BACKGROUND
rna viruses evolve extremely rapidly, often with mutation rates one million times greater than vertebrate species  <cit> .
this rate of mutation allows viral populations to keep pace with rapidly changing environments.
viral pathogens, such as influenza virus, hiv, hepatitis c virus and measles virus, place a substantial burden on global human health.
often, after encountering a particular viral strain, an individual develops long-lasting immunity specific to this strain.
however, in some viruses, mutations to the virus genome may result in proteins that are recognized to a lesser degree by the human immune system, leaving individuals susceptible to future infection.
these mutations rapidly spread through the virus population in a process known as antigenic drift.
the capacity for rapid evolutionary change allows the virus population to flourish, despite substantial immune pressure.
understanding the process of viral adaptation is critical to our efforts to control the spread of viral pathogens.
the evolution of the influenza virus has been highly studied for these reasons.
repeated epidemics of seasonal influenza infect between 10% and 20% of the human population every year, causing  <dig>  to  <dig>  deaths annually  <cit> .
mutations to the hemagglutinin  and the neuraminidase  genes are the primary sources of antigenic change  <cit> .
we expect that natural selection will promote those mutations that alter the antigenic character of the virus without causing loss of function of the ha and na proteins.
previous studies have focused on rates of nucleotide and protein change, examining the ratio of the rates of nonsynonymous change to synonymous change  in the ha genealogical tree  <cit> .
deleterious mutations are weeded out from the population, resulting in an overabundance of deleterious mutations on the side branches of the tree, while advantageous mutations spread through the entire population, resulting in an overabundance of advantageous mutations on the trunk of the tree.
these studies have shown that epitope sites evolve extremely rapidly on the trunk of the genealogical tree, indicative of the presence of adaptive evolution  <cit> .
although it is well accepted that adaptive evolution occurs in influenza, there has been considerable debate as to the tempo of this adaptation.
understanding the relative importance of continuous vs. episodic change appears critical to an adequate explanation of influenza epidemiological dynamics.
some epidemiological models have assumed continuous antigenic change  <cit> , while others have assumed episodic antigenic change  <cit> .
these models have sought to understand the general patterns in genealogical trees of specific influenza a subtypes and in particular, the mechanisms that limit the genetic diversity of the virus despite its high transmissibility and mutation rate.
alternative hypotheses have resulted from these theoretical efforts, emphasizing on one hand selective sweeps and episodic antigenic change  <cit> , and on the other, continuous selection and short-lived strain-transcending immunity  <cit> .
in empirical studies of patterns of nucleotide and protein change, some authors have argued that adaptive change is continuous  <cit> , while others have argued that adaptive change is discontinuous, occurring in an episodic fashion  <cit> .
generally, much of this difficulty in analysis arises from the complex mapping of genotype to antigenic phenotype in influenza; antigenic character may change substantially without a corresponding genetic leap  <cit> .
because of the complexity of the genotype-phenotype map, it will necessarily be difficult to directly extrapolate the presence of sequence changes to an inference of antigenic innovation.
instead, we propose using temporally tagged genetic data to examine the large-scale dynamics of a viral population, searching for traces left by adaptive evolution in the shape of genealogical trees.
this analysis uses phylogenetic and population genetic techniques to characterize the strength and the timing of adaptive change using sequence data.
RESULTS
effective population size
the genealogical trees of the hemagglutinin genes of human influenza a  and human measles virus appear immediately distinct, with influenza exhibiting a ladder-like tree with a long trunk and very short side branches and measles presenting a bushier tree with deeper branchings .
in influenza, the trunk branch corresponds to the progenitor lineage; mutations that occur along the trunk are eventually fixed, persisting until 'over-written' by subsequent mutations.
in contrast, mutations that appear on side branches are eventually lost from the population.
we expect that a similar progenitor lineage exists in measles, but because the population turns over much more slowly, we do not have enough temporal resolution to identify this progenitor lineage.
the competitive mechanisms by which the viral populations replace themselves have important repercussions for their genealogical trees.
it is well known that influenza undergoes extensive antigenic drift, allowing a single individual to be repeatedly infected with successive strains of influenza differing in antigenic character  <cit> .
the influenza vaccine strain must be continually updated to remain effective against infection.
in contrast, primary infection by measles confers strong lifelong immunity, allowing vaccination to remain effective through time  <cit> .
in influenza, antigenic drift creates competition among strains, resulting in the emergence of selective forces.
here, selection that promotes antigenically novel strains results in rapid population turnover; in measles, the immune response is equally potent across strains, resulting in neutral evolutionary dynamics and slower strain turnover .
the interface between phylogenetic patterns and ecological dynamics has been referred to as 'phylodynamics'  <cit> .
previous work on phylodynamic patterns has focused on the obvious visible differences between the genealogical trees of influenza and of measles  <cit> .
by calculating the effective size of each viral population, we attempt to quantify and explain the differences between the sparse tree of influenza and the prolific tree of measles.
effective population size ne demarks the timescale at which population turnover occurs.
on average, we expect 2ne generations for a new mutation to fix in a haploid population, and we expect ne generations for two randomly chosen individuals to find a common ancestor, a process known as coalescence  <cit> .
the overall appearance of a genealogical tree will depend upon the rate at which lineages coalesce with one another, determined by ne, along with the degree of temporal spacing among samples.
if coalescence is fast relative to the rate at which sampling occurs, then the resulting genealogy will appear ladder-like and spindly, while if coalescence is slow relative to sampling patterns, then the resulting genealogy will appear dense and bushy .
the coalescent timescale exhibited by natural populations will depend on both effective population size ne and on generation time τ, often measured in years per generation.
thus, a population of ne =  <dig> effective individuals with τ =  <dig>  years per generation will have a timescale of coalescence of neτ =  <dig> year.
from sequence data alone, it is impossible to independently identify ne and τ; only their product neτ can be estimated.
we fit a phylogenetic model incorporating the coalescent process to sequence data to estimate genealogical trees and coalescent parameters for influenza and measles virus .
in this case, we estimate neτ for ha of influenza a  at  <dig>  years  and neτ for measles at  <dig>  years .
these estimates give quantification to the visual differences apparent in genealogical trees.
we arrive at independent estimates of τ via experimental and epidemiological data on the duration of infection, which we take as  <dig> days for influenza   <cit>  and  <dig> days for measles   <cit> .
our basic results do not depend on these exact estimates.
dividing by τ yields estimates of ne =  <dig>  for influenza and ne =  <dig>  for measles.
in the absence of complicating factors such as selection, spatial population structure or fluctuating population size, effective population size ne is expected to equal consensus population size n. we arrive at very rough estimates of the census sizes of influenza and measles via overall incidence.
there are approximately  <dig> ×  <dig> cases per year of influenza  <cit> , which spread out over  <dig> day intervals gives an average of n =  <dig> ×  <dig> cases per generation.
there are about  <dig> ×  <dig> cases per year of measles  <cit>  or n =  <dig> ×  <dig> cases per generation.
here, the difference between the census population size and the effective population size  of influenza is enormous, approximately  <dig> , while the difference in measles is much smaller, approximately  <dig>
the observed differences between ne and n in influenza and measles may be due to multiple causes.
anything that skews reproductive output, so that a small number of infections contribute disproportionately to the genetic legacy of viral population, will inflate n/ne.
factors could include spatial population structure or other variation in host contact patterns.
however, it is a well known population genetic finding that selection, especially positive selection, reduces the effective size of an evolving population  <cit> .
this is why selective sweeps are identified in drosophila and in humans by finding regions of the genome with low diversity, indicative of decreased effective population size  <cit> .
we may expect most of the discrepancy between influenza and measles to be due to the effects of natural selection, as both infections represent acute viral infections displaying strong seasonal epidemics.
thus, without looking at rates of evolution, we can infer that levels of selection are substantially greater in influenza than in measles.
if we were to assume complete equivalence of epidemiological factors such as seasonality and spatial structure, then we would estimate levels of selection in influenza as 13000/ <dig> =  <dig> times greater than in measles.
this level of selection is an average, and it may arise from frequent fixation of weakly adaptive mutations or from rare mutations of large adaptive impact.
we investigate a more detailed dataset in an attempt to distinguish between these hypotheses.
turnover of simulated sequences
to better describe the effects of modes of selection on tree topology, we undertook a simulation-based study, in which models of neutral evolution , purifying selection , constant positive selection  and episodic positive selection  were compared.
in each case, an evolving population of  <dig>  sequences was simulated according to a wright-fisher model with non-overlapping generations.
each sequence consisted of  <dig> bases and mutated at a rate of 10- <dig> per site per generation.
in the neutral simulation, each sequence was assigned equivalent fitness.
in the simulation of purifying selection, each mutation had a 99% chance to be deleterious, and deleterious mutants had a selective disadvantage of  <dig>  relative to their parent's fitness.
in the simulation of constant positive selection, each mutation had a 10% chance to be advantageous, and advantageous mutants had a selective advantage s of  <dig>  relative to their parent's fitness.
in the simulation of episodic positive selection, each mutation had a  <dig> % chance to yield a selective advantage of s =  <dig> .
these parameters were chosen so that the overall genetic diversity the population was similar in all three cases with selection.
in the cases of constant positive selection and episodic positive selection, it took an average of ~ <dig> generations for the population to double in fitness.
the population-scaled rate of advantageous mutation nμa was  <dig> per generation for constant selection and  <dig>  per generation for episodic selection.
the population-scaled selective advantage ns was  <dig> for constant selection and  <dig> for episodic selection.
in each simulation, sequences were sampled over the course of  <dig> generations at a rate of one sample per  <dig> generations to yield approximately  <dig> samples in total.
a bayesian coalescent approach was then used to estimate the gene genealogies connecting these sequences .
it is immediately obvious from these results that selection constrains tree topology, resulting in more narrow ladder-like trees in each case of selection relative to the case of neutrality.
both positive and negative selection constrain both genetic diversity and scaled effective population size neτ.
under purifying selection, the original phenotype remains throughout the simulation , but mutations to this lineage often result in less fit phenotypes.
these lineages are quickly purged from the population .
in this case, the mean fitness of the population remains roughly constant through time, while in both cases of positive selection fitness increases through time .
there are further differences between the case of constant positive selection and the case of episodic positive selection.
in the case of constant positive selection , the tree appears fairly uniform, although there are multiple cases where relatively major lineages die out.
here, the effects of clonal interference  <cit>  are apparent.
all major lineages continually accumulate beneficial mutations.
however, because there is no recombination, these mutations cannot be combined onto the same genetic background, and thus, they are in competition with one another.
the tree shows that lineages that stochastically accrue more beneficial mutations tend to outcompete less fortunate lineages.
in the case of episodic positive selection , we see that mutation events result in a rapid transition of the population to the new allelic state.
this rapid transition can be seen as a sudden crash in genetic diversity, corresponding to the loss of lineages  bearing the ancestral allele.
as opposed to what is seen with constant selection, the disappearance of these lineages is synchronous, e.g.
multiple green lineages simultaneously disappear when yellow emerges at around generation  <dig>
a gene tree represents a complex, high-dimensional description of the genealogical relation-ships among a sample of sequences, and cannot be completely summarized by a single statistic.
instead, summary statistics can be used to probe various aspects of tree topology.
common summary statistics applicable in this context include the time to the most common ancestor  of the sample and the mean pairwise diversity of the sample, which is the average branch length distance between pairs of tips on the tree.
here, both tmrca and diversity are measured in the same units  as the branches in the tree.
additionally, the rate of coalescence can be directly measured from a genealogy by weighting the number of coalescent events observed by the total opportunity for coalescence  <cit> .
the inverse of this rate of coalescence yields an estimate of the scaled effective population size neτ  <cit> .
for each of these three statistics, we analyzed the posterior sample of genealogical trees to get a mean estimate and a 95% credible interval at multiple points in time.
in the cases of tmrca and diversity, at each point in time we took a 'slice' of contemporaneous lineages and traced their ancestry backward in time until arriving at a common ancestor.
this effectively turns a tree with temporally heterogeneous tips into a tree with all tips at the same point in time.
temporal 'slices' were taken every  <dig> generations.
to calculate neτ, we analyzed the rate of coalescence in sliding windows of  <dig> generations in width, moving the center of the window  <dig> generations in each step.
for comparison, the 'bayesian skyline plot'   <cit>  popularized by the software package beast  <cit>  shows the same information as our plots of neτ through time in figures  <dig>   <dig>   <dig>   <dig>  if time is measured in generations then neτ will be measured in generations, and if time is measured in years then neτ will be measured in years.
however, in the literature the quantity measured by the bsp is sometimes referred to as 'relative genetic diversity'  <cit> .
we disagree with this terminology and prefer to use 'diversity' to describe the sequence or temporal distance between lineages, as is standard in the population genetics literature  <cit> .
at equilibrium, an increase in neτ won't result in an immediate increase in diversity; instead, diversity will slowly increase until an equilibrium compatible with the new value of neτ is reached.
under the neutral coalescent, tmrca and diversity are expected to equal 2n =  <dig>  generations and effective population size is expected to be equivalent in generations to the census population size of  <dig>  individuals.
coalescent statistics for the neutral case are in line with these expectations .
as predicted, measures of tmrca, diversity and to a lesser extent neτ are lower in cases with selection .
here, the ancestry of the population is funneled through a small number of superior individuals, resulting in a decrease in genetic diversity.
we observe that tmrca, diversity and neτ remain consistently low under constant negative and positive selection .
in the case of constant positive selection, there is some evidence of low amplitude cycles in levels of diversity .
however, under episodic selection, we observe large fluctuations in tmrca, diversity and neτ .
during periods of selective neutrality, neτ coincides with the expected  <dig>  generations and tmrca and diversity gradually increase over time.
this increase would continue until the neutral expectation of 2n generations were reached.
however, when a selectively advantageous mutation appears, it very quickly sweeps through the population.
we observe a crash in diversity coinciding with the appearance of the newly emerged, advantageous mutation and a drop in tmrca after the sweep is complete.
during the course of the selective sweep, neτ drops precipitously, but immediately recovers after the sweep is over.
<dig> measured in units of  <dig> generations.
we propose to use temporal patterns of diversity and scaled effective population size as tools to judge patterns of selection in viral genealogies.
both positive and negative selection result in a reduction of diversity.
if episodic selection predominates, then we should observe slow growth and occasional rapid decline in diversity coupled with a transient drop in neτ, while if constant selection predominates, then we should observe much flatter patterns of diversity and neτ through time.
here, our use of tmrca and diversity, complements and extends previous analyses relying on 'bayesian skyline plots' of neτ.
for a sweep to be found with neτ, it requires catching the sweep in action, while a sweep's effects on diversity are more long-lasting.
our use of genealogical summary statistics is similar to that of drummond et al.
<cit> .
we recognize that our application of a neutral coalescent prior in the phylogenetic inference process is non-ideal.
phylogenetic methods that directly incorporate the actions of selection into their models of tree topology would be preferred.
currently, there are theoretical efforts in directly modeling selection in a coalescent framework, e.g.
the ancestral selection graph  <cit> , but these approaches lack suitable implementations for the viral genealogies presented here.
in our approach, were use a flexible bayesian model that gives important insight into the effects of selection through the parameter neτ and through genealogy shape.
here, the data will push the final genealogical inference away from the neutral coalescent expectation.
as such, we can identify the presence of selection, even if a parameter such an selective effect s is lacking from the phylogenetic model.
interaction of selection and population size
it is clear that viral genealogies should be affected by changes in pathogen population size , as well as by selective dynamics.
in the absence of selection, we expect a general correspondence between increases in prevalence and increases in neτ.
in this case, ne should be strickly equivalent to prevalence.
however, τ will vary over the course of an epidemic as susceptibles become depleted  <cit> .
during the initial upswing, τ will be inversely proportional to contact rate, while at equilibrium, τ will be inversely proportional to rate of recovery.
other authors have extensively demonstrated this correspondence in simulation studies  <cit> .
however, with selection in play, it is not immediately clear what relationship we should expect between prevalence and neτ.
we investigated this relationship using further simulations.
as before, an evolving population of sequences was simulated according to wright-fisher dynamics.
mutations occurred at a rate of 10- <dig> per site per generation, and 1% of mutations were advantageous.
we ran a number of simulations to ascertain the nucleotide diversity, measured as the per-site proportion of nucleotide differences between random pairs of sequences in the population, as a function of the population size n and the selective coefficient of advantageous mutations s. in each case, diversity was estimated as the mean of  <dig> generations of simulation after  <dig> generations of burn-in across three replicate simulations.
the results show that with strong selection, genetic diversity is effectively divorced from increases in population size .
under neutrality, genetic diversity increases linearly with population size, but with selection, initial increases in genetic diversity occur at low population sizes, but diversity plateaus at higher population sizes.
this suggests that, in cases of strong selection, the ancestry of sequences is determined by selective dynamics and the rapid fixation of advantageous alleles, rather than by the forces of genetic drift as determined by population size  <cit> .
measles and influenza show vastly different genealogical patterns ; it appears that strains of influenza undergo strong selective pressures based upon their antigenic phenotypes, while strains of measles are antigenically similar and exhibit neutral dynamics.
our results suggest that the genealogical patterns of measles are strongly impacted by epidemiological patterns, where increases in prevalence more-or-less directly map to increases in neτ, while the genealogical patterns of influenza are primarily driven by selective dynamics.
still, it is clear that prevalence impacts the genealogical patterns of influenza.
looking just within the usa and within new zealand influenza samples, rambaut et al.
<cit>  show that neτ drops during the summer months and peaks during the winter months, in accordance with seasonal fluctuations.
selective dynamics of influenza a
a more detailed look at the recent evolutionary history of the hemagglutinin gene of influenza a  further reveals the impact of selection on tree topology.
world-wide samples of influenza a  taken between  <dig> and  <dig> show a pattern of rapid population turnover, with most side-branches persisting for 2- <dig> years .
the overall estimate of neτ for these  <dig> sequences is very similar to the estimate of neτ from many fewer sequences sampled over a longer time period .
as discussed previously, the overall scale of the influenza tree as seen in neτ is indicative of selection, however the shape of the influenza genealogy further suggests its pervasive influence.
if neutral dynamics are occurring, then we expect to find tmrca and diversity to be 2× greater than neτ.
this pattern is supported by our neutral simulation .
however, if selection is present then this ratio will be distorted, as it is the case of all simulations involving selection .
in influenza, we find that the ratio of tmrca to neτ is  <dig>   and the ratio of diversity to neτ is  <dig>   .
we are confident that most of these patterns are driven by positive, rather than negative, selection.
measles virus undergoes purifying selection to maintain its function  <cit> , yet its genealogy appears largely congruent with neutral dynamics.
other genetic studies of influenza have shown abundant evidence for adaptive evolution of the ha <dig> domain, the primary target of the human immune response  <cit> .
1measured in years.
interesting temporal dynamics are apparent in the turnover of the influenza population.
from  <dig> to  <dig>  two major lineages of influenza steadily diversified their ha genes.
coexistence of these lineages leads to a steady increase in tmrca and diversity during this time.
tmrca increases until one of the lineages disappears just before  <dig>  while diversity increases until mid- <dig>  at which point it begins to decline, reaching a minimum in  <dig>  after  <dig>  the dynamics of the influenza population appear distinct from the dynamics of the earlier period.
from  <dig> to  <dig>  side-branches continually emerge and die off, so that tmrca and diversity remain at a fairly low and constant level.
given previous simulation results, a reasonable hypothesis for the selective dynamics from  <dig> to  <dig> would be a period of somewhat relaxed selection from  <dig> to mid- <dig> allowing diversity to accumulate, a selective event in  <dig> that causes diversity to decline and tmrca to eventually drop, and a period of continuous selection from  <dig> to  <dig> that keeps diversity low.
however, even during the  <dig> to  <dig> period, neτ remains far below its neutral expectation, suggesting that some degree of selection is always present.
the slight increase in neτ after  <dig> is likely due to sampling effects, before  <dig> samples are restricted to china, oceania and the usa, while after  <dig>  sampling is more global.
during this time period, there were no major shifts in influenza prevalence which could explain these genealogical patterns.
the preceding description, gathered through genetic analysis alone, qualitatively agrees with known patterns of antigenic evolution in the ha gene.
from  <dig> to  <dig>  the virus population remained in the sydney/ <dig> antigenic cluster and evolved very little in antigenic phenotype, although continued to evolve in genotype  <cit> .
this pattern is corroborated by our finding of increasing diversity during this time period; antigenic change provides the fuel for selection among strains, and so without antigenic evolution we expect a build up of genetic diversity.
in  <dig>  the fujian/ <dig> strain emerged from the tropics and effected a large jump in antigenic phenotype  <cit> .
this antigenically novel variant rapidly spread through the global influenza population, and through this rapid spread displaced genetic diversity during the course of 2002- <dig>  the period from  <dig> to  <dig> saw a large amount of antigenic change, first with the california/ <dig> transition and later with more continuous, but rapid antigenic change, necessitating vaccine updates for wisconsin/ <dig> and brisbane/ <dig>  <cit> .
this pattern of sustained antigenic evolution agrees well with our observation of continuously low levels of genetic diversity.
the observed consistently low levels of diversity from  <dig> to  <dig> are indicative of continuous selection on the global influenza population.
however, we caution that this result is only applicable at a fairly coarse temporal resolution.
from simulation, it can be seen that if a selective events occur sufficiently close together, there will not be time for diversity to recover and thus the second selective event will remain to a large extent hidden .
it is thus possible that our observations of continuously low diversity from  <dig> to  <dig> can be explained by relatively few selective events, perhaps close to  <dig> in the  <dig> year period.
it is also, of course, possible for there to have been more than  <dig> such events during this time.
patterns of diversity may be influenced by the spatial structure of the global virus population.
indeed, previous studies have shown that metapopulation dynamics promote persistence and shape genealogical patterns  <cit> .
to gain insight into the confounding influence of spatial structure on our results, we repeated the analysis of diversity patterns on samples from within china and southeast asia .
as expected, overall levels of diversity and neτ are lower for the regional influenza population compared to the global population, although the impact was stronger on neτ than diversity .
we see a similar temporal pattern of growth and decline in genetic diversity for the regional china and southeast asia samples .
diversity grows from  <dig> to  <dig>  declines from  <dig> to  <dig> and increases slowly from  <dig> to 2007; there is more variation in post- <dig> diversity here than seen in the global analysis.
the fujian/ <dig> antigenic variant was first discovered in southeastern china.
consistent with this geographic origin, diversity within china and southeast asia begins to decline in early  <dig>  as opposed to the global decline observed in mid- <dig>  the vaccine strain fujian/ <dig> was not sampled until august  <dig>  our analysis suggests that the original antigenic variant that effected the cluster transition first appeared significantly earlier.
generally, it may be possible that the relatively slow decline in diversity observed during 2002- <dig> may be in part due to a spatially asynchronous global influenza population.
in this case, a selective sweep will necessarily be constrained by waiting for migration events to spread the novel variant throughout the world  <cit> .
thus, it appears that there is a broad correspondence between patterns of antigenic change and patterns of genetic diversity.
it is generally thought that the ha <dig> domain of the ha protein experiences the strongest degree of immune pressure because of its high concentration of epitope-associated sites  <cit> .
most antigenic changes in this period appear largely due to amino acid substitutions in epitopes a and b and the receptor binding domain of ha  <cit> .
however, it has recently been suggested that the evolution of antigenicity and receptor specificity are intimately linked, implying that selection on one will lead to changes in the other  <cit> .
this picture is further complicated by variation in the number of potential n-linked glycosylation sites  on the surface of ha over this period.
glycans attached to pngs have been shown to play a role in antibody escape, the strength of receptor binding, oligomerization, sorting, and transport  <cit> .
because the addition of pngs to h <dig> ha appears to increase viral clearance by components of innate immunity, the fact that there has been an overall increase in the number of pngs on h3n <dig> ha since  <dig> suggests its other functions have greater selective importance  <cit> .
it is feasible that amino acid substitutions in the epitopes in conjunction with the addition and removal of pngs result in frequent, incremental changes in strain fitness and antigenicity.
the effects of other genes on selection in h <dig> ha are probably secondary.
analysis of sequences collected in new york and new zealand from  <dig> to  <dig> showed that the ha gene had consistently the smallest tmrca  <cit> , indicating it is under strong selection and thus the least likely hitchhiker.
the gene whose function is most closely linked to that of ha is na, which must compensate for changes in the receptor binding affinity of ha.
after ha, na is under the strongest positive selection and is an antibody target  <cit> .
in denmark, amino acid substitutions in n <dig> na epitopes were observed in every season from 1999- <dig> to 2005- <dig>  in addition to substitutions in ctl epitopes in other genes  <cit> .
it is hard to gauge the extent to which genome segments evolve independently.
on the one hand, reassortment rates are high, with fourteen separate events estimated from analysis of relatively small populations over four seasons  <cit> .
on the other hand, subsets of the genome significantly differ in the amount of phylogenetic history they share with one another  <cit> , and their genes have uniquely different functions and constraints.
CONCLUSIONS
multiple epidemiological models have been put forward in an attempt to explain the observed patterns of diversity in the influenza virus  <cit> .
in standard population genetic models, selection based on malthusian fitness, or r <dig> in the case of pathogens, will always result in decreased genetic diversity and effective population size.
however, selection for antigenic novelty may result in extended or deep bifurcations of the pathogen population, where a sub-set of the population moves in one antigenic  direction and another subset moves in another antigenic direction.
typically, this bifurcation leads to stable coexistence of multiple lineages, despite the presence of strong immune pressure on the viral population.
any epidemiological explanation of influenza a dynamics must simultaneously generate strong immune pressure, while preventing prolonged bifurcation of the influenza population.
in this study, we have shown that observed patterns of population turnover corroborate patterns of antigenic change from  <dig> to  <dig>  in particular, an epidemiological model of influenza must be able to generate periods of relative antigenic stasis and increasing genetic diversity, as observed from  <dig> to  <dig>  but also periods of sustained antigenic change and consistently low genetic diversity, as observed from  <dig> to  <dig>  the results here provide partial support for the idea that periodic selective sweeps can play a role in the low diversity of flu   <cit> , but they also suggest that these sweeps are not necessary and cannot be the only mechanism at play .
thus, even if transitions between antigenic clusters play a strong role in shaping longer-term influenza dynamics  <cit> , it appears another force must at times be responsible for maintaining low diversity in ha.
in the limiting case of epochal evolution, we would expect to see very large values of neτ during periods of antigenic stasis indicative of selective neutrality.
however, results for neτ between  <dig> and  <dig> strongly suggest that selection is continuously operating in influenza.
the strength of selection appears to vary somewhat over time, but its presence is seen throughout the study period.
interestingly, none of the existing epidemiological models that explicitly incorporate both evolution in sequence space and selection through immunity and cross-immunity in phenotypic space appear able to explain the two different periods observed in the data.
a model with short-lived transcending immunity  <cit>  would be compatible with the latter but not the former period; while the opposite would be the case for a model of epochal evolution which tends to generate fairly regular intervals of time, and cannot explain constant diversity, between selective sweeps  <cit> .
we propose that future work on the dynamics of the influenza virus should attempt to replicate the detailed patterns of population turnover and antigenic evolution, rather than focusing on the larger scale assessment of general tree shape.
investigation of the effects of space and the shape/topology of the genotype-phenotype map should complement these efforts.

 rna viruses evolve extremely rapidly, often with mutation rates one million times greater than vertebrate species. this rate of mutation allows viral populations to keep pace with rapidly changing environments. viral pathogens, such as influenza virus, hiv, hepatitis c virus and measles virus, place a substantial burden on global human health. often, after encountering a particular viral strain, an individual develops long-lasting immunity specific to this strain. however, in some viruses, mutations to the virus genome may result in proteins that are recognized to a lesser degree by the human immune system, leaving individuals susceptible to future infection. these mutations rapidly spread through the virus population in a process known as antigenic drift. the capacity for rapid evolutionary change allows the virus population to flourish, despite substantial immune pressure. understanding the process of viral adaptation is critical to our efforts to control the spread of viral pathogens. the evolution of the influenza virus has been highly studied for these reasons. repeated epidemics of seasonal influenza infect between 10% and 20% of the human population every year, causing to deaths annually. mutations to the hemagglutinin and the neuraminidase genes are the primary sources of antigenic change. we expect that natural selection will promote those mutations that alter the antigenic character of the virus without causing loss of function of the ha and na proteins. previous studies have focused on rates of nucleotide and protein change, examining the ratio of the rates of nonsynonymous change to synonymous change in the ha genealogical tree. deleterious mutations are weeded out from the population, resulting in an overabundance of deleterious mutations on the side branches of the tree, while advantageous mutations spread through the entire population, resulting in an overabundance of advantageous mutations on the trunk of the tree. these studies have shown that epitope sites evolve extremely rapidly on the trunk of the genealogical tree, indicative of the presence of adaptive evolution. although it is well accepted that adaptive evolution occurs in influenza, there has been considerable debate as to the tempo of this adaptation. understanding the relative importance of continuous vs. episodic change appears critical to an adequate explanation of influenza epidemiological dynamics. some epidemiological models have assumed continuous antigenic change, while others have assumed episodic antigenic change. these models have sought to understand the general patterns in genealogical trees of specific influenza a subtypes and in particular, the mechanisms that limit the genetic diversity of the virus despite its high transmissibility and mutation rate. alternative hypotheses have resulted from these theoretical efforts, emphasizing on one hand selective sweeps and episodic antigenic change, and on the other, continuous selection and short-lived strain-transcending immunity. in empirical studies of patterns of nucleotide and protein change, some authors have argued that adaptive change is continuous, while others have argued that adaptive change is discontinuous, occurring in an episodic fashion. generally, much of this difficulty in analysis arises from the complex mapping of genotype to antigenic phenotype in influenza; antigenic character may change substantially without a corresponding genetic leap. because of the complexity of the genotype-phenotype map, it will necessarily be difficult to directly extrapolate the presence of sequence changes to an inference of antigenic innovation. instead, we propose using temporally tagged genetic data to examine the large-scale dynamics of a viral population, searching for traces left by adaptive evolution in the shape of genealogical trees. this analysis uses phylogenetic and population genetic techniques to characterize the strength and the timing of adaptive change using sequence data.  effective population size the genealogical trees of the hemagglutinin genes of human influenza a and human measles virus appear immediately distinct, with influenza exhibiting a ladder-like tree with a long trunk and very short side branches and measles presenting a bushier tree with deeper branchings. in influenza, the trunk branch corresponds to the progenitor lineage; mutations that occur along the trunk are eventually fixed, persisting until'over-written' by subsequent mutations. in contrast, mutations that appear on side branches are eventually lost from the population. we expect that a similar progenitor lineage exists in measles, but because the population turns over much more slowly, we do not have enough temporal resolution to identify this progenitor lineage. the competitive mechanisms by which the viral populations replace themselves have important repercussions for their genealogical trees. it is well known that influenza undergoes extensive antigenic drift, allowing a single individual to be repeatedly infected with successive strains of influenza differing in antigenic character. the influenza vaccine strain must be continually updated to remain effective against infection. in contrast, primary infection by measles confers strong lifelong immunity, allowing vaccination to remain effective through time. in influenza, antigenic drift creates competition among strains, resulting in the emergence of selective forces. here, selection that promotes antigenically novel strains results in rapid population turnover; in measles, the immune response is equally potent across strains, resulting in neutral evolutionary dynamics and slower strain turnover. the interface between phylogenetic patterns and ecological dynamics has been referred to as'phylodynamics'. previous work on phylodynamic patterns has focused on the obvious visible differences between the genealogical trees of influenza and of measles. by calculating the effective size of each viral population, we attempt to quantify and explain the differences between the sparse tree of influenza and the prolific tree of measles. effective population size ne demarks the timescale at which population turnover occurs. on average, we expect 2ne generations for a new mutation to fix in a haploid population, and we expect ne generations for two randomly chosen individuals to find a common ancestor, a process known as coalescence. the overall appearance of a genealogical tree will depend upon the rate at which lineages coalesce with one another, determined by ne, along with the degree of temporal spacing among samples. if coalescence is fast relative to the rate at which sampling occurs, then the resulting genealogy will appear ladder-like and spindly, while if coalescence is slow relative to sampling patterns, then the resulting genealogy will appear dense and bushy. the coalescent timescale exhibited by natural populations will depend on both effective population size ne and on generation time τ, often measured in years per generation. thus, a population of ne = effective individuals with τ = years per generation will have a timescale of coalescence of neτ = year. from sequence data alone, it is impossible to independently identify ne and τ; only their product neτ can be estimated. we fit a phylogenetic model incorporating the coalescent process to sequence data to estimate genealogical trees and coalescent parameters for influenza and measles virus. in this case, we estimate neτ for ha of influenza a at years and neτ for measles at years. these estimates give quantification to the visual differences apparent in genealogical trees. we arrive at independent estimates of τ via experimental and epidemiological data on the duration of infection, which we take as days for influenza and days for measles. our basic results do not depend on these exact estimates. dividing by τ yields estimates of ne = for influenza and ne = for measles. in the absence of complicating factors such as selection, spatial population structure or fluctuating population size, effective population size ne is expected to equal consensus population size n. we arrive at very rough estimates of the census sizes of influenza and measles via overall incidence. there are approximately × cases per year of influenza, which spread out over day intervals gives an average of n = × cases per generation. there are about × cases per year of measles or n = × cases per generation. here, the difference between the census population size and the effective population size of influenza is enormous, approximately, while the difference in measles is much smaller, approximately the observed differences between ne and n in influenza and measles may be due to multiple causes. anything that skews reproductive output, so that a small number of infections contribute disproportionately to the genetic legacy of viral population, will inflate n/ne. factors could include spatial population structure or other variation in host contact patterns. however, it is a well known population genetic finding that selection, especially positive selection, reduces the effective size of an evolving population. this is why selective sweeps are identified in drosophila and in humans by finding regions of the genome with low diversity, indicative of decreased effective population size. we may expect most of the discrepancy between influenza and measles to be due to the effects of natural selection, as both infections represent acute viral infections displaying strong seasonal epidemics. thus, without looking at rates of evolution, we can infer that levels of selection are substantially greater in influenza than in measles. if we were to assume complete equivalence of epidemiological factors such as seasonality and spatial structure, then we would estimate levels of selection in influenza as 13000/ = times greater than in measles. this level of selection is an average, and it may arise from frequent fixation of weakly adaptive mutations or from rare mutations of large adaptive impact. we investigate a more detailed dataset in an attempt to distinguish between these hypotheses. turnover of simulated sequences to better describe the effects of modes of selection on tree topology, we undertook a simulation-based study, in which models of neutral evolution, purifying selection, constant positive selection and episodic positive selection were compared. in each case, an evolving population of sequences was simulated according to a wright-fisher model with non-overlapping generations. each sequence consisted of bases and mutated at a rate of 10- per site per generation. in the neutral simulation, each sequence was assigned equivalent fitness. in the simulation of purifying selection, each mutation had a 99% chance to be deleterious, and deleterious mutants had a selective disadvantage of relative to their parent's fitness. in the simulation of constant positive selection, each mutation had a 10% chance to be advantageous, and advantageous mutants had a selective advantage s of relative to their parent's fitness. in the simulation of episodic positive selection, each mutation had a % chance to yield a selective advantage of s =. these parameters were chosen so that the overall genetic diversity the population was similar in all three cases with selection. in the cases of constant positive selection and episodic positive selection, it took an average of ~ generations for the population to double in fitness. the population-scaled rate of advantageous mutation nμa was per generation for constant selection and per generation for episodic selection. the population-scaled selective advantage ns was for constant selection and for episodic selection. in each simulation, sequences were sampled over the course of generations at a rate of one sample per generations to yield approximately samples in total. a bayesian coalescent approach was then used to estimate the gene genealogies connecting these sequences. it is immediately obvious from these results that selection constrains tree topology, resulting in more narrow ladder-like trees in each case of selection relative to the case of neutrality. both positive and negative selection constrain both genetic diversity and scaled effective population size neτ. under purifying selection, the original phenotype remains throughout the simulation, but mutations to this lineage often result in less fit phenotypes. these lineages are quickly purged from the population. in this case, the mean fitness of the population remains roughly constant through time, while in both cases of positive selection fitness increases through time. there are further differences between the case of constant positive selection and the case of episodic positive selection. in the case of constant positive selection, the tree appears fairly uniform, although there are multiple cases where relatively major lineages die out. here, the effects of clonal interference are apparent. all major lineages continually accumulate beneficial mutations. however, because there is no recombination, these mutations cannot be combined onto the same genetic background, and thus, they are in competition with one another. the tree shows that lineages that stochastically accrue more beneficial mutations tend to outcompete less fortunate lineages. in the case of episodic positive selection, we see that mutation events result in a rapid transition of the population to the new allelic state. this rapid transition can be seen as a sudden crash in genetic diversity, corresponding to the loss of lineages bearing the ancestral allele. as opposed to what is seen with constant selection, the disappearance of these lineages is synchronous, e.g. multiple green lineages simultaneously disappear when yellow emerges at around generation a gene tree represents a complex, high-dimensional description of the genealogical relation-ships among a sample of sequences, and cannot be completely summarized by a single statistic. instead, summary statistics can be used to probe various aspects of tree topology. common summary statistics applicable in this context include the time to the most common ancestor of the sample and the mean pairwise diversity of the sample, which is the average branch length distance between pairs of tips on the tree. here, both tmrca and diversity are measured in the same units as the branches in the tree. additionally, the rate of coalescence can be directly measured from a genealogy by weighting the number of coalescent events observed by the total opportunity for coalescence. the inverse of this rate of coalescence yields an estimate of the scaled effective population size neτ. for each of these three statistics, we analyzed the posterior sample of genealogical trees to get a mean estimate and a 95% credible interval at multiple points in time. in the cases of tmrca and diversity, at each point in time we took a'slice' of contemporaneous lineages and traced their ancestry backward in time until arriving at a common ancestor. this effectively turns a tree with temporally heterogeneous tips into a tree with all tips at the same point in time. temporal'slices' were taken every generations. to calculate neτ, we analyzed the rate of coalescence in sliding windows of generations in width, moving the center of the window generations in each step. for comparison, the'bayesian skyline plot' popularized by the software package beast shows the same information as our plots of neτ through time in figures if time is measured in generations then neτ will be measured in generations, and if time is measured in years then neτ will be measured in years. however, in the literature the quantity measured by the bsp is sometimes referred to as'relative genetic diversity'. we disagree with this terminology and prefer to use'diversity' to describe the sequence or temporal distance between lineages, as is standard in the population genetics literature. at equilibrium, an increase in neτ won't result in an immediate increase in diversity; instead, diversity will slowly increase until an equilibrium compatible with the new value of neτ is reached. under the neutral coalescent, tmrca and diversity are expected to equal 2n = generations and effective population size is expected to be equivalent in generations to the census population size of individuals. coalescent statistics for the neutral case are in line with these expectations. as predicted, measures of tmrca, diversity and to a lesser extent neτ are lower in cases with selection. here, the ancestry of the population is funneled through a small number of superior individuals, resulting in a decrease in genetic diversity. we observe that tmrca, diversity and neτ remain consistently low under constant negative and positive selection. in the case of constant positive selection, there is some evidence of low amplitude cycles in levels of diversity. however, under episodic selection, we observe large fluctuations in tmrca, diversity and neτ. during periods of selective neutrality, neτ coincides with the expected generations and tmrca and diversity gradually increase over time. this increase would continue until the neutral expectation of 2n generations were reached. however, when a selectively advantageous mutation appears, it very quickly sweeps through the population. we observe a crash in diversity coinciding with the appearance of the newly emerged, advantageous mutation and a drop in tmrca after the sweep is complete. during the course of the selective sweep, neτ drops precipitously, but immediately recovers after the sweep is over. measured in units of generations. we propose to use temporal patterns of diversity and scaled effective population size as tools to judge patterns of selection in viral genealogies. both positive and negative selection result in a reduction of diversity. if episodic selection predominates, then we should observe slow growth and occasional rapid decline in diversity coupled with a transient drop in neτ, while if constant selection predominates, then we should observe much flatter patterns of diversity and neτ through time. here, our use of tmrca and diversity, complements and extends previous analyses relying on'bayesian skyline plots' of neτ. for a sweep to be found with neτ, it requires catching the sweep in action, while a sweep's effects on diversity are more long-lasting. our use of genealogical summary statistics is similar to that of drummond et al.. we recognize that our application of a neutral coalescent prior in the phylogenetic inference process is non-ideal. phylogenetic methods that directly incorporate the actions of selection into their models of tree topology would be preferred. currently, there are theoretical efforts in directly modeling selection in a coalescent framework, e.g. the ancestral selection graph, but these approaches lack suitable implementations for the viral genealogies presented here. in our approach, were use a flexible bayesian model that gives important insight into the effects of selection through the parameter neτ and through genealogy shape. here, the data will push the final genealogical inference away from the neutral coalescent expectation. as such, we can identify the presence of selection, even if a parameter such an selective effect s is lacking from the phylogenetic model. interaction of selection and population size it is clear that viral genealogies should be affected by changes in pathogen population size, as well as by selective dynamics. in the absence of selection, we expect a general correspondence between increases in prevalence and increases in neτ. in this case, ne should be strickly equivalent to prevalence. however, τ will vary over the course of an epidemic as susceptibles become depleted. during the initial upswing, τ will be inversely proportional to contact rate, while at equilibrium, τ will be inversely proportional to rate of recovery. other authors have extensively demonstrated this correspondence in simulation studies. however, with selection in play, it is not immediately clear what relationship we should expect between prevalence and neτ. we investigated this relationship using further simulations. as before, an evolving population of sequences was simulated according to wright-fisher dynamics. mutations occurred at a rate of 10- per site per generation, and 1% of mutations were advantageous. we ran a number of simulations to ascertain the nucleotide diversity, measured as the per-site proportion of nucleotide differences between random pairs of sequences in the population, as a function of the population size n and the selective coefficient of advantageous mutations s. in each case, diversity was estimated as the mean of generations of simulation after generations of burn-in across three replicate simulations. the results show that with strong selection, genetic diversity is effectively divorced from increases in population size. under neutrality, genetic diversity increases linearly with population size, but with selection, initial increases in genetic diversity occur at low population sizes, but diversity plateaus at higher population sizes. this suggests that, in cases of strong selection, the ancestry of sequences is determined by selective dynamics and the rapid fixation of advantageous alleles, rather than by the forces of genetic drift as determined by population size. measles and influenza show vastly different genealogical patterns; it appears that strains of influenza undergo strong selective pressures based upon their antigenic phenotypes, while strains of measles are antigenically similar and exhibit neutral dynamics. our results suggest that the genealogical patterns of measles are strongly impacted by epidemiological patterns, where increases in prevalence more-or-less directly map to increases in neτ, while the genealogical patterns of influenza are primarily driven by selective dynamics. still, it is clear that prevalence impacts the genealogical patterns of influenza. looking just within the usa and within new zealand influenza samples, rambaut et al. show that neτ drops during the summer months and peaks during the winter months, in accordance with seasonal fluctuations. selective dynamics of influenza a a more detailed look at the recent evolutionary history of the hemagglutinin gene of influenza a further reveals the impact of selection on tree topology. world-wide samples of influenza a taken between and show a pattern of rapid population turnover, with most side-branches persisting for 2- years. the overall estimate of neτ for these sequences is very similar to the estimate of neτ from many fewer sequences sampled over a longer time period. as discussed previously, the overall scale of the influenza tree as seen in neτ is indicative of selection, however the shape of the influenza genealogy further suggests its pervasive influence. if neutral dynamics are occurring, then we expect to find tmrca and diversity to be 2× greater than neτ. this pattern is supported by our neutral simulation. however, if selection is present then this ratio will be distorted, as it is the case of all simulations involving selection. in influenza, we find that the ratio of tmrca to neτ is and the ratio of diversity to neτ is. we are confident that most of these patterns are driven by positive, rather than negative, selection. measles virus undergoes purifying selection to maintain its function, yet its genealogy appears largely congruent with neutral dynamics. other genetic studies of influenza have shown abundant evidence for adaptive evolution of the ha domain, the primary target of the human immune response. 1measured in years. interesting temporal dynamics are apparent in the turnover of the influenza population. from to two major lineages of influenza steadily diversified their ha genes. coexistence of these lineages leads to a steady increase in tmrca and diversity during this time. tmrca increases until one of the lineages disappears just before while diversity increases until mid- at which point it begins to decline, reaching a minimum in after the dynamics of the influenza population appear distinct from the dynamics of the earlier period. from to side-branches continually emerge and die off, so that tmrca and diversity remain at a fairly low and constant level. given previous simulation results, a reasonable hypothesis for the selective dynamics from to would be a period of somewhat relaxed selection from to mid- allowing diversity to accumulate, a selective event in that causes diversity to decline and tmrca to eventually drop, and a period of continuous selection from to that keeps diversity low. however, even during the to period, neτ remains far below its neutral expectation, suggesting that some degree of selection is always present. the slight increase in neτ after is likely due to sampling effects, before samples are restricted to china, oceania and the usa, while after sampling is more global. during this time period, there were no major shifts in influenza prevalence which could explain these genealogical patterns. the preceding description, gathered through genetic analysis alone, qualitatively agrees with known patterns of antigenic evolution in the ha gene. from to the virus population remained in the sydney/ antigenic cluster and evolved very little in antigenic phenotype, although continued to evolve in genotype. this pattern is corroborated by our finding of increasing diversity during this time period; antigenic change provides the fuel for selection among strains, and so without antigenic evolution we expect a build up of genetic diversity. in the fujian/ strain emerged from the tropics and effected a large jump in antigenic phenotype. this antigenically novel variant rapidly spread through the global influenza population, and through this rapid spread displaced genetic diversity during the course of 2002- the period from to saw a large amount of antigenic change, first with the california/ transition and later with more continuous, but rapid antigenic change, necessitating vaccine updates for wisconsin/ and brisbane/. this pattern of sustained antigenic evolution agrees well with our observation of continuously low levels of genetic diversity. the observed consistently low levels of diversity from to are indicative of continuous selection on the global influenza population. however, we caution that this result is only applicable at a fairly coarse temporal resolution. from simulation, it can be seen that if a selective events occur sufficiently close together, there will not be time for diversity to recover and thus the second selective event will remain to a large extent hidden. it is thus possible that our observations of continuously low diversity from to can be explained by relatively few selective events, perhaps close to in the year period. it is also, of course, possible for there to have been more than such events during this time. patterns of diversity may be influenced by the spatial structure of the global virus population. indeed, previous studies have shown that metapopulation dynamics promote persistence and shape genealogical patterns. to gain insight into the confounding influence of spatial structure on our results, we repeated the analysis of diversity patterns on samples from within china and southeast asia. as expected, overall levels of diversity and neτ are lower for the regional influenza population compared to the global population, although the impact was stronger on neτ than diversity. we see a similar temporal pattern of growth and decline in genetic diversity for the regional china and southeast asia samples. diversity grows from to declines from to and increases slowly from to 2007; there is more variation in post- diversity here than seen in the global analysis. the fujian/ antigenic variant was first discovered in southeastern china. consistent with this geographic origin, diversity within china and southeast asia begins to decline in early as opposed to the global decline observed in mid- the vaccine strain fujian/ was not sampled until august our analysis suggests that the original antigenic variant that effected the cluster transition first appeared significantly earlier. generally, it may be possible that the relatively slow decline in diversity observed during 2002- may be in part due to a spatially asynchronous global influenza population. in this case, a selective sweep will necessarily be constrained by waiting for migration events to spread the novel variant throughout the world. thus, it appears that there is a broad correspondence between patterns of antigenic change and patterns of genetic diversity. it is generally thought that the ha domain of the ha protein experiences the strongest degree of immune pressure because of its high concentration of epitope-associated sites. most antigenic changes in this period appear largely due to amino acid substitutions in epitopes a and b and the receptor binding domain of ha. however, it has recently been suggested that the evolution of antigenicity and receptor specificity are intimately linked, implying that selection on one will lead to changes in the other. this picture is further complicated by variation in the number of potential n-linked glycosylation sites on the surface of ha over this period. glycans attached to pngs have been shown to play a role in antibody escape, the strength of receptor binding, oligomerization, sorting, and transport. because the addition of pngs to h ha appears to increase viral clearance by components of innate immunity, the fact that there has been an overall increase in the number of pngs on h3n ha since suggests its other functions have greater selective importance. it is feasible that amino acid substitutions in the epitopes in conjunction with the addition and removal of pngs result in frequent, incremental changes in strain fitness and antigenicity. the effects of other genes on selection in h ha are probably secondary. analysis of sequences collected in new york and new zealand from to showed that the ha gene had consistently the smallest tmrca, indicating it is under strong selection and thus the least likely hitchhiker. the gene whose function is most closely linked to that of ha is na, which must compensate for changes in the receptor binding affinity of ha. after ha, na is under the strongest positive selection and is an antibody target. in denmark, amino acid substitutions in n na epitopes were observed in every season from 1999- to 2005- in addition to substitutions in ctl epitopes in other genes. it is hard to gauge the extent to which genome segments evolve independently. on the one hand, reassortment rates are high, with fourteen separate events estimated from analysis of relatively small populations over four seasons. on the other hand, subsets of the genome significantly differ in the amount of phylogenetic history they share with one another, and their genes have uniquely different functions and constraints.  multiple epidemiological models have been put forward in an attempt to explain the observed patterns of diversity in the influenza virus. in standard population genetic models, selection based on malthusian fitness, or r in the case of pathogens, will always result in decreased genetic diversity and effective population size. however, selection for antigenic novelty may result in extended or deep bifurcations of the pathogen population, where a sub-set of the population moves in one antigenic direction and another subset moves in another antigenic direction. typically, this bifurcation leads to stable coexistence of multiple lineages, despite the presence of strong immune pressure on the viral population. any epidemiological explanation of influenza a dynamics must simultaneously generate strong immune pressure, while preventing prolonged bifurcation of the influenza population. in this study, we have shown that observed patterns of population turnover corroborate patterns of antigenic change from to in particular, an epidemiological model of influenza must be able to generate periods of relative antigenic stasis and increasing genetic diversity, as observed from to but also periods of sustained antigenic change and consistently low genetic diversity, as observed from to the results here provide partial support for the idea that periodic selective sweeps can play a role in the low diversity of flu, but they also suggest that these sweeps are not necessary and cannot be the only mechanism at play. thus, even if transitions between antigenic clusters play a strong role in shaping longer-term influenza dynamics, it appears another force must at times be responsible for maintaining low diversity in ha. in the limiting case of epochal evolution, we would expect to see very large values of neτ during periods of antigenic stasis indicative of selective neutrality. however, results for neτ between and strongly suggest that selection is continuously operating in influenza. the strength of selection appears to vary somewhat over time, but its presence is seen throughout the study period. interestingly, none of the existing epidemiological models that explicitly incorporate both evolution in sequence space and selection through immunity and cross-immunity in phenotypic space appear able to explain the two different periods observed in the data. a model with short-lived transcending immunity would be compatible with the latter but not the former period; while the opposite would be the case for a model of epochal evolution which tends to generate fairly regular intervals of time, and cannot explain constant diversity, between selective sweeps. we propose that future work on the dynamics of the influenza virus should attempt to replicate the detailed patterns of population turnover and antigenic evolution, rather than focusing on the larger scale assessment of general tree shape. investigation of the effects of space and the shape/topology of the genotype-phenotype map should complement these efforts. 
viral pathogens, such as influenza virus, exploit this capacity for evolutionary change to persist within the human population despite substantial immune pressure. our results have important consequences for understanding the epidemiological and evolutionary dynamics of the influenza virus. we quantify the degree of ongoing adaptation in influenza and measles virus through comparison of census population size and effective population size inferred from genealogical patterns, finding a 60-fold greater deviation in influenza than in measles. through analysis of simulated populations and sequence data from influenza a and measles virus, we show how phylogenetic and population genetic techniques can be used to assess the strength and temporal pattern of adaptive evolution. the action of natural selection affects the shape of the genealogical tree connecting members of an evolving population, causing deviations from the neutral expectation. additionally, these general techniques may prove useful to assess the strength and pattern of adaptive evolution in a variety of evolving systems. the magnitude and distribution of these deviations lends insight into the historical pattern of evolution and adaptation in the viral population. they are especially powerful when assessing selection in fast-evolving populations, where temporal patterns become highly visible. rna viruses evolve extremely quickly, allowing them to rapidly adapt to new environmental conditions.
 rna viruses evolve extremely quickly, allowing them to rapidly adapt to new environmental conditions. viral pathogens, such as influenza virus, exploit this capacity for evolutionary change to persist within the human population despite substantial immune pressure. understanding the process of adaptation in these viral systems is essential to our efforts to combat infectious disease.  through analysis of simulated populations and sequence data from influenza a and measles virus, we show how phylogenetic and population genetic techniques can be used to assess the strength and temporal pattern of adaptive evolution. the action of natural selection affects the shape of the genealogical tree connecting members of an evolving population, causing deviations from the neutral expectation. the magnitude and distribution of these deviations lends insight into the historical pattern of evolution and adaptation in the viral population. we quantify the degree of ongoing adaptation in influenza and measles virus through comparison of census population size and effective population size inferred from genealogical patterns, finding a 60-fold greater deviation in influenza than in measles. we also examine the tempo of adaptation in influenza, finding evidence for both continuous and episodic change.  our results have important consequences for understanding the epidemiological and evolutionary dynamics of the influenza virus. additionally, these general techniques may prove useful to assess the strength and pattern of adaptive evolution in a variety of evolving systems. they are especially powerful when assessing selection in fast-evolving populations, where temporal patterns become highly visible. 