
–
2.32
0.83
–
–
–
–
0.11
23.5
14.11
8.97
0.5
3.29
3.29
5.9
3.4
1.54
–
1.29
1.29
1.12
1.52
1.69
0.36
1.19
1.36
6.13
–
0.53
1.11
0.64
–
0.83
0.83
–
2.32
0.83
–
–
–
–
3.29
3.49
28.5
15.23
9
0.5
5.37
4.37
3.37
4.44
0
–
0.21
0.46
0
1.25
1.46
0.54
0
1.04
0.25
–
0.25
2.75
0.83
0
–
0
0.33
0
0
0
0.25
0
0
6.37
0
0.13
0.14
0
1.13
2.13
3.13
1.09
1.38
–
1.09
1.09
1.09
0.19
0.19
0.19
1.19
0.19
4.46
–
0.42
0.68
0.68
0.42
–
1.88
1.41
0.82
0.83
3.25
0.28
2.42
7.72
0.13
28.5
15.36
9.14
0.5
6.5
6.5
6.5
5.53
1.38
–
1.3
1.55
1.09
1.44
1.65
0.73
1.19
1.23
4.71
–
0.67
3.43
1.51
0.42
–
1.88
1.74
0.82
0.83
3.25
0.53
2.42
7.72
6.5
4.08
31.5
18.23
9.83
0.5
2.7
1.7
4.11
6.17
0.5
0
0.21
0.46
0
1.25
1.96
0.54
0
1.38
0.25
0
0.25
2.92
0.83
0
0
0
0.33
0
0
0
0.25
0
0
3.7
0
0.11
0.12
0
1.11
2.11
3.35
1.1
1.29
2.59
1.1
1.1
1.1
0.19
0.19
0.19
1.19
0.19
4.37
0.3
0.3
0.54
0.54
0.3
0.73
1.78
1.34
0.45
0.73
3.11
0.19
2.2
7.44
0.11
31.5
18.34
9.95
0.5
3.81
3.81
7.46
7.27
1.79
2.59
1.31
1.56
1.1
1.44
2.15
0.73
1.19
1.57
4.62
0.3
0.55
3.46
1.37
0.3
0.73
1.78
1.67
0.45
0.73
3.11
0.44
2.2
7.44
3.81
3.85
28.5
15.66
9.67
0.5
3
2
3
3.42
0
–
0.17
0.42
0
1.42
2.08
0.5
0
1
0
–
0
3.17
1.08
–
0
0
0.33
0
0
0
0.25
0
0
4
0
0.11
0.14
0
1.11
2.11
3.22
1.09
1.51
–
1.09
1.09
1.09
0.19
0.19
0.19
1.19
0.19
4.42
–
0.52
0.77
0.77
–
0.5
1.84
1.39
0.49
0.79
3.27
0.3
2.48
0.89
0.11
28.5
15.77
9.81
0.5
4.11
4.11
6.22
4.51
1.51
–
1.26
1.51
1.09
1.61
2.27
0.69
1.19
1.19
4.42
–
0.52
3.94
1.85
–
0.5
1.84
1.72
0.49
0.79
3.27
0.55
2.48
0.89
4.11
3.65
For example, the bottom-up keystone index of the bay anchovy Žspecies a22, see Appendix A. in summer is K bsu s 2.92. This means that
if the bay anchovy is removed, 2.92 higher AspeciesB extinct secondarily because of reduced bottom-up effects.
the worst one Žconversed, 31-18-23-22. in minimum
six steps, where a step means the exchange of two
neighbors Žfor example, 22-23-18-31
22-2331-18
22-31-23-18
31-22-23-18
31-22-1823 31-18-22-23 31-18-23-22.. The number of
minimal steps from the best to the worst sequence
characterizes their distance Ži.e., how similar they
are; which depends on the length of the sequence..
The next sequence is always worse by 1r6 than the
previous one. Hence, the congruence for the sequences is 100%, 83%, 66%, 50%, 33%, 17% and
™™
™™
™™
0%, respectively. Of course, many alternative pathways do exist but the number of minimal steps
between two sequences characterizes how they differ
Žtwo pathways of equal length mean similar distance.. The sequence of preys in the flounder’s menu
corresponds to 83% congruence between important
positions and large flows.
In the case of two preys, sequences correspond to
0% or 100% congruence. In the case of three preys,
they do to 0%, 33%, 66% or 100%, and in the case
of, for example, six preys, the congruence of se-
Table 3
The sequence of preys according to flow ratios is given for each non-specialist consumer, for each season
Preys w
Congruence w Ž%.
Preys sp
Congruencesp Ž%.
Preys su
Congruencesu Ž%.
Preys f
Congruence f Ž%.
7
8
9
10
11
12
13
17
19
22
23
25
26
27
28
29
30
32
33
Averagre
6-1-2
1-2-7
8-Ž2-7.
–
1-2-7
1-2-7
1-2-7
3-4
16-3-18-11-15-12
8-2-1
8-1-2
14-15-18
14-Ž15-18.-12
–
15-14-22
14-18-15
–
–
–
33
100
17
–
100
100
100
100
53
0
33
66
75
–
100
33
–
–
–
65
6-Ž1-2.
2-1-7
8-Ž2-7.
–
1-2-7
1-2-7
1-2-7
3-4
16-3-18-11-15-12
8-2-1
8-2-1
–
14-Ž15-18.-12
16-15-14-22
14-15-22
14-18-15
27-22-23
22-23-31-18
22-23-19-21
17
66
17
–
100
100
100
100
33
0
0
–
50
17
0
33
66
83
66
50
1-2-6
Ž1-2.-7
8-Ž2-7.
8-9
1-2-7
1-2-7
1-2-7
3-4
16-3-18-11-15-12
8-2-1
8-2-1
14-15-18
14-Ž15-18.-12
14-15-16-22
15-22-14
14-18-15
27-Ž22-23.
22-23-31-18
22-23-19-21
100
83
17
100
100
100
100
100
47
0
0
33
42
33
66
0
50
66
66
58
6-1-2
Ž1-2.-7
8-Ž2-7.
–
1-2-7
1-2-7
1-2-7
3-4
16-3-18-11-15-12
8-2-1
8-2-1
14-15-18
14-Ž15-18.-12
14-15-16-22
15-22-14
14-18-15
27-Ž22-23.
22-23-31-18
22-23-Ž19-21.
33
83
17
–
100
100
100
100
33
0
0
66
58
33
66
33
17
83
58
54
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
Consumer
For example, white perch Žspecies a28, see Appendix A. eats mainly Nereis Ža15. in winter, then Aother polychaetesB Ža14., and finally, some bay anchovy Ža22.. Energy
flows are shown at Table 1. The congruence of this sequence of preys and their positional importance Žsee Table 2. is also given. For white perch, it is 100%, because the
K-values of these preys are 1.69, 1.5 and 1.11, respectively. For the perch eats more bay anchovy than Aother polychaetesB in summer, its congruence value is only 66% in this
season. The last row gives seasonal average congruence values for the whole web. For detailed explanation, see the text.
297
298
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
quences changes in 15 steps from 0% to 100%, each
one is better by approximately 7%.
If K was equal for two preys Žparentheses in
Table 3., the average congruence values for the two
sequences was calculated. If the flow magnitude was
equal for the preys, the better choice was considered,
for simplicity. This does not affect seriously our
results.
In cases when a trophic group does not feed
seasonally on another which is present and otherwise
eaten by the given group, the group with zero flux is
included in prey sequences. Two reasons might be
considered. At one hand, a zero flux is hard to detect
independently on data collecting methods, thus, a
typical prey not eaten in a season may mean only a
very low level of consumption. On the other hand, if
a prey is really out of the seasonal diet, but present
in the community, I consider this as a case of prey
choice Žattempted to analyze..
Table 3 shows prey sequences according to flow
magnitude for each non-specialist consumer in each
season, and the congruence of positional importance
and flow magnitude. The last row shows average
congruence for the whole network.
4. Reliable energy flows
Elsewhere, we have shown that high average keystone index in a web results in less reliable network
flows ŽBarlow and Proschan, 1965; Jordan
´ and
Molnar,
´ 1999; Jordan
´ et al., 1999.. Here, reliability
means the probability that a sink species remains
connected to any of the sources, despite AfailuresB
Ži.e., probabilistic deletion of edges, according to the
model cited above.. Comparison of the average seasonal K values Ž3.49 for winter, 3.65 for fall, 3.85
for summer and 4.08 for spring. suggests that winter
is the season when trophic flows reach sinks in the
most reliable way.
flows. Phytoplankton Ža1. and suspended POC Ža2.
are evidently important in energy flow networks.
Beside them, some other species can also be characterized as being generally in key position, like the
blue crab Ža19. or the bay anchovy Ža22, except in
winter.. Some components are not in very important
positions of the network, e.g., benthic diatoms Ža4.
or herrings Ža21.. Nevertheless, they can be important members of the community, too, independently
of trophic effects. Moreover, a model based on carbon flows cannot predict the importance of species if
the dynamics of other nutrients have stronger control
on the community ŽUlanowicz and Baird, 1999..
Analyses of the N and P flow networks as well as an
analysis of the flow network showing control-linkages could contribute to a better prediction of positional importance of the trophic components in the
Chesapeake Bay.
The congruence of important positions and large
flows has been analyzed. In the case of better congruence, we suggest that predation and other trophically mediated indirect interactions may be more
important in community regulation. Trophic control
seems to have the largest effect in winter, less in
summer, and the least in fall and springtime.
The reliability of the network flows depends on
trophic structure and correlates with the average
positional keystone index of the members of the
web. Energy supply is the most safety in winter,
while trophic flows are the least reliable during
springtime. These results are in concert with the
well-known Chesapeake field observations depicting
poor phytoplankton production in winter and excess
production in springtime: a poor source of nutrients
has larger regulatory power Žnote that exploitative
competition emerges indirectly from trophic interactions..
This study was a macroscopic, quantitative attempt to connect the structure and dynamics of whole
trophic networks, and to investigate the relationship
between pattern and process in ecology ŽPimm, 1991;
Polis and Winemiller, 1996..
5. Results and conclusions
The seasonal positional keystone indices are given
for each trophic component of the Chesapeake Bay
ecosystem. These numbers characterize the seasonal
importance of components in maintaining carbon
Acknowledgements
I am grateful to Istvan
´ Molnar
´ for many useful
discussions. I thank Robert Ulanowicz for comments
F. Jordanr
´ Journal of Marine Systems 27 (2001) 289–300
on an earlier form of the MS and Katalin Jaszkuti
for
´
preparing the manuscript. Two anonymous referees
are acknowledged for helpful criticism. This work
was funded by the grant OTKA F 029800.
Appendix A
The list of the 34 major components of the Chesapeake Bay ecosystem’s carbon flow network. Trophic
groups are identified by Baird and Ulanowicz Ž1989..
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
phytoplankton
suspended bacteria
sediment bacteria
benthic diatoms
free bacteria
heteromicroflagellatae
microzooplankton
zooplankton
ctenophore
sea nettle
other suspension feeders
Mya
oysters
other polychaetes
Nereis
Macoma spp.
meiofauna
crustacean deposit feeders
blue crab
fish larvae
alewife and blue herring
bay anchovy
menhaden
shad
croaker
hog choker
spot
white perch
catfish
blue fish
weak fish
summer flounder
striped bass
dissolved organic carbon
299
Appendix B
Flow data not shown or slightly inconsistent
Žcomparing annual data to seasonal sums. in the
original figures of Baird and Ulanowicz Ž1989.: in
spring, flows from 23 to 30, from 22 to 27, from 22
to 30, and from 6 to suspended POC are 0.7, 1.5, 0.8
and 4016, respectively; in summer, flows from 3 to
19, from 11 to 19, from 12 to 19, and from 15 to 19
are 940, 300, 120 and 160, respectively. In the
annual web, the flow from 2 to 3 is 288 913; the
edge from 14 to 28 is not shown Žflow: 71.. Sporadic
differences between seasonal sums and annual data
are negligible Žfrom 1 to 8, from 2 to 9, from 8 to 9,
from 7 to 13, from 14 to 27, and from 15 to 28 these
are 37 139 instead of 37 149, 3457 instead of 3439,
6842 instead of 6878, 306 instead of 304, 316 instead of 314, and 64 instead of 59, respectively.. In
winter, the flow from 7 to 13 is 23 instead of 25. In
fall, the sum of flows to 9 may also have been
mistyped. The loop from 19 to 19 is not considered
here; this does not affect the results of my calculations.
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