×

The genetical bandwidth mapping: a spatial and graphical representation of population genetic structure based on the Wombling method. (English) Zbl 1124.92031

Summary: Characterizing the spatial variation of allele frequencies in a population has a wide range of applications in population genetics. This article introduces a new nonparametric method, which provides a two-dimensional representation of a structural parameter, called the genetical bandwidth, which describes genetic structures around arbitrary spatial locations in a study area. This parameter corresponds to the shortest distance to areas of significant allele variation, and its computation is based on W. Womble’s systemic function [Differential systematics. Science 28, 315–322 (1951)]. A simulation study and application to data sets taken from the literature give evidence that the method is particularly demonstrative when the fine-scale structure is stronger than the large-scale structure, and that it is generally able to locate genetic boundaries or clines precisely.

MSC:

92D10 Genetics and epigenetics
92D15 Problems related to evolution

Software:

STRUCTURE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Balloux, F., EASYPOP (version1.7): a computer program for the simulation of population genetics, J. Hered., 92, 301-302 (2001)
[2] Bamshad, M. J.; Wooding, S.; Watkins, W. S.; Ostler, C. T.; Batzer, M. A.; Jorde, L. B., Human population genetic structure and inference of group membership, Am. J. Hum. Genet., 72, 578-589 (2003)
[3] Barbujani, G., Geographic patterns: how to identify them and why?, Hum. Biol., 72, 133-153 (2000)
[4] Barbujani, G.; Oden, N. L.; Sokal, R., Detecting regions of abrupt change in maps of biological variables, Syst. Zool., 38, 376-389 (1989)
[5] Berry, A.; Kreitman, M., Molecular analysis of an allozyme cline: alcohol deshydrogenase in Drosophila melanogaster on the East Coast of North America, Genetics, 134, 869-893 (1993)
[6] Bocquet-Appel, J. P.; Bacro, J. N., Generalized Wombling, Syst. Biol., 43, 442-448 (1994)
[7] Cann, H. M.; de Tomas, C.; Cazes, L., A human genome diversity cell line panel, Science, 296, 261-262 (2002)
[8] Csillag, F.; Kabos, S., Wavelets, boundaries and the spatial analysis of landscape patterns, Ecoscience, 9, 177-190 (2002)
[9] Fagan, W. F.; Fortin, M.-J.; Soykan, C., Integrating edge detection and dynamic modelling in quantitative analysis of ecological boundaries, Bioscience, 53, 730-783 (2003)
[10] Fan, J.; Gijbels, I., Local Polynomial Modelling and its Applications (1996), Chapman & Hall: Chapman & Hall London · Zbl 0873.62037
[11] Fortin, M.-J., Edge detection algorithms for two-dimensional ecological data, Ecology, 75, 956-965 (1994)
[12] Fortin, M.-J.; Dale, M., Spatial Analysis. A Guide for Ecologist (2005), Cambridge University Press: Cambridge University Press Cambridge
[13] Fortin, M.-J.; Olson, R. J.; Ferson, S.; Iverson, L.; Hunsaker, C.; Edwards, G.; Levine, D.; Butera, K.; Klemas, V., Issues related to the detection of boundaries, Landscape Ecol., 15, 453-466 (2000)
[14] François, O.; Ancelet, S.; Guillot, G., Bayesian clustering using hidden markov random fields in spatial population genetics, Genetics, 174, 805-816 (2006)
[15] Jacquez, G.; Maruca, S.; Fortin, M.-J., From fields to objects: a review of geographic boundary analysis, J. Geogr. Syst., 2, 221-241 (2000)
[16] Kayser, M.; Lao, O.; Anslinger, K.; Augustin, C.; Bargel, G.; Edelmann, J.; Elias, S.; Heinrich, M.; Henke, J.; Henke, L., Significant genetic differentiation between Poland and Germany follows present-day political borders, as revealed by Y-chromosome analysis, Hum. Genet., 117, 428-443 (2005)
[17] Klopfstein, S.; Currat, M.; Excoffier, L., The fate of mutations surfing on the wave of a range expansion, Mol. Biol. Evol., 23, 482-490 (2006)
[18] Malécot, G., The Mathematics of Heredity (1968), Freeman & Company: Freeman & Company New York (USA)
[19] Manel, S.; Schwartz, M.; Luikart, G.; Taberlet, P., Landscape genetics: combining landscape ecology and population genetics, Trends Ecol. Evol., 18, 157-206 (2003)
[20] Manel, S.; Bellemain, E.; Swenson, J.; François, O., Assumed and inferred spatial structure of populations: the Scandinavian brown bears revisited, Mol. Ecol., 13, 1327-1331 (2004)
[21] Mantel, N., The detection of disease clustering and a generalised regression approach, Cancer Res., 27, 173-220 (1967)
[22] Marjanovic, D.; Fornarino, S.; Montagna, S.; Primorac, D.; Hadziselimovic, R.; Vidovic, S.; Pojskic, N.; Battaglia, V.; Achilli, A.; Drobnic, K., The peopling of modern Bosnia-Herzegovina: Y-chromosome haplogroups in the three main ethnic groups, Ann. Hum. Genet., 69, 757-763 (2005)
[23] Monmonier, M., Maximum-difference barriers: an alternative numerical regionalization method, Geogr. Anal., 3, 245-261 (1973)
[24] Moran, P. A., Notes on continuous stochastic phenomena, Biometrika, 37, 17-23 (1950) · Zbl 0041.45702
[25] Pritchard, J. K.; Stephens, M.; Donnelly, P., Inference of population structure using multilocus genotype data, Genetics, 155, 945-959 (2000)
[26] R Installation and Administration (2006), R Foundation for Statistical Computing: R Foundation for Statistical Computing Vienna, Austria
[27] Ramachandran, S.; Rosenberg, N.; Zhivotovsky, L.; Feldman, M., Robustness of the inference of human population structure: a comparison of X-chromosomal and autosomal microsatellites, Hum. Genomics, 1, 87-97 (2004)
[28] Rosenberg, N. A.; Pritchard, J. K.; Weber, J. L.; Cann, H. M.; Kidd, K. K.; Zhivotovsky, L. A.; Feldman, M. W., Genetic structure of human populations, Science, 298, 2381-2385 (2002)
[29] Rosenberg, N.; Saurabh, S.; Ramachandran, S.; Zhao, C.; Pritchard, J.; Feldman, M. W., Clines, clusters, and the effect of study design on the influence of human population structure, PLoS Genet., 1, 660-671 (2005)
[30] Rousset, F., Genetic Structure and Selection in Subdivided Populations (2004), Princeton University Press: Princeton University Press Princeton, NJ, USA
[31] Serre, D.; Pääbo, S., Evidence for gradients of human genetic diversity within and among continents, Genome Res., 14, 1679-1685 (2004)
[32] Silvermann, B. W., Density Estimation for Statistics and Data Analysis (1986), Chapman & Hall: Chapman & Hall New York
[33] Sokal, R.; Oden, N., Spatial autocorrelation in biology. I-Methodology, Biol. J. Linn. Soc., 10, 199-228 (1978)
[34] Weir, B. S.; Cockerham, C. C., Estimating \(F\)-statistics for the analysis of population structure, Evolution, 38, 1358-1370 (1984)
[35] Womble, W., Differential systematics, Science, 28, 315-322 (1951)
[36] Wright, S., Isolation by distance, Genetics, 28, 114-138 (1943)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.