Appendix
Table 3 Objective function and constraints of taxon selection problems for the pheasant example
Maximize |
l1 y1 +¼+ l20 y20 |
(1) |
Subject to
Size constraint: |
xPB + xPC + xPE + xPG + xPI + xPM + xGG + xGL + xGS + xGV £ k |
(2) |
Binary constraints: |
xi ∈{0,1}∀ taxon i |
(3) |
ys Î{0,1} "s = 1,..,20 |
(4) |
|
Split constraints: |
yi ≤ xi∀ taxon i |
(5) |
y11 £ xPB + xPC |
||
y11 £ xPE + xPG + xPI + xPM + xGG + xGL + xGS + xGV |
||
y12 £ xPB + xPC + xPI |
||
y12 £ xPE + xPG + xPM + xGG + xGL + xGS + xGV |
||
y13 £ xPB + xPC + xPG + xPI |
||
y13 £ xPE + xPM + xGG + xGL + xGS + xGV |
||
y14 £ xPB + xPC + xPG + xPI + xPM |
||
y14 £ xPE + xGG + xGL + xGS + xGV |
||
y15 £ xPB + xPC + xPE + xPG + xPI |
||
y15 £ xPM + xGG + xGL + xGS + xGV |
||
y16 £ xPB + xPC + xPE + xPG + xPI + xPM |
||
y16 £ xGG + xGL + xGS + xGV |
||
y17 £ xPB + xPC + xPE + xPG + xPI + xPM + xGS |
||
y17 £ xGG + xGL + xGV |
||
y18 £ xPB + xPC + xPE + xPG + xPI + xPM + xGG + xGS |
||
y18 £ xGL + xGV |
||
y19 £ xPB + xPC + xPE + xPG + xPI + xPM + xGV |
||
y19 £ xGG + xGL + xGS |
||
y20 £ xPB + xPC + xPE + xPG + xPI + xPM + xGL + xGV |
||
y20 £ xGG + xGS |
(continued)
Table 3 (continued)
Budget constraint: |
cPB xPB + cPC xPC +¼+ cGV xGV £ B |
(6) |
Viability constraints: |
xPB £ xPE |
(7) |
xPC £ xGG + xGV |
||
xPG £ xPB |
||
xPI £ xGL |
||
xPM £ xPC + xGL |
||
xGL £ xPB |
||
xGS £ xPM + xPG |
||
xGV £ xGG + xPE |
Table 4 Objective function and constraints of reserve selection problems for the pheasant example. Due to the fact that G. gallus is contained in all but one area there are many area-split constraints of the form ys £ zBT + zID + zIN + zLK + zPH + zMY + zTH + zVN . Such constraints are redundant since k ≥ 2, and thus omitted
Maximize |
l1 y1 +¼+ l20 y20 |
(1) |
Subject to
Size constraint: |
zID + zLK + zBT + zIN + zPH + zMY + zTH + zVN £ k |
(8) |
Binary constraints: |
zr ∈{0,1}∀ area r |
(9) |
ys Î{0,1} "s = 1,..,20 |
(4) |
|
Area-split constraints: |
y1 £ zBT + zTH |
(10) |
y2 £ zID |
||
y3 £ zPH |
||
y4 £ zVN |
||
y5 £ zMY |
||
y6 £ zMY |
||
y7 £ zBT + zID + zIN + zPH + zMY + zTH + zVN |
||
y8 £ zLK |
||
y9 £ zIN |
||
y10 £ zID |
||
y11 £ zBT + zID + zTH |
||
y12 £ zBT + zID + zMY + zTH |
||
y13 £ zBT + zID + zMY + zTH + zVN |
||
y14 £ zBT + zID + zMY + zTH + zVN |
||
y15 £ zBT + zID + zPH + zMY + zTH + zVN |
||
y16 £ zBT + zID + zPH + zMY + zTH + zVN |
||
y17 £ zBT + zID + zIN + zPH + zMY + zTH + zVN |
||
y18 £ zBT + zID + zIN + zPH + zMY + zTH + zVN |
||
y18 £ zID + zLK |
||
y19 £ zBT + zID + zPH + zMY + zTH + zVN |
||
y20 £ zBT + zID + zLK + zPH + zMY + zTH + zVN |
||
y20 £ zBT + zID + zIN + zPH + zMY + zTH + zVN |
||
Budget constraint: |
cID zID + cLK zLK +¼+ cVN zVN £ B |
(11) |
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