Perhaps the most useful indices to result from the Input/Output section of NETWRK are the "total dependency coefficients" (Szyrmer & Ulanowicz 1987) or, more appropriately, the "indirect diets" of each taxon. By reading down the column of these dependency coefficients one notes the quantitative trophic history of material reaching that given compartment.

The total dependency coefficients (TDC’s) of the heterotrophs in the graminoid ecosystem reveal that a significant fraction of the carbon reaching many of the predators originates in the periphyton compartment (Figure 1). The aquatic invertebrates (7-12) and fish (14-35) depend on the periphyton compartment (3) on the average for 80% of their sustenance. Periphyton contributes a significant amount of carbon to the diets of some birds, aquatic herpetofauna and aquatic mammals. Tadpoles (#41) have the highest dependency on periphyton ~ 96% in the wet season and 97% in the dry season, while large frogs (#38) depend on periphyton for 94% and 96% of their energy in the wet and dry seasons, respectively. The indirect dependency of otter (51) on periphyton varies between 79-88% between wet and dry season, whereas snail kites depend on periphyton for 94-95% of their sustenance during the wet and dry season respectively. By way of contrast, only very small flows link periphyton with terrestrial mammals and terrestrial herpetofauna, which feed mainly upon terrestrial invertebrate species. Such is the case for lizards (44), muskrats (46), rabbits (48), bobcats (54) and Florida panthers (55), which obtain virtually none of their carbon via periphyton pathways.

One may employ the total dependency matrix to test how dependent each single compartment is on the other major groups. For example, looking at how much various groups are dependent on invertebrates (compartments 7 to 14) reveals that the salamanders and smaller frogs show the highest dependencies (Figure 2). More than 100% of the carbon reaching salamanders (36) during the dry season, medium frogs (39) and small frogs (40) during both seasons passes through invertebrates. Similarly, approximately 100% of the carbon that reaches the snail kites (59) and nighthawks (60) pass through invertebrates. (The values greater than 100% simply mean that the same carbon is spending time in more than one invertebrate compartment.) There is a very low dependency of birds, mammals and herpetofauna upon fishes, with only fishing spiders (14) showing more than 50% dependency on fish (Figure 3).

Dependencies on the remaining three big groups (herptofauna, birds and mammals) do not exceed 20% in most cases. The exceptions here are the dependencies of snakes (24%), alligators (28%) and mink (22%) on lizards during the wet season, although their dependencies on lizards remain much lower during the dry season. Dependency coefficients generally decline as one proceeds from invertebrates up to mammals, however, the dependencies of bobcats and panthers on muskrat are very high — 90% and 94% for bobcats in the wet and dry respectively, and 80% for both wet and dry seasons for panthers.

Summing the dependencies on all primary producers for each compartment, one sees that, in most instances, the result is close to 100% (Figure 4). This indicates that the system depends mainly on internal carbon fixation and receives only a small subsidy from outside the system. There are some exceptions, with lizards (# 44) being the most obvious — it only depends on 2% of internal carbon in both wet and dry season. The very low dependency on internal carbon by lizards is because they import most of their diet from outside the system. Snakes and alligators (#’s 43 and 45) depend on internal carbon for 77-95% and 73-94% respectively (for wet and dry seasons) and import their remaining sustenance from outside the system. Similarly, mink (#52) depend on internal carbon for 78-96% (wet and dry season, respectively), the panthers (# 55) 96-99%, and passerine birds (#63) 91-94% for wet and dry season, respectively.

In general, there is a difference in indirect diets between wet and dry seasons. The dependencies on primary producers (Figure 4), and especially on periphyton (Figure 1), increase from the wet to the dry season. Conversely, the dependencies on invertebrates (Figure 2) are higher during the wet season than during the dry, while dependencies on fish (Figure 3) do not show any trend.

The dependencies of consumers on periphyton are very different from those of the consumers in the mangrove system, although the similarity of the graminoid system to that of the cypress is more evident. In the mangrove system (Ulanowicz, et al. 1999) the consumers depend mostly on carbon from the detrital compartments, while in the cypress system most of the consumers are supported via the grazing chain, and the importance of periphyton increases during the dry season (Ulanowicz, et al. 1997). This is similar to the increase in dependencies on periphyton seen in the graminoid system, although the magnitude of the dependencies is generally smaller in the cypress system. Comparison of the graminoid dependencies with those in the marine system (Florida Bay) is not as useful, although the dependencies on detritus also seem low in the Bay ecosystem (Ulanowicz, et al. 1998).

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Impact analysis is used to study both positive and negative indirect effects between compartments. In higher-dimensional networks, such as this ecosystem, every pair of compartments is connected in this way, at least indirectly. Coefficients in the impact matrix represent the aggregated net (positive and negative) indirect effects between two species.

Of special interest are those compartments that function as "beneficial predators". The direct impact of a predator on its prey is obviously negative. However, the overall effect can become positive, due to the potential for compensation via multiple indirect pathways. In such cases one speaks of "beneficial predators". In the three previous networks, beneficial predation was quite abundant. In the cypress swamp, for example, the American alligator was a net benefactor to 11 of its prey items. In the graminoid system during the wet season, redear sunfish and warmouth benefited two prey compartments (Table 1). During the dry season, the warmouth, redear sunfish and spotted sunfish benefited more than one (two) of their prey items (Table 2).

Table 1 and table 2 list all the beneficent predators during either season, together with the number of prey that each positively impacts. In the graminoid system there are 13 beneficial predators in the wet season and 17 in the dry, which is much lower than the 218 and 208 that was found in the wet and dry season mangrove systems respectively. The much lower number of beneficial predators in this system could be due to the fact that the main predators of the invertebrates and fish compartments, namely the wading birds, were excluded from this model. Of the 13 and 17 beneficial predator interactions, 8 predators are beneficial in both seasons, which indicates that some predators are beneficial to more than one prey type. In addition to the number of beneficial predators being low, the magnitudes of their actions are not very strong. The most significant positive impact during the wet season is that of gar on other macroinvertebrates — where the impact is 0.027, while the most significant positive impact during the dry season is the impact of snakes on crayfish (0.137).

Although only a small number of beneficial predator interactions achieve significant magnitude, in a few cases more than one predator affects the same prey in a net positive manner. Adding together all the positive effects by multiple predators, one obtains an aggregate positive impact by the several predators (Table 3). In addition to those links cited above, three other prey compartments receive significant benefit from a combination of predators during both wet and dry seasons: Living sediment (#1), living POC (#2) and periphyton (#3). During the both seasons, living POC receives the most benefit from their prey, but more so during the dry season (0.06 vs. 0.04).

Having considered and identified instances of beneficial predation, one should also consider whether the reverse relationship might be possible, i.e., that the overall effect of a host on its predator over all pathways, direct and indirect, can be negative. As mentioned above, in such case we talk of a "malefic prey". A search of the graminoid network uncovers 111 cases of "malefic" links during the wet season and 103 for the dry. A total of 36 prey affect their predators negatively in the wet period and 33 in the dry (Table 4). The compartment living POC (#2) produces the highest number of negative indirect effects on its predators during both seasons, adversely affecting some 18 prey during the wet season and 17 during the dry period. Next in line is the small frogs compartment (#40) with 6 negative impacts in the wet season, and 5 in the dry season. Similarly, killifishes (#22) and mesoinvertebrates (#10) also have 5 negative impacts on their predators.

The number of malefic prey species and the number of predators that they affect are lower in the graminoids than in the mangroves or Florida Bay systems. There are 186 and 185 malefic prey species in the wet and dry mangrove systems, and they affect 47 and 48 different predators in those two systems, respectively. In Florida Bay, the malefic prey species number 278 and 283 in the wet and dry seasons, respectively; and they affect 70 and 68 predators, respectively. The lower number of malefic prey in the graminoids might simply be due to the lower number of compartments in the system.

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As with most ecosystems studied by Network Analysis thus far, none of the compartments of the graminoid ecosystem feeds, on the average, at or above trophic level 5. In fact, none of the compartments feeds above the fourth trophic level. The highest feeders are the lizards (#44), which feed at an effective trophic level of 3.83 during the dry season and the mink (#52) and alligators (#45) that effectively feed at 3.49 during the wet season. The average trophic levels during both seasons are listed in Table 5. In general, there was very little difference between the trophic levels of the wet and dry seasons, although the trophic levels are generally higher in the dry season than in the wet. Only three compartments have seasonal differences larger than 0.2 — the freshwater prawns (#8), salamanders (#36) and lizards (#44) have differences of 0.21, 0.23 and 0.71, respectively, and all of their trophic levels are higher in the dry season than in the wet.

In the mangrove and Florida Bay systems, the raptors feed one full trophic level higher than the top predators of the graminoid or the cypress systems. In the mangrove system kites & hawks, eagles & ospreys and owls feed at effective trophic levels of 4.3, 4.2 and 4.5 respectively, while the top predators in the cypress are alligators and snakes, both feeding at an effective trophic level of 3.8. By way of inter- habitat comparison, the effective trophic level of alligators, mink and lizards in the graminoids (dry season only) resemble more those of the cypress than those of the mangrove system.

A quick perusal of the Lindeman transformation matrix, which apportions compartments among trophic levels, reveals that there are 16 trophic levels in the overall network. Thus, at least one non-redundant trophic pathway with 16 links can be found in the network. As usual, however, not much carbon persists beyond the fifth trophic stage, and the amounts calculated to reach the 16th level are absolutely infinitesimal (of the order 10^-32 grams.) The first six trophic levels during each season are depicted in Figure 5. One notices immediately that the trophic chains in the two seasons are quite similar, although the inputs and through-flows are generally smaller in the dry season, and the efficiencies are higher in the wet season. The efficiencies of the graminoid trophic levels are mostly lower than those observed in the other three ecosystems. The efficiencies of the higher trophic levels (V and VI) are higher, however, than the trophic efficiencies of levels V and VI of the cypress system. Similarly, the efficiency of trophic level V in the graminoid system is also higher than the efficiency of trophic level V in the mangrove system.

The ratio of detritivory:herbivory is a approximately 29:1 in the wet season and 45:1 in the wet season. This is much higher than the 7:1, 8:1 and 5:1 calculated for the mangrove, Florida Bay and cypress ecosystems, respectively. This higher detritivory suggests that the recycling of carbon is enormously important in the graminoid system. This result stands in stark contrast to the total dependency analysis, which showed that most compartments depend mainly on periphyton, and dependencies on detritus appear to be decidedly secondary. The discrepancy may be explained by the fact that most excretion and mortality from living compartments becomes refractory detritus (#66) and carbon in the sediment (#64), which in turn is utilized mainly by bacteria (TL2) in the sediment and in the water column (i.e., detritivory by TL2). Similarly, much of the production by plants (periphyton, macrophytes, floating vegetation and Utricularia) is not consumed by herbivores, but is broken down into labile and refractory detritus, which is then utilized by bacteria in the sediment and the water column (again detritivory). This augments the magnitude of detritivory and reveals that much of what is produced by the primary producers is not utilized by the higher trophic levels, but rather is recycled into the detritus and subsequently deposited as peat. The high dependencies by most heterotrophs on periphyton owe to the fact that the greater fraction of what is consumable among the primary producers consists of periphyton, and demonstrates how extremely important periphyton is to this system.

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The freshwater cypress biome and the mangrove ecosystem surround the graminoid ecotope, which is also proximal to the waters of Florida Bay. All of these networks have been estimated and analyzed previously as part of this contract, making it is possible to compare the system level indices calculated for the graminoid ecosystem to those of its neighbors. It is useful to bear in mind that in certain very real ways the graminoid system feeds its neighbors, and its characteristic indices might be expected to reflect that fact.

With respect to total activity, the graminoid system is far more active than any of the neighboring systems (Table 6). Its total system throughput is 19,949 gC.m^-2.y^-1 during the wet season and 10,992 gC.m^-2.y^-1 during the dry, while the throughputs of the other three systems are all approximately an order of magnitude smaller. The development capacity of the graminoid system (wet = 79,572 gC-bits.m^-2.y^-1 and dry = 39,854 gC-bits.m^-2.y^-1) is also significantly higher than that of the other systems. While one might attribute the latter inequality to the fact that the total system throughput serves as a scaling factor of the capacity, we note how the ascendency (normalized as a percentage of development capacity) in the graminoids is 48.6% in the wet season, and 52.6% in the dry season. This is much higher than the ascendency values for the mangroves (36%), Florida Bay (38%) or the cypress system (44%).

These values for ascendency reveal that the graminoid system appears to be the least stressed of the four communities studied. The graminoid system has been stressed by various modifications of its flow patterns, which resulted in loss of transitional glades, modification of flow patterns, reduced hydroperiods, unnatural pooling and over-drainage (Light & Dineen, 1994). The system has experienced the fewest changes to its faunal community, however, and is sustained by an abundance of flora and micro-bacterial communities. The mangrove system and the Florida Bay communities are more stressed than the graminoids because of the variations in osmolarity common to estuaries, and the recent hypersalinities noted in the Bay. The cypress ecosystem, like that of the graminoids is limited by a dearth of nutrients (probably phosphorus), which are abundant in the marine and estuarine waters and sediments. The graminoid system compensates for this dearth of nutrients through its profusion of periphyton, which exhibits a high P/B ratio, even under oligotrophic conditions. The natural stressors affecting the bay, mangroves and the cypress appear to have far greater effects, for they modulate the very rates of material and energy processing.

Information indices are usually applied only to whole systems. Evidence is accumulating however, that the various sub-components of the ascendency-like variables can serve to gauge the contributions of individual system elements to the performance of the whole system (Ulanowicz & Baird, 1999). For example, the ascendency is comprised of terms that are generated by each transfer in the system. If one sums up all the terms generated by the inputs to a given taxon (say, the jth one), the result is a measure of the contribution of that compartment to the full system ascendency (call it A_j). Because ascendency may be viewed as an indicator of efficient system performance (Ulanowicz, 1997), the same partial-sum, A_j, represents the contribution of taxon j to overall system performance. Furthermore, if one then divides A_j by the corresponding throughput for taxon j (call it T_j), the ratio A_j/T_j will represent the contribution per unit of activity of j to the total system ascendency.

Calculating and ranking these "relative contribution coefficients" proves to be a most interesting exercise. When the average trophic levels of the 66 compartments of the graminoid wetland ecosystem were calculated, for example, the lizards, alligators, snakes and large fishes were seen to feed at trophic levels higher than some other "charismatic megafauna", such as the snail kite, nighthawk, Florida panther or bobcat. The relative contributions to ascendency by the latter, however, actually outweighed those of the former. The relative values of these coefficients seem to accord well with most people's normative judgments of the specific "value" of the various taxa to the organization of the system as a whole (Table 7).

The system indices in the graminoid ecosystem show much larger variation between wet and dry seasons than do those of the other three systems. In the grassland prairies, the total systems throughput (T), development capacity (C) and ascendency (A) values are all nearly half in the dry season of what it is in the wet season, although the relative ascendency (A:C) increases during the dry season. This decrease in systems activity during the dry season is due to the lack of input into the system and the shutdown of some of the production activities during the dry season.

The relative contributions of the taxa of the graminoid ecosystem mirror some of the results obtained from the cypress ecosystem (Ulanowicz, et al. 1997). The avian and feline predators (snail kites, nighthawks, Florida panther and bobcats) ranked only 48, 39, 52 and 41 in terms of trophic level (average levels 3.13, 3.00, 3.17 and 3.02, respectively). Their relative contributions to the system ascendencies were highest of all taxa during both seasons. They were followed in relative contributions to the system ascendency by the fishing spiders, salamanders and larger fishes. The reduced sensitivity of crayfish (1.4 and 0.99 in wet and dry seasons) in the graminoids was not seen in the cypress, however. Crayfish ranked 16^th and 17^th in the cypress system with sensitivities of 1.9 and 2.2 respectively.

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5.5 Cycling

With 66 compartments in the trophic flow network the number of potential pathways for recycling carbon is roughly proportional to 66-factorial -- an immense number! The fact that the network is not fully connected reduces the number of potential cycles considerably. Nonetheless, the number of simple cycles in the graminoid network remains enormous. Using the standard algorithm in NETWRK 4.2a to calculate the number of cycles registered ca. 24 billion(!) cycles.

The situation is similar to what happened in previous years with the Florida Bay and mangrove networks, and the same approach taken then was followed with the graminoid systems: Most of the overwhelming number of simple cycles counted above include more than one detrital component. We make the approximation then, that one may choose to ignore those cycles that contain more than one nonliving compartment. The identification of such "single-detritus" cycles can than be achieved first by removing the cycles that contain no detrital links, and then by successively adding the detrital compartments into the search, one at a time. The number of cycles counted in this manner will be a radical underestimate of the total number of cycles present, but once they have been extracted from the network, the residual graph will contain no cycles. Even this simplification takes considerable computing power to execute. Unlike the mangrove system, where the dry season contained fewer routes for recycle, and the Florida Bay system, where the wet season showed a greater number of cycles, the number of cycles are the same in the wet and dry season models of the graminoids.

The first stage in the cycle analysis was the removal of the cycles that contain no nonliving compartments. These are generally rare in most ecosystems (Pimm, 1982). There were only 16 such cycles during both seasons in the graminoids. The cycle of greatest magnitude was cannibalism by snakes, but the amount cycled over this route is very small — 5.8 mgC.m^-2.y^-1 in the dry season and 14 mgC.m^-2.y^-1 in the wet season.

By far and away the greatest number of single-detrital cycles was generated by compartment #64, carbon in the sediment, which has 133,657 cycles in the dry season and 183,606 in the wet season. Of this huge number of cycles, only 8 cycles accounted for most of the recycling by the system: 457.29 gC.m^-2.y^-1 or 95.8% in the wet season, and 458.9 gC.m^-2.y^-1 or 96.2% in the dry season. The major routes for recycling were between the detritus compartments (both in the water column and in the sediment) and living sediments (Figure 6). Recycling between the detritus compartments included carbon cycled from living sediment (#1) to sediment carbon (#64), to refractory and labile detritus (#65 and 66) and from labile and refractory detritus to sediment carbon. Other than the cycles shown in Figure 6, the two next largest cycles (in magnitude) are:

1. Between living POC and labile detritus (± 2.6 gC.m^-2.y^-1 — wet and dry season) and
2. Between mesoinvertebrates, sediment carbon, living sediment and labile detritus (±1.1 gC.m^-2.y^-1 in the wet season and 0.7 gC.m^-2.y^-1 in the dry season).

Thus the linkage between the detrital cycle and the higher trophic levels is via the mesoinvertebrates feeding on living sediments and sediment carbon, which is a very small rate. One would expect that feeding on living POC, labile- and refractory detritus would be noticeable in the recycling of this system, because the detritivory:herbivory ratio is so large. This loop is largest, however, when the mesoinvertebrate-Utricularia-labile detritus-mesoinvertebrate loop is incorporated (0.5 gC.m^-2.y^-1 in the wet season and 0.4 gC.m^-2.y^-1 in the dry season).

The aggregate activities devoted to cycling in the graminoid ecosystem during the wet and dry seasons are 477.2 gC.m^-2.y^-1 and 476.8 gC.m^-2.y^-1, respectively, which puts the Finn Cycling Index at 2.4% and 4.3% for the wet and dry seasons, respectively. These Finn Cycling Index values are much lower than the 17.2% of the mangrove system, the 14.4% for Florida Bay, and the 8 - 9% occurring in the cypress swamps. Such a reduction in the FCI probably is due to the lower dependency by the higher trophic levels on the detritus (contrary to the fact that most of the carbon is shunted into the detritus) and the importance of periphyton to the higher trophic levels of the system.


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