Source-linked AI summary
Directional genetic differentiation and asymmetric migration
Lisa Sundqvist, Kevin Keenan, Martin Zackrisson, Paulo Prodöhl, David Kleinhans
TL;DR
Asymmetric gene flow is common, but conventional differentiation measures assume symmetry and complex alternatives are computationally demanding. The paper introduces a simpler method that derives directional differentiation from a hypothetical migrant pool and converts it into relative migration. Simulations show high-confidence detection when migration is present, with best performance at intermediate migration and reduced detection at high migration.
Problem
Conventional genetic differentiation measures assume symmetric gene flow, although asymmetric migration is common and important for interpreting genetic diversity and population management.
Method
The method compares populations with a hypothetical migrant pool, applies genetic differentiation measures, and uses the directional values to estimate relative migration and asymmetry.
Results
The method detected simulated gene-flow patterns with high confidence when migration was present, performed best at m = 0.005, and failed to detect patterns sufficiently often at m = 0.05.
Takeaways & Limitations
Directional differentiation and relative migration can support investigation of asymmetric gene flow, source-sink dynamics, and conservation or management decisions.
Takeaways & Limitations
The approach is influenced by historical demography and is developed under idealized conditions excluding recent common ancestry, unequal population sizes, and nonequilibrium populations.
Abstract
from arXiv · showhide
Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly used to gather this information. One potential caveat is that these measures assume gene flow to be symmetric. However, asymmetric gene flow is common in nature, especially in systems driven by physical processes such as wind or water currents. Since information about levels of asymmetric gene flow among populations is essential for the correct interpretation of the distribution of contemporary genetic diversity within species, this should not be overlooked. To obtain information on asymmetric migration patterns from genetic data, complex models based on maximum likelihood or Bayesian approaches generally need to be employed, often at great computational cost. Here, a new simpler and more efficient approach for understanding gene flow patterns is presented. This approach allows the estimation of directional components of genetic divergence between pairs of populations at low computational effort, using any of the classical or modern measures of genetic differentiation. These directional measures of genetic differentiation can further be used to calculate directional relative migration and to detect asymmetries in gene flow patterns. This can be done in a user-friendly web application called divMigrate-online introduced in this paper. Using simulated data sets with known gene flow regimes, we demonstrate that the method is capable of resolving complex migration patterns under a range of study designs.
1 Introduction
Genetic differentiation measures commonly infer population structure and migration but generally assume symmetric gene flow, despite asymmetric migration being common and consequential. The paper introduces a simpler approach that uses directional differentiation to estimate relative migration and detect asymmetries.
- Standard differentiation measures infer population structure and migration from allele-frequency data but assume migration is equal in all directions.
- Asymmetric migration commonly arises from wind, water currents, habitat-quality gradients, and density-dependent competition.
- Source-sink dynamics can skew differentiation, causing sink populations to appear unusually unique and potentially misdirecting conservation decisions.
- Estimating directional migration is important for interpreting evolutionary processes, identifying source populations, and improving conservation and management decisions.
- Existing asymmetric-migration analyses typically use computationally intensive maximum-likelihood or Bayesian models with many jointly estimated parameters.
- The proposed method compares each population with a hypothetical migrant pool, converts directional differentiation into relative migration, and supports applications such as source-sink identification and barrier testing.
2 Theory
The theory constructs directional differentiation by comparing populations with a shared hypothetical migrant pool derived from their allele frequencies. Standard differentiation measures are then used to estimate directional relative migration, with an idealized example recovering the expected asymmetry.
- The framework represents allele frequencies in an N × P matrix, where each element gives an allele’s frequency in a population.
- The hypothetical migrant pool is symmetric between populations and contains only alleles present at nonzero frequency in both populations.
- The selected pool function uses α1 = γ1 = 1/2 and K = 1, producing normalized geometrical means of corresponding allele frequencies.
- Directional differentiation compares each population with the shared migrant pool using standard measures such as Gst and D.
- In the idealized A → B example, Gst(b, f(a, b)) = 0.15 and D(b, f(a, b)) = 0.42, indicating lower potential migration from B to A than from A to B.
- The theoretical development considers idealized conditions and excludes recent common ancestry, unequal population sizes, and nonequilibrium populations.
- Directional relative migration is stored in matrix C, normalized from zero to one, and its elements estimate migration from population i to population j.
3 Simulations
Simulations evaluated directional migration detection across gene-flow regimes, migration rates, sample sizes, and numbers of loci. The method performed best at medium migration, detected symmetric flow without systematic asymmetry, and was less reliable at high migration.
- Simulation design: The simulations covered unidirectional, symmetric bidirectional, and asymmetric bidirectional gene flow across 180 scenarios with 1000 replicates each.Sample sizes and numbers of loci ranged from 10 to 100; evaluations varied one while fixing the other at 50.
- Unidirectional gene flow: At medium migration (m = 0.005), the correct direction exceeded 95% for both D and Gst with sample size 20 or more.With increasing loci, performance exceeded 95% at 40 loci for D and 20 loci for Gst; Gst reached 100% at 60 or more loci.
- Low migration: At low migration (m = 0.00025), D remained below 75% across sample sizes, whereas Gst reached 90% with 40 samples and 95% with 80 loci.For loci-based evaluations, D reached 90% at 70 loci, while Gst reached 90% at 50 loci and 95% at 80 loci.
- High migration: At high migration (m = 0.05), correct-direction estimates approached at most 75% only under the largest tested sample sizes and numbers of loci.Increasing sample size had its strongest effect between 10 and 30 samples.
- Symmetric bidirectional gene flow: Under symmetric bidirectional gene flow, estimates remained close to the expected 50% and did not systematically indicate asymmetry.Relative migration calculated from Gst was slightly more variable than migration calculated from D.
4 Program
divMigrate-online makes the directional migration method accessible through a web application with statistical testing, network visualization, and filtering. Simulated and Atlantic salmon examples illustrate how the software represents and evaluates gene-flow patterns, including an empirical founder-effect caveat.
- Software: divMigrate-online provides a web interface for estimating directional gene flow, visualizing population networks, and testing asymmetric links.The application analyzes simulated data and published Atlantic salmon microsatellite data.
- Visualization: Network graphics represent populations as nodes connected by reciprocal gene-flow components whose visual properties encode relative gene-flow strength.Only statistically significant asymmetric links can be plotted, and low values can be filtered for clearer visualization.
- Statistical testing: The statistical procedure bootstraps the data, estimates allele frequencies and user-selected differentiation measures, and compares directional 95% confidence intervals.Non-overlapping intervals designate significantly different directional gene-flow components.
- Simulated example: In the circular stepping-stone simulation, the application displayed additional migration directions because alleles could move indirectly through intermediate populations.Bootstrap confidence intervals were used to show only directions statistically higher than their reciprocal alternatives.
- Empirical example: In the Atlantic salmon example, no significant asymmetry occurred among landlocked populations, while all showed asymmetric gene flow toward the anadromous population.The authors suggest a strong recent founder effect may produce this apparent asymmetry because source populations can retain more private alleles.
- Access and flexibility: The application is browser-accessible and can also run locally in R, with source code freely available online.Specialized batch analyses are additionally supported through the divMigrate function in the diveRsity R package.
5 Discussion
The method detected asymmetric gene-flow patterns in simulations, especially at intermediate migration, but performance weakened when high gene flow homogenized populations. Its practical use is bounded by assumptions about population structure, demography, sampling, and allele-frequency data.
- Simulation performance: High migration (m = 0.05) prevented sufficiently reliable detection across all tested sample-size and locus combinations, likely because Fst ≈0.005 obscured directional signals.The authors attribute this to the homogenizing effect of high gene flow and note improved prospects with larger samples and more loci.
- Simulation performance: Intermediate migration (m = 0.005) produced the method’s best performance in detecting simulated gene-flow directions.
- Choice of differentiation measure: Relative migration calculated from Gst performed slightly better than estimates calculated from D in the simulations.The authors relate this result to guidelines recommending Gst under the simulation conditions and report similar performance for NmAlcala.
- divMigrate-online: Network plots cluster similar population samples, but their use for directional calculations requires populations to be predetermined and complements rather than replaces quantitative clustering methods.The filter threshold is useful for visualization, although its application is subjective and should be reported explicitly.
- Scope and assumptions: Directional relative migration can be difficult to interpret when historical demography, uneven population sizes, nonequilibrium conditions, or ghost populations influence genetic composition.The discussion specifically identifies founder effects, recent common ancestry, and small populations as important interpretive boundaries.
- Sampling and allele frequencies: Sampling effects can underestimate low-frequency alleles, potentially inflating migration estimates when rare or private alleles indicate absent gene flow.Because the method estimates relative migration, the authors argue that comparable underestimation across populations partly addresses this issue.
- Overall contribution: Compared with complex maximum-likelihood or Bayesian approaches, the method offers a simpler alternative for detecting asymmetric migration from allele-frequency data.The authors frame it as a lower-complexity complement to existing approaches rather than a replacement for all quantitative analyses.
8 Figures and tables
The figures evaluate directional migration accuracy across migration regimes and study designs, then visualize directional relative migration from simulated and empirical populations.
- Unidirectional migration: Figures 1 and 2 assess percent correct migration directions under unidirectional migration while varying sample size or number of loci.D and Gst are compared across high, medium, and low gene-flow conditions, with the other design variable fixed at 50.
- Bidirectional symmetric migration: Figures 3 and 4 assess directional estimates under symmetric migration across sample sizes and locus numbers, where 50% is the expected value.Both figures compare D and Gst while holding the other design variable at 50.
- Bidirectional asymmetric migration: Figures 5 and 6 assess percent correct directions under bidirectional asymmetric migration while varying sample size or number of loci.D and Gst are evaluated across high, medium, and low gene-flow conditions, with the other design variable fixed at 50.
- Directional relative migration: Figure 7 visualizes directional relative migration in a simulated circular stepping-stone model using calculated values, statistically asymmetric directions, and a 0.5 filter threshold.Panel b retains statistically higher directions, while panel c filters asymmetric values above 0.5.
- Directional relative migration: Figure 8 presents directional relative migration for populations A–G, then includes anadromous salmon and separately displays migration identified as asymmetric.The panels use a 0.35 filter for populations A–G and no filter for the anadromous-salmon and asymmetric-migration views.
- Thought experiment: Table 1 presents the allelic matrix for a two-population thought experiment with directional gene flow from population A to population B.The table is identified as the allelic matrix A for populations A and B.
9 Appendix
The appendix figures test directional-estimation accuracy under unidirectional, symmetric, and asymmetric migration across sample sizes, locus numbers, and gene-flow levels.
- Unidirectional migration: Figure A1 evaluates unidirectional migration accuracy as sample size and number of loci increase using NmAlcala.High, medium, and low gene flow are tested, with the non-varying design variable fixed at 50.
- Bidirectional symmetric migration: Figure A2 evaluates NmAlcala under bidirectional symmetric migration across sample sizes and locus numbers, with 50% as the expected value.The non-varying design variable is fixed at 50 for each analysis.
- Bidirectional asymmetric migration: Figure A3 evaluates NmAlcala under bidirectional asymmetric migration across sample sizes and locus numbers.High, medium, and low gene flow are tested while the non-varying design variable is fixed at 50.