The beak size variation of Galapagos finches is continuous variation. When a large enough number of genes influence a character, it will have a continuous, normal frequency distribution. despite the fact that the small number of genes on a large number of loci are controlling the character or vice versa.
We consider the case with a large number of loci and smaller genes for quantitative analysis. Quantitative genetics is concerned with
characters influenced by many genes, called polygenic characters. hundreds of genes are controlling the character. The pattern of inheritance, at the genetic level, is too complex. The value of a character, like a beak size, will usually also be influenced by the environment. Beak size is probably related to general body size and all characters to do with bodily stature will be influenced by the amount of food an organism happens to find during its life.
The behavior of same genotype individuals in two different environmental conditions:
Take identical genotype individuals to grow one in abundant food supply and the other is less. The first one will end up larger on average. Any pattern of discrete variation in the genotype frequency distribution is likely to be obscured by environmental effects and the discrete categories converted into a smooth curve.