This report responds to an assignment prompt requesting a Python implementation to decode the relationship between gene sequences that have undergone random mutations. Each base letter of a gene sequence has a probability of undergoing a mutation, which can take the form of an insertions, deletions or changes of a base letter to another.

The report specifically adresses the following requirements:

1. The implementation of an algorithmic strategy that outputs all Longest Common Subsequences (LCS) between two gene sequences.
2. Generating and studing a matrix of lentgths of LCSs for a given set of gene sequences.
3. The implementation of two strategies, a local and a global one, to reconstructing the genealogy of a given set of sequences.
4. A study of the computational complexity of each approach.
5. A discussion of which approach may be prefered in which situation.
6. An estimation of the probabilities of insertion, deletion and base changes based on the derived genealogical relationship.