As has been stated a number of times on this this it is assumed by evolutionary biologists that all life on Earth emerged from a single common ancestor. Charles Darwin was one of the first scientists to propose there may be a common ancestor for all life on this planet. That plants & animals, bacteria and archaea (single-celled organisms, similar in size to bacteria but different in molecular organization, the third domain of life) are all related, has given rise to a great deal of scepticism.
Universal common descent is an extremely difficult hypothesis to prove. Even demonstrating a common ancestor between various vertebrates or types of plants is difficult. We have to look at the fossil record, morphological analysis of living organisms and the genetic evidence that exists in every cell of every living organism to find this.
But to find proof that all living things have a universal common ancestor is magnitudes more complex and difficult. A letter published in the May 13 2010 issue of Nature, written by Douglas Theobald, assistant professor of biochemistry of Brandeis University (Waltham MA), gives us an idea of how these types of problems are solved. His paper provided convincing demonstration of universal common descent using statistical analysis techniques on the amino acid sequences in 23 universally conserved proteins across the three major divisions of life, but which have minor species-specific differences. Using advanced statistical modelling to replicate various relational and evolutionary models, He calculated that descent from one ancestor was 102,860 times more likely than descent from a number of ancestors.
What is interesting about this, is it demonstrates the predictability of the evolutionary model, even with a purely mathematical interegation. Whatever method of evaluation is chosen to test a a prediction, whether it be the study of fossils, the physical traits of an organism, or an analysis of DNA sequences, the model works. This is can be compared to sending people to the moon or a probe to Mars. If the h eliocentric theory of the solar system and the theory general relativity were wrong these achievements would be impossible. Likewise, it is the same with much of the work we are describing on this thread, if the theory of evolution was not robust, the predictions would be wrong. Biologists are not fitting evidence to their theory, as has been suggested above, the theory allows them to make predictions and then develop methodogies to test them.