Darwin's theory is correct but the smaller parts within that answer is called Gradualism which is more commonly used
Changes over species over long periods of time is known as evolution.
Evolution.
Selective breeding is used for more rapid evolution or artificial breeding.
punctuated equilibrium
Punctuated equilibrium.
Gradualism suggests that evolution occurs slowly and steadily over time, with small changes accumulating to result in major changes, while punctuated equilibria proposes that species remain relatively unchanged for long periods and undergo rapid evolution when faced with environmental pressures. In other words, gradualism emphasizes a constant rate of change whereas punctuated equilibria highlights long periods of stability punctuated by sudden bursts of change.
Punctuated equilibria is a theory in evolutionary biology that suggests species undergo long periods of relative stability (stasis) punctuated by sudden and rapid evolutionary change. This theory contrasts with gradualism, which proposes that evolution occurs steadily over long periods of time.
It's Evolution
Changes over species over long periods of time is known as evolution.
Evolution.
That's part of the theory of evolution by natural selection (Darwinism) but not the main principle, and some other (obsolete) theories also included this belief. I don't know if there is a more specific answer, but if you can't find one, just go with natural selection.
Gradualism proposes that evolution occurs through a slow and continuous process, with small changes accumulating over time. Punctuated equilibrium, on the other hand, suggests that evolution happens in rapid bursts of change separated by long periods of little to no change. Both theories address the concept of how species evolve over time, but they differ in the pace and patterns of these changes.
Some of the main evolutionary theories include Darwin's theory of natural selection, which proposes that species evolve over time through the process of adapting to their environment; the theory of genetic drift, which suggests that random changes in gene frequencies can lead to evolution; and the theory of punctuated equilibrium, which posits that evolution occurs in short bursts of rapid change followed by long periods of stasis.
The punctuated equilibrium theory suggests that species tend to evolve in rapid bursts of change followed by long periods of stability. This theory proposes that evolution does not always occur gradually and uniformly, but can involve abrupt shifts in traits due to significant environmental changes or genetic factors.
The punctuated equilibrium model of evolution holds that evolution occurs in spurts, with species evolving relatively rapidly, and then remaining unchanged for long periods.
Punctuated Equilibrium, I believe is the answer.
Punctuated Evolution or equilibrium