the corresponding indirect influences shown in the middle Table 4 matrix, compared 

 to the direct effects of the lower matrix of Table 1, seem incredible in view of the 

 simplicity of the Figure I system. They arethe basis for the proposition of this paper 

 that in most biotically well developed ecosystems the preponderance of causality is 



Table 3. Matrices for Indirect Paths of Length 3 in the Figure 1 Model. 

 Upper: Number of Length 3 Paths from Column to Row Com- 

 partments. 



Middle: Indirect Influence, as Daily Fractions of Carbon in 

 Column Compartments, Transferred to Row Compartments 

 Over Length 3 Paths. 



Lower: Total Influence, as Summed Daily Carbon Fractions of 

 Column Compartments, Transferred to Row Compartments 

 Over Paths of Lengths 1 Through 3. 



from 



1 



8 



to 



1 

 2 

 3 

 to 4 

 5 

 6 

 7 

 8 

 9 



3^ 



3 

 12 

 12 

 17 



9 

 17 





 11 



1 



1 



5 

 5 

 8 

 4 

 9 

 

 5 





 



'U 

 

 

 

 

 

 



3 



1 

 6 

 ^7~. 

 10 



6 

 13 







8 



1 





 4 

 4 



'6- 

 4 

 9 

 

 5 



5 



3 



14 



14 



19 



"IK 



21 







14 





 

 

 

 

 



•1- 





 



4 

 6 

 15 

 12 

 15 

 7 

 11 



•--I . 

 10 



from 

 4 5 



.729^.^0 

 .071 .729 





 



.003 .053^^04- 



.004 .004 



.014 Oil 



>0 >0 



>0 >0 

 



.023 >0 





 

 

 

 



>0 >0 



>0 



^0 >0 

 .858-^0 



.032 .857 



.025 >0 



.01 2 .008 







.001 .031 



from 



4 

 1 

 10 

 10 

 14 

 9 

 18 





 11 



98 



