Source: For the period 1300-1748 based on Andersson-Palm, L., 2001: Livet, kärleken och döden: Fyra uppsatser om svensk befolkningsutveckling 1300-1850, Historiska institutionen, Göteborgs universitet. For the period 1749-2004: http://www.scb.se (050428). Palm's figures have been adjusted for the period 1736-1748 so that the linking between 1748 and 1749 gives a realistic account.
According to Angus Maddison (http://www.ggdc.net/Maddison/Historical_Statistics/horizontal-file.xls), the population within the present borders of Sweden was 200000 in 1 AD and 400000 in 1000 AD. According to Stig Welinder (in Jordbrukets första femtusen år 4000 f. Kr.-1000e.Kr., 1998, Natur och Kultur/LTs förlag, Borås, p 218) studies in Sweden show that population increased 10-20-fold between 3900 BC and 500 BC. To this background, it is here assumed that the population in 4000 BC was 1/20 of the population in 1 AD. This gives a population of 10000 in 4000 BC, but the figures 5000 or 20000 could have been the true ones as well.