- Email: [email protected]
The spatial econometrics of elephant population change
EC O LO GIC A L E CO N O M ICS 6 0 ( 2 00 6 ) 3 2 0 –3 23
a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m
w w w. e l s e v i e r. c o m / l o c a t e / e c o l e c o n
ANALYSIS
The spatial econometrics of elephant population change A note Björn Frank a,b,1 , Per Botolf Maurseth c,⁎ a
German Institute for Economic Research (DIW Berlin), 14191 Berlin, Germany Clausthal University of Technology, Julius-Albert-Straβe 2, 38678 Clausthal-Zellerfeld, Germany c Norwegian Institute of International Affairs (NUPI), PO Box 8159 Dep., 0033 Oslo, Norway b
AR TIC LE I N FO
ABS TR ACT
Article history:
While previous research found no other variable than corruption to have a negative impact
Received 20 January 2005
on the growth rate of the elephant populations of African countries, we show that one
Received in revised form
further significant impact is exerted by ‘neighbourhood effects’. Elephants travel long
4 December 2005
distances, often crossing borders. Using spatial econometric tools, we find that elephant
Accepted 5 December 2005
population changes in one country have a positive impact on population changes in
Available online 20 February 2006
neighbouring countries. Our results have possible policy implications, as they suggest that spatial clustering of funds and of conservation efforts makes sense if the endangered
Keywords:
species move across borders.
Elephants
© 2006 Elsevier B.V. All rights reserved.
Spatial econometrics Corruption and ecology JEL classification: Q20 R15
1.
Introduction
The African elephant competes with humans for natural resources and is a species much sought after by poachers. At times, its extinction was deemed likely, and the conservation of the African elephant and its habitats is still on the political agenda. A related traditional research task is to estimate the size of elephant populations. Recently, there has also been a most interesting attempt to provide statistical evidence on the causes of changes in elephant populations. Smith et al. (2003) show that corruption has a negative impact on the growth rate of the elephant populations of African countries. No signifi-
cant control variables were found—e.g., GDP per capita was insignificant. In this article, we show that one further significant impact is exerted by what might be called ‘neighbourhood effects’. Searching for new food and water resources, elephants travel long distances. GPS (Global Positioning System) techniques have enabled researchers to track elephants who walked up to 55 km in 24 h, covering an area of 20,000 km2 in 500 days (Blake et al., 2003), although some elephants exhibit less wanderlust (Galanti et al., 2000). In any case, elephants often cross political borders.2 The nature of the resulting effects does not allow application of standard
⁎ Corresponding author. Tel.: +47 22 99 40 40; fax: +47 22 36 21 82. E-mail addresses: [email protected], [email protected] (B. Frank), [email protected] (P.B. Maurseth). 1 Fax: +49 5323 72 7659. 2 Cf. the maps of known African elephant ranges in Blanc et al. (2003) or the case study by Okoumassou et al. (1998).
0921-8009/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2005.12.007
321
EC O L O G IC A L E C O N O M IC S 6 0 ( 2 0 06 ) 32 0 –3 23
(Moran's I = 0.717)
Table 1 – Effects of corruption and neighbourhood on elephant population change
2
cpi Constant ρ
1
Neighbouring countries' average 0 elephant population
Coefficient
S.E.
z
P N |z|
13.49251 −55.72711 0.6404541
4.986211 19.99991 0.1406262
2.71 −2.79 4.55
0.007 0.005 0.000
Wald test of ρ = 0: χ2(1) = 20.742 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 10.993 (0.001). Variance ratio = 0.664. Squared corr. = 0.783.
-1 -2
-1
0
1
2
3
Elephant population change (normalised as deviations from the mean)
Fig. 1 – Moran scatterplot. regression techniques. Hence, we use spatial econometric tools.
2.
Hypotheses
Our basic idea is this: elephants move and they move across borders. This results in three possible links between elephant population changes in neighbouring countries: (1) If elephants move from country A to country B and do not return to A because they are poached in B, then conditions in B have an impact on the elephant population growth rate in A. (2) If elephants are poached, then food resources for elephants migrating from B increase, and that might keep these elephants from returning to A. (3) It might be that elephants react to sustained poaching by crossing international borders—leading to increased populations in neighbouring countries.3 Whereas the first two hypotheses suggest a positive relation between elephant population changes of neighbouring countries, the third suggests a negative one. It is not ex ante obvious what we will observe.
3.
Methods
In the following, we mainly use the data from Smith et al. (2003), as provided on Nature's home page.4 They report the elephant population change rate between 1987 and 1994 in 20 African countries, with a minimum of −100%, a maximum of 62.7% and a median figure of −35.35%. These 20 countries account for about 98% of the total African elephant population.5
3
We owe this observation to Robert J. Smith. 4 http://www.nature.com/nature/journal/v426/n6962/extref/ nature02025-s1.pdf. 5 Calculated from Blanc et al. (2003). The countries are Botswana, Cameroon, Congo, Cote d'Ivoire, DRC (Zaire), Ethiopia, Gabon, Ghana, Kenya, Malawi, Mozambique, Namibia, Nigeria, Somalia, South Africa, Sudan, Tanzania, Uganda, Zambia and Zimbabwe.
Douglas-Hamilton (1987, pp. 11–13) claims that, while parts of the elephant populations remain undetected, population trends are much clearer. As we use a cross-section of growth rates, we can hope for biases in the absolute values to cancel each other out. Unfortunately, we cannot estimate the following regression equation by using simple OLS: EPOPCHi ¼ a0 þ a1 dEPOPCHðNi Þ þ a2 dCPIi ;
ð1Þ
with EPOPCHi denoting country i's elephant population change, EPOPCH(Ni) denoting the average of the population changes in the neighbouring countries and CPIi being the corruption perception index. The regressand EPOPCHi has an impact on the explanatory variable EPOPCH(Ni) as well as the latter on the former, which is why one can speak of ‘spatial autocorrelation’. The error term is correlated with the explanatory variable EPOPCH(Ni); hence, OLS would lead to biased and inefficient estimates (Bao, 1999). To account for this problem properly, we need geographical information in addition to the elephant population data mentioned above. Specifically, a distance weights matrix of the following type is commonly used: 1=wij : Wij ¼ P j 1=wij
ð2Þ
Above wij is a measure of the distance between country i and country j. The variable Wij is therefore a function of the inverse of the distance between country i and j. This inverse distance measure is normalised with the sum of all such distances between country i and the other countries. This ‘row-standardisation’ makes it possible to construct weighted averages. In spatial econometrics analyses, the hypothesis is very often that a variable in one region will influence a variable in another region as a negative function of the distance between the two regions. This is what the variable Wij expresses. The distance variable, wij, can be constructed in various ways; often, geographical distance is used. Here, we use contiguity between countries. That is, spatial
Table 2 – OLS regression of elephant population change on corruption Epopch
Coefficient
S.E.
t
P N |t|
cpi Constant
27.33386 − 121.0664
6.062594 21.37114
4.51 −5.66
0.000 0.000
N = 20, R2 = 0.53.
322
EC O LO GIC A L E CO N O M ICS 6 0 ( 2 00 6 ) 3 2 0 –3 23
Table 3 – Effects of corruption and neighbourhood on change in forest cover
cpi Constant ρ
Coefficient
S.E.
z
P N |z|
0.0938317 −0.816207 0.2447276
0.0645974 0.2841509 0.242802
1.45 −2.87 1.01
0.146 0.004 0.313
Wald test of ρ = 0: χ2(1) = 1.016 (0.313). Likelihood ratio test of ρ = 0: χ2(1) = 0.937 (0.333). Variance ratio = 0.121. Squared corr. = 0.165.
Table 5 – Effects of corruption, neighbourhood and neighbouring corruption on elephant population change
cpi avneicpi Constant ρ
Coefficient
S.E.
z
P N |z|
12.43573 7.413634 −81.30833 0.5708323
4.890303 4.394885 25.89923 0.1539477
2.54 1.69 − 3.14 3.71
0.011 0.092 0.002 0.000
Wald test of ρ = 0: χ2(1) = 13.749 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 8.518 (0.004). Variance ratio = 0.724. Squared corr. = 0.799.
spillovers are measured on the basis of neighbourhood between countries and Wij is then defined slightly different from (2) as
neighbouring countries (see also a similar plea for the spatial lag model by Beck et al., 2005).
wij Wij ¼ P j wij
4.
ð3Þ
with wij = 1 in the case of contiguity between i and j, and 0 otherwise. Consider country j's elephant population change, EPCHj (normalised as deviations from the mean). For country i, the variable EPCHi ¼
X
Wij EPCHj
j
denotes the average of changes in the elephant population of that country's neighbours. Correlating this variable with the elephant population growth rate of the respective country i results in the ‘Moran's I', a common measure for spatial autocorrelation. This is a gross correlation in the sense that it does not take into account how elephant population change is influenced by other variables. For example, what seem to be positive neighbourhood effects might merely reflect a spatial pattern of corruption since corruption affects elephant population change. To account for this possibility, the spatial weight matrix Wij can be used in regression-based explorations, i.e. when control variables are considered. There are two basic approaches for integrating spatial correlation into regression techniques–spatial lag models and spatial error models–which have to be estimated by means of a maximum likelihood procedure (see, e.g., Anselin, 1992). Here, we report only results of the spatial lag model, because qualitatively the results are similar and the spatial lag model more directly improves on the intuitive approach indicated in Eq. (1): The variable of interest, here elephant population change, is partly determined by the value which the same variable takes in
Table 4 – Spatial autocorrelation of corruption levels, controlling for GDP per capita
gdpcap Constant ρ
Coefficient
S.E.
z
P N |z|
0.0002729 1.069353 0.585548
0.0001423 0.5356313 0.1548737
1.92 2.00 3.78
0.055 0.046 0.000
The growth rates of the elephant populations in African countries correlate with the growth rates in neighbouring countries: Moran's I is 0.717 and significant at the 99% level. The diagrammatic counterpart of this measure is the regression line in the Moran scatterplot (Fig. 1). The respective country's growth rate of the elephant population is plotted on the abscissa, EPCHi, as described in the previous section, on the ordinate. Observations in the northeast quadrant represent countries with both a relatively high elephant population change and neighbours who are similar in this respect. Similarly, the southwest quadrant shows countries with a below-average elephant population change and with neighbours who also do not seem to offer conditions favourable to this species. More dots are located in the northeast and in the southwest sector than in the other two: hence, a simple regression has a positive slope. Table 1 reports the main results of the regression analysis. Beginning from the bottom of the table, the squared correlation and the variance ratio are two quasi R2 statistics, indicating that a relatively high percentage of the variance can be explained. Rho is the estimated coefficient of neighbourhood effects. It is positive and significant; hence, controlling for corruption (cpi) leaves intact the initial result about neighbourhood. Corruption is also highly significant, but the coefficient has only half of the size that is estimated when we simply regress an elephant population change on corruption without considering neighbourhood effects: see Table 2. Note that the corruption index used runs from 0 to 10 with low values indicating high levels of perceived corruption. To check whether our results make sense, we applied the methods described above to the change in natural forest cover in the same countries. As forests do not ‘migrate’ across borders, we should not observe neighbourhood effects for forests.6 And indeed we do not: we see that ρ is clearly insignificant in Table 3.
6
Wald test of ρ = 0: χ2(1) = 14.295 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 8.631 (0.003). Variance ratio = 0.387. Squared corr. = 0.579.
Results
Note one qualification concerning this claim: There is no clear impact of corruption on forest cover, but other-unobservedvariables related to the environment or environmental policy could drive such a result. This does not seem to be the case here, however.
EC O L O G IC A L E C O N O M IC S 6 0 ( 2 0 06 ) 32 0 –3 23
However, an alternative explanation for our main result could relate to the finding that corruption is spatially autocorrelated (see Table 4). A likely consequence is that countries, which do not spend enough on anti-poaching strategies, also tend to share borders. This is fairly plausible: as one referee pointed out, poachers react to changes in anti-poaching strategies by moving from country to country; hence, a new anti-poaching strategy of one country could increase pressure on neighbouring countries to follow suit. A similar development of elephant populations in neighbouring countries should result. Yet if this were the main force leading to spatial autocorrelation in elephant growth rates, we should get regression results substantially different from those reported in Table 1 when controlling for the average level of corruption in the neighbouring countries, avneicpi. However, this is not the case, as shown in Table 5. (With r = 0.35, the correlation between cpi and avneicpi is not so strong that multicorrelation would be a major problem.) Hence, elephant movements across borders seem to be the main explanation of our results.
5.
Conclusion
We find a marked positive correlation of elephant population growth rates between neighbouring countries. Our results thus provide evidence that the first two mechanisms mentioned in Section 2 dominate over the third. These results have possible policy implications, as they suggest that spatial clustering of funds and of conservation efforts makes sense in cases where the endangered species move across borders. Although our statistical results are new, this kind of policy implication is evidently intuitively appealing, as several attempts in this direction have been implemented recently. The Biodiversity Support Program–a consortium of the World Wildlife Fund, the Nature Conservancy and the World Resources Institute–has not only stressed the importance of trans-boundary natural resource management projects, it also acknowledges wildlife migratory routes leading across political borders as a rationale (Griffin et al., 1999). For the same purpose, the government of Tanzania has agreed to work together with its neighbours in conserving trans-boundary ecosystems (Mpanduji et al., 2002). Our analysis suggests that such efforts are well founded.
323
Acknowledgements We are indebted to two anonymous referees for many suggestions, to Robert J. Smith and Matt Walpole of the Durrell Institute of Conservation and Ecology, University of Kent, for helpful discussions, and to Susan Høivik for polishing the text.
REFERENCES Anselin, Luc, 1992. Spacestat tutorial. Technical Report S 92 1, National Center for Geographical Information and Analysis. University of California, Santa Barbara, California. Bao, Shuming, 1999. Literature Review of Spatial Statistics and Models, China Data Center, http://141.211.136.209/cdc/docs/ review.pdf. Beck, Nathaniel, Gleditsch, Kristian Skrede, Beardsley, Kyle, 2005. Space is more than geography: using spatial econometrics in the study of political economy. mimeo: http://www.nyu.edu/ gsas/dept/politics/faculty/beck/becketal.pdf. Blake, Stephen, Bouché, Philippe, Rasmussen, Henrik, Orlando, Anne, Douglas-Hamilton, Iain, 2003. The last Sahelian elephants. Ranging behavior, population status and recent history of the desert elephants of Mali. mimeo: http://www. save-the-elephants.org/PDF%20Files/finalmali_eng.pdf. Blanc, J.J., Thouless, C.R., Hart, J.A., Dublin, H.T., Douglas-Hamilton, I., Craig, C.G., Barnes, R.F.W., 2003. African Elephant Status Report 2002: an update from the African Elephant Database. IUCN/SSC African Elephant Specialist Group. IUCN, Gland, Switzerland. Douglas-Hamilton, I., 1987. African elephants: population trends and their cause. Oryx 21 (1), 11–24. Galanti, Valeria, Tosi, Guido, Rossi, Rossella, Foley, Charles, 2000. The use of GPS radio-collars to track elephants (Loxodonta Africana) in the Tarangire National Park (Tanzania). Hystrix 11 (2), 27–37. Griffin, John, Cumming, David, Metcalfe, Simon, t'Sas-Rolfes, Mike, Singh, Jaidev 'Jay', Chonguiça, Ebenizário, Rowen, Mary, Oglethorpe, Judy, 1999. Study on the Development of Transboundary Natural Resource Management Areas in Southern Africa. Biodiversity Support Program, Washington, DC. Mpanduji, D.G., Hofer, H., Hilderbrandt, T.B., Goeritz, F., East, M.L., 2002. Movement of elephants in the Selous-Niassa Wildlife Corridor, southern Tanzania. Pachyderm. (33), 18–31. Okoumassou, K., Barnes, R.F.W., Sam, M.K., 1998. The distribution of elephants in north-eastern Ghana and northern Togo. Pachyderm. (26), 52–60. Smith, R.J., Muir, R.D.J., Walpole, M.J., Balmford, A., LeaderWilliams, N., 2003. Governance and the loss of biodiversity. Nature 426 (6), 67–70.
a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m
w w w. e l s e v i e r. c o m / l o c a t e / e c o l e c o n
ANALYSIS
The spatial econometrics of elephant population change A note Björn Frank a,b,1 , Per Botolf Maurseth c,⁎ a
German Institute for Economic Research (DIW Berlin), 14191 Berlin, Germany Clausthal University of Technology, Julius-Albert-Straβe 2, 38678 Clausthal-Zellerfeld, Germany c Norwegian Institute of International Affairs (NUPI), PO Box 8159 Dep., 0033 Oslo, Norway b
AR TIC LE I N FO
ABS TR ACT
Article history:
While previous research found no other variable than corruption to have a negative impact
Received 20 January 2005
on the growth rate of the elephant populations of African countries, we show that one
Received in revised form
further significant impact is exerted by ‘neighbourhood effects’. Elephants travel long
4 December 2005
distances, often crossing borders. Using spatial econometric tools, we find that elephant
Accepted 5 December 2005
population changes in one country have a positive impact on population changes in
Available online 20 February 2006
neighbouring countries. Our results have possible policy implications, as they suggest that spatial clustering of funds and of conservation efforts makes sense if the endangered
Keywords:
species move across borders.
Elephants
© 2006 Elsevier B.V. All rights reserved.
Spatial econometrics Corruption and ecology JEL classification: Q20 R15
1.
Introduction
The African elephant competes with humans for natural resources and is a species much sought after by poachers. At times, its extinction was deemed likely, and the conservation of the African elephant and its habitats is still on the political agenda. A related traditional research task is to estimate the size of elephant populations. Recently, there has also been a most interesting attempt to provide statistical evidence on the causes of changes in elephant populations. Smith et al. (2003) show that corruption has a negative impact on the growth rate of the elephant populations of African countries. No signifi-
cant control variables were found—e.g., GDP per capita was insignificant. In this article, we show that one further significant impact is exerted by what might be called ‘neighbourhood effects’. Searching for new food and water resources, elephants travel long distances. GPS (Global Positioning System) techniques have enabled researchers to track elephants who walked up to 55 km in 24 h, covering an area of 20,000 km2 in 500 days (Blake et al., 2003), although some elephants exhibit less wanderlust (Galanti et al., 2000). In any case, elephants often cross political borders.2 The nature of the resulting effects does not allow application of standard
⁎ Corresponding author. Tel.: +47 22 99 40 40; fax: +47 22 36 21 82. E-mail addresses: [email protected], [email protected] (B. Frank), [email protected] (P.B. Maurseth). 1 Fax: +49 5323 72 7659. 2 Cf. the maps of known African elephant ranges in Blanc et al. (2003) or the case study by Okoumassou et al. (1998).
0921-8009/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2005.12.007
321
EC O L O G IC A L E C O N O M IC S 6 0 ( 2 0 06 ) 32 0 –3 23
(Moran's I = 0.717)
Table 1 – Effects of corruption and neighbourhood on elephant population change
2
cpi Constant ρ
1
Neighbouring countries' average 0 elephant population
Coefficient
S.E.
z
P N |z|
13.49251 −55.72711 0.6404541
4.986211 19.99991 0.1406262
2.71 −2.79 4.55
0.007 0.005 0.000
Wald test of ρ = 0: χ2(1) = 20.742 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 10.993 (0.001). Variance ratio = 0.664. Squared corr. = 0.783.
-1 -2
-1
0
1
2
3
Elephant population change (normalised as deviations from the mean)
Fig. 1 – Moran scatterplot. regression techniques. Hence, we use spatial econometric tools.
2.
Hypotheses
Our basic idea is this: elephants move and they move across borders. This results in three possible links between elephant population changes in neighbouring countries: (1) If elephants move from country A to country B and do not return to A because they are poached in B, then conditions in B have an impact on the elephant population growth rate in A. (2) If elephants are poached, then food resources for elephants migrating from B increase, and that might keep these elephants from returning to A. (3) It might be that elephants react to sustained poaching by crossing international borders—leading to increased populations in neighbouring countries.3 Whereas the first two hypotheses suggest a positive relation between elephant population changes of neighbouring countries, the third suggests a negative one. It is not ex ante obvious what we will observe.
3.
Methods
In the following, we mainly use the data from Smith et al. (2003), as provided on Nature's home page.4 They report the elephant population change rate between 1987 and 1994 in 20 African countries, with a minimum of −100%, a maximum of 62.7% and a median figure of −35.35%. These 20 countries account for about 98% of the total African elephant population.5
3
We owe this observation to Robert J. Smith. 4 http://www.nature.com/nature/journal/v426/n6962/extref/ nature02025-s1.pdf. 5 Calculated from Blanc et al. (2003). The countries are Botswana, Cameroon, Congo, Cote d'Ivoire, DRC (Zaire), Ethiopia, Gabon, Ghana, Kenya, Malawi, Mozambique, Namibia, Nigeria, Somalia, South Africa, Sudan, Tanzania, Uganda, Zambia and Zimbabwe.
Douglas-Hamilton (1987, pp. 11–13) claims that, while parts of the elephant populations remain undetected, population trends are much clearer. As we use a cross-section of growth rates, we can hope for biases in the absolute values to cancel each other out. Unfortunately, we cannot estimate the following regression equation by using simple OLS: EPOPCHi ¼ a0 þ a1 dEPOPCHðNi Þ þ a2 dCPIi ;
ð1Þ
with EPOPCHi denoting country i's elephant population change, EPOPCH(Ni) denoting the average of the population changes in the neighbouring countries and CPIi being the corruption perception index. The regressand EPOPCHi has an impact on the explanatory variable EPOPCH(Ni) as well as the latter on the former, which is why one can speak of ‘spatial autocorrelation’. The error term is correlated with the explanatory variable EPOPCH(Ni); hence, OLS would lead to biased and inefficient estimates (Bao, 1999). To account for this problem properly, we need geographical information in addition to the elephant population data mentioned above. Specifically, a distance weights matrix of the following type is commonly used: 1=wij : Wij ¼ P j 1=wij
ð2Þ
Above wij is a measure of the distance between country i and country j. The variable Wij is therefore a function of the inverse of the distance between country i and j. This inverse distance measure is normalised with the sum of all such distances between country i and the other countries. This ‘row-standardisation’ makes it possible to construct weighted averages. In spatial econometrics analyses, the hypothesis is very often that a variable in one region will influence a variable in another region as a negative function of the distance between the two regions. This is what the variable Wij expresses. The distance variable, wij, can be constructed in various ways; often, geographical distance is used. Here, we use contiguity between countries. That is, spatial
Table 2 – OLS regression of elephant population change on corruption Epopch
Coefficient
S.E.
t
P N |t|
cpi Constant
27.33386 − 121.0664
6.062594 21.37114
4.51 −5.66
0.000 0.000
N = 20, R2 = 0.53.
322
EC O LO GIC A L E CO N O M ICS 6 0 ( 2 00 6 ) 3 2 0 –3 23
Table 3 – Effects of corruption and neighbourhood on change in forest cover
cpi Constant ρ
Coefficient
S.E.
z
P N |z|
0.0938317 −0.816207 0.2447276
0.0645974 0.2841509 0.242802
1.45 −2.87 1.01
0.146 0.004 0.313
Wald test of ρ = 0: χ2(1) = 1.016 (0.313). Likelihood ratio test of ρ = 0: χ2(1) = 0.937 (0.333). Variance ratio = 0.121. Squared corr. = 0.165.
Table 5 – Effects of corruption, neighbourhood and neighbouring corruption on elephant population change
cpi avneicpi Constant ρ
Coefficient
S.E.
z
P N |z|
12.43573 7.413634 −81.30833 0.5708323
4.890303 4.394885 25.89923 0.1539477
2.54 1.69 − 3.14 3.71
0.011 0.092 0.002 0.000
Wald test of ρ = 0: χ2(1) = 13.749 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 8.518 (0.004). Variance ratio = 0.724. Squared corr. = 0.799.
spillovers are measured on the basis of neighbourhood between countries and Wij is then defined slightly different from (2) as
neighbouring countries (see also a similar plea for the spatial lag model by Beck et al., 2005).
wij Wij ¼ P j wij
4.
ð3Þ
with wij = 1 in the case of contiguity between i and j, and 0 otherwise. Consider country j's elephant population change, EPCHj (normalised as deviations from the mean). For country i, the variable EPCHi ¼
X
Wij EPCHj
j
denotes the average of changes in the elephant population of that country's neighbours. Correlating this variable with the elephant population growth rate of the respective country i results in the ‘Moran's I', a common measure for spatial autocorrelation. This is a gross correlation in the sense that it does not take into account how elephant population change is influenced by other variables. For example, what seem to be positive neighbourhood effects might merely reflect a spatial pattern of corruption since corruption affects elephant population change. To account for this possibility, the spatial weight matrix Wij can be used in regression-based explorations, i.e. when control variables are considered. There are two basic approaches for integrating spatial correlation into regression techniques–spatial lag models and spatial error models–which have to be estimated by means of a maximum likelihood procedure (see, e.g., Anselin, 1992). Here, we report only results of the spatial lag model, because qualitatively the results are similar and the spatial lag model more directly improves on the intuitive approach indicated in Eq. (1): The variable of interest, here elephant population change, is partly determined by the value which the same variable takes in
Table 4 – Spatial autocorrelation of corruption levels, controlling for GDP per capita
gdpcap Constant ρ
Coefficient
S.E.
z
P N |z|
0.0002729 1.069353 0.585548
0.0001423 0.5356313 0.1548737
1.92 2.00 3.78
0.055 0.046 0.000
The growth rates of the elephant populations in African countries correlate with the growth rates in neighbouring countries: Moran's I is 0.717 and significant at the 99% level. The diagrammatic counterpart of this measure is the regression line in the Moran scatterplot (Fig. 1). The respective country's growth rate of the elephant population is plotted on the abscissa, EPCHi, as described in the previous section, on the ordinate. Observations in the northeast quadrant represent countries with both a relatively high elephant population change and neighbours who are similar in this respect. Similarly, the southwest quadrant shows countries with a below-average elephant population change and with neighbours who also do not seem to offer conditions favourable to this species. More dots are located in the northeast and in the southwest sector than in the other two: hence, a simple regression has a positive slope. Table 1 reports the main results of the regression analysis. Beginning from the bottom of the table, the squared correlation and the variance ratio are two quasi R2 statistics, indicating that a relatively high percentage of the variance can be explained. Rho is the estimated coefficient of neighbourhood effects. It is positive and significant; hence, controlling for corruption (cpi) leaves intact the initial result about neighbourhood. Corruption is also highly significant, but the coefficient has only half of the size that is estimated when we simply regress an elephant population change on corruption without considering neighbourhood effects: see Table 2. Note that the corruption index used runs from 0 to 10 with low values indicating high levels of perceived corruption. To check whether our results make sense, we applied the methods described above to the change in natural forest cover in the same countries. As forests do not ‘migrate’ across borders, we should not observe neighbourhood effects for forests.6 And indeed we do not: we see that ρ is clearly insignificant in Table 3.
6
Wald test of ρ = 0: χ2(1) = 14.295 (0.000). Likelihood ratio test of ρ = 0: χ2(1) = 8.631 (0.003). Variance ratio = 0.387. Squared corr. = 0.579.
Results
Note one qualification concerning this claim: There is no clear impact of corruption on forest cover, but other-unobservedvariables related to the environment or environmental policy could drive such a result. This does not seem to be the case here, however.
EC O L O G IC A L E C O N O M IC S 6 0 ( 2 0 06 ) 32 0 –3 23
However, an alternative explanation for our main result could relate to the finding that corruption is spatially autocorrelated (see Table 4). A likely consequence is that countries, which do not spend enough on anti-poaching strategies, also tend to share borders. This is fairly plausible: as one referee pointed out, poachers react to changes in anti-poaching strategies by moving from country to country; hence, a new anti-poaching strategy of one country could increase pressure on neighbouring countries to follow suit. A similar development of elephant populations in neighbouring countries should result. Yet if this were the main force leading to spatial autocorrelation in elephant growth rates, we should get regression results substantially different from those reported in Table 1 when controlling for the average level of corruption in the neighbouring countries, avneicpi. However, this is not the case, as shown in Table 5. (With r = 0.35, the correlation between cpi and avneicpi is not so strong that multicorrelation would be a major problem.) Hence, elephant movements across borders seem to be the main explanation of our results.
5.
Conclusion
We find a marked positive correlation of elephant population growth rates between neighbouring countries. Our results thus provide evidence that the first two mechanisms mentioned in Section 2 dominate over the third. These results have possible policy implications, as they suggest that spatial clustering of funds and of conservation efforts makes sense in cases where the endangered species move across borders. Although our statistical results are new, this kind of policy implication is evidently intuitively appealing, as several attempts in this direction have been implemented recently. The Biodiversity Support Program–a consortium of the World Wildlife Fund, the Nature Conservancy and the World Resources Institute–has not only stressed the importance of trans-boundary natural resource management projects, it also acknowledges wildlife migratory routes leading across political borders as a rationale (Griffin et al., 1999). For the same purpose, the government of Tanzania has agreed to work together with its neighbours in conserving trans-boundary ecosystems (Mpanduji et al., 2002). Our analysis suggests that such efforts are well founded.
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Acknowledgements We are indebted to two anonymous referees for many suggestions, to Robert J. Smith and Matt Walpole of the Durrell Institute of Conservation and Ecology, University of Kent, for helpful discussions, and to Susan Høivik for polishing the text.
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