That was the pattern according to an article by The New England Historical Society: In 1640, More Puritans Left New England Than Arrived. We liked this article for several reasons. One is the format where they link to prior articles. We have been trying to do that, except a post can become full of links. Another is that the subject relates to the focus of TGS, Inc. in a general and personal sense. In terms of the latter, there is mention of George Downing. His sister married Joseph Gardner. The couple was childless and deserves attention. Too, Elihu Yale was a returnee as a child; his grandmother married Theophilus Eaton, brother of Nathaniel who is a forebear of Dr. Frank. We could pull more out of the article.
According to the NEHS, the inflow was due to the policies of Charles I. We know many came over as indicated by the size of the publications by the NEHGS on the Great Migration (note, NEHS is not NEGHS).
Then, there was the English Civil War and the ebb. Lots of questions could be asked and answered: What happened in the British North American colonies during the English Civil War? One thing that we can note is that for a period, there was a lot of intermarrying of families in New England as the influx of new people went to almost nil. When it did pick up later, the rate was much smaller.
The NEHS article provided a few numbers. One can say that 21,000 immigrants came to New England before 1640. The majority of these were after Winthrop's 1630 arrival. Between 1640 and 1650, the number of people in the area would have been between 13K and 17.6K. By 1650, the number was over 22.8K. Some of the increase came through large families; there is a case of one couple having 25 kids. As the NEHS article mentions, some of the 'baby boomers' lived to be quite old with a huge amount of kids themselves.
In regard to this in-breeding, the article ends by noting that the immigration between 1640 and 1845 was only 1% which a very slight inflow.
Remarks: Modified: 11/21/2019
11/21/2019 -- Need to add in some information about the southerners: Stephen Tempest, graduated Oxford.