First of all, you should distinguish between the fitness of the gene and the fitness of the people. Second, I am using as input the empirical observation that the fitness of the achondroplasia gene is 1⁄4. Third, and tangentially, you should distinguish between the fitness of the children and parents.
(1 gene vs parents) Let us consider the 3 surviving children. Out of the 6 copies of the gene, 4 are wild type and 2 are achondroplasia. But in the parents, half of the genes are achondroplasia. Thus, regardless of how many children the parents have, the fitness of the gene is 2⁄3 the fitness of the parents.
(2) Empirically, 1⁄4 of achondroplasia births are inherited and 3⁄4 are de novo. Assuming equilibrium, the gene is producing 1⁄4 of replacement fertility, so it has a fitness of 1⁄4. If dwarfs only reproduce with non-dwarfs, they, too, have a fitness of 1⁄4. But if they only reproduce with dwarfs, they have a fitness 3⁄2 of the gene, thus 3⁄8.
(3 parents vs children) The 3⁄4 you compute is the reduction in the proportion of pregnancies yield children. This is a kind of infertility, though more emotionally difficult. It is only relevant if the parents are trying to reproduce as fast as possible. In the modern world, parents usually target a small fixed number of children and infertility has little effect. In both farmer and forager societies, children were probably modulated to available food supply. Such a wasted pregnancy does not reduce the number of children by 1, but probably delays future children by a year. If the usual interval is 4, this might reduce fitness by 1⁄4. But the effect is probably significantly smaller. If people are reproducing at the optimal speed, taking into account risk of famine, a small perturbation probably has little effect.
First of all, you should distinguish between the fitness of the gene and the fitness of the people. Second, I am using as input the empirical observation that the fitness of the achondroplasia gene is 1⁄4. Third, and tangentially, you should distinguish between the fitness of the children and parents.
(1 gene vs parents) Let us consider the 3 surviving children. Out of the 6 copies of the gene, 4 are wild type and 2 are achondroplasia. But in the parents, half of the genes are achondroplasia. Thus, regardless of how many children the parents have, the fitness of the gene is 2⁄3 the fitness of the parents.
(2) Empirically, 1⁄4 of achondroplasia births are inherited and 3⁄4 are de novo. Assuming equilibrium, the gene is producing 1⁄4 of replacement fertility, so it has a fitness of 1⁄4. If dwarfs only reproduce with non-dwarfs, they, too, have a fitness of 1⁄4. But if they only reproduce with dwarfs, they have a fitness 3⁄2 of the gene, thus 3⁄8.
(3 parents vs children) The 3⁄4 you compute is the reduction in the proportion of pregnancies yield children. This is a kind of infertility, though more emotionally difficult. It is only relevant if the parents are trying to reproduce as fast as possible. In the modern world, parents usually target a small fixed number of children and infertility has little effect. In both farmer and forager societies, children were probably modulated to available food supply. Such a wasted pregnancy does not reduce the number of children by 1, but probably delays future children by a year. If the usual interval is 4, this might reduce fitness by 1⁄4. But the effect is probably significantly smaller. If people are reproducing at the optimal speed, taking into account risk of famine, a small perturbation probably has little effect.
sorry; point 2 again, (Aa x aa should product a 1⁄2 not a 1⁄4)
acondroplasia X normal
............A.............a
...a.......Aa..........aa
...a......Aa...........aa
50%Aa acondroplasia
50%aa normal
or am I confused somewhere? Is that not the punnet square?
Sure, that’s the punnet square. You should stop drawing punnet squares and ask yourself why you are drawing them and ask what role they play.
The number 1⁄4 is the empirical fitness. It is mainly about how many children dwarfs have. You cannot guess that number by looking at punnet squares.