Establishing a Long Term System
for Monitoring the Illegal Killing of Elephants (MIKE)
Annex 4: Selection of a representative sample of sites
R W Burn Statistical Services Centre, University of Reading
1 OBJECTIVES
The aim of this exercise is to obtain a representative samples of sites from elephant range states for use in the proposed new information system MIKE (Monitoring the Illegal Killing of Elephants).
Representatives of range states were invited to submit lists of potential sites. The African and Asian Elephant Specialist Groups (AfESG and AsESG) compiled these lists and preselected a total of 69 sites from African elephant range states and 30 from Asian elephant range states. These lists of sites are supplied with data on criteria to assist in the site selection. These criteria follow the recommendations of the Workshop on the Monitoring of Trade in Elephant Products and Illegal Killing of Elephants held by TRAFFIC and IUCN/SSC in Nairobi (812 December 1997).
The idea is to use the available information to select a sample of sites to be used for MIKE which is as far as possible representative and "balanced" with respect to the criteria, and which is determined according to an objective and transparent method of selection.
2 METHODOLOGY
The sampling procedure was conducted completely separately for African and Asian range states.
African sites
After ensuring that the available data were completed as far as possible, the selection criteria were prioritised in consultation with the IUCN/SSC.
The Nairobi Workshop Report organised the criteria into two lists: list (a) consisting of factors which are thought likely to affect the incidence of illegal killing, and list (b) comprising other factors which will affect the ability to collect data from the sites. Criteria in the first list were regarded as having the role of stratification criteria for a stratified sample design, although for reasons explained below, the usual methods of sampling within strata were not appropriate. A system of numerical weights, reflecting the prioritisation of criteria, was devised for the factors of list (b). The information contained in these factors was thus condensed into a single score which was used for rating the sites according to the difficulty of collecting monitoring data. The weighted averages of these scores were computed for each subregion and the score was rescaled to the range 0  100, a lower score representing the least difficult site. The factors used in list (b), and the weights used are given in Annex I.
After examination of the available data, the stratification criteria (list (a)), and the coding used in subsequent analysis, were as follows:
Subregion:

East, West, Central and Southern Africa.

Ivory trade:

whether or not there is a significant domestic ivory trade and, if so, whether it is legal/illegal and local/international. The ivory trade data were coded


0 = no trade


1 = legal trade


2 = illegal trade (or both legal and illegal)

The data on local/international were not utilised because they were rather uncertain and (after consultation) thought to be less important.
CITES registration: whether or not the country was involved in the CITES COP 10 decisions (10.1 and 10.2); coded 0 for "no" and 1 for "yes".
Habitat type: savannah or forest habitat (a few sites were listed as both).
Enforcement capacity: low (0) or high (1).
Protection: whether or not the site is (or lies in) a protected area; coded 0 for "nonprotected" and 1 for "protected".
Civil strife: sites where there is current or recent civil strife (including in neighbouring areas); coded 0 for "no" and 1 for "yes".
Hunting: sites with a history of heavy illegal killing pressure were coded 1, otherwise 0.

It was decided (after consultation) that the size of elephant populations was also a possible candidate for inclusion as a stratification criterion. This variable was primarily included in list (b), but including it in list (a) also would have little effect on the overall results if, in the event, it turned out to be unimportant for stratification. It was therefore used in both lists.
The sizes of elephant populations differ widely between the four African subregions. For this reason, and also because there is confounding of habitat type with subregion, the sampling exercise was carried out separately for each of the subregions.
Uncertainties in the data on population sizes were dealt with by further enquiries and, in some cases, by reference to the African Elephant Database (Said et al, 1995). The coding scheme was as follows:
East and Southern Africa
0

= low

< 1,000

1

= med

1,000  9,999

2

= high

10,000 +

Central Africa
0

= low

< 1,000

1

= med

1,000  4,999

2

= high

5,000 +

West Africa
0

= low

< 100

1

= med

100  499

2

= high

500 +

Within each subregion, there are thus seven stratification criteria to be used for selecting a sample. These (with their numbers of levels) are: ivory trade (3), CITES reg (2), enforcement cap (2), protection (2), civil strife (2), hunting (2) and population (3). The complete crossclassification would therefore contain 3^{2} ´ 2^{5} = 288 cells. The normal procedure for constructing a stratified sample would be to select a random sample of units (sites) within each cell in the stratification table, usually with probabilities proportional to size, or according to some similar rule. In the present case, with an initial list of only 69 sites, this procedure would clearly be impossible.
What is required is a method which makes optimal use of the information contained in the stratification data to produce a sample which is the most representative that can be attained, given the constraints outline above. The procedure adopted here was first to split the sites into groups which, according to the stratification criteria, are as different from each other as possible, while the individual sites within each group are as similar as possible. This was achieved by means of hierarchical cluster analysis using Ward's method (Everitt, 1980). The advantage of a hierarchical classification is that it provides a natural way of choosing several sample sizes, so that different scenarios can be derived in an objective way.
In addition to cluster analysis, an attempt has been made to simplify the selection criteria by means of a dimension reduction technique (factor analysis with varimax rotation  Krzanowski, 1988). This provides some corroboration of the clustering and, at the same time, gives a simpler picture of what the cluster groups actually represent. The factor analysis was performed on all 69 cases together.
The cluster analysis was carried out separately for each subregion and the results subjected to crosschecking of "balance" with respect to habitat type and the values of the factor scores resulting from the factor analysis. In a few cases slight adjustments were made to the selections to correct for imbalance.
Site selection was performed on site ID codes, without reference to site identifications. The idea of this was to avoid any unconscious subjective bias in selection. The ID codes for all sites are listed in Annex II. The entire selection procedure was determined only by the statistical methods outlined above. The method is objective, transparent and repeatable.
Asian Sites
The methodological approach for the Asia sites was basically identical to that adopted for the Africa sites. There were a few minor differences, however, and these are listed here:
(1)

Since there were just 30 sites presented for inclusion, there was little point in splitting them into subregions for separate analysis, as was done for Africa. A pooled analysis was done for all 30 together.

(2)

None of the Asian range states registered under CITES 10.2, so this variable was excluded from the analysis.

(3)

Whereas the question on government cooperation was excluded for Africa (because virtually all of the responses were the same), it has been included for Asia.

(4)

While habitat type (forest/ savannah) was a factor to consider with the African elephant, it is not an really issue in Asia (although the question was asked and it has been reported).

(5)

Less information was available on elephant population sizes in Asia. Population size has been classified as simply low or high for each site.

Aside from these minor points, the method of analysis was identical to that used for Africa.
3 RESULTS OF ANALYSIS
African sites
FACTOR ANALYSIS
Total Variance Explained
Initial Eigenvalues

Rotation Sums of Squared Loadings

Component

Total

% of Variance

Cumulative %

Total

% of Variance

Cumulative %

1

1.83

26.10

26.10

1.73

24.71

24.71

2

1.45

20.76

46.86

1.54

22.02

46.74

3

1.35

19.30

66.16

1.36

19.42

66.16

4

0.86

12.35

78.51




5

0.53

7.59

86.10




6

0.52

7.46

93.56




7

0.45

6.44

100.00




Extraction Method: Principal Component Analysis.
Rotated Component Matrix

Component


1

2

3

Ivory trade

0.047

0.857

0.058

CITES reg

0.126

0.716

0.041

Enf't. cap.

0.020

0.380

0.669

Protection

0.130

0.167

0.820

Civil strife

0.813

0.153

0.219

Hunting

0.829

0.119

0.017

Pop'n. size

0.588

0.290

0.431

Rotation Method: Varimax with Kaiser Normalization.
Interpretation of rotated factors:
Factor

Dominant contributions

1

Hunting + civil strife

2

Ivory trade + CITES registration

3

Protection + enforcement capacity
(+ some contribution from population size)

About twothirds of the variation between sites can be explained by the above three factors. The analysis therefore results in a reasonable simplification.
CLUSTER ANALYSIS
The main analysis from which the site selections were derived was the cluster analysis. The method used was Ward's method with squared eucidlean distances. This was applied to each subregion separately. The dendrograms resulting from the analysis follow. For each site, the difficulty score is noted, together with the population level, the habitat type and the factor scores (lo or hi according to whether they are below or above their median values). Note that the factor scores correspond quite closely to the clustering  sites in the same group tend to have a similar pattern of factor scores, while different groups tend to have different scores.
East Africa
Rescaled Distance Cluster Combine
Site hab fac1 fac2 fac3 pop diff 0 5 10 15 20 25
ID itat score ++++++
10 s hi lo hi med 11 +
11 s hi lo hi med 11 ++
2 s hi lo hi med 39 + ++
3 f hi lo lo lo 50 + ++
4 s lo lo lo med 78 + ++
9 s lo lo lo hi 0 + ++
7 s hi lo hi lo 22 + I I
8 s hi lo hi lo 22 ++ I
6 s hi lo hi lo 22 + I
1 s hi lo lo lo 92 ++ I
12 s hi hi lo lo 47 + ++
5 s hi lo lo lo 100 +
Central Africa
Rescaled Distance Cluster Combine
Site hab fac1 fac2 fac3 pop diff 0 5 10 15 20 25
ID itat score ++++++
12 f hi hi lo med 36 ++
13 f hi hi lo med 36 + ++
11 f hi lo hi med 36 + ++
5 f lo hi lo med 61 ++ I I
7 s lo hi lo med 29 + ++ I
6 f hi hi lo lo 61 ++ I I
9 s hi hi lo med 14 + ++ I
10 f hi lo lo med 100 + I
14 s lo hi hi med 39 ++ I
16 f lo hi hi hi 25 + ++ I
8 f lo lo hi med 14 + ++
2 f lo hi hi hi 0 ++ I
15 f lo hi lo hi 11 + ++
1 s hi hi lo med 14 ++ I
4 f hi hi lo med 18 + ++
3 s hi hi hi hi 0 +
West Africa
Rescaled Distance Cluster Combine
Site hab fac1 fac2 fac3 pop diff 0 5 10 15 20 25
ID itat score ++++++
22 s hi lo hi lo 38 +
23 s hi lo hi lo 38 ++
24 s hi lo hi med 25 + ++
6 s hi lo lo lo 84 ++ I I
9 f/s hi hi lo lo 53 + ++ I
25 s hi hi lo lo 38 ++ I I
26 f hi hi hi hi 9 + ++ I
7 f hi hi hi med 9 ++ I
8 s lo hi hi hi 0 + I
4 s lo lo hi hi 13 + I
5 s lo lo hi med 25 ++ I
2 f/s lo lo hi hi 9 + I I
20 s lo lo hi hi 53 + ++ I
1 f/s lo lo hi med 22 + I I I
3 f/s lo lo hi med 22 + I I I
16 s lo hi hi hi 9 + ++
11 s lo hi lo lo 75 ++ I
15 s lo hi lo med 88 + ++ I
21 s lo lo lo med 100 + I I
10 s lo hi hi hi 16 ++ ++
12 f lo lo hi med 28 + ++ I
14 s lo lo lo med 88 + ++
17 s lo hi hi hi 0 ++ I
19 f lo hi hi med 9 + ++
13 f lo hi lo med 47 ++
18 s lo hi lo med 13 +
Southern Africa
Rescaled Distance Cluster Combine
Site hab fac1 fac2 fac3 pop diff 0 5 10 15 20 25
ID itat score ++++++
11 s hi lo hi med 0 +
13 s hi lo hi med 38 ++
12 s hi lo hi lo 54 + ++
9 s hi hi lo med 35 ++ ++
10 s hi hi lo lo 38 + I I
7 s hi hi hi med 0 ++ I
8 s hi hi hi lo 15 + I
3 s lo lo lo med 27 ++ I
15 s lo lo lo lo 31 + I I
1 s lo hi lo hi 46 ++ ++
6 s lo lo lo hi 54 + ++ I
4 s lo lo lo med 69 + I I I
14 s lo hi lo med 38 ++ ++
5 s lo lo lo lo 100 + I
2 s lo hi lo hi 23 +
Asian Sites
FACTOR ANALYSIS
Total Variance Explained
Initial Eigenvalues

Rotation Sums of Squared Loadings

Component

Total

% of Variance

Cumulative %

Total

% of Variance

Cumulative %

1

2.219

36.988

36.988

2.219

36.988

36.988

2

1.484

24.740

61.728

1.484

24.740

61.728

3

0.871

14.513

76.241

0.871

14.513

76.241

4

0.675

11.254

87.495




5

0.433

7.211

94.706




6

0.318

5.294

100.00




Extraction Method: Principal Component Analysis.
Rotated Component Matrix

Component


1

2

3

Ivory trade

0.199

0.811

0.293

Enf't. cap.

0.289

0.198

0.747

Protection

0.861

0.068

0.223

Hunting

0.097

0.850

0.301

Pop'n. size

0.081

0.132

0.817

No civil strife

0.875

0.153

0.108

Rotation Method: Varimax with Kaiser Normalization.
Interpretation of rotated factors:
Factor

Dominant contributions

1

No civil strife + protection

2

Hunting + ivory trade

3

Population size + enforcement capacity

CLUSTER ANALYSIS
4 SITE SELECTIONS
African sites
Three sampling scenarios have been derived from the analysis. These correspond to approximate sampling fractions of 25%, 40% and 65% of all sites, respectively. Within subregion sampling fractions have been held as close as possible to these overall percentages.
The method for obtaining a sample from the cluster analysis is to take a cut across the dendrogram at the point on the distance scale which gives the required number of sites for the sample. Note that there is not necessarily a solution for every possible sample size. The available sample sizes for each subregion, corresponding to the results of the hierarchical clustering are as follows:

East Africa:

1, 2, 3, 5, 6, 7, 8, 12


Central Africa:

1, 2, 4, 5, 6, 8, 10, 13, 14, 16


West Africa:

1, 2, 3, 4, 5, 6, 9, 10, 16, 26


Southern Africa:

1, 2, 3, 4, 5, 6, 8, 9, 15

The selection method was first to sample at random from a selected group (unless there was only one site in the group). The final selection was reviewed for balance according to habitat types and to ensure that the difficulty scores were not too high. Changes (in all cases minor) were made to the selections to correct for any deficiencies in this regard. The overall distribution of habitat types for the 69 sites provided was:
Habitat

No.

%

Forest

17

24%

Savannah

48

70%

Both

4

6%

Wherever possible, up to two alternative sites have been proposed for each site given. These are chosen from the same group as the selected site. However, it should be noted that taking one of these alternative sites may disturb the overall balance of the sample.
Although it is possible to derive certain intermediate solutions by selecting additional sites from cluster groups, with total sample size between the three proposed, it is important to note that there would be no rational basis for doing this.
Scenario 1
Subregion

No. of sites

Site IDs

Alternative sites

East Africa

3

9

2, 4



7

6, 8



12

1, 5

Central Africa

4

13

11, 12



5

7, 9



8

14, 16



3

2, 15

West Africa

6

24

22, 23



9

6



2





15





17





26

8, 7

Southern Africa

4

11

13, 12



9

10



7

8



2

1, 6

Total

17
(approx. 25%)



Overall sample distribution of habitat types:
Habitat

No.

%

Forest

4

24%

Savannah

11

65%

Both

2

12%

Scenario 2
Subregion

No. of sites

Site IDs

Alternative sites

East Africa

5

10

11, 2



9





7

6, 8



12

1



5



Central Africa

8

12

13, 11



5

7



9

6



16

14



8





2

15



1

4



3



West Africa

9

24

22, 23



9

6



26

25



7

8



2

4, 1



16





15

11



10

12



17

19, 18

Southern Africa

6

11

13, 12



9

10



7

8



3

15



1

6, 14



2



Total

28
(approx. 40%)



Overall sample distribution of habitat types:
Habitat

No.

%

Forest

7

25%

Savannah

19

68%

Both

2

7%

Scenario 3
Subregion

No. of sites

Site IDs

Alternative sites

East Africa

8

10

11, 2



3





4





9





7

6, 8



1





12





5



Central Africa

13

12

13



11





5





7





9

6



10





16

14



8





2





15





1





4





3



West Africa

16

24

22, 23



6





9





25





26





7





8





2

4, 1



16





15

11



21





10

12



14





17

19



13





18






\ .. continued





Scenario 3 continued




Subregion

No. of sites

Site IDs

Alternative sites

Southern Africa

8

11

13, 12



9





10





7

8



3





15





1

6, 14



2



Total

45
(approx. 65%)



Overall sample distribution of habitat types:
Habitat

No.

%

Forest

13

29%

Savannah

30

67%

Both

2

4%

Asian Sites
As with the Africa sites, three sampling scenarios have been derived. The choice of solutions is limited by the way the cluster analysis works out (i.e. the sample sizes that can be obtained by taking cuts across the dendrogram). The possible sample sizes are: 1, 2, 3, 4, 6, 7, 10, 15 and 30.
The three scenarios listed below consist of 6, 10 and 15 sites, respectively, corresponding to sampling rates of 20%, 33% and 50%.
Scenario

No. of sites

Site IDs

Alternative sites

1

6

26

27, 17



11

25, 28



1

2



7

3, 22



9

14, 30



8

4, 10

2

10

26

27, 17



18





11

25, 28



1

2



7

3



15

12



22





9

14, 30



8

4, 10



5



3

15

26

27, 17



18





21

20, 19



11

25



28

29



1





2





3





7





15

12



22





9

14, 13



30





8

4, 10



5



5 ESTIMATES OF SAMPLING ERROR AND PRECISION
To appreciate the potential sources of sampling error, it should be noted that the data obtained will be the result of a twostage sampling procedure. The first level of sampling is the selection of sites, as above. The second level of sampling is the selection of sampling units (transects, quadrats, or whatever) within sites. Both of these sampling processes contribute to the overall error of the observed variable. Little information is available for this project which can be used to assess the withinsite sampling error. However, it is generally true that in twostage sampling, it is the betweensite error which is dominant (Cochran 1977).
Statistical measures of sampling variation rest on the assumption of random sampling. In the present case, a sort of stratified sample design has been proposed (so as to take account of , or "balance", factors which are thought likely to affect illegal killing). With stratified samples, the selection of units (sites) within strata should be random. For reasons explained above, the element of randomness in the selection procedure has been inevitably rather less than ideal.
These two limitations make an accurate assessment of precision virtually impossible to achieve. However, very rough estimates can be made by making certain assumptions. First, we assume that a simple comparison between two successive observation periods (years, say) will be sufficient, thus eliminating the need to look at longer term time trends. (This assumption effectively ensures that the resulting estimates are conservative, in the sense that longer term trends provide more data and it is automatically easier to detect changes.) We can therefore reduce the problem to a simple paired ttest, assuming that the response variable is suitably transformed to approximate normality.
The next assumption is that carcass counts follow an overdispersed Poisson distribution. This is very likely to be at least approximately correct (overdispersal implying a spatial clustering of carcasses). Such data tend to follow Taylor's power law quite closely (Taylor 1961). The most common power law for such data is that the variance is proportional to the square of the mean. This fact allows the simplification of not having to obtain a prior estimate of variance; it also implies that a simple logtransformation will stabilise the variance (Green, 1994). With these assumptions it is easy to show that the fractional change detectable, d , is related to sample size (n) by means of the formula
where a is the significance level of the test and b is the type II error rate, so that the power of the test is 1b (the power of a test is the probability of detecting a difference when there really is one). t_{n1}(a ) is the percentage point of the tdistribution on n1 degrees of freedom corresponding to a onesided test (since we are estimating the precision of detecting an increase). This formula is an adaptation of that given by Green in the above reference.
Plots of % detectable change against power are given below for a = 0.05 and 0.10.
The interpretation of these plots is as follows: looking at Scenario 2 in the first graph, for example, the probability is 0.8 that a difference of 41% will be detected at a significance level of 0.05.
If these estimates seem disappointing, it should be noted that they are almost certainly very conservative due to the fact that the sample design has not been taken into account (in addition to the other reason concerning time trends, above). The effect of stratification in sample design is generally to reduce sampling errors, which in turn increases precision and power. But for reasons outlined above, there is insufficient information to attempt a rational quantification of this effect. Another mitigating factor is that we are only looking at the first level of sampling in a twostage sampling procedure. If more information were available on withinsite sampling, then the above calculations could probably be applied to the second level, with an effective increase in sample size. Ideally, a multilevel modelling approach should be adopted. These refinements would undoubtedly lead to more encouraging estimates of precision. The above estimate can be regarded as worstcase upper bounds for the genuine precision.
Overall, global estimates of error and power have been derived by combining the results of Asia with those of Africa. This has been done by simply adding the sample sizes, so the overall numbers of sites for the three scenarios are 23, 38 and 60, respectively.
THE INTERPRETATION OF THIS ANALYSIS SHOULD BE APPRAOACHED WITH CAUTION:
Annex I. Factors Used to Assess Difficulty
The following scoring system resulted from consultations with IUCN/SSC. Note that one of the variables supplied with the data, namely the answer to the questions "Is the government cooperative with data collection at the site level and within the Wildlife Department?", was not used. The answer was "Yes" for all sites but one and the variable therefore has negligible discriminating power.
Variable

Weight

NGO capacity

10

Existing research

1

Pre97 data

2

Post97 data

1

Population size

4

Existence of limits

4

Homogeneity

6

Existence of key staff

1

Single agency

4

Annex II. Site ID Codes CONFIDENTIAL
REFERENCES
Cochran W.G.  Sampling Techniques (Third Edition), Wiley, New York, 1977.
Everitt, B.  Cluster Analysis (Second Edition), SSRC/ Halsted Press, London, 1980.
Green, R.H.  Aspects of power analysis in environmental monitoring; in Fletcher D.J. & Manly
B.F.J. (Ed.)  Statistics in Ecology and Environmental Monitoring, Univ. of Otago Press, Dunedin, N.Z., 1994.
Krzanowski, W.J.  Principles of Multivariate Analysis, Clarendon Press, Oxford, 1988
Said M.Y., Chunge R.N., Craig G.C. Thouless C.R., Barnes R.F.W., Dublin H.T.  African Elephant Database 1995, IUCN/SSC, 1995.
Taylor L.R.  Aggregation, variance and the mean, Nature 189, 1961.
Annex 5 Detailed budget breakdown
Annex 3 Methods of counting elephants