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Introduction
Despite many therapeutic and epidemiological advances, infectious diseases—the number
one cause of death among children—remain directly responsible for roughly 15 million
(>25%) of the annual deaths that occur worldwide (1). Of particular concern are emerging
infections (EIs) that include novel entities like HIV/AIDS and severe acute respiratory
syndrome and previously existing but rapidly spreading diseases like cholera and the
plague (2, 3). Zoonosis is a rich source of such EI transmission into human hosts
(4), suggesting that pathogen surveillance of animals, as well as humans, is an important
method of early detection of potential outbreaks and of capturing the entire biodiversity
of a pathogen population at any given place and time.
Clinical, serologic, and genomic surveillance systems serve as invaluable tools for
detecting early outbreaks, determining the genetic variation of a population, improving
vaccine design, and evading antibiotic resistance. In the case of influenza A virus,
coordinated global efforts like those of the World Health Organization (WHO) identify
cases of influenza-like symptoms, conduct serology studies, and sequence viral isolates
(5). Despite such efforts, there remain areas of sparse data, particularly in potential
tropical influenza hot spots like India, Africa, or South America. Such sampling bias
in strain selection can skew the predicted dominant virus used in annual vaccine design
(6, 7).
Similarly, influenza virus surveillance has historically centered on human influenza
cases but ignored animal hosts, despite the importance of zoonosis in influenza virus
transmission. One particular animal host that deserves special attention is poultry,
which has played a crucial role in the transmission of highly pathogenic avian influenza
(HPAI) virus H5N1 to humans. First reported in Hong Kong in 1997 and 2003, this virus
has spread quickly from waterfowl to chickens, crows, pigeons, and other birds in
Europe, Africa, and particularly Asia, leading to the deaths by infection and forced
culling of millions of birds and resulting in appreciable economic losses (8). Concurrently,
sporadic infections among humans and other mammals have claimed, as of January 2012,
a high rate of 340 deaths out of 578 confirmed human infections since 2003 (9).
At present, no human-to-human transmission of HPAI virus has been documented. However,
scientists have recently discovered the set of mutations that enable the transmission
of avian influenza virus between ferrets (10), the animal model most closely mimicking
human pathogenesis because of shared host cellular receptors for viral attachment
(11). These developments, combined with the virus’s atypically high rate of mortality
and apparent resistance to oseltamavir (12), have raised worldwide concerns about
whether our current avian influenza virus surveillance is sufficient to identify wild
strains that have the potential for mammalian adaptation.
The swine is another animal that demands adequate surveillance (13). Researchers have
observed that epithelial cells in the pig trachea contain sialyloligosaccharides SAα2,3
and SAα2,6, which are unique host determinants for birds and humans, respectively
(14). This feature confers tropism in pigs on both avian and human influenza viruses
(15), allowing swine to serve as mixing vessels for antigenic shift, in which different
strains infecting the same host can reassort RNA segments to create a novel viral
strain (16). Such reassortments have engendered at least two major human pandemics
in the 20th century, in 1957 and 1968 (17). The most recent pandemic of swine origin
influenza virus (SOIV) in 2009, in particular, was a reassortant between Eurasian
and North American swine lineages, and although the virus most likely came from a
pig, a definitive geographic origin has yet to be determined (13, 18). Interestingly,
the closest ancestors of the 2009 pandemic virus were related to viruses isolated
from swine more than a decade prior (13, 19), suggesting that relevant strains circulating
in swine herds have escaped detection because of inadequate sampling (18).
In response to the dearth of avian and swine influenza virus isolates, invaluable
programs like the Global Initiative on Sharing Avian Influenza Data (GISAID) and the
PREDICT program sponsored by the U.S. Agency for International Development Emerging
Pandemic Threats were established to focus the monitoring of circulating strains on
wildlife, as well as to collect and make public clinical, epidemiological, and molecular
data on influenza virus (20, 21). Despite such initiatives, many countries with the
greatest number of poultry or pig stocks do not proportionately contribute avian and
swine influenza virus sequences to public repositories (7).
Currently, there is no standard quantitative measurement of the appropriate level
of genomic surveillance of a given pathogen. One immediate approach might be to consider
the absolute number of sequenced isolates, but this method fails to account for the
diversity and time information of the population sampled. A comparatively large number
of sequences may be insufficient to capture high genetic diversity in a pathogen population.
Another possible strategy appeals to clustering techniques. After representing sequences
as points in a mutational landscape, a highly clustered structure could potentially
reflect highly biased sampling. Once again, this method ignores time and can be confounded
by evolutionary processes like bottlenecks. A final tactic might be to measure the
genetic diversity within a sample of the pathogen. Phylogenetic reconstruction and
tallying of species richness is one method that characterized the subclades of avian
H5N1 (8), but such analyses are cumbersome, with arbitrary boundaries for classifying
clades. Techniques more grounded in information theory include Shannon’s entropy and
Rao’s quadratic entropy (22), but high diversity in a sample does not necessarily
correlate with high surveillance either.
In this paper, we propose a readily interpretable and computable quantitative measurement
for genomic surveillance of a pathogen that directly accounts for the number of isolates,
the evolutionary rate, and the time of sample collection without the need to define
arbitrary clades or species or the need for a full phylogenetic reconstruction. This
measure ranks a surveillance system as more complete if it is able to capture a greater
proportion of the pathogen’s diversity. We apply this measure to influenza virus and
compare the surveillance of different influenza virus strains in different hosts and
geographic regions. We find that, compared to human seasonal strains, sampling is
indeed substantially lower for swine H1N1 and avian non-H5N1 influenza virus, historically
overlooked strains despite their pandemic potential. We also find that avian H5N1
influenza virus surveillance in the WHO transmission zones of northern and western
Africa; eastern, southern, and southeastern Asia; and eastern, southwestern, and northern
Europe is high and may potentially serve as an effective early warning system given
a list of genetic determinants of mammalian adaptation. Avian H5N1 influenza virus
surveillance in North America, however, is much less comprehensive. We similarly apply
our methodology to other RNA viruses and show inadequate surveillance of both dengue
and West Nile viruses. Finally, we perform a comparative analysis of the q2 coefficient
and other methods, particularly phylogenetic and clustering alternatives, and find
that the q2 coefficient produces similar results with negligible computation time.
RESULTS
Measurement of surveillance: the q2 coefficient.
We propose a quantitative measure of pathogen surveillance that reflects both the
evolutionary rate and the biodiversity of a given population. For each host and subtype,
sequences were first temporally ordered from the oldest sequence to the newest. For
each sequence, we identified the sequence from the past with the highest homology
and recorded its genetic distance, such that for N sequences, we compiled a vector
of N distances. We defined the surveillance measurement q2 coefficient, a measurement
between 0 and 1, as the proportion of sequences within genetic distance R of the most
closely related ancestor.
q
2
=
G
e
n
e
t
i
c
D
i
s
t
a
n
c
e
<
R
N
Given a viral evolutionary rate of μ substitutions per site per year, R = t × μ is
thus the expected proportion of mutations that have accumulated over the span of t
years. In this report, we examine short time periods on the order of a decade and
do not expect the true genetic distance to diverge greatly from the Hamming distance.
However, we calculate the q2 coefficient by using a number of distance methods, including
Hamming distance, Jukes-Cantor, Kimura, Tamura, Tajima-Nei, Hasegawa, and Nei-Tamura,
and find little significant change (see Results). If the surveillance of a pathogen
in a given time and place is sufficient, we would therefore expect a maximal number
of viral isolates to have a closest ancestor in the sequence database with a sequence
identity of greater than 1 − R. For the q coefficient, we chose to use t = 2 years
since antigenic variant strains of influenza virus emerge and become predominant over
a period of roughly 2 to 5 years (23); however, any value of t can be used. One consideration
is that substitution rates can vary over time and across different lineages. To incorporate
such variability into our calculation of the q2 coefficient, we used the 95% highest
posterior density (HPD) interval of the evolutionary rate collected from the literature
(see Table S1 in the supplemental material) (24–26).
A major motivation behind use of the q2 coefficient is the ability to evaluate the
surveillance of different strains, hosts, and geographic regions. Sampling during
variable windows of time, however, can compromise an appropriate comparison. For example,
a high q2 coefficient derived from a local weeklong outbreak should not be extrapolated
to surveillance during an entire season. For any comparisons of surveillance over
a span of years, we therefore exclude from analysis any groups not sampled for more
than a month.
Influenza virus surveillance.
Complete coding sequences of hemagglutinin (HA), the major antigenic segment of influenza
virus, were collected from the NCBI (National Center for Biotechnology Information)
and GISAID databases and multiply aligned. To compare the levels of surveillance of
different strains, we separately considered sequences for human (H3N2, seasonal H1N1
pre-2009, SOIV H1N1 post-2009, and H5N1), avian (H5N1 and non-H5N1), and swine H1N1
influenza viruses. Figure 1A and B depict the absolute number of sequences isolated
across time as a first measure of surveillance. However, we wanted a measure of surveillance
that would take into account the evolutionary rate of the virus, as well as the biodiversity
of the viral pool. Calculation of Shannon’s entropy in Fig. 1C is an effective measure
of genetic diversity but, by itself, is no measure of surveillance.
FIG 1
Surveillance of influenza A virus. (A) Numbers of human H3N2 and H1N1 sequences over
time. (B) Numbers of H5N1 and swine H1N1pdm sequences over time. (C) Measurement of
influenza A virus genetic diversity by entropy. (D) Measurement of influenza A virus
surveillance by the q2 coefficient over time. The width of each plotted line denotes
the interval of q2 based on the 95% HPD of the evolutionary rate. n = 7,083 H3N2 human
(dark blue), 2,567 H1N1 human (blue), 11,626 H1N1pdm human (cyan), 878 H1N1 swine
(green), 1,193 H5N1 avian (yellow), 158 H5N1 human (orange), and 3,418 non-H5N1 avian
(red) influenza virus sequences.
Toward a measure that synthesizes both the absolute number of isolates and the evolutionary
rate, we calculated the q2 coefficient as a function of time for each influenza virus
strain in Fig. 1D as a representation of surveillance history. We also tabulated their
final q2 coefficients (see Tables S2 and S3 in the supplemental material) and mapped
these values among WHO transmission zones (27) in Fig. 2 (and Fig. S2 in the supplemental
material) to denote the present state of surveillance around the world. We showed
that our q2 coefficient calculations did not drastically change for different genetic
distances (<0.035 difference in the q2 coefficient).
FIG 2
Global map of influenza A virus surveillance in animal hosts by transmission zones.
The strains depicted include swine H1N1 (A) and non-H5N1 (B) avian influenza virus
strains. Each zone is colored in the blue-to-red spectrum to indicate the q2 coefficient.
Gray areas denote regions with viruses isolated over a span of no more than 1 month.
Analysis of each strain reflects a different state of geographic and host surveillance.
Overall, surveillance of human seasonal strains was high; the q2 coefficient values
of both human seasonal H3N2 and seasonal H1N1 viruses, which had been sampled and
sequenced long before 2003, approached 1 from 2003 to the present (Fig. 1D). Clustering
of sequences by transmission zone began to uncover weakness in the surveillance of
seasonal H3N2, particularly in central Asia (see Fig. S1A and S2A in the supplemental
material). In addition to central Asia, several parts of Europe, western Asia, and
especially central Africa, yielded lower q2 coefficients of seasonal H1N1 (see Fig. S1B
and S2B in the supplemental material). As a testament to the global response to the
pandemic, human SOIV H1N1 shot up to a q2 coefficient of 1 shortly after its arrival
in March 2009 in all transmission zones except central and southern Africa and central
Asia (Fig. 1D; see Fig. S1C and S2C in the supplemental material).
In contrast, despite a moderate increase in the number of sequences following H1N1pdm’s
arrival (Fig. 1B), the q2 coefficient of classical H1N1 swine isolates has lagged
much further behind (Fig. 1D) and is consistently high only in the eastern Asian (q2
coefficient = 0.753, Hamming distance) and North American (q2 coefficient = 0.877,
Hamming distance) transmission zones (Fig. 2A; see Fig. S1D in the supplemental material).
These findings suggest that surveillance of pigs is still not enough to capture the
high biodiversity of swine flu, as indicated by entropy (Fig. 1C).
Analysis of H5N1 influenza virus describes the effects of implementing international
sequencing initiatives like GISAID. Immediately following the second outbreak of HPAI
virus among humans in 2003, the q2 coefficient of H5N1 in both human and avian hosts
rose to approximately 0.7 to 0.85. With the establishment of GISAID in 2006, both
human and avian H5N1 influenza virus q2 coefficients increased further to high levels
of around 0.9, affirming the effectiveness of the global consortium. Beyond 2007,
however, the surveillance of human H5N1 influenza virus has waned compared to that
of avian H5N1 influenza virus (Fig. 1D). This discrepancy is most likely due to the
fact that human HPAI cases represent a subsampling of avian H5N1 influenza virus genotypes,
as reflected by the slight drop in human H5N1 entropy compared to that in birds (Fig. 1C).
Within H5N1, there is biased sampling in different transmission zones. Following particularly
large outbreaks, H5N1 human surveillance is high, with q2 coefficients of roughly
0.9 in northern Africa and eastern and southeastern Asia. Over time, the q2 coefficient
has decreased in eastern and southeastern Asia most likely because of a decline in
the number of sporadic introductions into the local human populations compared to
that in northern Africa, specifically Egypt (see Fig. S1E and S2D in the supplemental
material). H5N1 avian influenza virus surveillance is high in northern and western
Africa; eastern, southeastern, and southern Asia; and eastern, southwestern, and northern
Europe. On the other hand, the q2 coefficient indicates less avian H5N1 influenza
virus surveillance in North America. In the United States, for example, only until
2006 were the reporting and tracking of H5 in birds mandated by the USDA (28). The
smaller push for reporting stems from the low pathogenicity displayed by North American
avian H5N1 influenza virus strains, which have antigenic and genetic differences from
the Asian HPAI virus lineage (see Fig. S1F and S2E in the supplemental material) (29).
These results indicate that H5N1 influenza virus surveillance of avian hosts is much
more complete than H1N1 surveillance of swine. However, potential zoonotic transmission
from other avian strains is possible, as well. Performance of the same analysis of
non-H5N1 avian influenza virus strains yielded a low q2 coefficient beginning at 0.5
in 2003 and plateauing at a level just below 0.7 in spite of GISAID (Fig. 1D) and
the resulting increase in sequenced isolates (Fig. 1B). This finding potentially reflects
the extremely high genetic diversity of influenza A virus in its natural reservoir
(Fig. 1C) that is not fully captured by current surveillance systems. Transmission
zone analysis of non-H5N1 avian influenza virus strains indicates that non-H5N1 surveillance
is concentrated in southwestern Europe, the Central American-Caribbean region, North
America, northern Africa, and eastern and southeastern Asia (Fig. 2B; see Fig. S1G
in the supplemental material).
Calculation of the q2 coefficient for other complete coding segments of influenza
virus was also performed. Since observed differences in sequences should reflect the
evolutionary rates of each segment, any differences in the q2 coefficient should reflect
differences in sampling alone. For H3N2, H1N1pdm, and seasonal H1N1, the q2 coefficient
exhibited little change among different segments (differences of <0.02) and moderate
change for other strains. The largest change in the q2 coefficient was 0.186 between
swine H1N1 HA and PB2. Despite such differences between segments, results showed that
generally surveillance of human H3N2, H1N1pdm, and seasonal H1N1 across all segments
surpassed that of human H5N1, avian H5N1, swine H1N1, and non-H5N1 avian influenza
viruses (see Tables S2 and S3 in the supplemental material).
Dengue and West Nile virus surveillance.
As a proof of concept, we have also shown that the q2 coefficient can be used to monitor
surveillance efforts for other RNA viruses, such as dengue virus and West Nile virus.
Here, we focus on the env gene of these viruses, as it encodes the longest of the
structural proteins, which is prevalently sequenced for subtyping and has the best-documented
evolutionary rates of all flavivirus proteins (25, 26, 30, 31).
Calculation of the q2 coefficients of dengue virus subtypes 1, 2, and 3 depicts poor
surveillance in general (Fig. 3; see Fig. S3 and Table S4 in the supplemental material).
These sampling gaps may reflect the current limited funding and staff in many tropical
countries around the world (32). The incorporation of other genetic distances besides
Hamming distance produced a <0.118 change in the q2 coefficient of dengue virus.
FIG 3
Global map of dengue virus (DENV) surveillance in different countries. The strains
depicted include DENV-1 (A), DENV-2 (B), and DENV-3 (C). Each zone is colored in the
blue-to-red spectrum to indicate the q2 coefficient. Gray areas denote regions with
viruses isolated over a span of no more than 1 month.
The q2 coefficient of West Nile virus in the United States, on the other hand, was
higher in the first few years after its introduction into the United States (see Fig. S4
and Table S5 in the supplemental material). However, despite the implementation of
early warning systems for West Nile virus, by sampling dead birds (33) and mosquito
populations (34), the q2 coefficient beyond 2003 dropped over time, even with the
addition of multiple isolates within a short period of time. This decline in the q2
coefficient coincided with a rapid population growth of West Nile virus in the United
States during 2002 and 2003 spurred by the establishment of the WN02 strain marked
by a V159A mutation in its E protein (35). This analysis suggests that current surveillance
is being outpaced by the growing diversity of the virus in the New World. Other genetic
distances besides the Hamming distance produced a <0.094 change in the q2 coefficient
of West Nile virus.
Comparison to phylogenetic methods.
One may wonder if other alternative methods that account for pathogen evolution may
suffice to characterize the genetic surveillance of a pathogen. Phylogenetics has
been used in many studies to characterize pathogen surveillance qualitatively without
producing a quantitative measure of sampling completeness (36). A possible phylogenetic
analogue to the q2 coefficient might entail the reconstruction of a tree based on
available sequences and measurement of the distribution of branch lengths. The true
distance between two isolates, A and B, is represented by the sum of their patristic
distances, d
A and d
B, which are the branch lengths from each respective sequence to their common ancestral
node. Sequences are time ordered, however, and if we assume an approximate molecular
clock, then d
A < d
B given that sequence A occurs before sequence B. An estimate of distance is then
the larger patristic distance. A parallel to our q2 coefficient would predict high
surveillance to correspond to a maximal number (#) of patristic distances d to their
closest ancestor in the past less than 2 years as follows:
p
2
=
#
branch lengths
d
<
2
years
Total
#
branch lengths
d
Moreover, homogeneity of surveillance can be confirmed if branch lengths d have low
variance.
Phylogenies can be divided into those that are distance based and those that are character
based. Since the q2 coefficient readily incorporates different genetic distance methods,
it is equivalent to any p2 coefficient calculated from distance-based trees. On the
other hand, character-based trees, including maximum-likelihood and Bayesian inference
methods, incorporate site heterogeneity by considering one character (a site in the
alignment) at a time to reconstruct a tree (37); moreover, Markov chain Monte Carlo
(MCMC) methods like BEAST (38) can incorporate relaxed clock rates. The q2 coefficient
does not take into account either site or clock rate heterogeneity.
To determine the impact of site and clock rate heterogeneity in quantifying surveillance
completeness, we calculated the p2 coefficient of the human H5N1 HA data set of 158
sequences by using BEAST (see Materials and Methods). We accounted for site heterogeneity
by using the gamma model (39) and reconstructed trees under both strict and relaxed
molecular clocks. We calculated the p2 coefficients to be 0.848 (0.740 to 0.917) and
0.860 (0.721 to 0.911) for the strict and relaxed clocks, respectively. Given our
q2 coefficient of 0.821 (0.795 to 0.848) for human H5N1 HA, we concluded that incorporating
site heterogeneity and a relaxed molecular clock did not make a significant difference.
While these phylogenetic techniques can examine the fit of a number of evolutionary
models, they suffer from problems of robustness. For example, tree topology can be
highly unstable; the addition or deletion of a single sequence can radically restructure
the tree. Moreover, different methods of phylogenetic inference, such as maximum likelihood
or Bayesian inference, can lead to variable results, rendering interpretation of surveillance
complicated. Finally, computation time, particularly for BEAST, can be very expensive;
for data sets of more than 1,000 sequences, several weeks may be needed for the MCMC
to converge to a stable tree solution. In our analysis of 158 human H5N1 HA sequences,
p2 coefficients needed days of computation to complete, whereas q2 coefficient analysis
was finished in a matter of seconds.
Comparison to clustering methods.
Another possible surveillance measurement characterizes the cluster structure of isolates.
In an ideal situation, a well-sampled population of sequences separated by genetic
distance would be represented by points densely and homogeneously spread across a
continuum. Therefore, clustering techniques such as hierarchical, k-means, or expectation-maximization
clustering can be used to ascertain how poorly sampled a pathogen is on the basis
of the number of clusters in a data set. Bar coding is an alternative strategy based
on the field of persistent homology that identifies topologically invariant clusters
in cloud data; in particular, it calculates the b
0 Betti number, the number of connected components in a set of simplicial complexes
constructed from sequences at different filtration Hamming distances (see Materials
and Methods) (40). A lower b
0 would indicate better sampling.
As a comparison to the q2 coefficient, we applied bar coding to determine the b
0 values of different influenza virus strains at filtration Hamming distances ε ranging
from 0 to 200 (Fig. 4A). This threshold ε is analogous to the R threshold of the q2
coefficient: 2 years of influenza virus evolution equivalent to 2 × (5 × 10−3) = 1%
genetic distance. We therefore considered b
0 at a Hamming distance of 1% of the length of HA, or roughly 17 nucleotides, to be
appropriate for comparison to the q2 coefficient (Fig. 4B). For the most part, the
q2 coefficient and b
0 are inversely correlated. For example, the low b
0 and high q2 coefficient of human H3N2, seasonal H1N1, and H1N1pdm indicate good
surveillance. Non-H5N1 avian influenza virus has an extremely high b
0 and a low q2 coefficient. It should be noted that the non-H5N1 avian influenza virus
data set contains 15 different HA subtypes, as opposed to all of the other single-subtype
HA data sets considered. Thus, b
0 may need to be normalized by the expected number of HA subtypes. Nevertheless, b
0 for non-H5N1 avian influenza virus remains high even with normalization. However,
as with p2, calculation of b
0 demands substantial computing power and time on the order of hours.
FIG 4
Persistence homology analysis of influenza virus. (A) Bar coding plots of b
0 for each strain of influenza virus. b
0, or the number of simplicial complexes, can be determined by counting the bars present
at each filtration Hamming distance. A lower b
0 value indicates better surveillance, although this number may be higher in a setting
of bottleneck effects. (B) Comparison of persistence homology and the q2 coefficient
applied to influenza virus. The top bar plot displays b
0 at a Hamming distance of 17, roughly 1% of the length of HA. The bottom bar plot
displays q2 coefficients, with a threshold of 2 years of influenza virus evolution,
or 2 × (5 × 10−3) = 1%.
Comparison to diversity metrics.
Other alternative methods of gauging sampling bias may exist. For instance, there
are many diversity metrics in ecology, including Chao’s estimate of asymptotic species
richness (41), and in information theory, techniques like Shannon’s entropy, which
was applied in Fig. 1C. In particular, it is well known that the empirical Shannon
entropy of a sample underestimates the entropy of the true distribution. Bootstrapping
techniques can be used to estimate the bias produced by a low number of sequences.
This method is attractive for its ability to measure surveillance by assaying the
diversity of a pathogen directly. However, like the phylogenetic and bar coding methods
considered, implementation for a large number of trials is substantially more difficult,
computationally expensive, and time-consuming.
DISCUSSION
In this paper, we offer a quantitative method of measuring the quality of surveillance
of a particular pathogen that reflects its evolutionary rate and genetic diversity.
The q2 coefficient represents an easily interpretable quantitative measure of genomic
surveillance that does not rely on a full phylogenetic reconstruction. A number between
0 and 1, the q2 coefficient reflects the fraction of isolates with a closest isolate
in the past within 2 years of evolution. However, in its simplicity, the q2 coefficient
does not capture the complexity of evolutionary processes such as variable evolutionary
rates, recombination, reassortment, and population genetic effects. We decided on
the q2 coefficient instead of other equally valid metrics (Q1, q5, or q100) because
2 years represents the median influenza A virus vaccine update time. However, different
metrics may be applicable, depending on the specific aim of the surveillance program.
We applied this measure to multiple influenza virus strains and found that current
surveillance is generally complete for humans, particularly H1N1pdm, H3N2, and seasonal
H1N1, but poor for other hosts, particularly swine. Indeed, the calculated q2 coefficient
of swine H1N1 is most likely an overestimate, considering that influenza virus evolves
more slowly in swine than in humans because of a lesser degree of immune selection
(42). This finding reaffirms the need for increased surveillance of swine, which can
serve as mixing vessels for pandemic strain selection.
Compared to human H3N2 and H1N1 surveillance, human and avian H5N1 influenza virus
surveillance is lower at q2 coefficients of 0.838 and 0.923, respectively. Although
these the q2 coefficients are already high, the difference in the q2 coefficient may
suggest that there are strains of H5N1 circulating in bird and even possibly human
hosts that remain undetected. Given the recent discovery of molecular determinants
that enable ferret-to-ferret transmission of H5N1 virus (10), it is all the more important
to increase viral isolation to match or exceed the levels of human H3N2 and H1N1 surveillance.
In our analysis, we also noted geographic disparities; a preponderance of H5N1 avian
influenza virus isolates derived from northern and western Africa; eastern, southeastern,
and southern Asia; and eastern, southwestern, and northern Europe. Although North
America’s surveillance of non-H5N1 avian influenza virus sequences is trending upward,
it is particularly deficient in the sampling of H5N1 avian influenza virus. Even though
only low-pathogenicity avian influenza virus has been discovered in North America,
it is clear that current surveillance is not sufficient to capture the complete diversity
of even this H5N1 population.
One may wonder whether factors beyond the completeness of surveillance, such as natural
selection, may influence the q2 coefficient. For instance, bottlenecks and selective
sweeps can reduce the diversity of a pathogen population, thus increasing the q2 coefficient.
However, it is important to note that in such cases, the q2 coefficient behaves appropriately,
for it simply reflects surveillance completeness. If only a few sequences are enough
to capture the reduced biodiversity following a bottleneck, the q2 coefficient will
be close to 1.
Another possible confounding effect stems from selection bias in the submission of
sequences to public databases. We account for any possible duplication of sequences
by considering only unique sequences from each date and location. Beyond this safeguard,
we acknowledge that the q2 coefficient may fall prey to selection bias. However, without
prior knowledge of such biases, it would be difficult for any method to address these
confounders satisfactorily.
We compared the q2 coefficient to other possible quantitative methods, including those
based on phylogenetics and clustering. A drawback common to many of these surveillance
methods is that they are slow, computationally expensive techniques that are not explicitly
designed to capture pathogen diversity. For this reason, we developed the q2 coefficient,
which is readily computable and captures surveillance at any given time point. Applying
the q2 coefficient revealed deficient sampling of swine H1N1 and nonavian H5N1, dengue,
and West Nile viruses. These results bear great potential to guide the future allocation
of energy and resources for gathering viral isolates. We also foresee further ecological
applications of the q2 coefficient as an effective measure of asymptotic species richness
without relying on arbitrary criteria for defining species, unlike classic techniques
like Chao’s estimate. This feature can be particularly valuable for assessing the
number of additional samples needed to represent all of the species of an organism
in metagenomic studies. In conclusion, the scientific community as a whole must improve
its surveillance networks and share information for the advancement of scientific
inquiry and public health interventions, and we offer the q2 coefficient as a means
of evaluating the effectiveness of such efforts.
MATERIALS AND METHODS
Sequence collection, annotation, and alignment.
Complete coding sequences of all influenza virus coding segments were collected from
the NCBI influenza virus resource (43) and the GISAID database (20) downloaded as
of October 2012 for human, avian, and swine hosts. Complete coding sequences for the
envelope (env) gene of dengue virus subtypes 1, 2, and 3, as well as West Nile virus,
were collected from the Virus Pathogen Resource and Broad Institute downloaded as
of May 2012. All sequences were filtered for year and month information. If no day
information was provided, isolation was assumed to have occurred on the 15th of the
month. To avoid the effect of depositing duplicated sequences, only unique sequences
were considered for each date and location. Sequences were then aligned using ClustalW2
v. 2.0.12, using default parameters, and then manually curated. Influenza virus sequences
were annotated by transmission zones, defined by the WHO as geographically contiguous
regions with similar peaks in the influenza season (27). All alignments and the code
used are available upon request.
Shannon’s entropy as a measurement of genetic diversity.
Our measurement of pathogen surveillance incorporates the evolutionary rate, which
contributes to population diversity. To measure genetic diversity directly, we chose
to employ Shannon’s entropy, a popular and intuitive measure that avoids cumbersome
phylogenetic reconstruction, and applied it to the distribution of alleles at each
nucleotide position within an alignment. This calculation recovers the number of bits
of information per base. Assuming the independence of each position, the total entropy
of a population is the sum of the entropies of each base position of the alignment.
To correct for bias stemming from a variable number of isolates (n), we estimate Shannon’s
entropy (H) for a given base position on the basis of the following algorithm of Miller
et al., where m is the number of alleles (44):
H
=
m
−
1
2
n
−
Σ
i
=
1
n
p
i
log
2
p
i
Phylogeny as a measurement of surveillance.
Sequences were analyzed by using BEAST v1.7.4, a Bayesian MCMC approach, to sample
time-structured evolutionary trees from their joint posterior probability distribution.
Because of computational and time limits, we restricted our phylogenetic analysis
to human H5N1, as BEAST analysis of data sets of over a thousand sequences can take
weeks to converge to a stationary condition. This data set was analyzed by using an
exponential-growth coalescent as a tree prior with an HKY + Γ model of nucleotide
substitution. Relaxed and strict molecular clocks were employed. For the strict (relaxed)
clock, 20 independent runs of 750,000 (1,500,000) steps each were performed, compared
for convergence, and combined, with a burn-in of 150,000 (500,000) steps from each.
Each run finished after an average of 32.47 (19.14) h using one 3.00-GHz Intel Xeon
CPU with 12 GB of random-access memory. A single maximum clade credibility (MCC) tree
was created from each set of simulations with the average length determined for each
branch. We found the corresponding evolutionary rates to be 5.11 × 10−3 (range, 4.58
× 10−3 to 5.62 × 10−3) and 5.39 × 10−3 (range 4.39 × 10−3 to 5.80 × 10−3), similar
to the evolutionary rate we used for influenza virus HA analysis. The 95% HPD of each
branch length of the MCC tree was used to set a confidence interval for each p2 coefficient.
Persistence homology as a measurement of surveillance.
Another possible surveillance measure can be derived by using persistence homology
techniques like bar coding (40), a method of identifying topological invariants in
cloud data. First, sequenced isolates can be transformed in high-dimensional space
by using distance measures, such as pairwise genetic distance. From these cloud data,
points can be linked together on the basis of certain criteria to form a simplicial
complex, i.e., a network of points, line segments, triangles, and even n-dimensional
counterparts. When this criterion is a distance less than some ε, a filtered simplicial
complex or Vietoris-Rips stream is created.
An objective in the study of topology is to identify features of filtered simplicial
complexes that persist across all values of ε. A useful characteristic is the Betti
number, which in dimension 0 is b
0, the number of connected components in a particular simplicial complex. Trivially,
with a large enough ε, b
0 is 1, but what is interesting is the minimum value of ε that yields a b
0 value of 1. Low values would indicate a higher degree of surveillance.
The calculation of Vietoris-Rips streams for large point cloud data can be computationally
expensive, and an alternative method called witness streams (45) can be used to estimate
ε. Suppose a landmark subset of points (L) is preselected from point cloud data either
at random or using a max-min scheme. Let d(L, p) be a vector of distances between
a point p and all points in L. In dimension 0, a pair of points is then linked if
there exists a witness point z such that the maximum d(L, p) is less than the sum
of ε and the minimum d(L, p).
Using the Javaplex software package at http://code.google.com/p/javaplex, we implemented
a witness stream to filter different strains of influenza virus. Of N total sequences
per strain, n sequences were chosen as landmarks by using the max-min selection algorithm,
such that N/n = 3 (45). Bar coding was performed at filtration Hamming distances ε
at intervals of 20 from 0 to 100.
SUPPLEMENTAL MATERIAL
Figure S1
Influenza A virus surveillance by the q2 coefficient in different transmission zones.
The strains depicted include human H3N2 (A), human seasonal H1N1 (pre-2009 lineage)
(B), human H1N1pdm (post-2009 lineage) (C), swine H1N1 (D), human H5N1 (E), avian
H5N1 (F), and non-H5N1 avian (G) influenza virus strains. Download
Figure S1, PDF file, 0.4 MB
Figure S2
Global map of influenza A virus surveillance by transmission zone. The strains depicted
include human H3N2 (A), human seasonal H1N1 (pre-2009 lineage) (B), human H1N1pdm
(post-2009 lineage) (C), human H5N1 (D), and avian H5N1 (E) influenza virus strains.
Each zone is colored in the blue-to-red spectrum to indicate the q2 coefficient. Gray
areas denote regions with viruses isolated over a span of no more than 1 month. Download
Figure S2, PDF file, 0.1 MB
Figure S3
Dengue virus surveillance by the q2 coefficient in different countries. The strains
depicted include DENV-1 (A), DENV-2 (B), and DENV-3 (C). Download
Figure S3, PDF file, 0.2 MB
Figure S4
West Nile virus surveillance by the q2 coefficient in the United States in mosquito
and bird hosts. Download
Figure S4, PDF file, 0.1 MB
Table S1
Evolutionary rates of viral genes used for calculation of the q2 coefficient. The
95% HPD intervals are also provided.
Table S1, XLSX file, 0.1 MB.
Table S2
Current q2 coefficients of influenza virus. Intervals based on the 95% HPD of the
evolutionary rate are also provided.
Table S2, XLSX file, 0.1 MB.
Table S3
Current q2 coefficients of influenza virus HA by transmission zone. Entries designated
NaN represent transmission zones that were not sampled for longer than a month. Intervals
based on the 95% HPD of the evolutionary rate are also provided.
Table S3, XLSX file, 0.1 MB.
Table S4
Current q2 coefficients of dengue virus by country. Intervals based on the 95% HPD
of the evolutionary rate are also provided.
Table S4, XLSX file, 0.1 MB.
Table S5
Current q2 coefficients of West Nile virus by host. Intervals based on the 95% HPD
of the evolutionary rate are also provided.
Table S5, XLSX file, 0.1 MB.
Table S6
Number of sequences of each viral gene.
Table S6, XLSX file, 0.1 MB.

- Record: found
- Abstract: not found
- Article: not found

P. Daszak (2000)

- Record: found
- Abstract: found
- Article: not found

S. S. Morse (1995)

- Record: found
- Abstract: found
- Article: not found

T. Ito, J Couceiro, S Kelm … (1998)