Table 2.

Ecological network indicators calculated for the western Baffin Bay ecosystem

IndicatorDescriptionFormulaUnitsSource
Size, growth, and development 
Total system throughput, TST Sum of input, output, and internal biomass flows in the food web. It measures the size and activity of the system, indicating the amount of biomass production in the food web. TST here differs from total system throughflow (TSTflow), which is the sum of either all the inputs or all the outputs. ∑(internal flows+inputs+outputs) tons km−2 year−1 Ulanowicz, 1986  
Average mutual information, AMI Pathways of biomass flows among functional groups. It is calculated based on the joint probability of a certain biomass flow occurring, the marginal probability of a biomass flow entering functional group j, and the conditional probability that this flow leaves functional group i. It thus indicates the specialization and constriction of biomass flows within the food web. k.∑ijflowijTST.logflowij.TSTflowi..flow.j bits Ulanowicz, 1986; Fath et al., 2019  
Ascendency, A Measures both the growth (TST) and development (AMI) of the system. It can indicate the level of activity and organization within the system, representing the efficient part of the food web. TST*AMI bits Ulanowicz, 1986  
Relative ascendency, A/C Ratio between ascendency (A) and development capacity (C). It is the maximal value of ascendency (or organization) that the food web can reach. A−∑ijflowij.logflowijTST no units Ulanowicz, 1986; Fath et al., 2019  
Robustness Combines organization and efficiency of a system (ascendency), rendering it resistant, with redundant options in case of disturbance (redundancy), rendering it resilient. It varies between 0 and 1, with optimal results falling in the middle. −AC.logAC no units Fath, 2015  
Cycling 
Finn’s cycling index, FCI Indicates the fraction of the TSTflow that is recycled in the system, that is, how much of the biomass flow revisits the same functional group multiple times before exiting the system. High FCI indicates that the biomass stays in the system longer. ∑TSTflowcycledTSTflow no units Finn, 1976; Fath et al., 2019  
Indirect flow intensity, IFI Proportion of TSTflow derived from indirect pathways of biomass flows. ∑indirectflowsTSTflow no units Borrett et al., 2006  
Average path length, APL Average number of functional groups biomass inputs or outputs pass through before exiting the food web. It measures the retention of biomass within a system. A high APL is generally associated with a longer food chain. TSTflow∑inputs no units Finn, 1976  
Control 
Control difference, cd Quantifies pair-wise dependencies between each pair of functional groups, i.e. functional group i controls functional group j if the direct and indirect biomass flow from i to j exceeds that from j to i, within the flow environments of i and j. For component i to be controlling j, it must be more important in the input environment Ej’ than in the output environment Ej, and vice-versa. In terms of TSTflow, the control can be defined based on the difference between the fractional transfer values between i and j. The magnitude of cd indicates the level of control while the direction of control is quantified as positive or negative. cdij=EijTSTflowiout−Eji′TSTflowiin no units Dame and Patten, 1981; Schramski et al., 2006  
System control Relative influence of each functional group towards the movement of biomass through the entire food web. If positive, the group controls the system, and if negative the group is controlled by the system. It corresponds to the sum of cdij. ∑cdij no units Schramski et al., 2006; 2007  
IndicatorDescriptionFormulaUnitsSource
Size, growth, and development 
Total system throughput, TST Sum of input, output, and internal biomass flows in the food web. It measures the size and activity of the system, indicating the amount of biomass production in the food web. TST here differs from total system throughflow (TSTflow), which is the sum of either all the inputs or all the outputs. ∑(internal flows+inputs+outputs) tons km−2 year−1 Ulanowicz, 1986  
Average mutual information, AMI Pathways of biomass flows among functional groups. It is calculated based on the joint probability of a certain biomass flow occurring, the marginal probability of a biomass flow entering functional group j, and the conditional probability that this flow leaves functional group i. It thus indicates the specialization and constriction of biomass flows within the food web. k.∑ijflowijTST.logflowij.TSTflowi..flow.j bits Ulanowicz, 1986; Fath et al., 2019  
Ascendency, A Measures both the growth (TST) and development (AMI) of the system. It can indicate the level of activity and organization within the system, representing the efficient part of the food web. TST*AMI bits Ulanowicz, 1986  
Relative ascendency, A/C Ratio between ascendency (A) and development capacity (C). It is the maximal value of ascendency (or organization) that the food web can reach. A−∑ijflowij.logflowijTST no units Ulanowicz, 1986; Fath et al., 2019  
Robustness Combines organization and efficiency of a system (ascendency), rendering it resistant, with redundant options in case of disturbance (redundancy), rendering it resilient. It varies between 0 and 1, with optimal results falling in the middle. −AC.logAC no units Fath, 2015  
Cycling 
Finn’s cycling index, FCI Indicates the fraction of the TSTflow that is recycled in the system, that is, how much of the biomass flow revisits the same functional group multiple times before exiting the system. High FCI indicates that the biomass stays in the system longer. ∑TSTflowcycledTSTflow no units Finn, 1976; Fath et al., 2019  
Indirect flow intensity, IFI Proportion of TSTflow derived from indirect pathways of biomass flows. ∑indirectflowsTSTflow no units Borrett et al., 2006  
Average path length, APL Average number of functional groups biomass inputs or outputs pass through before exiting the food web. It measures the retention of biomass within a system. A high APL is generally associated with a longer food chain. TSTflow∑inputs no units Finn, 1976  
Control 
Control difference, cd Quantifies pair-wise dependencies between each pair of functional groups, i.e. functional group i controls functional group j if the direct and indirect biomass flow from i to j exceeds that from j to i, within the flow environments of i and j. For component i to be controlling j, it must be more important in the input environment Ej’ than in the output environment Ej, and vice-versa. In terms of TSTflow, the control can be defined based on the difference between the fractional transfer values between i and j. The magnitude of cd indicates the level of control while the direction of control is quantified as positive or negative. cdij=EijTSTflowiout−Eji′TSTflowiin no units Dame and Patten, 1981; Schramski et al., 2006  
System control Relative influence of each functional group towards the movement of biomass through the entire food web. If positive, the group controls the system, and if negative the group is controlled by the system. It corresponds to the sum of cdij. ∑cdij no units Schramski et al., 2006; 2007  
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