HIGHER ORDER (INDIRECT) CAUSES AND EFFECTS 



Second Order 



If each Table 1 matrix is multiplied by itself (Notes, h), the product matrices 

 represent, respectively, the number of paths of length 2 and the daily fractional 

 carbon flow summed over these paths from each column compartment to each 

 corresponding row compartment. These matrices appear as the upper and middle 

 matrices of Table 2. The upper one shows there are more paths of length 2 in the 



Table 2. Matrices for Indirect Paths of Length 2 in the Figure 1 Model. 

 Upper: Number of Length 2 Paths from Column to Row Com- 

 partments. 



Middle: Indirect Influence, as Daily Fractions of Carbon in 

 Column Compartments, Transferred to Row Compartments 

 Over Length 2 Paths. 



Lower: Total Influence, as Summed Daily Carbon Fractions of 

 Column Compartments, Transferred to Row Compartments 

 Over Paths of Lengths 1 Through 2. 



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