What ideas compete with evolution to explain population changes?
There are multiple ideas which offer alternative theories regarding population changes. While scientists support the idea of evolution, they do not accept that natural selection is the primary mechanism involved. Evolution continues to be viewed and accepted as the main ideology behind population changes.
natural selection: a function of the effect of inherited traits on the differential reproductive success of organisms interacting with their environment ("Natural Selection," Wikipedia)
During the 19th century, four alternative theories to natural selection emerged: theistic evolution, neo-Lamarckism, orthogenesis, and saltationism.
As for theories which offer alternatives to evolution itself, most of the alternative ideas exist within Christian ideologies. For some, Creationism exists as an alternative to evolution. Other alternatives (which derived from the original idea of Creationism) are Creation Science, neocreationism, and Intelligent Design.
Unfortunately for the religious world, many researchers have found the alternative thought to evolution as invalid (since not based upon actual scientific laws).
Definitions of alternative thoughts:
Creationism--the doctrine that matter and all things were created substantially as they now exist, by an omnipotent Creator, and not gradually evolved or developed (Dictionary.com).
Creation Science-- a form of creationism advocated as an alternative to the scientific theory of evolution and holding that the creation of the universe and everything in it was supernatural and relatively recent (Dictionary.com).
Intelligent Design--the theory that the universe and living things were designed and created by the purposeful action of an intelligent agent (Dictionary.com).