Final answer:
The idea that plants and animals do not share a common ancestor is false. Evolutionary theory posits that all organisms, including plants and animals, share a common ancestor from which they have evolved through mechanisms such as natural selection and mutation.
Step-by-step explanation:
The statement that the central idea of biological evolution is that plants and animals do not share a common ancestor is false. The theory of evolution is based on the idea that all life on Earth, including plants and animals, descends from a common ancestor. This commonality of descent is the core principle that explains the diversity of life forms we see today. Through processes such as natural selection and mutation, species diversify and adapt to their environments over time, giving rise to the rich biodiversity we observe. It is important to understand that natural selection is a key mechanism of evolution, which acts upon the genetic variation within populations to favor traits that enhance survival and reproduction. Mutations are the raw material for genetic variation and can lead to new traits that, if beneficial, may become more common in a population through natural selection. To directly address the question, under evolutionary theory, a single ancestral lineage can evolve into distinct new lineages, and relationships among species do show they all relate back to a single ancestral lineage. Furthermore, convergence can result in organisms that appear closely related but are not, due to evolving similar traits independently.