A major problem in population genetics is understanding how the genomic pattern of polymorphism is shaped by natural selection and the demographic history of populations. Complex population dynamics confounds patterns of variation and poses serious challenges for identifying genomic imprints of selection. We examine patterns of polymorphism using computer simulations and provide analytical predictions for hitchhiking effects under two models of adaptive niche expansion. The population split (PS) model assumes the separation of a founding population followed by directional selection in the new environment. Here, the new population undergoes a bottleneck and later expands in size. This model has been used in previous studies to account for demographic effects when testing for signatures of selection under colonization or domestication. The genotype-dependent colonization and introgression (GDCI) model is proposed in this study and assumes that a small number of migrants carrying adaptive genotype found a new population, which then grows logistically. The GDCI model also allows for constant migration between the parental and the new population. Both models predict reduction in variation and excess of high frequency of derived alleles relative to neutral expectations, with and without hitchhiking. Under comparable conditions, the GDCI model results in greater reduction in expected heterozygosity and more skew of the site frequency spectrum than the PS model. We also find that soft selective sweeps (fixation of multiple copies of a beneficial mutation) occurs less often in the GDCI model than in the PS model. This result demonstrates the importance of correctly modeling the ecological process in inferring adaptive evolution using DNA sequence polymorphism.