Movement changes allele frequencies when migrants contribute genes to the recipient population.
By the end: Calculate a mixing step and distinguish organism movement, reproductive gene flow, and horizontal transfer.
Let residents have A frequency 0.2 and the immigrant source frequency 0.8. If immigrants supply one quarter of gene copies to the newly mixed population, its frequency is three quarters times 0.2 plus one quarter times 0.8, or 0.35. The weights refer to genetic contribution, not necessarily the fraction of visitors.
Movement only creates gene flow when genetic material enters the population’s reproductive history. A bird passing through without breeding does not by that fact change the local breeding gene pool. Migrants can also have different reproductive success after arrival, so arrival counts alone may not give their contribution.
Gene flow concerns genetic material entering a population's reproductive history. Movement is one possible route, not the quantity being averaged. A pollen grain can carry alleles between stationary plant populations if it contributes to fertilization. An animal can travel across the same boundary without contributing any genes. Defining the recipient population therefore requires a reproductive and temporal context. Counts of organisms present at a site, counts of breeding adults, and counts of copies in their descendants can describe different mixtures.
Consider an invented diploid population with eighty resident breeders and twenty immigrant breeders. Suppose each group contributes the same expected number of copies per breeder to the offspring pool. At one autosomal locus, the resident contribution is proportional to 160 parental copies and the immigrant contribution to forty. Immigrants then supply one fifth of the genetic input. This inference needs equal contribution per breeder. It would fail if the migrants did not breed, arrived after reproduction, or had different reproductive success.
Now change only their contribution. Suppose each immigrant breeder supplies twice the expected genetic contribution of each resident. Resident weight is eighty times one, or eighty contribution units. Immigrant weight is twenty times two, or forty units. The immigrant share becomes forty divided by 120, or one third, even though only one fifth of the observed breeders are immigrants. These contribution units measure expected input, not literal offspring counts. Unequal success must be included before normalizing the two sources.
| Group | Breeders | Input per breeder | Total input units |
|---|---|---|---|
| Residents | 80 | 1 | 80 |
| Immigrants | 20 | 2 | 40 |
| Combined | 100 | Not uniform | 120 |
If residents have A frequency 20% and the immigrant source has 80%, that one-third input produces a new frequency of 40%. The resident term is two thirds times 0.2, about 0.1333. The immigrant term is one third times 0.8, about 0.2667. Their sum is 0.4. No allele has changed its sequence in this calculation. A becomes more common locally because copies already present elsewhere contribute to the recipient pool. Local appearance is not the same as mutational origin.
The same arithmetic can describe an actual standardized pool of three hundred contributed copies. Two hundred resident-derived copies at 20% A supply forty A copies. One hundred immigrant-derived copies at 80% A supply eighty. Together they supply 120 A copies out of three hundred, or 40%. This example counts gene copies, not 120 carriers. In a diploid offspring population, the carrier fraction would also depend on how A copies pair with one another and with a copies.
| Origin | Contributed copies | A frequency | A copies |
|---|---|---|---|
| Resident | 200 | 20% | 40 |
| Immigrant | 100 | 80% | 80 |
| Combined | 300 | 40% | 120 |
That distinction prevents another inference error. Even after measuring the A frequency exactly, we cannot infer the fraction expressing a phenotype without a genotype-to-phenotype model. Dominance, environmental effects, and other loci may matter. Nor does an increased A frequency establish a fitness benefit in the recipient environment. It can arise entirely through input from a source where A was already common. The mixture identifies the bookkeeping of contributions; additional evidence is needed to explain reproductive differences or trait consequences.
Migration often makes connected populations more similar at loci that differ between them. It can introduce useful variation, restore an allele lost by drift, or continually bring alleles favored elsewhere but costly in the recipient environment. The resulting frequency depends on migration, selection, drift, and their life-cycle order.
There is no universal rule that migration improves or harms a population. A variant’s effects, ecological conditions, and genetic associations matter. The mixing lab holds source and resident frequencies fixed for one step; it is not a model of long-term migration-selection balance or demographic growth.
Let the immigrant share be one quarter, as in the original worked example. Residents retain three quarters of the weight. Their A frequency of 0.2 contributes 0.15 to the final frequency, while the source frequency of 0.8 contributes 0.20. Adding gives 0.35. The increase over the resident value is 0.15, or fifteen percentage points. It is a 75% relative increase because 0.15 divided by 0.2 equals 0.75. Those two descriptions use different denominators and should not be substituted for each other.
Subtracting the original resident frequency gives a useful general rule. The frequency change equals the immigrant share multiplied by the source-minus-resident frequency difference. Here one quarter of the 0.6 difference is 0.15. This also explains the direction without calculation. Input raises A when its source frequency exceeds the resident frequency, lowers A when the source frequency is smaller, and leaves A unchanged when the frequencies match. No judgment about whether A is beneficial is required for any of these predictions.
Because the weights are nonnegative and sum to one, a mixture must lie between its two source frequencies. At zero immigrant input the result equals the resident frequency. At complete immigrant input it equals the source frequency. If an alleged two-source mixture produced 90% A from sources at 20% and 80%, something beyond that mixture happened or a measurement is wrong. Selection after mixing, a third source, or incorrect contribution weights could explain the discrepancy. The arithmetic supplies a check on the proposed explanation.
Repeated input requires updating the recipient, unlike the one-step lab. As a paper example, hold the source at 80% A and the immigrant share at one quarter each generation. Starting at 20%, the first mixture is 35%. The second is three quarters times 0.35 plus one quarter times 0.8, giving 46.25%. The third gives 54.6875%. The source does not change in this imagined reservoir model. Each generation closes one quarter of the remaining gap, so equal input does not mean equal percentage-point changes.
This repeated-input result depends on the source remaining fixed and on excluding other mechanisms. If the source is small enough that emigration changes it, both populations need tracking. If selection in the recipient opposes A, the trajectory need not approach the source frequency. If drift is strong, the realized changes can fluctuate around deterministic predictions. The one-step weighted average still describes the input stage when its inputs are known, but it does not by itself describe the full reproductive cycle.
| Step | Recipient A frequency | Gap below 80% source |
|---|---|---|
| Initial | 20% | 60 percentage points |
| First mixture | 35% | 45 percentage points |
| Second mixture | 46.25% | 33.75 percentage points |
| Third mixture | 54.6875% | 25.3125 percentage points |
Gene flow can therefore reduce an existing difference without eliminating all differences everywhere. Consider two environments in which different inherited variants have higher reproductive contribution. Exchange tends to mix their copies; local selection can continually favor different subsets after arrival. Whether divergence persists depends on the strengths and timing of those processes. A claim that movement necessarily erases local adaptation ignores selection, while a claim that locally favorable alleles necessarily exclude immigrants ignores recurring input. Neither conclusion follows from the mixture alone.
The resident contribution is 75%; the immigrant contribution is 25%. Each source's A frequency is held fixed for this step.
New A frequency: 35%. Resident weight 75%; immigrant weight 25%.
| Contribution | Weight | A frequency | Weighted A |
|---|---|---|---|
| Resident | 0.75 | 0.2 | 0.15 |
| Immigrant | 0.25 | 0.8 | 0.20 |
| Mixture | 1 | 0.35 |
In the migration lab, each source panel is standardized to one hundred gene copies. The resident panel always shows twenty A copies and eighty a copies; the source panel always shows eighty A and twenty a. These panels describe frequencies, not actual population sizes. They do not imply that the source and recipient contain equal numbers of organisms. The control specifies what fraction of the resulting contribution pool comes from the source, independently of the standardized panel sizes.
Choose no gene flow and inspect all three panels. The source remains different from the residents, but the resulting pool matches the residents. Physical existence of a nearby source does not change the recipient unless copies contribute. Now choose quarter immigrant input. In a standardized result of one hundred copies, seventy-five contributions are resident-derived and twenty-five are source-derived. Their expected A counts are fifteen and twenty respectively, giving thirty-five A copies. The panel represents this exact constructed mixture rather than a randomly sampled migrant group.
Before selecting half immigrant input, predict both allele counts. Fifty resident-derived contributions supply ten A and forty a copies. Fifty source-derived contributions supply forty A and ten a. The total is fifty of each type. The result is halfway between the source frequencies because the contribution weights are equal, not because each source population contains the same number of organisms. Changing the slider updates the weights immediately. It does not move identifiable individuals between panels or show births occurring through time.
Try an immigrant share of 5% using the slider. The new A frequency is 0.95 times 0.2 plus 0.05 times 0.8, giving 0.23. Each additional five percentage points of immigrant input increases the output by three percentage points, because 0.05 times the fixed source difference of 0.6 equals 0.03. This linear relationship applies across the slider because both source frequencies remain fixed. It is different from the shrinking changes in the repeated-generation example, where the resident frequency changes between steps.
A second paper calculation asks how much input would produce 50% A from these sources. The needed increase above the residents is 0.3, and the entire available source difference is 0.6. Dividing 0.3 by 0.6 gives an immigrant share of one half. Check that answer against the half-input preset. An output of 90% would require a share above one and is therefore impossible in this two-source model. Solving backward can expose a mistaken interpretation of a measured mixture.
| Target A frequency | Required immigrant share | Possible from 20% and 80% sources? |
|---|---|---|
| 23% | 0.03/0.60 = 5% | Yes |
| 50% | 0.30/0.60 = 50% | Yes |
| 90% | 0.70/0.60 ≈ 116.67% | No |
Do not treat exact displayed counts as predictions of unavoidable biological outcomes. If twenty-five immigrant copies were randomly drawn from a large source at 80% A, their A count could differ from twenty. Offspring sampling could introduce further variation. The lab intentionally omits that randomness to isolate weighted averaging. It also omits population growth and selection after arrival. Use its simultaneous pools to check which source supplies each contribution, then decide whether a real case needs additional sampling or life-cycle stages.
Ordinary gene flow among sexually reproducing populations often follows interbreeding. Introgression is transfer of genetic material between differentiated lineages through hybridization and subsequent breeding. Horizontal gene transfer can move DNA without that pattern of whole-organism ancestry.
These processes can make different genomic regions tell different histories. A gene’s presence does not always mean all of an organism’s ancestry followed the same route. To infer exchange, scientists compare multiple loci, population samples, and competing explanations rather than treating a single similarity as conclusive.
The order of mixing and selection can change the outcome even when each mechanism has the same stated strength. Consider a constructed haploid recipient starting at 20% A, a source at 80%, and a one-quarter immigrant share. In the recipient environment, suppose A has twice the expected reproductive contribution of a. If mixing occurs first, A reaches 35%. Selection then gives A weight 0.35 times two, or 0.70, against a weight 0.65. Normalizing gives 0.70 divided by 1.35, about 51.85% A.
Reverse the order while keeping the source frequency fixed. Selection first changes the resident pool from 20% A to 0.4 divided by 1.2, or one third A. Mixing that selected resident pool with one quarter source input gives three quarters times one third plus one quarter times 0.8, or 45% A. The difference arises because immigrants experience the recipient selection stage in the first sequence but enter after it in the second. These are explicit paper models, not additional settings in the lab.
| Order | Intermediate A frequency | Final A frequency |
|---|---|---|
| Mix, then select | 0.75 × 0.2 + 0.25 × 0.8 = 0.35 | 0.70/1.35 ≈ 51.85% |
| Select residents, then mix | 0.40/1.20 = 1/3 | 0.75 × 1/3 + 0.25 × 0.8 = 45% |
In both sequences, the assigned advantage belongs to a specified environment and reproductive stage. It is not an intrinsic superiority of immigrant or resident ancestry. If A were costly in the recipient, selection could instead reduce its frequency after input. If visitors changed food availability without leaving descendants, they might change selection while producing no gene flow themselves. Movement can have ecological effects and genetic effects, but evidence for one does not automatically establish the other. Follow actual genetic contribution when naming the mechanism.
Introgression also requires following descendants rather than stopping at a first encounter. A hybrid can inherit copies from two differentiated lineages. If its descendants breed with one parental lineage, some copies from the other lineage can persist in that population. At a focal locus, a hybrid carrying Aa crossed with aa gives half Aa and half aa offspring under ordinary Mendelian segregation and equal viability. The A copy can cross the lineage boundary even though much of the descendant genome comes from repeated breeding with the recipient lineage.
Horizontal transfer is a different route. A lineage can acquire a segment of DNA without receiving half its genome through hybrid reproduction. Consequently, the history of that segment need not match the ancestry inferred from most other loci. A shared allele alone cannot identify the route: it might reflect recent exchange, an ancestral variant retained by both populations, or independent sequence changes. Multiple genomic regions and their surrounding sequence context help compare those explanations. A single similarity does not demonstrate whole-organism migration or establish a complete ancestry history.
For a new observation, ask separately where the allele originated, how it entered the recipient, and why its descendants increased afterward. Mutation can explain origin, gene flow or transfer can explain arrival, and selection or drift can explain subsequent frequency changes. None of those stages requires organisms to anticipate an environmental need. Local usefulness now also does not establish why the variant first evolved elsewhere. A defensible account specifies the population boundary, contribution denominator, life-cycle order, and evidence that distinguishes inherited history from a proposed adaptive explanation.
Residents have A frequency 0.8; immigrants have 0.2 and supply 10% of the new gene pool. Find the mixture.
Keep the weights tied to their source populations.
| Contribution | Weighted A |
|---|---|
| Residents | 0.72 |
| Immigrants | 0.02 |
| Total | 0.74 |
The result is 0.9 × 0.8 + 0.1 × 0.2 = 0.74. Migration reduces A frequency here. With no other processes, the mixture must lie between the two source frequencies.
Twenty percent of animals observed at a site are migrants, but none reproduce there. Does the local offspring generation necessarily receive 20% of its genes from them?
Observation and reproductive contribution have different denominators.
| Measurement | What it counts |
|---|---|
| Visitors at a site | Observed organisms |
| Migration parameter in the model | Fraction of contributed gene copies |
| Given no contribution | Parameter is zero |
No. Under the stated absence of reproduction or other genetic transfer, those visitors contribute no genes to local offspring. Their presence might alter ecology and thus selection, but that is a separate mechanism. The mixing parameter must describe actual genetic contribution.
The explanations and exercises are complete without these optional links. The references cover inheritance, population mechanisms, and evidence for ancestry. Source annotations distinguish textbook explanations, secondary history, and a primary paper whose bibliographic identity alone was checked. The examples are constructed teaching models, not empirical estimates or professional decision advice.
Drift, gene flow, and other contributors to population change. The labs isolate mechanisms rather than estimate real populations.
Reproductive barriers, geographic separation, and polyploidy. Species concepts have different domains of applicability.