## An application to Asian elephants

I used the simulation model Vortex, developed by Robert Lacy (1993), to model Asian elephant population viability. Because a majority of Asian elephant populations are small and found in fragmented habitats, my primary goal was to determine the probability of extinction of small populations and what constitutes a viable population. Apart from looking at chance variations in birth and death processes (demographic stochasticity), I also looked at how varying sex ratios influenced population viability. The sex ratio factor was important in the context of the selective hunting of male Asian elephants for tusks.

The presentation in chapter 9 of conservation gives definitions of population viability analysis (PVA) and minimum viable population (MVP). Briefly, PVA is a process that evaluates data and models to arrive at a probability that a population will survive over a given period of time. The MVP has a predefined probability (say, 95% or 99%) of surviving for a given period of time (100 or 1,000 years, for instance).

The simulation program Vortex has capabilities for modeling demographic, environmental, and genetic stochasticity, catastrophes, and trends in carrying capacity. Monte Carlo simulations are used to determine the outcome of population events. I modeled Asian elephant populations of up to 150 individuals over a period of 100 years. Demographic stochasticity was modeled by assigning age-specific probabilities of birth and death based on field data. The demographic parameters used in the simulations were largely based on my study of the southern Indian populations. The reproductive life span of female elephants was taken to be 15-60 years. Birth probability was 0.20-0.22 per mature female per year, while 80% of males above 15 years old were assumed to be in the breeding pool. Mortality rates (given in table 7.3) were varied to yield a desired population growth rate and sex ratio under a deterministic analysis.

Environmental stochasticity is modeled as variation in the year-to-year probability of birth or death. This is achieved by sampling a statistical distribution, with the standard deviation (SD) of the mean probability of birth or death specifying the interannual fluctuations. To capture this, I set the SD to 20% and 40% of the mean probability of death to represent low and moderate environmental variation, respectively. Correspondingly, the SD on fecundity was set at 25% and 50% of the mean probability of births. I also allowed for two types of catastrophes. A serious drought could occur with a 2% probability (once every 50 years on average), reduce birth by 40%, and kill 20% of individuals in the population. A disease epidemic could occur every 200 years and kill 25% of individuals. The carrying capacity K of the population was set at 150 (SD = 20%).

In small populations, there could be additional demographic problems arising from inbreeding depression. This was incorporated using a "heterosis model," in which homozygotes with lethal genes have higher juvenile mortality compared to heterozygotes.

The age structure of the initial population was set to reflect a stable age distribution under constant fecundity and mortality. The female fecundity and mortality probabilities were adjusted to yield annual population growth rates of zero (r = 0), 0.5% (r= 0.005), and 2% (r = 0.02) under a deterministic scheme. For the scenario with a 2% growth rate, the male mortalities were varied to give adult male-to-female ratios of 1 : 4, 1 : 8, and 1 : 16 at stable age distribution. Under any one scenario, the population was simulated 500 or 1,000 times for 100 years.

The simulations showed that, under a potential growth rate of 2%, a population of 25-30 elephants would have a 99% probability of surviving for 100 years (fig. 7.8). When growth rates were potentially lower at 0.5% or stable, a population size of 65-80 individuals was needed to ensure its survival with the same probability. These sizes are arrived at when the adult sex ratios begin at 1 male to 4 female elephants. With a skewing of the ratios to 1 : 8 or 1 : 16, which is more commonly observed at present in most southern Indian populations, the probabilities of extinction increase considerably even at 2% potential growth rate. With a 1 : 16 ratio, for instance, a starting population of 150 elephants (at K = 150) has only a 92% probability of surviving for 100 years. It is only when K is increased to about 250 that this population would have a 99% survival probability.

The fact that a population of a certain size has a high probability of surviving over a period of a century does not necessarily imply its continued viability. When fecundity and mortality schedules indicate a low growth rate, such a population would almost certainly show an average negative growth rate under stochastic modeling. In brief, a population may be expected to survive for 100 years, but it would almost certainly be reduced in size at the end of this period. This would have a bearing on its future viability. Extending the time frame of the simulations, Peter Armbruster and colleagues found a 200-year lag during which extinction probabilities were low, but then increased significantly.

Simulations incorporating inbreeding depression and those omitting this factor showed negligible differences in survival probabilities for population sizes above 30 individuals. Interestingly, the survival probabilities for populations with low and moderate levels of environmental variation were hardly distinguishable, suggesting that long-lived species such as the elephant are relatively well buffered against moderate environmental fluctuations seen in Asian habitats. In semiarid regions of Africa, the degree of environmental variation could be much higher and hence be a more important consideration in determining population viability.

In brief, populations of 100-300 individuals, depending on demography, sex ratio, and ecological pressures, are indicated for their viability in the relatively short term of one or two centuries.

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