Infer quartet scores from an explicit original character matrix

1. Orient: Infer quartet scores from an explicit original character matrix

A character matrix records taxa as rows and comparable characters as columns. Missing data, correlated characters and coding choices must remain visible. A tree score is interpretable only when a learner can trace it back to this matrix and the stated model of character change.

2. Explain the evidence and inference model

For an unordered binary character, the Fitch rule combines state sets at internal nodes. If two descendant sets overlap, retain their intersection without adding a change. If they do not overlap, retain the union and add one change. Summing over internal combinations gives the minimum changes for that topology under equal transition costs.

The original core columns, in taxon order A,B,C,D, are1100,1010,1001 and1000. The first three each favor a different quartet split; the last is a singleton and costs one on every split. The controls add copies of two patterns to examine sensitivity. Copied columns are not independent new empirical observations; their purpose is to reveal weighting effects.

Maximum parsimony selects the smallest total under its assumptions, not the tree known to be true. Rapid evolution, unequal rates, repeated gains/losses and insufficient sampling can mislead a simple minimum-change criterion. Other methods model explicit substitution probabilities, but they too depend on data quality and assumptions.

3. Reconstruct a worked example

Core scores are6 for all three splits: each has one favored informative column costing1, two conflicting columns costing2 each, and the singleton costing1. Adding two1100 columns gives AB|CD8, AC|BD10 and AD|BC10.

4. Predict and investigate

Predict first: Does an extra singleton character resolve a tie among these quartet relationships?

Draw each quartet split and reproduce its core score using state-set intersections/unions. Add two1100 columns, then two1010 columns. Keep ties visible and distinguish an added independent measurement from copying an existing column.

Retain the complete matrix, topology, branch lengths or detection assumptions with the first prediction and all conflicting results. These original hypothetical data are not actual specimen observations or measured evolutionary histories.

5. Transfer and defend a changed case

Apply the mechanism to a changed case

Add one1100 and one1010 column to the core. Calculate the three total scores.

Retain your calculation, units and assumptions in the lesson notebook before opening this public practice response.

Compare a worked response

AB|CD=6+1+2=9; AC|BD=6+2+1=9; AD|BC=6+2+2=10. Two equally short trees remain; neither listed order nor a visual rotation breaks the tie.

6. Reflect and preserve uncertainty

Explain which conclusion is conditional on the model, identify an alternative and propose independent discriminating evidence. Use the General Biology II workspace to preserve a first argument, human critique and revision. Public practice and submitted prose do not establish independent phylogenetic, sampling or practical competence.

Supporting scientific reference, checked 30 October 2026. Original prose, numerical packets and diagrams; no source artwork or exercise is reproduced and no organism handling is requested.