Drift, Gene Flow and Competing Explanations

Buri kept 16 fruit flies as the parents of every generation, in 107 separate bottles, and within 19 generations many of those bottles had ended up with only one of the two alleles they started with. No one chose which allele won in which bottle. This lesson is about that kind of change, chance change, and about the movement of genes between populations, and about how you decide whether a pattern you see came from chance, from gene flow or from selection.

The idea: sampling error in a finite population

Think of an election poll. Ask 20 people and the result can be far from the true vote; ask 2,000 and it will be close. Nobody biased the small poll. It was just small.

Each generation of a population is a poll of the previous one. The gene copies that make up the offspring are a sample of the parents’ copies, and some parents leave more offspring than others by luck. Genetic drift is the change in allele frequency that comes from this random sampling of parents. It needs no difference in fitness, where fitness means the relative number of surviving offspring an individual leaves in a given environment. Drift acts on neutral, beneficial and harmful alleles alike, so it can carry a harmful allele up or a beneficial one to loss, especially when the population is small.

The standard model of drift is the Wright-Fisher model: a closed population of N diploid individuals, constant in size, with non-overlapping generations, random mating, no selection, no mutation and no migration. Each generation’s 2N gene copies are drawn at random from the parents’ pool. If the model’s assumptions hold, it predicts:

expected next frequency = p variance of next frequency = p(1 - p) / 2N

So drift has no direction on average, and its scatter shrinks as the population grows. Given long enough, one allele fixes, and for a neutral allele the model predicts the chance that it is the one to fix equals its current frequency. A neutral allele at 0.60 is lost 40% of the time. Population genetics in the Genetics course works through the algebra; here you need what it predicts and how to test it.

Real populations break the assumptions. Some parents leave many offspring and others none, the sex ratio is uneven, and the size swings from year to year. Each of these makes drift stronger than the census suggests. Biologists therefore describe drift with the effective population size (Ne): the size of an idealized Wright-Fisher population that would drift at the same rate as the real one. Ne is usually below the census size N.

Two short episodes of small size get their own names. A bottleneck is a sharp drop in numbers that leaves a chance sample of the original gene pool. A founder effect occurs when a new population starts from a few individuals who carry an unrepresentative sample of their source population’s variation.

Worked problem. These numbers are illustrative. A neutral allele has frequency 0.60 in a resident population and 0.20 among immigrants. After migration, immigrants make up m = 0.10 of the breeding pool. The next generation is 100 diploid offspring, formed by randomly sampling 200 gene copies, with no selection, no mutation and no further migration during sampling.

1. Migration. The mixed frequency is a weighted average: p = 0.90 x 0.60 + 0.10 x 0.20 = 0.54 + 0.02 = 0.56. Gene flow shifted the frequency by 0.56 - 0.60 = -0.04, and that shift is deterministic: it would happen the same way every time.
2. Expected outcome of drift. The expected number of copies in the offspring is 200 x 0.56 = 112, so the expected frequency is 112 / 200 = 0.56. Drift adds no push in either direction.
3. Scatter from drift. The variance is 0.56 x 0.44 / 200 = 0.2464 / 200 = 0.001232. The standard deviation is the square root, 0.035, about 3.5 percentage points. Repeat this generation many times and most outcomes fall within a few points of 0.56.
4. A smaller population. With 10 offspring (20 copies), the standard deviation is the square root of 0.2464 / 20 = 0.01232, which is 0.111, about 11 points. Ten times fewer parents gives about three times the scatter (the square root of 10 is 3.16).

The lesson of the numbers: migration moves the mean, drift spreads the outcomes around it, and the spread depends on Ne, not on how many animals you can count.

Immigrants in the breeding pool, m 0.10

Offspring number N (diploid, so 2N gene copies)

10 25 50 100 200

Resample

Expected from the rules, beside observed in this run of 500 resamples

	Expected	Observed
Mean offspring frequency
Standard deviation
Copies of the allele out of 2N

In this sketch: one generation; neutral Wright-Fisher, with 2N gene copies drawn at random from the mixed pool; no selection, no mutation, no further migration during sampling; resident 0.60 and immigrant 0.20 are the lesson’s illustrative numbers. m (0 to 0.5) and N (10 to 200) are free settings here; the lesson works m = 0.10 with N = 100 and N = 10. 500 resamples is this sketch’s choice; the lesson says “many times”.

Migration moves the mean, deterministically; drift spreads the outcomes around it, in neither direction, and the spread shrinks as the number of gene copies grows. This is a sketch of the logic, not a prediction for a real population.

Buri’s 107 fly lines: drift as a distribution

Peter Buri, publishing in 1956, ran a large version of a laboratory design that Warwick Kerr and Sewall Wright had introduced in 1954, using Drosophila melanogaster. He used two alleles at the brown eye-colour locus, started every line at a frequency of 0.5, and each generation picked 16 flies as the parents of the next. His first series had 107 lines, carried for 19 generations.

The key is replication. Any one line wanders up or down, and you cannot tell from it alone whether something pushed it. Across 107 lines, the distribution of frequencies spread out from 0.5 toward 0 and 1, with more and more lines fixed or lost, while the frequency pooled over all lines showed no systematic change. That pairing, spread without a shift in the mean, is the drift prediction.

Buri also asked what Ne would produce the spread he saw. For the first series the mean estimate was 9.0, not 16. The usual reading is that the flies in a bottle did not contribute equally to the next generation, so chance acted on fewer effective parents than were in the bottle.

Founders and frontiers: anoles on islands, bacteria on agar

Founder effects in nature are usually reconstructed after the fact. Jason Kolbe, Jonathan Losos and colleagues made them happen. They released one randomly drawn male-female pair of brown anoles, Anolis sagrei, from a single source island onto each of seven small islands in the Bahamas, where the vegetation was narrower than on the source. Their 2012 report in Science found two things together. Genetic and morphological differences that tracked the founding pairs persisted throughout the experiment. And all the populations evolved shorter hindlimbs, the direction predicted for lizards on narrow perches. Founder history and adaptive change acted in the same populations at once, and the design let the authors see each against the other. Founder effects alone are not a cause of new species, and this experiment did not test that.

A large population is not safe from drift either. Oskar Hallatschek and colleagues (2007, PNAS) mixed two Escherichia coli strains that differed only in a fluorescent label and let the colony spread across agar. It broke into single-colour sectors. Only a thin band of pioneer cells at the edge founds each new stretch of colony, and random fluctuations in that band, not the mass of cells behind it, decided which colour got carried outward. Range expansion is a run of founder events.

Gene flow: swamping or rescue

Gene flow is the movement of alleles between populations by individuals or gametes, pollen included. It pulls the populations’ frequencies toward each other, as step 1 of the worked problem showed. Whether that helps or harms depends on what the incoming alleles do in the new place.

It can harm. Migration load is a drop in a population’s mean fitness caused by immigrant alleles that suit somewhere else. Timema cristinae walking-sticks live on two host plants, and colour morphs differ in how well they are camouflaged on each. Daniel Bolnick and Patrik Nosil (2007, Evolution) compared 25 natural populations and found that those receiving more immigrants from the other host were more poorly matched, and that more poorly matched populations showed stronger selection within a generation. This is a comparison across populations, a correlation that fits the migration-load prediction rather than a manipulation of migration.

It can also help. Sarah Fitzpatrick and colleagues (2020, Current Biology) studied gene flow into two small, isolated guppy populations in the Caigual and Taylor streams of Trinidad after fish from a different source were introduced upstream. Following the onset of gene flow, both recipient populations grew nearly tenfold. On average, hybrids lived longer and reproduced more than residents or immigrants, and alleles putatively associated with local adaptation were not entirely swamped. This is genetic rescue: an increase in a small population’s fitness or growth after new alleles arrive. In the Houston Ship Channel and Galveston Bay region of Texas, Gulf killifish in polluted water carry tolerance-associated variants that Oziolor and colleagues (2019, Science) inferred had entered by introgression from Atlantic killifish, followed by strong selection. Introgression is the movement of alleles from one species into another through hybridization. Gene flow is neither good nor bad in general; each of these results belongs to its system.

Two explanations for one pattern

Suppose one allele is common on an island and rare on the mainland. Selection predicts that the change is repeatable: replicate populations in the same environment shift the same way, and carriers outperform non-carriers when fitness is measured directly. Drift predicts that replicates scatter in both directions, with a mean that stays at the starting frequency, and that carriers do no better in a fitness assay. Gene flow predicts frequencies that track the amount and source of immigration.

The tools that separate them are the ones you have met: replicates, so that a mean can be compared with scatter (Buri, Kolbe); a neutral null, a model of what chance alone would produce (Wright-Fisher, or a colony model); and an independent fitness assay that does not rely on the pattern itself. Often the answer is both, as with the anoles. The earlier lessons on testing an evolutionary explanation and selection in ecological context use the same logic.

Design problem

In expanding bacterial colonies, one fluorescent strain forms large sectors. Is it fitter, or did it get lucky at the frontier? Design the experiment.

One way to do it

Grow many replicate colonies from the same starting mix, say 20 colonies at 50:50. The neutral expectation, which Weinstein and colleagues (2017, PLOS Computational Biology) used, is that the mean fraction across replicates stays at the starting fraction while individual colonies scatter widely. Large sectors in a few colonies are what drift produces; a consistent shift in the mean fraction across replicates, beyond what a neutral model calibrated to your colonies allows, is evidence of selection.

Then remove two confounds. Swap the fluorescent labels between the strains and repeat, so that any cost of carrying a particular marker shows up. And measure each strain’s expansion speed growing alone, as an independent fitness assay that does not depend on the sector pattern.

Finally, keep the scope. Fitness on agar during expansion may differ from fitness in a well-mixed liquid culture: Weinstein and colleagues found that the ranking of their strains changed between the two. A strain that wins on a plate has been shown to win on a plate.