are african elephants an endangered species?

A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

A

S P E C I E S ?

RE AFRICAN ELEPHANTS AN ENDANGERED SPECIES? by Greg Hertzler and Maxwell Gomera

i

Published by:

IUCN – The World Conservation Union (Regional Office for Southern Africa)

Sponsored by:

Ford Foundation International Development and Research Centre, Australian AID and Australian Research Centre

Copyright:

2004. IUCN The World Conservation Union This publication may be produced in whole or part and in any form for education or non-profit uses, without special permission from the copyright holder, provided acknowledgement of the source is made. IUCN would appreciate receiving a copy of any publication which uses this publication as a source. No use of this publication may be made for resale or other commercial purpose without the prior written permission of IUCN. The views expressed in this publication do not necessarily reflect those of IUCN or of the sponsors of this publication.

Citation:

Hertzler Greg and Gomera Maxwell (2004). Are African Elephants an Endangered Species? IUCN – ROSA , Harare, Zimbabwe.

ISBN:

1-77931-018-8

Layout and Design:

Design@7 Visual Works

Photograph:

IUCN - Library

Available from:

IUCN Regional Office for Sothern Africa, 6 Lanark Rd, Box 745, Harare Zimbabwe

THE IUCN-ROSA SERIES ON TRANSBOUNDARY NATURAL RESOURCES MANAGEMENT-PAPER 4

ii

A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

IUCN - THE WORLD CONSERVATION UNION IUCN - The World Conservation Union was founded in 1948 and brings together 79 states, 112 government agencies, 760 NGOs, 37 affiliates, and some 10,000 scientists and experts from 141 countries in a unique worldwide partnership. Its mission is to influence, encourage and assist societies throughout the world to conserve the integrity and diversity of nature and to ensure that any use of natural resources is equitable and ecologically sustainable. Within the framework of global conventions IUCN has helped over 75 countries to prepare and implement national conservation and biodiversity strategies. IUCN has approximately 1000 staff, most of whom are located in its 42 regional and country offices while 100 work at its Headquarters in Gland, Switzerland.

IUCN - REGIONAL OFFICE FOR SOUTHERN AFRICA The IUCN Regional Office for Southern Africa was established in Zimbabwe in 1987 to serve the Southern African Region and the Southern African Development Community (SADC) in the development of modern skills in conservation and natural resource management. IUCN-ROSA coordinates such regional services to over 69 members in 11 countries through its regional support programmes, regional networks, and its country offices in Botswana, Mozambique, South Africa, and Zambia. IUCN ROSA’s operational vision is to be a Development Partner of First Choice but the vision for IUCN’s environmental and natural resource management work in the region is “Greater Environmental and Human Security in Southern Africa”. Its mission for Southern Africa is to facilitate and strengthen an integrated approach for the sustainable and equitable use of natural resources and the conservation of biological diversity. The underlying objective in all IUCN-ROSA’s activities and programmes is capacity building and catalysing action. Developing, coordinating, and supporting programmatic partnerships is the preferred operational mechanism supporting this objective. Additional services include the provision of objective and scientifically-based advisory services and technical assistance, training inputs and programmes, and fora for national and inter-regional dialogue, networking, debate, and conflict resolution. At the regional level, IUCN-ROSA spearheads the World Conservation Union’s efforts to integrate the Union’s secretariat, membership and commissions in common purpose within the framework of the Union’s mission.

iii

ABSTRACT

1

INTRODUCTION

2

BIOECONOMIC MODELS

4

CALIBRATING THE MODELS

12

RESULTS

19

CONCLUSION

29

REFERENCES

31

LIST OF GRAPHS Figure:1 Figure:2 Figure:3 Figure:4 Figure:5 Figure:6 Figure:7 Figure:8 Figure:9 Figure:10 Figure:11

Recruitment, Mortality and Surplus Yield of Elements Demand Curve for Ivory, Hides and Meat Damage to Agricultural Production Effort Function for Culling Actual and Predicted Stocks for the Biomass Model Actual and Predicted Stocks for the Age Structural Model Biomass Model with Open Access Biomass Model with Optimal Management Steady State Supply Age Structural Model with Open Acess Age Structural Model with Optimal Management

5 6 7 8 14 16 20 22 23 25 27

LIST OF TABLES Table:1 Table:2 Table:3 Table:5 Table:6 Table:7 Table:8

Parameters for the Population Dynamics of the Biomasss Model Parameters for the Population Dynamics of the Age Structural Model Parameters for the Objective Functions of the Biomass and Age Structured models Biomass Model with Open Access Biomass Model with Optimal Management Age Structural Model with Open Acess Age Structural Model with Optimal Management


iv

14 15 17 20 23 26 27

ARE AFRICAN ELEPHANTS AN ENDANGERED SPECIES? Abstract In the late 1980s there were two campaigns to save African elephants. One banned international trade in ivory. The other established common property rights to elephants for local communities. Has either campaign saved the elephants? To answer this question, we constructed and solved two models, a biomass model and an age structured model. We conclude that in countries which successfully establish property rights, local communities will conserve elephants. In countries with poor property rights or open access, poachers will exterminate the elephants. The world cannot save African elephants by banning trade. Instead, African countries must save them by establishing property rights.

1

INTRODUCTION From 1981 to 1989, the elephant population of Africa fell from 1.3 million to 650 thousand (Barbier et al., 1990, Table 1.1). Eastern and central African countries allowed poachers to slaughter elephants for their ivory. Southern African countries controlled poaching and maintained their populations. Although conservationists questioned the population estimates (Cumming, 1989), many people feared that African elephants would soon disappear from the earth (Beddington, et al., 1989). Two campaigns were begun to save the elephants. One was political lobbying to ban international trade in ivory. The other was a strategy to create common property rights and give local communities an incentive to conserve elephants. The campaign to ban trade was launched with the “Urgent Memorandum” by the African Wildlife Foundation (AWF). Sent to AWF members, it warned of the rapid decline in elephant numbers and asked for tax deductible donations (Bonner, 1993, p. 53). In response, the World Wide Fund for Nature (WWF) convened a hasty meeting in Zambia to discuss their elephant conservation policy (Bonner, 1993, p. 89). Scientists within WWF did not support a ban on ivory trade. The scientists did not prevail. First to propose a ban were the Humane Society of the United States (Thompson, 1992). They wished to upgrade African elephants from Appendix II to Appendix I of the Convention on International Trade in Endangered Species of Flora and Fauna (CITES), declaring elephants an endangered species. Not to be outdone, Friends of Animals organised a public relations campaign to convince WWF to support the ban (Bonner, 1993, p. 112) and the Environmental Investigation Agency worked covertly with an individual within WWF to draft a proposal to CITES (Bonner, 1993, p. 127; Sugg and Kreuter, 1994, p. 31). The Environmental Investigation Agency persuaded Tanzania in eastern Africa to submit the proposal to the parties of CITES (Bonner, 1993, p. 128). Neighbouring Kenya quickly installed Richard Leakey as head of its wildlife department and became leader of the “ban” wagon (Bonner, 1993, p. 130). The most famous spectacle of the campaign soon followed. Kenya built a pyre of $US3 million worth of ivory and burned it in front of the cameras (Bonner, 1993, p. 149). What seemed like a waste was actually good public relations as Leakey then raised donations of $US143 million (Satchell, 1993). Intellectual support for the ban on ivory trade came from the Ivory Trade Review Group (ITRG, 1989). Economists within the ITRG argued that even optimally managed elephant populations may be driven to extinction (Barbier et al., 1990, pp. 11-14). On the one hand, elephants products

2

are valuable, elephants are easy to harvest and the proceeds of the harvest can be invested in the economy at the social discount rate. On the other hand, elephants reproduce and grow slowly. The rate of return to dead elephants may exceed the rate of return to living elephants and it may be optimal to shoot the elephants and invest the proceeds.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

The economists did not support a complete ban, however, because this would have deprived African countries of the funds needed to protect wildlife. Instead, they proposed a temporary ban, giving time to implement a “truly effective package of regulation”. (Barbier et al., 1990, p. 138). The economists were overruled and, in October 1989, African elephants were listed in Appendix I of CITES. The second campaign to save the elephants began in January 1989, when the people of Nyaminyami, a village in north western Zimbabwe, were granted authority to manage wildlife in their district (Bonner, 1993, p. 253). This was the first trial of the Communal Areas Management Programme for Indigenous Resources (CAMPFIRE). CAMPFIRE was the brainchild of the Department of National Parks and Wildlife Management (DNPWM), Marshall Murphree from the Centre for Applied Social Sciences at the University of Zimbabwe, with help from WWF in Harare and from Zimbabwe Trust. The principle is simple. Local communities with property rights over wildlife, in particular elephants, will have the incentive to sustain the populations. Many people in Africa aren’t interested in sustaining elephants. Bonner (1990, p. 222) cites an article from a newspaper in Kenya which may explain this attitude: “A woman, who was eight months pregnant, was gored to death by elephants in Wundanyi District on Friday morning... Ms Henrita Mkankjala Mwamburi (40) was trying to scare the elephants which had invaded her maize plantation... One of the elephants charged at Ms Mwamburi and hurled her about 10 metres away. Her stomach burst open and the unborn child was thrown out. Both died on the spot.” In the early 1990s, an average of 27 people were killed every year by elephants in Kenya (Dublin, Milliken and Barnes, p. 25, undated). Most were farmers protecting their crops. For this reason, farmers are suspected of encouraging poachers. If local communities are to sustain elephant populations, farmers must be compensated for any crop damage and elephants must be worth more alive than dead. Who is right? Are the economists correct in concluding that even optimally managed elephant populations are in danger of extinction? Are the proponents of CAMPFIRE correct in thinking that local communities with property rights over elephants will manage them sustainably? The economists based their conclusions on a biomass model which assumes all elephants are the same. They argued from theory rather than from empirical results. In this study we quantify and solve a biomass model which predicts that elephant populations should be maintained at about one third the carrying capacity of the habitat. However, a biomass model is inadequate for elephants which have a complex life cycle and become more valuable as they grow older. Letting young elephants grow into older and more valuable elephants provides an additional rate of return to living elephants which cannot be included in a biomass model. In this study we construct an age structured model to track individual elephants through their life cycle. We then quantify and solve the model which predicts that elephant populations should be sustained just below the carrying capacity of the habitat.

3

BIOECONOMIC MODELS Both biomass and age structured models will include the multiple uses for elephants. The models will differ, however, in their description of the population dynamics.

Biomass Model Disregarding the age and sex of individuals, the population dynamics of elephants can be described by a single equation for the change in stocks.

(1)

S (t + 1) − S (t ) = R(S (t ))− M (S (t ))− C(t ) − H (t ); t = 0,K, ∞.

The change in elephant stocks in the current year, S(t+1)-S(t), increases with recruitment, R(S(t)), and decreases with natural mortality, M(S(t)), culling, C(t), and hunting, H(t). Culling removes entire family groups across all ages. Hunting is predominantly for trophy bulls. Because the biomass model does not distinguish age groups, an additional constraint may be needed to keep hunting to realistically low levels. Recruitment and mortality depend upon the stock of elephants. The recruitment rate is calculated as a product of the proportion of breeding female elephants, the intrinsic rate of recruitment and an environmental interaction term. Multiplying the recruitment rate by the elephant stocks gives recruitment. ( 2)

R(S (t )) = 05 . fr S (t ) e − S ()t S (t ).

The proportion of females in the population is 0.5, the proportion of these which are fertile is ƒ and so the proportion of breeding females if 0.5ƒ. The intrinsic recruitment rate for each breeding female is r and the recruitment rate in an ideal environment is 0.5ƒr. The environmental interaction

S, ( and S (( are parameters which help determine the minimum viable e population, the carrying capacity of the habitat and the maximum sustainable yield from the population. Multiplying the recruitment rate in an ideal environment by the environmental . fr S (t ) e − S (t ) . Finally, multiplying the recruitment interaction term gives the recruitment rate, 05 rate by the stock of elephants, S(t), gives total recruitment in equation (2). term is

S (t ) e

− S ()t

S where

)

The mortality rate is the intrinsic mortality rate multiplied by an environmental interaction term. Multiplying the mortality rate by the stock of elephants gives natural mortality. (3)

4

S t M (S (t )) = me () S (t ).

The intrinsic mortality rate is m and the environmental interaction term isme S ()t ,Swhere S( is a

me

parameter which helps to determine the carrying capacity of the habitat and the maximum sustainable yield of the population. Natural mortality in equation (3) is called a Ricker relationship (Getz and Haight, p. 72, 1989).


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

5

Figure 1: Recruitment, Mortality and Surplus Yield of Elephants.

Recruitment minus mortality is surplus yield. If, in equation (2), Sequals one and (

)

equals zero,

e

recruitment becomes a Ricker relationship and the minimum viable population will be zero. Further, if Sin ( equation (2) equals

me

Sin equation (3), the environment affects recruitment and

mortality to the same extent and the resulting surplus yield is numerically indistinguishable from that of a logistic growth model. For elephants, however, the minimum viable population will be above zero and the environment will affect recruitment more than it affects mortality, as shown in Figure 1. Substituting recruitment from equation (2) and mortality from equation (3) into equation (1) gives another formulation for the population dynamics of elephants.

(4)

S (t + 1) − S (t ) = 05 . fr S (t ) e − S (t )S (t ) − me S (t )S (t )

− C(t ) − H (t ); t = 0,K , ∞.

This formulation will be compared with the age-structured model to be presented below. Elephants have multiple uses. Benefits are the revenues from the culling and hunting of elephants, from any agricultural production within the elephants’ range and from the amenity or existence value of elephants. Costs are the costs of effort expended in culling and hunting. Benefits above costs are discounted and summed over time to get the net present value which is the wealth generated for a country by its elephants. ∞

( 5)

t

(1+1 ) [pc (C(t))C(t) + ph H(t) C, H t =0

J(S(0)) = max ∑

]

+ pa A(S(t)) + p s S(t) − p x X (S(t), C(t)) − p y Y(S(t), H(t)) .

1

)

The net present value, J, is the sum over time of revenues above costs, discounted at the rate+ .

Revenue from culling, pcC, is the price of an elephant’s ivory, hide and meat, pc, multiplied by the

quantity culled, C. The price may depend upon the quantity sold. Revenue from hunting, phH, is the trophy fee plus a daily rate for the hunter and any guests, ph , multiplied by the quantity hunted, H. Revenue from agriculture, paA, is a gross margin, pa , multiplied by the quantity of agricultural production, A. Damage to crops and livestock caused by elephants reduces agricultural production. No allowance is made for the cost of human lives lost in protecting crops from elephants. Instead, it is assumed that farmers are compensated for losses and will not risk their lives to save their crops. Amenity and existence values, psS, include use values such as revenue collected from tourists who view elephants, option values for people who may wish to view elephants in the future and existence values as contributions by people who are willing to pay to preserve elephants, where ps is the value per elephant and S is the stock of elephants. The costs of effort for culling and hunting, pxX and pyY, are the prices of effort, px and py , multiplied by the quantities of effort, X and Y. The effort expended in culling and hunting will depend upon the stock of elephants and on the quantities to be culled and hunted. If culling supplies a significant proportion of Africa’s ivory and hides, the price of ivory, hides and meat may fall. This will be modelled by an isoelastic demand function.

( 6)

pc (C(t )) = C(t ) . −

If the price flexibility,− , is zero, the price will be constant and equal to the scale parameter, = C. . Otherwise, the price will decline with increased culling, as shown in Figure 2.

6

Figure 2: Demand Curve for Ivory, Hides and Meat.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

Agricultural production will be a simple linear function of the stock of elephants.

(7)

A(S (t ))= u − vS (t ).

In the absence of elephants, agricultural production would be at its maximum, u. Each elephant decreases production by the competition coefficient between elephants and agriculture, v. To consider only the damage caused by elephants, maximum production can be set to zero as shown in Figure 3.

7

Figure 3: Damage to Agricultural Production.

The effort expended in culling and hunting will be derived from Cobb-Douglas production functions. 1

(8)

 C(t ) X (S (t ), C(t )) =   S (t )

(9)

 H (t )  a  . Y (S (t ), H (t ))=   cS t b   () 

  .   1

For example, the Cobb-Douglas function for culling, as an output produced by the two inputs of 1 1  X  effort and stocks, is C=  S Sß, where Sis the catchability coefficient,  is the effort elasticity and ß is the stock elasticity. Inverting this production function gives the effort function in equation (8). Effort will increase with culling and decrease with stock. To ensure this, the elasticities

1

and ß

should be greater than zero. As explained later, these elasticities proved impossible to estimate and are assumed to be one, giving the effort function for culling shown in Figure 4.

Figure 4: Effort Function for Culling.

The effort function for hunting in equation (9) is similar. An optimal management strategy for elephants chooses culling and hunting in every year to maximise the net present value in equation (5) subject to the change in stock in equation (4). Alternatively, the conditions for optimal management can be derived from the Hamiltonian which can be interpreted as a dynamic profit function.

(10)

(t ) = (1+1 ) [pc (C(t ))C(t ) + ph H (t ) + pa A(S (t ))+ ps S (t ) t

+

[

]

− p x X (S (t ),C(t ))− p y Y (S (t ), H (t ))

(t + 1) 05. fr S (t )

e

− S (t )

S (t )− me

S (t )

S (t )

− C (t )− H (t )]; t = 0,K ,∞ .

Discounted dynamic profits, (t), equal discounted annual profits minus total user costs. Annual profits are the revenues from culling, hunting, agricultural production and amenity and existence values minus the costs of culling and hunting effort. Total user costs are the costs of using elephants now rather than saving them for the future. They are similar to other costs in which a price is + (t+1), which is the multiplied by a quantity. In this case, the “price” is the marginal user cost,

8

value of an elephant in the wild before it is culled or hunted. The “quantity” is the net quantity of elephants used, in other words, recruitment minus natural mortality, culling and hunting. Typically, elephants are more valuable for culling, hunting, and amenity and existence than they are pests to agriculture. The marginal user cost will be positive. If the population of elephants is decreasing, total user costs will be negative, as the costs of depreciating the stocks. Conversely, if


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

the population of elephants is increasing, total user costs will be positive, as the benefits of investing in the stocks. The first-order conditions for optimal culling and hunting are found by differentiating dynamic profit.

(11)

(t ) = 0 = C(t )

(1+1 )  pc (C(t ))− px

(t ) = 0 = H (t )

(1+1 )  ph − p y

t



t



X (⋅)  − C(t )

Y (⋅)  − H (t )

(t + 1);

(t + 1);

t = 0,K, ∞.

Under the assumption of no market power, the first order conditions equate output prices with marginal costs. Because the model is dynamic, there are two types of marginal costs: the marginal effort costs and the marginal user cost. Marginal effort costs are for labor, ammunition, vehicles and fuel as inputs needed to harvest elephants. The marginal user cost is for elephants in the wild as an input. Suppose people have open access to elephants and exploit them to make as much money as possible today with no regard for the future. People would maximise annual profits instead of dynamic profits by setting the marginal user cost to zero. This is a complete market failure. Or suppose people have property rights which are imperfect. They will set the marginal user cost above zero but still too low. This is an incomplete market failure. Finally, suppose people have perfect property rights. The marginal user cost will be as high as possible, reflecting the full value of an elephant in the wild, and elephants will be optimally managed. Unlike other prices, the marginal user cost cannot be observed in a marketplace. Therefore, a major purpose of a bioeconomic model is to calculate the marginal user cost and determine whether there is market failure. If so, policies can be designed to ensure that the value of an elephant in the wild is included in people’s culling and hunting decisions.

The Age Structured Model For elephants, recruitment, natural mortality and hunting are age-specific. Although the actual model to be solved later has 61 age groups, only 3 age groups are sufficient to discuss the life cycle of elephants. The number of new born elephants is the number recruited. Natural mortality, culling and hunting will be accounted for later by considering the number of new born elephants which survive to one year of age. (12)

− S (t )+ S1(t )+ S2 (t )) S 0 (t + 1) = 05 . fr [S 0 (t ) + S1 (t ) + S 2 (t )] e ( 0 [S1 (t ) + S 2 (t )];

t = 0,K , ∞. S 0 (0) = S 0 .

9

Subscripts on stocks denote age groups, with S0(t), S 1(t) and S 2(t) being new born, one year old and two year old elephants, respectively. In this equation, only the female elephants which are one or two years old can reproduce but the environmental interaction term depends on the total elephants of all ages. The number of one year old elephants next year is the number of new born elephants this year, minus the number that died from natural causes, and minus the number that were culled. There is culling but no hunting of new born elephants.

(13)

S ( t) + S1( t) + S2( t)) S1(t + 1) − S 0(t) = − m0 e ( 0 [S 0(t) − C0(t)]

S1 (0) = S 1.

− C0 (t ); t = 0,K, ∞.

The intrinsic mortality rate for the new born elephants is m0. Multiplying the intrinsic mortality rate by the environmental interaction term gives the rate at which elephants die naturally before reaching the age of one. Some elephants are culled instead. Subtracting the number of new born elephants that are culled, C0(t), from the total number of new born elephants, S0(t), gives the number of new born elephants that are susceptible to natural mortality. Similarly the number of elephants surviving to become two years old next year is the number of elephants which were one year old this year, minus natural mortality and minus the number harvested by culling and hunting.

(14)

S t +S t +S t S 2 (t + 1) − S1 (t ) = − m1e ( 0 ( ) 1( ) 2 ( ))[S1 (t ) − C1 (t ) − H1 (t )]

S 2 (0) = S 2 .

− C1 (t ) − H1 (t );

t = 0,K, ∞.

The intrinsic mortality rate for the one year olds is m1, and the number of one year old elephants susceptible to natural mortality is the number left after culling and hunting. Some elephants may live to be 60 years old but, to simplify the presentation of the model, elephants are assumed to die before they reach the age of three. The mortality rate of two year olds equals one. S (t )+ S1(t )+ S2 (t )) m2 e ( 0 = 1.

This mortality rate is substituted into the equation for the number surviving to be three years old.

10

S () t + S1 () t + S2 () t ) S 3 (t + 1) − S 2 (t ) = − m2 e ( 0 [S 2 (t ) − C2 (t ) − H 2 (t )]

− C2 (t ) − H 2 (t ).

Simplifying shows that the number of three year olds must equal zero. S 3 (t + 1) = 0.

The manager has the option of letting the elephants die naturally and collecting the ivory, or culling and hunting them. The only restriction is that culling and hunting cannot exceed the available stock.


A R E

(15)

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

S 2 (t ) ≥ C2 (t ) + H 2 (t ); t = 0,K, ∞.

Culling is not specific to each age group. Instead, culling of age groups, C0(t), C1(t) and C2(t) in equations (13), (14) and (15), are fractions of the total culling, C(t). To calculate the fractions, total culling is multiplied by the proportions of each age group within the total population. Similarly, hunting of the mature age groups, H1(t) and H2(t) in equations (14) and (15), are fractions of total hunting, H(t).

(16)

C0 (t ) =

S 0 (t )

S 0 (t ) + S1 (t ) + S 2 (t )

C(t );

S1 (t ) C(t ); S 0 (t ) + S1 (t ) + S 2 (t )

C1 (t ) = C2 (t ) = H1 (t ) = H 2 (t ) =

S 2 (t )

S 0 (t ) + S1 (t ) + S 2 (t ) S1 (t )

S1 (t ) + S 2 (t ) S 2 (t )

S1 (t ) + S 2 (t )

11

C(t );

H (t ); H (t ); t = 0,K, ∞.

In summary, equations (12) through (16) account for the lag before elephants reach sexual maturity, different natural mortality rates among age groups, indiscriminate culling across all age groups and discriminate hunting of mature animals only. The net present value for the age structured model is similar to that for the biomass model. ∞

(17)

J (S 0 (0 ), S1 (0 ), S 2 (0 ))= max ∑

( )t [pc (C (t ))C (t )+ ph H (t )

1 C , H t = 0 1+

+ pa A (S 0 (t )+ S1 (t )+ S 2 (t ))+ ps [S 0 (t )+ S1 (t )+ S 2 (t )]

]

− p x X (S 0 (t )+ S1 (t )+ S 2 (t ), C (t ))− p y Y (S1 (t )+ S 2 (t ), H (t )).

The revenue from culling and hunting are the same as before and the revenue from agriculture, the amenity and existence values and the total cost of culling all depend upon the total stock of elephants. Only the cost of hunting is age-specific, depending upon the number of elephants in the older age groups. An optimal management strategy chooses culling and hunting to maximise the net present value in equation (17), subject to constraints for age groups in equations (12) through (16). In each year, the dynamic profit function has total user costs for different age groups.

(18)

(t ) = (1+1

)t [pc (C(t ))C(t ) + ph H (t )

+ pa A(S 0 (t ) + S1 (t ) + S 2 (t ))+ p s [S 0 (t ) + S1 (t ) + S 2 (t )]

]

− p x X (S 0 (t ) + S1 (t ) + S 2 (t ), C(t ))− p y Y (S1 (t ) + S 2 (t ), H ) +

0

+

1

+

2

+

3

(t + 1)05. fr

[S 0 (t ) + S1 (t ) + S 2 (t )] e − (S0 (t )+S1(t )+S2 (t ))[S1 (t ) + S 2 (t )]

(t + 1)− m0 e (S0 (t )+ S1(t )+ S2 (t ))[S 0 (t ) − C0 (t )]− C0 (t ) (t + 1)− m1e (S0 (t )+ S1(t )+ S2 (t ))[S1 (t ) − C1 (t ) − H1 (t )]− C1 (t ) − H1 (t )

(t + 1)[S 2 (t ) − C2 (t ) − H 2 (t )];

t = 0,K, ∞.

The marginal user costs for age groups are + 0(t+1),+ 1 (t+1) and+ 2 (t+1). To calculate total user costs, these marginal user costs are multiplied by the net changes in the stocks of age groups from the right hand sides of equations (12), (13) and (14). In addition, the inequality constraint on culling and hunting of two year old elephants in equation (15) is multiplied by its shadow + 3(t+1). As before, the first order conditions for optimal culling and hunting are derived by price, differentiating dynamic profit.

(19)

(t ) = 0 = (1+1 C(t )



)t  pc (C(t ))− px 

X (⋅)   C(t )

(t + 1)1 − m0 e (S0 (t )+ S1(t )+ S2 (t ))

−

1

−

2

−

3

S 0 (t ) S 0 (t ) + S1 (t ) + S 2 (t )

S1 (t )  S 0 (t ) + S1 (t ) + S 2 (t )

(t + 1)1 − m1e (S0 (t )+ S1(t )+ S2 (t )) 

(t + 1)

(t ) = 0 = (1+1 H (t ) −

2

−

3

S 2 (t ) ; S 0 (t ) + S1 (t ) + S 2 (t )



)t  ph − p y 

Y (⋅)   H (t )

(t + 1)1 − m1e (S0 (t )+ S1(t )+ S2 (t )) (t + 1)

S1 (t ) S1 (t ) + S 2 (t )

S 2 (t ) ; t = 0,K, ∞. S1 (t ) + S 2 (t )

These first-order conditions include a weighted average of marginal user costs across age groups. Open access would drive these marginal costs to zero and policies should be designed to ensure that the full values for elephants of all ages are included in peoples’ culling and hunting decisions.

Calibrating the Models The population dynamics and objective functions of the models are calibrated from published research and primary data.

Population Dynamics Ideally, the population dynamics would be estimated statistically. Data for elephant stocks, the quantities culled and hunted (Price Waterhouse, 1996) and the effort expended in culling and hunting (DNPWLM, undated) are available for 1980 through 1995 and, in principle, the estimation method of Hertzler, Harman and Lindner (1997) could be applied. Unfortunately, the data show

12

a very rapid and unpredictable increase in elephant stocks beginning in 1989, probably due to migration into Zimbabwe from other countries. Attempts at statistical estimation gave unrealistically high rates of recruitment. Instead, the population dynamics were calibrated to give biologically reasonable predictions.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

Recruitment depends on the calving interval defined as the number of years between live births for females. In Zimbabwe, calving intervals of 5 years (Chizarira), 4.3 years (Hwange), 4.1 years (Gona ReZhou), 4.0 years (Chirisa) and 3.4 years (Mana Pools) have been reported (Craig, 1989). These data are consistent with calving intervals of 4.6 years and 8.6 years reported for Murchison Falls and Bunyoro populations in Uganda (Laws, Parker and Johnstone, 1975). The shortest calving interval reported for the Uganda elephant population was 2.75 years while the longest was 9.1 years (Laws, 1969). Gestation in elephants is 22 months (Buss and Smith, 1966) and a calving interval of 2.75 years, or 33 months, still allows an effective nursing period of 11 months before the next calf is born. This places an upper bound on the rate of recruitment of 1/2.75 or 0.36 calves per year under ideal conditions. Calf mortality rates of 20%, 15%, 10%, 10% and 5% per year were reported for the new born, the one year old, two year old, three year old and four year old calves respectively in the Uganda elephant population (Laws, Parker and Johnstone, 1975). Adult mortality rates were an average of 5% per year. These mortality rates are much higher than recruitment rates and are not sustainable. Other studies place adult mortality at 2 to 3% (Corfield, 1973; Douglas-Hamilton, 1972). Ages at which female elephants become sexually mature can vary. Ages ranging from 11 to 19 years have been reported for different populations (Laws, 1966). Craig (1989) reported that observations based on known-age populations had shown the age at sexual maturity to be between 9 and 10 years. This is consistent with observations for populations in East Africa (Laws and Parker, 1968; Laws, 1969). Adding two years for gestation gives the age at first calving of around 12 years. The age at which female elephants reach menopause is not known, but is probably around 55 years of age. The maximum lifespan of an elephant was estimated by Laws (1966) to be about 60 years. Craig (1989) estimated the maximum lifespan to be about 50 years. However, Craig’s estimate is not based on any actual observation, but on conservative deductions on the study by Laws. In Zimbabwe, the Department of National Parks and Wild Life Management (DNPWLM) estimate the carrying capacity of the country to be 35,000 elephants (personal communication). This refers to the maximum number of elephants that can be maintained without affecting the habitat for other species. The 1995 elephant population estimate for Zimbabwe is 63,780 and the population of elephants has been increasing (Booth, 1989, Price-Waterhouse, 1996). The stock of elephants that can be sustained is probably much higher than 35,000, if damage to the habitat is not considered. Large stocks will decrease recruitment and increase natural mortality through the environmental interaction terms of the model.

13

Table 1: Parameters for the Population Dynamics of the Biomass Model.

Parameter

Description

Value

Recruitment f

proportion of fertile animals 0.5

r

intrinsic recruitment rate

S ( environmental interaction

interaction ) Se( environmental environmental interaction

0.36 0.004796 0.5483 0.00002127

Mortality m

me

intrinsic mortality rate

S environmental interaction

0.03210 0.000005580

Parameters for the population dynamics of the biomass model are summarised in Table 1. The proportion of fertile animals in the population was inferred from simulation experiments with the age-structured model which showed that half the population is between the ages of sexual maturity and menopause. The intrinsic recruitment rate was set at 0.36 elephants per year and the natural mortality rate was set at 3.2%. The environmental interaction parameters were varied to adjust the carrying capacity of the habitat, the minimum viable population and the maximum sustainable yield. As shown previously in Figure 1, the carrying capacity of the habitat is set at 66,172 elephants, a bit larger than the 63,780 elephants in Zimbabwe in 1995. The minimum viable population is set at 3,000 elephants. The maximum sustainable yield at the highest point on the surplus yield curve is set at 863 elephants per year. The recruitment, mortality and environmental interaction parameters were chosen to predict elephant stocks during the 1980s, as shown in Figure 5. No reasonable combination of parameters was able to predict elephant stocks after 1989.

14

Figure 5: Actual and Predicted Stocks for the Biomass Model.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

Parameters for the population dynamics of the age structured model are summarised in Table 2. The intrinsic recruitment rate and the environmental interaction parameters are the same as in Table 1. However, the proportion of fertile animals is set to 1 because only animals between the age of first calving and menopause enter the recruitment relationship in the age structured model. Intrinsic mortality rates decline from 8% for new born elephants to 2.62% for elephants 5 years old and older. Table 2 also lists important ages in the life cycle of elephants. Table 2: Parameters for the Population Dynamics of the Age Structured Model.

Parameter

Description

Value

year of sexual maturity

10

year of first calving

12

year reaching trophy size

41

year of menopause

56

years of lifespan

60

Ages

Recruitment f

proportion of fertile animals 1

r

intrinsic recruitment rate

S ( environmental interaction

) Se( environmental interaction environmental interaction

0.36 0.004796 0.5483 0.00002127

Mortality m0


0.08

m1


0.07

m2


0.06

m3


0.04

m4


0.03

m5 through m60


0.02620

me

S environmental interaction

0.000005580

15

In Figure 5, the biomass model began with initial stocks of 46,426 elephants in 1980. The age structured model requires 61 initial stocks for age groups from 0 to 60 years old. This age distribution is unknown. It was estimated using the age structured model by simulating until elephant stocks reached a steady state at the carrying capacity of the habitat. Then the age distribution from this steady state was used allocate the 46,426 elephants into age groups. Figure 6 shows the predicted stock of elephants and their age distribution.

Figure 6: Actual and Predicted Stocks for the Age Structured Model.

As did the biomass model, the age structured model predicts the decline in stocks beginning in 1980 but not the rapid and erratic increases in stocks beginning in 1989. Predicted stocks are broken down into age groups. The lowest line in the figure represents the number of new born elephants less than 1 year old. The next line up represents all elephants less than two years old. Continuing this process, the top line represents all elephants less than 60 years old which is the total stock of elephants. The distances between lines represent the elephants in each age group. There are many elephants in the younger age groups and, as not all of them survive, fewer elephants in older age groups.

Objective Function Parameters are the same for the objective functions of both the biomass and age structured models. These are summarised in Table 3. Prices are reported in US dollars using an exchange rate of 10 Zimbabwe dollars to 1 US dollar. Social discount rates are thought to range from 8% to 12% for

16

developing countries. The behaviour of Zimbabwe in managing its elephants suggests a patience which may be inconsistent with such high discount rates. As a baseline, 5% will be used but results will be obtained for social discount rates up to 15%. Due to the CITES ban on trade, the demand for culled elephants is difficult to determine. Ivory and hides can still be traded among countries in the Southern Africa Convention for Wildlife


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

Management (SACWM) which took reservations to the CITES listing of the African elephant. The value of the ivory among these countries is negligible. The expected yield of hide from a culled elephant is 80 kilograms and the approximate export price for good quality chrome crust hide in 1989 was $US12.35 per kilogram, giving a price per hide of $US988 (Dawe and Hutton, 1994). It is probable that a hide from a culled elephant would still fetch about $US988 within SACWM and the carcass could be worth about $US200 for meat. Therefore, an estimate for the price of a culled elephant would be the price of the hide plus that of the carcass, or $US1,188. The scale and flexibility parameters for the demand for culled elephants were calibrated to give a price of $US1,188 at a culling of 256 elephants per year as shown previously in Figure 2. The scale parameter will be increased to simulate the possibility of renewed trade in ivory. Table 3: Parameters for the Objective Functions of the Biomass and Age Structured Models.

Parameter

Description

Value

Prices social discount rate C scale parameter for culling price flexibility for culling − . ph price for trophy hunting pa gross margin for agriculture ps amenity or existence value px price of culling effort py price of hunting effort Agric. Yield u maximum yield v competition coefficient Culling Effort 1  elasticity on culling effort  S elasticity on stock ß catchability coefficient Hunting Effort a elasticity on hunting effort b elasticity on stock c catchability coefficient 1+

0.05 2,068 0.1 21,584 12.78 0 7,136 5,290 0 0.7 1 1 0.005488 1 1 0.0002240

The price of hunting is estimated from the charges for an elephant hunting safari. Fergusson (1994) reported that an elephant hunt took an average of 10.9 days. Hunts are marketed as 21 day safaris by the Zimbabwe Association of Tourism and Safari Operators (ZATSO). Therefore each safari will shoot at least one elephant, but probably no more than one. The average price for a trophy elephant in 1993 was $US7,724 (DNPWLM, undated). In addition, an average daily rate for an elephant hunt of $US660 is charged, giving a price for a 21 day safari of US$21,584. This is somewhat less than the estimate of Clarke et al. (1986).

17

The price for agricultural production is the gross margin per livestock unit. The gross margin per livestock unit was calculated from results by Jansen, Bond and Child (1993), who reported a weighted average return from cattle enterprises of $US0.83 per hectare per year. The number of cattle was calculated from the stocking rates and average herd size, giving an average gross margin of $US12.78 per livestock unit. The amenity value of elephants could not be estimated from the data. Viewing by tourists is difficult to divide among species because tourists visit National Parks to see, not just elephants, but the diversity of wildlife. In addition, people may be willing to pay for the option of viewing elephants in the future and for ensuring their existence. Although, the price of amenity and existence is set to zero in Table 3, it is surely much greater than zero. For example, Brown and Henry (cited in Barbier et al., p. 18, 1990) estimated the value of viewing elephants in Kenya to be $US25 million per year. Rather than estimate people’s willingness to pay, sensitivity analysis will be used to determine the minimum amount people could pay to local communities in Zimbabwe to preserve elephants. The price of effort for culling comprises the cost of labour, ammunition, vehicles, an aircraft and fuel. Culling may be performed by government workers whose wages are guaranteed regardless of the nature of the activity to which their effort is directed. Therefore, the opportunity cost of the labour used in culling is assumed to be zero. There are no data on the other costs of culling operations. Instead the cost used in this study was estimated from unpublished data on 1996 budgeted costs for a plains game hunt obtained from ZATSO (personal communication). The total expenses for the hunt, excluding trophy expenses, marketing and management, food and drinks, camp hire and labour, are $US7,136 per year. If property rights to elephants are poorly established, culling may also be done by poachers for which no costs are available. To test the sensitivity to costs, results will be obtained for prices of effort up to $US15,000. The cost of effort for hunting was also estimated using the data from ZATSO. The cost for elephant safaris is assumed to be the same as a plains game hunt. The costs per day, excluding trophy expenses, were multiplied by 21 days to give the costs per safari of $US5,290. Rather than consider total benefits from agriculture, the maximum yield for agriculture is set to zero so the model will calculate just the damage caused by elephants. The competition coefficient is the number of cattle displaced or the crop yields damaged by an elephant. In Zimbabwe, elephants live in natural farming regions which are more suitable for cattle and wildlife (Jansen, Bond and Child, 1993). Laws (1981) reported that, in grasslands and woodlands, 80% to 90% of the elephant’s stomach fill was grass. This figure suggests that there is considerable competition between elephants and cattle. In other areas, 60% of stomach fill was herbaceous material and

18

40% was woody material. There is no data on how often elephants encroach onto cattle range in Zimbabwe. However, Laws, Parker and Johnstone (1975) reported numerous observations of elephants leaving the sanctuary of Uganda National Parks at dusk to feed in adjacent country or in farmers’ holdings. Even if elephants are in their own range for the day, they probably encroach onto livestock range for most of the night. It is assumed that 10% of the elephants encroach onto cattle range at any one time. Based on calculations using body mass, an elephant consumes 7


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

times more forage than a cow and calf as a livestock unit. Thus the competition coefficient, as the number of livestock units displaced per elephant, equals 7 multiplied by 10%, or 0.7. Ideally, the catchability coefficients and elasticities for culling and hunting should be estimated statistically but the available data are insufficient. It was assumed that the elasticities are equal to one as in the Schaefer model of fisheries economics. The catchability coefficient for culling was calculated as the proportion of elephants stocks culled in a year. In a typical year prior to 1989, 350 elephants were culled. Out of a stock of 63,780 elephants, the proportion caught is 350/ 63,780, or 0.005488. The catchability coefficient for hunting is the proportion of trophy animals shot per safari. Each safari will shoot at least one elephant, but probably no more than one. Simulations of the age structured model give an estimate of 4,465 trophy elephants out of the total population. Therefore, the catchability coefficient for hunting is 1/4,465, or 0.0002240.

Solution Procedure The bioeconomic models are implemented in MicroSoft Excel and copies are available from the authors. The models can be used both for simulation and optimisation. Optimisation is by the GRG2 solver which has a reduced gradient algorithm for non-linear objective functions and a Newton-Raphson method for non-linear constraints. This solver was originally developed for the GINO mathematical programming package (Liebman et al., 1986) and is now incorporated into microcomputer spreadsheet software. The standard solver in Excel is not big enough to solve the age structured model, however, and the Premium Solver from Frontline Systems, Inc. (1996) is used instead.

Results Some countries, Kenya is one example, have failed to enforce the state’s rights to the elephants. Even with elephants listed in Appendix I of CITES there will be open access. In Zimbabwe, local communities have property rights to elephants through the CAMPFIRE program. These property rights are not perfect (Muir and Bojö, 1994; IIED, 1994) but at least open access is eliminated. To approximate the different situations in Kenya and Zimbabwe, we solve the biomass and age structured models for both open access and optimal management.

Biomass Model With open access, farmers and poachers maximise annual profits instead of dynamic profits and ignore the user costs of elephants in the wild. Figure 7 shows the stocks of elephants, culling and hunting over time as predicted by the biomass model.

19

Figure 7: Biomass Model with Open Access.

Because the biomass model cannot predict how many trophy animals are in the population, hunting is restricted to be less than or equal to 350 elephants per year. The model predicts that massive culling will drive the stock of elephants from 63,780 to below the minimum viable population of 3,000 elephants by year 5. The elephants are “mined” generating a net present value of $US69 million. This describes the situation in Kenya which had approximately 65,000 elephants in 1981 and only 16,000 elephants in 1989 (Barbier et al., 1990, Table 1.1). Many parameters in the model are imprecise. The baseline parameters in Tables 1 and 3 can be varied to gauge the sensitivity of the open access solution. Table 5 shows the year when stocks are driven below the minimum viable population and the net present value (NPV) for selected scenarios. Table 5: Biomass Model with Open Access.

20

Scenario Minimum Viable Population

NPV

(year)

($US million)

Open Access (baseline) No Appendix I ( C =4,680)

5

69

2

104

No hunting (ph=0)

3

34

No damage to agriculture (pa=0)

5

70

Amenity (ps=200)

5

90

Higher cost of culling (px=15,000)

8

78

Kenya was a key supporter for listing elephants in Appendix I of CITES. Suppose, however, that elephants had not been listed and the price for culling was higher. The ivory from older aged elephants could be worth about $US4,200, assuming 10 kilograms of ivory per elephant estimated to sell for $US420 per kilogram (Barbier et al., 1990, pp. 4-5). The ivory from middle aged elephants


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

could be worth about $US2,100, assuming 5 kilograms per elephant. The ivory from juvenile elephants is worth nothing. From simulations of the age structured model, there are approximately 11% older aged and 49% middle aged elephants. With these assumptions, a weighted average value of ivory from culled elephants would be about $US1,500 per elephant. This scenario can be modelled by increasing the scale parameter for culling from 2,068 to 4,680 which increases the price for culling by $US1,500 to $US2,688 per elephant at a culling of 256 elephants per year. With the higher price for culling, elephants are still exterminated but the wealth generated by elephants increases by $US35 million to $US104 million. Kenya also banned trophy hunting of elephants, although this ban may soon be reversed (Baskin, 1994). Banning of trophy hunting is modelled by setting the price of hunting to zero. The ban cannot save the elephants. It simply reduces wealth of the country by another $US35 million. Kenya was reported to receive $US143 million in donations (Satchell, 1993). Perhaps, this explains its support for the listing of elephants in Appendix I of CITES and its ban on hunting which together reduced the country’s wealth by only $US70 million. If elephants were not pests to agriculture, the price for damage to agriculture would be zero but it would make little difference. Elephants would still be driven to extinction and the wealth of the country would only be $US1 million larger. Since the economy of Kenya depends upon tourism, elephants might be credited for their contribution to the tourist industry. To model this, the price for amenity and existence value was set to $US200 per elephant. This value is unknown and chosen somewhat arbitrarily. With this value, results for the age structured model to follow show that elephants will be optimally managed near the carrying capacity of the habitat, even in the worst case scenario. This amenity and existence value contributes $US21 million to the economy of Kenya before the elephants are driven to extinction. Efforts to enforce the state’s rights to elephants would increase the costs to poachers of shooting elephants. This could be modelled by more than doubling the price of effort for culling to $US15,000. Elephants are exterminated in 8 years instead of 5 and wealth increases by $US9 million. Enforcement is not free, however. It could easily cost the government $US9 million to enforce its property rights (Sugg and Kreuter, 1994, pp. 42-43) and the wealth of the country would be unchanged. If property rights work perfectly, local communities will maximise dynamic profits and capture the full user costs of elephants. Elephants will be optimally managed. The biomass model predicts that stocks will be dramatically culled but still be sustained above the minimum viable population, as shown in Figure 8.

21

Figure 8: Biomass Model with Optimal Management.

Eventually the stocks approach a steady state of 18,207 elephants with culling of 159 elephants and hunting of 350 elephants per year. The net present value of optimally managed elephants is $US184 million which is $US115 million higher than with open access. Demand and supply in the steady state are shown in Figure 9. The demand curve is the same as in Figure 1. The steady state supply curve increases until quantities of culling and hunting reach the maximum sustainable yield of 863 elephants per year. Then the supply curve bends backward, increasing further as quantities decrease. Its shape is determined by the shape of the surplus yield curve in Figure 1.

22


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

23

Figure 9: Steady State Supply.

In the steady state, optimal culling and hunting total 509 elephants per year. At a culling of 159 elephants per year, the price of a culled elephant is $US1,246 and the marginal effort cost of culling is only $US97. The difference between the price and the marginal effort cost is the marginal user cost of $US1,149 per elephant, which is the value of an elephant in the wild. Thus, the marginal effort cost contributes 8% and the marginal user cost contributes 92% of the final sale price of a culled elephant. The baseline parameters in Tables 1 and 3 are varied to gauge the sensitivity of the optimal management solution. Table 6 shows the stocks of elephants in the steady state and the net present value (NPV) for the baseline parameters and several scenarios. Table 6: Biomass Model with Optimal Management.

Scenario

Steady State Stocks

NPV

(head)

($US million)

18,207

184

15,217

235

Optimal Management (baseline) No Appendix I ( C=4,680) No hunting (ph=0)

3,013

43


20,875

189

Amenity (ps=200)

59,703

403


18,948

182

Higher surplus yield (MSY=1,487)

24,544

194

Higher discount rate1+( =0.10) and No Appendix I ( C=4,680)

14,163

111

3,025

158

28,450

227

and Amenity (ps=200)

According to the biomass model, if elephants had not been listed in Appendix I of CITES, a viable population would still be sustained and Zimbabwe would be about $US51 million wealthier. By agreement with other southern African countries, this added wealth would have been used for wildlife management (SACIM, 1994). Animal rights groups argue that elephants should not be treated as a resource but be preserved without exploitation. In addition to a ban on trade in ivory, they would prefer an international ban on the importation of trophy animals. This would set the price of hunting to zero. Unfortunately, elephants still have value for hides and meat and are pests to agriculture. With no trophy hunting, elephant stocks would be reduced to a steady state of 3,013 elephants after 40 years. An international ban on the import of trophies would jeopardise the survival of elephants and reduce the wealth of Zimbabwe by $US141 million. The model assumes a fixed carrying capacity of the habitat with competition between elephants and humans modelled as damage to agriculture. If elephants did not damage agriculture, there would be little change in optimal management. The damage reduces the wealth of Zimbabwe by only $US5 million and is a minor factor in explaining the decline in elephant populations. This result must be qualified, however. In the past, a major reason for the decline in elephant populations has been the reduction in habitat from the increase in agriculture (WWF, 1997). On the other hand, elephants increase their own habitat and the habitat of other grazing animals by changing woodlands into grasslands. In a more complete model with a variable carrying capacity, it may be optimal to establish more agriculture and reduce the habitat for elephants, or it may be optimal to increase the habitat for elephants because they are more profitable than livestock (Jansen, Bond and Child, 1992). In Zimbabwe, revenues from tourism are distributed to local communities (Muir and Bojö; 1994, IIED, 1994) who make the life or death decisions for elephants. If elephants have an amenity and existence value of $US200 per elephant, stocks will be sustained just below the carrying capacity of the habitat, providing the money actually reaches the local communities. This would increase the wealth of the Zimbabwe by about $US219 million. Zimbabwe must also enforce property rights to elephants by discouraging poachers. Enforcement costs might be added to the price of culling, increasing it to, for example, $US15,000 per culling. The higher price has a negligible effect on optimal management and reduces wealth by only $US2 million because elephants are still extremely cheap to manage. The maximum sustainable yield (MSY) is determined by the environmental interaction parameters in Table 1. Because the parameters could not be estimated, a conservative estimate of 863 elephants

24

per year is used. Increasing the MSY to 1,487 elephants per year, while holding the carrying capacity of the habitat and the minimum viable population constant, increased the steady state stock by 6,337 elephants and the wealth of Zimbabwe by $US10 million but does not change the basic conclusions from the model.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

The social rate of discount is set to 5% in the baseline which may be low for developing countries. Doubling the discount rate to 10% reduces the steady state stock of elephants by 4,044 elephants, but does not drive them toward extinction. The net present value is significantly reduced but is not comparable with other net present values in Table 6 because the future is discounted much more. Suppose the discount rate is 10% and there was no listing of elephants in Appendix I. The stocks of elephants would slowly be reduced to around the minimum viable population by year 50. With a discount rate of 10% and no listing, adding an amenity and existence value of $US200 would help sustain the stock of elephants well above the minimum viable population.

Age Structured Model The open access solutions from the biomass model are consistent with decisions in a country such as Kenya where elephant stocks plummeted from 65,000 to 16,000 between 1981 and 1989 (Barbier et al., p. 2). However, the optimal management solutions are not consistent with decisions in a country such as Zimbabwe where stocks have been sustained above 60,000 elephants, near the carrying capacity of the habitat. Solutions to the age structured model may be consistent because the additional rate of return to letting young animals grow older and more valuable will increase the optimal stocks of elephants. Figure 10 shows the open access solution for the age structured model. For ease of presentation, the age groups for elephants are aggregated into juveniles from 0 to 9 years, middle aged from 10 to 39 years and old aged from 40 to 50 years. Juveniles have not yet reached sexual maturity. Middle aged and many of the old aged elephants are fertile. Only old aged elephants are can be hunted as trophy animals.

Figure 10: Age Structured Model with Open Access.

As with open access in the biomass model, massive culling drives the stocks below the minimum viable population in 4 years. Unlike in the biomass model, however, hunting is not restricted to 350 elephants but is chosen from the old aged stocks, allowing more hunting in early years and giving a higher net present value (NPV) of $US106 million.

25

Table 7 shows the same scenarios for the age structured model as for the biomass model in Table 5. Table 7: Age Structured Model with Open Access.

Scenario

Minimum Viable

NPV

Population (year)

($US million)

Open Access (baseline) No Appendix I ( C=4,680)

4

106

2

89

No hunting (ph=0)

3

35


4

108

Amenity (ps=200)

4

136


6

102

The wealth generated by elephants in a country such as Kenya with open access and a ban on hunting is predicted to be almost the same by the two models. Curiously, if elephants had not been listed in Appendix I, the wealth of the country would be less. Listing in Appendix I reduces the incentive for poaching and allows more hunting which is more profitable. The best strategy for a country such as Kenya would be to allow hunting, but lobby for the ban on international trade by listing elephants in Appendix I. Unfortunately, the elephants are exterminated, regardless, because there are no property rights. Figure 11 shows that it is optimal for a country with established property rights, such as Zimbabwe, to conserve its elephants near the carrying capacity of the habitat.

26


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

27

Figure 11: Age Structured Model with Optimal Management.

The old aged elephants are hunted but there is no culling. Rather, juvenile and middle aged elephants are left to grow into old age. In the steady state, 494 elephants are hunted per year and stocks are 59,826 elephants. Optimal management generates a net present value of $US201 million. Table 8 contains the steady state stocks and net present values (NPV) for the same scenarios as in Table 6 for the biomass model. The age structured model predicts that a ban on hunting would exterminate the elephants in 16 years. For most other scenarios, the model predicts that stocks should be sustained just below the carrying capacity. Table 8: Age Structured Model with Optimal Management.

Scenario

Steady State

NPV

Stocks (head)

($US million)

Optimal Management (baseline)

59,826

201

No Appendix I ( C =4,680)

42,437

201

0

43


59,840

212

Amenity (ps=200)

60,083

449


59,824

201

Higher surplus yield (MSY=1,487)

61,946

208

Higher discount rate1(+ =0.10) and No Appendix I ( C=4,680)

59,204

140

0

165

59,110

270

No hunting (ph=0)

and Amenity (ps=200)

A major argument against listing elephants in Appendix I was that countries which managed elephants wisely would be unduly penalised by the ban on trade. The age structured model suggests that a ban on trade has had negligible effect on the wealth of Zimbabwe because trophy

hunting is more profitable than culling for ivory, even without a ban. This result does not consider the stockpile of ivory collected from past culls, problem animal control and natural deaths. In June of 1997, the parties to CITES approved limited export of ivory under strict quotas from Zimbabwe, Botswana and Namibia to Japan (CITES, 1997). Limited trade may allow these countries to sell their stockpiles and gain the funds needed for wildlife management (SACIM, 1994). These results change, however, if the social discount rate is higher than 5%. First suppose the rate is 10%. With a ban on trade in ivory, elephant stocks are sustained near the carrying capacity. With free trade in ivory, stocks are culled below the minimum viable population in 16 years. Next suppose the rate is 15%. Although not shown in the table, even with a ban on trade, stocks are culled below the minimum viable population in 11 years. Therefore listing elephants in Appendix I is ineffective at both lower and higher discount rates. The ban on international trade has played a role in saving elephants only if the social discount rate of Zimbabwe is around 10%. This result must also be qualified, however. If the amenity and existence value is $US200 per elephant, elephants are sustained near the carrying capacity even with a social discount rate of 10% and free trade in ivory. For the 59,110 elephants in the steady state, $US200 per elephant is $US11,822,00 per year. This is less than half the estimate of Brown and Henry (cited in Barbier et al., p. 18, 1990) for the contribution of elephants to tourism in Kenya. Tourism is only one aspect of amenity and existence values and $US200 is surely a very low estimate.

28


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

CONCLUDING REMARKS Are African elephants an endangered species? No. Did the listing of African elephants in Appendix I of CITES, which banned international trade in ivory, help save the elephants? No. The true campaign to save elephants began in the village of Nyaminyami in north western Zimbabwe. Villagers were granted authority to manage wildlife in their district as part of the CAMPFIRE program (Bonner, 1993, p. 253). With property rights, local communities collect a significant portion of the marginal user costs, which are the values of elephants in the wild, conserve their elephants and generate wealth for the country. So long as farmers are compensated for any crop damage and don’t risk their lives to protect their livelihood, the damage to agriculture caused by elephants is relatively small. The value of elephants for trophy hunting exceeds their value for ivory. Therefore, it is not optimal to cull elephants. Instead, elephant populations should be sustained just below the carrying capacity of the habitat so that as many as possible can be hunted for trophies. Adding their contribution to tourism ensures the future of African elephants, even in the worst case scenario. The campaign to list African elephants in Appendix I of CITES and ban international trade in ivory was a noisy distraction. The slaughter of elephants in eastern and central African countries (Barbier et al., 1990) was caused by corruption in governments like that of Kenya (Kenya Wildlife Service, 1990, as cited in Bonner, 1993, p. 134). Corruption led to open access in which the marginal user costs of elephants in the wild were zero. Poachers slaughtered elephants for their ivory and destroyed wealth. Even if a ban on trade makes ivory worthless, the hide and meat give revenue in excess of the very low costs of harvest and elephants will still be slaughtered. On the other hand, the ban on trade has not severely penalised the southern African countries because it is not optimal for them to harvest elephants for their ivory. The ban has only prevented them from selling stockpiles of ivory which accumulated in the 1980s before the CAMPFIRE program, with small additions from the control of problem animals and natural deaths. The approval by the 10th conference of parties to CITES for Zimbabwe, Botswana and Namibia to sell limited quantities under strict quotas to Japan (CITES, 1997) will provide funds which the countries have agreed to use for wildlife management (SACIM, 1994). During the campaign to ban international trade in ivory, concerned people around the world contributed to animal rights and environmental groups. Their contributions were wasted. Instead of working to ban ivory trade, animal rights and environmental groups should have been working with African countries to establish programs like CAMPFIRE. Instead of spending on lobbying and salaries, they should have paid local communities an existence value for each elephant preserved. Animal rights groups, particularly in the United States and the United Kingdom, also campaigned against trophy hunting. The irony is that banning trophy hunting is the quickest way to drive elephants to extinction.

29

Using theoretical results from a biomass model, economists of the Ivory Trade Review Group (ITRG) argued against the textbook conclusion that optimally managed populations are sustained at high stocks. They pointed out that ivory and hides are very valuable and elephants are inexpensive to shoot. Investing in the economy of an African country has a return on investment equal to the social discount rate of, say, 10%. Surplus yield from elephants is only about 5%. Therefore it may be optimal to shoot the elephants and invest the proceeds in the economy (Barbier et al., 1990, pp. 11-14). However, the question must be answered empirically. We quantified and solved a biomass model which predicts that elephants should be maintained at about one-third the carrying capacity of the habitat and well above the minimum viable population. Moreover, elephants are not biomass. They have a complex life cycle in which reproduction and mortality are age specific and the value of an individual elephant grows as it ages. Biomass models do not include the rate of return from letting young animals grow into older and more valuable trophy animals. We also constructed, quantified and solved an age structured model which predicts that elephant populations should be sustained just below the carrying capacity of the habitat. Younger elephants should be left to grow into trophy animals. Finally, we end with another question. What does the rate of return to letting young animals grow into older more valuable animals mean for fisheries and wildlife management in general? Most management strategies are based on biomass models which do not include this rate of return. Therefore, even “optimally managed” stocks are being over exploited-but by how much?

30


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

REFERENCES Barbier, E. B., J. C. Burgess, T. M. Swanson and D. W. Pearce (1990) Elephants, Economics and Ivory, Earthscan Publications Ltd., London. Baskin, Y., (1994) “There’s a New Wildlife Policy in Kenya: Use It or Lose It”, Science, Vol 265, pp. 733-734. Beddington, J., R. Mace, M. Basson and E-J. Gulland (1989) “The Impact of the Ivory Trade on the African Elephant Population”. Renewable Resources Assessment Group, report to the Ivory Trade Review Group, London. Bonner, R., (1993) At the Hand of Man: Peril and Hope for Africa’s Wildlife, New York, USA. Booth, V., (1989) “The Number of Elephants Killed in Zimbabwe: 1960-1988”, in Elephant Management in Zimbabwe, ed. R. B. Martin, G. C. Craig and V. R. Booth, Department of National Parks and Wild Life Management, Harare, Zimbabwe. Buss, I. O., and N. S. Smith (1966) “Observations on Reproduction and Breeding Behaviour of the African Elephant”, Journal of Wildlife Management, Vol 30, pp. 375-388. CITES (1997) “List of Proposed Amendments to the Appendices: Mammal Proposals 11, 12 and 13”, World Wide Web URL, http://www.fws.gov/~r9dia/citeprop.html Clarke, V. J., D. H. M. Cumming, R. B. Martin, and D. A. Peddie (1986) “The Comparative Economics of African Wildlife and Extensive Cattle Production”, African Forestry Commission Working Party on Wildlife Management and National Parks, FAO, Rome. Corfield, T., (1973) “Elephant Mortality in Tsavo National Park, Kenya”, East African Wildlife Journal, Vol. 11, pp. 339-368. Craig, G. C., (1989) “Population Dynamics of Elephants” in Elephant Management in Zimbabwe, ed. R. B. Martin, G. C. Craig and V. R. Booth, Department of National Parks and Wild Life Management, Harare, Zimbabwe. Cumming, D. H. M., (1989) “Review of Elephant Numbers and Trends: A Brief Summary Report of the Work of Iain Douglas-Hamilton and Richard Barnes” in ITRG, Review of the Ivory Trade and the Future of the African Elephant, Vol. 2, pp. 8-15. Dawe, M., and J. M. Hutton (1994) “An Analysis of the Production and Economic Significance of Elephant Hide in Zimbabwe”, Africa Resources Trust, Harare, Zimbabwe. DNPWLM (undated) National Parks 9 Database, Department of National Parks and Wild Life Management, Harare, Zimbabwe.

31

Douglas-Hamilton, I., (1972) On the Ecology and Behaviour of the African Elephant, unpublished Ph.D. thesis, Oxford University. Dublin, H. T., T. Milliken and R. F. W. Barnes (undated) Four Years After the CITES Ban: Illegal Killing of Elephants, Ivory Trade and Stockpiles, The World Conservation Union, Species Survival Commission. Fergusson, R. A., (1994) “Sport Hunting In Zimbabwe-1993”, Zimbabwe Professional Hunters and Guides Association, Harare, Zimbabwe. Frontline Systems, Inc. (1996) Microsoft Excel Enhanced Solver. User’s Guide, V. 2.0. World Wide Web URL, http://www.frontsys.com/ Getz, W. M., and R. G. Haight (1989) Population Harvesting: Demographic Models of Fish, Forest and Animal Resources. Princeton University Press, Princeton. Hertzler, G., J. Harman and R. K. Lindner (1997) “Estimating a Stochastic Model of Population Dynamics with an Application to Kangaroos”, Natural Resource Modeling, Vol. 10, pp 1-41. IIED (1994) Whose Eden? An Overview of Community Approaches to Wildlife Management, International Institute for Environment and Development, London. ITRG (1989) The Ivory Trade and the Future of the African Elephant, Vol. 1, International Development Centre, Oxford. Jansen, D., I. Bond and B. Child (1992) Cattle, Wildlife, Both or Neither: A Summary of Survey Results for the Commercial Ranches in Zimbabwe. WWF Project Paper No. 30. Harare, Zimbabwe. Laws, R. M., (1966) “Age Criteria for the African Elephant, Loxodonta africana”, East African Wildlife Journal, Vol. 4, pp. 1-37. Laws, R. M., (1969) “Aspects of Reproduction in the African Elephant, Loxodonta africana”, Journal of Reproductive Fertility, Vol. 6, pp. 193-217. Laws, R. M., (1981) “Large Mammal Feeding Strategies and Related Overabundance Problems”, in Problems in Management of Locally Abundant Wild Animals, ed., P. A. Jewell and S. Holt, Academic Press, New York, pp. 217-232.

32

Laws, R. M., and I. S. C. Parker (1968) “Recent Studies on Elephant Populations in East Africa”, Symposia of the Zoological Society, Vol. 21, pp. 319-359. Laws, R. M., I. S. C. Parker and R. C. B. Johnstone (1975) Elephants and their Habitats: The Ecology of Elephants in North Bunyoro, Uganda, Clarendon Press, Oxford.


A R E

A F R I C A N

E L E P H A N T S

A N

E N D A N G E R E D

S P E C I E S ?

Liebman, J., L. Lasdon, L. Schrage and A. Waren (1986). Modeling and Optimisation with GINO, The Scientific Press, Palo Alto. Muir, K., and J. Bojö (1994) “Economic Policy, Wildlife and Land Use in Zimbabwe”, Environment Working Paper No. 68, World Bank, Washington D. C. Price Waterhouse (1996) Elephant Census In Zimbabwe 1980 to 1995: An Analysis and Review. Report to the Ministry of Environment and Tourism, Harare, Zimbabwe. SACIM (1994) “Sustainable Use, CITES and the African Elephant”, Southern African Centre for Ivory Marketing, a position paper presented at a meeting of the African Parties to CITES, 1924 September, Kasane, Botswana. Satchell, M., (1993) “Wildlife’s Last Chance”, US News & World Report, 15 November, pp. 68-76. Sugg, I. and U. Kreuter (1994) Elephants and Ivory: Lessons from the Trade Ban, Institute of Economic Affairs, Studies on the Environment No. 2, London. Thomson, R., (1992) The Wildlife Game. The Nyala Wildlife Publications Trust, South Africa. WWF (1997) “Conserving Africa’s Elephants: Current Issues & Priorities for Action”, World Wide Fund for Nature, Gland, Switzerland.

33