It's utterly incredible that Paraguay, in the 1860s, managed to attain such a horrifying death toll, which proportionately far exceeds that of even WWII Japan or Russia.
One thing that's always intrigued me - how did Paraguay manage to get its population back up in time for the Chaco War? I remember hearing that they legalised polygamy, but I've never seen any actual evidence for it.
That's because simply there is no numbers about the real population of Paraguay in that age that can really be trusted.
The most know version about the Paraguayan losses states that the country had, just before the war, a population between 800,000 and 1,337,439 people, the last number being registered in the 1857 census. In 1886 a new census registered 236.751, and due to this several authors state that Paraguaian losses in the war reached 70% of the general population and 99% of the male population.
The problem of these numbers is that the census of 1857 simply can't be trusted, as the census of 1846 had registered a population of 250,000 people. Therefore, in order to Paraguay have 1.3 million people they should have an annual population increase of 17%! Nowadays it's believed that by 1864 the population of Paraguay was between 285,000 and 450,000, depending on the rate of annual populational growth used for the period between 1846 and 1864.
Also, there is the 1870 census, made by the provisional government, that indicated a population of 116.351 just right after the war. If we project information of communities that didn't send any data for the government, then the total population should be between 140,000 and 165,000 people in 1870.
However, this census of 1870 can't really be trusted too, as the provisional government, in a country devastated by war and with no roads, simply didn't have the conditions to organize it properly (and the local rulers probably had other concerns to be worried about). Also, it has no numbers of how many people fled the country to Argentina and Mato Grosso.