Le Monde tells us (in French) that researchers found 47-million-year-old fossils of nine mating pairs of turtles of species Allaeochelys crassesculpta in a lake in Germany. These fossils, which, according to the researchers, are the only fossils of mating pairs of animals to be found, taught the researchers a lot on this extinct species. But what caught my eye is a probabilistic statement made by one of the researchers:
“Des millions d’animaux vivent et meurent chaque année, et nombre d’entre eux se fossilisent par hasard, mais il n’y a vraiment aucune raison que ça arrive lorsque vous êtes en train de vous reproduire. Il est hautement improbable que les deux partenaires meurent en même temps, et les chances que les deux soient fossilisés à la fois sont encore plus maigres”, a expliqué Walter Joyce, de l’université allemande de Tübingen. Avec plusieurs couples, les probabilités s’amoindrissent encore.
Since the name Walter Joyce sounds English speaking, I searched for a version in English. I found this:
“No other vertebrates have ever been found like these, so these are truly exceptional fossils,” Joyce said. “The chances of both partners dying while mating are extremely low, and the chances of both partners being preserved as fossils afterward even lower. These fossils show that the fossil record has the potential to document even the most unlikely event if the conditions are right.”
The difference between the English version and the French version are slight yet important. The French reader learns that it is improbable that a pair of animals will die together while mating, and that it is even less probable that they will be fossilized together. The chances that this will happen to several mating pairs is even smaller. This is true if the death-while-mating+being-fossilized events of the different couples were independent. However, the article itself explains to the readers that here the events are dependent. During the mating process the turtles freeze, and sometimes sink to the bottom of the lake, where the water is poisonous. Thus, in this lake the probability of finding a fossil of a single turtle is less probable than finding the fossil of a mating pair of turtles, and the probability of finding several fossils of mating pairs is not necessarily lower than the probability of finding a single fossil of a mating pair… The English version does not correct this inaccuracy, but it does end with a note that can be interpreted as a correction of previous mistakes: “These fossils show that the fossil record has the potential to document even the most unlikely event if the conditions are right.”
Next week the semester starts, and I will get a new bunch of first-year undergrad students who are eager to study Introduction to Probability. I will ask them to read this article and spot the mistakes. I wonder how many will find what is wrong in this article.