Final answer:
Cladistics is the analysis focusing on the sequence of derived character emergence in organisms, using homologous traits and the principle of maximum parsimony to construct phylogenetic trees, reflecting evolutionary relationships.
Step-by-step explanation:
The type of analysis that focuses on the order in which derived characters appeared in organisms is cladistics. Cladistics involves organizing organisms into clades, which are groups that descended from a single ancestor. This method pays particular attention to homologous traits, which indicate shared evolutionary history. Using cladistics, scientists apply the concept of maximum parsimony to determine the simplest and most probable evolutionary pathway. This pathway is one with the fewest major divergences but is well supported by the available evidence.
In practice, phylogenetic trees are constructed to visualize these relationships and the emergence of derived traits relative to ancestral ones. The relative appearance of these traits helps scientists to understand the sequence of evolutionary events. Hence, when reconstructing a phylogeny for organisms based on characteristics such as their circulatory system traits, those with the most primitive features would appear towards the base of the tree, while derived features would place an organism higher on the tree.