Two-locus clines on the real line with a step environment
The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We investigate a two-locus model in which two diallelic, recombining loci are subject to selection caused by an abrupt environmental change. The habitat is one-dimensional and unbounded, selection at each locus is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious. We admit an environmentally independent, intermediate degree of dominance at both loci, including complete dominance. First, we derive an explicit expression for the single-locus cline with dominance, thus generalizing classical results by Haldane (1948). We show that the slope of the cline in the center (at the step) or, equivalently, the width of the cline, is independent of the degree of dominance. Second, under the assumption of strong recombination relative to selection and migration, the first-order approximations of the allele-frequency clines at each of the loci and of the linkage disequilibrium are derived. This may be interpreted as the quasi-linkage-equilibrium approximation of the two-locus cline. Explicit asymptotic expressions for the clines are deduced as $x\to\pm\infty$. For equivalent loci, explicit expressions for the whole clines are derived. The influence of dominance and of linkage on the slope of the cline in the center and on a global measure of steepness are investigated. This global measure reflects the influence of dominance. Finally, the accuracy of the approximations and the dependence of the shape of the two-locus cline on the full range of recombination rates is explored by numerical integration of the underlying system of partial differential equations.
Code (0)
등록된 구현이 없습니다.
Tasks
Numerical IntegrationVocal Bursts Valence PredictionSimilar Papers 제목 키워드 기반
A Geospatial Approach to Predicting Desert Locust Breeding Grounds in Africa
Desert locust swarms present a major threat to agriculture and food security. Addressing this challenge, our study develops an operationally-ready model for predicting locust breeding grounds, which has the potential to …
Earth ObservationLOCUS: A Distribution-Free Loss-Quantile Score for Risk-Aware Predictions
Modern machine learning models can be accurate on average yet still make mistakes that dominate deployment cost. We introduce Locus, a distribution-free wrapper that produces a per-input loss-scale reliability score for …
LOCUS-DT: Localization via Observation-Conditioned Uncertainty Scoring with Digital Twins
Accurate indoor localization is essential for emerging applications in robotic navigation and search and rescue. While classical methods typically focus on single-point estimates, complex indoor environments with heavy b…
A neural model of the locust visual system for detection of object approaches with real-world scenes
In the central nervous systems of animals like pigeons and locusts, neurons were identified which signal objects approaching the animal on a direct collision course. Unraveling the neural circuitry for collision avoidanc…
Collision AvoidanceOn pseudo-absence generation and machine learning for locust breeding ground prediction in Africa
Desert locust outbreaks threaten the food security of a large part of Africa and have affected the livelihoods of millions of people over the years. Machine learning (ML) has been demonstrated as an effective approach to…
regression