Chapter 3
Selection of sites for in situ conservation
- a logical approach

3.1 Introduction


Management decisions should be based on the information about
the resources to be managed and the management objectives under
consideration. Suppose we want to set aside some areas for in situ
conservation of plant genetic resources and the objective is to
maximize the number of species being conserved. For this, we should
know: 1. which species do we want to conserve? 2. where are those
species located? 3. how much area do we want to set aside for in
situ conservation purpose? and 4. whether the conservation area
should be in one big piece or many small pieces? etc. This chapter
deals with some of these issues.
In a presence/absence matrix (Appendix 3.1), we have 430 plant
species listed from 46 sites in the study area. The areas sampled
at each site is 0.25 hectares. If we have enough resources then we
can choose all the 46 sampled sites to conserve all the 430
species. This could be one approach. However, if we have limited
resources or we are willing to save only a certain fraction of
these plant species/sites then the question arises about which
combination of sites should be chosen to maximize the number of
species being saved.
The number of possible combinations of sites taking 0, 1, 2,
3, . . ., 46 site(s) at a time out of 46 sites are given by the
coefficients of the binomial expansion 46Cr, where r ranges from 0
to 46. In each group of combinations, there will be one or more
combinations of sites that would help save the maximum number of
species. It is relatively easy to obtain the combination of
site(s) giving maximum number of species when the number of sites
(more importantly) and the number of species are a few. But, as the
number of sites increases, the number of all possible combinations
to be tested increases exponentially. For n sites, the total number
of possible combinations to be tested will be 2n (which is the sum
of the binomial coefficients) in n+1 groups (which is number of
terms in binomial expansion). The first and the last groups will
have one combination each with zero and all sites and thus with
zero and all species respectively. But it becomes very much time
consuming even for computers to get the answers for rest of the
groups. The time taken to get the answer for these groups will be
proportional to the coefficients of binomial for respective groups.
In our case, 246-2 combinations will have to be tested in 45 groups.
3.2 Data Analysis
3.2.1 Testing all possible combinations
Our computer program testall.c (Appendix 3.3) tests for all
possible combinations of site(s) in each group and lists the
following: 1. maximum number of species being saved and the
combination of site(s) giving that number, 2. minimum number of
species being saved and the combination of site(s) giving that
number, and 3. the average number of species that would be expected
to be saved from all possible combinations. This program works well
for small number of sites (maximum up to 20 or so) in reasonable
time, but as the number of sites increases, the number of possible
combinations to be tested increases exponentially, and it would
take enormous amount of time even for fast computers to test all
possible combinations especially in the middle groups. Therefore,
another set of two programs was developed to answer this question
in case of large number of sites where all possible combinations
are not tested.
3.2.2 Testing limited combinations which are more likely to have
optimal solution
Our computer program gencomb.c (Appendix 3.4) generates
combinations of sites. Using these combinations and the
presence/absence matrix, our computer program, testlim.c (Appendix
3.5) lists (again like testall.c) the following three outputs: 1.
maximum number of species being saved and the combination of
site(s) giving that number, 2. minimum number of species being
saved and the combination of site(s) giving that number, and 3. the
average number of species that would be expected to be saved from
all tested combinations. But for every group of combinations of
site(s), the program gencomb.c must be modified to generate
combinations to be tested for next number of sites taken at a time
out of n (in our case 46) sites. Therefore, in our case, after 3rd
site, program gencomb.c was modified (by fixing the previous site
added) so that it would generate only 46C3 (= 15180) combinations to
be tested. Here the assumption is that the site previously selected
is more likely to be selected in the later combinations
representing optimal solutions. This way the computation was fast
and each group was taking a few minutes time to get the answer.
3.2.3 Pooling similar sites into clusters of site(s) of manageable
number and testing all possible combinations
The results obtained in above fashion (by using gencomb.c and
testlim.c) are expected to be fairly closer to or most probably
hitting at the correct answer or optimal solution, but still there
are chances of missing it. Therefore, 46 sampled sites were
classified based on presence/absence of 430 species by complete
linkage clustering and a manageable number of clusters of site(s)
was obtained by putting cutoff point at a suitable distance (Figure
3.3). The 14 clusters thus obtained were used to prepare a
presence/absence matrix of 430 species distributed over 14 clusters
of site(s) (Appendix 3.2). Now, with small number of clusters of
site(s), it was possible to test all possible combinations (using
testall.c) to find out which combinations of clusters would give
maximum number of species taking 1, 2, ..., 14 clusters at a time
out of 14 clusters. Species-area curves were made from these
results.
3.2.4 Greedy method
The question at hand comes under one of the computationally
hard problems. If there are only a few sites (up to 20 or so) then
the first approach is manageable and preferable. But as the number
of sites increases, the first approach becomes unmanageable whereas
other two approaches also become a little laborious. Therefore,
another approach called greedy method (Horowitz and Sahni, 1995)
was used. This method was also used by Daniels et al. (1991) though
not stated explicitly. In this method, first the site having
maximum number of species is selected. Then all the species that
are present at that site are knocked out from the presence/absence
matrix. Again from the remaining matrix the site having maximum
species is selected and all the species present at that site are
knocked out. This procedure is repeated till the cumulative number
of species of selected sites plateaus. A FORTRAN program -
GREEDY.FOR (Appendix 3.7) does this job. This procedure was tested
manually in other packages also and the results were the same.
3.3 Results
3.3.1 Testing all possible combinations
For 430 x 46 matrix, program testall.c works well and gives
perfectly correct results. But for middle groups it is not
manageable. Therefore, only for initial four and last four groups
the results are given in tables 3.1a, 3.1b and 3.1c.
3.3.2 Testing limited combinations that are more likely to have
optimal solution
The results of testing limited combinations that are more
likely to give optimal solution are given in Tables 3.2a, 3.2b and
3.2c. Table 3.2a gives the combination of site(s) giving maximum
number of species being saved in each group. Similarly Table 3.2b
gives the combination of sites giving minimum number of species.
Table 3.2c gives the average number of species that would be
expected to be saved if all possible (or tested) combinations are
considered.
Table 3.1 Results of testall.c for initial four and last four groups of
combinations for 430 x 46 matrix.
Table 3.1a Maximum number of species being saved and the combinations
of sites giving those number of species.
----------------------------------------------------------------------
1 2 3
----------------------------------------------------------------------
1 125 22
2 179 22 38
3 209 14 22 38
4 235 14 22 38 46
. . . . . .
(Dor middle groups, it is not manageable).
. . . . . .
43 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 30 32 33 34 35 37 38 39 40 41 42 43 44 45 46
44 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 32 33 34 35 37 38 39 40 41 42 43 44 45 46
45 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46
46 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
---------------------------------------------------------------------

Table 3.1b Minimum number of species being saved and the combinations
of sites giving those number of species.
----------------------------------------------------------------------
1 2 3
----------------------------------------------------------------------
1 2 3
2 12 3 13
3 23 1 3 8
4 31 1 3 4 8
. . . . . .
(For middle groups, it is not manageable).
. . . . . .
43 401 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 45 46
44 409 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 45 46
45 419 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46
46 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
---------------------------------------------------------------------

Table 3.1c Average number of species that would be expected to be saved
if all possible combinations of sites are considered.
----------------------------------------------------------------------
1 2
----------------------------------------------------------------------
1 58.46
2 101.8
3 135.1
4 161.8
. .
(For middle groups, it is not manageable).
. .
43 421.5 Legends for columns in table 3.1:
44 424.4 1 = No. of sites taken at a time out of 46 sites.
45 427.2 2 = No. of species being saved.
46 430 3 = Combination of sites giving that number of species.
----------------------------------------------------------------------

Table 3.2 Results of testing limited number of combinations which are
more likely to have optimal solution (for 430 x 46 matrix).
Table 3.2a Maximum number of species being saved and the combinations of
sites giving those number of species.
-------------------------------------------------------------------------
1 2 3
-------------------------------------------------------------------------
1 125 22
2 179 22 38
3 209 14 22 38
4 235 22 14 38 46
5 255 38 22 14 42 46
6 272 14 38 22 26 42 46
7 288 46 14 38 22 26 42 44
8 301 26 46 14 38 22 16 42 44
9 313 44 26 46 14 38 22 16 34 42
10 324 16 44 26 46 14 38 22 34 37 42
11 334 34 16 44 26 46 14 38 22 9 42 45
12 343 45 34 16 44 26 46 14 38 22 9 12 42
13 351 37 45 34 16 44 26 46 14 38 22 12 13 42
14 359 12 37 45 34 16 44 26 46 14 38 22 13 23 42
15 366 23 12 37 45 34 16 44 26 46 14 38 22 9 13 42
16 372 9 23 12 37 45 34 16 44 26 46 14 38 22 13 21 42
17 378 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 39 42
18 383 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 24 42
19 388 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 25 42
20 392 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 6 13 42
21 396 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 41 42
22 399 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 10 13 42
23 402 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 19 42
24 405 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13 20
42
25 408 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 13
30 42
26 411 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22
13 33 42
27 414 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38
22 13 35 42
28 417 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14
38 22 13 42 43
29 419 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46
14 38 22 2 13 42
30 421 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26
46 14 38 22 13 32 42
31 422 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44
26 46 14 38 22 4 13 42
32 423 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16
44 26 46 14 38 22 7 13 42
33 424 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34
16 44 26 46 14 38 22 8 13 42
34 425 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45
34 16 44 26 46 14 38 22 11 13 42
35 426 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37
45 34 16 44 26 46 14 38 22 13 15 42
36 427 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12
37 45 34 16 44 26 46 14 38 22 13 17 42
37 428 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23
12 37 45 34 16 44 26 46 14 38 22 13 18 42
38 429 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9
23 12 37 45 34 16 44 26 46 14 38 22 13 27 42
39 430 27 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21
9 23 12 37 45 34 16 44 26 46 14 38 22 13 40 42
40 430 40 27 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39
21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 13 42
----------------------------------------------------------------------------

Table 3.2b Minimum number of species being saved and the combinations of
sites giving those number of species.
----------------------------------------------------------------------------
1 2 3
----------------------------------------------------------------------------
1 2 3
2 12 3 13
3 23 1 3 8
4 134 22 3 8 22
5 180 38 22 3 22 38
6 209 14 38 22 14 22 38
7 235 46 14 38 22 14 22 38
8 253 26 46 14 38 22 14 22 26
9 269 44 26 46 14 38 22 14 22 26
10 282 16 44 26 46 14 38 22 14 16 22
11 294 34 16 44 26 46 14 38 22 14 16 22
12 305 45 34 16 44 26 46 14 38 22 14 16 22
13 318 37 45 34 16 44 26 46 14 38 22 3 14 16
14 327 12 37 45 34 16 44 26 46 14 38 22 3 12 14
15 335 23 12 37 45 34 16 44 26 46 14 38 22 1 3 12
16 342 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
17 348 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
18 358 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
19 363 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
20 368 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
21 372 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
22 376 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
23 379 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3 5
24 382 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 3
5
25 385 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22 1
3 5
26 388 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38 22
1 3 5
27 391 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14 38
22 1 3 5
28 394 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46 14
38 22 1 3 5
29 398 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26 46
14 38 22 1 3 5
30 400 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44 26
46 14 38 22 1 2 3
31 402 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16 44
26 46 14 38 22 1 2 3
32 403 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34 16
44 26 46 14 38 22 1 2 3
33 404 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45 34
16 44 26 46 14 38 22 1 2 3
34 405 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37 45
34 16 44 26 46 14 38 22 1 2 3
35 406 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12 37
45 34 16 44 26 46 14 38 22 1 2 3
36 407 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23 12
37 45 34 16 44 26 46 14 38 22 1 2 3
37 408 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9 23
12 37 45 34 16 44 26 46 14 38 22 1 2 3
38 409 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21 9
23 12 37 45 34 16 44 26 46 14 38 22 1 2 3
39 410 27 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39 21
9 23 12 37 45 34 16 44 26 46 14 38 22 1 2 3
40 411 40 27 18 17 15 11 8 7 4 32 2 43 35 33 30 20 19 10 41 6 25 24 39
21 9 23 12 37 45 34 16 44 26 46 14 38 22 1 2 3
----------------------------------------------------------------------------

Note: In the above table (Table 3.2b), there is a problem for which there is an explan
However, this table itself is not important and could be ignored. This was kept for dr
a graph in Figure 3.1 represented by 'Minimum'.

Table 3.2c Average number of species expected to be saved if all possible
(or tested) combinations are considered.
-----------------------------------------------------------------------
1 2
-----------------------------------------------------------------------
1 59
2 102
3 135
4 192
5 225
6 242
7 261
8 276
9 289
10 301
11 310
12 319
13 329
14 337
15 344
16 350
17 355
18 364
19 368
20 373
21 376
22 380
23 383
24 386
25 388
26 391
27 394
28 396
29 400
30 402
31 404
32 405
33 406
34 407
35 408
36 409
37 409
38 410
39 411
40 412
----------------------------------------------------------------------
Legends for columns in Table 3.2a, 3.2b and 3.2c:
1 = serial number/number of sites taken at a time.
2 = no. of species being saved.
3 = combination of sites giving that no. of species.

The species-area curves from Table 3.2 are given in Figure
3.1. It is clear from Table 3.2 and Figure 3.1 that just by
choosing proper combination of sites, one can maximize the number
of species being saved. The Table 3.2 and Figure 3.1 also show that
when the proper combinations of site(s) are chosen then the
species-area curve rises faster and peaks/plateaus earlier as
compared to the any other possibilities.
3.3.3 Pooling similar sites into clusters of site(s) of manageable
number and testing all possible combinations
Though the results in Table 3.2a are expected to be fairly
closer to the ideal combinations of sites to be chosen for
maximizing the number of species being saved, one is not sure
because all possible combinations could not be tested in all
groups. Therefore, 46 sampled sites were classified based on
presence/absence of 430 species by complete linkage clustering
(Figure 3.3). The results of the analysis after clustering 46 sites
into 14 clusters of sites are given in Table 3.3a, 3.3b & 3.3c.
These results are ideal because it was possible to test all
possible combinations since there were only 14 clusters. Table 3.3a
gives the combinations of cluster(s) giving maximum number of
species. Table 3.3b gives the combinations of cluster(s) giving
minimum number of species and Table 3.3c lists the average number
of species that would be expected to be saved if all possible
combinations are considered. The species-area curves based on Table
3.3 are given in Figure 3.2. Here again, it is clear from the Table
3.3 and Figure 3.2 that one can maximize the number of species
being saved just by choosing the proper combinations of cluster(s)
of sites. Again here also, species-area curve in Figure 3.2
peaks/plateaus earlier as compared to the other possibilities
showing importance of choosing proper combinations of
clusters/sites.
Table 3.3 Results of testing all possible combinations in each group
for 430 x 14 matrix using testall.c.
Table 3.3a Maximum number of species being saved and the combinations
of sites giving those number species.
-----------------------------------------------------------------------
sn 1 2
-----------------------------------------------------------------------
1 250 12
2 322 12 13
3 355 6 12 13
4 380 6 9 12 13
5 400 6 7 9 12 13
6 408 6 7 9 12 13 14
7 414 6 7 9 11 12 13 14
8 419 3 6 7 9 11 12 13 14
9 423 3 6 7 9 10 11 12 13 14
10 426 1 3 6 7 9 10 11 12 13 14
11 429 1 3 4 6 7 9 10 11 12 13 14
12 430 1 2 3 4 6 7 9 10 11 12 13 14
13 430 1 2 3 4 5 6 7 9 10 11 12 13 14
14 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14
-----------------------------------------------------------------------

Table 3.3b Minimum number of species being saved and the combinations
of sites giving those number of species.
-----------------------------------------------------------------------
sn 1 2
-----------------------------------------------------------------------
1 2 5
2 12 5 14
3 24 2 5 14
4 41 2 5 8 14
5 66 1 2 5 8 14
6 85 1 2 3 5 8 14
7 111 1 2 3 4 5 8 14
8 165 1 2 3 4 5 8 10 14
9 201 1 2 3 4 5 8 10 11 14
10 242 1 2 3 4 5 6 8 10 11 14
11 275 1 2 3 4 5 6 7 8 10 11 14
12 312 1 2 3 4 5 6 7 8 9 10 11 14
13 382 1 2 3 4 5 6 7 8 9 10 11 12 14
14 430 1 2 3 4 5 6 7 8 9 10 11 12 13 14
-----------------------------------------------------------------------
Legends for columns in Tables 3.3a & 3.3b:
sn = serial number/number of site(s)/cluster(s) chosen.
1 = number of species being saved.
2 = combination of site(s)/cluster(s) giving that many species.





Table 3.3c Average number of species that would be expected to be saved
if all possible combinations are considered.
-----------------------------------------------------------------------
sn 1 sn n cl n
-----------------------------------------------------------------------
1 83.36 1 34 12 250
2 146.4 2 13 13 224
3 195.7 3 42 6 136
4 235.3 4 54 7 124
5 268.1 5 2 11 97
6 295.8 6 136 10 83 Legends for columns in Table 3.3c:
7 319.7 7 124 9 79 sn = serial no./no. of clusters chosen.
8 340.7 8 19 4 54 1 = no. of species being saved.
9 359.4 9 79 3 42 n = number of species.
10 376.2 10 83 1 34 cl = cluster number.
11 391.4 11 97 8 19
12 405.3 12 250 2 13
13 418.1 13 224 14 10
14 430 14 10 5 2
-----------------------------------------------------------------------

Table 3.4 Percentage of species being saved and trend in beta diversity
(for 430 x 46 matrix).
-----------------------------------------------------------------------
Maximum Minimum Average
-----------------------------------------------------------------------
sn 1 2 3 1 2 3 1 2 3
-----------------------------------------------------------------------
1 125 0.302 29.07 2 0.833 0.465 59 0.422 13.72
2 179 0.144 41.63 12 0.478 2.791 102 0.244 23.72
3 209 0.111 48.6 23 0.828 5.349 135 0.297 31.4
4 235 0.078 54.65 134 0.256 31.16 192 0.147 44.65
5 255 0.063 59.3 180 0.139 41.86 225 0.07 52.33
6 272 0.056 63.26 209 0.111 48.6 242 0.073 56.28
7 288 0.043 66.98 235 0.071 54.65 261 0.054 60.7
8 301 0.038 70 253 0.059 58.84 276 0.045 64.19
9 313 0.034 72.79 269 0.046 62.56 289 0.04 67.21
10 324 0.03 75.35 282 0.041 65.58 301 0.029 70
11 334 0.026 77.67 294 0.036 68.37 310 0.028 72.09
12 343 0.023 79.77 305 0.041 70.93 319 0.03 74.19
13 351 0.022 81.63 318 0.028 73.95 329 0.024 76.51
15 366 0.016 85.12 335 0.02 77.91 344 0.017 80
16 372 0.016 86.51 342 0.017 79.53 350 0.014 81.4
17 378 0.013 87.91 348 0.028 80.93 355 0.025 82.56
18 383 0.013 89.07 358 0.014 83.26 364 0.011 84.65
19 388 0.01 90.23 363 0.014 84.42 368 0.013 85.58
20 392 0.01 91.16 368 0.011 85.58 373 0.008 86.74
21 396 0.008 92.09 372 0.011 86.51 376 0.011 87.44
22 399 0.007 92.79 376 0.008 87.44 380 0.008 88.37
23 402 0.007 93.49 379 0.008 88.14 383 0.008 89.07
24 405 0.007 94.19 382 0.008 88.84 386 0.005 89.77
25 408 0.007 94.88 385 0.008 89.53 388 0.008 90.23
26 411 0.007 95.58 388 0.008 90.23 391 0.008 90.93
27 414 0.007 96.28 391 0.008 90.93 394 0.005 91.63
28 417 0.005 96.98 394 0.01 91.63 396 0.01 92.09
29 419 0.005 97.44 398 0.005 92.56 400 0.005 93.02
30 421 0.002 97.91 400 0.005 93.02 402 0.005 93.49
31 422 0.002 98.14 402 0.002 93.49 404 0.002 93.95
32 423 0.002 98.37 403 0.002 93.72 405 0.002 94.19
33 424 0.002 98.6 404 0.002 93.95 406 0.002 94.42
34 425 0.002 98.84 405 0.002 94.19 407 0.002 94.65
35 426 0.002 99.07 406 0.002 94.42 408 0.002 94.88
36 427 0.002 99.3 407 0.002 94.65 409 0 95.12
37 428 0.002 99.53 408 0.002 94.88 409 0.002 95.12
38 429 0.002 99.77 409 0.002 95.12 410 0.002 95.35
39 430 0 100 410 0.002 95.35 411 0.002 95.58
40 430 0 100 411 0 95.58 412 0 95.81
---------------------------------------------------------------------------
Legends for columns in Table 3.4:
sn = serial number.
1 = Number of species being saved.
2 = beta diversity between currently and previously selected combinations.
3 = percentage of species being saved.

Table 3.5 Percentage of species being saved and trend in beta diversity
(for 430 x 14 matrix).
---------------------------------------------------------------------------
Maximum Minimum Average
---------------------------------------------------------------------------
sn 1 2 3 1 2 3 1 2 3
---------------------------------------------------------------------------
1 250 0.224 58.14 2 0.833 0.465 83.36 0.430718 19.38605
2 322 0.093 74.88 12 0.5 2.791 146.4 0.251686 34.05349
3 355 0.066 82.56 24 0.415 5.581 195.7 0.168381 45.50698
4 380 0.05 88.37 41 0.379 9.535 235.3 0.122179 54.72093
5 400 0.02 93.02 66 0.224 15.35 268.1 0.093721 62.33721
6 408 0.014 94.88 85 0.234 19.77 295.8 0.074851 68.78372
7 414 0.012 96.28 111 0.327 25.81 319.7 0.06161 74.34884
8 419 0.009 97.44 165 0.179 38.37 340.7 0.05198 79.23023
9 423 0.007 98.37 201 0.169 46.74 359.4 0.044635 83.57442
10 426 0.007 99.07 242 0.12 56.28 376.2 0.038937 87.47907
11 429 0.002 99.77 275 0.119 63.95 391.4 0.034367 91.02326
12 430 0 100 312 0.183 72.56 405.3 0.030636 94.26279
13 430 0 100 382 0.112 88.84 418.1 0.027581 97.24186
14 430 0 100 430 0 100 430 0 100
---------------------------------------------------------------------------
Legends for columns in Table 3.5:
sn = serial number/number of site(s)/cluster(s) chosen.
1 = number of species being saved.
2 = beta diversity between previously chosen & next site/cluster to be chosen.
3 = percentage of species being saved.










Table 3.6 Number of species listed from 46 sites.
---------------------------------------------------------------------------
1 2 1 2
---------------------------------------------------------------------------
1 15 22 125 Legends for columns in Table 3.6:
2 21 38 114 1 = site number.
3 2 21 103 2 = number of species present.
4 16 24 99
5 26 14 99
6 28 23 97
7 22 32 92
8 13 31 88
10 66 17 86
11 50 29 82
12 76 45 81
13 10 37 80
14 99 12 76
15 40 34 74
16 88 18 71
17 86 27 71
18 71 46 70
19 33 25 69
20 58 26 68
21 103 35 68
22 125 10 66
23 97 44 66
24 99 9 61
25 69 41 60
26 68 20 58
27 71 33 55
28 19 11 50
29 82 30 48
30 48 42 45
31 88 15 40
32 92 36 39
33 55 39 35
34 74 19 33
35 68 40 31
36 39 43 30
37 80 6 28
38 114 5 26
39 35 7 22
40 31 2 21
41 60 28 19
42 45 4 16
43 30 1 15
44 66 8 13
45 81 13 10
46 70 3 2
---------------------------------------------------------------------------

Table 3.7 Results of greedy method (for 50 x 46 matrix).
---------------------------------------------------------------------------
1 2 3 4 5
---------------------------------------------------------------------------
1 14 23 23 23 Legends for columns in Table 3.7:
2 24 22 11 34 1 = Serial number.
3 42 9 6 40 2 = Site number.
4 26 14 3 43 3 = Total number of species present at that site.
5 45 18 3 46 4 = Maximum number of species after knocking out
6 5 7 1 47 species of previously selected site.
7 13 2 1 48 5 = Cumulative number of species being saved.
8 39 7 1 49
9 41 11 1 50
-------------------------------------------------------------------------

Table 3.7a Maximum number of species being saved and the combinations
of sites giving those number of species (for 50 x 46 matrix).
-------------------------------------------------------------------------
Output of greedy method for 50 WRCPs. (After arranging in proper format.)
-------------------------------------------------------------------------
1 2 3 4
-------------------------------------------------------------------------
1 23 23 14
2 34 11 14 24
3 40 6 14 24 42
4 43 3 14 24 42 26
5 46 3 14 24 42 26 45
6 47 1 14 24 42 26 45 5
7 48 1 14 24 42 26 45 5 13
8 49 1 14 24 42 26 45 5 13 39
9 50 1 14 24 42 26 45 5 13 39 41
-------------------------------------------------------------------------
Legends for table 3.7a:
1 = serial number or number of sites taken at a time out of 46 sites.
2 = maximum number of species being saved.
3 = number of species being added or beta diversity between currently
and previously selected combinations.
4 = combination of site(s).












Table 3.8 Results of greedy method (GREEDY.FOR) for 430 x 46 matrix.
---------------------------------------------------------------------
1 2 3 4 5
---------------------------------------------------------------------
1 22 125 125 125
2 38 114 54 179
3 14 99 30 209
4 46 70 26 235
5 42 45 20 255
6 26 68 17 272
7 44 66 16 288
8 16 88 13 301
9 34 74 12 313
10 37 80 11 324
11 45 81 10 334
12 12 76 9 343
13 13 10 8 351
14 23 97 8 359
15 9 61 7 366
16 21 103 6 372
17 39 35 6 378
18 24 99 5 383
19 25 69 5 388
20 6 28 4 392
21 41 60 4 396
22 10 66 3 399
23 19 33 3 402
24 20 58 3 405
25 30 48 3 408
26 33 55 3 411
27 35 68 3 414
28 43 30 3 417
29 2 21 2 419
30 32 92 2 421
31 4 16 1 422
32 7 22 1 423
33 8 13 1 424
34 11 50 1 425
35 15 40 1 426
36 17 86 1 427
37 18 71 1 428
38 27 71 1 429
39 40 31 1 430
---------------------------------------------------------------------
Legends for columns in Tables 3.8 & 3.9:
1 = Serial number. 2 = Site number.
3 = Total number of species present at that site/cluster of site(s).
4 = Maximum number of species after knocking out species of previously
selected site.
5 = Cumulative number of species being saved.

Table 3.9 Results of greedy method (GREEDY.FOR) for 430 x 14 matrix.
---------------------------------------------------------------------
1 2 3 4 5
---------------------------------------------------------------------
1 12 250 250 250
2 13 224 72 322
3 6 136 33 355
4 9 79 25 380
5 7 124 20 400
6 14 10 8 408
7 11 97 6 414
8 3 42 5 419
9 10 83 4 423
10 1 34 3 426
11 4 54 3 429
12 2 13 1 430
---------------------------------------------------------------------

3.3.4 Greedy method
The output of GREEDY.FOR for both the matrices (430 x 46 and
430 x 14) are given in tables 3.8 and 3.9 respectively. On
arranging these outputs into a proper format of output of testall.c
or testlim.c, we get the same results (same combinations giving
same numbers of species) as from earlier approaches.

3.4 Discussion
Figure 3.0 shows the species-area curves based on tables 3.1a,
3.1b, and 3.1c. The results for the middle groups are difficult to
get as they would take a lot of time. However, if number of sites
are less (as we have seen for a 430X14 matrix) then we can get
complete results and the full range of options. It is possible,
from Table 3.2 and 3.3 to compute the percentage of species being
saved by saving 1, 2, 3, ..., 46 site(s) (or 1, 2, 3, ..., 14
cluster(s) of sites as the case may be) when the combinations
giving maximum and minimum number of species are being chosen as



























well as the average number of species being saved when all possible
(or tested) combinations are considered. These are given in tables
3.4 and 3.5 respectively. These tables give options that by saving
how many sites (how much area) how much percentage of species can
be saved. Table 3.4 and 3.5 also give diversity between
previously and currently selected combinations. It is clear from
the tables 3.4 & 3.5 that we are getting high diversity when
there are major habitat changes. Therefore, we are getting proper
combinations of sites/clusters if we are considering both the and
diversity together. It is noticeable in tables 3.4 & 3.5 that in
case of proper combinations of sites/clusters represented by
maximum, the diversity is decreasing gradually. In case of
average, it is fluctuating in table 3.4 whereas it is gradually
decreasing in table 3.5. In case of minimum it is increasing
gradually. Figures 3.4 and 3.5 show these trends in the behaviour
of beta diversity. This clue might help in reducing the computation
time for getting proper combinations of sites/clusters. In
species-area curves, the slope of the curve is proportional to the
diversity, while the intercept reflects diversity (Crawley
1986). From figures 3.1 and 3.2 it is also clear that in case of
proper combinations, the curve rises smoothly with gradual decrease
in slope, whereas in other combinations, it takes major jumps where
diversity is high showing major habitat changes.
After applying greedy method on a presence/absence matrix of
50 WRCPs (which are being selected for detailed discussion in other
chapters) from 46 sites (Appendix 3.6) the results are as given in
table 3.7. We can select these combinations of sites for in situ
conservation if we consider only these 50 WRCPs. But these WRCPs
cannot be conserved in isolation. Other associated plant species,
other organisms and all the components of the ecosystems will have
to be maintained simultaneously. Combinations of sites selected for
conservation based on criteria of maximizing the number of species
of a certain group of organisms (e.g., angiosperms, avifauna or
mammals etc.) may not necessarily result in maximizing total
species diversity. Quite often (especially in species rich tropical
ecosystems) it will be difficult to prepare an exhaustive list of
species and the presence/absence data for such a list. Therefore,
such exercises would rarely be based on exhaustive presence/absence
data. Nevertheless, such exercises might have considerable
implications for conservation.
Species-area relationship depends on how organisms of
different kind are distributed spatially. This topic seems to have
attracted enough attention of researchers and is really
interesting. A number of researchers have strived to find uses of
this relationship. These include: 1. Inferring biological processes
like disturbance (Lawrey 1991), competition (Leps 1990) and
division of niche space (Sugihara 1980). 2. Defining minimal area
of a community and delineating types of communities (Cain 1938;
Rice and Kelting 1955; Oosting 1956; Goldsmith and Harrison 1976;
Kershaw and Looney 1985; Colinvaux 1993). 3. Use in island
biogeography (MacArthur and Wilson 1963, 1967; MacArthur 1965;
Patrick 1967; Williamson 1981, 1988) and design of nature reserves
(Diamond and May 1981; Higgs 1981; Dzwonko and Loster 1989;
Bierregaard et al. 1992). 4. Estimating biodiversity of a larger

region by extrapolation (Evans et al. 1955; Williams 1964; Kilburn
1966; Hubbel and Foster 1983; Lauga and Joachim 1987; Westfall et
al. 1987; Gentil and Dauvin 1988; May 1988; Palmer 1990; Gitay et
al. 1991; Grassle and Maciolek 1992). Some others had been
interested in finding out functional form of species-area
relationship (Gleason 1922, 1925; Arrhenius 1923; Williams 1964;
Williamson 1981) and their theoretical justification (Williams
1964; May 1975; Coleman 1981; Williamson 1981). There are also
debates and criticisms attached with such studies. The debate over
value of z in the standard species-area relationship S = cAz and
its biological meaning makes an interesting reading (May 1975;
Sugihara 1981). Crawley (1986) criticised the erroneous ideas
attached with the concept of minimal area, and illustrated the
expected shapes of species-area curves under a variety of spatial
distribution of species. Similarly a well-designed experiment to
tear apart the effect of "grain, extent and number of samples" by
Palmer and White (1994) gives much insight in the species-area
relationship. Although here the main theme of this chapter is
maximization of number of species being saved and not the
species-area relationship itself, yet the species-area relationship
issue comes in. From this kind of data set, the number of possible
species-area curves would be equal to the product of binomial
coefficients. The curve represented by maximum would be one of them
and would be the topmost one. Similarly the curve represented by
minimum would also be one of them and would be the bottommost one
(Figure 3.2). Rest of the curves would be in between and all the
curves will converge at two points. For in situ conservation
purpose, one will be interested in curve represented by maximum
only. In principle, one can be as bad in his/her selection as the
curve represented by minimum, but it would hardly ever happen
because at least one will be tempted to select sites with number of
species arranged in decreasing order and the species-area curve
resulting from this selection scheme will not be the one
represented by minimum one. For estimating total number of species
present in a particular region based on species-area curve by
extrapolation, the curve represented by average is considered to
give good estimate. But for in situ conservation purpose this curve
will be meaningless because a deterministic event of selecting a
definite combination of site(s) would happen during decision making
and the number of species being saved will be quite more than the
average value.
Finding out combinations of sites saving maximum number of
species is of much practical use in in situ conservation but very
difficult to arrive at especially when there are a large number of
sites. Lomolino (1994) tested all possible combinations for a total
number of reserves or islands ranging from nine to 22 and the
number of target species from nine to 25. It is possible to get
answer for small number of sites. Here we are testing all possible
combinations for 430 x 14 matrix and the results of greedy method
are exactly similar to it. Therefore, for this dataset the greedy
algorithm is giving correct answer. But consider the following
example for which greedy algorithm will give a wrong answer when we
take two sites at a time. The greedy method will give A D
combination with 14 species whereas testall.c will give the correct
answer as B C combination with 16 species.
The example:
Sites Species
A 1 2 3 4 5 6 7 8 9 10
B 1 2 3 4 5 11 12 13
C 6 7 8 9 10 14 15 16
D 17 18 19 20

Similarly, Underhill (1994) has given an example in which only two
sites are enough to preserve all species but greedy algorithm
chooses three sites. Underhill (1994) has also shown that
algorithms that minimize the number of reserves to conserve every
species (Margules et al., 1988; Rebelo & Siegfried 1990;
Vane-Wright et al. 1991; Nicholls & Margules 1993; Pressey et al.,
1993) are essentially manifestations of the greedy algorithm.
Therefore, it seems worthwhile putting in some research effort in
following two areas: 1. Develop a short cut method to answer this
question even for large number of sites. Altogether a different
logic needs to be used unlike the simple logics used in the above
approaches. Though the first approach is foolproof, since it tests
for all possible combinations in all groups, yet it is not
practicable in cases of a large number of sites. The second
approach is fairly good but one cannot be 100% sure and also it is
time consuming. The third approach may not be desirable on certain
grounds (like why to pool more similar sites etc.). On a second
thought, the third approach of pooling similar sites into less
number of clusters of site(s) and then testing all possible
combinations is no way superior to the second one. For example, if
we have option of choosing five sites then according to Table 3.2a
sites 14, 22, 38, 42 & 46 would give 255 species. If we classify
the 46 sites to reduce them into 14 clusters of sites and then test
all possible combinations then site-cluster 12 is giving 250
species. Even though this site-cluster has seven sites (sites 21,
22, 25, 32, 35, 38 & 45), it is saving less species than what we
are getting from the second approach by selecting only five sites.
Therefore, for a large number of sites the second approach seems to
be better than the third approach. The fourth approach of greedy
method is smart and fast enough even for a large number of sites
but still it is not foolproof as shown in the above example. Such
examples of more patchy distribution of species, where greedy
method is more likely to give wrong results, are easy to visualize.
Therefore, there is still scope to look for novel logics/approaches
to solve this problem. This is very important because just by
choosing right combinations we will be saving more number of
species and therefore leaving more options for our future
generations though setting aside same amount of area for
conservation. The possible solutions might come from bit level
programming and clues from behabiour of diversity. 2. Increase
the computation speed of computers so that they can do this job in
less time even using testall.c. Clearly the second approach poses
the challenge before computer scientists.
In the absence of such a logical approach one more possibility
is that one would be tempted to choose the sites with maximum
number of species for successive addition of sites. This also would
not necessarily result in maximization of number of species being
saved. For example, according to table 3.6 the first site to be
chosen will be 22. The second site to be added would be 38 which is
correct according to logical approach also (Table 3.2). But for
adding third site, one would think of adding site number 21 that
would (in combination with other previously chosen sites) result in
saving only 197 species whereas site 14 (which is below site 21 in
species richness) would (in proper combination of sites) save 209
species. Therefore, it is very important to select right
combination of site(s)/region(s) etc. to maximize the number of
species being saved. The maximization of number of species being
saved is one thing that cannot be ignored.
The method discussed above could be used in decision making
about selection of sites/areas/regions for in situ conservation at
any level/scale (individual, village, block, district, state,
national or international). This way it would be possible to
maximize the number of species being saved at all spatial scales.
The sites/regions that have very few species exclusive to them
could be set aside for non-conservation purposes if those species
are rehabilitated elsewhere. However, rehabilitating elsewhere
should not mean to ignore the demand of striving to conserve more
variation specially in the life supporting species of the
locality/regions/states etc. The sites selected for conservation at
various levels of spatial scales could be nested. In adopting this
approach, however, there will be a crisis if the conservation sites
selected at a lower level of spatial scale will not fit to maximize
the number of species being saved when higher level of spatial
scale is considered. Then owners (individuals/communities/states
etc.) will have to be cooperative then only the number of species
being saved can be maximized at the higher level though sacrificing
the maximization of number of species being saved at lower level of
spatial scale for certain regions. If all the owners conserve all
the species they own then also there will be no problem. This
approach could also be used in ex situ conservation for
maximization of number of accessions conserved/maintained at
various ex situ conservation centres, gene banks, field gene banks
and cryopreservation centres.