The Key deer ("Odocoileus virginianus clavium") is an endangered deer that lives only in the Florida Keys.
 It is a subspecies of the white-tailed deer ("O. virginianus").
 It is the smallest North American deer.
Odocoileus lucasi, historically incorrectly confused with "Navahoceros fricki", and known as the American mountain deer, is an extinct species of North American deer.
Foster's rule (also known as the island rule or the island effect) is an ecogeographical rule in evolutionary biology stating that members of a species get smaller or bigger depending on the resources available in the environment.
 For example, it is known that pygmy mammoths evolved from normal mammoths on small islands. Similar evolutionary paths have been observed in elephants, hippopotamuses, boas, deer (for example Key deer) and humans.
The Irish elk ("Megaloceros giganteus") also called the giant deer or Irish giant deer, is an extinct species of deer in the genus "Megaloceros" and is one of the largest deer that ever lived.
 Its range extended across Eurasia during the Pleistocene, from Ireland to Siberia to China.
 A related form is recorded in China during the Late Pleistocene.
 The most recent remains of the species have been carbon dated to about 7,700 years ago in Siberia.
 Although most skeletons have been found in bogs in Ireland, the animal was not exclusive to Ireland and was not closely related to either of the living species currently called elk - "Alces alces" (the European elk, known in North America as the moose) or "Cervus canadensis" (the North American elk or wapiti).
 For this reason, the name "Giant deer" is used in some publications, instead of "Irish elk".
 A study has suggested that the Irish elk was closely related to the Red deer ("Cervus elaphus").
 However, other phylogenetic analyses support the idea of a sister-group relationship between fallow deer ("Dama dama") and the Irish elk.
The Columbia Basin pygmy rabbit is an isolated population of pygmy rabbit ("Brachylagus idahoensis"), that is native only to a single Columbia Basin area of Washington state.
 The Columbia Basin pygmy rabbit is the smallest North American rabbit.
 While the IUCN considers the species as a whole to be of least concern, the US Fish & Wildlife Service considers this a distinct population segment, and as thus merits protections under the Endangered Species Act.
 The last purebred Columbia Basin pygmy rabbit died in 2008, marking the end of the pure genetic line.
Pampas deer ("Ozotoceros bezoarticus") live in the grasslands of South America at low elevations.
 They are known as "venado" or "gama" in Spanish and as "veado-campeiro" in Portuguese.
 Their habitat includes water and hills, often with winter drought, and grass that is high enough to cover a standing deer.
 Many of them live on the Pantanal wetlands, where there are ongoing conservation efforts, and other areas of annual flooding cycles.
 Human activity has changed much of the original landscape.
 They are known to live up to 12 years in the wild, longer if captive, but are threatened due to over-hunting and habitat loss.
 Many people are concerned over this loss, because a healthy deer population means a healthy grassland, and a healthy grassland is home to many species, some also threatened.
 Many North American birds migrate south to these areas, and if the Pampas deer habitat is lost, they are afraid these bird species will also decline.
 There are approximately 80,000 Pampas deer total, with the majority of them living in Brazil.
Merycomyia is a genus of North American deer flies in the family Tabanidae.
The bog turtle ("Glyptemys muhlenbergii") is a critically endangered species of semiaquatic turtle endemic to the eastern United States.
 It was first scientifically described in 1801 after an 18th-century survey of Pennsylvania.
 The smallest North American turtle, its carapace measures about 10 cm long when fully grown.
 Although the bog turtle is similar in appearance to the painted or spotted turtles, its closest relative is actually the somewhat larger wood turtle.
 The bog turtle can be found from Vermont in the north, south to Georgia, and west to Ohio.
 Diurnal and secretive, it spends most of its time buried in mud and – during the winter months – in hibernation.
 The bog turtle is omnivorous, feeding mainly on small invertebrates.
The pudús (Mapudungun "püdü" or "püdu", Spanish: pudú , ] ) are two species of South American deer from the genus Pudu, and are the world's smallest deer.
 The name is a loanword from Mapudungun, the language of the indigenous Mapuche people of southern Chile and south-western Argentina.
 The two species of pudús are the northern pudú ("Pudu mephistophiles") from Venezuela, Colombia, Ecuador, and Peru, and the southern pudú ("Pudu puda"; sometimes incorrectly modified to "Pudu pudu") from southern Chile and south-western Argentina.
 Pudús range in size from 32 to tall, and up to 85 cm long.
 As of 2009, the southern pudu is classified as near threatened, while the northern pudu is classified as vulnerable in the IUCN Red List.
Thaumastocera is a genus of North American deer flies in the family Tabanidae.

Question: What animal subject to the Foster's rule is the smallest North American deer?
Answer: Key deer