Kin Selection, Relatedness and When Helping Pays · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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When helping family pays

Science · Ecology & Conservation · ages 20-22
Name ______________________   Date ____________
  1. For autosomal allele copies under the lesson's outbred diploid pedigree assumptions, what does expected relatedness r = 1/4 mean?

    • An expected quarter is shared by recent descent.
    • A quarter of behavior is inherited; the rest is learned.
    • A quarter of each benefit returns directly to the helper.
  2. Two full siblings share both parents in a diploid pedigree. Their ancestors are unrelated and non-inbred. Each shared parent gives a two-link path between them. What is their expected relatedness r?

    • 1/4: use one shared-parent path and leave out the other.
    • 1/2: add both shared-parent paths, each contributing 1/4.
    • 2: add the four link factors without multiplying along paths.
  3. Two unrelated individuals take turns removing parasites from each other. Which mechanism could maintain helping through later returns?

    • Kin selection: familiarity raises pedigree relatedness.
    • Kin selection: belonging to one species gives every pair full-sibling relatedness.
    • Reciprocity: later help provides a return benefit to the earlier helper.
  4. In the lesson's additive model, r = 0.5, B = 8 and C = 4 in matching fitness units. Does the claim 'there is no net advantage from helping in this comparison' fit these values?

    • Yes. The weighted benefit equals the cost, giving zero net gain.
    • No. A positive raw benefit is enough to favor helping.
    • No. At equality, the heritable helping trait is selected against.
  5. In the lesson's additive model, r = 0.5, B = 6 and C = 2 in matching fitness units. What is the relatedness-weighted benefit r times B?

    Answer: ______________

  6. A nonreproducing worker helps the queen raise related offspring. What can this add without the worker producing its own offspring?

    • Direct fitness, because the queen's offspring count as the worker's own offspring.
    • Indirect fitness, by helping related offspring survive and reproduce.
    • Pedigree relatedness, because feeding relatives changes their inherited ancestry.
  7. In the lesson's additive model, a recipient has r = 0 and the helper has C > 0. A positive benefit B to this recipient alone makes r times B > C.

    Circle one:   True   False

  8. In the lesson's one-recipient additive model, the same helping act has B = 12 and C = 4 in matching fitness units. Compare a full sibling with r = 0.5 and a recipient assigned r = 0. For which recipient is helping favored, and why?

    • Neither: the direct cost of 4 prevents helping even when the recipient is a full sibling.
    • Both: the benefit of 12 exceeds 4, so relatedness does not change whether helping is favored.
    • Only the full sibling: its weighted benefit is 6, while the other recipient's is 0.
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Answer key

For grown-ups. Fold this page away before handing over the rest.

When helping family pays W1-mt_scVf8G34WI-s1

  1. An expected quarter is shared by recent descent. · The quarter concerns expected sharing by descent from recent common ancestors. It is not a percentage of inherited behavior or a promised return of benefits.
  2. 1/2: add both shared-parent paths, each contributing 1/4. · Each shared-parent path contributes 1/2 times 1/2 = 1/4. Add the two paths: 1/4 + 1/4 = 1/2.
  3. Reciprocity: later help provides a return benefit to the earlier helper. · A later return of help is reciprocity. Familiarity does not raise pedigree relatedness, and members of one species are not all full siblings.
  4. Yes. The weighted benefit equals the cost, giving zero net gain. · 0.5 times 8 = 4, equal to the cost of 4. The net gain is zero. Equality does not satisfy Hamilton's strict inequality.
  5. 3 · The weighted benefit is 0.5 times 6 = 3. The direct cost is used when comparing the weighted benefit with the cost.
  6. Indirect fitness, by helping related offspring survive and reproduce. · Helping related offspring survive and reproduce can add indirect fitness. Whether helping is favored depends on relatedness-weighted reproductive gains and direct fitness costs.
  7. False · With r = 0, the weighted benefit is 0. It cannot exceed a positive direct cost. This does not rule out other explanations of cooperation.
  8. Only the full sibling: its weighted benefit is 6, while the other recipient's is 0. · For the full sibling, 0.5 times 12 = 6 > 4, so helping is favored. For the recipient assigned r = 0, 0 times 12 = 0 < 4, so helping is not favored through this comparison. The benefit and cost stay the same.
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