Measured Games · Paper 15 of 07 · Evolutionary epidemiology

The evolution of virulence

After R. M. Anderson and R. M. May (1982); the myxomatosis record from F. Fenner and F. N. Ratcliffe (1965)

Abstract

A parasite that exploits its host harder transmits better but kills faster, and the two effects trade off in the basic reproduction number. Selection therefore favours an intermediate level of harm rather than either avirulence or maximum exploitation. Where several strains share a host the calculation changes, because within-host competition rewards growth that the strain would not choose if it had the host to itself.

Keywordstransmission trade-off · basic reproduction number · coinfection · myxomatosis

1Setup

Setup

It is often said that a well-adapted parasite evolves towards harmlessness, on the grounds that killing your host is bad for business. The claim is intuitive and wrong, and the reason it is wrong is a trade-off.

Exploiting a host harder generally produces more of the parasite and so more transmission. It also shortens the time the host is alive and infectious. Selection acts on the product of the two, not on either alone, so the favoured level of harm is generally neither zero nor as much as possible.

2The model

The model

# virulence v is the extra host mortality the parasite imposes # transmission rises with exploitation but saturates β(v) = B √v # an infection ends when the host recovers, dies of other causes, or dies of this R0(v) = β(v) / ( d + v ), d = background loss rate # selection maximises R0, giving an interior optimum dR0/dv = 0 → v* = d # with several strains sharing a host, within-host competition # rewards faster growth regardless of what it costs the infection fitness ∝ R0(v) · vs → v* rises with s

The single-infection optimum lands exactly on the rate at which infections were going to end anyway. That is the whole logic in one line: harm the host faster than it was going to be lost and you waste transmission; slower and you leave transmission unclaimed.

Figure 1Selection on a heritable exploitation rate

This figure needs JavaScript. The panels below are live simulations rather than images, so with scripting turned off they stay empty and the controls do nothing. Everything the figure demonstrates is also stated in the surrounding text: the model is given in full in section 2 and the result in section 3.

Mean virulence in the population against the optimum

Reproduction number against virulence · hover to read the trade-off

Distribution of strains in the current generation

Mean virulence Predicted optimum R₀

Charts are focusable. With a chart focused, use the left and right arrow keys to read values along the horizontal axis.

Background loss rate d

Transmission coefficient B

Within-host competition s

Mutation size

Predicted v*—

Mean virulence—

R₀ at the mean—

Max attainable R₀—

Deviation—

Generation0

Figure 1. Strains carry a heritable virulence and reproduce in proportion to fitness, so the mean arrives at the optimum by selection rather than by being set there. Start avirulent and it climbs: harmlessness is not stable. The competition slider is the important one. At zero it reproduces the single-infection result v* = d exactly; raise it and the population evolves past the level that maximises its own reproduction number, which is what coinfection does in nature.

3Results

Results

Anderson and May (1982) formalised the trade-off and drew the conclusion that displaced the avirulence folklore: selection favours an intermediate level of harm, set by how the parasite's transmission responds to exploitation and by how long infections last for other reasons. Avirulence is not an endpoint, it is a strategy that gets invaded.

The coinfection result runs the other way and matters more for management. When strains share a host, the one that grows fastest wins the within-host contest even though its aggression shortens the infection for everyone present, including itself. That is a tragedy of the commons operating inside a single body, and it selects for virulence above the level that would maximise the parasite's own reproduction number.

The practical implication is that anything raising the rate of multiple infection, higher transmission, crowding, or vaccines that reduce symptoms without blocking transmission, shifts selection towards more harm rather than less.

4Evidence

Evidence

Myxomatosis in Australian rabbits is the standard case because the whole sequence was watched and measured. The strain released in 1950 killed essentially every rabbit it infected, with a case fatality rate around 99.8 per cent and an average survival time of ten to twelve days. Fenner and Marshall (1957) built a grading scale from field isolates tested in laboratory rabbits, running from grade I, lethal to almost all with survival under about thirteen days, to grade V, killing fewer than half.

Within about two years, slightly attenuated strains were displacing the original in the field. They still killed most infected rabbits, but the rabbits lived longer while infectious, and since transmission depends on mosquitoes picking up virus from skin lesions, longer survival meant more transmission. For roughly the following thirty years the field was dominated by intermediate grades, with case fatality rates in the range of 70 to 95 per cent. Crucially the virus did not keep going towards harmlessness: highly attenuated strains were cleared quickly by the rabbit's immune system and transmitted poorly, which is the far arm of the trade-off doing its work.

The experiment was then repeated by accident. A different South American strain was released in France in 1952, and the European epidemic produced strikingly similar outcomes, with attenuated strains emerging and resistant rabbits selected for. Independent replication on another continent is rare in evolutionary epidemiology and is a large part of why this case carries the weight it does.

De Roode and colleagues (2008) provided a clean quantitative test in monarch butterflies and their protozoan parasite, measuring transmission and host lifespan across parasite genotypes and finding the intermediate optimum the model predicts. Alizon and colleagues (2009) review the wider evidence and are candid that support is strong in some systems and thin in others.

5Limitations

Limitations

The trade-off curve is the weak point. The model requires transmission to rise with virulence at a decreasing rate, and for most pathogens that relationship has never been measured. Where it has not been, the theory predicts an intermediate optimum without saying where, which is close to unfalsifiable.

The framework also assumes virulence is a parasite trait under parasite control. Much observed harm is immunopathology, damage done by the host's own response, which the parasite does not choose and may not benefit from. In those cases the optimisation is being applied to the wrong quantity.

The myxomatosis case is also less finished than its textbook status suggests, and the site should not present a freeze-frame as an endpoint. Field isolates collected in the 1990s were found to produce a disease that is not classical myxomatosis at all: rather than the cutaneous form Fenner described, the virulent strains caused acute collapse, a phenotype absent from the 1950s isolates. The virus and the rabbit population have gone on coevolving, with rabbit resistance changing what a given viral grade means in the wild, and there was no systematic phenotyping of Australian field isolates between the early 1980s and that work. The thirty years of stability at intermediate virulence is real; treating it as where the story ended is not.

Alizon and colleagues put the honest summary well: the hypothesis is theoretically compelling, well supported in a handful of carefully measured systems, and routinely assumed rather than tested in the rest. Treat the myxomatosis story as the best available case rather than as typical.

References

Alizon, S., Hurford, A., Mideo, N., & Van Baalen, M. (2009). Virulence evolution and the trade-off hypothesis: History, current state of affairs and the future. Journal of Evolutionary Biology, 22(2), 245–259. https://doi.org/10.1111/j.1420-9101.2008.01658.x
Anderson, R. M., & May, R. M. (1982). Coevolution of hosts and parasites. Parasitology, 85(2), 411–426. https://doi.org/10.1017/S0031182000055360
de Roode, J. C., Yates, A. J., & Altizer, S. (2008). Virulence-transmission trade-offs and population divergence in virulence in a naturally occurring butterfly parasite. Proceedings of the National Academy of Sciences, 105(21), 7489–7494. https://doi.org/10.1073/pnas.0710909105
Fenner, F., & Marshall, I. D. (1957). A comparison of the virulence for European rabbits (Oryctolagus cuniculus) of strains of myxoma virus recovered in the field in Australia, Europe and America. Journal of Hygiene, 55(2), 149–191. https://doi.org/10.1017/S0022172400037098
Fenner, F., & Ratcliffe, F. N. (1965). Myxomatosis. Cambridge University Press.
Kerr, P. J., Cattadori, I. M., Liu, J., Sim, D. G., Dodds, J. W., Brooks, J. W., Kennett, M. J., Holmes, E. C., & Read, A. F. (2017). Next step in the ongoing arms race between myxoma virus and wild rabbits in Australia is a novel disease phenotype. Proceedings of the National Academy of Sciences, 114(35), 9397–9402. https://doi.org/10.1073/pnas.1710336114
Frank, S. A. (1996). Models of parasite virulence. The Quarterly Review of Biology, 71(1), 37–78. https://doi.org/10.1086/419267
Read, A. F., & Taylor, L. H. (2001). The ecology of genetically diverse infections. Science, 292(5519), 1099–1102. https://doi.org/10.1126/science.1059410

Verification Every reference on this page has been checked against Crossref. The claims this page makes about what those sources report have also been checked against the sources, and any corrections that check produced are recorded in the project’s claims log.