key: cord-0334273-x208ou74
authors: Kennedy, David A.
title: Detection, not mortality, constrains the evolution of virulence
date: 2021-11-14
journal: bioRxiv
DOI: 10.1101/2021.11.14.468516
sha: 1189bfb6bd9d0c7e586e640b702b453e0d28933b
doc_id: 334273
cord_uid: x208ou74

Why would a pathogen evolve to kill its hosts when killing a host ends a pathogen’s own opportunity for transmission? A vast body of scientific literature has attempted to answer this question using “trade-off theory,” which posits that host mortality persists due to its cost being balanced by benefits of other traits that correlate with host mortality. The most commonly invoked trade-off is the mortality-transmission trade-off, where increasingly harmful pathogens are assumed to transmit at higher rates from hosts while the hosts are alive, but the pathogens truncate their infectious period by killing their hosts. Here I show that costs of mortality are too small to plausibly constrain the evolution of disease severity except in systems where survival is rare. I alternatively propose that disease severity can be much more readily constrained by a cost of behavioral change due to the detection of infection, whereby increasingly harmful pathogens have increasing likelihood of detection and behavioral change following detection, thereby limiting opportunities for transmission. Using a mathematical model, I show the conditions under which detection can limit disease severity. Ultimately, this argument may explain why empirical support for trade-off theory has been limited and mixed.

The seminal works of Anderson and May (Anderson and May 1982; May and Anderson 1983) 24 changed the way that biologists thought about the evolution of pathogen virulence, defined 25 as the severity of disease signs or symptoms caused by infection with a particular pathogen. 26 Before Anderson and May, the conventional wisdom was that pathogens would evolve to 27 be avirulent over time (Alizon and Michalakis 2015), since a highly virulent pathogen risks 28 killing its host and by killing its host a pathogen truncates its own infectious period and 29 reduces its own fitness. Anderson and May articulated that natural selection favors pathogen 30 variants that maximize their own fitness. If virulence were correlated with other epidemio-31 logical parameters such as infectiousness or time to recovery, intermediate levels of virulence 32 could maximize fitness, and thus be evolutionarily adaptive. The idea they proposed, "trade-33 off theory", is that the cost of virulence, which they assumed was a truncated duration of 34 infectiousness caused by host mortality, trades off against other benefits such as an increased

The cost of mortality 101 The original formulation of the virulence-transmission trade-off arises from analysis of a 102 classic SIR model based on the models of Kermack and McKendrick (1991) and Anderson 103 and May (1979) .

Above, S, I, and R are the respective densities of susceptible, infectious, and recovered 105 hosts. N is the total population density derived by summing S, I, and R. r is the maximum 106 per capita birth rate, φ is that rate at which immunity wanes, β is the transmission rate, 107 γ is the recovery rate, µ is the baseline host mortality rate, and α is the pathogen-induced 108 host mortality rate.

mizes the basic reproductive number R 0 will competitively exclude all other pathogen strains 114 once the system reaches an equilibrium. It thus follows that natural selection will lead to 115 the evolution of a pathogen strain that maximizes R 0 (Anderson and May 1982). 116 In the above model, the basic reproductive number is 

According to the principle of R 0 maximization, a new pathogen variant would be able 126 to invade and displace an existing pathogen strain provided the new value of R 0 is greater 127 than the old value of R 0 . Under the assumption that recovery rate γ is the same for two 128 pathogen variants, this can be reduced to (Supplemental Information): impact pathogen fitness, and presumably, moreso for increasingly severe disease.

To formalize this concept, consider an alternative SIR-type model, with modification from 185 Eqs 1-3. The differences are that 1) host mortality has been removed, and 2) the infectious 186 class has been split up into three groups.

As before, N is the sum of host density in all classes, S is the density of susceptible hosts, while the reused parameters φ, β and γ can still take any non-negative value.

As before, we can readily derive the basic reproductive number, 217

if we relaxed the assumption that was unchanged by evolution, the numerator on the left one can combine Inequalities 6 and 13 to ask:

When the left-hand side of the above expression is larger than the right-hand side, mortality 260 will impose a stronger constraint on virulence evolution than detection, and vice versa. For 261 a pathogen with low virulence, the denominators on both sides are close to one meaning that 262 we can visualize this inequality using only the numerators (Fig. 4 ). This demonstrates that 263 for pathogens with relatively low virulence, detection will generally be a stronger constraint 264 on virulence evolution than mortality.

The new conventional wisdom says that pathogens evolve to balance the cost and benefits 267 of virulence and its associated traits. Typically, the cost of virulence is assumed to be a 268 truncated infectious period due to disease-induced host mortality. Here I have argued that At some level, this conclusion may be obvious. Both mortality and detection could in 306 principle constrain virulence evolution, but death is usually a rare outcome of infection 307 whereas detection is usually a common outcome. It thus follows that detection costs may 308 often be larger than mortality costs.

Few data are yet available to quantify precisely how large detection costs are, but the data 310 that do exist suggest these costs are quite large in comparison to fully asymptomatic infec- 

Perhaps the greatest challenge moving forward is to test this theory experimentally. The 381 difficulty of doing so stems from being able to create conditions that are close enough to field 382 conditions such that they allow for changes in behavior that limit transmission following the 383 detection of infection. Such laboratory experiments may prove too difficult to design, and 384 may ultimately mean that tests of this theory must be performed in the field.

It is worth noting that virulence has been defined differently by different researcher 

Here I have assumed that the benefits of virulence come from a correlation with trans-404 mission rate (Fig. 1) . As shown by Inequality 14, the precise benefit of virulence does not 405 impact whether virulence is more strongly constrained by mortality or detection. Numerous 

Substituting equation 4 into inequality 5 yields

Multiplying both sides by α o + γ o + µ and dividing both sides by β n N yields

Multiplying both sides by negative 1 and then adding 1 to each side yields

Under the assumptions of a virulence-transmission trade-off constrained by disease-induced 443 mortality, γ o = γ n and so the above can be rewritten

where ∆α ≡ α n − α o and ∆β ≡ β n − β o . 

Multiplying both sides by γ o and dividing both sides by

Again multiplying both sides by negative 1 and adding 1 to each side yields: Infection fatality rate (%)

Influenza A (flu)

Plasmodium falciparum (malaria)

Variola major (smallpox)

HIV (AIDS) Figure 2 : Under the assumption that host mortality constrains virulence, moderate changes in transmission rates can justify large increases in the infection fatality rate. Open circles indicate approximate infection fatality rates for various pathogens and parasites (values are for illustration purposes and may not be exact). Filled circles indicate the maximum infection fatality rate that would be evolutionarily favored under current theory if it were accompanied by a 10% increase in the transmission rate ( ∆β βo ). Note that this change in transmission is enough justify an otherwise harmless pathogen evolving to become as virulent as the 2003 SARS virus. Figure 4 : A graphical representation of Inequality 14 for a pathogen with initially low virulence. The cost from an x% reduction in average transmission is equivalent to the cost from an x% increase in the infection fatality rate. The dashed line is the 1:1 line. Above the dashed line, virulence is constrained by mortality costs, and below it, detection costs. The dotted red arrow depicts the example provided in the main text of a pathogen with initially low virulence that evolves higher virulence in the form of either killing 1% of infected hosts (i.e. roughly equivalent to SARS-CoV-2 infection) or causing infected hosts to stay home for one day (roughly equivalent to infection with a virus that causes the flu or the common cold). Notably, the cost of the former is much smaller than the cost of the latter despite the fact that most would consider the former more virulent than the latter.

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