Dollo's law is the statistically true statement that evolution never runs backwards. That is, once an organism evolves into a new form, its descendants will never return to exhibit the old traits in exactly the same way.

This is subject to a number of caveats; evolutionary trends such as neoteny and trait loss can cause an organism to appear to reverse their evolution. However, an axolotl or a blind cave fish does not look exactly like their ancestors; while they have lost traits that their ancestors took millennia to evolve, they do not actually look like their ancestor, and they bear clear traces of their intervening developmental history.

Additionally, in the short term, mutations -- especially negative mutations -- can appear in a population, and then in a few generations can disappear again; just because your great-grandfather had hemophilia, it does not necessarily follow that any of his living descendants do. Dollo's law, insofar as it applies, does not apply on the level of sub-population genetics.

This point is worth emphasizing; many populations have such wide variation in phenotypes that a trait may entirely disappear in a sub-population, but still be in a species' gene pool; a finch population may change beak shape through evolution, but future generations may regain the original shape through breeding with an sub-population that never lost the original shape; likewise, a dog may never evolve back into a wolf, but if a German shepherd breeds with a wolf, their descendants will quickly start to show wolf-like traits that German shepherd had lost.

However, the general statement holds: once a species evolves into a new species, the chances of it ever evolving back into a member of the original species is so extraordinarily low that we may as well treat it as impossible.

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