expected of its ecosystems. This is reflected in the Figure 1 carbon flow network. Of 

 72 possible interactions between the compartments, not counting the self interactions 

 of each compartment, 27 are realized for 38% connectivity. The upper matrix of 

 Table 1 is an adjacency matrix representing the interactions shown in Figure 1. 

 "Adjacency" because each entry of "1" represents a direct carbon exchange from a 

 column compartment to the corresponding row compartment over a path of length 1 . 



These carbon flows are quantified in the lower matrix of Table 1 , where each entry 

 represents the daily fraction of carbon in each column compartment transferred by 

 each row compartment (Notes, 0- The columns in this matrix sum to 1 over the entire 

 ecosystem model, and hence are < 1 (in principle, < 1 actually) within the Figure 1 

 subsystem. Thus, the entries quantify daily carbon exchanges on a scale between 

 and 1 , and will here be taken to exemplify influences of the column compartments on 

 the row compartments (Notes, g). The largest values are intracompartmental, along 

 the principal diagonal, reflecting strong predator-prey interactions between the 

 species within each compartment and also the tendency of carbon not to be 

 transferred to other compartments in a given day. As strong as these diagonal values 

 are, and as relatively small as the intercompartmental interactions appear in 

 comparison (0.021 is the largest nondiagonal value), it will be shown that indirect 

 influences are predominant. 



Table 1. Adjacency Matrices for the Figure 1 Model. 



Upper: Presence ( 1 ) or Absence (0) of Direct Feeding Flow from 

 Column to Corresponding Row Compartments. 

 Lower: Direct Influence, as Daily Fractions of Column Com- 

 partments Contributed as Food Over Length 1 Paths Identified in 

 the Upper Matrix. 



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