What is evolution?
The first step is to remind ourself of the definition of the term "evolution". Evolution is most often defined as "any change in allele frequency in a population". I will assume that you are willing to use this standard definition.
If one were to use another definition of evolution (see How to define “evolution”? for a discussion), of course the below list of mechanisms that are driving evolution would be different.
Forces that drive evolution
Categorizing the processes that affect allele frequencies might be subject to issues of semantics. Without going into the details, we generally recognize 4 forces that drives evolution
- Natural selection
- Natural selection refers to the deterministic change in allele frequency due to a differential in fitness among different genotypes. Sexual selection and artificial selection are typically considered as part of natural selection (although that may vary from author to author)
- Genetic Drift
- Genetic Drift refers to the stochastic sampling process of individuals
- A mutation refers to any spontaneous change (substitution, indel, chromosome duplication, etc...) in an individual's genotype.
- Gene flow (aka. migration)
- Gene flow refers to the transfer (migration) of DNA sequences among populations.
KennyPeanuts's answer, random mating and hardy-weinberg equilibrium
In his answer, @KennyPeanuts also talk about random mating. Random mating refers to the condition where the probability of two individuals to mate depends only on their respective fitness. Many people phrase random mating as absence of mate choice but it actually refers to the absence of variation for mate choice in the population.
Hardy-Weinberg states that under the above four conditions and random mating, then the frequency of the genotype that has the allele $i$ derived from the mother and the allele $j$ derived from the father, where $x_i$ and $x_j$ are the frequency of these alleles is $\cdot x_i \cdot x_j$. This means that for a bi-allelic locus, the allele frequency of the genotypes
BB are $x^2$, $x(1-x)$, $x(1-x)$ and $(1-x)^2$, respectively where $x$ is the frequency of the allele
A. For the heterozygotes (
BA), we often care little which of the two allele is inherited by the mother and which is inherited by the father (assuming there are genders) and we therefore call
BA genotypes (which can eventually be confusing). As such, the frequency of the
AB genotype is $2 x(1-x)$.
The condition of random mating ensure that there is no deviation of genotype frequencies from the Hardy-Weinberg's expectations and it ensure that there is no change in genotype frequencies from the first to the second generation considered (after one generation, the equilibrium genotype frequency is immediately reached). Random mating is therefore not a condition for evolution to not occur.