Annie's parents were Howard Turner Meek born 1841 and died about 1879 in either Arkansas or Missouri.
His wife was Mary Jane Cochran Turnbold Meek born 1840 in Missouri. They can be found living in Graves County, KY in the 1870 census:
Name: Howard Meek
Age in 1870: 25
Birth Year: abt 1845
Birthplace: Tennessee
Home in 1870: Lynnville, Graves, Kentucky
Race: White
Gender: Male
Post Office: Lynnville
Value of Real Estate: View image
Household Members:
Name Age
Howard Meek 25
Mary J Meek 30
Arumissa Meek 2
Ann E Meek 1
William Tumbold 9
Thomas J Tumbold 7

Sometime between 1870 and 1880 they moved to either Missouri (according to my mother-in-law) or Arkansas (according to my mother-in-law's brother) where they both died. I do not know how they died but they left three orphan children, Annie, James and Joseph.
A brother of Howard's went to wherever it was they were living and brought the children back to Dickson County, Tennessee. This brother, Moses Harvey Meek, took the two boys to raise as can be seen in this 1880 census:
1880 census shows:
District 4, Dickson, TN page 294B
J. H. Meek Self M M W 40 TN
Occ: farmer Fa: TN Mo: TN
Martha J. Meek wife F M W 42 TN
Occ: Keeps House Fa: VA Mo: TN
James Jeff Meek son M S W 17 TN
Alex Meek son M S W 15 TN
Martha L. Meek Dau F S W 11 TN
Susan A. Meek Dau F S W 9 TN
Ida Arizona Meek Dau F S W 7 TN
Edgar Meek Son M S W 5 TN
Missouri A. Meek Dau F S W 3 TN
Babe Meek Son M S W 8M TN
James C. Meek Nephew M S W 9 KY
Joseph H. Meek Nephew M S W 7 MO
Fa: TN Mo: KY
Anna Meek Aunt F S W 64 TN
Fa: NC Mo: NC

The sister, Annie, was raised by Howard and Moses Harvey, sister Lucinda Meek Brown:
1880 census page 294A shows:
John W. Brown self M M W 25 TN
Occ: farmer Fa: TN Mo: TN
S. Lucinda Brown wife F M W 26 TN
Occ: Keeps House Fa: TN Mo: TN
Edgar Brown son M S W 3 TN
Andrew J. Brown Son M S W 1 TN
Anna E. Meek Niece F S W 12 KY
Occ: at home Fa: TN Mo: KY

Howard, Moses Harvey and Lucinda were three of twelve children of Moses Christopher Meek and Clemency Laws Meek.