Division of Parasitic Diseases, Centers for Disease Control and Prevention, Atlanta, Georgia
Division of Parasite and Vector Biology, Liverpool School of Tropical Medicine, Liverpool, England
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Abstract |
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Introduction |
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Recently, methods have been developed to test for mutation-drift equilibrium (MDE), which should be approached more slowly than migration-drift equilibrium, and to trace past population demography from mitochondrial (e.g., Rogers and Harpending 1992
) and microsatellite loci (e.g., Kimmel et al. 1998
; Reich and Goldstein 1998
). In this study, we apply these methods to mtDNA and 18 microsatellite loci from populations of A. gambiae and A. arabiensis to address the following questions: (1) Are populations of A. gambiae and A. arabiensis at MDE? (2) If not, was disequilibrium a result of population expansion or contraction? (3) Do populations within a species and/or across species show similar historical demographics? (4) What is the likely influence of the observed demographic history on estimates of gene flow? The answers to these questions not only will elucidate the historical demographics of these species, but will also clarify the utility of the estimates of gene flow derived from differentiation indices.
To maximize independence of populations, we selected two populations for each species that had been shown by earlier work to exhibit the greatest differentiation (Lehmann et al. 1999
; Donnelly and Townson 2000
). The two populations of A. gambiae within Kenya showed higher differentiation than did the same western Kenyan population and one from Senegal (Lehmann et al. 1999
). We selected analytical methods that exploited different aspects of the data in order to maximize independence between tests. Together, these tests can provide a comprehensive picture of the past demographics of these species. Selection can produce patterns of variation that are indistinguishable from those produced by demographic changes (e.g., Tajima 1989
; Fu and Li 1993
). To avoid confusing selection (which is locus-specific) with demographic instability, we relied on the composite signature of all 19 loci, representing two marker systems, mtDNA and microsatellites.
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Materials and Methods |
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Slatkin (1994b)
demonstrated that the probability of detecting linkage disequilibrium between closely linked (neutral) loci is greatly diminished in a recently expanded population. This is a result of the accumulation of new mutations when haplotype loss is minimal. Ancestral haplotypes will persist in the population and will be indistinguishable from putative recombination events, thereby confounding tests of linkage disequilibrium. Calculations of linkage disequilibrium between polymorphic sites in the mtDNA were performed using DnaSP, version 3.
Analyses of the mismatch distribution (the frequency distribution of pairwise differences in mtDNA sequences) as proposed by Slatkin and Hudson (1991)
, Rogers and Harpending (1992)
, and Rogers (1995)
distinguish between the smooth unimodal distribution of a recently expanded population that is shaped by accumulation of mutations with minimal lineage loss and the "ragged" multimodal distributions that are shaped by mutations in equilibrium with stochastic lineage loss. Harpending et al. (1993)
suggested a "raggedness" statistic based on the sum of the squared differences between the frequencies of successive entries (the number of mutational differences between sequences) in the distribution. The statistical significance of this value may be determined from the distribution of the statistic determined by simulations. All calculations were performed using DnaSP, version 3.
Methods to Infer Historic Population Demographics from Microsatellite Data
Cornuet and Luikart (1996)
have extended the single-locus homozygosity test (Watterson 1978
) to multiple loci under a range of mutation models, including the infinite-alleles model (IAM), the stepwise mutation model (SMM), and the two-phase model (TPM). This approach, analogous to the Tajima test, compares the homozygosity (or its complementexpected heterozygosity) calculated on the basis of allele frequencies with that calculated on the basis of the number of alleles and the sample size, which are expected to be identical in a neutral locus in a population at MDE. To evaluate the sensitivity of the results to the mutation model, we performed the tests under the SMM, the TPM with mutations of more than one repeat occurring at frequencies of 10%, 20%, and 30%, and even under the IAM. Significant departure between the estimates of heterozygosity under the correct mutation model implies that the population is not at MDE. Tests were performed using the Bottleneck program (Cornuet and Luikart 1996
).
Kimmel et al.'s (1998)
approach follows a rationale similar to that of Tajima (1989)
, Fu and Li (1993)
, and Cornuet and Luikart (1996)
in that it contrasts an estimate of
(=4Neµ; diploid autosomes) calculated from allele frequencies with an estimate calculated on the basis of the variance in repeat numbers. In neutral loci in a population at MDE, the estimates will be equal. The quotient of the two estimates, termed the imbalance index (ß =
var/
freq) will depart from 1 after a demographic change. ß, and 95% confidence intervals estimated by bootstrapping over loci were calculated using programs written in the SAS language (SAS Institute 1990
).
The k-test of Reich and Goldstein (1998)
exploits differences between the expected distributions of alleles in populations at MDE and populations that have recently expanded. The expected distribution of a recently expanded population tends to be unimodal, and more peaked than the multimodal and heavier-tailed distribution of a population at MDE (Reich and Goldstein 1998
). The g-test of Reich and Goldstein (1998)
compares the between-loci variance in the number of repeats with a theoretical expectation derived assuming that the loci follow an SMM and that the population size is stable. We performed both the k- and the g-tests using programs written in the SAS language. k-statistics were calculated for each locus, and the significance of the proportion of positive k values was based on a binomial distribution with the probability of a positive k set conservatively as 0.515 (Reich, Feldman, and Goldstein 1999
). Significance levels for the g-test are given in Reich, Feldman, and Goldstein (1999)
.
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Results |
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Microsatellites
The polymorphism of the 18 microsatellite loci in A. gambiae and A. arabiensis was moderate to high (table 1
). The higher genetic diversity of A. gambiae may reflect an ascertainment bias, as the loci were originally isolated from this species or a lower effective population size in A. arabiensis, as suggested by previous studies (Taylor et al. 1993
; Lehmann et al. 1998
; Simard et al. 2000
). Genetic diversity of the A. gambiae population from eastern Kenya was lower than that of western Kenya (expected heterozygosity: Wilcoxon signed-ranks test, n = 18, P < 0.02; number of alleles: sign test, n = 18, P < 0.001), in accordance with previous reports based on a subset of nine of the loci (Lehmann et al. 1998, 1999
). No significant differences in genetic diversity were detected between the populations of A. arabiensis. Exact tests of linkage disequilibrium, using the sequential Bonferroni correction to accommodate the number of tests, showed no significant departure from equilibrium between any locus pair in any population, thereby demonstrating the independence of loci. Using 18 independent loci would allow us to distinguish between a locus-specific effect, such as that caused by selection, and a genomewide effect, caused by a demographic change.
The results of the homozygosity test (Cornuet and Luikart 1996
) were dependent on the mutation model (table 4
). We emphasize the results based on the SMM and TPM models, since the consensus is that they better approximate the mutation process at microsatellite loci than the IAM (e.g., Weber and Wong 1993
; Di Rienzo et al. 1994
; Primmer et al. 1998
). Higher heterozygosity based on the number of alleles was significant for A. gambiae populations under the SMM and the TPM with multiple repeat mutations at frequencies of 10% and 20%. Similarly, A. arabiensis remained significant, with up to 10% multiple repeat mutations (table 4 ). Higher heterozygosity based on the number of alleles across many independent loci indicates a recent expansion of the population. Another possible cause, a recent influx of rare alleles from genetically distinct populations (Cornuet and Luikart 1996
), is unlikely given that the same signature was observed in all populations and that allele frequency distributions are relatively homogeneous between populations (Lehmann et al. 1996, 1999
; Donnelly and Townson 2000
). Similarly to mtDNA, the pattern of departure from MDE due to a recent expansion was stronger in A. gambiae, as the average deviation from expectation under MDE was larger and departures from equilibrium persisted under a wider range of mutation models (table 4
).
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The interlocus g-test showed no evidence for deviation from equilibrium in any of the populations (table 5 ). This may reflect the decreased power of this test with extensive variation in mutation rate across loci as may be the case with our data set, which combines dinucleotide and trinucleotide microsatellite loci.
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Discussion |
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MDE was rejected by six of the eight tests in the A. gambiae populations from western Kenya and by three of these tests in eastern Kenya. In both populations, departures were detected in mtDNA- and microsatellite-based tests (table 6
). All departures from equilibrium in the western Kenyan population were consistent with a recent population expansion, and the same trend was also apparent in the two nonsignificant tests. Departures from equilibrium in the eastern Kenyan population showed traces of both a recent expansion and a bottleneck (table 6
). Indeed, previous studies have suggested that a bottleneck had occurred in eastern Kenya, based on its lower genetic diversity, the presence of all eastern Kenyan microsatellite alleles (with frequency > 5%) in western Kenya but the absence of several western Kenyan alleles in eastern Kenya, and evidence that differentiation in mtDNA and microsatellites was generated primarily by drift and not by mutation-drift (Lehmann et al. 1998, 1999, 2000
). The lack of significant linkage disequilibrium in the mtDNA, even between mutations shared by three or more individuals (table 3
), and the unimodal, relatively smooth, and narrow-tailed mismatch distributions of these populations (fig. 3
) suggest that expansion started from a virtually monomorphic population, and the expansion, whose traces are found in both populations, preceded the bottleneck in eastern Kenya.
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The weaker signal of expansion in A. arabiensis may reflect an earlier expansion, a smaller change in effective population size between the pre- and postexpansion populations, and/or a smaller current population size. The expansion detected in these species may be contemporaneous with the agricultural revolution in sub-Saharan Africa (4,00010,000 years ago). Coluzzi (1982)
proposed that because these species were dependent on humans for feeding and breeding sites, mosquito populations may have mirrored the growth in populations of humans and domestic animals during this period. Estimates of current Ne for A. arabiensis (Taylor et al. 1993
; Simard et al. 2000
) are an order of magnitude lower than those for A. gambiae (Lehmann et al. 1998
). A lower effective population size would mean that A. arabiensis would approach MDE more rapidly after an expansion. Whether the expansion was a result of the agricultural revolution or was, for example, associated with ameliorating conditions after an extensive drought remains to be resolved.
Dependence on Assumed Mutation Models
Microsatellite-based tests of past demographic stability assume a certain mutation model, and an incorrectly specified model can influence the outcomes of tests (e.g., the homozygosity test; table 4
). Most empirical and theoretical work suggests that the SMM and the TPM are more appropriate mutation models for microsatellite loci than is the IAM (Shriver et al. 1993
; Di Rienzo et al. 1994
; Schlötter et al. 1998
). If the mutation process approximates an IAM, then the k-test may falsely reject a stable population size (Reich, Feldman, and Goldstein 1999
). Conversely, as demonstrated by King, Kimmel, and Chakraborty (2000)
, the imbalance index ß, will become more conservative as loci approach an IAM, because the estimate of
derived from variance in allele size will be higher than that estimated from allele frequency. Therefore, even under an IAM, MDE would be rejected in A. gambiae as a result of a significant imbalance index ß and mtDNA tests, but no significant departure from MDE would be detected in A. arabiensis populations. However, an IAM, or a TPM with a high frequency of multiple steps, is unlikely for our microsatellite data because allele arrays have virtually no gaps in the series of allele size, which must be expected under the these models (for allele arrays, see Lehmann et al. 1999
; Donnelly and Townson 2000
).
The current findings help reconcile the discrepancy between ecological studies, suggesting limited dispersal (Adams 1940
), and indirect genetic studies, suggesting high rates of migration across vast distances (Lehmann et al. 1996
; Donnelly and Townson 2000
). Estimates of migration derived from differentiation indices are inflated by a recent expansion. The opposite effect may apply to populations to the east of the eastern Rift Valley, where a recent bottleneck resulted in an underestimation of gene flow (see Lehmann et al. 1999, 2000
). The degree of bias in estimates of gene flow that the demographic changes cause is unknown, which highlights the need for new methods to infer contemporary gene flow in nonequilibrium populations. Large current Ne values and recent dramatic population size changes are likely to be common in many "pest species," and therefore tests of MDE should be performed before gene flow is inferred from differentiation indices.
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Conclusions |
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Acknowledgements |
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Footnotes |
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1 Keywords: Anopheles
malaria
mosquitoes
population genetics
expansion
2 Address for correspondence and reprints: Martin J. Donnelly, Centers for Disease Control and Prevention, MS F22, 4770 Buford Highway, Chamblee, Georgia 30341. E-mail: mpd7{at}cdc.gov
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