Which of the following statements is NOT true, according to natural selection? (1) organisms that are well adapted to their environments...

Statement four is the incorrect statement—"Organisms in a changing environment must adapt to acquire necessary traits and survive."

This statement seems a great deal like Jean Baptiste Lamarck's theory of Use and Disuse and the Inheritance of Acquired Characteristics. This theory was an earlier one than Darwin's Natural Selection Theory. 

Lamarck believed if an organism acquired an ability or trait during its lifetime that allowed it to adapt, it would pass along this trait to its offspring. Also, if an organism didn't use a body part, it would wither and eventually disappear from the species. For example, he believed giraffes inherited longer necks from ancestors who stretched their necks to try to reach the food supply high up in the trees. According to Lamarck, this acquired trait would then be passed down. This can easily be disproved by August Weisman's experiment where he removed tails from mice, allowed them to breed for several generations, and all offspring still had tails.

In Natural Selection theory, all individuals have variations and these variations may prove to be advantageous in a certain environment. The variations are not acquired but are present when the organism was born and are a result of genetic differences (a concept not known at the time of Darwin). New traits arise by mutation and natural selection operates on these as well. 

If an organism has an adaptation that allows it to survive and reproduce—known as differential reproduction, its offspring may inherit the beneficial trait. As time goes by, natural selection operates on populations that allow the best-suited individuals to have a selective advantage. As enough beneficial traits are inherited over time, a population may evolve to become a new species. Conversely, if the environment changes, if a population can't adapt, it may become extinct.