The Price equation framework to study disease within-host evolution

The Price equation and evolutionary epidemiology

The Price equation has found widespread application in many areas of evolutionary biology, including the evolutionary epidemiology of infectious diseases. In this paper, we illustrate the utility of this approach to modelling disease evolution by first deriving a version of Price's equation that can be applied in continuous time and to populations with overlapping generations. We then show how this version of Price's equation provides an alternative perspective on pathogen evolution by considering the epidemiological meaning of each of its terms. Finally, we extend these results to the case where population size is small and generates demographic stochasticity. We show that the particular partitioning of evolutionary change given by Price's equation is also a natural way to partition the evolutionary consequences of demographic stochasticity, and demonstrate how such stochasticity tends to weaken selection on birth rate (e.g. the transmission rate of an infectious disease) and enhance selection on mortality rate (e.g. factors, like virulence, that cause the end of an infection). In the long term, if there is a trade-off between virulence and transmission across parasite strains, the weaker selection on transmission and stronger selection on virulence that arises from demographic stochasticity will tend to drive the evolution of lower levels of virulence. This article is part of the theme issue 'Fifty years of the Price equation'.

Effects of contact structure on the transient evolution of HIV virulence

Early in an epidemic, high densities of susceptible hosts select for relatively high parasite virulence; later in the epidemic, lower susceptible densities select for lower virulence. Thus over the course of a typical epidemic the average virulence of parasite strains increases initially, peaks partway through the epidemic, then declines again. However, precise quantitative outcomes, such as the peak virulence reached and its timing, may depend sensitively on epidemiological details. Fraser et al. proposed a model for the eco-evolutionary dynamics of HIV that incorporates the tradeoffs between transmission and virulence (mediated by set-point viral load, SPVL) and their heritability between hosts. Their model used implicit equations to capture the effects of partnership dynamics that are at the core of epidemics of sexually transmitted diseases. Our models combine HIV virulence tradeoffs with a range of contact models, explicitly modeling partnership formation and dissolution and allowing for individuals to transmit disease outside of partnerships. We assess summary statistics such as the peak virulence (corresponding to the maximum value of population mean log₁₀ SPVL achieved throughout the epidemic) across models for a range of parameters applicable to the HIV epidemic in sub-Saharan Africa. Although virulence trajectories are broadly similar across models, the timing and magnitude of the virulence peak vary considerably. Previously developed implicit models predicted lower virulence and slower progression at the peak (a maximum of 3.5 log₁₀ SPVL) compared both to more realistic models and to simple random-mixing models with no partnership structure at all (both with a maximum of ≈ 4.7 log₁₀ SPVL). In this range of models, the simplest random-mixing structure best approximates the most realistic model; this surprising outcome occurs because the dominance of extra-pair contact in the realistic model swamps the effects of partnership structure.

Pathogens such as HIV can evolve rapidly when the environment changes. One important aspect of a pathogen’s environment is the probability that an infectious contact (a sneeze for a respiratory disease, or an unprotected sex act for a sexually transmitted disease) encounters an uninfected person and thus has a chance to transmit the pathogen. As an epidemic grows the number of uninfected people shrinks, changing evolutionary pressures on the pathogen. While researchers have used models to explore pathogen evolution during epidemics, their models usually neglect important processes such as people entering and leaving sexual partnerships. We compared several evolutionary models for HIV that include partnership dynamics as well as sexual contact outside of stable partnerships. Models of intermediate complexity predicted lower virulence midway through the epidemic (a minimum of 15 years to progress to AIDS) than either more realistic models or simple models with no partnership structure (both with a minimum of 7.25 years to progress to AIDS), because random sexual contacts tended to wash out the effects of stable partnerships. Researchers trying to predict the evolution of pathogens must try to understand the implications of their modeling choices; models of intermediate complexity may not produce intermediate conclusions.

Evolutionary rescue: linking theory for conservation and medicine

Evolutionary responses that rescue populations from extinction when drastic environmental changes occur can be friend or foe. The field of conservation biology is concerned with the survival of species in deteriorating global habitats. In medicine, in contrast, infected patients are treated with chemotherapeutic interventions, but drug resistance can compromise eradication of pathogens. These contrasting biological systems and goals have created two quite separate research communities, despite addressing the same central question of whether populations will decline to extinction or be rescued through evolution. We argue that closer integration of the two fields, especially of theoretical understanding, would yield new insights and accelerate progress on these applied problems. Here, we overview and link mathematical modelling approaches in these fields, suggest specific areas with potential for fruitful exchange, and discuss common ideas and issues for empirical testing and prediction.

Antimicrobials, stress and mutagenesis

Cationic antimicrobial peptides are ancient and ubiquitous immune effectors that multicellular organisms use to kill and police microbes whereas antibiotics are mostly employed by microorganisms. As antimicrobial peptides (AMPs) mostly target the cell wall, a microbial ‘Achilles heel’, it has been proposed that bacterial resistance evolution is very unlikely and hence AMPs are ancient ‘weapons’ of multicellular organisms. Here we provide a new hypothesis to explain the widespread distribution of AMPs amongst multicellular organism. Studying five antimicrobial peptides from vertebrates and insects, we show, using a classic Luria-Delbrück fluctuation assay, that cationic antimicrobial peptides (AMPs) do not increase bacterial mutation rates. Moreover, using rtPCR and disc diffusion assays we find that AMPs do not elicit SOS or rpoS bacterial stress pathways. This is in contrast to the main classes of antibiotics that elevate mutagenesis via eliciting the SOS and rpoS pathways. The notion of the ‘Achilles heel’ has been challenged by experimental selection for AMP-resistance, but our findings offer a new perspective on the evolutionary success of AMPs. Employing AMPs seems advantageous for multicellular organisms, as it does not fuel the adaptation of bacteria to their immune defenses. This has important consequences for our understanding of host-microbe interactions, the evolution of innate immune defenses, and also sheds new light on antimicrobial resistance evolution and the use of AMPs as drugs.

Cationic antimicrobial peptides are ancient and ubiquitous immune effectors that multicellular organisms use to kill and police microbes, whilst antibiotics are mostly employed by microorganisms. Here we provide a new hypothesis to explain this widespread adoption of antimicrobial peptides. We show that cationic antimicrobial peptides (AMPs) do not increase bacterial mutagenesis, as they do not elicit bacterial stress pathways. Those stress pathways increase the mutation rate when bacteria are treated with antibiotics. Employing AMPs hence seems advantageous for multicellular organisms, as it does not fuel the adaptation of bacteria to their immune defenses. This has important consequences for our understanding of host-microbe interactions, the evolution of innate immune defenses, and also sheds new light on antimicrobial resistance evolution and the use of AMPs as drugs.

Pathogen life-history trade-offs revealed in allopatry

Trade-offs in life-history traits is a central tenet in evolutionary biology, yet their ubiquity and relevance to realized fitness in natural populations remains questioned. Trade-offs in pathogens are of particular interest because they may constrain the evolution and epidemiology of diseases. Here, we studied life-history traits determining transmission in the obligate fungal pathogen, Podosphaera plantaginis, infecting Plantago lanceolata. We find that although traits are positively associated on sympatric host genotypes, on allopatric host genotypes relationships between infectivity and subsequent transmission traits change shape, becoming even negative. The epidemiological prediction of this change in life-history relationships in allopatry is lower disease prevalence in newly established pathogen populations. An analysis of the natural pathogen metapopulation confirms that disease prevalence is lower in newly established pathogen populations and they are more prone to go extinct during winter than older pathogen populations. Hence, life-history trade-offs mediated by pathogen local adaptation may influence epidemiological dynamics at both population and metapopulation levels.

Parallel patterns of increased virulence in a recently emerged wildlife pathogen

A bacterial pathogen of wild songbirds evolved higher virulence following its emergence in two separate regions of the host range.

The evolution of higher virulence during disease emergence has been predicted by theoretical models, but empirical studies of short-term virulence evolution following pathogen emergence remain rare. Here we examine patterns of short-term virulence evolution using archived isolates of the bacterium Mycoplasma gallisepticum collected during sequential emergence events in two geographically distinct populations of the host, the North American house finch (Haemorhous [formerly Carpodacus] mexicanus). We present results from two complementary experiments, one that examines the trend in pathogen virulence in eastern North American isolates over the course of the eastern epidemic (1994–2008), and the other a parallel experiment on Pacific coast isolates of the pathogen collected after M. gallisepticum established itself in western North American house finch populations (2006–2010). Consistent with theoretical expectations regarding short-term or dynamic evolution of virulence, we show rapid increases in pathogen virulence on both coasts following the pathogen's establishment in each host population. We also find evidence for positive genetic covariation between virulence and pathogen load, a proxy for transmission potential, among isolates of M. gallisepticum. As predicted by theory, indirect selection for increased transmission likely drove the evolutionary increase in virulence in both geographic locations. Our results provide one of the first empirical examples of rapid changes in virulence following pathogen emergence, and both the detected pattern and mechanism of positive genetic covariation between virulence and pathogen load are consistent with theoretical expectations. Our study provides unique empirical insight into the dynamics of short-term virulence evolution that are likely to operate in other emerging pathogens of wildlife and humans.

A long-standing paradox in the study of infectious diseases is why pathogens evolve to cause harm to the very hosts they depend on to survive and reproduce. Research over several decades suggests that this harm, or virulence, is an inevitable by-product of the pathogen replication needed to maximize the chance that a given pathogen will be transmitted to another host. Here we demonstrate that a recently emerged bacterial pathogen of a North American songbird species has gradually become more virulent during each of two emergence events in different regions of the host range. This evolution of higher virulence appears to have been driven by selection for high rates of pathogen replication, because bacterial isolates that are more virulent in finches also attain the highest loads in infected host tissues. Overall, our results indicate that emerging pathogens can evolve to become more virulent in their hosts, at least in the short term, when an increase in the pathogen's ability to replicate is linked with higher virulence. Our findings have important implications for understanding and predicting the severity of disease caused by emerging pathogens in wildlife, domestic animals, and humans.

Modelling the course of an HIV infection: insights from ecology and evolution

The Human Immunodeficiency Virus (HIV) is one of the most threatening viral agents. This virus infects approximately 33 million people, many of whom are unaware of their status because, except for flu-like symptoms right at the beginning of the infection during the acute phase, the disease progresses more or less symptom-free for 5 to 10 years. During this asymptomatic phase, the virus slowly destroys the immune system until the onset of AIDS when opportunistic infections like pneumonia or Kaposi’s sarcoma can overcome immune defenses. Mathematical models have played a decisive role in estimating important parameters (e.g., virion clearance rate or life-span of infected cells). However, most models only account for the acute and asymptomatic latency phase and cannot explain the progression to AIDS. Models that account for the whole course of the infection rely on different hypotheses to explain the progression to AIDS. The aim of this study is to review these models, present their technical approaches and discuss the robustness of their biological hypotheses. Among the few models capturing all three phases of an HIV infection, we can distinguish between those that mainly rely on population dynamics and those that involve virus evolution. Overall, the modeling quest to capture the dynamics of an HIV infection has improved our understanding of the progression to AIDS but, more generally, it has also led to the insight that population dynamics and evolutionary processes can be necessary to explain the course of an infection.

Natural selection. IV. The Price equation

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen.

Epidemiological and clinical consequences of within-host evolution

Many viruses and bacteria are known to evolve rapidly over the course of an infection. However, epidemiological studies generally assume that within-host evolution is an instantaneous process. We argue that the dynamics of within-host evolution has implications at the within-host and at the between-host levels. We first show that epidemiologists should consider within-host evolution, notably because it affects the genotype of the pathogen that is transmitted. We then present studies that investigate evolution at the within-host level and examine the extent to which these studies can help to understand infection traits involved in the epidemiology (e.g. transmission rate, virulence, recovery rate). Finally, we discuss how new techniques for data acquisition can open new perspectives for empirical and theoretical research.

The evolutionary dynamics of a rapidly mutating virus within and between hosts: the case of hepatitis C virus

Many pathogens associated with chronic infections evolve so rapidly that strains found late in an infection have little in common with the initial strain. This raises questions at different levels of analysis because rapid within-host evolution affects the course of an infection, but it can also affect the possibility for natural selection to act at the between-host level. We present a nested approach that incorporates within-host evolutionary dynamics of a rapidly mutating virus (hepatitis C virus) targeted by a cellular cross-reactive immune response, into an epidemiological perspective. The viral trait we follow is the replication rate of the strain initiating the infection. We find that, even for rapidly evolving viruses, the replication rate of the initial strain has a strong effect on the fitness of an infection. Moreover, infections caused by slowly replicating viruses have the highest infection fitness (i.e., lead to more secondary infections), but strains with higher replication rates tend to dominate within a host in the long-term. We also study the effect of cross-reactive immunity and viral mutation rate on infection life history traits. For instance, because of the stochastic nature of our approach, we can identify factors affecting the outcome of the infection (acute or chronic infections). Finally, we show that anti-viral treatments modify the value of the optimal initial replication rate and that the timing of the treatment administration can have public health consequences due to within-host evolution. Our results support the idea that natural selection can act on the replication rate of rapidly evolving viruses at the between-host level. It also provides a mechanistic description of within-host constraints, such as cross-reactive immunity, and shows how these constraints affect the infection fitness. This model raises questions that can be tested experimentally and underlines the necessity to consider the evolution of quantitative traits to understand the outcome and the fitness of an infection.

Rapidly mutating viruses, such as hepatitis C virus, can escape host immunity by generating new strains that avoid the immune system. Existing data support the idea that such within-host evolution affects the outcome of the infection. Few theoretical models address this question and most follow viral diversity or qualitative traits, such as drug resistance. Here, we study the evolution of two virus quantitative traits—the replication rate and the ability to be recognised by the immune response—during an infection. We develop an epidemiological framework where transmission events are driven by within-host dynamics. We find that the replication rate of the virus that initially infects the host has a strong influence on the epidemiological success of the disease. Furthermore, we show that the cross-reactive immune response is key to determining the outcome of the infection (acute or chronic). Finally, we show that the timing of the start of an anti-viral treatment has a strong effect on viral evolution, which impacts the efficiency of the treatment. Our analysis suggests a new mechanism to explain infection outcomes and proposes testable predictions that can drive future experimental approaches.