Universal features of surname distribution in a subsample of a growing population

We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions. In the first, we construct the family size distribution for the subsample from the stable distribution for the full population. This latter distribution is calculated for an arbitrary growth process in the limit of slow growth, and is seen to depend only on the average and variance of the number of children per individual, as well as the mutation rate. The distribution for the subsample is shifted left with respect to the original distribution, tending to eliminate the part of the original distribution reflecting the small families, and thus increasing the mean family size. From the subsample distribution, various bulk quantities such as the average family size and the percentage of singleton families are calculated. In the second approach, we study the past time development of these bulk quantities, deriving the statistics of the genealogical tree of the subsample. This approach reproduces that of the first when the current statistics of the subsample is considered. Surname statistics for the US in 1790 and 2000 and for Norway in 2008 are analyzed in the light of the theory and show satisfactory agreement, when the time-dependence of the growth rate is taken into account for the two contemporary data sets.     

Ethnicity and malaria affect surname distribution in consenza Province (Italy)

Three samples of surnames reported in the telephone directory of Cosenza province, Italy, are used, singly and together, to detect the presence of genetic barriers and to analyze the genetic relationship between the Italian and the Italo-Albanian communities living in this area. The genetic structure of the population seems characterized by the distinction between the northern and southern regions of the province. The Sibari plain, endemic with malaria until recently, probably constituted a genetic barrier. In the southern region of the province, the valley along the Crati river (also occupied by malarial fenlands), constituted a genetic barrier between the northern Sila upland and the western coast. Surname similarities between Italians and Italo-Albanians could be the result of gene flow and/or an initial choice of similar surnames; the second possibility accords with the persistence of the Albanian cultural identity and the level of endogamy in Albanian communities. In fact, the coefficient of relationship by isonomy (Ri), which is significantly higher in Italo-Albanians than in Italians, may be the result of genetic isolation and endogamy.     

Medical genetic study of the Rostov oblast population: analysis of surname distribution in seven districts

Data on the surname frequency distribution in seven districts (districts) of the Rostov oblast (region) have been used to calculate random inbreeding varying from 0.000064 to 0.000186 in the Volgodonsk and Millerovo districts, respectively. Schematic surname landscapes have been constructed for six districts. The observed spectrum of frequent surnames is compared with that of the complete register of surnames in Russia.     

Medical genetic study of the Rostov oblast population: Analysis of surname distribution in seven districts

Data on the surname frequency distribution in seven raions (districts) of the Rostov oblast (region) have been used to calculate random inbreeding varying from 0.000064 to 0.000186 in the Volgodonsk and Millerovo districts, respectively. Schematic surname landscapes have been constructed for six districts. The observed spectrum of frequent surnames is compared with that of the complete register of surnames in Russia.     

Evolution of the distribution of dispersal distance under distance‐dependent cost of dispersal

Abstract We analyse the evolution of the distribution of dispersal distances in a stable and homogeneous environment in one‐ and two‐dimensional habitats. In this model, dispersal evolves to avoid the competition between relatives although some cost might be associated with this behaviour. The evolutionarily stable dispersal distribution is characterized by an equilibration of the fitness gains among all the different dispersal distances. This cost‐benefit argument has heuristic value and facilitates the comprehension of results obtained numerically. In particular, it explains why some minimal or maximal probability of dispersal may evolve at intermediate distances when the cost of dispersal function is an increasing function of distance. We also show that kin selection may favour long range dispersal even if the survival cost of dispersal is very high, provided the survival probability does not vanish at long distances.     

Sicilian provinces: population subdivisions revealed by surname frequencies

The Sicilian population has a complex history of colonization and invasions that have influenced the genetic composition of the nine provinces of the island. Because surnames are patrilineally inherited, they simulate a Y-chromosome nonrecombinant genetic locus. We used surname data and a specific sampling strategy to describe the major subdivisions in each province and for the whole island of Sicily. The high number of families per surname in two provinces can be related to inbreeding as a result of founder events. Each province shows a major division, which, according to local historical events, likely represents cultural and probably genetic differences between east and west, between north and south, or between the inner regions and the coastal area. On the island level surnames reproduce the same separation, obtained by others with genes, of the eastern area from the western area. The separation is attributed to Greek influence in the east and to Phoenician-Carthaginian-Norman influence in the west. This separation crosses the two central provinces of Agrigento and Caltanissetta.     

Delimitation and aggregation between populations analyzed by surname structure

The surname distribution, taken from the lists of telephone subscribers in 1979 and 1988, was used to analyze the similarity-distance relationships between human populations. The study used 43 neighbouring Italian communal populations, situated along the Apennine mountains. These communes were chosen to determine the effects of the territorial geomorphological structure, the presence of communication routes, and different administrative jurisdictions on the communes aggregation or differentiation. Overall communication routes are shown to be the most important factor in group aggregation. The presence of communication routes is also predominant in group differentiation due to the Apennine ridge. The ridge has an influence only when routes are absent, and in any case, its effect is lessened in the presence of communication routes. Aggregation due to adherence to the same political division, either on the provincial or regional level was found to be a secondary effect which occurs only when the borders of the administrative subdivisions coincide with the factors considered above.     

The application of gene diversity analyses to surname diversity data

The use in the literature of statistics and measures derived for the measurement and the analysis of inbreeding from data on gene frequency diversity and applied to data on surname diversity is discussed. To overcome the difficulties encountered with this approach, a simple mathematical model for analysing isonymy data is proposed. Finally some further measures of surname diversity are given based on measures developed for gene diversity analysis and for community diversity analysis in ecology.     

Evolution under multiallelic migration-selection models

The loss of a specified allele and the convergence of the gene frequencies at a single multiallelic locus under the joint action of migration and viability selection are investigated. The monoecious, diploid population is subdivided into finitely many panmictic colonies that exchange adult migrants independently of genotype. Sufficient conditions are established for global fixation and for global loss of a particular allele. When migration is either sufficiently weak or sufficiently strong relative to selection, the equilibria are described, convergence of the gene frequencies is demonstrated, and sufficient conditions for the increase of a suitably defined mean fitness are offered. If the selection pattern is the same in every colony and such that in a panmictic population there is a globally asymptotically stable, internal (i.e., completely polymorphic) equilibrium point, then under certain weak assumptions on migration, the gene frequencies in the subdivided population converge globally to that equilibrium point. Thus, in this case, the ultimate state of the population is unaffected by geographical structure.     

Evolution and distribution of class II-related endogenous retroviruses

Endogenous retroviruses (ERVs) are widespread in vertebrate genomes and have been loosely grouped into "classes" on the basis of their phylogenetic relatedness to the established genera of exogenous retroviruses. Four of these genera-the lentiviruses, alpharetroviruses, betaretroviruses, and deltaretroviruses-form a well-supported clade in retroviral phylogenies, and ERVs that group with these genera have been termed class II ERVs. We used PCR amplification and sequencing of retroviral fragments from more than 130 vertebrate taxa to investigate the evolution of the class II retroviruses in detail. We confirm that class II retroviruses are largely confined to mammalian and avian hosts and provide evidence for a major novel group of avian retroviruses, and we identify additional members of both the alpha- and the betaretrovirus genera. Phylogenetic analyses demonstrated that the avian and mammalian viruses form distinct monophyletic groups, implying that interclass transmission has occurred only rarely during the evolution of the class II retroviruses. In contrast to previous reports, the lentiviruses clustered as sister taxa to several endogenous retroviruses derived from rodents and insectivores. This topology was further supported by the shared loss of both the class II PR-Pol frameshift site and the class II retrovirus G-patch domain.     

Delineating Europe's cultural regions: population structure and surname clustering

Surnames (family names) show distinctive geographical patterning and in many disciplines remain an underutilized source of information about population origins, migration and identity. This paper investigates the geographical structure of surnames, using a unique individual level database assembled from registers and telephone directories from 16 European countries. We develop a novel combination of methods for exhaustively analyzing this multinational data set, based upon the Lasker Distance, consensus clustering and multidimensional scaling. Our analysis is both data rich and computationally intensive, entailing as it does the aggregation, clustering and mapping of 8 million surnames collected from 152 million individuals. The resulting regionalization has applications in developing our understanding of the social and cultural complexion of Europe, and offers potential insights into the long and short-term dynamics of migration and residential mobility. The research also contributes a range of methodological insights for future studies concerning spatial clustering of surnames and population data more widely. In short, this paper further demonstrates the value of surnames in multinational population studies and also the increasing sophistication of techniques available to analyze them.     

Evolution under the multiallelic Levene model

The evolution of the multiallelic Levene model is investigated. New sufficient conditions for nonexistence of a completely polymorphic equilibrium and for global loss of an allele and information on which allele(s) will be lost are deduced from some new results on multidimensional recursion relations. In the absence of dominance, a more detailed analysis is presented. Sufficient conditions for global fixation of a particular allele are established. When the number of alleles equals the number of demes, necessary and sufficient conditions for the existence of an isolated, globally asymptotically stable, completely polymorphic equilibrium point are derived, and this equilibrium is explicitly determined. Three examples, one with arbitrarily many alleles and two with three alleles, illustrate the theory.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

Evolution under Fertility and Viability Selection

Evolution at a single multiallelic locus under arbitrary weak selection on both fertility and viability is investigated. Discrete, nonoverlapping generations are posited for autosomal and X-linked loci in dioecious populations, but monoecious populations are studied in both discrete and continuous time. Mating is random. The results hold after several generations have elapsed. With an error of order s [i.e., O(s)], where s represents the selection intensity, the population evolves in Hardy-Weinberg proportions. Provided the change per generation of the fertilities and viabilities due to their explicit time dependence (if any) is O(s2), the rate of change of the deviation from Hardy-Weinberg proportions is O(s2). If the change per generation of the viabilities and genotypic fertilities is smaller than second order [i.e., o(s2)], then to O(s2) the rate of change of the mean fitness is equal to the genic variance. The mean fitness is the product of the mean fertility and the mean viability; in dioecious populations, the latter is the unweighted geometric mean of the mean viabilities of the two sexes. Hence, as long as there is significant gene frequency change, the mean fitness increases. If it is the fertilities of matings that change slowly [at rate o(s2)], the above conclusions apply to a modified mean fitness, defined as the product of the mean viability and the square root of the mean fertility.     

Evolution of age-dependent sex-reversal under adaptive dynamics

We investigate the evolution of the age (or size) at sex-reversal in a model of sequential hermaphroditism, by means of the function-valued adaptive dynamics. The trait is the probability law of the age at sex-reversal considered as a random variable. Our analysis starts with the ecological model which was first introduced and analyzed by Calsina and Ripoll (Math Biosci 208(2), 393–418, 2007). The structure of the population is extended to a genotype class and a new model for an invading/mutant population is introduced. The invasion fitness functional is derived from the ecological setting, and it turns out to be controlled by a formula of Shaw–Mohler type. The problem of finding evolutionarily stable strategies is solved by means of infinite-dimensional linear optimization. We have found that these strategies correspond to sex-reversal at a single particular age (or size) even if the set of feasible strategies is considerably broader and allows for a probabilistic sex-reversal. Several examples, including in addition the population-dynamical stability, are illustrated. For a special case, we can show that an unbeatable size at sex-reversal must be larger than 69.3% of the expected size at death.     

Evolution of genetic architecture under directional selection

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.     

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.