Dispersal of Mycobacterium tuberculosis via the Canadian fur trade

Caitlin S. Pepperell; Julie M. Granka; David C. Alexander; Marcel A. Behr; Linda Chui; Janet Gordon; Jennifer L. Guthrie; Frances B. Jamieson; Deanne Langlois-Klassen; Richard Long; Dao Nguyen; Wendy Wobeser; Marcus W. Feldman

doi:10.1073/pnas.1016708108

New Research In

Edited by Simon A. Levin, Princeton University, Princeton, NJ, and approved March 3, 2011 (received for review November 9, 2010)

Abstract

Patterns of gene flow can have marked effects on the evolution of populations. To better understand the migration dynamics of Mycobacterium tuberculosis, we studied genetic data from European M. tuberculosis lineages currently circulating in Aboriginal and French Canadian communities. A single M. tuberculosis lineage, characterized by the DS6^Quebec genomic deletion, is at highest frequency among Aboriginal populations in Ontario, Saskatchewan, and Alberta; this bacterial lineage is also dominant among tuberculosis (TB) cases in French Canadians resident in Quebec. Substantial contact between these human populations is limited to a specific historical era (1710–1870), during which individuals from these populations met to barter furs. Statistical analyses of extant M. tuberculosis minisatellite data are consistent with Quebec as a source population for M. tuberculosis gene flow into Aboriginal populations during the fur trade era. Historical and genetic analyses suggest that tiny M. tuberculosis populations persisted for ∼100 y among indigenous populations and subsequently expanded in the late 19th century after environmental changes favoring the pathogen. Our study suggests that spread of TB can occur by two asynchronous processes: (i) dispersal of M. tuberculosis by minimal numbers of human migrants, during which small pathogen populations are sustained by ongoing migration and slow disease dynamics, and (ii) expansion of the M. tuberculosis population facilitated by shifts in host ecology. If generalizable, these migration dynamics can help explain the low DNA sequence diversity observed among isolates of M. tuberculosis and the difficulties in global elimination of tuberculosis, as small, widely dispersed pathogen populations are difficult both to detect and to eradicate.

Migration of human pathogens between host populations is of clear biomedical interest, because global spread of infectious diseases is predicated on pathogen dispersal. For obligate human pathogens, the paths of migration are shaped by social networks among hosts and, at a broader scale, by human migrations and patterns of comingling. The shape and magnitude of these processes may be inferred from genetic data from both extant populations of humans (1, 2) and microorganisms carried by humans (3). Statistical genetic inferences about pathogen migration have been buttressed by a variety of independent data types, such as linguistic (3), epidemiological (4), and ecological (5).

Human tuberculosis (TB) is caused by Mycobacterium tuberculosis. By current estimates, M. tuberculosis infects one third of the world's population; a minority of these infections progress to disease and account for 9–10 million new, transmissible cases per year (6). Genetic data from M. tuberculosis are characterized by low DNA sequence diversity (7) and significant population subdivision, both at continental (8, 9) and fine geographic scales (10). TB is characterized by variable transmissibility, depending on environmental conditions, and irregular disease dynamics (11, 12). Variation in temporal dynamics of disease is introduced by the phenomenon of clinical latency, whereby a host may be infected with M. tuberculosis for decades before reactivating the infection, becoming ill, and thus able to transmit the infection to others. These features and other aspects of disease ecology would be expected to affect migration of M. tuberculosis among host populations. Broad outlines of M. tuberculosis migratory history have been described based on the geographic range of specific bacterial clades and lineages (9). However, very little is known about M. tuberculosis migratory patterns and rates, population dynamics during migration, or effects of migratory history on M. tuberculosis population genetic diversity.

In this paper, we present evidence suggesting that M. tuberculosis dispersed into Canadian Aboriginal populations as a result of contact with European fur traders in the 18th century. Although contact between the populations involved small numbers of individuals, it was extensive enough to result in the development of the Métis society of both European and Aboriginal ancestry. (Additional historical details are given in SI Background Material.) Large-scale TB epidemics were not evident among Western Canadian Aboriginal populations until the late 19th and 20th centuries (10, 13–15), suggesting that epidemics may be uncoupled from the process of M. tuberculosis dispersal.

Our analyses of historical, epidemiological, and M. tuberculosis genetic data suggest that (i) M. tuberculosis may be spread by small numbers of human migrants; (ii) M. tuberculosis populations can persist at low levels over historical time scales; (iii) these small bacterial populations may be sustained by ongoing migration and possibly by slow disease dynamics; and (iv) shifts in host ecology favoring the pathogen may be accompanied by bacterial population expansions, with marked effects on genetics of M. tuberculosis populations.

Results

Results of M. tuberculosis population screening for lineage-defining polymorphisms (16, 17) are shown in Fig. 1 and Table S1. DS6^Quebec is the most frequent lineage among bacteria from all four populations: the French Canadian population of Quebec (QU), and Aboriginal populations in Ontario (ON), Saskatchewan (SK), and Alberta (AB). Within Saskatchewan, DS6^Quebec was found in all of eight intraprovincial regions (fine-scale geographic data are available only for this population; see ref. 10 for definitions of within-Saskatchewan regions). Frequencies of other M. tuberculosis lineages were more variable among populations. A minimum spanning tree, based on 12 minisatellite loci from bacteria with the DS6^Quebec polymorphism, reveals a distinctly star-like network structure (Fig. 2), with little evidence of population differentiation. Networks based on minisatellite data within other common lineages (Rd 182, Rd 219, and H37Rv-like) were not star-like (Fig. S1). Lineage-specific patterns also were evident in analyses of population genetic structure (Analysis of Molecular Variance, AMOVA; Table 1). Overall, a modest level of differentiation was observed among populations [fraction of minisatellite variation among populations (F_ST) = 0.08]. However, differentiation varied substantially between lineages, with the least variation seen within the DS6^Quebec lineage (F_ST = 0.04) and the greatest within the H37Rv-like lineage (F_ST = 0.52). These results suggest that (i) the DS6^Quebec lineage was introduced into these populations in the relatively remote past, resulting in a similarly high frequency across populations; (ii) M. tuberculosis belonging to the DS6^Quebec lineage were, or are, exchanged freely among study populations; (iii) the DS6^Quebec lineage underwent rapid population expansion, reflected in a star-like network topology, possibly coincident with its introduction into new host populations; and (iv) there has been temporal and/or spatial variation in patterns of bacterial migration among human populations, reflected in variable differentiation within bacterial lineages.

Fig. 1.

Fur trade geography, regional frequencies of M. tuberculosis lineages, and historical timeline. (A) Map of Canada from Natural Resources Canada (49). The main fur trade canoe route from the St. Lawrence River to the Beaufort Sea (Montreal route) is shown in light blue. Canoe routes from Hudson's Bay to the interior are shown in red. Geography of canoe routes is based on a map by A. Ray in ref. 24 and was checked against a map of fur trade posts (50). Geography of railways, steamship lines, and areas classified as remote/traditional on the basis of archival evidence (all ca. 1920) are from figure 38 in ref. 21 and ref. 24. Proportional lineage frequencies of M. tuberculosis isolates are shown as pie charts in the corresponding province (see also Table S1). Nomenclature of M. tuberculosis lineages is from refs. 16 and 17. Pie charts are the same size for clarity, although total sample sizes differed among populations. Lineage frequencies were unavailable for the MB population. (B) Events shown in the timeline are the founding of New France (Quebec) in 1608; incursion of fur traders to the Northwest around 1710; British conquest of New France (and end of migration from France to Quebec) in 1760; merger of North West Company and Hudson's Bay Company (HBC) in 1820 (with subsequent abandonment of the Montreal route in favor of Hudson's Bay routes); completion of the Canadian Pacific Railway (CPR) in 1885, by which time Western buffalo herds were severely depleted; and, finally, widespread use of bush planes to reach remote areas, starting in the 1930s. Gray boxes indicate the estimated timing of processes in M. tuberculosis demographic history: dispersal of M. tuberculosis to indigenous populations (light gray), and expansion of M. tuberculosis populations as a result of shifts in host ecology (dark gray).

Fig. 2.

Minimum spanning tree of minisatellite haplotypes (12 loci) from M. tuberculosis within the DS6^Quebec lineage, in QU, ON, SK, and AB populations. The size of nodes is proportional to the frequency of TB cases associated with that M. tuberculosis haplotype. Scale is indicated by the line at the bottom of the figure, which represents a difference of one minisatellite repeat. Minisatellites were not available from the MB population.

View this table:

Table 1.

Within- and between-lineage AMOVA based on 12 minisatellite loci for M. tuberculosis from Quebec, Ontario, Saskatchewan, and Alberta

Although the Quebec population is now geographically and socially isolated from Aboriginal populations in Ontario, Saskatchewan, and Alberta, there is a history of comingling in the context of the Canadian fur trade (Fig. 1). Table 2 outlines the expected history of the DS6^Quebec lineage, assuming it was introduced to Canada by a French immigrant to Quebec and dispersed to Aboriginal populations via fur trade transportation and social networks. Estimates derived from M. tuberculosis minisatellite data of the time to most recent common ancestor (TMRCA) (18) and divergence time between bacterial populations (T_D) (19) suggest that genetic exchange between QU and Western Aboriginal M. tuberculosis populations occurred over ∼100 y; timing of this exchange is consistent with historical human migrations connected with the trade in furs. (Additional estimates are given in SI Results.)

View this table:

Table 2.

Genetic timing estimates for DS6^Quebec M. tuberculosis lineage in calendar years

Levels of overall genetic diversity of M. tuberculosis restriction fragment length polymorphism (RFLP) (20) haplotypes from four populations are shown in rarefaction curves in Fig. 3A. Published data were available from Manitoba (MB) and are included along with data from QU, SK, and AB; data from ON are not included because of the small sample size (SI Results). The number of distinct haplotypes is highest in QU, consistent with its being a source population for pathogen migration. Levels of diversity are lowest in SK and MB, with intermediate diversity in AB. Diversity thus does not decrease in an east-to-west pattern, as we might expect with a serial founder effect (1) originating in Quebec.

Fig. 3.

Genetic diversity of M. tuberculosis populations. (A) Number of distinct RFLP haplotypes as a function of the number of sampled chromosomes obtained using rarefaction (Materials and Methods). Populations include QU, MB, SK, and AB; ON is not included because of its low sample size (SI Results). Every fourth data point is presented for clarity. (B) RFLP haplotype diversity (Shannon index), correcting for sample size by repeatedly sampling the total number of isolates in the smallest sample from each population (NRS, n = 123). Boxplots indicate values obtained over all samples; value for the smallest sample (NRS) is indicated by a line. Populations are as in the left panel, except that SK is split into RS and NRS populations. Although Manitoba contains both remote and nonremote regions (Fig. 1), detailed geographic data were not available for the MB sample; diversity shown here is for the entire sample.

Epidemics of TB among Canadian indigenous populations occuring post-European contact have been associated with dramatic social, economic, and environmental changes that characterized the industrial era (late 19th century and beyond; SI Background Material). There is evidence of regional differences in the pace of these changes: Published analyses of archival fur trade documents indicate that some indigenous populations remained remote from the cash-based industrial economy as late as the 1920s (21). Regions within Saskatchewan and Manitoba fall into this historically remote/traditional category, whereas Alberta does not contain any such regions (Fig. 1A). Later development of transportation networks (starting with the widespread use of bush planes in the 1930s) allowed commercial development of previously remote regions (21).

Given associations between industrialization, attendant shifts in host ecology, and TB epidemic expansion among indigenous populations (SI Background Material), we hypothesized that M. tuberculosis diversity in Saskatchewan and Manitoba was low relative to Alberta because of the more recent expansion of the M. tuberculosis population in remote/traditional areas. To test this hypothesis, minisatellite and RFLP haplotypes from SK were divided into historically “remote” (RS) and “nonremote” (NRS) regions according to the classification of trading districts outlined in ref. 21. Consistent with this classification, diversity in NRS regions is similar to that in AB (Alberta contains no remote regions), with the lowest diversity observed in RS (Fig. 3B and Fig. S2). Permutation procedures identified RS and QU as having lower and greater diversity, respectively, than would be expected under a random distribution of minisatellite haplotypes among populations (Fig. S3).

We analyzed DS6^Quebec minisatellite data with rejection sampling, an Approximate Bayesian Computation (ABC) method, to assess whether a demographic model allowing an expansion in RS (in which the historical bacterial effective population size, N_e, was smaller than the current N_e) is more likely than a null model of constant size. We estimated the parameter ω, the ratio of historical N_e to contemporary N_e (Materials and Methods and SI Materials and Methods). Results using this method indicate that the posterior probability of the expansion model (versus the null constant-size model) is 1; based on simulations under the null model, the P value of this posterior probability is 0. We estimate ω to be 0.08 (95% credibility interval 0.01–0.29; Fig. S4A). Translating these results to absolute numbers (current N_e = 30) generates an estimate of effective number of TB cases in RS before 1930 (the time fixed for the expansion, based on the social history described above) equal to 2.35 individuals (95% credibility interval 0.35–8.80). SI Results gives parameter estimations under alternative mutation rate assumptions, all of which reject the constant-size model in favor of the expansion model.

Based on the size and dynamics of the population involved in the French (Montreal-based) trade in the West before 1870 and the prevalence of TB in European cities in the 18th century, we estimated the absolute number of M. tuberculosis infections transmitted to Western indigenous populations (SI Results and Table S2). The historical estimate of N_em, the product of population size (N_e) and fraction of the indigenous M. tuberculosis population replaced by immigrants (m) per generation, is 0.16. In an island model, N_em <1 results in substantial population differentiation caused by genetic drift (22). Estimates of N_em derived from bacterial minisatellite data were higher than this historical estimate: For pooled lineages, N_em derived from F_ST (AMOVA) is 6.16, and the private alleles method of Barton and Slatkin (23) generated an estimate of 3.62 (empirical 95% confidence interval 2.47–4.72).

Discussion

The recent history of human migration to Western Canada informs the analyses of M. tuberculosis genetic data presented here. Most importantly, substantial contact between French Canadian and Western indigenous populations is limited to a specific historical period, the fur trade era. The early bound on this period of contact is provided by the dates of incursion of fur traders into the Western interior [∼1710 (24)], and the later bound is provided by historical and demographic analyses indicating that westward migration of French Canadians ceased in the latter half of the 19th century for economic and other reasons (25).

Based on the observed pattern of M. tuberculosis lineage frequencies in this historical context, as well as bacterial population genetic diversities consistent with Quebec as a source population, genetic timing estimates, and patterns of genetic differentiation between populations, we infer that the DS6^Quebec lineage was dispersed to indigenous populations by French Canadian fur traders about a century before epidemic forms of TB were manifest in Western Aboriginal communities.

Several features of the human migration associated with trade in furs are noteworthy. First, the absolute number of human migrants was small: By our estimate, 5,419 individuals migrated from east to west during 160 y of trade between Montreal and Western Canadian indigenous populations (SI Results). These early migrations are dwarfed by population movements of the late 19th and early 20th centuries. Facilitated by massive interprovincial and international migration to the Canadian prairies—from which French Canadians were largely absent—the census of Western Canada grew from 110,000 in 1871 to 750,000 in 1911 (26). Between 1900 and 1917, a total of 1,671,414 foreign-born individuals migrated to Western Canada from the United Kingdom, the Ukraine, Russia, Germany, Austria, Hungary, Norway, Denmark, China, and elsewhere (27). Despite the enormous number of migrants from regions of high TB incidence, who would be expected to introduce a broad range of Euro-American and East Asian M. tuberculosis lineages (8), bacterial populations in Western indigenous communities are dominated by the DS6^Quebec lineage, present at a frequency similar to that in the French Canadian population of Quebec (Fig. 1A).

The apparent lack of M. tuberculosis gene flow from 19th century homesteaders to indigenous populations may be explained by social distance between populations. International migrants to the prairies, particularly those facing language and cultural barriers to assimilation, were socially and geographically isolated (27). By the late 19th century, prairie indigenous populations also were socially segregated, at times forcibly (15, 27), from the non-Aboriginal population. This isolation is in contrast to the earlier fur trade era, which was characterized by intermarriage and trading collaborations between European immigrants and First Nations groups (ref. 28 and SI Background Material). Although contact between populations involved small numbers of individuals, we speculate that close social ties between the sending and receiving host populations permitted migration of M. tuberculosis through the fur trade. Given that transmission of M. tuberculosis requires sustained, close contact [exemplified by efficient transmission in high-density shared living environments such as prisons (11)], this observation is likely to be generalizable, with structure of global M. tuberculosis populations strongly influenced by the social architecture of host populations.

Although by no means a disease-free interval for Native peoples (there were devastating epidemics of smallpox and other infectious diseases), epidemics of TB were not a feature of the fur trade era (1710–1870). TB epidemics among Western Canadian indigenous populations occurred later, starting in the late 1800s (10, 13–15). Expansion of rail and steamship networks into Western Canada in the late 19th century permitted agricultural development, industrial-scale extraction of natural resources, development of government institutions, and mass immigration. TB epidemics were among a chain of sequelae for Aboriginal populations that included displacement, loss of traditional food sources, crowding, and institutionalization (ref. 29 and SI Background Material).

Indigenous populations in some regions (e.g., Northern Saskatchewan and Manitoba; the shaded areas of Fig. 1A) remained remote from the evolving industrial economy into the 1920s (21). We find that the genetic diversity of M. tuberculosis in lowest in RS and is highest in QU (Fig. 3); we did not have detailed geographic data that would allow us to classify M. tuberculosis strains from Manitoba according to the scheme we used in Saskatchewan (i.e., NRS vs. RS). We note that molecular epidemiological studies of other historically remote/traditional regions are consistent with low genetic diversity of the M. tuberculosis population (30, 31).

Differences in genetic diversity may result from two distinct phenomena. First, the process of M. tuberculosis migration is likely to involve serial founder events, so that diversity is highest in the source population (QU) and lower in the subsequently founded populations (ON, RS, NRS, AB, and MB). Another explanation is that QU, the oldest M. tuberculosis population (founded by 17th and 18th century migrants from France; Table 2), may be closer to an equilibrium distribution of haplotype frequencies; the youngest populations still may show evidence of a “founder flush” (32). As an historically remote/traditional population, RS was probably shielded from at least some of the ecological antecedents of epidemic TB until the regional incursion of air travel networks in the 1930s (21) and thus had the most recent expansion in its pathogen population. Demographic modeling with ABC demonstrated a very high probability of expansion in the RS M. tuberculosis population since 1930; the magnitude of the bacterial expansion was ∼13-fold.

Although our historical estimates of M. tuberculosis migration rates were low (direct N_em = 0.16), the lack of genetic differentiation among populations (DS6^Quebec F_ST = 0.04) and estimates of N_em from the genetic data (indirect N_em = 3.62) would suggest a high rate of M. tuberculosis migration. Slatkin (33, 34) has observed that indirect (genetic) estimates of gene flow may be higher than direct measurements of population dispersal, especially in populations characterized by colonization-extinction-recolonization dynamics, which can limit population differentiation even when rates of migration are low. Taken together, our results suggest that absolute numbers of M. tuberculosis migration events were low (N_em <1, an order-of-magnitude estimate based on historical data), and patterns of genetic differentiation have been affected by unstable dynamics of small, preindustrial M. tuberculosis populations.

We have delineated two asynchronous processes involved in the spread of TB from European immigrants to native Canadians (Fig. 1B). The first is dispersal of the etiologic agent, M. tuberculosis, populations of which were sustained at very low levels (N_e ≅ 2) for ∼100 y by small numbers of human migrants who had intimate, sustained contact with susceptible hosts. In addition to sustained migration, variable transmission dynamics of TB may have cushioned small bacterial populations against extinction (35). The second process is expansion of the bacterial population, following a shift in host ecology favoring the pathogen. We find evidence of bacterial population expansions in the DS6^Quebec M. tuberculosis haplotype network (Fig. 2), patterns of genetic diversity (Fig. 3), and coalescent-based demographic analysis of bacterial minisatellite data.

This work is a study of a specific historical phenomenon, and it is unknown whether the observed patterns of M. tuberculosis migration are applicable to other settings. Asynchronicity of pathogen migration and epidemiological phenomena is likely to render control of TB more difficult and could help explain global persistence of the pathogen despite extensive efforts at eradication. Because M. tuberculosis is an obligate human pathogen that requires specific environmental conditions and sustained contact for transmission, barriers to geographic spread of M. tuberculosis are largely social and therefore somewhat fluid. Perseverance of tiny bacterial populations would permit gradual accrual of a large geographic range despite significant population subdivision. As a result, by the time the spread of TB is obvious, M. tuberculosis populations already may be well established.

Materials and Methods

Population Descriptions.

Clinical isolates of M. tuberculosis in this study are from five Canadian populations: the French Canadian population of Quebec (QU), and Aboriginal populations in Ontario (ON), Manitoba (MB), Saskatchewan (SK), and Alberta (AB). The QU sample (n = 297) is described in ref. 16. The ON sample (n = 45) derives from TB cases that occurred between 1997–2009 in First Nations communities in a single region of the province (total population ∼25,000). MB data (n = 163) are from a published study (36): The total number of TB cases, number of different bacterial RFLP haplotypes, number of singletons, and the configuration distribution of the five most common M. tuberculosis haplotypes from First Nations reserve communities in Manitoba (1992–1999) are reported. We made the conservative assumption that the remaining (unreported) haplotypes were doubletons. The SK sample (n = 444) is described in ref. 10. AB samples (n = 283) are from TB cases among First Nations individuals in the province, excluding urban areas, from 1990–2008.

Genotyping Methods.

Isolates of M. tuberculosis were genotyped by RFLP, based on the number and location of IS6110 elements (20). The number of tandem repeats at 12 minisatellite loci also was determined for each isolate using a standard methodology (37). M. tuberculosis lineage typing, based on genomic deletions (16, 17), was done with real-time PCR (details are given in SI Materials and Methods and Dataset S1).

Mutation Rate Estimate.

We estimated a mutation rate (μ) per transmission generation (10) for minisatellite loci based on simulations using empirical estimates of intrahost M. tuberculosis population dynamics and in vitro estimates of mutations per cell doubling for bacterial minisatellite loci. Given a known per annum RFLP mutation rate (38), we made additional estimates by examining the number of RFLP types per minisatellite haplotype and comparing estimates of θ (θ = 2 N_eμ, product of effective population size, N_e, and mutation rate, μ) from RFLP and minisatellite data. All estimates were of a similar order of magnitude and were consistent with published estimates (39); we used 0.001 mutations per locus (SI Materials and Methods, Table S3).

Statistical Calculations.

Genetic differentiation.

AMOVA, implemented in Arlequin version 3.5 (40), was used to calculate F_ST values from M. tuberculosis minisatellite haplotype data.

Network analysis.

BioNumerics 5.0 (Applied Maths) was used to generate minimum spanning trees of M. tuberculosis minisatellite haplotypes. This program implements the Prim–Jarnik algorithm; the BURST priority rule maximizing single- and double-locus variants, was used during network searches.

Genetic timing estimates.

We estimated TMRCA of the DS6^Quebec lineage in each population using minisatellite genotypes and the method of Ytime (18). We selected as the root the haplotype at the center of the DS6^Quebec network (Fig. 2), present at high frequency in QU, SK, and AB populations. We obtained bootstrap confidence intervals with Ytime assuming a star-like genealogy and neutrality (SI Materials and Methods). Divergence times for DS6^Quebec isolates between pairs of populations were estimated from minisatellite genotypes by the T_D estimator, which is robust to population size changes and weak gene flow (SI Materials and Methods) (19). This procedure requires an estimate of the average variance in repeat number in the ancestral population at the time of divergence (V₀); we estimated T_D using three different values of V₀ for each pair of populations (Results and SI Materials and Methods). Alternative mutation rate and demographic assumptions have little effect on our main conclusions (SI Results).

Population genetic diversity.

We assessed diversity of minisatellite and RFLP haplotypes in each population, for all lineages, by calculating the number of distinct haplotypes using rarefaction (41), calculating haplotype diversity with resampling to the lowest sample size to correct for unequal sample sizes (42), and implementing a permutation procedure to assess whether observed diversities of minisatellite haplotypes could be explained by a random partitioning of isolates from all populations (details are given in SI Materials and Methods).

Migration.

Under a simple island model, assuming an equilibrium population where each “island” (QU, SK, and AB) has equal size N_e, we applied Slatkin's private alleles method with minisatellite haplotype data from all lineages to estimate N_em, where m is the probability that an individual is a migrant in each generation (33, 43). N_em estimates were converted to F_ST values, and vice versa, using the standard expectation for a haploid population F_ST = 1/(1+2Nm) (43) (SI Materials and Methods).

Demographic Modeling.

Motivated by the results of the diversity calculations, we used minisatellite genotypes and rejection sampling, an ABC procedure, to estimate the factor (ω) by which the size of the DS6^Quebec lineage in Remote Saskatchewan (RS) before its likely expansion is related to its current size.

Assuming a constant population size after the expansion, we estimated the current effective population size of RS as 544 (multiplying the harmonic mean of fluctuating DS6^Quebec TB case counts in RS from 1986–2004 by 18, the number of years over which exhaustive samples were obtained). This epidemiological estimate of N_e was interpreted in the standard population genetic manner (discussed further in SI Materials and Methods). One million coalescent simulations of minisatellite haplotypes under a population-expansion model were performed using SIMCOAL 2.0 (44, 45). The time of expansion was fixed at 54 generations, with ω drawn from a prior Uniform distribution on [0.01, 1]. The simulated data were summarized with four statistics (number of distinct and singleton haplotypes, haplotype diversity, and mean variance in locus repeat sizes), which produced reliable estimates in our method validation (SI Materials and Methods) and have been used in previous studies (2, 46–48). Values of ω resulting in simulations with summary statistics within a threshold Euclidean distance from those observed in RS were retained to produce a posterior distribution. We also estimated the posterior probabilities of the population expansion and null constant-size models by the acceptance probabilities of each model.

We tested the method's performance using simulated data with known expansion sizes. The method is most powerful for pronounced expansions (ω ∼ 0.1); with high accuracy, it both can estimate ω and can distinguish between the population-expansion and constant-size models (SI Materials and Methods and Fig. S5).

Acknowledgments

We thank V. Hoeppner for providing data and bacterial strains, T. MacMillan and A.D. Popescu for data collection; A. Avelar, T. Van, E. Heinemeyer, and C.-Y. Wu for technical assistance; and G. Dolganov for help with real-time PCR assays. This work was supported by National Institutes of Health Grants 5K08AI67458-2 (to C.S.P.) and GM28016 (to M.W.F.). J.M.G. is the recipient of a National Science Foundation Graduate Research Fellowship.

Footnotes

↵¹C.S.P. and J.M.G. contributed equally to this work.
↵²To whom correspondence should be addressed. E-mail: pepperc{at}stanford.edu.

Author contributions: C.S.P., J.M.G., and M.W.F. designed research; C.S.P. and J.M.G. performed research; C.S.P., D.C.A., M.A.B., L.C., J.G., J.L.G., F.B.J., D.L.-K., R.L., D.N., and W.W. contributed new reagents/analytic tools; C.S.P., J.M.G., and M.W.F. analyzed data; and C.S.P., J.M.G., and M.W.F. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1016708108/-/DCSupplemental.

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References

↵
1. Ramachandran S,
2. et al.
(2005) Support from the relationship of genetic and geographic distance in human populations for a serial founder effect originating in Africa. Proc Natl Acad Sci USA 102:15942–15947.
OpenUrl Abstract/FREE Full Text
↵
1. Ray N,
2. et al.
(2010) A statistical evaluation of models for the initial settlement of the american continent emphasizes the importance of gene flow with Asia. Mol Biol Evol 27:337–345.
OpenUrl Abstract/FREE Full Text
↵
1. Moodley Y,
2. et al.
(2009) The peopling of the Pacific from a bacterial perspective. Science 323:527–530.
OpenUrl Abstract/FREE Full Text
↵
1. Viboud C,
2. et al.
(2006) Synchrony, waves, and spatial hierarchies in the spread of influenza. Science 312:447–451.
OpenUrl Abstract/FREE Full Text
↵
1. Biek R,
2. Henderson JC,
3. Waller LA,
4. Rupprecht CE,
5. Real LA
(2007) A high-resolution genetic signature of demographic and spatial expansion in epizootic rabies virus. Proc Natl Acad Sci USA 104:7993–7998.
OpenUrl Abstract/FREE Full Text
↵
1. WHO
(2009) Global Tuberculosis Control, Global tuberculosis control: A short update to the 2009 report (World Health Organization, Geneva).
↵
1. Achtman M
(2008) Evolution, population structure, and phylogeography of genetically monomorphic bacterial pathogens. Annu Rev Microbiol 62:53–70.
OpenUrl CrossRef PubMed
↵
1. Hirsh AE,
2. Tsolaki AG,
3. DeRiemer K,
4. Feldman MW,
5. Small PM
(2004) Stable association between strains of Mycobacterium tuberculosis and their human host populations. Proc Natl Acad Sci USA 101:4871–4876.
OpenUrl Abstract/FREE Full Text
↵
1. Hershberg R,
2. et al.
(2008) High functional diversity in Mycobacterium tuberculosis driven by genetic drift and human demography. PLoS Biol 6:e311.
OpenUrl CrossRef PubMed
↵
1. Pepperell C,
2. et al.
(2010) Bacterial genetic signatures of human social phenomena among M. tuberculosis from an Aboriginal Canadian population. Mol Biol Evol 27:427–440.
OpenUrl Abstract/FREE Full Text
↵
1. Iseman MD
(2000) A Clinician's Guide to Tuberculosis (Lippincott Williams and Wilkins, Philadelphia).
↵
1. Aparicio JP,
2. Castillo-Chavez C
(2009) Mathematical modelling of tuberculosis epidemics. Math Biosci Eng 6:209–237.
OpenUrl CrossRef PubMed
↵
1. Daschuk JW,
2. Hackett P,
3. MacNeil S
(2006) Treaties and tuberculosis: First Nations people in late 19th-century western Canada, a political and economic transformation. Can Bull Med Hist 23:307–330.
OpenUrl PubMed
1. Ferguson R
(1928) Tuberculosis among the Indians of the Great Canadian Plains (Adlard and Sons Ltd. London)
↵
1. Lux M
(2001) Medicine that Walks: Disease, Medicine, and Canadian Plains Native People, 1880-1940 (Univ of Toronto Press, Toronto).
↵
1. Nguyen D,
2. et al.
(2004) Genomic characterization of an endemic Mycobacterium tuberculosis strain: Evolutionary and epidemiologic implications. J Clin Microbiol 42:2573–2580.
OpenUrl Abstract/FREE Full Text
↵
1. Gagneux S,
2. et al.
(2006) Variable host-pathogen compatibility in Mycobacterium tuberculosis. Proc Natl Acad Sci USA 103:2869–2873.
OpenUrl Abstract/FREE Full Text
↵
1. Behar DM,
2. et al.
(2003) Multiple origins of Ashkenazi Levites: Y chromosome evidence for both Near Eastern and European ancestries. Am J Hum Genet 73:768–779.
OpenUrl CrossRef PubMed
↵
1. Zhivotovsky LA
(2001) Estimating divergence time with the use of microsatellite genetic distances: Impacts of population growth and gene flow. Mol Biol Evol 18:700–709.
OpenUrl Abstract/FREE Full Text
↵
1. van Embden JD,
2. et al.
(1993) Strain identification of Mycobacterium tuberculosis by DNA fingerprinting: Recommendations for a standardized methodology. J Clin Microbiol 31:406–409.
OpenUrl Abstract/FREE Full Text
↵
1. Ray AJ
(1990) The Canadian Fur Trade in the Industrial Age (Univ of Toronto Press, Toronto).
↵
1. Wright S
(1931) Evolution in Mendelian populations. Genetics 16:97–159.
OpenUrl PubMed
↵
1. Barton NH,
2. Slatkin M
(1986) A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population. Heredity 56:409–415.
OpenUrl CrossRef PubMed
↵
1. Innis HA
(1930) The Fur Trade in Canada (Univ of Toronto Press, Toronto) Ed 1970 reprinted 1999 with a new introductory essay.
↵
1. Green A,
2. MacKinnon M,
3. Minns C
(2005) Conspicuous by their absence: French Canadians and the Settlement of the Canadian West. J Econ Hist 65:822–849.
OpenUrl
↵
1. Urquhart MC,
2. Buckley KAH
, eds (1965) Historical Statistics of Canada (Macmillan, Toronto).
↵
1. Waiser B
(2005) Saskatchewan: A New History (Fifth House, Calgary,AB, Canada).
↵
1. Francis RD
1. Francis D
(1985) in The Prairie West Historical Readings, Traders and Indians, ed Francis RD (Pica Pica, Edmonton, AB, Canada), pp 58–70.
↵
1. Friesen G
(1984) The Canadian Prairies: A History (Univ of Toronto Press, Toronto).
↵
1. Kunimoto D,
2. Chedore P,
3. Allen R,
4. Kasatiya S
(2001) Investigation of tuberculosis transmission in Canadian Arctic Inuit communities using DNA fingerprinting. Int J Tuberc Lung Dis 5:642–647.
OpenUrl PubMed
↵
1. Nguyen D,
2. et al.
(2003) Tuberculosis in the Inuit community of Quebec, Canada. Am J Respir Crit Care Med 168:1353–1357.
OpenUrl Abstract/FREE Full Text
↵
1. Templeton A
(2006) Population Genetics and Microevolutionary Theory (John Wiley & Sons, Hoboken, NJ).
↵
1. Slatkin M
(1985) Gene flow in natural populations. Annu Rev Ecol Syst 16:393–430.
OpenUrl
↵
1. Slatkin M
(1987) Gene flow and the geographic structure of natural populations. Science 236:787–792.
OpenUrl Abstract/FREE Full Text
↵
1. Blaser MJ,
2. Kirschner D
(2007) The equilibria that allow bacterial persistence in human hosts. Nature 449:843–849.
OpenUrl CrossRef PubMed
↵
1. Blackwood KS,
2. Al-Azem A,
3. Elliott LJ,
4. Hershfield ES,
5. Kabani AM
(2003) Conventional and molecular epidemiology of tuberculosis in Manitoba. BMC Infect Dis, 10.1186/1471-2334-3-18.
↵
1. Supply P,
2. et al.
(2006) Proposal for standardization of optimized mycobacterial interspersed repetitive unit-variable-number tandem repeat typing of Mycobacterium tuberculosis. J Clin Microbiol 44:4498–4510.
OpenUrl Abstract/FREE Full Text
↵
1. Tanaka MM,
2. Rosenberg NA
(2001) Optimal estimation of transposition rates of insertion sequences for molecular epidemiology. Stat Med 20:2409–2420.
OpenUrl CrossRef PubMed
↵
1. Reyes JF,
2. Tanaka MM
(2010) Mutation rates of spoligotypes and variable numbers of tandem repeat loci in Mycobacterium tuberculosis. Infect Genet Evol 10:1046–1051.
OpenUrl CrossRef PubMed
↵
1. Excoffier L,
2. Lischer HEL
(2010) Arlequin suite ver 3.5: A new series of programs to perform population genetics analyses under Linux and Windows. Molecular Ecology Resources, in press.
↵
1. Kalinowski ST
(2004) Counting alleles with rarefaction: Private alleles and hierarchical sampling designs. Conserv Genet 5:539–543.
OpenUrl CrossRef
↵
1. Shannon CE
(1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423, 623–656.
OpenUrl
↵
1. Slatkin M,
2. Barton NH
(1989) A comparison of three indirect methods for estimating average levels of gene flow. Evolution 43:1349–1368.
OpenUrl CrossRef
↵
1. Excoffier L,
2. Novembre J,
3. Schneider S
(2000) SIMCOAL: A general coalescent program for the simulation of molecular data in interconnected populations with arbitrary demography. J Hered 91:506–509.
OpenUrl FREE Full Text
↵
1. Laval G,
2. Excoffier L
(2004) SIMCOAL 2.0: A program to simulate genomic diversity over large recombining regions in a subdivided population with a complex history. Bioinformatics 20:2485–2487.
OpenUrl Abstract/FREE Full Text
↵
1. Estoup A,
2. Wilson IJ,
3. Sullivan C,
4. Cornuet JM,
5. Moritz C
(2001) Inferring population history from microsatellite and enzyme data in serially introduced cane toads, Bufo marinus. Genetics 159:1671–1687.
OpenUrl PubMed
1. Beaumont MA,
2. Zhang W,
3. Balding DJ
(2002) Approximate Bayesian computation in population genetics. Genetics 162:2025–2035.
OpenUrl PubMed
↵
1. Estoup A,
2. Beaumont M,
3. Sennedot F,
4. Moritz C,
5. Cornuet J-M
(2004) Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus. Evolution 58:2021–2036.
OpenUrl CrossRef PubMed
↵
1. NaturalResourcesCanada
(2007) Rivers and Names of Canada, Lakes. Available at http://atlas.nrcan.gc.ca/site/english/maps/reference/outlinecanada/canada06. Accessed September 29, 2010.
↵
1. NaturalResourcesCanada
(1974) Posts of the Canadian Fur Trade, Available at: http://atlas.nrcan.gc.ca/site/english/maps/archives/4thedition/historical/079_80. Accessed September 29, 2010.
↵
1. Charbonneau H,
2. et al.
(1993) The first French Canadians. Pioneers in the St. Lawrence Valley (Univ of Delaware Press, Newark, NJ).

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Proceedings of the National Academy of Sciences: 108 (16)

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Article Classifications

Biological Sciences
Evolution

[1] ↵
Ramachandran S,
et al.
(2005) Support from the relationship of genetic and geographic distance in human populations for a serial founder effect originating in Africa. Proc Natl Acad Sci USA 102:15942–15947.
OpenUrl Abstract/FREE Full Text

[2] Ramachandran S,

[3] et al.

[4] ↵
Ray N,
et al.
(2010) A statistical evaluation of models for the initial settlement of the american continent emphasizes the importance of gene flow with Asia. Mol Biol Evol 27:337–345.
OpenUrl Abstract/FREE Full Text

[5] Ray N,

[6] et al.

[7] ↵
Moodley Y,
et al.
(2009) The peopling of the Pacific from a bacterial perspective. Science 323:527–530.
OpenUrl Abstract/FREE Full Text

[8] Moodley Y,

[9] et al.

[10] ↵
Viboud C,
et al.
(2006) Synchrony, waves, and spatial hierarchies in the spread of influenza. Science 312:447–451.
OpenUrl Abstract/FREE Full Text

[11] Viboud C,

[12] et al.

[13] ↵
Biek R,
Henderson JC,
Waller LA,
Rupprecht CE,
Real LA
(2007) A high-resolution genetic signature of demographic and spatial expansion in epizootic rabies virus. Proc Natl Acad Sci USA 104:7993–7998.
OpenUrl Abstract/FREE Full Text

[14] Biek R,

[15] Henderson JC,

[16] Waller LA,

[17] Rupprecht CE,

[18] Real LA

[19] ↵
WHO
(2009) Global Tuberculosis Control, Global tuberculosis control: A short update to the 2009 report (World Health Organization, Geneva).

[20] WHO

[21] ↵
Achtman M
(2008) Evolution, population structure, and phylogeography of genetically monomorphic bacterial pathogens. Annu Rev Microbiol 62:53–70.
OpenUrl CrossRef PubMed

[22] Achtman M

[23] ↵
Hirsh AE,
Tsolaki AG,
DeRiemer K,
Feldman MW,
Small PM
(2004) Stable association between strains of Mycobacterium tuberculosis and their human host populations. Proc Natl Acad Sci USA 101:4871–4876.
OpenUrl Abstract/FREE Full Text

[24] Hirsh AE,

[25] Tsolaki AG,

[26] DeRiemer K,

[27] Feldman MW,

[28] Small PM

[29] ↵
Hershberg R,
et al.
(2008) High functional diversity in Mycobacterium tuberculosis driven by genetic drift and human demography. PLoS Biol 6:e311.
OpenUrl CrossRef PubMed

[30] Hershberg R,

[31] et al.

[32] ↵
Pepperell C,
et al.
(2010) Bacterial genetic signatures of human social phenomena among M. tuberculosis from an Aboriginal Canadian population. Mol Biol Evol 27:427–440.
OpenUrl Abstract/FREE Full Text

[33] Pepperell C,

[34] et al.

[35] ↵
Iseman MD
(2000) A Clinician's Guide to Tuberculosis (Lippincott Williams and Wilkins, Philadelphia).

[36] Iseman MD

[37] ↵
Aparicio JP,
Castillo-Chavez C
(2009) Mathematical modelling of tuberculosis epidemics. Math Biosci Eng 6:209–237.
OpenUrl CrossRef PubMed

[38] Aparicio JP,

[39] Castillo-Chavez C

[40] ↵
Daschuk JW,
Hackett P,
MacNeil S
(2006) Treaties and tuberculosis: First Nations people in late 19th-century western Canada, a political and economic transformation. Can Bull Med Hist 23:307–330.
OpenUrl PubMed

[41] Daschuk JW,

[42] Hackett P,

[43] MacNeil S

[44] Ferguson R
(1928) Tuberculosis among the Indians of the Great Canadian Plains (Adlard and Sons Ltd. London)

[45] Ferguson R

[46] ↵
Lux M
(2001) Medicine that Walks: Disease, Medicine, and Canadian Plains Native People, 1880-1940 (Univ of Toronto Press, Toronto).

[47] Lux M

[48] ↵
Nguyen D,
et al.
(2004) Genomic characterization of an endemic Mycobacterium tuberculosis strain: Evolutionary and epidemiologic implications. J Clin Microbiol 42:2573–2580.
OpenUrl Abstract/FREE Full Text

[49] Nguyen D,

[50] et al.

[51] ↵
Gagneux S,
et al.
(2006) Variable host-pathogen compatibility in Mycobacterium tuberculosis. Proc Natl Acad Sci USA 103:2869–2873.
OpenUrl Abstract/FREE Full Text

[52] Gagneux S,

[53] et al.

[54] ↵
Behar DM,
et al.
(2003) Multiple origins of Ashkenazi Levites: Y chromosome evidence for both Near Eastern and European ancestries. Am J Hum Genet 73:768–779.
OpenUrl CrossRef PubMed

[55] Behar DM,

[56] et al.

[57] ↵
Zhivotovsky LA
(2001) Estimating divergence time with the use of microsatellite genetic distances: Impacts of population growth and gene flow. Mol Biol Evol 18:700–709.
OpenUrl Abstract/FREE Full Text

[58] Zhivotovsky LA

[59] ↵
van Embden JD,
et al.
(1993) Strain identification of Mycobacterium tuberculosis by DNA fingerprinting: Recommendations for a standardized methodology. J Clin Microbiol 31:406–409.
OpenUrl Abstract/FREE Full Text

[60] van Embden JD,

[61] et al.

[62] ↵
Ray AJ
(1990) The Canadian Fur Trade in the Industrial Age (Univ of Toronto Press, Toronto).

[63] Ray AJ

[64] ↵
Wright S
(1931) Evolution in Mendelian populations. Genetics 16:97–159.
OpenUrl PubMed

[65] Wright S

[66] ↵
Barton NH,
Slatkin M
(1986) A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population. Heredity 56:409–415.
OpenUrl CrossRef PubMed

[67] Barton NH,

[68] Slatkin M

[69] ↵
Innis HA
(1930) The Fur Trade in Canada (Univ of Toronto Press, Toronto) Ed 1970 reprinted 1999 with a new introductory essay.

[70] Innis HA

[71] ↵
Green A,
MacKinnon M,
Minns C
(2005) Conspicuous by their absence: French Canadians and the Settlement of the Canadian West. J Econ Hist 65:822–849.
OpenUrl

[72] Green A,

[73] MacKinnon M,

[74] Minns C

[75] ↵
Urquhart MC,
Buckley KAH
, eds (1965) Historical Statistics of Canada (Macmillan, Toronto).

[76] Urquhart MC,

[77] Buckley KAH

[78] ↵
Waiser B
(2005) Saskatchewan: A New History (Fifth House, Calgary,AB, Canada).

[79] Waiser B

[80] ↵
Francis RD
Francis D
(1985) in The Prairie West Historical Readings, Traders and Indians, ed Francis RD (Pica Pica, Edmonton, AB, Canada), pp 58–70.

[81] Francis RD

[82] Francis D

[83] ↵
Friesen G
(1984) The Canadian Prairies: A History (Univ of Toronto Press, Toronto).

[84] Friesen G

[85] ↵
Kunimoto D,
Chedore P,
Allen R,
Kasatiya S
(2001) Investigation of tuberculosis transmission in Canadian Arctic Inuit communities using DNA fingerprinting. Int J Tuberc Lung Dis 5:642–647.
OpenUrl PubMed

[86] Kunimoto D,

[87] Chedore P,

[88] Allen R,

[89] Kasatiya S

[90] ↵
Nguyen D,
et al.
(2003) Tuberculosis in the Inuit community of Quebec, Canada. Am J Respir Crit Care Med 168:1353–1357.
OpenUrl Abstract/FREE Full Text

[91] Nguyen D,

[92] et al.

[93] ↵
Templeton A
(2006) Population Genetics and Microevolutionary Theory (John Wiley & Sons, Hoboken, NJ).

[94] Templeton A

[95] ↵
Slatkin M
(1985) Gene flow in natural populations. Annu Rev Ecol Syst 16:393–430.
OpenUrl

[96] Slatkin M

[97] ↵
Slatkin M
(1987) Gene flow and the geographic structure of natural populations. Science 236:787–792.
OpenUrl Abstract/FREE Full Text

[98] Slatkin M

[99] ↵
Blaser MJ,
Kirschner D
(2007) The equilibria that allow bacterial persistence in human hosts. Nature 449:843–849.
OpenUrl CrossRef PubMed

[100] Blaser MJ,

[101] Kirschner D

[102] ↵
Blackwood KS,
Al-Azem A,
Elliott LJ,
Hershfield ES,
Kabani AM
(2003) Conventional and molecular epidemiology of tuberculosis in Manitoba. BMC Infect Dis, 10.1186/1471-2334-3-18.

[103] Blackwood KS,

[104] Al-Azem A,

[105] Elliott LJ,

[106] Hershfield ES,

[107] Kabani AM

[108] ↵
Supply P,
et al.
(2006) Proposal for standardization of optimized mycobacterial interspersed repetitive unit-variable-number tandem repeat typing of Mycobacterium tuberculosis. J Clin Microbiol 44:4498–4510.
OpenUrl Abstract/FREE Full Text

[109] Supply P,

[110] et al.

[111] ↵
Tanaka MM,
Rosenberg NA
(2001) Optimal estimation of transposition rates of insertion sequences for molecular epidemiology. Stat Med 20:2409–2420.
OpenUrl CrossRef PubMed

[112] Tanaka MM,

[113] Rosenberg NA

[114] ↵
Reyes JF,
Tanaka MM
(2010) Mutation rates of spoligotypes and variable numbers of tandem repeat loci in Mycobacterium tuberculosis. Infect Genet Evol 10:1046–1051.
OpenUrl CrossRef PubMed

[115] Reyes JF,

[116] Tanaka MM

[117] ↵
Excoffier L,
Lischer HEL
(2010) Arlequin suite ver 3.5: A new series of programs to perform population genetics analyses under Linux and Windows. Molecular Ecology Resources, in press.

[118] Excoffier L,

[119] Lischer HEL

[120] ↵
Kalinowski ST
(2004) Counting alleles with rarefaction: Private alleles and hierarchical sampling designs. Conserv Genet 5:539–543.
OpenUrl CrossRef

[121] Kalinowski ST

[122] ↵
Shannon CE
(1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423, 623–656.
OpenUrl

[123] Shannon CE

[124] ↵
Slatkin M,
Barton NH
(1989) A comparison of three indirect methods for estimating average levels of gene flow. Evolution 43:1349–1368.
OpenUrl CrossRef

[125] Slatkin M,

[126] Barton NH

[127] ↵
Excoffier L,
Novembre J,
Schneider S
(2000) SIMCOAL: A general coalescent program for the simulation of molecular data in interconnected populations with arbitrary demography. J Hered 91:506–509.
OpenUrl FREE Full Text

[128] Excoffier L,

[129] Novembre J,

[130] Schneider S

[131] ↵
Laval G,
Excoffier L
(2004) SIMCOAL 2.0: A program to simulate genomic diversity over large recombining regions in a subdivided population with a complex history. Bioinformatics 20:2485–2487.
OpenUrl Abstract/FREE Full Text

[132] Laval G,

[133] Excoffier L

[134] ↵
Estoup A,
Wilson IJ,
Sullivan C,
Cornuet JM,
Moritz C
(2001) Inferring population history from microsatellite and enzyme data in serially introduced cane toads, Bufo marinus. Genetics 159:1671–1687.
OpenUrl PubMed

[135] Estoup A,

[136] Wilson IJ,

[137] Sullivan C,

[138] Cornuet JM,

[139] Moritz C

[140] Beaumont MA,
Zhang W,
Balding DJ
(2002) Approximate Bayesian computation in population genetics. Genetics 162:2025–2035.
OpenUrl PubMed

[141] Beaumont MA,

[142] Zhang W,

[143] Balding DJ

[144] ↵
Estoup A,
Beaumont M,
Sennedot F,
Moritz C,
Cornuet J-M
(2004) Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus. Evolution 58:2021–2036.
OpenUrl CrossRef PubMed

[145] Estoup A,

[146] Beaumont M,

[147] Sennedot F,

[148] Moritz C,

[149] Cornuet J-M

[150] ↵
NaturalResourcesCanada
(2007) Rivers and Names of Canada, Lakes. Available at http://atlas.nrcan.gc.ca/site/english/maps/reference/outlinecanada/canada06. Accessed September 29, 2010.

[151] NaturalResourcesCanada

[152] ↵
NaturalResourcesCanada
(1974) Posts of the Canadian Fur Trade, Available at: http://atlas.nrcan.gc.ca/site/english/maps/archives/4thedition/historical/079_80. Accessed September 29, 2010.

[153] NaturalResourcesCanada

[154] ↵
Charbonneau H,
et al.
(1993) The first French Canadians. Pioneers in the St. Lawrence Valley (Univ of Delaware Press, Newark, NJ).

[155] Charbonneau H,

[156] et al.

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Dispersal of Mycobacterium tuberculosis via the Canadian fur trade

Abstract

Results

Discussion

Materials and Methods

Population Descriptions.

Genotyping Methods.

Mutation Rate Estimate.

Statistical Calculations.

Genetic differentiation.

Network analysis.

Genetic timing estimates.

Population genetic diversity.

Migration.

Demographic Modeling.

Acknowledgments

Footnotes

References

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Dispersal of Mycobacterium tuberculosis via the Canadian fur trade

Abstract

Results

Discussion

Materials and Methods

Population Descriptions.

Genotyping Methods.

Mutation Rate Estimate.

Statistical Calculations.

Genetic differentiation.

Network analysis.

Genetic timing estimates.

Population genetic diversity.

Migration.

Demographic Modeling.

Acknowledgments

Footnotes

References

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