Abstract
Characterizing spatial patterns in allele frequencies is fundamental to evolutionary biology because such patterns can inform on underlying processes. However, the spatial scales at which changing selection, gene flow, and drift act are often unknown. Many of these processes can operate inconsistently across space (causing non-stationary patterns). We present a wavelet approach to characterize spatial pattern in genotype that helps solve these problems. We show how our approach can characterize spatial patterns in ancestry at multiple spatial scales, i.e. a multi-locus wavelet genetic dissimilarity. We also develop wavelet tests of spatial differentiation in allele frequency and quantitative trait loci (QTL). With simulation we illustrate these methods under a variety of scenarios. We apply our approach to natural populations of Arabidopsis thaliana and traditional varieties of Sorghum bicolor to characterize population structure and locally-adapted loci across scales. We find, for example, that Arabidopsis flowering time QTL show significantly elevated scaled wavelet variance at ∼ 300 − 1300 km scales. Wavelet transforms of population genetic data offer a flexible way to reveal geographic patterns and underlying processes.
Author summary Biologists can learn about evolutionary processes by studying spatial/geographic changes in the genotype of organisms in nature. However, many previous approaches to measure spatial genetic patterns have been limited by forcing individual samples into bins of discrete size and location, hindering our ability to learn about evolution. Here we present a new continuous approach to spatial genetics that allows us to resolve patterns that change in space and opposing patterns that occur at different spatial scales.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
↵* lasky{at}psu.edu
