After the "lexical" phase of model building, the next step involves connecting the selected compartments to one another via feeding and detrital pathways. This topology is determined from information about the diets of each taxon. But the purpose here is not merely to formulate a qualitative "food web". We wish to quantify the connections as well. Toward this end, it is useful to concentrate first on assessing the densities, or stocks of the participating taxa. Knowing the concentration of biomass is the key to scaling all the activities of a particular population.
4.1 Estimation Techniques
Four different models were estimated: two for the wet season (long and short hydroperiod) and two for the dry season (long and short hydroperiod). These models were then combined into two models: one for wet season and one for dry season.
The biomass values of some species are known to reasonable precision. For example, the number of animals per cubic meter or liter is available for some of the compartments. As the standard units used in NA are grams of carbon per square meter (gC.m-2), the available data had to be transformed to maintain dimensional consistency. Towards this end, information on the average weight (grams) of animals was gathered from technical manuals. The percentage of carbon per gram of dry weight was then combined with wet weight/dry weight ratio to obtain gC.m-3. Busch et al. (1998) gives the average depth for short and long hydroperiod sites as 22 and 42 cm respectively, and by assuming these average water depths, the carbon biomass in the required units (g.m-2) could be calculated. In the case of primary producers, macrophyte biomass data was reported in gram dry weight.m-2 (Daoust & Childers, 1999), while periphyton (Browder, et al. 1982), floating vegetation and Utricularia data were reported in grams ash free dry weight.m-2 (Trexler, pers. comm.). In this case only the wet weight/dry weight ratio and the percentage of carbon per gram of dry weight (Jorgensen, et al. 1991) were necessary to convert the biomass into the correct units.
Water column detritus data for the graminoid marshes includes only TOC (total organic carbon). This compartment includes both dead organic carbon (POC — particulate organic carbon - and DOC — dissolved organic carbon) and living matter (bacteria etc.). The TOC data of Flora & Rosendahl (1982) was then divided into DOC and POC by using a 95% DOC, 5% POC split (Scinto, pers. comm.). POC was divided into living and dead POC by using a concentration of 5% living POC (Christian, pers. comm.). The remaining 95% dead POC and the DOC were divided into labile and refractory detritus by using a 20% labile, 80% refractory split (Dierberg & Ewel, 1985). Concentrations were reported in gC.l-1, and the above procedure was followed. Sediment detritus data was approximated by using bulk densities (g.cm-3) and organic carbon percentages of dry weight (45% for long hydroperiod and 0.6% for short hydroperiod) given by Brown et al. (1990). Due to lack of information it was assumed that the sediment detritus does not change significantly between wet and dry seasons.
In most cases, suitable estimates of fish and invertebrate density were available. These densities could be used in conjunction with published animal body masses for fishes and common invertebrates (Kushlan, et al. 1986) to estimate biomass per unit area. While the primary data on fishes came almost entirely from one source (Trexler, et al. 1996), the invertebrate biomass values were estimated from several different data sets.
Once the densities were determined, each value was multiplied by an average individual body mass in order to generate estimates of biomass per unit area. In most cases, the individual body masses used were those from Kushlan, et al. (1986). For several invertebrate compartments (mesoinvertebrates, other macroinvertebrates and large aquatic insects), body mass estimates appearing in Ulanowicz (1994) were used. In some fish compartments, body masses were calculated using collection data from Fury, et al. (1999). These data were used to augment or fill in missing or underrepresented species that were not suitably covered by the body mass estimates reported in Kushlan, et al. (1986). Conversion to grams carbon per square meter were carried out under the convention reported in Jorgensen, et al. (1991): 20% of wet weight is dry weight, and 45% of dry weight is carbon weight.
Data for all herpetofauna except alligators were obtained from Diffendorfer et al. (1999) in grams wet weight per hectare and converted using the wet weight/dry weight ratio and the percentage of carbon per gram of dry weight given by Jorgensen et al. (1991). Dalrymple (pers. comm.) suggests an average number of 10,000 alligators in the ENP, of which 75% occur in long hydroperiod areas, and with a 50:50 sex ratio. Wulff (pers. comm.) suggests that there are about 5,000 adult alligators in the Park and the average weight is 20 kg each. For this study an average value of 10,000 alligators was used, with 30:70 split between adults and juveniles. An average weight of approximately 20 kg was used for adults and 5 kg for juveniles.
Mammals have been very poorly monitored in the graminoid system. In many cases the data for the cypress system had to be used and adjusted to pertain to the graminoids. In general, the average wet mass per animal was obtained from Burt & Grossenheider (1961 or 1976), and the dry weight/wet weight and dry weight/carbon ratios from Jorgensen, et al. (1991).
Bird densities were obtained from the Christmas Bird Count (CBC) and the Breeding Bird Survey (BBS). CBC data from http://www.mbr-pwrc.usgs.gov/cgi-bin/cbcgrids2.pl/numcols=7/cellsize=100?478,578 and BBS from http://www.mbr-pwrc.usgs.gov/id/check/25.html. The BBS (abundance per route) data is converted by using Robbins, et al. 1986 methodology, where they observe 50 stops 0.5 miles apart, and observe 0.25 miles in each direction — thus an area of 12.5 miles2. The CBC data is converted by using the circle with diameter 15km — an area of 458 km2 (Bolte & Bass, 1980). The relative abundance of birds in the CBC is given in number/100 party hours (John R. Sauer, pers. comm., Patuxent Wildlife Research Center) and this abundance was used as is, as it gives a good abundance for the area of the circle counted (Sauer, pers. comm.). It was assumed that the birds that the number of birds that do not feed in the area for the whole day are offset by those birds that were not counted in the survey. Average mass per individual was obtained from Dunning (1993) and Stevenson and Anderson (1994).
Once the biomass had been approximated, information was sought on the production, respiration and consumption rates per unit biomass of each species. Multiplying any biomass density by these factors establishes the total input to and outputs from the compartment in question. If one also has solid data on the dietary proportions of heterotrophs, the total input can be apportioned among the various prey compartments, and the magnitudes of the intercompartmental inputs can be established at this time. Unfortunately, the dietary components of some taxa were not available as quantitative proportions -- only as a list of species. In such cases the total input was assumed to derive from the various prey in proportion to the production or biomass values of those prey.
The consumption, production, respiration and egestion values for each compartment were calculated either by using P/B, P/C, P/R ratios, or by employing known formulas for calculating metabolism, assimilation efficiency, etc. For microbial compartments the P/B, P/R and P/C values from the cypress model were used. For primary producers:
Herpetofauna energetics values were calculated by using the following methodology:
For muskrats, rabbits, raccoons, otter, mink, white tailed deer, bobcats and panthers respiration values were calculated by using Kleiber (1961)'s formula,
Metabolism (Kcal.gww-1.d-1) = 70 x wet weight (kg)0.75, the mean food caloric content of 4.5 Kcal.gdw-1, a mean food carbon content of 45% (Jorgensen, et al. 1991) and using the rule- of- thumb that free living metabolism is approximately twice basal metabolism (McNab, 1980). Fournier & Weber (1994) give the average basal metabolism for opossums as 11,150 ml O2.kg-1.day-1 and finds that the cost of transport is 15-80% (we used 50%) higher than for the average of other mammals of equivalent mass. For the remaining mammals, Banse & Mosher's (1980) formula [P/B = 1.11 x wet mass(kg)-0.33] was invoked to calculate production in conjunction with a metabolic equivalent of 1.5 kcal = 1gww. An assimilation efficiency of 65% was used to calculate the egestion rates of muskrats, rabbits, raccoons, opossum and white tailed deer, while a figure of 80% was applied to otters, mink and panthers (Jorgensen, et al. 1991). Bobcat assimilation efficiency was calculated at 73.75% (Powers, et al. 1989).
Respiration values for rats and mice were calculated from an O2 consumption = 3.27 ml O2.g-1.hour-1 of live weight, to yield an R/C ratio of 0.62 (Odum, et al. 1962). Odum et al. (1962) give an annual turnover rate (P/B) of 2.5 for mice in unfavorable (long hydroperiod) habitat, and 4.9 in favorable (short hydroperiod) areas. Only 2% of the total energy utilized during a season or annual cycle is channeled into production, so that the P/C ratio is 0.02 (Odum, et al. 1962). These ratios were used in conjunction with the estimated biomass of rats and mice to quantify their energetics.
For all bird compartments the annual ratios of P/B (0.015), C/B (0.24) and E/C (0.25) were used to quantify the energetics (Christian & Luczkovich 1999). Respiration was calculated by subtracting the production and egestion from the consumption.
The two seasonal networks were assumed to balance over each period. Although this assumption is not entirely realistic, balance is required for the critical input/output phase of NA (described below). Furthermore, assuming balance facilitates the estimation of many rates. For example, when a component is balanced, its total output can be equated to its total input as a quantity known as the compartmental throughput. It remains to apportion this throughflow among the output processes, namely, respiration, excretion, natural mortality and losses to predation. Fortunately, respiration and excretion rates per unit biomass are available for most species from the literature, so that these outputs can be established immediately. Most of the losses to predation are reckoned from the predator (input) side, as described above.
At this point, the balance is almost complete. It remains to estimate the exchanges of carbon with the outside world. Exogenous imports and exports occur in four different ways: (1) Carbon from the atmosphere may be fixed as biomass through the process of photosynthesis. The magnitude of this import is assessed by multiplying the standing stock of the autotroph with its primary productivity per unit carbon, as mentioned above. (2) Biomass may enter or leave the system with water flowing into and out of the study area. These exchanges are usually estimated from the overall water budget for the area, but in this system that data was not available, and it was therefore assumed that no carbon was imported in this manner. (3) Carbon is accumulated in the sediment and so exported from the system as peat soils. (4) Biomass may enter and leave the system as animal populations migrate across the boundaries of the study area.
Migration applies to many animal species in the model, including invertebrates, fishes and birds. Flowing in the opposite direction are the inputs to the system, for example lizards. Lizards are presumed to stay mostly in the tree hummocks, so that they feed outside the system, and therefore some of their diet would be obtained outside the system. Emigrations of populations, i.e., flows of carbon leaving the system, are considered similar to any other export, but immigrations are treated differently. The network analysis routine, NETWRK, was amended so that migratory imports would be considered separately so as to avoid compartments like lizards from mistakenly being perceived as primary producers. Exactly how this was done will be explained more in detail in the next section.
Movements by avifauna are different than those of fish. Some of the birds may nest or roost on the graminoid prairies, but then leave temporarily to feed elsewhere — such as the cypress and mangroves. Such feeding should be classified as an import to the system. The exclusion of wading birds from this system implies that most of the invertebrates, fishes and herpetofauna consumed by the birds will now appear as an export of carbon to the mangrove and cypress systems. Furthermore, different types of birds exhibit different feeding techniques. For example, some need high water levels and others, low water. These activities are all built into the estimates of imports to- and exports from the ecosystem and impart to the system the role of a "food basket" for the cypress and mangrove systems.
The estimates of all the flows entering and leaving each compartment have now been described. Of course, uncertainties inherent in these partially independent estimations will mean that many of the compartments will not balance exactly. The degree of imbalance can be computed by entering the estimated flows into a spreadsheet format (EXCEL[TM] was used for this purpose). Doing this allows one to compare the marginal sums of inputs to and outputs from each compartment in order to identify those that are most out-of-balance. The investigator has several options for treating an imbalance in a compartment. If the imbalance is severe, it is probably best to check the sources and the arithmetic. Failing the discovery of an error, one might search for other references to crosscheck the data being used.
If no amendments to a compartmental budget can be made on the basis of new data, some investigators prefer to bring the system nearly into balance by adjusting the least-well known flows. Others would rather maintain the flow proportions for each compartment as they appear in the literature and then re-balance the whole system under the covering assumption of linear, donor-control, which always maintains flows positive (Ulanowicz 1989). In this study all compartments could be balanced to within a few percent using literature values, and a final balance was achieved using the program DATBAL, which assumes linear, donor control.
The resulting networks are too large and complicated for easy illustration. Even a matrix representation of one such network spans several pages and is extremely cumbersome to use. For these reasons, detailed results are probably best presented in hypertext format, which can be accessed over the World Wide Web at http://www.cbl.umces.edu/~atlss. Using hypertext, one follow simple instructions to locate the estimated value of any stock or flow in either the wet or dry season. Furthermore, the entire rationale and associated references pertaining to the estimation of any particular value have also been documented in hypertext. Thus, by pointing and clicking one may examine a trophic flow network in minute detail.
This format for disseminating
the details of the network should have important benefits for ecosystem science
in general and for the visibility of the ATLSS endeavor in particular. We are
aware of no other single source where the structural elements of entire ecosystems
can be examined and scrutinized so readily. Even if a user has no idea of the
benefits of NA, he/she can begin with the species that interests them most and
trace the sources and fates of material into and out of that compartment --
simply by pointing and clicking. The presentation also makes it easier to critique
the networks, and online suggestions for improvements and amendments are welcomed
4.2.1. Background
Sometime during the mid-1970's it became apparent that ecological modeling in the form of a set of coupled, deterministic differential equations was a problematical undertaking that required support from other, independent methods of systems analysis. In the search for parallel methods of describing the behavior of total ecosystems, various computations performed on the network of trophic flows have figured prominently (SCOR, 1981).
The original impetus for diverting attention from dynamics and concentrating analysis on flow structure came from the field of economics, where success in elucidating indirect economic effects had been achieved by manipulations on matrices of economic flows (Leontief, 1951; Hannon, 1973). Thereafter followed a number of other topological treatments of the underlying flow graph (e.g., Finn, 1976; Levine, 1980; Patten, et al. 1976; Ulanowicz & Kemp, 1979). Eventually, Ulanowicz collected most of the methods for analyzing flow networks into a single executable package, called NETWRK (Ulanowicz & Kay 1991.) NETWRK 4.2a is the version used in this analysis.
Four types of analyses are performed by NETWRK. First, input-output structure matrices are calculated. These allow the user to look in detail at the effects, both direct and indirect, that any particular flow or transformation might have on any other given species or flow. Next, the graph is mapped into a concatenated trophic chain (after Lindeman 1942). Then global variables describing the state of development of the network are presented. Finally, all the simple, directed biogeochemical cycles are identified and separated from their supporting dissipative flows. NETWRK 4.2a and its accompanying documentation may be downloaded from the World Wide Web at http://www.cbl.umces.edu/~ulan/ntwk/network.html.
In addition to NETWRK, a package called IMPACTS was used to gauge both the positive and negative, direct and indirect impacts that heterotrophic predation may cause. The method was described in Ulanowicz & Puccia (1990). Of particular interest is how negative impacts at one level can ramify to become positive indirect effects.
The data required to run either of these programs have already been discussed. It was detailed above how, for each compartment, it is necessary to know: (1) all the inputs from outside the system, (2) all the various inputs flowing from other compartments of the system, (3) all the outputs which flow as inputs to other compartments, (4) all exports of useful medium outside the system, and (5) all rates of dissipation of medium. Each of these flows can be represented by a positive scalar element of a matrix or a vector; the absence of a flow can be represented by a zero.
The initial section of the NETWRK package is founded upon an ecological variation of economic input-output analysis. "Total contribution coefficients" (Szyrmer & Ulanowicz, 1987) describe exactly what fraction of the total amount leaving compartment i (prey or row designation) eventually enters compartment j (predator or column designation) over all pathways, both direct and indirect. Alternatively, the "total dependency coefficients" portray the fraction of the total ingestion by j, which passed through compartment i along its way to j. The columns of this matrix are particularly useful, because they portray the "extended diet" of the species in question (or, correspondingly, the trophic "pyramid" that supports each heterotroph). As was demonstrated with the cypress wetland ecosystem, such indirect ratios can provide valuable information about how a system is functioning.
As an example of indirect diet coefficients, consider the snail kites (#59). They depend on the apple snails (#7) and other macroinvertebrates (#11) for 100% of their sustenance. These prey items in their turn depend upon primary producers, such as periphyton, macrophytes and other floating vegetation (#3, 4, 5 and 6), and living detritus (#1 and 2), so that ca. 95% of the consumption by snail kites originates from periphyton. Thus, carbon is counted more than once as it passes up the food chain, and the fact that all of the above dependencies sum to over 270% is entirely consistent with the fact that snail kites feed, on the average, at about trophic level 3.
Hannon
(1973), Finn (1976), Levine (1980) and Patten,
et al. (1976) give various examples of how one may employ input-output
analysis. One highly useful application is the decomposition of the graph according
to each input. That is, the eventual fate of each of the nonzero inputs to the
system is traced independently of the other inputs to the system. Not only does
this decomposition portray the isolated effects of the various inputs, but these
sub-networks can be linearly recombined to recreate what the effects of any
arbitrary linear combination of inputs would be, if the flow structure were
kept the same.
The second section of output from NETWRK interprets the given network according to the trophic concepts of Lindeman (1942). Of course, it is impossible to relegate omnivorous heterotrophs entirely to a single trophic level, but Ulanowicz & Kemp (1979) indicated how input-output techniques could be used to apportion the activities of omnivores among a series of integer trophic levels. This method has been expanded to include the effects of biogeochemical cycles by Ulanowicz (1995a).
In order for trophic aggregation to be meaningful, it is necessary that trophic pathways among living compartments remain finite in length, otherwise one is forced to interpret an infinite regress of trophic levels. Fortunately, Pimm (1982) states that cycles among living taxa are rare in ecosystem networks (although we encountered some interesting exceptions in the three previous networks). The absence of such feeding cycles avoids trophic pathways of infinite length. As a preliminary to trophic aggregation, therefore, all cycles flowing through only living compartments are first removed from the network. So long as the Finn cycling index for such heterotrophic cycling (see below) remains sufficiently small (say, below two percent or so), no appreciable distortion of results should ensue. The 2% requirement is more than satisfied by the graminoid networks.
When the fractions by which each component feeds at a particular trophic level are weighted by the value of that trophic level and the results are summed, one arrives at the effective trophic level for the given species (Levine, 1980.) For example, if a species or compartment is receiving 15 units of medium along a pathway of length 2 and 5 units along a pathway of length 3, then it is acting 75% as a herbivore (trophic level = 2) and 25% as a carnivore (level = 3). The effective trophic position becomes (0.75 x 2) + (0.25 x 3) = 1.75. It is often interesting to compare the average trophic position of species under different circumstances (as, for example, between wet and dry seasons).
The section of NETWRK dealing with trophic aggregation culminates with the partitioning of system activity into a trophic "chain" of transfers, along linear aggregations of heterotrophs. Each such aggregation feeds back into detrital return loops. Such a depiction of the underlying trophic dynamics has been termed "canonical" by Ulanowicz (1995a), because any ecosystem can be mapped into this equivalent and simple form to allow the relative magnitudes of corresponding flows to be compared directly.
One change made recently as part of NETWRK version 4.2a was to treat migratory inputs of heterotrophs differently than inputs to autotrophs (primary production). NETWRK now treats inputs to heterotrophs as coming into the system at exactly the same trophic level as the receiving compartment would otherwise occupy within the system. Previously such inputs were treated as primary production by default, and this unrealistic assumption artificially deflated many of the reported trophic levels.
The next section of output from NETWRK yields estimates for global attributes of the network that have been defined with the help of information theory to assess the pattern of development in ecosystems (Ulanowicz, 1980,1986; Hirata & Ulanowicz, 1984; Ulanowicz & Norden, 1990). The first such property is the "total system throughput", or the gross sum of all transfers, which provides a measure of the size of the system. Multiplying the total throughput by the system indeterminacy (according to the Shannon Wiener formula) of the individual flows yields what has been termed the "development capacity" of the system. This quantity serves as an upper bound on the ascendency, which is a measure of the network's potential for competitive advantage over other real or putative network configurations. Ascendency is the product of a factor of size (total system throughput) times a factor representing the coherence of the flows (the average mutual information of the flow structure).
The difference between the realized structure and its upper bound is the overhead (Ulanowicz, 1986). Overhead has contradictory interpretations. On one hand, it is a catchall for the system's inefficiencies in processing material and energy. What is a disadvantage under benign conditions can turn in the system’s favor when it is perturbed in some novel way, however. Then, the overhead represents a "strength-in-reserve" of degrees of freedom, which the system can utilize to adapt to the new threat. Overhead is generated in any of four ways: three components of overhead are due to indeterminacies in imports, exports, dissipations (respirations), and a fourth is related to the indeterminacy over which of several parallel pathways flow will proceed between any two nodes (flow redundancy). The fractions of the development capacity encumbered by the ascendency and by each of the overhead components provide a profile of the structural composition of the system that often is useful for assessing the organizational status of an ecosystem.
Most networks of ecosystem flows contain cycles of material or energy, and the magnitudes and structure of these cycles are fully assessed by NETWRK. The program enumerates all of the simple cycles in the given matrix of exchanges. Furthermore, the simple cycles are grouped into "nexuses" of cycles that share the same "weak arc." A weak arc is defined here as the smallest flow in a given directed cycle. The assumption is that the weak arc is the limiting or controlling link in a cycle, and that by grouping according to critical links, one identifies the domain of influence for each weak arc. Presumably, any change in a weak arc will propagate throughout its associated nexus. The nexuses are listed roughly according to ascending order of the magnitude of their defining weak arcs.
The cycles are then subtracted from the network in a fashion described in detail by Ulanowicz (1983). Briefly, the magnitude of flow in the smallest weak arc is distributed over the flows in that particular nexus, and the resulting amounts are subtracted from each arc in that nexus. This process zeroes the weak arc, thereby eliminating all the cycles in that nexus, but it does not disturb the balance around any compartment, nor does it change any exogenous input, export or respiration. None of the remaining arcs of the nexus are driven negative. After that nexus has been removed, the next smallest weak arc is located; and nexuses are subtracted iteratively until all cycles have been removed from the network.
As each cycle is removed, the flow associated with that cycle is added to the magnitudes of other cycles of the same trophic length. The end result is a distribution of the magnitude of cycling according to the trophic length of cycles. This profile could be useful in assessing system response to perturbation. For example, cycling via the larger loops is often more sensitive to disturbance. The cycle distribution is then normalized by the total system throughput. Summing this normalized distribution yields the Finn cycling index, which is the fraction of total activity that is devoted to cycling (Finn, 1976).
Finally, the separation of cycled from transient flow is reported in the form of separate matrices for each type of flow. The row sums and column sums of the matrix of aggregated cycles will always balance; no further reference to exogenous exchanges is necessary. The visual structure of the aggregated cycles existing in more complicated networks very often reveals separate domains of control in the network (e.g. Baird & Ulanowicz 1989). Finally, it should be remarked that the starting network has been neatly decomposed into an acyclic "tree" of dissipative flows and a wholly conservative nexus of cycled flows.
NETWRK treats only positive
mass flows and does not consider the propagation of the negative effects that
accompany predation. Ulanowicz & Puccia (1990)
outlined how to treat the propagation of both positive and negative trophic
effects, and their technique has been implemented in the algorithm, IMPACTS.
For any particular component (designated as the "focal taxon"), IMPACTS
provides a ranked listing of all the positive and negative impacts (both direct
and indirect) upon that focal species. Also a ranked listing of all the direct
and indirect trophic effects that focal species has upon all the other taxa
is likewise provided. Of special interest are those predators that exert a direct
negative impact upon a prey, but whose combined indirect positive influences
more than compensate the prey for its direct losses. Such "beneficial predators"
are more common than might be supposed and often highlight particular ecological
roles that otherwise might have gone unnoticed. In similar fashion, one can
identify various prey species that indirectly have an adverse effect upon their
predators. These are referred to as "malefic prey". IMPACTS can be
downloaded from http://www.cbl.umces.edu/~ulan/ntwk/network.html.
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