Equilibrium models of isolation by distance predict an increase in genetic differentiation with geographic distance. Here we find a linear relationship between genetic and geographic distance in a worldwide sample of human populations, with major deviations from the fitted line explicable by admixture or extreme isolation. A close relationship is shown to exist between the correlation of geographic distance and genetic differentiation (as measured by F ST) and the geographic pattern of heterozygosity across populations. Considering a worldwide set of geographic locations as possible sources of the human expansion, we find that heterozygosities in the globally distributed populations of the data set are best explained by an expansion originating in Africa and that no geographic origin outside of Africa accounts as well for the observed patterns of genetic diversity. Although the relationship between F ST and geographic distance has been interpreted in the past as the result of an equilibrium model of drift and dispersal, simulation shows that the geographic pattern of heterozygosities in this data set is consistent with a model of a serial founder effect starting at a single origin. Given this serial-founder scenario, the relationship between genetic and geographic distance allows us to derive bounds for the effects of drift and natural selection on human genetic variation.genetic distance ͉ genetic drift ͉ HGDP-CEPH ͉ human origins ͉ microsatellites A regular decrease of genetic similarity with increasing geographic distance has been predicted by the theory of isolation by distance (1) and by the stepping-stone model (2), under the assumption that movement connected with mating is usually restricted to short distances (3, 4). Data on genetic polymorphisms have confirmed a strong association between genetic and geographic distance; early studies were generally limited to short geographic ranges and within-regional analyses (5, 6), but later studies have been extended to wider areas (7-9). Here, we regress a measure of genetic differentiation on geographic distance at the global level using 783 microsatellite loci from the Human Genome Diversity Project-Centre d'Etude du Polymorphisme Humain (HGDP-CEPH) worldwide sample of populations (10, 11). We then use simulations to examine a serial founder effect scenario as a possible explanation for the observed relationship between genetic and geographic distance. Materials and MethodsData.
The increasing abundance of human genetic data has shown that the geographical patterns of worldwide genetic diversity are best explained by human expansion out of Africa. This expansion is modelled well by prolonged migration from a single origin in Africa with multiple subsequent serial founding events. We discuss a new simulation model for the serial founder effect out of Africa and compare it with results from previous studies. Unlike previous models, we distinguish colonization events from the continued exchange of people between occupied territories as a result of mating. We conduct a search through parameter space to estimate the range of parameter values that best explain key statistics from published data on worldwide variation in microsatellites. The range of parameters we use is chosen to be compatible with an out-of-Africa migration at 50-60 Kyr ago and archaeoethno-demographic information. In addition to a colonization rate of 0.09-0.18, for an acceptable fit to the published microsatellite data, incorporation into existing models of exchange between neighbouring populations is essential, but at a very low rate. A linear decay of genetic diversity with geographical distance from the origin of expansion could apply to any species, especially if it moved recently into new geographical niches.
We investigate reliable multipath provisioning of traffic in high-capacity backbone mesh networks, e.g., next-generation SONET/SDH networks supporting virtual concatenation (VCAT). VCAT enables a connection to be inversely multiplexed on to multiple paths, a feature that may lead to significantly improved performance over conventional single-path provisioning. Other mesh networks such as those employing optical wavelength-division multiplexing (WDM) and multiprotocol label switching (MPLS) can also benefit from this multipath provisioning approach. We propose effective multipath bandwidth as the metric to provision a connection while satisfying its reliability requirements (measured in terms of availability). We demonstrate that effective multipath bandwidth provides more flexibility and lower blocking probability without the cost and the complexity associated with traditional protection schemes developed for optical WDM and MPLS networks. We also investigate the practical problem of provisioning effective multipath bandwidth with cost constraints. We analyze the tractability of the problem and present a heuristic which results in significantly reduced number of blocked connections due to cost constraints.Index Terms-Degraded service, effective multipath bandwidth, flexible provisioning, multiconstrained paths, multipath provisioning, virtual concatenation (VCAT).
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