ARTICLE
Received 1 Jun 2010 | Accepted 1 Oct 2010 | Published 2 Nov 2010
DOI: 10.1038/ncomms1104
Global distribution of the sickle cell gene and
geographical confirmation of the malaria
hypothesis
Frédéric B. Piel1, Anand P. Patil1, Rosalind E. Howes1, Oscar A. Nyangiri2, Peter W. Gething1, Thomas N. Williams2,
David J. Weatherall3 & Simon I. Hay1
It has been 100 years since the first report of sickle haemoglobin (HbS). More than 50 years
ago, it was suggested that the gene responsible for this disorder could reach high frequencies
because of resistance conferred against malaria by the heterozygous carrier state. This
traditional example of balancing selection is known as the ‘malaria hypothesis’. However, the
geographical relationship between the transmission intensity of malaria and associated HbS
burden has never been formally investigated on a global scale. Here, we use a comprehensive
data assembly of HbS allele frequencies to generate the first evidence-based map of the
worldwide distribution of the gene in a Bayesian geostatistical framework. We compare this
map with the pre-intervention distribution of malaria endemicity, using a novel geostatistical
area-mean comparison. We find geographical support for the malaria hypothesis globally; the
relationship is relatively strong in Africa but cannot be resolved in the Americas or in Asia.
Spatial Ecology and Epidemiology Group, Tinbergen Building, Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK.
Kenya Medical Research Institute/Wellcome Trust Programme, Centre for Geographic Medicine Research-Coast, PO Box 230, Kilifi District Hospital,
Kilifi 80108, Kenya. 3 Weatherall Institute of Molecular Medicine, John Radcliffe Hospital, Oxford OX3 9DS, UK. Correspondence and requests for materials
should be addressed to F.B.P. (email: [email protected]) or S.I.H. (email: [email protected]).
1
2
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I
t has been a century since the first description of abnormally elongated red blood cells in an anaemic patient and the link with the
clinical symptoms of what is now called sickle cell anaemia (SCA)
was published1. Sickle haemoglobin (HbS), a structural variant of
normal adult haemoglobin, results from a single amino acid substitution at position 6 of the beta globin molecule (β 6Glu→Val)2. When
HbS is inherited from only one parent, the heterozygous child is
usually an asymptomatic carrier2. When inherited from both parents,
the homozygous child suffers from SCA. HbS is the most common
pathological haemoglobin variant worldwide3. Without treatment,
which is rarely available in low-income, high-burden countries4,
the vast majority of children born with SCA die before the
age of 5 years3. Natural selection should therefore have purged this
mutation from human populations, but allele frequencies of HbS in
excess of 15% have been observed5.
In 1949, it was suggested that the Darwinian paradox of high
frequencies of genetic blood disorders could result from a selective
advantage conferred by such disorders in protecting against Plasmodium falciparum malaria infection in heterozygotes6. This balancing selection, commonly referred to as the ‘malaria hypothesis’,
was originally suggested to explain the geographical correspondence between the distribution of thalassaemia and malaria in the
Mediterranean region, and was later confirmed7 in many locations
including Sardinia8, Melanesia9,10 and Kenya11. At the same time, a
similar relationship between HbS and malaria was independently
discovered in Africa12,13. In vitro and in vivo studies have since added
support for the protective role of HbS against malaria14,15.
Despite significant bibliographic assemblies of information on
the distribution of HbS5,16, important limitations exist with previous
mapping efforts17–19. These include (i) the inclusion of non-random
population samples (such as those including patients with malaria
or samples from related individuals) that could bias HbS allele frequency estimates; (ii) poor discrimination between indigenous and
recently migrated populations that could confound evidence of the
relationship between HbS allele frequency and historical malaria
endemicity; (iii) the lack of inclusion of HbS allele frequency local
geographical heterogeneities; and (iv) limited documentation on the
cartographic methodology used to generate maps, making them difficult to reproduce and evaluate objectively. More importantly, the
geographical support for the malaria hypothesis has never advanced
beyond visual comparison20–24.
In this study, we conduct a formal investigation of the geographical evidence in support of the malaria hypothesis at the global scale.
In brief, we first updated previous data collections5,16 with online
searches of the published literature, which we augmented using
unpublished data from the Malaria Genomic Epidemiology Network Consortium (MalariaGEN, http://www.malariagen.net)25, to
create a comprehensive geodatabase of HbS allele frequency. These
were reviewed using criteria devised to exclude sources of bias, such
as those resulting from the inclusion of data from non-representative or non-indigenous populations. We then mapped these data
using a Bayesian model-based geostatistical framework26–28. This
enabled a comparison, for each pixel, between the modelled HbS
allele frequency and the endemicity of malaria based on a unique
categorical map reflecting its distribution before the era of interventions for malaria control29. Finally, a geostatistical test for geographical association was devised, by computing the areal mean HbS allele
frequency associated with each historical malaria endemicity class
and calculating the probability that these mean values increased in
each successive class.
Results
HbS allele frequency database and map. Searches of the literature
identified 41,445 references (see Methods), 90% of which did not
include data allowing allele frequency calculations. The application
of additional inclusion criteria further restricted the total to 278
informative references (see Supplementary References 64–342,
cited in alphabetical order by surname), which have been used as
inputs to our model. A total of 699 spatially unique data points were
abstracted from these sources and entered into our georeferenced
database with 74 additional surveys from MalariaGEN. Of these, 29
(4%) were located in the Americas, 618 (80%) in Africa and Europe
(mostly subSaharan Africa) and 126 (16%) in Asia (Fig. 1a and
Supplementary Fig. S1).
Using our model (see Methods), we produced a continuous
10 × 10 km resolution global raster grid of HbS allele frequency,
with predictions drawn from the median of the posterior predictive
distribution for each pixel (Fig. 1b), accompanied by a per-pixel estimate of prediction uncertainty (Fig. 2). Empirical model performance was judged by comparing observed HbS allele frequencies with
predicted values for a randomly removed subset of 10% of the data
points, which revealed a mean error and a mean absolute error in HbS
allele frequency predictions of − 0.15 and 6.76%, respectively (see
Methods). This global map of HbS allele frequencies should not be
interpreted as showing the contemporary geographical distribution
of this gene. It is the first global map of the distribution of the HbS
gene, based on representative and indigenous population samples
(see Methods).
Our HbS map (Fig. 1b) showed an HbS allele frequency of > 0.5%
to be present throughout most of the African continent, the Middle
East and India and in localized areas in Mediterranean countries.
The maximum predicted value of HbS allele frequency was 18.18%
in northern Angola. A large contiguous area with frequencies above
9% was observed stretching from southern Ghana to northern Zambia. The map also indicated similar frequencies in an area extending
from southern Senegal to northern Liberia, in localized patches in
eastern Côte d’Ivoire, the eastern shores of Lake Victoria, southeast
Tanzania and oases on the east coast of Saudi Arabia, as well as in
the southern Chhattisgarh and southern Karnataka regions of India.
Areas with frequencies above 6% were predicted in Madagascar,
central Sudan, the west coast of Saudi Arabia, southeastern Turkey
and in the Chalkidiki region of Greece. The many records of absence
(Fig. 1a) and the very low HbS allele frequencies predicted by our
model (Fig. 1b) also confirmed that HbS was largely absent from the
Horn of Africa and from areas south of the Zambezi.
Spatial validation of the malaria hypothesis. To test the geographical association between HbS and malaria, we used the only available global map of preintervention malaria transmission intensity
(endemicity; see Methods)29. On the basis of an assembly of historical malariometric information, this map categorized the world circa
1900 into six classes of successively higher endemicity: malaria free,
epidemic, hypoendemic, mesoendemic, hyperendemic and holoendemic (see Fig. 1c for endemicity class definitions)29,30.
The relationship between the predicted HbS allele frequencies
and the level of malaria endemicity was summarized graphically
in violin plots (Fig. 3), which illustrate the density distributions of
predicted HbS allele frequencies within each endemic area. HbS
was absent from epidemic areas, which were found only in northern America and Eurasia. Globally, predicted HbS allele frequencies were similar in malaria-free, hypoendemic and mesoendemic
zones, but were substantially higher in hyperendemic and holo­
endemic areas (Fig. 3a). In Africa and Europe (Fig. 3b), an increase
in HbS allele frequencies from hypoendemic through to holo­
endemic malaria zones was more pronounced. In Asia (Fig. 3c),
no relation between predicted HbS allele frequencies and malaria
endemicity was found. HbS was absent in the indigenous populations of the Americas.
Although the maps and violin plots provided a valuable insight
into the covariation of HbS allele frequency and malaria endemicity, our aim was to formally quantify the significance of any such
relationship. Measurement of the difference between the areal mean
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HbS data points
Presence
Absence
HbS allele frequency (%)
0 – 0.51
0.52 – 2.02
2.03 – 4.04
4.05 – 6.06
6.07 – 8.08
8.09 – 9.60
9.61 – 11.11
11.12 – 12.63
12.64 – 14.65
14.66 – 18.18
Malaria endemicity
Malaria free
Epidemic
Hypoendemic
Mesoendemic
Hyperendemic
Holoendemic
Figure 1 | Global distribution of the sickle cell gene. (a) Distribution of the data points. Red dots represent the presence and blue dots the absence of the
HbS gene. The regional subdivisions were informed by Weatherall and Clegg19, and are as follows: the Americas (light grey), Africa, including the western
part of Saudi Arabia, and Europe (medium grey) and Asia (dark grey); (b) Raster map of HbS allele frequency (posterior median) generated by a Bayesian
model-based geostatistical framework. The Jenks optimized classification method was used to define the classes45; (c) The historical map of malaria
endemicity29 was digitized from its source using the method outlined in Hay et al.44 The classes are defined by parasite rates (PR2 − 10, the proportion of
2- up to 10-year olds with the parasite in their peripheral blood): malaria free, PR2 − 10 = 0; epidemic, PR2 − 10 ≈ 0; hypoendemic, PR2 − 10 < 0.10; mesoendemic,
PR2 − 10 ≥ 0.10 and < 0.50; hyperendemic, PR2 − 10 ≥ 0.50 and < 0.75; holoendemic, PR0 − 1 ≥ 0.75 (this class was measured in 0- up to 1-year olds)29,30.
HbS allele frequency calculated within each endemicity area allowed
us to quantify the statistical strength of such differences, taking into
account the inherent uncertainty of the predicted HbS allele frequencies (see Methods). Differences in areal means between endemicity regions were calculated for 100 unique realizations of the
HbS allele frequency map generated by the Bayesian model (Fig. 4
and Supplementary Fig. S2). When combined, these realizations
produced predictive probability distributions for the difference in
areal mean HbS allele frequency between each successive endemicity class (see Table 1 and Methods).
These geostatistical measures provide the first quantitative
evidence for a geographical link between the global distribution
of HbS and malaria endemicity. At the global level, we found clear
High : 0.47
Low : 0.00
Figure 2 | Map of the uncertainty of the HbS allele frequency prediction.
Interval between the 2.5 and 97.5% quantiles (95% probability) of the
per-pixel predicted allele frequency using a continuous scale.
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0.10
HbS allele frequency
HbS allele frequency
0.12
0.15
0.10
0.05
0.08
0.06
0.04
0.02
0.00
0.00
Epidemic Hypoendemic Mesoendemic Hyperendemic Holoendemic
Malaria free
n = 1,847,900 n = 394,356 n = 594,008
n = 552,032
n = 339,100
n = 105,744
Malaria free
Epidemic
Hypoendemic Mesoendemic Hyperendemic Holoendemic
Malaria free
Epidemic
Hypoendemic Mesoendemic Hyperendemic Holoendemic
Malaria free
Epidemic
Hypoendemic Mesoendemic Hyperendemic Holoendemic
0.10
HbS allele frequency
HbS allele frequency
0.12
0.15
0.10
0.05
0.08
0.06
0.04
0.02
0.00
Malaria free
n = 328,662
0.00
Epidemic Hypoendemic Mesoendemic Hyperendemic Holoendemic
n = 64,252 n = 155,146
n = 101,344
n = 143,998
n = 168,576
0.10
HbS allele frequency
HbS allele frequency
0.12
0.15
0.10
0.05
0.00
0.06
0.04
0.02
0.00
Malaria free
n = 704,970
Epidemic Hypoendemic Mesoendemic Hyperendemic Holoendemic
n = 4,400
n = 258,584 n = 320,756 n = 210,568
n = 132,802
Figure 3 | Comparison of the distribution of HbS and malaria. Violin plots
of the predicted median HbS allele frequency for each pixel, within each
malaria endemicity class, for the world (a), Africa and Europe (b) and Asia
(c). The plot for the Americas is not shown as the predicted median was
in the lowest histogram bin (between 0 and 0.5%) everywhere. The green
areas match the colours used in the historical map of malaria endemicity
(Fig. 1c) and show a smoothed approximation of the frequency distribution
(a kernel density plot) of the predicted allele frequency within each
endemicity class. The black central bar indicates the interquartile range
and the white circles indicate the median values. The plots have been
adjusted to an equal-area projection of the Earth.
differences between high endemicity classes (Fig. 4a), associated
with a high probability of HbS allele frequency increases ( > 90%)
from mesoendemic to hyperendemic and hyperendemic to holoendemic areas, as well as from epidemic to hypoendemic areas (Table
1). In Africa, we observed a gradual increase from epidemic to
holoendemic (Fig. 4b). High probabilities of increase were found
between the same classes as in the global analysis, but also from
hypoendemic to mesoendemic areas (87%). In Asia, differences
between classes were much smaller (Fig. 4c) and the probabilities of
increase were much lower between most classes, especially in areas
of high endemicity.
Discussion
A strong geographical link between the highest HbS allele frequencies and high malaria endemicity was observed at the global scale
(Fig. 4a), but this observation is influenced primarily by the relationship found in Africa (Fig. 4b). The gradual increase in HbS
allele frequencies from epidemic areas to holoendemic areas in
Africa is consistent with the hypothesis that malaria protection by
HbS involves the enhancement of not only innate but also acquired
immunity to P. falciparum31. Interactions with haemoglobin C32,33
might explain the lower HbS allele frequencies in West Africa24.
0.08
Figure 4 | Quantitative validation of the geographical support for the
malaria hypothesis. Violin plots of the predictive distribution of the areal
mean of HbS prevalence over each endemicity region, for the world (a),
Africa and Europe (b) and Asia (c). The green areas match the colours
used in the historical map of malaria endemicity (Fig. 1c) and show a
smoothed approximation of the frequency distribution (a kernel density
plot) of the predicted allele frequency within each endemicity class. The
black central bar indicates the interquartile range and the white circles
indicate the median values. The plots have been adjusted to an equal-area
projection of the Earth.
Despite the presence of large malarious areas, HbS is absent in the
Americas and in large parts of Asia2 (Fig. 1a). Therefore, no geographical confirmation of the malaria hypothesis could be identified
in these regions. Although several haemoglobin variants have been
identified in the Americas5, none of the malaria protective polymorphisms have been observed in the indigenous populations of this
continent19. The combination of the low likelihood of an independent HbS mutation arising and a relatively low selection pressure
(due to the absence of holoendemic areas, the more recent arrival of
malaria, as well as the predominance of P. vivax) could contribute to
the absence of HbS in that region. In Southeast Asia34, other malaria
protective polymorphisms have been identified (haemoglobin E
(HbE), the thalassaemias, glucose-6-phosphate dehydrogenase
deficiency and Southeast Asian ovalocytosis) and levels of malaria
endemicity were relatively high. It is suspected that HbE and Southeast Asian ovalocytosis in particular may have had epistatic interactions35,36, altering the selection pressure for the HbS gene in that
region37. The complex social structure and the predominance of
P. vivax38 are also considered as likely to contribute to the unresolved
geographical relationship in India. Ongoing work to create an
open-access database for several malaria protective polymorphisms
will allow more comprehensive distribution mapping and improve
our understanding of their geographical interaction.
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Table 1 | Probabilities of an increase in the areal mean for each pair of consecutive malaria endemicity classes.
World
The Americas
Africa
Asia
Malaria free–
epidemic
Epidemic–
hypoendemic
0.0366
0.1312
0.0030
0.0966
0.9729
0.5170
0.9939
0.9210
Hypoendemic–
mesoendemic
Mesoendemic–
hyperendemic
0.6570
0.4245
0.8744
0.7646
Hyperendemic–
holoendemic
0.9996
0.4202
0.9964
0.6047
0.9998
NA
0.9422
0.0041
Abbreviation: NA, not applicable.
The Monte Carlo s.e. of the estimate were all lesser than 0.001.
Substantial variations in HbS allele frequencies over short distances (up to 10% over < 50 km) have been described in literature5,
for example, in relation to altitude, rainfall or Anopheles survival39,
which underlie variations in selection40. Such spatial heterogeneity was observed in the geodatabase. The combination of a detailed
georeferencing process, the use of a geostatistical model able to
incorporate the multiple scales of variation within the data and a
semicontinuous gradient of HbS allele frequencies allowed us to
describe the global distribution and the high geographical variability of this gene more rigorously than achieved in previous maps17–19.
The uncertainty measure (see Fig. 2) provides an important estimate of the limitations associated with a retrospective data set,
and can highlight areas prone to small population samples and/or
areas lacking observations (for example, New Zealand).
Among the factors that might contribute to the heterogeneity
observed in the HbS allele frequency in hyperendemic areas in Africa
(Fig. 3b), we identified (i) a component of geographical sampling
error from an ‘opportunistic sample’ of surveys that we were able to
source from literature; (ii) the kinetics of the spread of the HbS gene,
which leads to an exponential increase in areas in which a selective
pressure appears, but to a much slower decrease in areas in which the
selective pressure disappears41; (iii) long-term (sociological or physical) isolation of local populations, which could result in pockets of
lower HbS allele frequencies observed on the map (Fig. 1b).
One hundred years after the first description of SCA, we used a
comprehensive search combined with a rigorous selection of survey
data and modern mapping methods to create a new, evidence-based
map of the worldwide distribution of HbS allele frequency and to
quantify the uncertainty in these mapped predictions. Using a novel
geostatistical approach that accounts for this uncertainty, we have
compared this new map with a historical map of the global endemicity of malaria. We provide the first geographical and quantitative
confirmation of the malaria hypothesis at the global scale.
Methods
Creating a global database of sickle cell allele frequencies. A schematic
overview of the methods used is provided as Figure 5. To identify publications
with HbS allele frequency data, a comprehensive electronic data search was
undertaken using PubMed (http://www.pubmed.gov), ISI Web of Knowledge
(http://isiwebofknowledge.com) and Scopus (http://www.scopus.com), using
the following keyword string: ‘sickle cell’ or ‘haemoglobin S’ or ‘hemoglobin S’
or ‘Hb S’. Initial searches were conducted on 12 December 2007 and updated on
20 October 2009. A total of 18,336 (in Text terms), 28,908 (in Title/Keywords/
Abstract) and 22,732 (in Article Title/Abstract/Keywords) references were found
in the three respective databases and exported using bibliographic management
software. The 2,220 references from Livingstone’s extensive but out-of-date database on frequencies of haemoglobin variants5 were then added. Duplicates were
removed manually. Titles and abstracts, when available, were then reviewed to
identify references that met the following selection criteria: first, that the population sample was representative of an indigenous population. When multiple
surveys included similar subsets of population samples, only the larger one was
included, provided that all the other inclusion criteria were fulfilled. When multiple surveys were totally independent, each survey was included in the model. Few
studies corresponded to a purely random or universal sample of the population
studied; therefore, all unselected samples were included. Studies of patients, with
sickle cell or any other condition, were excluded. We considered population surveyed as indigenous, if no information was available from the author to suspect
that the population did not evolve locally in relation to the historical prevalence
Online searches (1950–2009)
ISI Web of
Knowledge
(n = 28,908)
PubMed
(n = 18,336)
Scopus
(n = 22,732)
Without duplicates
(n = 41,445)
HbS strict inclusion criteria
Global geodatabase of HbS data
(1950–2009)
Model input (n = 773)
AA
AS
LAT
LON
Nested Bayesian geostatistical model
Predicted distribution of
HbS allele frequency in local populations
(at 10 km × 10 km grid locations)
Lysenko malaria
endemicity map
Geographical validation of themalaria hypothesis
Figure 5 | Schematic overview of the data collection and mapping
processes. Blue diamonds describe input data. Orange boxes denote
models and experimental procedures. Green rods indicate output data.
of malaria. Non-native populations surveyed in the Americas or Western Europe,
for example, were therefore excluded. Surveys explicitly surveying a specific ethnic group, not representative of the overall population at the sampling site, were
excluded. Although ethnic group information was recorded when available, it was
not used in the model because of (i) inconsistency of information provided by the
sources and ethnic group definitions used and (ii) contradicting local results in
the relationship between ethnicity and HbS allele frequency. Second, details were
needed on the number of individuals sampled and on the AA and AS genotypes
identified. Sources reporting an allele frequency but no sample size were thus
excluded. Because of (i) the complexity of the multiple compound status when
HbS is inherited with another structural variant, haemoglobin C or HbE, or with
a thalassaemia, α- or β-, (ii) the small number of individuals involved (apart from
in the Mediterranean countries) and (iii) the inconsistencies in the identification
of such cases, these individuals were not included in the calculations of the HbS
allele frequency. Third, the survey description needed to be spatially explicit so
that it could be georeferenced (see below). Using these strict criteria for inclusion,
we identified 278 references with data allowing us to calculate an allele frequency
for HbS (see Supplementary References 64–342). Data on absences of HbS in
populations, such as native Americans, were also included in this study, as they
usually constituted isolated data points that are very informative for a global
predictive model. Finally, genotype data collected by the Malaria Genomic Epidemiology Network Consortium (MalariaGEN, http://www.malariagen.net)25 were
added to the database as they represent a significant source of standardized data
from malaria-endemic countries.
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Georeferencing. We used the georeferencing procedure developed by the Malaria
Atlas Project (MAP, http://www.map.ox.ac.uk), which is described in Guerra
et al.42 Geographic coordinates could be found for 459 population samples, located
as points ( < 10 km2). The centroid of polygons was used for the 314 population
samples that could be georeferenced to district level (admin2 unit) or to a smaller
area clearly defined by the author (for example, detailed map of the study area).
Studies that could only be located to province (admin1 unit) or country (admin0
unit) level were excluded.
Creating a continuous map of sickle cell allele frequency. The number of
individuals with AA and AS genotypes was used to calculate allele frequencies.
Individuals described as sicklers were all considered as heterozygotes (AS). All
SS individuals were assumed to die shortly after birth, meaning we discarded the
few records of SS individuals in the database. Preliminary analysis (not shown)
indicated that the resulting likelihood functions at points with SS individuals were
very similar to those obtained using standard Hardy–Weinberg assumptions. Even
today, medical services for improving the survival of sickle cell patients (SS) are
rarely available outside economically developed countries, where the burden of
sickle cell is greatest, and would have been more rudimentary before the 1990s,
when two-thirds of the surveys were conducted. It seems reasonable therefore to
assume that the few surviving HbS homozygous individuals were unlikely to substantively affect HbS allele frequency estimates. When only an allele frequency and
the sample size were given, the number of AA and AS individuals was calculated
by assuming that the genotypes of newborns were in Hardy–Weinberg proportions
but that all SS individuals had died by the time of the surveys. The sample size was
recalculated as the sum of AA and AS individuals. Information on age could not
be taken into account as it was provided in only 45% of the sources. Among these,
samples were taken from cord blood/neonates (n = 23,152), children (n = 26,205),
adults (n = 219,966) and mixed groups (n = 78,111). The inputs to the geostatistical model were the coordinates of the population studied (lat/long in decimal
degrees, WGS84) and the number of AS (positive) and AA (negative) individuals. A
Bayesian geostatistical model involving a two-part nested covariance function was
fitted to these data and 500,000 Markov chain Monte-Carlo iterations43 were used
to predict HbS allele frequencies at unsampled locations and generate continuous
maps. Because of the high heterogeneity of allele frequencies in areas in which HbS
is present, the small set of HbS absences, for example, in the Americas, was not sufficient to rule out the possibility that HbS allele frequency could be relatively high in
some places. For that reason, the posterior predictive distribution of allele frequencies in the Americas tended to have a long right-hand tail, and point estimates of
allele frequency tended to be surprisingly high. A thinned 10% sample of the data
was used to map various summary statistics of the posterior predictive distribution
of HbS allele frequency at unsampled locations. To validate the predictions of the
model, the analysis was repeated with 90% of the data set, and predictions at the
locations of the held-out data points were evaluated. See Supplementary Methods
for details on the statistical analysis.
Comparing with a precontrol map of malaria endemicity. In the late 1960s, a
team of Russian researchers conducted a synthesis of historical records, documents
and maps of several malariometric indices used to record malaria endemicity29.
Combined with expert opinion and data on temperature and rainfall, this review
allowed them to create a unique global map of the precontrol distribution of
malaria, at the peak of its hypothesized distribution44. We chose to use this malaria
map for reasons detailed in Supplementary Methods. Similar to traditional box
plots, violin plots allow the comparison of a semicontinuous variable (HbS allele
frequency) with a categorical variable (malaria endemicity class). In addition, they
show the density distribution of the observations or predictions. The analysis of the
violin plots of the allele frequencies within each endemicity class is supported by a
visual interpretation of the plots. To quantify the differences between malaria endemicity classes, we calculated the probability of finding a higher allele frequency
in one class than in the class just below on the basis of their geographical pattern.
The posterior predictive distribution of the areal mean of the HbS allele frequency
over each endemicity class was plotted by region (Fig. 4). The posterior probability
of an increase in the areal mean HbS allele frequency for each pair of consecutive
malaria endemicity classes, along with the Monte-Carlo standard errors associated
with those estimates, was then calculated. Probabilities of zero and one indicate
that the HbS allele frequency in an endemicity class is certainly lower or higher,
respectively, than in the adjacent class. A probability of 0.5 corresponds to an equal
chance of an increase or decrease. Further details are provided in Supplementary
Methods. These comparisons have been made globally and regionally for Europe
and Africa, and for Asia. The separation into these two regions was based on the
distinct haplotypes occurring east and west of Saudi Arabia (see Fig. 1a)19,37.
References
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2. Serjeant, G. R. & Serjeant, B. E. Sickle Cell Disease (Oxford University Press, 2001).
3. Weatherall, D., Akinyanju, O., Fucharoen, S., Olivieri, N. & Musgrove, P.
in Disease Control Priorities in Developing Countries (eds Jamison, D. T. et al.)
Ch. 34, 663–680 (Oxford University Press, 2006).
4. Modell, B. & Darlison, M. Global epidemiology of haemoglobin disorders and
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Acknowledgments
Trust. T.N.W. is funded by a Senior Clinical Fellowship (#076934) from the Wellcome
Trust. D.J.W. is funded by the Wellcome Trust. The authors are also grateful for
support from the Philippe Wiener–Maurice Anspach Foundation. This paper is
published with the permission of the director of KEMRI. This work forms part of
the output of the Malaria Atlas Project (MAP, http://www.map.ox.ac.uk), principally
funded by the Wellcome Trust, UK.
Author contributions
F.B.P. and S.I.H. helped to assemble the data, developed the conceptual approach and
wrote the first draft of the manuscript. R.E.H. and O.A.N. assembled and abstracted
the data. A.P.P. and P.W.G. conceived and helped to implement the modelling and all
computational tasks. All authors contributed to the study design and data interpretation
and to the revision of the final manuscript.
Additional information
Supplementary Information accompanies this paper on http://www.nature.com/
naturecommunications
We are grateful to Archie Clements, Marius Gilbert, Charles Godfray, Sunetra Gupta,
Bridget Penman, Graham Serjeant, Robert Snow and William Wint for providing
comments on the manuscript, and to Anja Bibby for proofreading. Data from the
MalariaGEN Consortium (http://www.malariagen.net) have been shared for inclusion
in the database. We acknowledge all the contributing collaborators and members for
collecting, preparing and genotyping the samples. We also thank Anabel Arends and
Gilberto Gòmez for sharing complementary unpublished data from Venezuela. F.B.P.,
R.E.H. and O.A.N. are funded by a Biomedical Resources Grant (#085406)
from the Wellcome Trust (to S.I.H.) and acknowledge contributions from its
Technical Advisory Group. S.I.H. is funded by a Senior Research Fellowship
(#079091) from the Wellcome Trust that also supports P.W.G. A.P.P. is funded by a
Principal Research Fellowship (#079080) awarded to Robert Snow by the Wellcome
Competing financial interests: The authors declare no competing financial interests.
Reprints and permission information is available online at http://npg.nature.com/
reprintsandpermissions/
How to cite this article: Piel, F.B. et al. Global distribution of the sickle cell gene
and geographical confirmation of the malaria hypothesis. Nat. Commun. 1:104
doi: 10.1038/ncomms1104 (2010).
License: This work is licensed under a Creative Commons Attribution-NonCommercialShare Alike 3.0 Unported License. To view a copy of this license, visit http://
creativecommons.org/licenses/by-nc-sa/3.0/
nature communications | 1:104 | DOI: 10.1038/ncomms1104 | www.nature.com/naturecommunications
© 2010 Macmillan Publishers Limited. All rights reserved.
Supplementary Information
The content of this supplementary information is summarised as:
1. Supplementary Figures
Supplementary Figure S1. Violin plots of the HbS posterior predictive distribution
Supplementary Figure S2. Temporal distribution of the data points
2. Supplementary Methods
The choice of a malaria map
Bayesian model-based geostatistical framework
3. Supplementary References
Supplementary Figures
Supplementary Figure S1. Violin plots of the HbS posterior predictive distribution.
Predictive distribution of HbS prevalence at a uniformly-distributed point within each
endemicity region for the world (a), Africa-Europe (b), and Asia (c). The green areas
match the colours used in the Lysenko map (Fig. 2c) and show a smoothed
approximation of the frequency distribution (a kernel density plot) of the predicted
allele frequency within each endemicity class. The black central bar indicates the interquartile range and the white circles indicate the median values. The plots have been
adjusted to an equal-area projection of the Earth
3
Supplementary Figure S2. Temporal distribution of the data points. The regional
sub-divisions (the Americas in light grey; Africa, including the western part of Saudi
Arabia, and Europe in medium grey; and Asia in dark grey), are shown in Figure 2a of
the main manuscript.
4
Supplementary Methods
The choice of a malaria map
The Malaria Atlas Project (MAP, www.map.ox.ac.uk) has recently invested
considerable efforts in refining the limits and the malaria endemicity maps for
Plasmodium falciparum46 and P. vivax47. Despite the quality of such products, these
contemporary maps cannot be used to investigate the spatial link between the
distribution of haemoglobin S (HbS) and malaria. Here we are interested in the
historical spatial relationship between HbS and malaria, not in their contemporary
distributions, which have changed considerably over the last 50 years due to human
migration (as, for instance, indicated by the prevalence of HbS in African Americans or
Mediterranean immigrants in North America), epidemiological transition, and human
interventions. Amongst numerous global malaria maps46, 48-55, only one56,57 provides a
reliable global proxy of pre-intervention malaria endemicity. Its main advantages lie in
the efforts made by its authors to gather comprehensive information from the literature
and from expert opinion, in order to map malaria globally at the peak of its distribution
(c.1900).
5
Bayesian model-based geostatistical framework
The model for HbS allele frequency. The HbS allele frequency
was modelled using
a Bayesian spatial generalized linear model (GLM)58. The core of the model was a
Gaussian process (GP)58, denoted
. A GP is a probability distribution for functions,
which can be used as a prior for unknown functions in Bayesian statistics58,59. In this
model, a Gaussian process prior was assigned to transformed HbS allele frequency. The
model form can be defined using the following statements:
The mean function simply returned constant
, and no covariates were used. We used a
“nested” covariance function consisting of two components: a long‐range Gaussian
6
component and a short‐range Matern component59. The range parameters of the two
components were
and
, respectively. The overall amplitude parameter
was
partitioned between the long-scale and short-scale components with proportions
and , respectively, to obtain component-specific amplitude parameters
degree of differentiability
the Americas and
. The
of the Matern component was learned from the data
alongside the other parameters. A global “nugget variance”
The distance function
and
was assumed.
gave the great‐circle distance between
and , unless
was in
was in Eurasia or Africa, in which case it returned
. This
modification prevented data in Africa from unduly influencing the east coast of South
America. This method was preferred to a regional covariate which would influence the
mean and covariance within each region.
7
Likelihoods. We assumed that Hardy‐Weinberg60,61 assumptions applied in all sampled
populations, so newborns were in proportions:
where AA corresponds to the normal homozygous individuals, AS to the heterozygous
carriers of HbS, and SS to the homozygous individuals with sickle cell anaemia. The
“0” subscript denotes newborns. However, we assumed that all SS individuals died
before reaching the age of reproduction, so to preserve equilibrium the reproductive
population would be in proportions:
where the coefficient
can be determined from
and from the fact that allele
frequencies in newborns have to match allele frequencies in reproductive individuals.
We assumed that the observed frequencies more closely matched those of the
reproductive population than of the newborn population. Accordingly, we discarded the
few SS records in the database.
A binomial sampling model was assumed for the number
individuals observed at each data location , given the number
frequency .
of heterozygous
sampled and the allele
8
This likelihood specification completes the Bayesian probability model in the previous
section.
A sensitivity analysis (not presented here) revealed that, for the small SS prevalences
observed, the likelihood functions did not change substantially when the SS individuals
were incorporated and Hardy‐Weinberg frequencies were assumed.
Implementation. The model was implemented in the Python (http://www.python.org)
programming language. The code is available from the MAP’s code repository
(http://github.com/malaria-atlas-project/ibd-world). It was fitted with the Markov chain
Monte Carlo algorithm62 using the open‐source Bayesian analysis package PyMC63. All
scalar parameters in the model were updated using the standard one-at-a-time
Metropolis algorithm with a normal transition density62. The evaluation of
at the data
locations, which has a multivariate normal full conditional distribution, was updated
using Gibbs steps62. Dynamic traces62 are available upon request. Maps were generated
using Python and Fortran code available from the MAP’s code repository
(http://github.com/malaria-atlas-project/generic-mbg).
9
Map Uncertainty. Bayesian geostatistical analysis58 makes it possible to estimate the
uncertainty associated with model predictions. In comparison, when using traditional
uncertainty measures (such as the kriging standard deviation) it is not possible to
determine the probability of finding a value within a certain range (e.g. the probability
of finding an allele frequency of between 10% and 15% in one location) or to find the
range of values most likely to be found in an area where no data is available. High
uncertainties are typically associated with a high heterogeneity of variables in an area
(e.g. presence of both high and low allele frequencies separated by short distances in
Africa) or with the absence of data over a large area (e.g. in Mauritania, Niger, Libya
and Iran within the sickle cell area, in western parts of Russia and China outside the
sickle cell area). Non-zero uncertainty predicted in parts of Oceania represent a local
artefact of the model due to the very low density of data points in that part of the world.
In the Americas, a similar effect was prevented by the higher number of data points
showing absences and the artificially increased distance across the Atlantic, to avoid
HbS AF from Western Africa influencing the prediction in Brazil. See Figure 3.
Validation metrics. In order to estimate the predictive skill of our geostatistical model,
a 10% semi-random sample of the data was held out. A minimum distance of 100 km
between points was imposed during the random sampling process to insure a good
coverage of the hold out sample. The model was run with the thinned 90% of the data,
allowing a comparison between the model’s predictions and the observed allele
frequencies of the 10% of the data which had been held out, and allowing the
calculation of the prediction’s mean error and mean absolute error. The mean error is
the average distance between the actual data points and the predicted values. The
10
absolute mean error is a measure of the average magnitude of the errors in the predicted
values. They provide a measure of the model’s overall bias and overall accuracy,
respectively.
Probabilities of categorical increases. The difference in the mean values of
between Lysenko56 regions 1 (malaria free) and 2 (epidemic) is:
where the random variable
1, and likewise for
realizations
is a location uniformly distributed within Lysenko region
. This figure can be approximated using
of
and a corresponding set of realizations for
This procedure was conducted using
and
independent
:
of the parameter samples in the
dynamic trace, selected at random. To assess the Monte Carlo standard error of the
approximation, the procedure was repeated to compute the standard deviation using
different realizations of
Supplementary Figure S2).
and
and subsets of the dynamic trace (see Figure 5 and
11
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