Final answer:
The program used to compare two sequences to determine their similarity is BLAST (basic local alignment search tool), used in sequence alignments to construct phylogenetic trees.
Step-by-step explanation:
The mathematical program that allows two sequences to be compared with each other to determine the degree of similarity between them is known as BLAST (basic local alignment search tool). Using BLAST, scientists can perform a sequence alignment, which is the arrangement of proteins, DNA, or RNA sequences to identify similar regions that may indicate conservation of function or structure. These alignments are essential in constructing phylogenetic trees and understanding evolutionary relationships among various species. The process helped revolutionize our understanding of phylogeny by confirming some morphological studies and rearranging others based on molecular information.
Sequence homology derived from these comparisons can estimate the evolutionary distance between DNA sequences and reflect how long it's been since those genes diverged from a common ancestor. This method is more effective than just using morphological data for determining phylogenic relationships.