Clines with partial panmixia in an environmental pocket

Area of Science:

• Population genetics
• Evolutionary biology
• Mathematical modeling

Background:

• Geographically structured populations exhibit complex dynamics.
• Clines, representing allele frequency gradients, are shaped by migration and selection.
• Panmixia, or random mating, is a key factor influencing population structure.

Purpose of the Study:

• To investigate the impact of partial panmixia on allele frequency clines.
• To determine conditions for cline maintenance in a spatially heterogeneous environment.
• To analyze the influence of environmental dimensionality and selection strength.

Main Methods:

• Mathematical modeling of allele frequency dynamics.
• Analysis of asymptotically stable equilibria for single-locus clines.
• Derivation of critical parameters for cline maintenance.

Main Results:

• A cline is maintained only if the scaled panmictic rate (β) is less than 1 and the pocket radius exceeds a critical value (an).
• The critical radius (an) increases with the ratio of selection coefficients (-α), panmictic rate (β), and dimensionality (n).
• Explicit formulas for critical radii were derived for specific dimensionalities (n=1, 3).

Conclusions:

• Partial panmixia can prevent the fixation of favored alleles in localized environments.
• Clines are more difficult to maintain in higher dimensional spaces or with stronger selection.
• The study provides quantitative insights into the interplay of migration, selection, and spatial structure.