A Population Viability Analysis
for African Elephant (Loxodonta
afr/cana): How Big Should
Reserves Be?
PETER ARMBRUSTER
RUSSELL LANDE
Department of Biology
University of Oregon
Eugene, OR 97403, U.S.X.
Abstract: We present an age.structure~ density-dependent
model o f elephant population dynamics in a fluctuating
environmeng drawing p r i m a ~ l y upon the life history parameters obtained f r o m studies in semi-arid land at Tsavo
National Parig Kenyct Density regulation occurs by changes
in the age o f first reproduction and calving interval We
model environmental stochasticity with drought events affecting sex- and age-specific survivorship~ Results indicate a
m a x i m u m p o p u l a t i o n growth rate o f 3% p e r year and an
equilibrium elephant density o f 3.1~mile e. Analysis o f the
demographic results and their sensitivity to &banges in juvenile survivorship and drought f r e ~ i e ~
supported by genetic constderatior~ suggests that in semi-arid regions a
m i n i m u m reserve size o f 1000 m i l d is necessary to attain a
99% probability o f p o p u l a t i o n persistence f o r 1000 year~
The effect o f age-independent culling on population viability is also analyzed
Anilisis de la viabilidad de poblaciones del elefante africano
(Loxodonta afr/cana): ~Cu~mgrande deben set las r--t~,ervas?
Resumen: Presentamos un modeio densodependiente y
estructurado p o r edades de la dindmica poblacional de ele.
fantes en un ambiente fluctuant~ basado principalmente en
los pardmetros de historia de vida obtenidos a partir de estadios en dreas seraidridas del Parque Nacionai Tsat~ Ken i ~ La regulaci6n densodependiente se manifiesta como
cambios en la edad de primera reproducct6n y en los intervalos "calving" (calving intervals). La estocasticidad ambient a l e s modelada con eventos de sequla que afectan las
supervivencias espectficas para cada edad y sexcx Los resultados indican que la tasa de crecimiento m d x i m a es del
3% anual y la densidad de equilibrlo es de 3.1 elefantes/
milla?. El andlisis de los resultados demogrdficos y su sensihilidad a los cambios eft la supervivencia j u v e n i l y a la
frecuencia de sequla~ apoyado p o r consideraciones gendtica~ sugiere q u e e n regiones semidridas se necestta un
tamaFio de reservas de p o r 1o menos 1000 m i l l a s z para
obtener una probabilidad de persistencia pohlacional para
1000 atios del 99%. Tambic~n es analizado el efecto que la
eliminaci6n independiente p o r edad (age.independent cull.
ing) tiene sobre la viabilidad poblacionaL
Introduction
The plight of the African elephant (Loxodonta afrtcana) has received much attention and generated much
Paper submitted April 15, 1992; revised manuscript accepted January 14, 1993.
602
Conservation Biology
Volume 7, No. 3, September 1993
debate in recent years. Overall numbers are in decline,
and in several areas localized extinctions have already
taken place(Parker & Amin 1983) or appear imminent
(Malpas 1981). In East Africa, few elephants are predicted to survive beyond 1995 outside high security
Armbnn~ & lande
areas, and a similar trend is predicted for the continent
as a whole within 20 years (Caughley et al. 1990). Habitat loss and poaching are the two factors most responsible for the African elephant's current decline, and both
are a d i r e c t p r o d u c t o f h u m a n p o p u l a t i o n g r o w t h
throughout Afric~ With the rapid growth of the human
population, and with economic development in Africa,
the implementation of a conservation plan for the survival of L o x o d o n t a a f r l c a n a is imperative.
The 1989 ban o n ivory trade by the Convention on
International Trade in Endangered Species (CITES) was
initiated in an attempt to r e d u c e the threat of poaching
on the African elephant. Although the ivory ban has received a great deal of positive press in the West, a formal
analysis of the success of this program is not yet complete, and preliminary evidence of its effectiveness is
mixed. That African r h i n o c e r o s a r e c u r r e n t l y o n t h e
verge of extinction in the wild indicates that the ban on
international trade in rhino horn has been less than totally effective. As rhinos are driven locally extinct,
poaching pressure may turn to elephants, as has been
d o c u m e n t e d in the Luwanga valley in Zambia (MilnerGulland & Leader-Williams 1992).
Although the issue of habitat loss has been discussed
(Parker & Graham 1989), w e feel it has not received the
attention it deserves as an important threat to the persistence of the African elephant. Consequently, w e
present a demographic analysis that may be useful as
one c o m p o n e n t in the development of comprehensive,
site-specific management strategies for African elephant
populations. Such management strategies will need to
be sensitive to local ecological, social, and economic
conditions. However, an understanding of basic elephant population dynamics will always be fundamental
to a successful conservation program.
In this paper w e develop an age-structured, densitydependent model of elephant population dynamics in a
fluctuating environment. We present an estimate of
equilibrium elephant density and the reserve size necessary to provide a 99% probability of persistence for
1000 years, as suggested by Shaffer's ( 1 9 8 1 ) discussion
of population viability. A high probability of population
persistence has b e e n chosen due to the difficulty of reestablishing viable elephant populations in isolated areas w h e r e extinctions have occurred, and a long time
frame is considered appropriate due to the long generation time (Leslie 1966) of the African elephant (30.8
years, estimated from our model with a stable age distribution at carrying capacity in a favorable environment). The effects of cullirtg o n the relationship between reserve size and probability of extinction are
examined. Age-independent culling is cutTently practiced in southern Africa, especially during prolonged
droughts, to r e d u c e elephant densities and to alleviate
habitat destruction by elephant populations.
~/ep/~t Popu/~on giahm0,
603
The Model
Several models of elephant population dynamics have
been proposed. Fowler and Smith ( 1 9 7 3 ) used a Leslie
matrix and incorporated density d e p e n d e n c e to determine an equilibrium density and age structure. However, the determims"tic nature of their model and the
lack of any environmental parameters render their conclusions questionable. Wu and Botkin ( 1 9 8 0 ) developed a stochastic model that accounted for the life history of individuals in the population. They concluded
that the population of Hwange National Park in Zimbabwe exhibited a nonstable age structure and suggested
that rainfall is the most likely factor'causing short-term
variations in age structure. Finally, Croze et al. ( 1 9 8 1 )
found that the g r o w t h rate of a m o d e l p o p u l a t i o n
changed q u l d d y in response to cyclical habitat disturbances they simulated. Their simulation was deterministic and assumed no density dependence.
Our model incorporates aspects of the previous models, treating individual births and deaths, and environmentally driven fluctuations in life-history parameters,
as stochastic processes. Both males and females are
modeled in 12 five-year age classes, and discrete fiveyear time steps are employed. Density d e p e n d e n c e is
modeled using the relationships derived by Fowler and
Smith (1973), affecting only reproduction. Age-specific
survivorships, influenced by environmental fluctuations,
have been adopted in most cases from studies of elephant populations in Tsavo National Park, Keny~ The
semi-arid nature of this park may be characteristic of the
type of land gazetted to game reserves as expanding
human populations occupy the wettest lands for agriculture (Parker & Graham 1989).
Reproduction is modeled with the age of first reproduction in years, Mx~, and the calving interval in years,
C/, varying as a function of population density in elephants per square mile, D, as described by Fowler and
Smith (1973), such t h a t M x x = 10 + D and Car = 4Dr3
or 2.75, whichever is larger. Fowler and Smith derived
their equation for age of first reproduction versus density based on data from five populations. Their relationship between calving interval and density was based o n
data from 11 populations. Laws ( 1 9 6 9 a ) suggests that
physiological, nutritional, and social stresses p r o d u c e a
delayed age of first reproduction and prolonged calving
intervals in populations with higher densities.
In our stochastic model, if the calving interval is
greater than 5 years, the probability of an individual
female giving birth to a single offspring in one five-year
interval is F x = 5/C/, and the probability of zero offspring is 1 - (5/C/). If the calving interval is less than
five years, all females will give birth to at least one offspring in a five-year interval, and the probability of a
female giving birth to two offspring in five years is F x =
ComervationBiology
Volume7, No. 3, Septemlaca"1993
604
F2e/~nt ~ o Q
v/O/t/o/
(5 -- C/)/CL To approximate reproduction in the first
fertile age class, total reproductive output is multiplied
by the p r o p o r t i o n of the five-year interval occurring
after age of first reproduction. Females are assumed to
give birth to male and female offspring with an equal
probability. Reproduction cannot o c c u r unless there is
at least one male at least 10 years old in the population.
Environmental stochasticity is simulated with the assumption of three different drought regimes. The basis
for this approach lies in Phillipson's ( 1 9 7 5 ) analysis of
rainfall patterns in Tsavo N.P., Kenya. Phillipson described a mild 10-year drought superimposed on a m o r e
severe 50-year drought. This description is generally
supported by annual rainfall records of Tsavo N.P. since
1948 and by previous records of major events (phillipson 1975). In an attempt to describe conditions over a
longer t i m e scale, w e also i n c o r p o r a t e a 250-year
drought in o u r simulation. Such an event is suggested by
Phlllipson's probability data, c o r r e s p o n d i n g to three
consecutive years of low rainfall. The probability of any
five-year time step experiencing a given drought regime
is as follows: P(10-year d r o u g h t ) = 1 - (0.9) 5, P(50year drought) -------5/50, P(250-year drought) -----5/250.
Survivorship data for five-year intervals are presented
in Table 1. The values for the first age class during normal years are modified for b o t h males and females from
Laws's ( 1 9 6 9 b ) value of 0.388, which was based on an
estimate of natality and extrapolation from adult mortality rates. This value suggests that 40% of the population w o u l d b e comprised of the 0-5-year age class, an
estimate that Corfield ( 1 9 7 3 ) argues is significantly
higher than estimates r e p o r t e d by other investigators.
The survivorship figures for the ten-year drought w e r e
interpolated from Laws's data. They reflect limited mortality f r o m such an e v e n t as suggested by Corfield
( 1 9 7 3 ) and affect only the first two age classes. The
50-year drought survivorship figures w e r e taken from
Corfield's ( 1 9 7 3 ) analysis of mortality during the twoyear drought at Tsavo in 1970-1971, c o m b i n e d with
Laws's data from normal years to reflect survivorship
over a five-year period with two consecutive drought
years and three normal years. Finally, survivorship during a five-year period with a 250-year drought was extrapolated to represent a severe effect on mortality of
three consecutive drought years.
Individual birth and death during each five-year interval are simulated in accordance with Leslie ( 1 9 4 5 ) as
follows. We use the numerical routine RAN2 (Press et al.
1989) to generate uniform r a n d o m numbers. The reproductive probabilities, Fag are evaluated based on the size
of the total population from the last time step. Individual
females give birth to zero, one, or two offspring With
density-dependent probabilities as described above. A
random n u m b e r then determines the state of the environmental parameter, and the corresponding survivor-
~ o n
Biology
Volume7, No. 3, September1993
Armbtuscer~
Table l.
~
fer ave-yeR time aefJ.
Female survfvorsl~ip
Age class
0-5 Years
5-10 Years
10-15 Years
15-20 Years
20-25 Years
25-30 Years
30-35 Years
35-40 Years
40-45 Years
45-50 Years
50-55 Years
55-60 Years
Normal
years
lO-Year
droughts
50-Year
droughts
250-Year
droughts
0.500*
0.887
0.884
0.898
0.905
0.883
0.881
0.875
0.857
0,625
0.400
0.000
0.477
0.877
0.884
0.898
0.905
0.883
0.881
0.875
0.857
0.625
0.400
0.000
0.250*
0.639
0.789
0.819
0.728
0.464
0.475
0.138
0.405
0.086
0.016
0.000
0.01
0.15
0.20
0.20
0.20
0.10
0.10
0.05
0.10
0.01
0.01
0.00
Male survivorship
Age class
0-5 Years
5-10 Years
10-15 Years
15-20 Years
20-25 Years
25-30 Years
30-35 Years
35-40 Years
40-45 Years
45-50 Years
50-55 Years
55-60 Years
Normal
years
l O-Year
droughts
50-Year
droughts
250.Year
droughts
0.500*
0.887
0.884
0.898
0.923
0.694
0.674
0.695
0.622
0.118
0.333
0.000
0.477
0.877
0.884
0.898
0.923
0.694
0.674
0.695
0.622
0.118
0.333
0.000
0.250*
0.639
0.791
0.902
0.891
0.745
0.690
0.621
0.663
0.149
0.244
0.000
0.01
0.15
0.35
0.60
0.60
0.20
0.20
0.20
0.20
0.01
0.01
0.00
* Values modified from those of Laws (1969b) and Corfield (1973),
see tex£
Note Normal years take place in afire.year time step with a probability of 0.47, lO.year droughts with a probability of O.41, 50-year
droughts with a probability of O.1, arid 250-year drot~hts with a
lz~abiUty of 0 02.
ship values from Table 1 are applied. Individuals survive
to the next age class or die based on the evaluation of a
random n u m b e r versus survivorship. This yields the
state of the population at the end of o n e five-year step.
In the case w h e r e culling is being simulated, the population is reduced to a percentage of carrying capacity
( % K ) at the beginning of each time step if it has g r o w n
above (% K) in the previous time step. Such a reduction
is achieved by multiplying the n u m b e r in each sex and
age class by the fraction (% K)/TP and truncating to the
nearest integer, w h e r e TiP represents the total size of the
population (which is greater than %K).
The relationship b e t w e e n habitat area and the probability of extinction was examined in simulations b o t h
with and without c~llitlgr In Figure 3, for areas of 20, 50,
100, and 200 mile 2, 1000 simulatious w e r e run; for the
area of 500 mile 2, 30,000 simulations w e r e run; for the
area of 1000 mile 2, 20,000 simulations w e r e run. A
greater n u m b e r of simulations w e r e utilized for larger
areas in order to attain acceptable statistical confidence
Armbrgs~"& Lmde
rdeplmt Popu~oa VlablliO,
in the smaller extinction probabilities associated with
such areas. Simulations w e r e initiated with an elephant
density of 3.1/mile 2 at a p p r o x i m a t e equilibrium agedistribution based o n the survivorship curve for normal
years. For each area, considered simulations w e r e run
for 200 time steps ( 1 0 0 0 years). Extinction o c c u r r e d
w h e n no individuals remained or w h e n all remaining
individuals w e r e of the same sex. Extinction events
w e r e r e c o r d e d b y the five-year period in which they
occurred. From this information a cumulative distribution of extinctions for a 1000-year period was constructed.
Results
To initially assess the validity of this model, its behavior
without environmental stochasticity in a constant envir o n m e n t (without droughts) is c o m p a r e d with the relevant p a r a m e t e r estimates from the Tsavo population in
1967 (Laws 1969a). The six years p r e c e d i n g 1967
w e r e c h a r a c t e r i z e d b y above-average rainfall (Laws
1969b), and Laws's ( 1 9 6 9 a ) speculation of a decline in
recruitment beginning in 1965 w o u l d suggest that the
population was approaching a demographic equilibrium
in 1967.
Figure 1 illustrates the simulation of an initial population of 11 males and 11 females in an area of 4000
mile 2 over 625 years without environmental stochasticity. The model p r o d u c e s a nearly logistic growth curve
up to a carrying capacity of 3.1 elephants/mile 2. The
equilibrium elephant density of 3.1/mile 2 is very close
15,000
¢D
N
. m
0"J
e'- 1 0 , 0 0 0
O
.
605
to Laws's ( 1 9 6 9 b ) estimate of 3.0/mile 2. Based on the
density-dependent relationships of Fowler and Smith
(1973), the m o d e l predicts an equilibrium calving interval of 5.8 years and age of first reproduction at 13
years. Laws's estimate for the calving interval was 6.5
years and for age of first reproduction was 12.5 years.
Laws estimated the sex ratio in 1967 to b e 53.1% female, while the simulation m e a n sex ratio is 53.4% female. In the simulations, the population growth rate at
l o w d e n s i t y in a c o n s t a n t e n v i r o n m e n t ( w i t h o u t
droughts) averages 3% p e r year. Observational estimates of population growth rates in favorable environmerits average 4% to 5% p e r year (Laws et al. 1975;
Martin et al. 1989). Due to the wide margins of error in
the aerial surveys upon which m a n y such estimates are
based, the potential for immigration to further elevate
these estimates, and the uncertainty with regard to agestructure data (Corfield 1973), a simulation growth rate
of 3% p e r year appears to be a reasonable approximation.
The dynamics of the population o v e r a 50OO-year period with environmental stochasticity in an area of 4000
mile 2 are displayed in Figure 2. The simulation was initiated with a density of 3.1 elephants/mile 2 and w i t h t h e
p o p u l a t i o n at an a p p r o x i m a t e e q u i l i b r i u m agedistribution as described above. The s o m e w h a t volatile
dynamics indicate that the simulation is sensitive to the
o c c u r r e n c e of droughts. Without long-term information
on elephant population n u m b e r s it is difficult to assess
the accuracy of this simulation. Because the rainfall data
support the 10- and 50-year drought regimes, and because of the d o c u m e n t e d effects of major droughts on
elephant mortality, w e have incorporated this type of
environmental stochasticity in subsequent analysis.
The effect of habitat area on the probability of population extinction is presented in Figure 3. The results
suggest that an area of 500 mile 2 is required to yield a
99% probability of persistence for 1000 years. Figure 4
12,000
i
m
°N
~
Q..
O
O_
e"
5000
o
.m
6000
Q.
O
3000
0
0
200
400
600
Time (years)
Figure 1. Growth from an initial population o f 11
males and 11 females in an area o f 4000 mile 2 for
625 years with no environmental stochasticity.
0
I
I
I
1000
2000
3000
400t
5000
Time (years)
Figure 2. Simulation o f total population size with
10; 50-, and 250-year droughts over 5000 year~
Conservation
Biology
V o l u m e 7 , N o . 3, S e p t e m b e r
1993
606
£~ph~t Popul~ion V~bilO,
0
eX
UJ
>
probabilities of extinction are considerably less semitive to culling below 50% of carryin 8 capacity than are
those for smaller areas.
Finally, Figure 5 presents the yield per five-year interval averaged over 10,000 time steps in a fluctuating environment as a function of the level to which the population is culled. The results are based on an area of
4000 mile 2, with the population initiated at approximate equilibrium age-distribution. Age-independent
cullirig Was simulated as described above. Figure 5 indicates that the maximum sustainable yield of individual
animals will be realized by culling to approximately
20% of carrying capacity. An analysis of Figure 4 suggests that culling to achieve a maximum sustainable
yield will substantially increase extinction probabilities
for all areas considered.
20 io2
_....----
.Q
..Q
0•Q.
(0
Armbn~er &
' -
0.1
0.01
//r
200 m i l e
~ . /
0.001
E 0.0001
/
:i e
|
l
400
600
800
00
200
1000
Time (years)
ro
Figure ~ Log o f cumulative probability of population extinction over 1000 years f o r six habitat areas
without culling.
presents the effect of habitat area on the probability of
population extinction as a function of the level of culling. The results indicate that the probability of extinction for each area considered is not seriously affected
until culling reaches approximately 50% of carrying capacity. Furthermore, for areas of 500 and 1000 mile 2,
cO
0
e"
or)
k.
tO
0.)
00
mile 2
200 mile 2
-~-
'
; -
'
~'-
200
>-
la3
= m
X
UJ
A degree of uncertainty with regard b o t h to survivorship in the first age class (O-5 years) and to long-term
drought regimes warrants an analysis of the sensitivity of
our model to variations in these parameters. Table 2
presents probabilities of extinction and standard errors
for all areas considered, with first age-class survivorship
values of 0.45, 0.50 and 0.55. Results indicate that the
model is sensitive to variations in this parameter, and
that a survivorship in the first age class of 0.45 necessitates an area of 1000 mile 2 to predict a 99% probability
of population persistence over 1000 years.
50 mile 2
~
4.o
Sensitivity
0.1
t,-
500
O)
fa.
mile 2
1,1-,.
"tO
O)
0
>,
m
100
>-
.'~ .001
.O
¢0
..Q
0It,..,
}
la.
I
0.01
0
20
I
40
I
I
60
80
1 O0
Culling Target (%g)
Figure 4. Log o f probability of population extinction
over 1000 years f o r six habitat areas as a function
o f the percentage o f carrying capacity (% K) to which
age.independent culling reduces the populatiott
Biology
Volume 7, No. 3, ~-'ptember 1993
~"
0
0
'
20
'
40
60
80
1 O0
Culling Target
Figure 5. Average equilibrium yield per five-year interval over a lO, O00 year period as a function o f the
percentage o f carrying capacity (% K) to which ageindependent culling reduces the populatiott
At~ms~er & L ~
Elepl~t Population ViablliO~
Table 2. Sensitivity of aflnctioa peobabilities to mu'vlvorshlp
values of the O..-5-yenrage clam ( ~ 0 .
I
Probability o f extinction + £ £
Area
(mild)
20
50
100
200
500
1000
Sxl = 0.45
0.985
0.690
0.367
0.147
0.032
+- 0.004
-+ 0.015
-+ 0.015
+ 0.011
-+ 0.002
0.011 +--0.001
Sxl = 0.50
0.917
0.485
0.197
0.061
0.012
-+ 0.009
-+ 0.016
+ 0.013
- 0.003
- 0.002
0.003 +- 0.001
Sx I = 0.55
0.815
0.299
0.089
0.031
0.005
+- 0.012
+ 0.014
--- 0.009
--+0.005
-+ 0.001
0.001 +- 0.000
Table 3 presents probabilities of extinction and standard errors w h e n mild, medium, and severe droughts
are m o d e l e d respectively as occurring with 10-, 25-, and
125-year frequencies; 10-, 50-, and 250-year frequencies; or 10-, 100-, and 1000-year frequencies. The results
demonstrate that the m o d e l is quite sensitive to the
frequency of droughts, and for the 10-, 25-, 125-year
regime an area of 1000 m i l e s is sufficient to predict only
a 97.8% probability of p o p u l a t i o n persistence o v e r
1000 years.
Until it is possible to d e t e r m i n e survivorship and
long-term w e a t h e r patterns m o r e accurately, the m o s t
responsible m a n a g e m e n t decision d e a r l y dictates assuming that such values will lie on the conservative side
of our current estimates. The potential for global climate change, edge effects, and a synergistic interaction
b e t w e e n these t w o factors and m o r e frequent droughts
strongly suggests that an area of 1000 m i l e 2 be adopted
as the m i n i m u m reserve size necessary to provide a 99%
probability of population persistence over 1000 years.
607
section and less than 250 m m rain p e r year in the drier
eastern section (Corfield 1973). In m a n y cases, application to other areas may b e appropriate, because wildlife
parks and preserves are allocated to the driest land least
hospitable for agriculture. Less arid areas may well b e
able to support s o m e w h a t higher elephant densities and
may require smaller areas to provide equivalent probabilities of population persistence (Parker & Graham
1989). The figure of 1000 mile 2 as a r e c o m m e n d a t i o n
for m i n i m u m habitat area necessitates further considerations of habitat heterogeneity and seasonal variations in
habitat quality. Also, m a n y factors that m a y play an important role in p r o m o t i n g extinctions, such as disease,
parasites, grazing competition, edge effects, and metapopulation structure, have not b e e n incorporated into
this analysis (Mace & Lande 1991). Despite such limitations, the outputs of our demographic model for a
constant environment appear to be in good a g r e e m e n t
with Laws's ( 1 9 6 9 a ) estimates of population parameters
for Tsavo N.P., Kenya, prior to the 1970-1971 drought.
Figure 6 presents the sizes of 20 parks and game reserves in central and southern Africa (Kenya, Tanzania,
Uganda, Zimbabwe ). Only 35% of these areas are larger
than 1000 mile s. Our analysis predicts that areas smaller
than this size may need to be artificially repopuiated
(unless management can mitigate risk factors, including
droughts). Linking these smaller reserves with o t h e r
habitat patches through habitat corridors m a y alleviate
16
14
Discussion
12
In considering the implications of this model certain
limitations should b e noted. Conclusions applied to
other areas should account for habitat comparisons with
Tsavo N.P., w h i c h is characterized as semi-arid, receiving less than 500 m m of rain p e r year in the western
Table 3. ~nslliv~ of extinction probabilities to the frequency
of droqht evem.
.~
10
E
8
Z
6
4
Extinction probabilities +. SE.
Area
(mile 2)
20
50
100
200
500
1000
lO/25/125-Year
droughts
lO/50/250-Year
droughts
1
0.976
0.888
0.707
0.431
0.272
0.917
0.485
0.197
0.061
0.012
0.003
-+ 0
-+ 0.005
-+ 0.010
-+ 0.014
-+ 0.007
-+ 0.006
-+ 0.009
-+ 0.016
-+ 0.013
-+0.003
-+ 0.002
-+ 0.0008
lO/lO0/500.Year
droughts
0.573
0.098
0.020
0.003
0.002
0
-+ 0.049
-+ 0.009
-+ 0.004
- 0.0008
-+ 0.0006
+ 0
Note: The 10; 25; 50; 100; 125; 250-, and 5OO-year droughts occur
toith probabilities o f 0. 41, 0.2, 0.1, 0.05, 0.04, 0.02, and O.O1, respec.
tively. Simulations incorporate three levels o f drought severl~, as
describ~ in the text and Table 1.
2
0
1
2
3
4
5
6
7
8
9
Park Size (xlO00 mile 2)
Figure ~ A frequency distribution o f the size o f 20
parks and g a m e reserves in Keny¢ Tanzant4g
Ugand~ a n d Z i m b a b u ~ From Sould et aL (1979)
a n d Martin et aL (1989).
Conservation Biology
Volume 7, No. 3, September 1993
608
EleplumtPopul~on V~blli~
such a necessity. Cumming ( 1 9 9 0 ) has shown that the
average size of newly established reserves has been
shrinking since 1923 in south-central Africa (Botswana,
Malawi, Mozambique, Namibia, Tanzania, Zimbabwe).
With the qualifications mentioned above, our analysis
suggests that 1000 mile 2 be adopted as a minimum size
criteria w h e r e v e r possible for areas expected to maintain viable elephant populations.
Genetic considerations also support adopting an area
of nearly 1000 mile 2 as the minimum habitat size for
elephant populations. With an equilibrium elephant
density of 3.1/mile 2, an 807-mile 2 area will support a
population of 2500 elephants. Assuming a ratio of effective population size (Ne) to total population size (N) of
NJN = 0.2 (Mace & Lande 1991), such an area will
support an effective population of 500 individuals. This
is consistent with the generally accepted effective population size of 500 necessary to maintain typical levels
of genetic variability for quantitative characters in a
population (Franklin 1980; Lande 1988). Where populations are culled to levels below 3.1 elephants/mile 2, a
concomitant increase in habitat area to maintain an effective population size of 500 should be applied.
The equilibrium elephant density of 3.1/mile 2 and Figure 4 suggest that culling down to densities of 1.6 elephants/mile 2 (i.e. 50% of equilibrium density) in reserves larger than 100 mile 2 may not pose a serious
threat to population persistence. At Tsavo (8068 mile2),
Laws's ( 1 9 6 9 b ) recommendation to cull from an elephant density of 3/mile 2 to 2/mile 2 may have been reasonable with regard to this model, although no longer
an issue due to poachers reducing densities to much
lower levels. Barnes's ( 1 9 8 3 ) recommendation to reduce the elephant population of Ruaha N.P., Tanzania
(9730 mile2), to a density of 2.7 elephants/mile 2 seems
reasonable in light of this model. In Zimbabwe, culling
to elephant densities of 2.7/mile 2 as r e c o m m e n d e d by
Martin et al. ( 1 9 8 9 ) will not seriously increase extinction probabilities for parks larger than 100 mile 2, according to our model.
An analysis of Figures 4 and 5 suggests that efforts to
maximize sustainable yields of individual animals by
culling to 20% of carrying capacity will seriously increase the probability of such populations going extinct.
However, less drastic harvesting strategies and density
control operations that maintain populations within
50% of carrying capacity may not seriously endanger
population viability.
Efforts to formulate harvesting quotas must also take
into account that maximizing ivory yields will dictate a
different strategy than maximizing meat yields. Because
ivory can be collected from natural mortalities, a lower
harvesting rate than predicted for meat yields will maximize ivory population in elephant populations (Basson
et al. 1991).
Conservation Biology
Volume 7, No. 3, September 1993
Armbms~ ~ l~de
~ - t
Considerations
Poaching has played a major role in reducing elephant
numbers in Africa. One of the many examples comes
from Kenya, w h e r e poaching is estimated to have reduced the elephant population by two-thirds b e t w e e n
1973 and 1980 (Barnes 1983). The African elephant
was listed in the Convention on International Trade in
Endangered Species (CITES) in 1989, and the subsequent ban on ivory trade adopted by 105 m e m b e r countries was initiated in an attempt to reduce poachin~,r
However, Botswana, Malawi, Zambia, South Africa, and
Zimbabwe favor lifting the ban o n ivory trade, arguing
that it hinders their conservation efforts by preventing
them from exploiting ivory as a sustainable resource.
Successful antipoaching enforcement has b e e n demonstrated to require annual expenditures of approximately
U.S. $200/km 2 (Cumming et al. 1990), an amount that
most African countries have b e e n unwilling to allocate
to wildlife preservation w h e n wildlife is not generating
revenues. Our analysis suggests that limited exploitation
of elephant populations, while fraught with ethical concerns and a great potential for corruption, may be a
biologically feasible means of generating revenue to
support conservation efforts, at least in the near future.
Certainly an analysis of the effectiveness of the CITES
ivory ban and the socio-economic ramifications of such
a program would need to be carefully evaluated before
it could be recommended.
Habitat loss may be of even greater importance than
poaching in threatening the survival of the African elephant (Parker & Graham 1989). A rapidly expanding
human population and economic development in Africa
are motivating habitat loss and contributing to poaching. Any attempt to confront these impending realities
necessitates viable economic alternatives to the ivory
trade. One potential solution currently being explored
is communal game management. Such programs involve
local residents in managing wildlife populations for sustainable yields instead of agriculture and cattle ranching.
Well managed safari hunts provide the greatest economic return on harvested animals, with minimum demographic impact on the population. Initial attempts at
these management programs indicate that they may be
more profitable than cattle ranching or agriculture,
which are often only marginally successful in the arid
climate of central and southern Africa. Furthermore,
these programs have demonstrated that w h e n local residents have a financial interest in preserving game,
poaching is effectively eradicated (Campfire Association
1990). In addition to sustainable harvesting such wildlife management programs may generate considerable
income through tourism. It should b e emphasized that
communal game management should not take place in
established parks, but rather adjacent to them. Manage-
Armbr~er~/ande
ment areas w o u l d provide buffer z o n e s b e t w e e n wilderhess and developed areas, diminishing edge effects and
wildlife/human conflicts.
The potential problems with this strategy, however,
are serious. Historical examples of bureaucracy and government corruption in Africa are daunting. The past involvement of Kenya's g o v e r n m e n t officials in illegal
ivory trade exemplifies the potential pitfalls of such programs (Parker & Amin 1983). Also, relying on the exploitation of wildlife to sustain an increasing human
population may set a dangerous precedent.
The successful conservation of African elephant populations will necessitate a multi-disciplinary approach.
We present an analysis, based on demographic and genetic evidence, w h i c h suggests that 1000 mile 2 be
adopted as a general guideline for the minimum habitat
area necessary to sustain viable populations of African
elephants on semi-arid land. Efforts to integrate such
recommendations into a socio-economically viable conservation program may include communal game mana g e m e n t as an option. Such m a n a g e m e n t s c h e m e s
would Facilitate the integration of a sustainable wildlife
management ethic into African society, which is ultimately the only real hope for effective species c~nservation in Africa.
Acknowledgments
We thank G. C. Craig, T. Foose, I. S. C. Parker, M. L Shaffer, and U. S. Seal for critical comments. This w o r k was
partially supported by NSF grant DEB-9225127 to I~
Lande.
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