This example of convergence is highly similar to what occurred with the various lizard species discovered in New Mexico -- as environments change, organisms that already occupy a similar niche in their environment but that are taxonomically different often change in similar ways, developing the same adaptations to the environmental changes. In this way, the separate evolutionary branches of each of these organisms converges in a way that produces highly similar characteristics that are not closely related. An extreme example of convergence is given by the case of the anteater, of which there are several varieties on different continents. But though these anteaters might all be called by the same common name, they are completely different taxonomically. They did not evolve from a common ancestor (at least, not one high up on any evolutionary branch), but...

It is somewhat astounding that despite the variety of life and the multitude of ways in which organisms might develop, there are so many similarities between so many different organisms. This is what makes convergent evolution one of the most astounding and compelling evolutionary mechanisms.
References

Fountain, H. (2010). "White Lizards Evolve in New Mexico Dunes." The New York Times. Accessed 9 January 2010. http://www.nytimes.com/2010/01/05/science/05oblizard.html

Hall, B. & Hallgrimsson, B. (2007). Strickberger's Evolution. New York: Jones 7 Bartlett.

WGBH. (2010). "Convergent evolution." Accessed 9 January 2010. http://www.pbs.org/wgbh/evolution/library/01/4/l_014_01.html