In haplodiploid organisms, males are haploid and females are diploid. Consider the relatedness diagram shown below. Female A has a full-sister, Y, who has a daughter, B. The relatedness between A and B is ___________. (Rounded off to three decimal places)
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For two-species diet problems, set up a linear system (coefficients are counts of animals). Align coefficients to eliminate one variable, solve, and verify in the other equation to catch arithmetic slips.
Step 1: State transmission rules under haplodiploidy.
\(\bullet\) A haploid father contributes \emph{all} his genome to each daughter \(\Rightarrow\) \(r(\text{father}\!\to\!\text{daughter})=1\).
\(\bullet\) A diploid mother contributes a random half to each offspring \(\Rightarrow\) \(r(\text{mother}\!\to\!\text{offspring})=\tfrac12\).
\(\bullet\) By symmetry, the probability that two offspring share the same maternal allele at a locus is \(\tfrac12\).
Step 2: Recall full-sister relatedness in haplodiploids.
Two full sisters (same father and mother) share:
\(\circ\) \textit{Paternal set}: identical (from haploid father) \(\Rightarrow\) contribution \(1\times\tfrac12 = 0.5\) (the factor \(\tfrac12\) weights the paternal genome in each sister).
\(\circ\) \textit{Maternal set}: expected half in common \(\Rightarrow\) \( \tfrac12 \times \tfrac12 = 0.25\).
Total \(r_{\text{sisters}} = 0.5 + 0.25 = 0.75\).
Step 3: Chain relatedness from A to B through Y (aunt \(\to\) niece).
A \(\xrightarrow{\,0.75\,}\) Y (full sisters), and Y \(\xrightarrow{\,0.5\,}\) B (mother to daughter).
Multiply along the path (path method):
\[
r_{A,B} \;=\; r_{A,Y}\times r_{Y,B} \;=\; 0.75 \times 0.5 \;=\; 0.375.
\]
Step 4: Sanity check via allele-tracking.
Pick a random locus in A. Probability it is shared with Y is \(0.75\); conditional on sharing with Y, the chance Y transmits that allele to B is \(0.5\). Product \(0.75\times0.5=0.375\) \(\Rightarrow\) consistent.
Final Answer:\;
\[
\boxed{0.375}
\]
