Recovering geography from a matrix of genetic distances

¹ Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università dell'Aquila - L'Aquila, Italy
² Istituto per le Applicazioni del Calcolo “Mauro Picone” (IAC-CNR) - Roma, Italy
³ Mathematics & Statistics, Texas Tech University - Lubbock, TX, USA
⁴ Sichuan University of Science and Engineering - Sichuan, Zigong, China
⁵ Dipartimento di Fisica, Università di Roma “Sapienza” - Roma, Italy
⁶ Centro Interdisciplinare “B. Segre”, Accademia dei Lincei - Roma, Italy

Received: 25 May 2017
Accepted: 5 July 2017

Abstract

Given a population of N elements with their geographical positions and the genetic (or lexical) distances between couples of elements (inferred, for example, from lexical differences between dialects which are spoken in different towns or from genetic differences between animal populations living in different faunal areas) a very interesting problem is to reconstruct the geographical positions of individuals using only genetic/lexical distances. From a technical point of view the program consists in extracting from the genetic/lexical distances a set of reconstructed geographical positions to be compared with the real ones. We show that geographical recovering is successful when the genetic/lexical distances are not a simple consequence of phylogenesis but also of horizontal transfers as, for example, vocabulary borrowings between different languages. Our results go well beyond the simple observation that geographical distances and genetic/lexical distances are correlated. The ascertainment of a correlation, in our perspective, merely is a prerequisite.