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A single idealized migration step shifts a population allele frequency toward that of the incoming gene pool.
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Formula
p and m are dimensionless fractions from 0 to 1; t denotes a generation
| Symbol | Meaning | Unit |
|---|---|---|
| Allele frequency after migration | fraction | |
| Resident-population allele frequency before migration | fraction | |
| Fraction of the gene pool contributed by migrants in the step | fraction per generation | |
| Allele frequency in the migrant population | fraction |
p_{t+1}=(1-m)p_t+mp_m=p_t+m(p_m-p_t)The mixing balance weights allele frequencies in resident and immigrant gene pools. It assumes random mixing, a constant migrant frequency and no additional selection, mutation or drift in the step. m is the fraction of introduced genes, not necessarily the fraction of visible individuals when reproductive success differs. Repeated migration uses the recurrence step by step; this equation alone does not describe spatial spread or all population-genetic forces.
A migrant gene pool mixes randomly with residents; other evolutionary forces are excluded during the single step.
The post-migration allele frequency is the weighted mean of resident and migrant gene pools.
Migrant frequency
Only meaningful for m>0; p and pm must refer to the same allele.
p=0.40; pm=0.70; m=0.10. Calculate p′ and Δp.
p′=0.43 and Δp=0.03=m(0.70−0.40).
Using m as the fraction of visible individuals rather than the gene pool.
Define m by gene contribution and account for unequal reproduction if it changes those contributions.
Formula cluster
p′ lies between resident p and migrant pm when m lies between zero and one.
Residents have p=0.40, migrants pm=0.70 and m=0.10. Then p′=0.9·0.40+0.1·0.70=0.43. Check: Δp=0.03=m(pm−p)=0.10·0.30; frequency moves toward the migrant value without reaching it immediately.
Quantify gene flow as an evolutionary force in island–mainland and population-mixture models
Here is how to work through a typical Gene Flow and Migration: Allele-Frequency Change (p′ = (1−m)p + m·pm) task step by step:
Task
p=0.40; pm=0.70; m=0.10. Calculate p′ and Δp.
Solution path
p′=0.43 and Δp=0.03=m(0.70−0.40).
how one gene-flow step shifts a population allele frequency. Its output is the mixed frequency p′ after weighting two gene pools.. p′ lies between resident p and migrant pm when m lies between zero and one. The quantity answers a specific biological or statistical question, not automatically the full cause of an observed pattern. Tie it to the population, sample or model level from which inputs came. A number without that reference can be misleading across studies. Keep description separate from explanation: the metric summarizes data but does not by itself establish the underlying mechanism.
Use p is resident, pm migrant and m the gene fraction contributed in the step. The units are frequencies and m are unitless fractions; one generation is the stated time step.. Check that numerator and denominator refer to the same time interval, target population and scale. Proportions entered as percentages usually need conversion to values between zero and one. Write units and definitions beside the observations. This helps catch swapped groups, mismatched age intervals or a wrong denominator before they distort the result. Also document measurement definitions and preprocessing, because studies can operationalize the same symbols differently.
The central assumption is: migrant and resident populations use the same allele definition and mix randomly. additional selection, mutation and drift during the step are negligible. If reproductive advantage, assortative mating or multiple migrant sources alter the weighting., interpretation changes or the formula no longer fits. State sampling, measurement method and biological scale. A model is useful because it simplifies a question, but its limits belong in the report. Do not automatically transfer parameters to different species, populations, laboratories or sampling conditions. Report these assumptions with the result so readers can judge which populations and conditions the conclusion can cover.
In the example, p=0.40, pm=0.70 and m=0.10 give p′=0.43. The check is: Δp=0.03 equals m(pm−p)=0.10·0.30. Substitute calculated values back into the original relation and check whether ranges and units are biologically plausible. Rounded data can create a small discrepancy, but should not change direction or order of magnitude. Also test a simple limiting case, such as zero, complete detection or equal groups. This separates arithmetic errors from model limitations. Round intermediate values only at the end, and check the order of magnitude against the biological question.
A nearby quantity is Hardy–Weinberg equilibrium without evolutionary forces. The substantive distinction is that migration changes p between populations; Hardy–Weinberg describes genotype frequencies at fixed p. Both can appear in the same biological analysis, but they use different inputs and answer different questions. Choose by the requested output and verify the data definition before comparing values. A related name does not imply identical units or interchangeable interpretation. This matters when a descriptive statistic is reported alongside a model parameter. Before comparing values, align definitions, populations, observation periods and analysis rules; otherwise the difference may be methodological.
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Curated exam set for "Gene Flow and Migration: Allele-Frequency Change":
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Which formula describes Gene Flow and Migration: Allele-Frequency Change?
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How do you rearrange Gene Flow and Migration: Allele-Frequency Change for Migrant frequency?
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