The Burgar/Burgess families in Shetland
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Growth and origin of the Burgar family in Shetland.
The graph below shows an estimate of the number of Burgar persons present in Shetland from 1600 to 1800.

It can be seen that the numbers increase almost exponentially in the above time period. It must be emphasised that these figures are based on the written records. A lot of people would have been unrecorded at the earlier dates. However, from 1700 onwards the written records probably give a good estimate of the population.
The graph suggests that the Burgar family were not in Shetland in the early 1500s. The question then arises as to where did they come from if they did not originate in Shetland? The obvious answer would be from Orkney, which also has a large family of Burgar. The present day Orkney Burgar, have Norse DNA, whereas the the Shetland Burgar/Burgess are of Celtic origin, so are not related. However, it is possible that two different Burgar families could have co-existed in Orkney. Without carrying out DNA testing on all the branches of the Orkney and Shetland Burgar it is not possible to say whether the Burgar families originated in Orkney.
Apparently, some Vikings had Celtic ancestry, maybe as a result of intermingling with Celts early in the times of the Viking invasions, or even because Celts also co-inhabited Norway soon after it was settled after the end of the ice age. So it is possible that the Shetland Burgar/Burgess, may have originated in Norway, but from Celtic stock. Thus they would be Vikings.
However, It is possible that the Shetland Burgar family might ultimately have come from Scotland.
The Baillie Court Rolls of 1694 show that there were only 3 Burgar heads of family out of about 135 families. This amounts to 2% of the population of Dunrossness.
See other people present in Dunrossness in 1694
The data for the above graph has been estimated as shown below.
1600
Burgar in the Shetland Isles are James in Yell, Magnus in Fetlar and William in Dunrossness (maybe).
1650
Possibly the only 2 Burgar in Dunrossness were George and David Burgar
1700
There may have been about 10 Burgar persons in 1700, the children of George Burger and Jean Williamson.
1716
In the Gifford Rentals there are 5 Burgar persons listed in Dunrossness as having crofts. Thus with children there might be say 20 altogether. There were no Burgar in other parts of Shetland.
1750
The Communicants List contains 21 Burgher adults and estimates from later marriages indicate that there were about 20 juveniles at this time making a total of 40 Burgher.
1800
About 100 Burgar were recorded as being born between 1750 and 1800, which together with Burgar born pre-1750 but still living but minus children that died would make about 100 persons.