Chapter 4: Comparative analysis of carbon and nitrogen dynamics of three estuaries on the east
4.2. Materials and Methods
4.2.5. Ecological network analysis
The mass-balanced carbon and nitrogen networks were analysed using the software WAND (Allesina and Bondavalli, 2004) to examine the flow of energy and material in the seasonal networks of the East Kleinemonde, Mlalazi and Mpenjati estuaries through Ecological Network Analysis (ENA). Zooplankton biomass for the East Kleinemonde Estuary was available as total zooplankton biomass and not as biomass per species; therefore the biomass of the different zooplankton species at the Mlalazi and Mpenjati estuaries were aggregated into one compartment, “total zooplankton”, to generate another set of networks that allowed for comparisons between estuaries. A total of 16 networks (two estuaries, two nutrients and four seasons) were also analysed, with the results from the aggregated and original networks being presented in the Results section below.
To quantify the contribution of detritus, primary producers (phytoplankton and microphytobenthos) and consumers (zooplankton, macrobenthos, fish) to the carbon and nitrogen requirements of the system, as well as the dependencies of each system on the above-mentioned groups, an input-output analysis was conducted (Szyrmer and Ulanowicz, 1987). The input-output analysis provides information about the influence that direct and indirect predator-prey interactions have on other compartments of the food web;
the fractions of direct and indirect relationships between compartments are represented as components of the total contribution and total dependency matrix (Szyrmer and Ulanowicz, 1987). Input-output analysis is based on information of the matrix of dietary proportions (G), the elements in this matrix represent the fraction of compartment i in the diet of compartment j. By multiplying matrix (G) by itself (G)2, one can determine all the pathways of length 2 connecting i to j. This procedure is repeated until the pathways of maximum length (m) are determined (G)m. The series of matrix powers reach a limit:
lim{(I)+(G)+(G)2 +(G)3+(G)4+ ….} → (I-G)-1
the matrix (I), which equals (G)0, is named the identity matrix, and consists of 0’s for i≠j and 1’s for i=j. The limit or matrix inverse (I-G)-1 is named the Leontief structure matrix (S), where Sij represents the fraction of total input into j that left i and passed through all pathways to fulfil a final demand of j of one unit. The transformation of the (S) matrix calculate the intermediate transfers between compartments, this transformed matrix is named total dependency matrix (D). The elements of the (D) matrix represents the fraction of the total diet of j that passed through compartment i on its way to j over all direct and indirect pathways.
are the elements of the identity matrix and describes the entries of the dependency matrix, which are termed dependency coefficients, represents the flows from compartment i entering all other compartments in the system and represents all flows entering j. The sum of the coefficients in the jth column of the dependency matrix represents its extended diet or dependency on the production of each compartment in the system via all direct and indirect pathways. Conversely, the row sum of the coefficients in the dependency matrix represents the dependencies of all the other compartments in the system on a particular compartment.
The contribution matrix (C) is calculated from the matrix of host coefficients (F), the output structure matrix (Σ) and the flows (T). The elements of the matrix of host coefficients represents the fraction of total activity of compartment i that flows directly to compartment j. The output structure matrix (Σ) equals (I-FT)-1
(Augustinovics, 1970), FT is the transposed matrix of host coefficients indicating that the rows of this matrix were exchanged with its columns. The elements of the contribution matrix (C) represents the fraction of total flow that left compartment i and enters compartment j over all direct and indirect pathways.
represents the amount of production of compartment j generated by one unit of input to i, is the exports from compartment i entering all other compartments in the system, represents all flows entering j and Cij represents the entries of the contribution matrix or contribution coefficients. The row sum of the contribution coefficients determines the total contribution of each compartment to all other compartments in the system.
To determine the contribution of or dependency on a given compartment in the system, the contribution and dependency coefficients of each compartment were row summed. The total contribution of or dependency on the major groups in the system (phytoplankton, microphytobenthos, zooplankton, macrobenthos, fishes, suspended and sediment detritus) was then evaluated.
The Total System Throughput (T..) is a measure of the size and activity of a system (Ulanowicz and Kay, 1991). The Total System Throughput equals the sum of all flows of energy or material through all the compartments in the food web.
In order to determine the trophic status of each system, indices such as the number of discrete trophic levels, efficiency of trophic transfers, and amount of detritivory and herbivory were calculated using the Lindeman trophic analysis. This analysis transformed each trophic interaction in a network into a food chain with discrete trophic levels (Ulanowicz and Kemp, 1979, Ulanowicz 1995a). Lindeman analysis first allocated a discrete trophic level to parts of each compartment in the network based on their feeding activities, detritus and primary producers were apportioned to the first trophic level (Ulanowicz and Kemp, 1979). Based on their discrete trophic levels, parts of compartments were grouped according to the trophic level they feed on. The efficiency of trophic transfer or the amount of energy and material passed from one discrete trophic level to another is quantified. The exports, respirations and returns to the detrital pool of each discrete trophic level, as well as the total amount of detritivory and herbivory in a system were also determined.
To examine the cycling of energy and material within these estuaries, a cycle analysis was conducted.
This determines the topology of pathways over which energy or material is recycled within a system
(Ulanowicz, 1983). The Finn Cycling Index (FCI) represents the ratio of the total amount of energy or material cycled through the system to the system total throughput (Finn, 1980).
FCI = – /
where Ti is the total throughput through group i and (Sii -1) is the throughput through group i resulting from cycling. The Average Path Length (APL) measures the average number of transfers that a unit of energy experiences since it enters to the system until it leaves the system (Kay et al., 1989). The Average Path Length is calculated as APL: (TST-Z)/Z, where TST is the total system throughput and Z is the sum of all the imports to the system, and
To determine the size, development and organization of each estuary, system information indices were calculated (Ulanowicz, 1986). The ascendency (A) provides an indication of the organization and specialization of the flows within a system, and is calculated by multiplying the TST by the average mutual information or measure of flow specialization in a system. Thus, A combines the total activity of a system (T..) with the efficiency of flows in the system,
A = log (
where Tij represents a quantum of flow leaving compartment i and entering compartment j, T.. is the total system throughput and represents the sum of flows over all combinations of Tij, T.j represents all flows entering j. Higher A values indicate a well organized system, with higher internalization of resources and more specialized pathways (Ulanowicz, 1986). An increase in A is expected during the dry season or closed phase of TOCEs due to the lower disturbance caused by reduced freshwater inflow.
The development capacity (DC) determines the potential of a system to develop and is the maximum limit to the ascendency. The DC is calculated as the product of the total system throughput (TST) and the diversity of individual flows,
DC = - log (
where Tij/T.. represents the actual flow from compartment i to j.
The system overhead (O) equals the difference between the development capacity and the ascendency, this represents the flexibility of a system to adapt to disturbances (Ulanowicz, 1986). The overhead is
formed by the magnitudes and diversity of pathways of imports and exports to and from the system, dissipation of energy (or energy) and redundancy (R, parallel pathways). Since the overhead represents the capacity of a system to withstand perturbations, the integrity of an ecosystem depends on a balance between the ascendency and overhead. The overhead on imports and exports is expected to be higher during the wet season as a result of the increased rainfall and river inflow to these estuaries.
The ratio of the ascendency to the development capacity or relative ascendency (A/DC) is a measure of the degree of system order, where lower A/DC values are indicative of systems with low order (Ulanowicz, 2012). The relative redundancy (R/DC) is the ratio of the redundancy or flow on parallel pathways to the development capacity. R/DC represents the capacity of a system to adapt to novel perturbations, since parallel pathways of energy act as a buffer against perturbations (Ulanowicz, 2012). Higher A/DC values are expected during the dry season or closed phase of the TOCEs because of the reduced flushing and disturbance during this season (Scharler, 2012).
The above suite of indices was calculated for the carbon and nitrogen networks of the East Kleinemonde, Mlalazi and Mpenjati estuaries. The indices obtained are described, compared and related to the physical and biological conditions of the systems during a particular season.