Tract Length and Cline Shape Are Separately Encoded Signatures in Subdivided Populations

Question: How do spatial population structure and migration-selection balance shape the genomic signatures of adaptive introgression, such as ancestry tract length and allele frequency clines, in subdivided populations?

Answer

Across the retrieved papers, the consistent position is that spatial structure breaks the tight coupling between the two canonical signatures of adaptive introgression: allele frequency tracks the local migration-selection-drift equilibrium, while introgressed tract length tracks recombination time along the path the allele has travelled, and these two clocks only agree when an unconditionally advantageous allele is spreading as a wave through space. Le Goff et al. make this explicit by showing that under local adaptation allele frequency depends on the local balance between selection and migration, which generally destroys the frequency–tract-length relationship that holds during wave spread [1]. The corollary, supported by the modelling literature here, is that subdivision adds signatures with no panmictic counterpart — distance-from-source gradients in introgressed ancestry proportion, cline steepness set by an effective migration rate shared among barrier loci, and a strong dependence of equilibrium polymorphism on habitat geometry rather than on mean migration alone. The practical implication is that a single low-frequency introgressed allele in a subdivided system is genuinely ambiguous unless tract structure, spatial position, and cline shape are read jointly.

Tract length and allele frequency are driven by different clocks, and subdivision is what decouples them

During the spread of a globally advantageous introgressed allele, tracts are progressively eroded by recombination with the recipient background, so that tract length, like allele frequency, reflects the distance the wave has travelled [1]. Ancestry tract structure has an independent and well-behaved demographic expectation: the number of ancestry switches per segment is predicted analytically from recombination rate, ancestry heterozygosity, and effective population size, and these predictions match forward simulations and empirical African American data without invoking selection [10]. Tract-based inference is nonetheless confounded by linked selection in ways that mimic introgression age: background selection introduces a systematic upward bias in apparent tract lengths, and selective sweeps produce an asymmetric distortion of the length distribution around the selected site whose directional signal dissipates quickly while the local reduction in effective size persists [12]. In structured populations these linked effects are attenuated by gene flow, with FST and genealogical topologies remaining close to neutral expectations under migration while diversity and coalescence times stay robust [13], so the tract-length signal is least contaminated exactly where migration is high.

The frequency–tract-length correlation is the diagnostic that distinguishes a spreading wave from local adaptation

Le Goff et al. frame the ambiguity precisely: in a subdivided population a low-frequency adaptive allele may be the leading edge of a travelling wave or may simply sit in a subpopulation where the introgressed allele is locally selected against, and simulations predict a positive frequency–tract-length correlation in the first case and no correlation in the second [1]. Applying this to Ciona intestinalis with haplotagging-based phased genomes and local ancestry, they found no relationship between adaptive allele frequency and introgressed tract length, supporting local adaptation rather than an ongoing wave [1]. The signature of a genuine wave is that the ancestry increase is initially genome-wide because of linkage disequilibrium and only later becomes heterogeneous: in threespine stickleback, all chromosomes showed large increases in immigrant ancestry in the first generations after a discrete immigration event, with genomic variation in introgression extent emerging over a decade [2].

Where selection is local, cline shape is governed by habitat geometry rather than by mean migration rate

Under local adaptation the relevant equilibrium is a selection–migration–drift balance, and this balance is far more sensitive to spatial and temporal structure than a single migration parameter implies. In a three-habitat multilocus model, persistence of polymorphism is characterised by Ns, Nm, and the ratio of favourable to unfavourable habitat size, with the polymorphic range widening as gene flow decreases and habitat symmetry increases, and drift substantially lowering the critical migration threshold [7]. Environmental spatial autocorrelation strongly promotes maintenance of locally adaptive alleles in two-dimensional landscapes [14]. Temporal organisation matters independently of the mean: holding the time-averaged migration rate fixed in a two-deme Moran model with heterogeneous selection, periodic migration drives the population toward neutrality, most strongly for out-of-phase seasonal migration, and the response to period is non-monotonic, so populations with identical mean migration rates can reach different evolutionary outcomes [5]. Empirically, local adaptation in maize and teosinte operates at an intermediate geographic scale—larger than individual populations but smaller than the species range—with selective sweeps shared among populations most often via migration [8].

Barrier loci steepen clines through a shared effective migration rate, coupling ancestry clines genome-wide

Cline steepness at introgressed loci is not locus-autonomous: an effective migration rate encapsulating the effects of all other selected loci predicts allele frequencies at barrier loci and neutral coalescence times along the genome, and this approximation remains accurate across a broad parameter range in mainland-island models [15]. The same effective-migration framing relates divergence at individual trait loci to measurable fitness components of migrants and early-generation hybrids and clarifies how tipping points arise, including how assortative mating shifts the critical migration level beyond which divergence collapses [9]. Genome-wide cline scans in Antirrhinum hybrid zones confirm the predicted clustering: most steep clines fall in seven genomic regions, only four of which were recovered by pairwise FST scans, and one region shows a cline approaching fixation on one side of the zone while remaining polymorphic on the other [16]. Where divergence is highly polygenic, however, this clustering gives way to genomically widespread and moderate peaks of both differentiation and introgression rather than discrete islands of divergence [18].

Subdivision superimposes a distance-from-source gradient in ancestry proportion that tract length does not record

Spatial position adds a signature orthogonal to tract length. In a Plateau Fence Lizard hybrid zone, introgression proportions of hybrid populations are correlated with geographic distance from the parental populations, a pattern repeated with admixture proportions and hybrid index values, alongside asymmetric migration biased toward the northern end and cline analyses indicating a slow northward shift of the zone centre [6]. Simulations of post-admixture range expansions show that the mean genomic proportion of introgressed DNA forms a cline that increases with distance from the population expansion source until reaching the hybrid zone boundary and persists over time, and comparison with Eurasian paleogenomic data supports a prolonged Neanderthal admixture pulse extending far beyond the Levant [19]. Comparable spatial dependence appears within species pairs: in Mimulus, genomic patterns of hybrid ancestry are correlated across population groups, with correlations highest between geographically proximal populations, indicating that introgression is not locally constrained but spreads via migration across the landscape [4]. Replicated damselfly hybrid zones add that demographic history explains geographic heterogeneity in which loci are introgressed while chromosome architecture—steeper X-linked clines—imposes consistent constraints [17].

Conflicts and gaps

The central inference rule is weaker than it appears. "No frequency–tract-length correlation" is consistent with local adaptation, but also with an old wave whose tract signal has been erased, and the Ciona test rests on a two-scenario dichotomy between a travelling wave and local adaptation rather than on a fitted spatial model [1]. The measurement itself is the weak link: at low divergence, no local ancestry method exceeds 0.575 accuracy, and the most per-site-accurate method produces 78.8 times too many tracts, implying an admixture time 61.2 times too old—precisely the within-species divergence regime where subdivided adaptive introgression is studied [11]. Background-selection bias in apparent tract lengths compounds this and is not addressed by the two-scenario design [12]. The role of selection in structuring ancestry across space is directly contested: Farnitano et al. find that ancestry variation is probably not driven by simple linked selection against hybrid ancestry and that known reproductive-isolation loci are poor predictors, with selection highly polygenic and its architecture varying across space [4]—in tension with the clustered barrier model [15] and with cline-scan results [16]. Whether polygenic barriers yield clustered or widespread differentiation peaks therefore remains unresolved [18]. Finally, no retrieved paper derives joint analytical predictions for cline shape and tract-length distribution within one explicit spatial model; the components—effective migration rates [15], tract-length expectations [10], and spatial polymorphism thresholds [7]—exist separately but are not integrated.

What would change the answer

The decisive test is a joint forward-simulation and inference study over an explicit spatial model (stepping-stone and continuous-space), generating local ancestry and identity-by-descent tracts under matched global versus local selection, and asking which combinations of frequency, tract length, distance-from-source, and cline steepness are jointly identifiable—the effective-migration machinery of Zwaenepoel provides a natural analytic backbone for such a comparison [15]. Temporal sampling would break the wave-versus-equilibrium degeneracy directly: serially sampled genomes analysed with time-lagged F2 statistics, which recover directional migration rates from metapopulation time series [3], or the ancient-DNA approach that localises hybrid zones from clines in introgressed proportion [19], would show whether ancestry is still moving. Empirically, replicated transects with haplotype-resolved local ancestry [1] spanning a known connectivity gradient, combined with tract-length bias corrections for background selection [12], and systems with an observable time zero such as the stickleback immigration event [2], would supply the parameter contrasts that current designs lack.

References

[1] Le Goff, M., Cerqueira, F., Penaud, B., Gagnaire, P.-A., Viard, F., Bierne, N.. "Adaptive introgression in subdivided populations leaves distinct genomic footprints under global and local selection: a case study in Ciona intestinalis". bioRxiv. 2026-10-19T00:00:00.000Z. URL: https://doi.org/10.64898/2026.09.29.754965

[2] Flanagan, B. A., Padhiar, A., Peng, F., Quraishi, S., Roth-Monzon, A. J., Gilani, F., Simonse, L., Maciejewski, M. F., Reid, N., Malinsky, M., Hund, A. K., Bolnick, D. I.. "Rapid genome-wide introgression reveals fitness advantage of immigrant genotypes". bioRxiv. 2025-08-28T00:00:00.000Z. URL: https://doi.org/10.1101/2025.08.27.672692

[3] Isacchini, G., Okada, T., Schmid, C., Popli, D. R., Peter, B. M., Schiffels, S., Hallatschek, O.. "Inferring Migration Networks with Time-Lagged F2 Statistics". bioRxiv. 2026-03-12T00:00:00.000Z. URL: https://doi.org/10.64898/2026.03.12.710875

[4] Farnitano, M. C., Sotola, V. A., Sweigart, A. L.. "On the causes of correlated genomic ancestry across contrasting hybridization histories in a monkeyflower species pair.". bioRxiv. 2026-04-04T00:00:00.000Z. URL: https://doi.org/10.64898/2026.04.02.716215

[5] Mohammad Amin Masoumi, Kamran Kaveh, Mohammad Reza Ejtehadi. "Effects of Periodic Migration on Selection in Subdivided Populations". arxiv. 2026-10-07T00:00:00.000Z. URL: https://arxiv.org/abs/2610.0816

[6] Leache, A., Davis, H. R., Singhal, S.. "Hybrid zone analysis using coalescent-based estimates of introgression and migration". bioRxiv. 2025-01-25T00:00:00.000Z. URL: https://doi.org/10.1101/2025.01.21.634130

[7] Olusanya, O., Barton, N. H., Polechova, J.. "Local adaptation in a metapopulation - a multi-habitat perspective". bioRxiv. 2025-05-07T00:00:00.000Z. URL: https://doi.org/10.1101/2025.05.03.652039

[8] Tittes, S., Lorant, A., McGinty, S., Holland, J. B., Sanchez-Gonzalez, J. d. J., Seetharam, A. S., Tenaillon, M. I., Ross-Ibarra, J.. "Not so local: the population genetics of convergent adaptation in maize and teosinte.". bioRxiv. 2024-12-03T00:00:00.000Z. URL: https://doi.org/10.1101/2021.09.09.459637

[9] Surendranadh, P., Sachdeva, H.. "Effect of assortative mating and sexual selection on polygenic barriers to gene flow". bioRxiv. 2025-01-05T00:00:00.000Z. URL: https://doi.org/10.1101/2024.07.30.605898

[10] Nataneli, S., Karatas, A. L., Ferrari, T., Patel, R. A., Mooney, J. A.. "Analytical expectations for ancestry junction accumulation in admixed genomes". bioRxiv. 2026-02-17T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.28.685223

[11] Tian, Q.. "What limits local ancestry inference at low divergence: a feasibility threshold, a metric that conceals failure, and a deficit of input more than architecture". bioRxiv. 2026-08-03T00:00:00.000Z. URL: https://doi.org/10.64898/2026.07.30.741148

[12] Enrique Santiago. "From IBD tracts to runs of homozygosity: a unified coalescent framework including selection". arxiv. 2026-07-14T00:00:00.000Z. URL: https://arxiv.org/abs/2605.03498

[13] Lesturgie, P., Blanckaert, A., Sousa, V. C.. "The Joint Impact of Deleterious Mutations, Dominance, and Gene Flow on Linked Neutral Variation in Structured Populations". bioRxiv. 2026-05-16T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.15.724312

[14] Sakamoto, T., Yeaman, S.. "Maintenance of polymorphism in spatially heterogeneous environments". bioRxiv. 2025-04-29T00:00:00.000Z. URL: https://doi.org/10.1101/2025.04.25.650679

[15] Zwaenepoel, A.. "Predicting barrier architecture and the genomic landscape of differentiation under polygenic divergent selection". bioRxiv. 2026-09-07T00:00:00.000Z. URL: https://doi.org/10.64898/2026.09.03.749118

[16] Field, D. L., Stankowski, S., Reiter, T., Polechova, J., Bradley, D., Richardson, D., Pal, A., Shipilina, D., Boell, L., Pickup, M., Xue, Y., Coen, E., Barton, N. H.. "Genome-wide cline analysis identifies new locus contributing to a barrier to gene flow across an Antirrhinum hybrid zone". bioRxiv. 2025-02-20T00:00:00.000Z. URL: https://doi.org/10.1101/2025.02.17.638607

[17] Stand-Perez, M., Arce Valdes, L. R., Ordaz-Morales, J. E., Swaegers, J., Chavez-Rios, J. R., Gutierrez-Rodriguez, C., Ibarra-Laclette, E., Hansson, B., Baena-Diaz, F., Sanchez-Guillen, R. A.. "From divergence to contact: demographic history and genomic context shape introgression across independent damselfly hybrid zones". bioRxiv. 2026-04-10T00:00:00.000Z. URL: https://doi.org/10.64898/2026.04.09.717498

[18] Harencar, J. G., Uckele, K., Kay, K. M.. "Divergent habitat selection across many loci maintains species boundaries during introgression". bioRxiv. 2026-07-27T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.28.728564

[19] Di Santo, L. N., Quilodran, C. S., Cerrito, P., Currat, M.. "Tracing the Neanderthal-Modern Human hybrid zone using paleogenomic data". bioRxiv. 2026-01-06T00:00:00.000Z. URL: https://doi.org/10.64898/2026.01.06.697899

How this survey was made

This survey answers one question: “How do spatial population structure and migration-selection balance shape the genomic signatures of adaptive introgression, such as ancestry tract length and allele frequency clines, in subdivided populations?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 19 papers whose work this text draws on, chosen from the 101 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 21, 2026 and covered work from the previous two years.