You said: "It is one "family" line of the root person [Think of it this way: For example, your mother is part of your "family" just as your father is, and I think you would not consider her a separate family or family "line" just because she has a different surname than your father has]"
Sure I would. Mother has a completely different ancestry than my father. Her paternal ancestry is one line. Her mother's paternal ancestry is another line.
"2 family lines for the 1st ancester generation
4 lines or the 2nd generation
No, when arranging a person's ancestry by line, one starts, man or woman with their paternal ancestry to the paternal progenitor.
After that, females marrying into your ancestry introduce new ancestry lines.
So, your paternal line (Gen 1 - base) is your dad's line.
So, your next line (Gen 2) is your mom's paternal line
Each of your grandmothers introduce the next 2 lines with their paternal lines. Each line (except the very first one) ends with a female marrying into one of your male lines.
As an example, here is the typical presentation of a person's ancestral line for their Lane line. As you can see, it is much easier to follow than an ahnentafel. Also note how it ends with a female that marries into a male line at pg 45, where the Studley line is shown. As you can see, this can be done without a numbering system. Also note that Sarah Harris and Hannah Hersey have their own "lines-chapters" that follow their paternal line - which starts with Harris and Hersey progenitors and ends with them - females marrying into a male line.http://books.google.com/books?ei=X_aXUMG6DK2I2gX27oHYAw&
William-1 Lane was a resident of Dorchester, Mass., as early as 1635. He came from Norfolk Co., England. In his will dated Feb. 28, 1(550, he gave his sons George and Andrew £8 apiece. He died 1654.
* George-2 Lane, son of William,1 was among the thirty proprietors of land in Hingham, and Sept. 18, 1635, drew his house-lot of five acres, situated on the main street, now North street. He had ten shares in the 1st, 2d, 3d and 4th Divisions, ten acres at Nutty Hill, and thirteen acres in common lands; selectman 1669 and 1678; freeman Oct. 8, 1672; died June 4, 1689. In 1680 he had assigned to him in the old Unitarian Church "the seate under ye pulpit," and his wife, Sarah Harris, daughter of Walter and Mary # (Fry) Harris, had assigned to her "the fore-seate for the women in the body of the meeting house." She died March 26, 1694-5. Walter Harris came to Weymouth in the ship "William & Francis" 1632, lived there twenty years, died in Dorchester, Nov. 6, 1654. His wife died Jan. 1655.
Ebenezer-3 Lane, baptized Aug. 25, 1650, son of George2, married Dec. 27, 1688, Hannah Hersey, born in Hingham, Feb. 13, 1668, died March 31, 1745, daughter of William and Rebecca (Chubbuck) Hersey. "Ebenezer3 served with distinguished bravery in Capt. Joshua Hobart's Co. in Philip's Indian War, Oct. 1675, and was on the roll of Capt. Isaac Johnson's Co. of Roxbury, Dec. 13, 1675, which enlisted for the Narragansett campaign of July, 1675. He died Dec. 12, 1726, aged 76."
Susanna-4 Lane, daughter of Ebenezer3, married Dec. 31, 1724, Jonathan Studley. (Line continued on page 45.)"