At the heart of the anti-science, anti-intellectual movement that conservapedia represents there is the Theory of Evolution. A quick glance at the entry over there will reveal much. Much of the debate can be distilled into an argument against common descent. Once a person accepts common descent the literal interpretation of the Bible is no longer possible and can be tossed out. Common descent is a fact, there is no denying it, any objective analysis of the evidence will reveal this. Talk.origins has an excellent essay on over 29 pieces of evidence that prove common descent  review that for a devastating blow to Biblical literalism. The goal for this article is to distill all that evidence down to a few key facts that can not be explained through anything other than common descent.
The article is constructed to begin with a short description of each piece and to point to why it is irrefutable proof of common descent. Then each section will be expanded into more detail with included examples.
- 1 Irrefutable evidence for common descent
- 2 Anatomical homology
- 3 Endogenous retroviral insertions
- 4 Pseudogenes and shared errors
- 5 Embryology
- 6 Chromosome fusion
- 7 Convergence
- 8 References
Irrefutable evidence for common descent
- Anatomical homologies- Through out the domains of life organisms show a distinct pattern of constraints based on homology in development and construction of the body. Tetrapods have five digits because the ancestor of tetrapods had five digits. When a tetrapod does not seem to have five obvious digits a review of their development will show that they start out with 5 and that the fuse together later to form fewer numbers. All organisms use the same 3 letter code for translating RNA into proteins, the choice of which letters represent which amino acids is an inherently arbitrary event the code is shared because the last universal ancestor to life had that code.
- Endogenous retroviral insertions - These are inactivated viral genes that were inserted by ancient retroviruses. In order for a retrovirus to be inherited in all members of a species many highly improbable events must happen. The virus must insert into a gamete cell, it must mutate so it is inactive, that gamete cell must be used to make an embryo that lives to reproduce and whose genome fixates into the population. This is a very rare event, and ERV's are usually species specific and insert themselves nearly randomly into the genome of the host. The fact that we share ERVs with simians is proof we share a common genome. Even more than that phylogenetic trees can be constructed based on the pattern of ERVS, humans share more ERVs with chimps than either share with Gorillas. This is absolute proof of common descent.
- Pseudogenes - Share errors is a powerful argument for a common source. If two text books describe the same event in similar language its possible they just both converged on the same wording. But if they both share the same grammar or spelling errors it becomes impossible to say they did not derive from a common source. There are genes that no longer code for a protein due to a mutation or error. Species often share the same pseudogene, with the same inactivating mutation. A famous example of this is the L-gulonolactone oxidase which synthesizes vitamin c, all simians including humans share this pseudogene but the guinea pig which also has an inactivated L-gulonolactone oxidase gene has a different mutation.
- Embryology - The pharyngula stage of embryonic development appears to be highly conserved over time. At this stage it is difficult to tell the difference between various vertebrate species. This conserved state screams common ancestory, and the field of evolutionary development, which is highlighting the role of such things as HOX genes, has expanded our knowledge of embryo ontogeny to amazing new levels of detail. All thanks to acknowledging the fact of common descent.
- Chromosome fusion - Chimpanzee's have one more chromosome than humans do. If it is true we share a common ancestor we should be able to figure out what happened to that chromosome. Researchers have found it. Chromosome 2 in humans is actually the fusion of two chimpanzee chromosomes. At the end of each chromosome is a marker called a telomere which usually appears only on the ends. But in human chromosome 2 it there two appearing in the center, marking where the two ends fused. Another knock down win for common descent.
- Convergence - The phylogenetic trees constructed using anatomical homology, DNA homology, pseudogenes, endogenous retroviral insertions, and many other methods all converge on a similar looking tree. There are slight differences but the general relationships of the trees are intact. If all of these methods were flawed you would not expect each of them to converge on the same tree.
Section in progress
What is a retrovirus
A retrovirus is a virus in the family Retroviridae. While many viruses use DNA to store genetic information, a retrovirus uses RNA. Because the infected cell will only replicate the retrovirus' genes if they are also DNA, the virus must rely on reverse transcriptase to transcribe its RNA into DNA and then insert it into the host genome. The retrovirus has significant clinical importance since HIV, which causes AIDS, is a retrovirus.
The retrovirus consists of a protein capsid, base, RNA genome, and the reverse transcriptase. Since RNA is never coded back into DNA in an uninfected cell there is no endogenous reverse transcriptase in the cytoplasm. The retrovirus must bring it with it. The discovery of reverse transcriptase in retroviruses has been a major boon for the biomedical industry where conversion of RNA to DNA is used in many genetic treatments and research.
Reverse transcriptase is prone to making errors in transcription. Sometimes these errors will inactivate the retrovirus' genes and the host cell will not produce new viruses. These mutated strands of retrovirus DNA are still integrated in the host genome. In some cases in a multicellular organism this will be in a germ line cell. This means that the any offspring created from that germ line cell will have the inactivated retrovirus gene in its genome. These are referred to as endogenous retroviral insertions, it has been estimated that up to 10 percent of the human genome consists of these types of inserts.
ERV's are usually species specific, insert almost randomly in the host genome, and the error or mutation that inactivated the gene is random. If two organisms share the same ERV, in the same location with the same inactivation mutations than they must share them due to common inheritance and not two separate infections. Researchers analyze shared ERV insertions across species in order to construct phylogenetic trees.
What is a pseudogene
Pseudogenes are genes present in an organism's genome that have lost the ability to code for proteins due to mutation.  They were first identified and dubbed in the late 1970s when researchers began finding non-coding regions in some organisms that were similar to actual coding genes in other organisms.  So far an estimated 19,000 pseudogenes have been identified in the human genome, this is almost equal to the total number of coding genes (21,000).  Humans have many pseudogenes including L-gulonolactone oxidase which is used to synthesize vitamin c. Research reports that this gene was inactivated in the common ancestor of all simians. 
Pseudogenes have been identified in a wide range of organisms from bacteria to mice to humans, the total number of pseudogenes in a given genome is not predictable but specific pseudogenes are often compared across species to elucidate complex evolutionary relationships 
Pseudogenes are often difficult to parse from the large amount of non-coding base pairs in the genome. Convention requires two elements to be present to label a sequence a pseudogene. The first is homology which is the requirement that a sequence be demonstrated to descend from a functional copy of the gene and the second is non-functionality which is the requirement that the gene not code for a protein in the organism in question. 
Since all pseudogenes are asserted to be descended from a functioning gene the first step is to find the parent gene that it descended from. This is done by using computer programs to compare sequences of DNA across species.  This is a large computational problem but by keeping in mind the phylogenetic relationships between species the search time can be decreased by looking at species that share a more recent common ancestor. Once a functioning copy of a gene is detected its sequence is compared to the pseudogene. A high correlation in base pairs is used to assign homology. Non-functionality can be demonstrated by attempting to transcribe the sequence in-vitro. 
In copyright law there is a problem when determining if one source has copied another source because it is possible, particularly with topics in narrow sub-fields, that two authors could converge on a similar sounding passage to describe the same thing. However, errors in the passages are independent of the subject of the text and of each other. So multiple shared errors, particularly in grammar or spelling, become increasingly improbable for two independent creations. If there are several shared errors between two passages the only reasonable explanation is that one is a copy of the other, or that both were created by the same common source.
This same concept applies to pseudogenes. While it is possible that two genes might look the same because they both do the same thing, once an error invalidates a gene the sharing of this same error between two species can only be explained as the fact that they derived from the same source where the error first appeared. Using pseudogenes and analyzing shared inactivation mutations in these genes can be used to construct phylogenetic trees and as a proof of common descent.
Vitamin C and our simian common ancestor
One of the most famous examples of a shared error is that of Gulonolactone oxidase. This is because it is proof of a shared ancestory between humans and other simians. Gulonolactone oxidase is an enzyme that catalyzes the reactions needed to produce ascorbic acid (vitamin c).  This gene is present in most animals however it has been inactivated due to mutation in some. Animals that can no longer synthesize vitamin c include: simians, guinea pigs, and several species of fruit bats. Since these organisms consume a large portion of their diet in fruit the inactivation of the gene was not a significant detriment. Humans that fail to eat sources of vitamin c can develop scurvy.
The mutation that causes the inactivation of the L-gulonolactone oxidase gene is different depending on the group the organism is in. All extant Guinea pigs share the same inactivation mutation, while all extant simians share a different one. The likelihood of two different species sharing the same inactivation mutation is statistically impossible and is actually shared due to common inheritance. The most recent common ancestor of all extant guinea pigs developed the mutation in the gene, while a different mutation developed in the most recent common ancestor in simians.
Conserved development and the pharyngula
Pharyngula is the term used to describe the phylotypic stage of development in embryology. Taxonomically diverse vertebrate embryos all seem to converge to a very similar morphology. The term was coined in 1981 and stems from the characteristic pharyngeal arches that appear. It is defined as:
The point during development when the basic body plan for a particular higher-level taxa is visible and when all the members of this taxon look most similar.
It is thought by most researchers that this stage represents the basic vertebrate body plan in the common ancestor of all vertebrates. Though there is some dispute as to how similar embryos are and to the reality of this stage. 
Their are six stages to embryonic development, and the pharyngula stage is towards the middle. In the early stages of development there is significant diversity in the morphology of embryos, this diversity decreases over time till the pharyngula stage where they are most similar (often difficult for anyone but trained embryologist to differentiate), and finally in the last stages of development morphology diversifies again.  It is hypothesized that the reason the pharyngula stage is so morphologically constrained is that this is the point where sequential activation of hox genes is initiated so any strong deviations from the developmental plan would lead to drastic changes in the final phenotype of the organism. 
Hox genes and ontogeny
Section in progress
Another piece of evidence that makes clear the factual reality of common descent is chromosome fusion. This can happen in a wide variety of ways, across a wide variety of species.  Fusion of chromosome creates cases where descendant species have different numbers of chromosomes. You can also get splits that increase the number rather than fusion which decreases. The pattern of these fusion events allow for the creation of very intricate phylogentic trees and offers proof of common descent.
One famous example is a fusion event that proves Humanities descent from a common ancestor of us and chimpanzees  Humans have 23 pairs of chromosomes, all other great apes have 24. Something happened to shrink the number of chromosomes in the descent that lead to Humans. This event was a chromosome fusion event. Human chromosome 2 looks almost identical to two of the chimpanzee's chromosomes stacked on one on top of the other. 
Chromosomes form light and dark bands on a karyotype that can be compared to see how similar they are. The light and dark banding patterns of the two chimp chromosomes match that of the single human one. Also on the end of each chromosome are a series of repetitive DNA sequences called telomeres. These sequences are only found on the tips of the chromosome. But for chromosome two you find them in the middle, as if two tips of a chromosome merged together. Also chromosomes have what are called a centromere which link the two sister chromatids toghther. These are distinct regions on the chromosome and there is usually only one. But on chromosome two we find two centromeres. One is "non-functional" but its genetic code matches the other centromere from the second chimpanzee chromosome.
Clearly from this evidence it is clear that the human chromosome 2 is a fusion event between two chimpanzee chromosomes. This means that we inherited these chromosomes from a common ancestor with chimpanzees. Another home run for the fact of common descent and another strike out for "special creation." Humans are Great Apes. This is an irrefutable fact.
Section in progress
- 29+ Evidences for Macroevolution on Talk.origins archive.
- Petrov, D.A, Hartl, D.L. (2000). Pseudogene evolution and natural selection for a compact genome. The American Genetic Association 91:221-227. 
- Gerstein, M, Zheng, D. (2006). The real life of pseudogenes. Scientific American 95:48-55. 
- Bensasson, D., Zhang, D., Hartl, D., Hewitt, G. (2001). Mitochondrial pseudogense: evolution's misplaced witness. Trends in Ecology and Evolution 16: 314-321. 
- Molecular basis for the deficiency in humans of gulonolactone oxidase, a key enzyme for ascorbic acid biosynthesis, American Journal of Clinical Nutrition, Vol 54, 1203S-1208S 
- Pharyngual Period
- Irie, N., Sehara-Fujisawa, S. (2007). The vertebrate phylotypic stage and an early bilaterian-related stage in mouse embryogenesis defined by genomic information. BMC Biology 5:1. 
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- SLACK, J. M. W., P. W. H. HOLLAND, AND C. F. GRAHAM. 1993. The zootype and the phylotypic stage. Nature 361:490–492.
- Callazo, A. (2000). Developmental variation, homology and the pharyngula stage. Systematic Biology 49:1, 3-18. 
- Embryo Stages
- Changes in chromosome number during evolution Talk Origins archive.
- MacAndrew, Alec Human Chromosome 2 is a fusion of two ancestral chromosomes. From evolution pages.
- IJdo JW, Baldini A, Ward DC, Reeders ST, Wells RA, Origin of human chromosome 2: an ancestral telomere-telomere fusion. Proc Natl Acad Sci U S A 1991 Oct 15;88(20):9051-5. Available here