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The mitochondria in the sperm are digested upon entry into the egg, making mDNA inheritance exclusively female. What is the advantage of this? Wouldn't some male mDNA be beneficial because of the advantages of (at least a little) sexual reproduction?

Reference: "Postfertilization autophagy of sperm organelles prevents paternal mitochondrial DNA transmission" (behind paywall, here's a ScienceDaily article discussing the results).

Edit:

Both answers seem valid but it is hard to quantify the relative costs.

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    $\begingroup$ cant be sure about this but sperm mitochondria have the main purpose of fuelling the sperm movement. There is a likelihood that these mitochondria have developed some mutation because of this excessive respiratory load. $\endgroup$ – WYSIWYG Aug 27 '13 at 16:57
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Maternal inheritance of mitochondrial DNA is very well conserved, although some species, such as some mussels, show paternal inheritance. As for why or what the advantage is, some of it is due to basic logistics: sperm cells have ~100-1000 mitochondria, egg cells have 105-106, so male contributions are largely washed out. Plus, most mitochondria in sperm are toward the tail, which does not always or necessarily get inside the egg.

For a more selection-based mechanism of the actual destruction, think about what sperm do. They are small packets of energy that do nothing but race until they die. That's it. Energy production, which occurs in the mitochondria, produces reactive oxygen that can damage genomes. The mt-genome in the egg is far less likely to be damaged.

Additionally, I might look to chromosome uniformity. Heteroplasmy does occur now and again, and it's not usually a good thing. Mitochondria are very important, so it makes sense to have an all-or-nothing approach, lest any deleterious genomes persist.

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The mainstream theory, I believe, is that it's a way of avoiding the inevitable destructive (organismal fitness-lowering) competition that the two parents' mitochondria would otherwise be in.

From Austin Burst and Robert Trivers' book Genes in Conflict (p. 146):

Selfish mitochondrial genomes... have a replication advantage over normal mitochondrial genomes in within-organism selection, but they lose out in conventional among-organism selection... Therefore, if a population is polymorphic for 2 mitochondrial types, one more selfish than the other, a nuclear gene that somehow reduces the efficacy of the within-individual selection will tend to become associated with the less selfish type, and so can increase in frequency due to among-organism selection.. That is, there will be selection for nuclear genes that modify mitochondrial behavior so as to reduce the efficacy of within-organism selection (just as there is selection on nuclear genes to suppress drive at unlinked loci)...

An even better way to limit within-organism mitochondrial selection is to ensure that only one parent transmits mitochondria to the next generation - that is, to impose uniparental inheritance...

I think the implication is that uniparental inheritance on the mtDNA, is imposed by adaptations acting in the interest of the nDNA. Without uniparental inheritance, within-cell selection on mitochondria would drive them to replicate faster than is optimal from the rest of the cell's (and the nDNA's) perspective.

Apparently this theory also plays a role in answering Fisher's question, from the preface to The Genetical Theory of Natural Selection:

No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes; yet what else should he do if he wishes to understand why the sexes are, in fact, always two?

Laurence Hurst and Bill Hamilton argue, in their paper Cytoplasmic Fusion and the Nature of Sexes (1992):

Binary mating types are proposed to arise in a three-stage process through selection of nuclear genes to minimize cytoplasmic gene conflict at the time of gamete fusion. In support of this view we argue that: (i) in systems with fusion of gametes, the mating type genes are typically binary and regulate cytoplasmic inheritance; (ii) binary sexes have evolved several times independently associated with fusion, although at least twice binary types have been lost, associated with a loss of fusion; further, in accordance with the theory are findings for isogamous species that (iii) close inbreeding may correlate with less than two sexes and biparental inheritance of cytoplasmic genes; and (iv) species with more than two sexes may have uniparental inheritance of cytoplasmic genes, be rare and be afflicted by deleterious cytoplasmic genes which attempt to pervert normal cytoplasmic genetics.

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