Mårten was born 31 January and was baptised 4 February 1855 in Fränninge parish. His parents were the åbo (a type of farmer) Anders Jönsson and his wife, Kjersti Nilsdotter. The parents lived in Starrarps Ohra (a small place in that parish.)
Mårten would have used the patronymic last name of Andersson (literally meaning Anders' son, son of Anders) because his father's given name was Anders.
I checked the household examination record for 1855-1859. This is a parish record similar in format to a census but FAR more detailed. It also was continually updated, so it is not a once-every-ten-years-record.