title: A reconsideration of Galton's problem (using a two-sex population).
abstract: The main purposes of this paper are to promote and expound the bisexual Galton-Watson branching process as a relevant model for the consideration of Francis Galton's problem regarding the extinction of surnames of "men of note." A scheme for adapting the bisexual process to consider Galton's problem is introduced. A necessary and sufficient condition for the certain extinction of a male-induced property in a two-sex species is presented. An approach for calculating the extinction of a male-generated characteristic in the two-sex species is proposed. That approach is then used to find the probability of the extinction of surnames in a bisexual population for Alfred Lotka's data based on an United States Census. Finally, these results are then compared with the classic extinction probabilities (from Lotka) associated with the traditional Galton-Watson branching process using asexual reproduction.
authors.affiliation: Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana, 46383, USA.
authors.forename: D M
authors.initials: DM
authors.lastname: Hull
mesh_terms: D005260:Female; D006801:Humans; D008297:Male; D008954:Models, Biological; D011157:Population Dynamics; D011336:Probability; D012098:Reproduction; D012723:Sex