Modeling hunting patterns from tusks in the ivory trade

The enormous volume of the international trade in African elephant tusks during the 1970s and 1980s generated the basic information on mortality patterns to explore population dynamics through simulations. Tom Pilgram and David Western used data on sizes of tusks that originated in Kenya and Tanzania to generate age structures for male and female elephants killed (appendix 2). They then used a deterministic Leslie matrix model to simulate and interpret the mortality patterns seen from the ivory trade. Reproduction was taken to be density dependent following Richard Laws and the Fowler-Smith model. Changes in birth rate with density, however, were varied in a stepwise fashion rather than as a continually varying function. Age at sexual maturity was set at 10 years and intercalving interval at 3 years at the lowest population density. These were increased by 0.5 year each year the population exceeded a set target. Mortality rates were based on studies by Richard Laws, Timothy Cor-field, and Iain Douglas-Hamilton. The lower juvenile mortality rates of about

10% during the first year and 2% subsequently until 5 years described by Douglas-Hamilton were used, while above 5 years, the more detailed data of Laws were incorporated.

Two hunting patterns were simulated with the freedom to choose the actual hunting rates. The first hunting pattern assumed was that of a random cropping across all ages and both sexes, much like that used in population control. The second pattern attempted to mimic selective hunting by relating effort to size of tusks. To achieve this, the base hunting intensity was multiplied by the average tusk weight for a given age and sex class being hunted. Older, and thus larger-tusked, elephants suffered proportionately higher mortality from hunting, while males suffered more than females. The hunting intensity factor was varied to achieve set targets of ivory harvest. For these two hunting scenarios and varying intensities, the simulations produced outputs of age structures of elephants alive, dying naturally, and killed. These were compared to the observed patterns for interpreting the prevailing hunting patterns.

The simulations showed that the observed mortality patterns were indicative of selective hunting of a relatively young population. The age structure during year 15 of such a selectively hunted young population showed a characteristic peak in the young-to-middle-age classes. This matched most closely with the age structure of the elephant population at Kasungu National Park, Malawi, studied by Hugo Jachmann. Here, a combination of high fecundity and selective poaching maintained the population at a relatively young stage.

Other simulations based on ivory trade data showed that random cropping or selective hunting of a mature population was unlikely. Pilgram and Western further explored the population consequences of hunting scenarios. Under one scenario, the amount of ivory harvested was fixed at a level equal to 150% of the yield from natural mortality of a mature population. With selective hunting, the population became younger, and mean tusk weight declined. Thus, the intensity of hunting increased to maintain the ivory harvest at a constant level, taking the population to the verge of collapse by the fifteenth year. Another scenario maintained a constant total number of deaths at 150% of natural mortality. Ivory harvest declined with time, but the population stabilized, with deaths being replaced by increased recruitment.

As with other models, the Pilgram-Western model makes various assumptions. In particular, their assumption that selective hunting has a linear relationship to tusk size is unlikely to be true. Their data on age and sex structures of hunted populations derived from tusk sizes in the trade are pooled for several populations in the continent. There may be differences in hunting patterns between various populations that would be obscured from pooled data from the ivory trade. Nevertheless, the Pilgram-Western model represented an important first step in understanding the patterns underlying the exploitation of African elephants for ivory. It also helped resolve one of the most contentious debates on the African ivory trade (chapter 8).

Ian Parker had claimed that most of the ivory came from natural deaths, commercial hunting was generally not a threat to African elephant populations, and competition from expanding human populations was the greatest threat to elephants. Opposing all these views, Iain Douglas-Hamilton contended that most of the ivory in the trade came from elephants killed illegally, and populations were being overexploited in all but the most inaccessible areas. Further, the increase in human populations and loss of habitat could not explain the increased rate of hunting of elephants. The results of the Pilgram-Western model clearly favored Douglas-Hamilton's explanations.

A different approach was used by M. P. Wells to model human-impacted African elephant populations. Instead of using data on tusks in the trade, Wells used the ratio of dead elephants found in the field to live elephants counted during surveys. The "carcass ratio" was used to infer trends in population growth and degree of selective hunting for tusks. This exercise showed that trends in carcass ratios over a period of 15 years showed distinct patterns related to the type of mortality experienced by an elephant population. If data on carcass ratios had been collected in the field during aerial censuses of elephant populations, it may have been possible to infer mortality patterns from the results of such models.

At the gross, continentwide scale, the data on ivory exports during 19501987 from Africa were used in another modeling effort by Graeme Caughley, Holly Dublin, and Ian Parker. They used the logistic function with a carrying capacity set by the estimated population size in 1950. Production of "live ivory" was substituted for elephant numbers in the function, with 1 tonne of ivory representing 100 elephants. Ivory offtake effort was related to standing crop of ivory such that the effort increased with declining standing ivory. Assuming an intrinsic rate of increase of r = 0.06 on an annual basis, the model produced trajectories of annual production of ivory and deduced elephant population size over the period 1950-2000. This model suggested an overall decline of elephant populations since 1950, with a 3.3% decline throughout Africa during 1990, when the production effort was about 10-fold that of 1950. The reported increases in elephant populations within national parks in East and Central Africa during this period obviously meant an even steeper decline outside the protected areas. The modeled trajectory predicted the near extinction of elephants by 2020. The significant decline in ivory offtake since 1990, however, changed the actual scenario such that the continentwide population probably stabilized during the decade of the 1990s.

One of the more ambitious modeling efforts in scale has possibly been that of E. J. Milner-Gulland and J. R. Beddington, who used continentwide data compiled by Ian Parker on the ivory trade since 1814. In an earlier effort, Milner-Gulland had teamed up with Ruth Mace (1991) to investigate the patterns of hunting for ivory in Africa during 1979-1987 using the Leslie matrix. This exercise showed that the harvest of 12%-13% of elephants annually with a preference for elephants with larger tusks could produce the tusk sizes and quantities of ivory seen in the international trade. Now, instead of a complex Leslie matrix, their model was a "robust simplification" incorporating the range of recruitment and mortality rates observed at several sites across Africa, a factor to describe the density-dependent response, and data on tusk weights in the trade. More important, they used information on elephant distribution areas in various vegetation types determined by Iain Douglas-Hamilton, fixed maximum carrying capacities for each type, and modeled the interaction of hunting for ivory and carrying capacity under different scenarios. Sensitivity analyses showed their model to be robust to the range of parameter values used. Their modeling suggested that reductions in carrying capacity (as a result of agricultural expansion) were the major cause of elephant population declines in the nineteenth century and the early part of the twentieth century, but that hunting for ivory has been the predominant cause of elephant decline since 1950 (fig. 7.10).

The use of changes in the sex ratio over time is another means of determining the levels of poaching for ivory, especially in Asian elephant populations, in which only males possess tusks. This could be especially useful in the case of populations for which reliable official records of poaching are unavailable. Using the basic Leslie matrix, I constructed a model to iteratively simulate changes in the sex ratio of an elephant population under pressure of ivory poaching and applied it to data from the Periyar Reserve with the help of my colleagues. The model made the following assumptions based on studies of

Figure 7.10

A comparison of the mean rate of population change when hunting alone (broken line), when carrying capacity alone (dotted-dashed line), and when both factors (solid line) are assumed responsible for population decline in African elephants. Until about 1970, both factors seemed to play a role, but after this time, hunting was the major factor in population decline. (From Milner-Gulland and Beddington 1993. Reproduced with the permission of the Royal Society of London.)

Figure 7.10

A comparison of the mean rate of population change when hunting alone (broken line), when carrying capacity alone (dotted-dashed line), and when both factors (solid line) are assumed responsible for population decline in African elephants. Until about 1970, both factors seemed to play a role, but after this time, hunting was the major factor in population decline. (From Milner-Gulland and Beddington 1993. Reproduced with the permission of the Royal Society of London.)

elephants at Periyar and elsewhere in Asia. The male-to-female ratio of various age classes, especially the adults, in Sri Lankan elephants was taken to be the natural situation that would prevail under the near absence of poaching. This "near-natural" age-sex distribution was therefore simulated using reasonable assumptions of birth rate (intercalving interval of about 4.5 years) and age-specific mortality for the sexes such that the population would be growing at r = 0.02 (see section 7.4.3).

Observations at Periyar during the 1950s and 1960s by naturalists such as M. Krishnan had indicated an abundance of large-tusked bulls. G. U. Kurup's survey in 1969 had indicated an adult male-to-female ratio of about 1 : 6, which changed to 1 : 122 by 1987-1989, when Mohana Chandran kept detailed records of elephant sightings. Our surveys during 1994 showed this ratio to be 1 : 101. The basic idea, therefore, was to simulate increased rates of male mortality across the various age classes for a starting population of about 1,000 elephants (from census estimates) with an adult sex ratio of 1 : 6 over a 20-year period (beginning in 1974) such that the resulting population structure (age-sex ratios) would match the observed structure in 1994. The difference between the increased mortality rates and the expected natural rates (of the Sri Lankan situation) would represent the rates of poaching for ivory.

Four scenarios of poaching were simulated: (1) the rate of mortality under poaching was constant over two decades (thus, most of the harvest was during the initial years); (2) the rate was low initially, but then increased as the absolute numbers of tusked bulls declined; (3) there was a background rate of mortality from poaching, but spurts occurred during years 5, 10, and 15; and (4) the spurts occurred during years 3, 6, 9, 12, 15, and 18 of the simulation. We also added a function to lower the birth rate progressively as adult male-to-female ratio skewed beyond 1 : 25 based on field observations.

All scenarios simulated the observed population structure quite well and came up with similar results of poaching intensity and ivory harvest. Over the 20-year period, an estimated 336-388 tuskers had been poached and 3,2563,334 kg of ivory harvested, with a large proportion of this coming from the 10- to 20-year-old age class (fig. 7.11). Interestingly, the population growth rates indicated even under the extremely skewed sex ratios were only marginally negative. This is actually to be expected because declining birth rates do not result in major changes in population growth compared to increase in death rates (of females). Our more recent observations at Periyar show an increased birth rate, perhaps the result of subadult bulls coming into the adult age category. It would be interesting to monitor changes in the tusker-to-makhna ratio in this population in the coming years.

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