Today, in the metro, I have finally understood what is the form of a genotype space.
A genotype space is a representation of all the possible genotypes that can possibly exist, and in which two neighbor points are different only for one single mutation (Hamming distance is 1).
Until now, in the book club slides, I represented it as a matrix:
genotype space represented as a matrix
However, this representation has many flaws… it should be at least a multi-dimensional matrix, since each node should have exactly n neighbors (where n is the length of the genotype), while in a matrix they can have only 4 (or 8 if you count diagonals).
So, a better representation of the genotype space is a graph, like the following:
genotype space represented as a graph
In this graph, the “genotype” of an organism is a chromosome composed by only 5 bases, and in which each base can take only two values. Each node is connected only to the nodes that differ by a single position; for example, “00000″ is connected to “10000″, “01000″, “00100″, “00010″ and “00001″. Thanks to “jts” from Biostar, now I also know that this is an Hamming graph H(5, 2).
Now that we have a representation of the genotype space, we can take any phenotype of our interest, and mark it in the genotype space. For example, imagine that all the genotypes in green correspond to individuals that suffer a congenital disease:
a genotype network. All the green nodes correspond to genotypes that are affected by a congenital disease (for example)
The genotypes in green correspond to what A. Wagner calls “genotype network”, and other authors call “neutral network”. It is a set of genotypes that have the same phenotype, and that are connected by at least one change.
By exploring the topology and structure of a genotype network, we may be able to make some nice observations. For example, how big is the genotype network of a congenital disease, in human populations? Or, how can a population of individuals explore a genotype network?
There are really a lot of questions that come to my mind when looking at these representation. So, it is a good time for me to search on new literature!!
note: I wrote a small python script to generate a Hamming Graph of binary strings. Here it is: https://gist.github.com/1854319