4- Use the Newton-Raphson method with three iterations to find the roo.docx
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4- Use the Newton-Raphson method with three iterations to find the root of the following equation with an initial guess of 1 f ( x ) = e x 2 x 1 = 0 .
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4.2 Evolution of terrestrial ecomorph The transition from scansorial to terrestrial forms has occurred independently at least five times in this radiation, which includes two clades of multiple terrestrial species and three lineages represented by single species (Figure 3). These terrestrial species predominantly occur in open habitats and grasslands in the dry zone of Peninsular India. The earliest diversification within the terrestrial lineages began within the H. gracilis clade. The first split between H. gracilis and the ancestor of H. reticulatus, H. albofaciatus, H. sataraensis, H. vijayraghovani and H. imbricatus was 15.9 Mya (95\% HPD: 18.5-12.4). Diversification within this clade occurred until 5.6 Mya (95\% HPD: 8.1-3.5). On the other hand, diversification within the H. triedrus clade began 7.9 Mya (95\% HPD: 9.9-6.2). The transition from scansorial to terrestrial ecomorph in the three lineages leading to H. scabriceps, H. malcolmsmithi and H. ff. gleadowi occurred after 12.6 Mya (95\% HPD: 16.1-10.3), 5.6 Mya (95\% HPD: 7.6-4.4) and 7.2 Mya (95\% HPD: 11.8 3.1 ) , respectively. Competition has been demonstrated to drive adaptive diversification, by facilitating character divergence (Schluter, 1994; Yoder et al., 2010). With the increase in the diversity of scansorial species, increased competition could have led to evolution of the terrestrial population. However, the evolution of the terrestrial lineages of Indian Hemidacty/us is broadly consistent with increased diversification in Ophisops and Sitana lizards largely distributed in open habitats (Agarwal \& Ramakrishnan, 2017; Deepak \& Karanth, 2018). This suggests that presence of a novel niche is likely to have played a role in the adaptive diversification of these geckos, although the role of competition cannot be ruled out. The repeated evolution of terrestrial lineages in Hemidactylus and increased diversification in other open habitat lizards act as independent replicates and point towards a common underlying process. The diversification within the terrestrial lineages of Hemidactylus is concurrent with the establishment and spread of open habitats and grasslands in the dry zone of Peninsular India, implicating the role of climate in the ecomorphological diversification of these geckos. The increased aridification during the late Miocene led to the expansion of C4 grassland on the Indian subcontinent. This appearance of a novel resource is likely to have shaped the diversification of open-habitat and grassland species. Although most of the diversification in the terrestrial Hemidactylus occurred during the late Miocene, the earliest diversification of terrestrial geckos is older than the dates available for expansion of C4 grasslands ( 9 Mya onwards). However, these dates of C 4 grassland expansion are based on palynological studies carried out in the sub-Himalayan region (Hoorn et al., 2000). Palynological studies from Peninsular india might shed light on the vegetation in.
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E. 4
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