A large discrepancy between the Amerindian contribution to the mitochondrial and nuclear genetic components of 55 Puerto Rican (PR) genomes from the 1000 Genomes Project is identified, with Amerindian mitochondrial haplotypes being highly represented (67.3%), in strong contrast to the Amerindian autosomal contribution (12.9%). I examine the potential causes behind this strong mitonuclear discordance. The Amerindian contribution to the X chromosome is 19.8%, implying assortative mating with Amerindian females during the establishment of the PR population. However, this scenario does not account for the extraordinarily high Amerindian mitochondrial contribution. Demographic simulation of simple assortative mating scenarios during establishment of the PR population indicates that the observed Amerindian mitochondrial contribution is higher than expected. The simulations show that expansion from a small founding population does not produce the observed frequencies, instead producing the frequencies expected under neutrality, with the Amerindian mitochondrial frequencies approximately twice the Amerindian autosomal proportion. In addition, multiple replicated simulations show that drift is an unlikely explanation for the elevated Amerindian mitochondrial frequency, as these are unable to produce the elevated Amerindian mitochondrial frequency observed in the PR genomic dataset, under a range of different starting conditions. I conclude that the mitonuclear discordance appears most consistent with adaptive mitochondrial benefit; however, the molecular mechanism(s) remain to be characterized before this can be confirmed and warrant further investigation. Lastly, I show potential evidence of selection on autosomes and allosomes, using admixture proportions. Interestingly, the major histocompatibility complex locus on chromosome 6 shows greatly elevated single nucleotide polymorphism density but is unaccompanied by strong admixture variance. The observations on mitonuclear discordance may affect the interpretation of apparent assortative mating in recent human admixture events, which should be treated with caution when relying only on mitochondrial haplotype frequencies.