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In this work, we investigated surname distribution in 4,348,021 Honduran electors with the aim of detecting population structure through the study of isonymy in three administrative levels: the whole nation, the 18 departments, and the 298 municipalities. For each administrative level, we studied the surname effective number, α, the total inbreeding, FIT , the random inbreeding, FST , and the local inbreeding, FIS . Principal components analysis, multidimensional scaling, and cluster analysis were performed on Lasker's distance matrix to detect the direction of surname diffusion and for a graphic representation of the surname relationship between different locations. The values of FIT , FST , and FIS display a variation of random inbreeding between the administrative levels in the Honduras population, which is attributed to the "Prefecture effect." Multivariate analyses of department data identified two main clusters, one south-western and the second north-eastern, with the Bay Islands and the eastern Gracias a Dios out of the main clusters. The results suggest that currently the population structure of this country is the result of the joint action of short-range directional migration and drift, with drift dominating over migration, and that population diffusion may have taken place mainly in the NW-SE direction.

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In order to describe the isonymic structure of Albania, the distribution of 3,068,447 surnames was studied in the 12 prefectures and their administrative subdivisions: the 36 districts and 321 communes. The number of different surnames found was 37,184. Effective surname number for the entire country was 1327, the average for prefectures was 653.3 ± 84.3, for districts 365.9 ± 42.0 and for communes 122.6 ± 8.7. These values display a variation of inbreeding between administrative levels in the Albanian population, which can be attributed to the previously published "Prefecture effect". Matrices of isonymic distances between units within administrative levels were tested for correlation with geographic distances. The correlations were highest for prefectures (r = 0.71 ± 0.06 for Euclidean distance) and lowest for communes (r = 0.37 ± 0.011 for Nei's distance). The multivariate analyses (Principal component analysis and Multidimensional Scaling) of prefectures identify three main clusters, one toward the North, the second in Central Albania, and the third in the South. This pattern is consistent with important subclusters from districts and communes, which point out that the country may have been colonised by diffusion of groups in the North-South direction, and from Macedonia in the East, over a pre-existing Illiryan population.

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In order to describe the isonymic structure of Paraguay, the distribution of 4,843,868 surnames of 2,882,163 persons was studied in the 18 departments and 237 districts of the nation. The correlations between isonymic and geographic distances for departments were r = 0.713 ± 0.052 for Euclidean distance, 0.597 ± 0.074 for Nei's and 0.582 ± 0.076 for Lasker's, and for districts r = 0.320 ± 0.007, 0.235 ± 0.009 and 0.422 ± 0.008, respectively. Average α was 151 for the entire country, 140.6 ± 6.5 for departments and 108.2 ± 2.7 for districts. The geographical distribution of districts'α is compatible with the settlement of subsequent groups of migrants moving from South towards the Centre and North of Paraguay. The geographical analysis of the first three components of Lasker's isonymy distance matrix is in agreement with such a process. The prevalence of Spanish-Amerindian ethnic groups and the relative absence of indigenous surnames (absence due mainly to the forced surname change of 1848) is in agreement with the diffusion of Spanish speaking males over a low-density area populated by indigenous groups. The present distribution of Y-markers and mt-markers in the available studies in most Latin American populations is compatible with this process.

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