Study of what affects viral life spans
Viral phylodynamics is the study of how epidemiological, immunological, and evolutionary processes act and potentially interact to shape viral phylogenies.
Since the term was coined in 2004, research on viral phylodynamics has focused on transmission dynamics in an effort to shed light on how these dynamics impact viral genetic variation. Transmission dynamics can be considered at the level of cells within an infected host, individual hosts within a population, or entire populations of hosts.
Many viruses, especially RNA viruses, rapidly accumulate genetic variation because of short generation times and high mutation rates.
Patterns of viral genetic variation are therefore heavily influenced by how quickly transmission occurs and by which entities transmit to one another.
Patterns of viral genetic variation will also be affected by selection acting on viral phenotypes.
Although viruses can differ with respect to many phenotypes, phylodynamic studies have to date tended to focus on a limited number of viral phenotypes.
These include virulence phenotypes, phenotypes associated with viral transmissibility, cell or tissue tropism phenotypes, and antigenic phenotypes that can facilitate escape from host immunity.
Due to the impact that transmission dynamics and selection can have on viral genetic variation, viral phylogenies can therefore be used to investigate important epidemiological, immunological, and evolutionary processes, such as epidemic spread, spatio-temporal dynamics including metapopulation dynamics, zoonotic transmission, tissue tropism, and antigenic drift.
The quantitative investigation of these processes through the consideration of viral phylogenies is the central aim of viral phylodynamics.
Sources of phylodynamic variation.
In coining the term "phylodynamics", Grenfell and coauthors postulated that viral phylogenies "... are determined by a combination of immune selection, changes in viral population size, and spatial dynamics".
Their study showcased three features of viral phylogenies, which may serve as rules of thumb for identifying important epidemiological, immunological, and evolutionary processes influencing patterns of viral genetic variation.
 Rapid expansion of a virus in a population will be reflected by a "star-like" tree, in which external branches are long relative to internal branches. Star-like trees arise because viruses are more likely to share a recent common ancestor when the population is small, and a growing population has an increasingly smaller population size towards the past. Compared to a phylogeny of an expanding virus, a phylogeny of a viral population that stays constant in size will have external branches that are shorter relative to branches on the interior of the tree. The phylogeny of HIV provides a good example of a star-like tree, as the prevalence of HIV infection rose rapidly throughout the 1980s (exponential growth). The phylogeny of hepatitis B virus instead reflects a viral population that has remained roughly consistent (constant size). Similarly, trees reconstructed from viral sequences isolated from chronically infected individuals can be used to gauge changes in viral population sizes within a host.
 Viruses within similar hosts, such as hosts that reside in the same geographic region, are expected to be more closely related genetically if transmission occurs more commonly between them. The phylogenies of measles and rabies virus illustrate viruses with spatially structured host population. These phylogenies stand in contrast to the phylogeny of human influenza, which does not appear to exhibit strong spatial structure over extended periods of time. Clustering of taxa, when it occurs, is not necessarily observed at all scales, and a population that appears structured at some scale may appear panmictic at another scale, for example at a smaller spatial scale. While spatial structure is the most commonly observed population structure in phylodynamic analyses, viruses may also have nonrandom admixture by attributes such as the age, race, and risk behavior. This is because viral transmission can preferentially occur between hosts sharing any of these attributes.
 The effect of directional selection on the shape of a viral phylogeny is exemplified by contrasting the trees of influenza virus and HIV's surface proteins. The ladder-like phylogeny of influenza virus A/H3N2's hemagglutinin protein bears the hallmarks of strong directional selection, driven by immune escape (imbalanced tree). In contrast, a more balanced phylogeny may occur when a virus is not subject to strong immune selection or other source of directional selection. An example of this is the phylogeny of the HIV envelope protein inferred from sequences isolated from different individuals in a population (balanced tree). Phylogenies of the HIV envelope protein from chronically infected hosts resemble influenza's ladder-like tree. This highlights that the processes affecting viral genetic variation can differ across scales. Indeed, contrasting patterns of viral genetic variation within and between hosts has been an active topic in phylodynamic research since the field's inception.
Although these three phylogenetic features are useful rules of thumb to identify epidemiological, immunological, and evolutionary processes that might be impacting viral genetic variation, there is growing recognition that the mapping between process and phylogenetic pattern can be many-to-one. For instance, although ladder-like trees could reflect the presence of directional selection, ladder-like trees could also reflect sequential genetic bottlenecks that might occur with rapid spatial spread, as in the case of rabies virus. Because of this many-to-one mapping between process and phylogenetic pattern, research in the field of viral phylodynamics has sought to develop and apply quantitative methods to effectively infer process from reconstructed viral phylogenies (see Methods). The consideration of other data sources (e.g., incidence patterns) may aid in distinguishing between competing phylodynamic hypotheses. Combining disparate sources of data for phylodynamic analysis remains a major challenge in the field and is an active area of research.
Applications.
Viral origins.
Phylodynamic models may aid in dating epidemic and pandemic origins.
The rapid rate of evolution in viruses allows molecular clock models to be estimated from genetic sequences, thus providing a per-year rate of evolution of the virus.
With the rate of evolution measured in real units of time, it is possible to infer the date of the most recent common ancestor (MRCA) for a set of viral sequences.
The age of the MRCA of these isolates is a lower bound; the common ancestor of the entire virus population must have existed earlier than the MRCA of the virus sample.
In April 2009, genetic analysis of 11 sequences of swine-origin H1N1 influenza suggested that the common ancestor existed at or before 12 January 2009.
This finding aided in making an early estimate of the basic reproduction number formula_1 of the pandemic. Similarly, genetic analysis of sequences isolated from within an individual can be used to determine the individual's infection time.
Viral spread.
Phylodynamic models may provide insight into epidemiological parameters that are difficult to assess through traditional surveillance means.
For example, assessment of formula_1 from surveillance data requires careful control of the variation of the reporting rate and the intensity of surveillance.
Inferring the demographic history of the virus population from genetic data may help to avoid these difficulties and can provide a separate avenue for inference of formula_1.
Such approaches have been used to estimate formula_1 in hepatitis C virus and HIV.
Additionally, differential transmission between groups, be they geographic-, age-, or risk-related, is very difficult to assess from surveillance data alone.
Phylogeographic models have the possibility of more directly revealing these otherwise hidden transmission patterns.
Phylodynamic approaches have mapped the geographic movement of the human influenza virus and quantified the epidemic spread of rabies virus in North American raccoons.
However, nonrepresentative sampling may bias inferences of both formula_1 and migration patterns.
Phylodynamic approaches have also been used to better understand viral transmission dynamics and spread within infected hosts. For example, phylodynamic studies have been used to infer the rate of viral growth within infected hosts and to argue for the occurrence of viral compartmentalization in hepatitis C infection.
Viral control efforts.
Phylodynamic approaches can also be useful in ascertaining the effectiveness of viral control efforts, particularly for diseases with low reporting rates. For example, the genetic diversity of the DNA-based hepatitis B virus declined in the Netherlands in the late 1990s, following the initiation of a vaccination program. This correlation was used to argue that vaccination was effective at reducing the prevalence of infection, although alternative explanations are possible.
Viral control efforts can also impact the rate at which virus populations evolve, thereby influencing phylogenetic patterns. Phylodynamic approaches that quantify how evolutionary rates change over time can therefore provide insight into the effectiveness of control strategies. For example, an application to HIV sequences within infected hosts showed that viral substitution rates dropped to effectively zero following the initiation of antiretroviral drug therapy. This decrease in substitution rates was interpreted as an effective cessation of viral replication following the commencement of treatment, and would be expected to lead to lower viral loads. This finding is especially encouraging because lower substitution rates are associated with slower progression to AIDS in treatment-naive patients.
Antiviral treatment also creates selective pressure for the evolution of drug resistance in virus populations, and can thereby affect patterns of genetic diversity. Commonly, there is a fitness trade-off between faster replication of susceptible strains in the absence of antiviral treatment and faster replication of resistant strains in the presence of antivirals. Thus, ascertaining the level of antiviral pressure necessary to shift evolutionary outcomes is of public health importance. Phylodynamic approaches have been used to examine the spread of oseltamivir resistance in influenza A/H1N1.
Methods.
Most often, the goal of phylodynamic analyses is to make inferences of epidemiological processes from viral phylogenies.
Thus, most phylodynamic analyses begin with the reconstruction of a phylogenetic tree.
Genetic sequences are often sampled at multiple time points, which allows the estimation of substitution rates and the time of the MRCA using a molecular clock model.
For viruses, Bayesian phylogenetic methods are popular because of the ability to fit complex demographic scenarios while integrating out phylogenetic uncertainty.
Traditional evolutionary approaches directly utilize methods from computational phylogenetics and population genetics to assess hypotheses of selection and population structure without direct regard for epidemiological models.
For example,
However, such analyses were not designed with epidemiological inference in mind and it may be difficult to extrapolate from standard statistics to desired epidemiological quantities.
In an effort to bridge the gap between traditional evolutionary approaches and epidemiological models, several analytical methods have been developed to specifically address problems related to phylodynamics.
These methods are based on coalescent theory, birth-death models, and simulation, and are used to more directly relate epidemiological parameters to observed viral sequences.
Coalescent theory and phylodynamics.
Effective population size.
The coalescent is a mathematical model that describes the ancestry of a sample of nonrecombining gene copies.
In modeling the coalescent process, time is usually considered to flow backwards from the present.
In a selectively neutral population of constant size formula_6 and nonoverlapping generations (the Wright Fisher model),
the expected time for a sample of two gene copies to "coalesce" (i.e., find a common ancestor) is formula_6 generations.
More generally, the waiting time for two members of a sample of formula_8 gene copies to share a common ancestor is exponentially distributed, with rate
 formula_9.
This time interval is labeled formula_10, and at its end there are formula_11 extant lineages remaining. These remaining lineages will coalesce at the rate formula_12 after intervals formula_13.
This process can be simulated by drawing exponential random variables with rates formula_14 until there is only a single lineage remaining (the MRCA of the sample).
In the absence of selection and population structure, the tree topology may be simulated by picking two lineages uniformly at random after each coalescent interval formula_15.
The expected waiting time to find the MRCA of the sample is the sum of the expected values of the internode intervals,
 formula_16
Two corollaries are :
Consequently, the TMRCA estimated from a relatively small sample of viral genetic sequences is an asymptotically unbiased estimate for the time that the viral population was founded in the host population.
For example, Robbins et al. estimated the TMRCA for 74 HIV-1 subtype-B genetic sequences collected in North America to be 1968.
Assuming a constant population size, we expect the time back to 1968 to represent formula_19 of the TMRCA of the North American virus population.
If the population size formula_20 changes over time, the coalescent rate formula_21 will also be a function of time.
Donnelley and Tavaré derived this rate for a time-varying population size under the assumption of constant birth rates:
 formula_22.
Because all topologies are equally likely under the neutral coalescent, this model will have the same properties as the constant-size coalescent under a rescaling of the time variable: formula_23.
Very early in an epidemic, the virus population may be growing exponentially at rate formula_24, so that formula_25 units of time in the past, the population will have size formula_26.
In this case, the rate of coalescence becomes
 formula_27.
This rate is small close to