I see 5 children to Alexander & Rosanna?s marriage:
Sarah 3.6.1868
James 27.5.1870
Ellen 5.1.1872
Martha 20.5.1875
William 28.2.1877
All registered in Ballymena.
I assume this is Alexander and Rose in 1901:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Shilvodan/Lisnevnagh/916723/
From that information we can see that one of the daughters married an Armstrong. James was born 8.5.1892, regd Antrim town. From that we find that Ellen Lyttle married Alexander Armstrong on 18.12.1891 in Ballymena. They appear to have had the following further children:
Ellen 17.5.1900
Annie 23.1.1904
Andrew 12.8.1906
Fanny 22.4.1910
Charles 25.2.1913
All registered in Belfast.
Alexander?s probate abstract:
Probate of the Will of Alexander Lyttle late of Lisnevenagh County Antrim Labourer who died 30 January 1907 granted at Belfast to John Beckett M'Clenahan and Robert Lyttle Farmers. Effects ?17 10s.
The full will can be read on the PRONI wills site:
http://applications.proni.gov.uk/DCAL_PRONI_WillsCalendar/willsSearchResultsDetails.aspx
It tells us that Martha married a Mr Downey. Can't find them in the 1911 census. Possibly they lived outside Ireland.
I think that Rose may have died 12.5.1909 aged 71, registered in Antrim. She seems to have been known as Agnes too. You would need to get the death certificate to know for certain. Latterly Rose & Alexander had been living on plot 8c in Lisnevenagh townland.
Regarding the migration from Scotland, the records don?t go back far enough to be able to tell exactly when most people arrived. All that we know is that the vast majority of Scots arrived in the 1600s, with a big rush in the 1690s due to famine in Scotland. The area around Ballymena was settled by the Adair family from Kinhilt, near Stranraer. They brought many of their kinsmen with them to the Ballymena area (which was briefly called Kinhiltstown). So some people in the Ballymena area originated there. But there has obviously been subsequent movement, and so it?s very difficult to say much more with any certainty.
During the 1600s, some 100,000 Scots settled in Ireland, representing something like 10% of the entire Scottish population. They came because land was in short supply in Scotland, rents were rising there but remained low in Ireland and because in many cases the major landowners where they lived in Scotland invited them to move. (The major landowners or undertakers, had been given various concessions in Ireland by King James I (a fellow Scot) in an effort to subdue the country. Part of the deal was that they took sufficient people with them from their Scottish estates to ensure Ireland was properly settled. Previous attempts to settle people in Ireland had failed due to lack of numbers). And I commented previously, famine was an additional reason for migrating to Ireland in the 1690s.