The graph shows the evolution of worldwide murder rate until 2100, if the murder rate in each country were to remain the same, and population grow as in the medium variant of the UN World Population Prospectus prediction. The current crime rates are taken from the the UN Global Study on Homicide. The code and data used to generate the plot can be found in this git repository.
Of course, it’s unrealistic to assume that murder rate will stay constant through time in a given country. And it’s also possible that their deviation follow a global trend, instead of canceling out, affecting them significantly the accuracy of the numbers in this extrapolation. For example, if one were to do such a chart using IQ, it seems quite likely that the Flynn effect would make it deviate strongly from the actual behavior. For murder rate there is a potential similar effect, more famously discussed in a recent book by Steven Pinker, but I remain less convinced about it representing a trend as likely to be projected in the future as the one in the Flynn effect.
Relatedly, one could argue that as many countries improve in “general well-being”, they will improve along these lines. I picked murder rate for this graph since economically developed countries already have values that differ on orders of magnitude from each other, and the same happens with really underdeveloped countries (compare Malawi with Madagascar, for example) so it seems like something that might not be so coupled with “general well-being” as other metrics.
Also, of course, even if the number was to increase for the next century there’s no reason to assume that it would just continue increasing for the next one – if it has decreased in the past, it seems possible that it would decrease in the future as well.
Note also that the number described in the Wikipedia page for the current global murder rate doesn’t agree with the beginning of the line in the graph. This seems to be because the UN Global Study on Homicide source doesn’t take the sum of the most recent murder totals for all countries in its data report tool (which would be 379845), but instead uses a more refined analysis, with a low estimate of 324000, a high estimate of 518000, and a chosen summary value of 437000. In any case, divergences about the starting point shouldn’t affect the trend itself noticeably.