Ok, here are two terms that are sometimes used interchangeably, sometimes not, and when they’re not, they are used in various ways.
Parallel evolution
Convergent evolution
For this installment of Talkin’ Terminology, do you consider these to be the same, or how do you differentiate them?
Parallelism implies common ancestry, albeit in the distant past. Convergent evolution implies no common ancestry.
Maybe Zen has it right, but they do seem to be used often interchangeably — considering that parallelism is normally the opposite of convergence, it's like another version of the joke that goes "Microbiology is the only field where multiplication and division mean the same thing."
Parallel evolution implies that the same phenotype evolved in two separate lines from the same ancestral phenotype. Convergent evolution means that two distinct phenotypes *converged* on the same phenotype, but that the ancestral phenotype giving rise to the convergence was not shared.
Example of parallel evolution: saber-toothed cats. In each case we can describe the evolution of sabers, in general, as parallel evolution: both are derived from cat teeth, basically. The same ones, even.
Contrast that with convergent evolution: wings for birds and wings for insects. The wings of birds are derived from tetrapod appendages. The wings of insects are derived from insect limbs (iirc).
Of course, at some point you can say that they shared common ancestry for the feature, e.g. limbs in general. The easiest way to spot the difference, for me, is to think about the extent of differentiation between the parallel/convergent populations. In the case of saber-toothed cats, it's basically the same animal, in differnet populations, evolving the same trait. In insects and birds, they derive wings in very different populations (and they're quite different wings, to boot).
Wikipedia's take is actually pretty close to how I think of the two.
Convergent evolution
A -> B
C -> B
Parallel evolution
A -> B
A -> B
There was a very interesting paper by Jeff Arendt and David Reznick in TREE on this topic a few years ago.
They argue that the convergence/parallel distinct is rather meaningless – biologists tend to use "convergence" if the two species in question are distantly related, and "parallel" when the species are closely related.
The problem is that no-one really distinguishes what "closely" or "distantly" related mean, and when you're dealing evolvability constraints, then the picture just gets really muddy:
"Closely related species of different populations might evolve the same phenotype using different genes. Distantly related organisms, even ones in different classes, might do so using the same genes. In the former case, the evidence for different genes or genetic pathways yielding the same phenotype in different populations of the same species or closely related species argues against the role of constraints in shaping how specific features of the phenotype evolve."
Their conclusion is:
If the use of the terms ‘parallelism’ and ‘convergence’ cannot be associated with a clear dichotomy, either at a phylogenetic level or a molecular level, then their continued use is not justified and can even be mis- leading. They are relics of a time when we could not evaluate the underlying causes of phenotypic similarity and were confined to inferences based on comparative anatomy. These terms are also relics of a time when there was not an appreciation of the complexity of genetic and developmental networks that underlie the determination of simple phenotypic traits, such as coloration. We argue that this might be a good time to simplify our vocabulary. We need only one term to describe the independent evol- ution of phenotypic similarity. ‘Convergent evolution’ will do nicely. If one is interested in how phenotypic similarity evolved, then we have the toolkit to find out.
Link to the Arendt and Reznick paper