Reconstruct Population History Research Articles

Diversity and genetic connectivity of heteropod (Pterotracheoidea) gastropods in the Tropical Eastern Pacific

AbstractPrevious research focusing on pelagic gastropods in the open ocean has demonstrated that many morphospecies comprise multiple distinct clades or cryptic species that can be distinguished with DNA sequence data. To date, the genetic diversity of the pelagic gastropod fauna of the tropical East Pacific, especially in shallow coastal waters, remains largely unexplored. To document the diversity of pterotracheoids (formerly heteropods) from the coastal waters of the Bay of Panama, we collected, photographed and sequenced fragments of mitochondrial cytochrome c oxidase subunit I (COI) and 16S ribosomal DNA for 60 atlantids, 3 carinariids and 6 pterotracheids. In addition to the COI barcode, our results include the first published 16S sequences for these groups. We found 11 operational taxonomic units (OTUs): 9 in the genus Atlanta, 1 Carinaria and 1 Firoloida. We report the presence of Atlanta oligogyra (Clades A and B), Atlanta turriculata, Atlanta lesueurii, Atlanta helicinoidea (Clade B), Atlanta plana, Atlanta echinogyra, Atlanta inflata and Atlanta frontieri through comparisons of our sequences with previously published sequences. We did not find Atlanta gaudichaudi, Atlanta inclinata, Atlanta tokiokai, Atlanta gibbosa, Atlanta peronii, or Oxygyrus inflatus, which have previously been reported from the region. Haplotype networks and estimates of ΦST illustrate how some species show population differentiation across the tropical Indo‐Pacific region, whereas others show little apparent population structure. For example, the most common haplotypes of A. inflata and of A. turriculata occur in the Indian Ocean, the Central and West Pacific and the tropical East Pacific, whereas individuals of A. frontieri from the Indian Ocean do not share haplotypes with individuals of A. frontieri from the Pacific Ocean. Analyses were limited by sample sizes, but these data suggest that population genetics approaches may be useful for reconstructing population histories of these important, but overlooked, components of the plankton.

Genotyping-in-Thousands by sequencing of archival fish scales reveals maintenance of genetic variation following a severe demographic contraction in kokanee salmon

Historical DNA analysis of archival samples has added new dimensions to population genetic studies, enabling spatiotemporal approaches for reconstructing population history and informing conservation management. Here we tested the efficacy of Genotyping-in-Thousands by sequencing (GT-seq) for collecting targeted single nucleotide polymorphism genotypic data from archival scale samples, and applied this approach to a study of kokanee salmon (Oncorhynchus nerka) in Kluane National Park and Reserve (KNPR; Yukon, Canada) that underwent a severe 12-year population decline followed by a rapid rebound. We genotyped archival scales sampled pre-crash and contemporary fin clips collected post-crash, revealing high coverage (> 90% average genotyping across all individuals) and low genotyping error (< 0.01% within-libraries, 0.60% among-libraries) despite the relatively poor quality of recovered DNA. We observed slight decreases in expected heterozygosity, allelic diversity, and effective population size post-crash, but none were significant, suggesting genetic diversity was retained despite the severe demographic contraction. Genotypic data also revealed the genetic distinctiveness of a now extirpated population just outside of KNPR, revealing biodiversity loss at the northern edge of the species distribution. More broadly, we demonstrated GT-seq as a valuable tool for collecting genome-wide data from archival samples to address basic questions in ecology and evolution, and inform applied research in wildlife conservation and fisheries management.

The Human in Humanity

For this conference theme “Variability and Scale in Psychiatric Neuroscience: How You Seek Determines What You Find”, I think it would be timely to start with a discussion on human origins and Africa’s place in understanding the evolutionary history of our species. In reconstructing the past, the genetic record contributes one narrative, which when used in conjunction with information from other fields such as archaeology, cultural anthropology, history, paleontological, linguistics, and oral traditions, contributes in building a clearer picture of the human journey up to the present. As a researcher who uses DNA as a tool to reconstruct population history, the starting point is a biological sample to get to the DNA. That intersection of science to engage with individuals who are members of the wider community, has had to build on trust, respect, honesty, justice and fairness, benefit sharing, among other values to ensure win-win scenarios for science and society.

Massively parallel sequencing of 165 ancestry-informative SNPs and forensic biogeographical ancestry inference in three southern Chinese Sinitic/Tai-Kadai populations

Ancestry informative markers (AIMs), which are distributed throughout the human genome, harbor significant allele frequency differences among diverse ethnic groups. The use of sets of AIMs to reconstruct population history and genetic relationships is attracting interest in the forensic community, because biogeographic ancestry information for a casework sample can potentially be predicted and used to guide the investigative process. However, subpopulation ancestry inference within East Asia remains in its infancy due to a lack of population reference data collection and incomplete validation work on newly developed or commercial AIM sets. In the present study, 316 Chinese persons, including 85 Sinitic-speaking Haikou Han, 120 Qiongzhong Hlai and 111 Daozhen Gelao individuals belonging to Tai-Kadai-speaking populations, were analyzed using the Precision ID Ancestry Panel (165 AISNPs). Combined with our previous 165-AISNP data (375 individuals from 6 populations), the 1000 Genomes Project and forensic literature, comprehensive population genetic comparisons and ancestry inference were further performed via ADMIXTURE, TreeMix, PCA, f-statistics and N-J tree. Although several nonpolymorphic loci were identified in the three southern Chinese populations, the forensic parameters of this ancestry inference panel were better than those for the 23 STR-based Huaxia Platinum System, which is suitable for use as a robust tool in forensic individual identification and parentage testing. The results based on the ancestry assignment and admixture proportion evaluation revealed that this panel could be used successfully to assign individuals at a continental scale but also possessed obvious limitations in discriminatory power in intercontinental individuals, especially for European-Asian admixed Uyghurs or in populations lacking reference databases. Population genetic analyses further revealed five continental population clusters and three East Asian-focused population subgroups, which is consistent with linguistic affiliations. Ancestry composition and multiple phylogenetic analysis further demonstrated that the geographically isolated Qiongzhong Hlai harbored a close phylogenetic relationship with Austronesian speakers and possessed a homogenous Tai-Kadai-dominant ancestry, which could be used as the ancestral source proxy in population history reconstruction of Tai-Kadai-speaking populations and as one of the representatives for forensic database establishment. In summary, more population-specific AIM sets focused on East Asian subpopulations, comprehensive algorithms and high-coverage population reference data should be developed and validated in the next step.

How Many Subpopulations Is Too Many? Exponential Lower Bounds for Inferring Population Histories.

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, such as the seminal work of Li and Durbin, attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure-the history of multiple subpopulations that merge, split, and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.

Distinguishing eastern North American forest moth pests by wing-scale ultrastructure: potential applications in paleoecology

The use of fossil moth wing scales has recently been introduced as a new method to reconstruct population histories of lepidopterans and provide a proxy for insect disturbance. We investigated the potential for using wing-scale ultrastructure to distinguish between the five most common outbreak species of moth pests in eastern North America: spruce budworm ( Choristoneura fumiferana Clemens), hemlock looper ( Lambdina fiscellaria Guenée), forest tent caterpillar ( Malacosoma disstria Hübner), blackheaded budworm ( Acleris variana Fernie), and jack pine budworm ( Choristoneura pinus Freeman). Using scanning electron images of scales, we made qualitative and quantitative comparisons of morphological traits at the ultrastructural level. We found that hemlock looper and eastern blackheaded budworm scales could be categorically separated from each other and from the three other species. We developed a quadratic discriminant function using measurements of ultrastructure traits that distinguishes scales of the three remaining species with an overall accuracy of 66%. We found that forest tent caterpillar could be well separated based on these traits, but we were less confident in distinguishing the closely related jack pine and spruce budworm. Our method offers potential advantages in scale identification for future studies in paleoecology, while providing the additional advantage of not requiring intact, unfolded, and undamaged scales.

Neutral Theory: From Complex Population History to Natural Selection and Sociocultural Phenomena in Human Populations.

Here, we present a synthetic view on how Kimura's Neutral theory has helped us gaining insight on the different evolutionary forces that shape human evolution. We put this perspective in the frame of recent emerging challenges: the use of whole genome data for reconstructing population histories, natural selection on complex polygenic traits, and integrating cultural processes in human evolution.

Using features of a Creole language to reconstruct population history and cultural evolution: tracing the English origins of Sranan.

Creole languages are formed in conditions where speakers from distinct languages are brought together without a shared first language, typically under the domination of speakers from one of the languages and particularly in the context of the transatlantic slave trade and European colonialism. One such Creole in Suriname, Sranan, developed around the mid-seventeenth century, primarily out of contact between varieties of English from England, spoken by the dominant group, and multiple West African languages. The vast majority of the basic words in Sranan come from the language of the dominant group, English. Here, we compare linguistic features of modern-day Sranan with those of English as spoken in 313 localities across England. By way of testing proposed hypotheses for the origin of English words in Sranan, we find that 80% of the studied features of Sranan can be explained by similarity to regional dialect features at two distinct input locations within England, a cluster of locations near the port of Bristol and another cluster near Essex in eastern England. Our new hypothesis is supported by the geographical distribution of specific regional dialect features, such as post-vocalic rhoticity and word-initial 'h', and by phylogenetic analysis of these features, which shows evidence favouring input from at least two English dialects in the formation of Sranan. In addition to explicating the dialect features most prominent in the linguistic evolution of Sranan, our historical analyses also provide supporting evidence for two distinct hypotheses about the likely geographical origins of the English speakers whose language was an input to Sranan. The emergence as a likely input to Sranan of the speech forms of a cluster near Bristol is consistent with historical records, indicating that most of the indentured servants going to the Americas between 1654 and 1666 were from Bristol and nearby counties, and that of the cluster near Essex is consistent with documents showing that many of the governors and important planters came from the southeast of England (including London) (Smith 1987 The Genesis of the Creole Languages of Surinam; Smith 2009 In The handbook of pidgin and creole studies, pp. 98-129).This article is part of the theme issue 'Bridging cultural gaps: interdisciplinary studies in human cultural evolution'.

Identifying source populations for the reintroduction of the Eurasian beaver, Castor fiber L. 1758, into Britain: evidence from ancient DNA

Establishing true phylogenetic relationships between populations is a critical consideration when sourcing individuals for translocation. This presents huge difficulties with threatened and endangered species that have become extirpated from large areas of their former range. We utilise ancient DNA (aDNA) to reconstruct the phylogenetic relationships of a keystone species which has become extinct in Britain, the Eurasian beaver Castor fiber. We sequenced seventeen 492 bp partial tRNAPro and control region sequences from Late Pleistocene and Holocene age beavers and included these in network, demographic and genealogy analyses. The mode of postglacial population expansion from refugia was investigated by employing tests of neutrality and a pairwise mismatch distribution analysis. We found evidence of a pre-Late Glacial Maximum ancestor for the Western C. fiber clade which experienced a rapid demographic expansion during the terminal Pleistocene to early Holocene period. Ancient British beavers were found to originate from the Western phylogroup but showed no phylogenetic affinity to any one modern relict population over another. Instead, we find that they formed part of a large, continuous, pan-Western European clade that harbored little internal substructure. Our study highlights the utility of aDNA in reconstructing population histories of extirpated species which has real-world implications for conservation planning.

Comparative performance of deciduous and permanent dental morphology in detecting biological relatives

Dental morphology plays a key role in reconstructing population history and evolutionary relationships at global, regional, and intracemetery scales. At the inter-individual level, it is assumed that close biological kin exhibit greater phenotypic similarity than non-relatives. Heritability estimates provide one measure of phenotypic resemblance but are not easily incorporated into analyses of archaeological samples. In this study we evaluate the assumption that relatives are more similar phenotypically than non-relatives. We compare results for permanent dental morphology to those obtained using deciduous dental morphology in a matched dataset (Paul & Stojanowski, ). Permanent trait expression was scored from dental casts representing 69 sibling pairs, curated as part of the longitudinal Burlington Growth Study. Simulating a biodistance approach, 22 morphological traits of permanent tooth crowns were used to generate 69 inter-relative and 2,076 non-relative Euclidean distances. Following distance ordination, family-specific dispersion values were calculated from multidimensional scaling coordinates. Output was compared to that of a previous study that focused on deciduous crown variation in the same set of individuals (Paul & Stojanowski, ). Mantel tests were used to evaluate the correlation of a proxy genetic distance matrix to both the permanent and deciduous dental distance matrices. On average, inter-relative distances generated from morphological traits of permanent tooth crowns were smaller than expected by chance based on resampling (p < 0.001). While family-specific dispersion varied greatly for both permanent and deciduous datasets, over 75% of the families exhibited greater dispersion with permanent traits. This suggests that morphological traits of the permanent dentition provide a less faithful reflection of biological relatedness than morphological traits of the deciduous dentition. Mantel tests indicate that both the deciduous and permanent distance matrices are significantly correlated with a matrix of genetic relatedness coefficients; however, the magnitude of the correlations was low. Overall, morphological traits of permanent tooth crowns perform moderately well in distinguishing relatives from non-relatives, but deciduous crown variations may provide a more direct reflection of the underlying genetic structure of intra-site or intra-cemetery samples. These findings have implications for bioarchaeological research and biodistance practices. In particular, morphological traits of the deciduous dentition should be incorporated into standard data collection protocols because of their stronger signal of relatedness.

THE SOCIAL CONSEQUENCES OF CLIMATE CHANGE IN THE CENTRAL MESA VERDE REGION.

The consequences of climate change vary over space and time. Effective studies of human responses to climatically induced environmental change must therefore sample the environmental diversity experienced by specific societies. We reconstruct population histories from A.D. 600 to 1280 in six environmentally distinct portions of the central Mesa Verde region in southwestern Colorado, relating these to climate-driven changes in agricultural potential. In all but one subregion, increases in maize-niche size led to increases in population size. Maize-niche size is also positively correlated with regional estimates of birth rates. High birth rates continued to accompany high population levels even as productive conditions declined in the A.D. 1200s. We reconstruct prominent imbalances between the maize-niche size and population densities in two subregions from A.D. 1140 to 1180 and from A.D. 1225-1260. We propose that human responses in those subregions, beginning by the mid-A.D. 1200s, contributed to violence and social collapse across the entire society. Our findings are relevant to discussions of how climate change will affect contemporary societies.

Ancient DNA reveals substantial genetic diversity in the California Condor (Gymnogyps californianus) prior to a population bottleneck

ABSTRACT Critically endangered species that have undergone severe population bottlenecks often have little remaining genetic variation, making it difficult to reconstruct population histories to apply in reintroduction and recovery strategies. By using ancient DNA techniques, it is possible to combine genetic evidence from the historical population with contemporary samples to provide a more complete picture of a species' genetic variation across its historical range and through time. Applying this approach, we examined changes in the mitochondrial DNA (mtDNA) control region (526 base pairs) of the endangered California Condor (Gymnogyps californianus). Results showed a >80% reduction in unique haplotypes over the past 2 centuries. We found no spatial sorting of haplotypes in the historical population; the periphery of the range contained haplotypes that were common throughout the historical range. Direct examination of mtDNA from California Condor museum specimens provided a new window into historical po...

Population history and its relationship with climate change on the Chinese Loess Plateau during the past 10,000 years

Based on compilation of a large number of archaeological and palaeosol 14C-ages, the Summed Probability Method is used to reconstruct population history and climatic patterns on the Chinese Loess Plateau during the period 8.5–3.5 cal. ka BP. During this period, the population experienced two major expansion periods and several climatic fluctuations. The first population expansion began at around 7.8 cal. ka BP, and the second at around 5.8 cal. ka BP. During the first period, although already in combination with cultivation of broomcorn millet the population growth was supported mainly by hunting and gathering. With the switch from broomcorn millet to foxtail millet, plant cultivation became the major factor promoting a second population increase. In this paper, we demonstrate that, initially, suitable climate and agriculture both can facilitate population growth and climate events had a significant influence on demographic fluctuations. However, when reaching the threshold of land capacity, population became increasingly more sensitive towards climate fluctuations.

Developmental Changes in Morphology of the Middle and Posterior External Cranial Base in Modern Homo sapiens.

The basicranium has been described as phylogenetically informative, developmentally stable, and minimally affected by external factors and consequently plays an important role in cranial size and shape in subadult humans. Here basicranial variation of subadults from several modern human populations was investigated and the impact of genetic relatedness on basicranial morphological similarities was investigated. Three-dimensional landmark data were digitized from subadult basicrania from seven populations. Published molecular data on short tandem repeats were statistically compared to morphological data from three ontogenetic stages. Basicranial and temporal bone morphology both reflect genetic distances in childhood and adolescence (5–18 years), but not in infancy (<5 years). The occipital bone reflects genetic distances only in adolescence (13–18 years). The sphenoid bone does not reflect genetic distances at any ontogenetic stage but was the most diagnostic region evaluated, resulting in high rates of correct classification among populations. These results suggest that the ontogenetic processes driving basicranial development are complex and cannot be succinctly summarized across populations or basicranial regions. However, the fact that certain regions reflect genetic distances suggests that the morphology of these regions may be useful in reconstructing population history in specimens for which direct DNA evidence is unavailable, such as archaeological sites.

DNA analysis of ancient dogs of the Americas: Identifying possible founding haplotypes and reconstructing population histories

As dogs have traveled with humans to every continent, they can potentially serve as an excellent proxy when studying human migration history. Past genetic studies into the origins of Native American dogs have used portions of the hypervariable region (HVR) of mitochondrial DNA (mtDNA) to indicate that prior to European contact the dogs of Native Americans originated in Eurasia. In this study, we summarize past DNA studies of both humans and dogs to discuss their population histories in the Americas. We then sequenced a portion of the mtDNA HVR of 42 pre-Columbian dogs from three sites located in Illinois, coastal British Columbia, and Colorado, and identify four novel dog mtDNA haplotypes. Next, we analyzed a dataset comprised of all available ancient dog sequences from the Americas to infer the pre-Columbian population history of dogs in the Americas. Interestingly, we found low levels of genetic diversity for some populations consistent with the possibility of deliberate breeding practices. Furthermore, we identified multiple putative founding haplotypes in addition to dog haplotypes that closely resemble those of wolves, suggesting admixture with North American wolves or perhaps a second domestication of canids in the Americas. Notably, initial effective population size estimates suggest at least 1000 female dogs likely existed in the Americas at the time of the first known canid burial, and that population size increased gradually over time before stabilizing roughly 1200 years before present.

Investigating population history using temporal genetic differentiation.

The rapid advance of sequencing technology, coupled with improvements in molecular methods for obtaining genetic data from ancient sources, holds the promise of producing a wealth of genomic data from time-separated individuals. However, the population-genetic properties of time-structured samples have not been extensively explored. Here, we consider the implications of temporal sampling for analyses of genetic differentiation and use a temporal coalescent framework to show that complex historical events such as size reductions, population replacements, and transient genetic barriers between populations leave a footprint of genetic differentiation that can be traced through history using temporal samples. Our results emphasize explicit consideration of the temporal structure when making inferences and indicate that genomic data from ancient individuals will greatly increase our ability to reconstruct population history.

The relative efficacy of functional and developmental cranial modules for reconstructing global human population history

This study tests the relative efficacy of human cranial modules, defined on the basis of developmental and functional criteria, for reconstructing neutral genetic population history. Specifically, two hypotheses were tested: 1) The "basicranial hypothesis" predicts that the endochondrally ossifying basicranium will be more reliable for reconstructing population history than intramembranously ossifying regions of the human cranium. This is based on the assumption that early ossification of the basicranium and its distinct functional constraints produce a cranial structure that is relatively immune to non-neutral evolutionary forces. 2) The "single function hypothesis" predicts that cranial regions associated with a single (sensory) function are less reliable indicators of neutral genetic history. Here the prediction is based on the logic that complex, multi-functional, integrated cranial regions are less likely toexhibit homoplasy and, therefore, provide a more accurate morphological proxy for genetic relationships. The congruence between craniometric affinity matrices and neutral genetic population matrices based on autosomal microsatellite and classical markers was assessed using a series of Mantel and Dow-Cheverud tests. The results did not support the predictions of the "basicranial hypothesis," as the endochondrally ossifying basicranium was not significantly more congruent with the genetic data than intramembraneously ossifying modules. Moreover, although the results provided some support for the "single function hypothesis," defining cranial modules on the basis of anatomical or functional complexity did not provide a consistent means of predicting their phylogenetic efficacy. These results have important implications for building an accurate inference model of cranial evolution in the human fossil record.

Population structure, dispersal and colonization history of the garden bumblebee Bombus hortorum in the Western Isles of Scotland

New methods of analysing genetic data provide powerful tools for quantifying dispersal patterns and reconstructing population histories. Here we examine the population structure of the bumblebee Bombus hortorum in a model island system, the Western Isles of Scotland, using microsatellite markers. Following declines in other species, B. hortorum is the only remaining long-tongued bumblebee species found in much of Europe, and thus it is of particular ecological importance. Our data suggest that populations of B. hortorum in western Scotland exist as distinct genetic clusters occupying groups of nearby islands. Population structuring was higher than for other bumblebee species which have previously been studied in this same island group (Fst = 0.16). Populations showed significant isolation by distance. This relationship was greatly improved by using circuit theory to allow dispersal rates to differ over different landscape features; as we would predict, sea appears to provide far higher resistance to dispersal than land. Incorporating bathymetry data improved the fit of the model further; populations separated by shallow seas are more genetically similar than those separated by deeper seas. We argue that this probably reflects events following the last ice age when the islands were first colonized by this bee species (8,500–5,000 ybp), when the sea levels were lower and islands separated by shallow channels would have been joined. In the absence of significant gene flow these genetic clusters appear to have since diverged over the following 5,000 years and arguably may now represent locally adapted races, some occurring on single islands.

Assessment and integration of genetic, morphological and demographic variation in Hagenia abyssinica (Bruce) J.F. Gmel to guide its conservation

Assessing and integrating genetic, morphological and demographic variation is instrumental for planning conservation, tree improvement and domestication programs. We discuss the variation of the gravely endangered tropical tree species Hagenia abyssinica in Ethiopia with regard to its morphological and genetic traits as well as its population demography in a conservation context. An analysis of variance (ANOVA) revealed a highly significant differentiation among 22 natural populations of H. abyssinica in all quantitative morphological traits assessed. Multivariate and univariate taxonomic distances of leaf traits among populations are not correlated with the corresponding genetic distances at AFLP markers (multivariate r = −0.03484 at p = 0.3926), showing that the genetic differentiation at AFLPs is not associated with the morphological differences among populations. Chloroplast microsatellite data allowed us to identify lineages and to reconstruct population history, while the AFLP data enabled us to identify populations of high genetic diversity. A weighted-score population prioritisation matrix (WPPM) that integrates genetic, morphological and demographic criteria was developed and used for the first time to prioritise populations for conservation and domestication. Action is needed to launch conservation and domestication programs of H. abyssinica to ensure the long-term survival of the species and to boost its economic and ecological value.

Reconstructing Population Histories from Single Nucleotide Polymorphism Data

Population genetics encompasses a strong theoretical and applied research tradition on the multiple demographic processes that shape genetic variation present within a species. When several distinct populations exist in the current generation, it is often natural to consider the pattern of their divergence from a single ancestral population in terms of a binary tree structure. Inference about such population histories based on molecular data has been an intensive research topic in the recent years. The most common approach uses coalescent theory to model genealogies of individuals sampled from the current populations. Such methods are able to compare several different evolutionary scenarios and to estimate demographic parameters. However, their major limitation is the enormous computational complexity associated with the indirect modeling of the demographies, which limits the application to small data sets. Here, we propose a novel Bayesian method for inferring population histories from unlinked single nucleotide polymorphisms, which is applicable also to data sets harboring large numbers of individuals from distinct populations. We use an approximation to the neutral Wright-Fisher diffusion to model random fluctuations in allele frequencies. The population histories are modeled as binary rooted trees that represent the historical order of divergence of the different populations. A combination of analytical, numerical, and Monte Carlo integration techniques are utilized for the inferences. A particularly important feature of our approach is that it provides intuitive measures of statistical uncertainty related with the estimates computed, which may be entirely lacking for the alternative methods in this context. The potential of our approach is illustrated by analyses of both simulated and real data sets.