Population Genetics and Evolution

Abstract

Darwin recognised the importance of the fact that many individuals of a species are destined to die before reaching reproductive age. He argued that as a consequence every slight modification that chanced to arise and that was advantageous to the individual that possessed it would tend to be preserved, and thus change the characteristics of the species as a whole; he called this evolution by natural selection. This assumes that such slight modifications are passed on through the generations, but how and under what circumstances this occurs was not known in Darwin’s time. The Bohemian monk Gregor Mendel did not publish his experiments on genetics until 1865, six years after The Origin of Species, and their significance was not recognised for decades after that. Yet, as Sigmund states in his delightful book Games of Life, the basics of inheritance could have been deduced a hundred years before Mendel by considering qualitative traits like eye-colour. (The inheritance of a quantitative trait like height tends to be more complex, and so less revealing.) Maupertuis, famous in mathematics for his “principle of least action”, tried to find a solution by studying the occurrence of the rare qualitative trait Polydactyly (“multi-fingeredness”) in a family over several generations. Elisabeth Horstmann of Rostock had six fingers on both hands, and so did her daughter. Four of her daughter’s eight children, among them the famous surgeon Jacob Ruhe of Berlin, had six fingers, and two of his six children also inherited the painful trait. It seemed that there were certain “factors” causing the trait, that were passed on unchanged through the generations, and that a child could inherit these factors from either its father or its mother. Everything is consistent with the hypothesis that each trait is caused by one factor, which comes with equal probability from either parent. The rarity of the trait, although it made it obvious that it was inherited, prevented Maupertuis from obtaining a crucial piece of evidence, that two polydactylous parents may have a five-fingered child (just as two brown-eyed parents may have a blue-eyed child). The trait is in fact determined by two factors, one inherited from each parent. What happens if you inherit different factors from your parents?