Step 1: Understanding the Concept: Pedigree analysis is a tool used to track the inheritance pattern of a specific genetic trait through generations in a family.
Step 2: Key Formula or Approach: Analyze the inheritance from affected parents to their offspring to deduce if the trait is dominant or recessive, and whether it is autosomal or sex-linked.
Step 3: Detailed Explanation:
Looking at the chart, in the first generation, both the father and the mother are affected (shaded).
They have some children who are completely unaffected (unshaded).
This is the hallmark of a dominant trait. If the trait were recessive, both affected parents would have the genotype "aa", meaning they could only produce "aa" (affected) children. Since they produce unaffected offspring, both parents must be heterozygous carriers of a dominant trait (Aa $\times$ Aa), capable of producing "aa" (unaffected) children.
Next, we determine if it is autosomal or sex-linked.
If it were an X-linked dominant trait, an affected father ($X^{A}Y$) would pass his affected $X$ chromosome to ALL his daughters, making them 100% affected.
However, the chart clearly shows the affected father has an unaffected daughter. This explicitly rules out X-linked dominant inheritance.
Therefore, the inheritance pattern must be Autosomal dominant.
Step 4: Final Answer: The correct identification is Autosomal dominant.