When several populations evolve from one species (ie. anole lizards), it is referred to as what?

When several population evolve from one species is referred to as speciation.

Speciation is referred to a s evolutionary process where population evolve to become extinct species. Four geographic modes of speciation in nature are parapatric, sympatric, peripatric and allopatric.

Speciation can be induced artificially through agriculture, laboratory experiment, and animal husbandry. Sympatric speciation can take place through polyploids. For example, doubling of chromosomes number.

It is called a common ancestor