The observation of high mitochondrial mutation rates in human pedigrees has led 
to the question of how such an asexual genetic system can survive the 
accumulation of slightly deleterious mutations caused by Muller's ratchet. I 
define a null model to quantify in unprecedented detail the threat from 
extinction caused by Muller's ratchet. This model is general enough to explore 
the biological significance of Muller's ratchet in various species where its 
operation has been suspected. For increased precision over a wide range of 
parameter space I employ individual-based simulations run by evolution@home, the 
first global computing system for evolutionary biology. After compiling 
realistic values for the key parameters in human mitochondrial DNA (mtDNA) I 
find that a surprisingly large range of biologically realistic parameter 
combinations would lead to the extinction of the human line over a period of 20 
million years - if accepted wisdom about mtDNA and Muller's ratchet is correct. 
The resulting genomic decay paradox complements a similar threat from extinction 
due to mutation accumulation in nuclear DNA and suggests evaluation of 
unconventional explanations for long-term persistence. A substantial list of 
potential solutions is given, including compensatory back mutations, mutation 
rate heterogeneity and occasional recombination in mtDNA. Future work will have 
to explore which of these actually solves the paradox. Nonetheless, the results 
presented here provide yet another reason to minimize anthropogenic increase of 
mutation rates.