Evolutionary invasion analysis, also known as adaptive dynamics, is a set of mathematical modeling techniques that use
differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
to study the long-term
evolution
Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
of
traits in
asexually reproducing populations. It rests on the following four assumptions about
mutation
In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, m ...
and
natural selection
Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Cha ...
in the population under study:
# Individuals reproduce clonally.
# Mutations are infrequent, and natural selection acts quickly. The population can be assumed to be at
equilibrium when a new mutant arises.
# The number of individuals with the mutant trait is initially