Darwin was troubled by elaborate male traits observed in many species that are seemingly maladaptive for survival, the peacock’s tail being the most iconic of all. He wrote "The sight of a feather in a peacock’s tail, whenever I gaze at it, makes me sick" because it challenged his theory of evolution by natural selection for adaptive traits. The extreme length of the tail may render a peacock more vulnerable to predation and therefore maladaptive for survival. To account for the evolution of apparently maladaptive traits he proposed the theory of sexual selection, wherein, traits that directly enhance mating success may be selected for, either as weapons in male-male competition for mates or as ornaments preferred by females. Male and female elephants in the proboscidean evolutionary radiation have had tusks and show extreme exaggeration in size and form. However, tusk in the Asian elephant (Elephas maximus) is sexually dimorphic as it is expressed only in the males, hinting at a possibility that opposing selection (sexual selection advantage to males and natural selection disadvantage to females) may have been the processes behind this pattern of tusk expression. Intriguingly, tuskless males (male dimorphism with respect to tusk) also occur at fairly high frequencies in some Asian elephant populations (∼50% in norteastern India and ∼95% in Sri Lanka). Theory states that dimorphic males can also occur in a population in stable frequencies as a consequence of sexual selection. I explored sexual selection on elephant tusks as possible mechanism leading to the observed patterns of tusk dimorphism in the elephants. All elephant populations on earth have been harvested for ivory, therefore, artificial selection (selective poaching of tusked elephants for ivory) is another possible cause of tusk dimorphism. I developed mathematical models of population genetics, population dynamics and conducted field observations of mating behavior of Asian elephant in Kaziranga National Park, Assam to understand the evolution of tusk dimorphism in elephants. Darwin’s sexual selection theory was controversial when proposed in 1871 and continues to remain so in 2014. In the introduction of my thesis I have discussed Darwin’s two classical mechanisms of sexual selection, namely, male-male combats for mates and female mate choice based on male traits. The latter was viewed with considerable skepticism by his con-temporary Alfred Russell Wallace and more recently deemed "fundamentally flawed" by Joan Roughgarden. Therefore, I have also discussed the arguments against female mate choice for male traits found in literature. I have reviewed current knowledge about sexual selection for sexually dimorphic male traits of body size and musth, in the African and Asian elephant and state why I have hypothesized that tusks may also be under sexual selection. Sexually selected traits are expected to be genetically determined, therefore, I explored mathematically (Chapter 1) the genetic basis of evolution of sexual dimorphism. Fisher proposed that sexually selected male display traits originate in both the sexes but are suppressed in the females by modifier genes, when the trait becomes deleterious to females. Thus, sexually antagonistic selection on a trait and sex-specific gene expression can lead to the evolution of sexual dimorphism. Tusk is sexually monomorphic in the probocideans that are ancestral to both the African (Loxodonta africana) and Asian elephant (Elephas maximus). Tusk continues to remain monomorphic in the African elephant but has become sexually dimorphic in the Asian elephant. Tusk, therefore could be a sexually selected male trait that evolved according to the Fisherian model. Intriguingly, tuskless males occur at very high frequencies in some Asian elephant populations. The tusked and tuskless male morphs could be alternate male mating strategies, occurring at evolutionarily stable frequencies. Alternatively, the observed male tusk dimorphism, could be a consequence of artificial selection against tusked individuals, due to selective harvest of tusked males. Furthermore, male African elephants are more intensely poached for ivory than female elephants. Yet the frequency of tuskless individuals has increased more rapidly among females than in males. In essence, sexual dimorphism could be evolving among such poached populations. Is such rapid, contemporary evolution of sexual dimorphism, possible through the Fisherian modifier gene mechanism? A 2-loci genetic model (with X-linked trait gene and an autosomal modifier gene) (Rice 1984), a slight variant of the model (with X-linked modifier gene, and an autosomal trait gene) and an entirely autosomal model, were analyzed for the rate of evolution of sexual dimorphism, under different selection pressures for tusk possession. Negative frequency dependent selection was introduced into the model of tusk evolution in accordance with Gadgil’s model for the evolution of male dimorphism as consequence of sexual selection (Gadgil 1972). In two of the 2-loci models (in which tusk gene in autosomal), tusklessness evolved much more rapidly in females than in males, under equal negative selection pressures. The models predict several combinations of time-lines and negative selection pressures for effecting a particular change in the frequency of tusklessness. Model predictions were com-pared with observed changes in the frequency of female tusklessness, in one South Ugandan, African elephant population (∼2% to 10% in 5 to 9 generations) and male tusklessness (∼5% to 50% in 25 to 40 generations) in one north eastern Indian, Asian elephant population. The models predict strong selection pressures of 30% to 50% reduction in fitness, that can effect an 8% increase in tusklessness, in the African elephant population, within time-lines of 9 to 5 generations (∼225 to 125 years) respectively. For the male Asian elephants, natural selection against tusked males on an already sexually dimorphic population, must have been in operation and shifted the population to 5% male tusklessness. The models predict that artificial selection with 20 to 30% fitness cost to tusked males, operating for 40 to 25 generations (∼1000 to 600 years) respectively, can further shift the population from ∼5% to ∼50% tusklessness. Asian elephant populations may already have been in a transient phase of evolution, tending towards tusklessness, with recent artificial selection hastening the process. The two major pre-dictions from this modeling exercise are (1) artificial selection could have played a significant role in the evolution of male tusk dimorphism in the Asian elephant (2) a lack of or very mild current sexual selection on tusks in the male Asian elephant. Both these predictions may be empirically verified. Chapters 2 and 3 are attempts at empirical verification of prediction (1) and Chapters 4 and 5 of prediction (2). From historical references to elephant harvest in Assam, we do know that artificial selection has been in operation, but whether it has played a major role in causing male tusk dimorphism needs to be established. It may be possible to detect signatures of significant past harvest from current demographic structure of an elephant population. Sustained biased harvesting of a particular sex and or age class from an animal population alters the sex ratio and age structure (relative proportion of individuals in each age and sex class) of a population considerably (Sukumar 1989). It may be possible to back infer the harvest scenario by studying the deviation of current age and sex ratios from natural age and sex ratios. In Chapter 2, I explored models of population dynamics under different harvest regimes and its effect on age and sex ratios. I described a method to infer unknown harvest rates and numbers from age and sex ratios, namely, adult female to male ratio, male old-adult to young-adult ratio, and proportion of adult males in the population using Jensen’s(2000) 2-sex, density-dependent Leslie matrix model. The specific combination of male and female harvest rates and numbers can be deter-mined from the history of harvest and an estimate of population size. I validated this model with published data on age and sex ratios of one Asian and African elephant population with fairly reliable data on elephant harvest as well. In Chapter 3, I applied this model to the demographic data that I collected from a wild Asian elephant population in Kaziranga National Park, Assam, India (where more than 50% of the adult males are tuskless). Male polymorphism of sexually-selected male traits occur at stable frequencies in populations of several species. The different male morphs of the trait are hypothesized to be alternate male mating strategies with equal life time reproductive fitness. Male Asian elephants of Kaziranga National Park, Assam are dimorphic with respect to tusk possession: ∼50% of the males are tuskless (and are locally called makhnas). Makhnas could be trading tusk for either longevity, larger body size, testicular volume and or duration of musth as alternate mating strategies. On the other hand makhnas may have increased to a very high frequency primarily due to selective removal (captures for domestication and hunting for ivory) of tusked males from the population for centuries. The aim of Chapter 3 was to examine the role of artificial selection in the evolution of makhnas. Prolonged male-biased harvest(removal from the population) is bound to alter the demographic structure of the population and leave a signature of the intensity and type of harvest on the residual population structure. The Kaziranga elephant population was considered as representative of elephant populations of north east India; A harvest modeling approach (described and validated in Chapter 2) was used to infer unknown harvest of elephants from demographic parameters estimated by sampling this elephant population during 458 field days in the dry season months of 2008–2011. The Kaziranga elephant population appears to have been harvested approximately for the past 700 to 1000 years with adult tusked males being harvested at approximately twice the rate of adult tuskless males, adult females and their immature offspring of both the sexes. The currently observed high frequency of tuskless males in Kaziranga therefore, may be a consequence of sustained artificial selection against tusked males for several centuries. The previous two Chapters have only examined some mechanisms for the loss of tusks in elephants. I proceeded to examine the possibility of evolution of tusks through Darwin’s mechanisms of male-male competition for mates and female mate choice. Elephant tusks are cited as an example of a male trait that has evolved as a weapon in male-male combats. In Chapter 4 I examined the role of tusks in establishing dominance along with two other known male–male signals, namely, body size and musth (a temporary physiologically heightened sexual state) in an Asian elephant population in northeastern India with equal proportions of tusked and tuskless males. I observed 116 agonistic interactions with clear dominance outcomes between adult (>15 years) males during 458 field days in the dry season months of 2008–2011. A generalized linear mixed-effects model was used to predict the probability of winning as a function of body size, tusk possession and musth status relative to the opponent. A hierarchy of the three male–male signals emerged from this analysis, with musth overriding body size and body size overriding tusk possession. In this elephant population tusk possession thus played a relatively minor role in male–male competition. An important implication of musth and body size being stronger determinants of dominance than tusk possession is that it could facilitate rapid evolution of tuskless males in the population under artificial selection against tusked individuals, which are poached for ivory. If not a weapon, tusks could be a male ornament that female elephants find attractive. I explored the interplay of the three male traits (body size, musth and tusk), male mating strategies and female mate choice in Chapter 5. In some species males obtain mating opportunities by harassment of females. Given the striking size difference between an adult male and female elephant, with males weighing at least 30% more than females, male coercion of females to mate is a possibility. A detailed study of the courtship behavior revealed that overt male harassment of females is rare and the ability of a male to mount and stay mounted on a female for copulation is under female control. Therefore female Asian elephants can exercise choice to mate but this is subtly different from exercising mate choice itself. Age-related male mating strategy (reported for the first time in the Asian elephant) exists in the Kaziranga elephant population and this strategy limits the ability of females to exercise choice. Young males (<25 years) predominantly show a sneak mating strategy. Middle-aged males (25–40 years), when in musth, mate–guarded oestrous females from sneakers and attempted mating but sometimes resorted to sneak mating when out of musth. Old males (> 40 years) attempted mating only during their musth phase and were seldom sneakers. Large/musth males received positive responses from estrous females towards courtship attempts significantly more often than did small/non–musth males. Tusked non–musth males attempted courtship significantly more often than did their tuskless peers, and had a higher probability of receiving positive responses than did tuskless males. A positive response, however, may not translate into mating because of mate–guarding by the dominant male. Females permitted large/musth males to stay mounted significantly longer than small/non-musth males. Musth and large body size may be signals of male fertility. Female mate choice in elephants thus seems primarily for traits that signal direct benefits of assurance of conception. Tusked males may attain sexual maturity faster than tuskless males. Therefore it is worth exploring if tusks function as signals of male fertility when males are young (15 to 25 years); this may be possible through hormonal and behavioral profiling of young tusked and tuskless males from 10 to 20 years of age. Overall all musth and body size appear to play a larger role in enhancing male mating success than tusks. Tusked males appear to have a weak sexual selection advantage (male-male domi-nance and female preference) over their tuskless peers, only in the young age class (15 to 25 years) in this population. Males in this age age class, seldom come into musth that would over-ride tusk as a signal of male dominance. Current sexual selection on tusks in this population, appeared to be insignificant and this may be verified through genetic analysis of paternity success. An important implication of musth and body size being stronger determinants of mating success than tusk possession is that, it could facilitate rapid evolution of tuskless males in the population under artificial selection against tusked individuals, even in a slow breeder such as the elephant. Musth may have evolved much later than tusks in elephants, therefore it is possible that tusks evolved under sexual selection before musth evolved. However, body size, in mammals in gen-eral appear to be under both natural and sexual selection. Gould has shown that the absurdly large and palmate antlers of the extinct Irish elk, scales allometrically with body size (Gould & Lewontin 1979). Phylogenetic studies of elephant evolutionary radiation indicate a general trends towards increase in body-size with size reduction and tendency towards dwarfism occurring only in island habitats (Palombo 2001). Tusk development, which is essentially tooth development may be closely linked to cranium development. Cranium development in turn may be linked to body size through allometric scaling laws. If so, any selection on body size is bound to act on tusk size. I propose that the evolution of elaborate tusks seen in elephants is primarily due to natural and or sexual selection acting on body size, and tusk just hitched a ride with body size. Tusks may be maintained in spite of tuskless males occurring in the population only because of a rather weak sexual selection advantage to tusk possession in contests in which males are symmetrical with respect to body size and musth status.