Test whether migration and selection can be swapped

1. Orient: Test whether migration and selection can be swapped

Gene flow moves inherited variants between populations when migrants or their gametes contribute to reproduction. Movement alone is not necessarily genetic contribution. A mixture model must define whether migrants replace residents, add to them or contribute only a fraction of the next generation.

2. Explain the population mechanism

The supplied haploid model replaces fraction m of a resident population at p=0.2 with donor material at pD=0.8. The resulting frequency is M(p)=(1−m)p+mpD. Selection then applies relative reproductive weight w to A and1 to a, producing S(p)=wp/[wp+(1−p)]. The denominator makes selection nonlinear in p.

Compare S(M(p)) with M(S(p)). In the first sequence, incoming variants undergo the supplied selection stage. In the second, migrants arrive after that stage. Identical parameter labels do not imply identical causal histories. At zero migration or no selective difference the two sequences coincide, but those are special boundaries.

An endpoint comparison cannot establish the actual stage order. Marked cohort arrival, reproductive timing and independent contribution records would be needed. These are conceptual evidence requirements, not instructions to introduce organisms or manipulate a population. Donor composition is held fixed and donor demography is omitted.

3. Work a complete evidence calculation

For m=0.2,w=2, migration first gives p=0.32 and selection then0.64/1.32=16/33≈0.48485. Selection first gives1/3; migration then0.8/3+0.16=32/75≈0.42667. The different endpoints reflect different stage histories.

4. Predict and investigate

Predict first: If both pathways use the same migration fraction and fitness ratio, must they predict the same endpoint?

Compare both stage orders at m0.2,w2, then set m0 or w1. Identify the algebraic reason for the equality at each boundary and an observation that could discriminate the stage order in a real life cycle.

Retain the original population definition, first prediction, controls and full numerical ledger, including conflicting or null results. These are original bounded teaching calculations, not measured populations.

5. Transfer and explain

Apply the mechanism to a changed case

Use m=0.25,w=2 with resident0.2 and donor0.8. Calculate both stage orders.

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

Compare a worked response

Migration then selection: mixture0.35, selected0.70/1.35=14/27≈0.51852. Selection then migration:0.75×1/3+0.25×0.8=0.45. Migration adds variants at a different stage in the two causal descriptions.

6. Reflect and retain evidence

State a competing mechanism, an observation that would distinguish it, and a limitation of the supplied sampling or life-cycle model. Preserve first reasoning and a criterion-linked human review in the General Biology II workspace. Public practice feedback and simulated evidence do not certify an independently demonstrated comparative argument, field investigation or practical skill.

Supporting scientific reference, checked 30 October 2026. All prose, numerical packets and diagrams are original. No organism collection, culture, breeding, release, personal genetic inference or clinical procedure is requested.