SCIENCE · INVESTIGATE AND EXPLAIN

Interpret a cooperation condition without treating it as a universal rule

Cooperative behavior can arise through several mechanisms. A direct mutual benefit differs from a cost to an actor that benefits a relative; repeated interactions and reciprocal effects add further possibilities. Merely observing a benefit to another organism does not identify the evolutionary mechanism.

Learning outcome: Compare relatedness 0, 0.5 and 1 at cost 3, including the equality boundary. Identify the independent demographic or competition evidence needed before applying this comparison to an actual population.

Starting recap

Connect behavioral mechanisms, demographic stages, community interactions and ecosystem budgets while preserving denominators, causal alternatives and external fieldwork gates.

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Try

At r = 0.5 and cost 2, weighted benefit is 3 and difference +1. At r = 0.25 with the same cost, weighted benefit is 1.5 and difference −0.5. Changing relatedness changes the conditional prediction without changing the recipient benefit.

Open the experiment

Predict

Would the same recipient benefit favor the behavior at every relatedness and cost?

Your prediction and reason

Experiment

Compare relatedness 0, 0.5 and 1 at cost 3, including the equality boundary. Identify the independent demographic or competition evidence needed before applying this comparison to an actual population.

Test an inclusive-fitness condition under fixed assumptions

Worked teaching model · synthetic values · Recipient benefit B=6 in the same reproductive-value scale as actor cost C. Simple marginal condition rB−C; relatedness is a population-relative genetic association, not the fraction of all DNA shared. No multiple recipients or local competition correction.

Relatedness coefficient: 0.5 relative coefficient Actor direct reproductive cost: 2 fitness units

Reset keeps your prediction, captures and practice history.

A benefit to another individual must be interpreted with relatedness, cost and population context.

The simple rB>C comparison has declared reproductive-value and marginal-effect assumptions. Direct reciprocity, mutual benefits and local competition are different or additional mechanisms; the sign is not moral value or a universal cooperation law.

Calculated quantities under stated assumptions
Quantity	Value	Unit
Recipient reproductive benefit	6	fitness units
Relatedness-weighted benefit	3	fitness units
Actor reproductive cost	2	fitness units
Marginal inclusive-fitness difference	1	fitness units
Positive simple-condition flag	1	1 yes / 0 no

Retain prior predictions, settings and quantities in the notebook. These are original supplied/calculated comparisons, not physical specimen observations or laboratory participation.

A benefit to another individual must be interpreted with relatedness, cost and population context.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Frame the biological question

2. Connect mechanisms and evidence

The simple marginal comparison uses actor cost C, recipient benefit B and relatedness r, all on compatible reproductive-value assumptions. The condition rB−C greater than zero identifies a positive weighted difference under those assumptions. Relatedness is a genetic association relative to a relevant population reference, not the fraction of all DNA that two organisms share.

Here B is fixed at 6 fitness units. The controls select r from 0 to 1 and cost from 1 to 5. Multiplying benefit by r and subtracting cost keeps the two sides on the stipulated scale. A zero difference is a boundary, not a positive prediction. The supported range omits negative relatedness and more complicated recipient structures.

Local competition can offset benefits, reproductive values can differ, and social effects can be nonlinear or frequency dependent. The simple sign therefore cannot establish the fate of an observed behavior by itself. It is also not a moral judgment, a claim of conscious calculation or a prescription for human social behavior.

3. Reconstruct a worked comparison

4. Predict and investigate

Predict first: Would the same recipient benefit favor the behavior at every relatedness and cost?

Retain the first prediction, controlled settings, complete ledgers and one conflicting or null comparison. These are original supplied calculations, not observed populations or completed fieldwork.

5. Transfer to a changed case

Apply the mechanism to a changed case

For r = 0.75 and cost 5, calculate the weighted benefit and marginal difference.

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

Compare a worked response

Weighted benefit 4.5 and difference −0.5. The simple positive condition is not met. This is conditional on the supplied marginal fitness units and omitted population effects.

6. Defend a conditional conclusion

Separate mechanism, population pattern and causal evidence. Identify a missing biological process and an independent observation that could discriminate alternatives. Preserve first reasoning and substantive human critique in the General Biology II workspace. Use supplied or ethically archived information only; no animal manipulation, habitat intervention or organism release is requested.

Supporting scientific reference, checked 30 October 2026. Original prose, models and packets; no source exercise or figure reproduced. Actual field sampling and independently assessed transfer remain separate evidence gates.

Relatedness and causal assumptions, checked 30 October 2026. The supplied numerical model is original, not an extracted field dataset.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

For r = 0.75 and cost 5, calculate the weighted benefit and marginal difference.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Evaluate a foraging return with search and handling included Next: Reconstruct cohort reproduction with the correct survival denominator

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