Nearly a Virgin Birth

From Nature Genetics, A human parthenogenetic chimaera by Strain et al, Nature Genetics 11, 164 - 169 (1995)

In mice, parthenogenetic embryos die at the early postimplantation stage as a result of developmental requirements for paternally imprinted genes, particularly for formation of extraembryonic tissues. Chimaeric parthenogenetic & normal mice are viable, however, due to non−random differences in distribution of their two cell types. Species differences in imprinting patterns in embryo and extra−embryonic tissues mean that there are uncertainties in extrapolating these experimental studies to humans. Here, however, we demonstrate that parthenogenetic chimaerism can indeed result in viable human offspring, and suggest possible mechanisms of origin for this presumably rare event.

I'll leave it to Melinda Wenner of Slate Magazine to explain:

An egg will only start dividing once it senses a spike in cellular calcium. This normally occurs as a result of a sperm's entry during fertilization. But if the egg happens to experience a spontaneous calcium spike, it will start reacting as if it's been fertilized. A defective sperm that lacks DNA can produce a spurious calcium spike. In the lab, scientists can coax unfertilized eggs into beginning the post-fertilization process by simply injecting them with calcium.

Once fertilization—or faux fertilization—occurs, an egg can complete the final stage of a cell division known as meiosis II, during which it loses half of its genetic material to make room for the sperm's DNA. But if there's no sperm, each half of the divided egg cell will end up short, and both will die. In order for our virgin birth to proceed, the faux-fertilized egg must, therefore, not complete meiosis.

Both of these events—the calcium spike and the division mistake—could occur as the result of random dysfunctions or genetic defects. Assuming they do, the egg cell may then begin the process of "parthenogenesis," or virginal development. When this happens to an egg-precursor cell, it can give rise to a tumor made up of many different types of tissue—liver, teeth, eye, and hair, for example.

Parthenogenesis in humans never produces viable embryos, though, because unfertilized eggs lack specific instructions about gene expression from the sperm.
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Are there any case reports of virgin births in the medical literature? Sort of. According to a 1995 report in the journal Nature Genetics, a mother brought her infant boy to the doctor after noticing that his head was developing abnormally. When doctors analyzed his blood, they found something truly bizarre: Despite his anatomically male features, the boy's blood cells were entirely female, consisting only of genetic material from his mother. Some of his other cells—such as those found in his urine—were normal, consisting of a combination of both maternal and paternal DNA. No one knows exactly how this occurred, but the best guess is that immediately after being fertilized, one of his mother's eggs fused with a neighboring unfertilized egg that was dividing parthogenetically. This gave rise to a boy who was considered half-parthenogenetic, since approximately half of his cells were derived from a "faux" conception, containing no remnants of his father's DNA.

When it comes to reproduction, genetics, the very definition of sex..It's not that simple. It's complicated. And these are not experimental animals - they're people. We're people.

"Nature loves diversity, society hates it.” (M. Diamond).

Exactly. So we try to educate society about things like this. That often clashes with religious belief, just as did the concept of a round Earth, a Heliocentric Solar System, Evolution...