The last property mentioned here is the signature property, the quantitative environ, both in the input and output orientation. Since each compartment has two distinct environs, there are in fact 2n environs in total. The output environ, E, for the ith node is calculated as:

where Nj is the diagonalized matrix of the ith column of N. When assembled, the result is the output-oriented flow from each compartment to each other compartment in the system and across the system boundary. Input environs are calculated as

where, gj=fj/T, and N' = (I — G')—1 These results comprise the foundation of network environ analysis since they allow for the quantification of all within-system interactions, both direct and indirect, on a compartment-by-compartment basis.

Table 2 Direct and integral relations in sample network from Figure 1

Direct Integral

Table 2 Direct and integral relations in sample network from Figure 1

Direct Integral

(sd2i |
sdi2) = |
+, -) |
! exploitation |
(su2i, sui2) = |
+ , |
-) |
! exploitation |

(sdsi |
sdi3) = |
+, -) |
! exploitation |
(su3i, sui3) = |
+ , |
-) |
! exploitation |

(sd41 |
sdi4) = |
0 , 0) - |
-> neutralism |
(su4i, sui4) = |
+ , |
+)- |
! mutualism |

(sdsi |
sdis) = |
- , +) |
! exploited |
(su5i, sui5) = |
+ , |
+)- |
! mutualism |

(sd32 |
sd23) = |
+, -) |
! exploitation |
(su32, su23) = |
-, |
-) |
! competition |

(sd42 |
sd24) = |
+, -) |
! exploitation |
(su42, su24) = |
+ , |
-) |
! exploitation |

(sd52 |
sd25) = |
0 , 0) - |
neutralism |
(su52, su25) = |
+ , |
+)- |
! mutualism |

(sd43 |
sd34) = |
+, -) |
! exploitation |
(su43, su34) = |
+ , |
-) |
! exploitation |

(sd53 |
sd35) = |
+, -) |
! exploitation |
(su53, su35) = |
+ , |
-) |
! exploitation |

(sd54 |
sd45) = |
+, -) |
! exploitation |
(su54, su45) = |
+ , |
-) |
! exploitation |

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