Agestructured model of sex ratio changes in Asian elephants

Even though some demographic data for Asian elephant populations were available from Sri Lanka, these had never been formally used in an appropriate model to study population dynamics. Based on my study of a southern Indian elephant population during 1981-1983, I used the Leslie matrix to model aspects of its dynamics. The models used for the African elephant populations described the dynamics of only the female segment of the population. In the conventional approach to modeling population dynamics, the male segment is often discarded as only females contribute directly to reproduction. However, in some Asian elephant populations, the male was being selectively killed for its tusks. Thus, I was interested in seeing how the differential mortality rates in females and males, the latter being selectively impacted by ivory poaching, would translate into changes in sex ratio and population growth.

The demographic data came from the elephant population of the Biligiriran-gans in southern India. The mean age of sexual maturity in female elephants was about 15 years, with the first calf being born at 17.5 years. Intercalving interval was 4.7 years. Mortality rates for both sexes were estimated from field data on carcasses discovered and from life table analysis for female elephants. For incorporation into the model, three rates of mortality—low, medium, and high—were used (table 7.3). The low mortality rates were the minimum rates that could be expected to operate in the population based on carcasses found in the field. The medium rates were those suspected to operate in the population over the long term, while the high rates could have been achieved during adverse periods such as a drought or a spurt in poaching. The mortality rates in any one category were higher for males than for females. Nine simulations were run using combinations of the three mortality rates each for the sexes (fig. 7.7).

The simulations began with an adult (>15 years old) sex ratio of 1 male to 5.4 females and made population projections over 50 years, by which time the stable age distribution was nearly reached. In all instances, the adult sex ratio skewed further in the short term (5 years). With low male mortality rates, the sex ratio narrowed after 5 years to stabilize between 1 : 2 and 1 : 3. With medium male mortality, the ratio stabilized at levels very close to the initial ratio. Thus, with medium male and medium female mortality schedules, the adult sex ratio eventually stabilized at 1 : 5.7. When male mortality was high, the sex ratios reached 1 : 13 or 1 : 27 under medium female and low female mortality, respectively. These simulations suggested that the medium male mortality schedules probably had been operating in this and other southern Indian populations over a long term. Sampling of age structures from the Nil-giris, a western extension of the Biligirirangans population, during 1981-1983

Table 7.3

Annual mortality rates for female and male Asian elephants used in population modeling.

For Deterministic Model For Stochastic Model Annual Death Rate (%) Annual Probability of Death (%)

Table 7.3

Annual mortality rates for female and male Asian elephants used in population modeling.

For Deterministic Model For Stochastic Model Annual Death Rate (%) Annual Probability of Death (%)

Age Class (years)

Female

Male

Female

Male

0-1

5-15

8-20

10-15

15

1-5

4-12

6-16

4-8

8

5-15

2-4

6-15

2-3

6-16

15-50

2-10

6-15

1.5-3.2

6-16

50-60

10-15

10-15

1.5-3.2

6-16

Source: Based on Sukumar (1985, 1989a, 1992, 1995b).

The mortality rates used in the deterministic modeling span the range from low to high (see text), while those for the stochastic modeling represent rates used to obtain potential intrinsic population growth rates r varying from 0 to 0.02.

Source: Based on Sukumar (1985, 1989a, 1992, 1995b).

The mortality rates used in the deterministic modeling span the range from low to high (see text), while those for the stochastic modeling represent rates used to obtain potential intrinsic population growth rates r varying from 0 to 0.02.

Elephant Population Since 1982

Figure 7.7

Simulated trends over 50 years (base year 1982) in the adult sex ratio of an Asian elephant population in southern India under different mortality schedules. (From Sukumar 1985, 1989a.)

Figure 7.7

Simulated trends over 50 years (base year 1982) in the adult sex ratio of an Asian elephant population in southern India under different mortality schedules. (From Sukumar 1985, 1989a.)

also indicated a 1 : 5 adult sex ratio, while a survey in Periyar during 1969 by G. U. Kurup gave an adult sex ratio of 1 : 6.

The increase in ivory poaching during the 1980s, however, strongly indicated that sex ratios would further skew. The model projected a decline in the proportion of adult males in the population, from the initial 6.5% to about 4% by the fifth year, corresponding to a further widening of the sex ratio to about 1 : 8. Field work during 1987 in the larger Nilgiris-Biligirirangans population showed that the proportion of adult males indeed had reduced to the level predicted by the model. If male mortality continued to be high, the sex ratios would widen to between 1 : 10 and 1 : 20 over the next decade, a level that was reached by 1997.

The model also explored population growth rates and age structure changes under the various scenarios. As with other elephant population models, this also showed that the most sensitive parameter of population growth is female mortality. Unlike some of the earlier estimates of maximum growth rate in African elephant populations, my simulations showed that Asian elephant populations would increase at lower rates of not more than about 2% per annum. Further, I showed that age distributions or ratios are not good predictors of population trends, a point that had also been argued from a theoretical viewpoint by Graeme Caughley. Thus, a population that was clearly declining under a high male-high female mortality schedule had a higher percentage of calves (7.5%) at stable age distribution than another population (5.7% calves) that was increasing under low male-low female mortality.

Consider two populations: A increases largely because of increase in birth rate, and B increases because of a decrease in death rate. In population A, the age distribution would shift toward the younger age classes, while in population B, there will be no change in age distribution if mortality is proportional for all age classes. The interpretation of growth rates in populations based merely on their standing age distributions can be very misleading unless other information is available. In the case of the Murchison Falls elephant population in Uganda, studied by Laws and associates, the sharp depletion of age classes below 20 years did suggest a declining birth rate, but did not necessarily reveal the value of r, the population's intrinsic growth rate.

My model had two possible limitations: it did not incorporate density-dependent relationships, unlike the Fowler-Smith model, and it did not provide for change in fecundity as a consequence of a skewing adult sex ratio. The issue of density dependence is obviously important in population regulation of large mammals. Later work by Charles Fowler strongly suggested that large herbivorous mammals are most productive when they are close to their carrying capacity (and not at half the carrying capacity, as implied in the standard logistic growth equation). Density-dependent brakes begin to operate only when such populations are very close to or have exceeded the carrying capacity. In my study population, I had no evidence that the elephants were near the carrying capacity and thus saw no need to invoke density dependence for the short-term projections.

On the issue of the link between sex ratio and fecundity, there was no empirical basis for deducing the relationship. However, I did carry out further simulations by increasing the calving interval and found that, with a low female mortality, the population growth became zero only at a calving interval of 7.7 years. In retrospect, this factor was again not important for applying the model to my study population. More recent studies by our team in southern India indicate that no measurable effect on fecundity is likely until the adult sex ratio has skewed to about 1 male to 20-25 females. In only one of the simulations did the sex ratio exceed 1 : 25 marginally. Thus, the results are broadly robust in describing the dynamics of the Nilgiris-Biligirirangans elephant populations.

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