Paternal mtDNA transmission
In genetics, paternal mtDNA transmission and paternal mtDNA inheritance refer to the incidence of paternal mitochondrial DNA (mtDNA) being passed on to offspring.  Paternal mtDNA inheritance is observed in a small number of species, but in the vast majority, mtDNA is believed to be passed unchanged from a mother to her offspring.

# In animals
Paternal mtDNA inheritance in animals varies.  For example, in Mytilidae mussels, paternal mtDNA "is transmitted through the sperm and establishes itself only in the male gonad."   In testing 172 sheep, "The Mitochondrial DNA from three lambs in two half-sib families were found to show paternal inheritance."
Mitochondria in mammalian sperm are usually destroyed by the egg cell after fertilization.  In 1999 it was reported that paternal sperm mitochondria (containing mtDNA) are marked with ubiquitin to select them for later destruction inside the embryo. Some in vitro fertilization techniques, particularly injecting a sperm into an oocyte, may interfere with this.

# In humans
Many sources, notably companies that sell genealogical DNA tests, state that paternal mtDNA is never transmitted to offspring.  This belief is central to mtDNA genealogical DNA testing and to the theory of mitochondrial Eve.  However, there have been some studies that claimed to have found some cases of paternal mitochondrial inheritance in humans (e.g. Schwarz & Vissing 2002), and it was proposed that in sexual reproduction, the tail of the sperm does enter the egg, and thus "paternal leakage" may occur.
The ideas about human paternal leakage were summed up in the 1996 study Misconceptions about mitochondria and mammalian fertilization: Implications for theories on human evolution: 
The mixing of maternal and paternal mtDNA has been found in humans and chimpanzees.  However, there has been only a single conclusively proven case of human paternal mitochondrial DNA transmission.  All other reported cases can be ascribed solely to contamination and sample mix up.
Responses to this evidence involves saying that so little paternal mtDNA is transmitted as to be negligible ("Some researchers argue that a fragment of the father's mtDNA is in fact passed on, though it represents much less than 1 percent of the total.") or saying that paternal mtDNA is so rarely transmitted as to be negligible ("Nevertheless, studies have established that paternal mtDNA is so rarely transmitted to offspring that mtDNA analyses remain valid...").  It has also been shown that about 1-2% of a person's mitochondria can be inherited from the father .
According to the 2005 study More evidence for non-maternal inheritance of mitochondrial DNA?:
  In addition, heteroplasmy is a "newly discovered form of inheritance for mtDNA. Heteroplasmy introduces slight statistical uncertainty in normal inheritance patterns."
On the other side of the issue are people who want to dismiss maternal mtDNA inheritance completely.  A surname project tutorial states, "A male will rarely get his father's mtDNA.  So far, this has been observed one time in the past 20 years of research."   This single instance is cited as evidence that the whole field of Human mitochondrial genetics is invalid.
In either case, these phenomena throw doubt on the theory that all mtDNA can be traced back to a single female.  This theory of mitochondrial Eve, which aims to trace all humans to "a woman living in sub-Saharan Africa about 200,000 years ago" allows no room for the inheritance of paternal mtDNA.

# In protozoa
Some organisms, such as Cryptosporidium, have mitochondria with no DNA whatsoever.

# In plants
It has also been reported that mitochondria can occasionally be inherited from the father, e.g. in bananas.  Some Conifers also show paternal inheritance of mitochondria, such as the coast redwood, Sequoia sempervirens.

# References and notes
-  The mtDNA is passed from mother to offspring unchanged except for the occasional genetic mutation, the rate of which is unknown but is sometimes estimated as once every 600 generations (see Mitochondrial DNA Mutation Rates).
The exceptional mitochondrial DNA system of the mussel family Mytilidae] by E. Zouros, December 2000.
-  The Fate of Paternal Mitochondrial DNA in Developing Female Mussels, Mytilus edulis: Implications for the Mechanism of Doubly Uniparental Inheritance of Mitochondrial DNA by Brent Sutherland, Donald Stewart, Ellen R. Kenchington, and Eleftherios Zouros
-  Male and Female Mitochondrial DNA Lineages in the Blue Mussel (Mytilus edulis) Species Group by Donald T. Stewart, Carlos Saavedra, Rebecca R. Stanwood, Amy 0. Ball, and Eleftherios Zouros
-  Further evidence for paternal inheritance of mitochondrial DNA in the sheep (Ovis aries) by X. Zhao1, N. Li, W. Guo1, X. Hu, Z. Liu, G. Gong, A. Wang1, J. Feng and C. Wu1, Nature, October 2004, Volume 93, Number 4, Pages 399-403
-  Sutovsky et al. 1999)
-  Misconceptions about mitochondria and mammalian fertilization: Implications for theories on human evolution by Friderun Ankel-Simons and Jim M. Cummins, 1996
-  Linkage Disequilibrium and Recombination in Hominid Mitochondrial DNA (PDF) by  Philip Awadalla, Adam Eyre-Walker, and John Maynard Smith, (view abstract), Science, 24 December 1999: Vol. 286
-  mtDNA Shows Signs of Paternal Influence by Evelyn Strauss, Science, 24 December 1999: Vol. 286. no. 5449, p. 2436; DOI: 10.1126/science.286.5449.2436a
-  NOVA Teachers: America's Stone Age Explorers Classroom Activity
-  evolutionary biologist Andrew Merriwether quoted in Debunking a myth about sperm's DNA. (research indicates paternal mitochondrial DNA does enter fertilized egg) by John Travis, Science News, 1/25/1997
-  "Mitochondria can be inherited from both parents", New Scientist article on Schwartz and Vissing's report; .  The report is: Marianne Schwartz and John Vissing (Aug 22, 2002). "Paternal inheritance of mitochondrial DNA" (PDF). New England Journal of Medicine. 347 (8): 57680. PMID 12192017..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"\"""\"""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{display:none;font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
-  Bandelt HJ, Kong QP,Parson W, and Salas A. (May 27, 2005). "More evidence for non-maternal inheritance of mitochondrial DNA?". American Journal of Medical Genetics. 42 (12): 95760. PMID 15923271.CS1 maint: Multiple names: authors list (link)
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