Modeling longterm trends in tusk inheritance

The exploitation of elephants would have had several population genetic consequences. Among African elephant populations, the selective hunting of both females and males has made qualitative and quantitative impacts on tusk inher-

Figure 7.11

Numbers of elephants killed (bars) and quantities of ivory harvested (solid circles) by poachers in various age classes over a 20-year period (19741994) in the Periyar Reserve, India. These represent the averages of four scenarios of poaching simulated by the model. (From Sukumar et al. 1998.)

Figure 7.11

Numbers of elephants killed (bars) and quantities of ivory harvested (solid circles) by poachers in various age classes over a 20-year period (19741994) in the Periyar Reserve, India. These represent the averages of four scenarios of poaching simulated by the model. (From Sukumar et al. 1998.)

itance. In qualitative terms, there is evidence for an overall reduction in tusk size. While the mean tusk size in the trade may have decreased because of a demographic shift to younger populations, there has also probably been a corresponding decrease in tusk size for a given age. At the same time, there has also been a noticeable increase in the proportion of tuskless elephants in heavily impacted regions such as Uganda and the Luangwa Valley in Zambia. Some of this change is obviously the outcome in the short term of the selective elimination of tusked elephants. When the poaching pressure decreases, there is again an increase in the proportions of tusked elephants, although not to the original levels, as has been observed in the Luangwa Valley.

The hunting of Asian elephants for tusks, of course, is confined to males. Interestingly, the capture of elephants also may have been biased toward tusked males. The premium on tusked elephants for use in war or ceremonial occasions through history would have resulted in higher rates of "mortality" among tusked males from wild populations. The Arthasastra, an ancient Indian manual on statecraft, prescribed the selective capture of 20-year-old tuskers from the wild (see chapter 2). The significant frequencies of tuskless males (fig.

7.12) in several Asian elephant populations hint at a selective advantage for the tuskless trait in the face of human exploitation.

The population genetics of the tusk trait is therefore of obvious interest to elephant biologists and modelers. To model changes in gene frequencies realistically, knowledge of the pattern of inheritance of the trait is needed. At present, there is no clear idea of tusk inheritance in elephants. It is likely that more than one gene locus is involved in the expression of tusks. Tuskless elephants may have rudimentary tusks or incisor teeth (called tushes among Asian elephants). These are much smaller than regular tusks. Size frequency distribution of incisors shows a distinct bimodal pattern, with some "tuskless" adult individuals possessing tusks weighing less than 1 kg, while others have full-blown tusks weighing several kilograms. A simple model of tusk inheritance would be a two-locus model in which one locus determines the presence or absence of rudimentary incisors, while the second locus determines if these develop into full-blown tusks. The considerable variation in the size of regular tusks among individuals in a population also suggests polygenic inheritance. Among Asian elephants, an additional complication is the total absence of regular tusks in females.

Attempts to model tusk frequency changes in elephant populations have used the simplest assumption possible. Andrew Dobson and associates, who

Figure 7.12

A tuskless male elephant at Minneriya, Sri Lanka. Such tuskless males are locally known as aliyas in Sri Lanka and as makhnas in India. They constitute over 95% of males in Sri Lanka, while in India, their proportion is variable across regions. (Photo courtesy of S. Wijeyamohan.)

Figure 7.12

A tuskless male elephant at Minneriya, Sri Lanka. Such tuskless males are locally known as aliyas in Sri Lanka and as makhnas in India. They constitute over 95% of males in Sri Lanka, while in India, their proportion is variable across regions. (Photo courtesy of S. Wijeyamohan.)

modeled this in African elephants, assumed a single locus, two-allele (T and t) determinant of the tusk trait. Homozygous dominant TT and heterozygous Tt individuals possess tusks, while homozygous recessive tt individuals are tusk-less. Ralph Tiedemann and Fred Kurt, who modeled Asian elephants, made a similar assumption with the additional condition that tusks are not expressed in females. This requires a role for females as carriers of genes for tusk expression in their sons. Limited records I have examined on tusk expression in sons sired by tuskless males in zoos suggest that females, indeed, play a role in tusk inheritance. A single locus model of tusk expression in elephants is certainly a caricature of reality. Nevertheless, it is a useful starting point in understanding the dynamics of tusk frequencies in elephant populations.

Dobson and his associates combined an age-structured, density-dependent demographic model with a single locus, two-allele population genetic model for tusk inheritance. The ability of males to obtain matings was a function of the proportion of tusked or tuskless males in the population. It was assumed that tuskless bulls would fail to win fights against tusked bulls and thus fail to obtain matings when the proportion of tusked bulls is high. The frequency of matings by tuskless bulls would then increase with a decrease in the frequency of tusked bulls in the population. The initial conditions of the population were set by allowing the simulation to run until age classes and gene frequencies reached stable frequencies and numbers. The population was then simulated with a 5% harvest across all age classes of tusked individuals only. Population numbers decline over the first 50 years to a low level, at which point they stabilize over the next 200 years. As the relative frequency of tusked and tusk-less individuals changes in favor of tusklessness, the mating success of tuskless bulls increases. A predominantly tuskless population then increases to the carrying capacity of the habitat.

The Tiedemann-Kurt model for Asian elephants has been described in much greater detail in their 1995 publication. Their model combines stochastic population dynamics with population genetics at the individual level. The demographic data on birth and death probabilities are based on Kurt's field observations in Sri Lanka during the late 1960s and 1970s and my work in southern India during the 1980s. Males were assumed to begin reproducing at 20 years of age and females at 8 years, giving birth 2 years later. Such an early age in female reproduction is likely to be true only of Sri Lankan elephants, but not other Asian populations. A constraint of an upper limit of six females mated annually by one adult male was set. The minimum intercalving interval was taken as 4 years, with a certain probability that a female would actually conceive in a given year 4 years after a previous conception; this translated into an average intercalving interval of 4.43 years, typical of observed populations.

The initial conditions of age and sex distribution, as well as allelic frequencies, were set by running the simulation for 100 years until equilibrium was established. For the initial simulation, the annual probability of death was set at 5.5% for females and 7% for all males. The above birth and female death rates also produced a stable population size under deterministic dynamics.

These rates were derived from averaging across all age classes for each sex; real populations have different age-class-specific death rates. Further simulations began with a stable age distribution and a population in Hardy-Weinberg equilibrium for allelic frequencies. Thus, the frequencies of genotypes and phe-notypes (makhnas and tuskers among males) were also stable under random mating between the sexes. The model, however, provides for sexual selection through a mating advantage for tuskers over makhnas to a specified degree.

The model was used to explore aspects of population growth in elephants, but the more interesting application was to track changes in gene frequencies for the tusk allele and relative proportions of tuskers and makhnas in the population under different selective regimes over a 2,000-year period (fourth century b.c. to early sixteenth century a.d.). Based on some historical data of elephants in Sri Lanka, collated by Fred Kurt and associates in a separate article, the model was applied to the island population. It was assumed that, at the beginning of this historical period, the tuskers constituted about 95% of the male segment, decreasing to less than 15% by the present time. Simple calculations using the Hardy-Weinberg law for allelic frequencies showed that, if tusks were to be determined by a dominant allele T, the initial frequency of this allele would have been 78% (say, 80%). If the allele for tusk expression is recessive (t), on the other hand, its frequency would have to be 97% (say, 95%) initially.

Simulations were run with both scenarios of the tusk allele as dominant and recessive in the absence of sexual selection, but with tuskers suffering a higher annual mortality (10%) compared to makhnas (7.5%). None of these simulated populations matched the condition of a decline in tusker proportion from 95% to about 10%-15% of the population over a 2,000-year period. Only when the tusk allele was taken to be dominant and a 50% sexual selection advantage was given for tuskers over makhnas in matings was this condition met (fig. 7.13). If the sexual selection advantage for tuskers was lower, at 10%-30%, the result was the extinction of the tusk allele.

The selection against tuskers through capture and hunting, however, has fluctuated historically. Even within the island of Sri Lanka, there are considerable differences in the relative numbers of tuskers and makhnas. While southeastern Sri Lanka has a 10%-15% tusker proportion, the Mahaweli basin has practically none. Using different initial population sizes and slightly differing historical mortality rates for tuskers in the two regions, the model was run to simulate the extinction of the tusk allele in the Mahaweli basin by about a.d. 1500. Based on these modeling results, the authors suggested a dominant inheritance of the tusk allele and a moderate degree (about 1.5 times) of sexual selection in favor of tuskers among Asian elephants.

Both the models of tusk dynamics in elephants make crucial assumptions, with little empirical basis, on sexual selection advantage for males. The model of Dobson and associates assumes that tuskless bulls fail to obtain any matings when they are present in low frequencies in relation to tuskless bulls. The mating success of a tuskless bull approaches parity with that of a tusker only when the

Figure 7.13

Simulated frequency of the (a) tusk allele over the long-term in reproductive adults and (b) the proportion of tuskers among reproductive male elephants under the conditions that the tusk allele is dominant, tusked males have a 60% reproductive advantage over tuskless males and tusked males suffer higher mortality than do tuskless males (these were simulated by R. Sukumar and G. Pradhan [unpublished results 2003] by modifying the model described in Tiedemann and Kurt 1995; see text for details).

Figure 7.13

Simulated frequency of the (a) tusk allele over the long-term in reproductive adults and (b) the proportion of tuskers among reproductive male elephants under the conditions that the tusk allele is dominant, tusked males have a 60% reproductive advantage over tuskless males and tusked males suffer higher mortality than do tuskless males (these were simulated by R. Sukumar and G. Pradhan [unpublished results 2003] by modifying the model described in Tiedemann and Kurt 1995; see text for details).

frequency of the latter falls to very low levels. This seems very unlikely. Among Asian elephants, the tuskless bulls are not necessarily inferior to tuskers in fighting ability. The Tiedemann-Kurt model does not explore other possibilities for the low frequency of tusked males in Sri Lanka, including the immigration of tusked males from imported captive elephants that may have become feral.

Gauri Pradhan and I have been modeling the possibilities of captive tuskers contributing the genes for tusks into a largely or entirely tuskless population. There is extensive historical evidence that rulers in Sri Lanka imported elephants, including tusked males, from several regions, including India and Burma, from as early as the sixth century a.d. (see chapter 2); this strongly suggests that tuskers were already scarce locally. Could some of these tusked males have escaped or been released into the wild and infused the tusk gene into the population? We thus explored three possibilities:

1. Tusked males had reduced in the population gradually in accordance with the Tiedemann-Kurt assumption.

2. The island was populated by an entirely tuskless elephant population, the result of genetic drift operating during the Pleistocene in a small founder population, but captive tuskers had successfully mixed with the population.

3. The depletion of tuskers occurred rapidly through selective capture until the sixth century, but the present frequency of the tusk gene has been maintained through the mixing of captive tuskers.

We modified the Tiedemann-Kurt model to incorporate more realistic features such as age-specific mortality for both sexes, age-dependent reproductive success in bull elephants, and frequency-dependent sexual selection of tuskers over makhnas. Our results showed that, while the gradual reduction in the tusk gene over the centuries was possible (see fig. 7.13) as in the earlier model, the frequency of the tusk gene (and proportion of tuskers) presently observed in the Sri Lankan elephant population could also have been the result of captive tuskers reverting to the wild in an entirely makhna population or mixing with a predominantly makhna population after elephant imports commenced during the sixth century a.d.

We are hopeful that the ongoing genetic studies of Asian elephant populations (see chapter 1) will provide more clarity on this issue.

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