Wesołowski T. 1999. Reduction of phallus in birds - an avian way to safe sex? Journal of Avian Biology 30: 483-485.

In contrast to other organisms with internal fertilization, males of the majority of birds do not posses a copulatory organ. Causes of this loss of phallus are not well understood. Copulations in birds are very short, indicating selection for fast transfer of sperm. I propose here that the loss of phallus is mainly a by-product of selection for rapid copulations, and present two hypotheses to explain this loss: (1)
Predation Avoidance - During copulation birds temporarily lose ability to fly, which strongly reduces their ability to escape predator attacks. Insemination with the phallus cannot be accomplished in a few seconds. Therefore, the reduction of phallus would result in acceleration of sperm transfer and shortening of the period of exposure to an elevated predation risk. (2) Copulation Efficiency. In most birds, the copulating male stands on the female's back in a very unstable position. A faster sperm transfer because of the loss of a phallus would result in fewer interrupted copulations due to loss of balance as well as in reduced risk of the female being injured if the male loses balance.