%0 Journal Article %1 christiansen1995genotypic %A Christiansen, Freddy Bugge %A Andreasen, Viggo %A Poulsen, Ebbe Thue %D 1995 %I Springer-Verlag %J Journal of Mathematical Biology %K clines diffusions diploidy heterozygote_disadvantage hybrid_zone %N 3 %P 225-249 %R 10.1007/BF00169562 %T Genotypic proportions in hybrid zones %U http://dx.doi.org/10.1007/BF00169562 %V 33 %X We study a hybrid zone between two populations of a diploid organism. The populations differ at one locus. Homozygotes have equal fitnesses and the heterozygote fitness is reduced by/~ + 6 (/~ is the birth rate deviation and 6 is the death rate deviation). The populations extend along a one dimensional continuous habitat, and migration occurs by diffusion of individuals. The model is formulated as a set of simple continuous time demographic models without age structure for the three genotypes, and the system is transformed into three new variables, the total population size N, the gene frequency p, and the deviation from Hardy-Weinberg proportions F. The gene frequency in a steady state cline always follows a hyperbolic tangent closely. Analysis of the asymptotic behavior of the cline far from the hybrid zone suggests a qualitative prediction of the shape of N, p and F over the zone. For weak selection the shape is determined by a central steepness of ,,/(~ + 6)/4D, as observed by Bazykin in 1969, where D is the diffusion coefficient. For strong selection the cline is less steep than the Bazykin cline, and the form is dominated by the migration process. The steepness at the center of the cline is close to x/-b/4D where b is the birth rate of homozygotes.

@article{christiansen1995genotypic, abstract = {We study a hybrid zone between two populations of a diploid organism. The populations differ at one locus. Homozygotes have equal fitnesses and the heterozygote fitness is reduced by/~ + 6 (/~ is the birth rate deviation and 6 is the death rate deviation). The populations extend along a one dimensional continuous habitat, and migration occurs by diffusion of individuals. The model is formulated as a set of simple continuous time demographic models without age structure for the three genotypes, and the system is transformed into three new variables, the total population size N, the gene frequency p, and the deviation from Hardy-Weinberg proportions F. The gene frequency in a steady state cline always follows a hyperbolic tangent closely. Analysis of the asymptotic behavior of the cline far from the hybrid zone suggests a qualitative prediction of the shape of N, p and F over the zone. For weak selection the shape is determined by a central steepness of ,,/(~ + 6)/4D, as observed by Bazykin in 1969, where D is the diffusion coefficient. For strong selection the cline is less steep than the Bazykin cline, and the form is dominated by the migration process. The steepness at the center of the cline is close to x/-b/4D where b is the birth rate of homozygotes.}, added-at = {2015-10-14T18:49:52.000+0200}, author = {Christiansen, Freddy Bugge and Andreasen, Viggo and Poulsen, Ebbe Thue}, biburl = {https://www.bibsonomy.org/bibtex/292fd3d32be3791bb08a253709fb25427/peter.ralph}, doi = {10.1007/BF00169562}, interhash = {9bcf322edb815c0846c585578be8380d}, intrahash = {92fd3d32be3791bb08a253709fb25427}, issn = {0303-6812}, journal = {Journal of Mathematical Biology}, keywords = {clines diffusions diploidy heterozygote_disadvantage hybrid_zone}, language = {English}, number = 3, pages = {225-249}, publisher = {Springer-Verlag}, timestamp = {2016-02-23T22:12:55.000+0100}, title = {Genotypic proportions in hybrid zones}, url = {http://dx.doi.org/10.1007/BF00169562}, volume = 33, year = 1995 }