Evan A. answered 09/04/23
Master's in Biology with Archaeology Education and Experience
If p is the frequency of an allele within the population, when p reaches 0 (meaning no individuals have the allele) or 1 (meaning all individuals have the allele), then the genes within the population will be the same for all subsequent populations unless new individuals with different alleles enter the population, or mutation changes the alleles that appear in new generations.
Evolution is defined as change over a period of time, and in biology, evolution specifically refers to a change in the types and frequency of heritable traits (usually traits that are genetically inherited) found within the population between generations. Evolution can be long-term, on the order of millions of years, or short-term like from one generation to their offspring. If all individuals within the population have the exact same genes, which can happen with genetic drift, then each new generation will have the exact same genes as their parents. That trend will continue indefinitely as long as the population survives, unless new individuals with different genes enter the population (migration) or mutation leads to new heritable alleles. Different frequencies of alleles in one generation compared to previous generations means that evolution has occurred, whereas generations remaining the exact same means no change has occurred over time in the population, and therefore the population is said to not have evolved.
In real-world scenarios, evolution will pretty much always occur over long periods of time due to mutation at least, or else the population will go extinct. However, this concept is important when you are thinking about how quickly a population is evolving, because if there are a lot of alleles in the gene pool, population change can occur frequently in a relatively short span of time due. In very small populations with a more limited gene pool, inbreeding is common, and genetic drift can cause some alleles to go extinct by chance, which means all members of the population can end up with very similar genes, and the population will tend to evolve much more slowly.