Mexico is estimated to have had about 35,000,000 people upon the arrival of the Spanish. Within the space of a generation the native population was reduced to less than 5,000,000 people. Unfortunately nobody worked up a really good census on this so the deaths have to be inferred from the estimates of the original population. Peru is another case where the Indians had a really tough time with Old World disease. The question arises "Hey, if they all died how come so many Latin Americans look like Indians". And, the answer is "they don't!". Frankly, they all look pretty Middle-Eastern and North African to me. Only a few look tremendously Indian. You have to remember that just about all of the people in the world with Indian ancestry have European, Asian and African ancestry added to the mix since Columbus' arrival. That is, we are all mestizos, and odds are that in the United States most such folks look so "white" or so "black" that they are thought of as "white" or "black". Indians without the requisite admixture of Old World genotypes die quickly of Old World diseases, usually as children. I've spent a great deal of time in both Latin America and the Middle East. This includes a good deal of time in Bolivia and Peru. Unlike the rest of Latin America, most of Bolivia and Peru were never really settled that much by Europeans. Today, the populations of Bolivian and the Peruvian interior (away from Lima) are still decended from 80-90% Indian stock, and, in fact, still speak Amayya and Quechwa as first-languages -- not Spanish.
They look very different from people we could characterize as "Latino" or "Hispanic."
Latinos and Hispanics also don't look Middle Eastern. I've seen plenty of Arabs and Sephardic Jews. They look nothing like Hispanics.
Rather, Hispanics look exactly like what they are: people of mixed descent amongst Indians, Europeans, and African slaves.
Latin America has many different people from many different places. There are even Hindus from India, and Moslems from Pakistan.
The deal is the original American Indian populations encountered by Columbus, et al, looked much more like Chinese than anybody else. Today few American Indian populations have more than a passing resemblance to the Chinese.
The statuary tells the story.