This document provides an overview of a presentation on eco-evolutionary models of pathogen virulence. It begins with background on the evolution of theories of host-pathogen interactions. It then presents a toy model combining epidemiological and evolutionary dynamics to examine how virulence may transiently peak when a pathogen emerges in a new host population before declining. The model is used to explore how the initial epidemic size and genetic variation affect the height and timing of the virulence peak. The discussion considers how the model may help explain observed patterns of high initial virulence sometimes seen in emerging infectious diseases.

1. Overview Emerging disease Seasonal disease Theory vs. data References
Eco-evolutionary virulence of pathogens:
models and speculations
Ben Bolker, McMaster University
Departments of Mathematics & Statistics and Biology
IGERT symposium
25 April 2014

2. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

3. Overview Emerging disease Seasonal disease Theory vs. data References
Acknowledgements
People Arjun Nanda and Dharmini Shah; Christophe Fraser;
Marm Kilpatrick; Anson Wong
Support NSF IRCEB grant 9977063; QSE3 IGERT; NSERC
Discovery grant

4. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

5. Overview Emerging disease Seasonal disease Theory vs. data References
Host-pathogen evolutionary biology
Why is it interesting?
Intellectual merit
Coevolutionary loops
Cryptic eects
Eco-evolutionary dynamics (Luo and Koelle, 2013)
Cool stories
Lots of data (sometimes)
Broader applications
Medical
Conservation and management
Outreach

6. Overview Emerging disease Seasonal disease Theory vs. data References
Host-pathogen evolutionary biology
Why is it interesting?
Intellectual merit
Coevolutionary loops
Cryptic eects
Eco-evolutionary dynamics (Luo and Koelle, 2013)
Cool stories
Lots of data (sometimes)
Broader applications
Medical
Conservation and management
Outreach

7. Overview Emerging disease Seasonal disease Theory vs. data References
Virulence: denitions
General public: badness
Plant biologists: infectivity
Evolutionists: loss of host tness
Theoreticians: rate of host mortality
(mortality rate vs. case mortality vs. clearance)

8. Overview Emerging disease Seasonal disease Theory vs. data References
Evolution of virulence evolution theory
Classical dogma monotonic trend toward avirulence
Ewald era virulence as an evolved (adaptive) trait. Tradeo
theory, modes of transmission.
post-Ewald more formal tradeo models, mostly based on R0
optimization. Adaptive dynamics
Now tradeo backlash
within-host dynamics/multi-level models
eco-evolutionary dynamics
host eects: resistance vs tolerance vs virulence

9. Overview Emerging disease Seasonal disease Theory vs. data References
Evolution of virulence evolution theory
Classical dogma monotonic trend toward avirulence
Ewald era virulence as an evolved (adaptive) trait. Tradeo
theory, modes of transmission.
post-Ewald more formal tradeo models, mostly based on R0
optimization. Adaptive dynamics
Now tradeo backlash
within-host dynamics/multi-level models
eco-evolutionary dynamics
host eects: resistance vs tolerance vs virulence

10. Overview Emerging disease Seasonal disease Theory vs. data References
Evolution of virulence evolution theory
Classical dogma monotonic trend toward avirulence
Ewald era virulence as an evolved (adaptive) trait. Tradeo
theory, modes of transmission.
post-Ewald more formal tradeo models, mostly based on R0
optimization. Adaptive dynamics
Now tradeo backlash
within-host dynamics/multi-level models
eco-evolutionary dynamics
host eects: resistance vs tolerance vs virulence

11. Overview Emerging disease Seasonal disease Theory vs. data References
Evolution of virulence evolution theory
Classical dogma monotonic trend toward avirulence
Ewald era virulence as an evolved (adaptive) trait. Tradeo
theory, modes of transmission.
post-Ewald more formal tradeo models, mostly based on R0
optimization. Adaptive dynamics
Now tradeo backlash
within-host dynamics/multi-level models
eco-evolutionary dynamics
host eects: resistance vs tolerance vs virulence

12. Overview Emerging disease Seasonal disease Theory vs. data References
Basic tradeo theory: assumptions
Homogeneous, non-evolving hosts
No superinfection/coinfection
Horizontal, direct transmission
Tradeo between rate of transmission
and length of infectious period
Infectious period ∝ 1/clearance
(= recovery+disease-induced mortality+natural mortality)

13. Overview Emerging disease Seasonal disease Theory vs. data References
Tradeos, R0, and r
Clearance+disease−induced mort.
Transmission
rate
mu 0 1 2 3 4 5

14. Overview Emerging disease Seasonal disease Theory vs. data References
Tradeos, R0, and r
Clearance+disease−induced mort.
Transmission
rate
mu 0 1 2 3 4 5

15. Overview Emerging disease Seasonal disease Theory vs. data References
Tradeos, R0, and r
Clearance+disease−induced mort.
Transmission
rate
mu 0 1 2 3 4 5

16. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

17. Overview Emerging disease Seasonal disease Theory vs. data References
Epidemiological model
SIR model
Constant population size
(birth=death)
Ignore recovery
Rescale: µ = 1, N = 1
(time units of host lifespan)
I
S
disease−
mortality
(α)induced
mortality
(µ)
birth
R
infection (β)
recovery

18. Overview Emerging disease Seasonal disease Theory vs. data References
Epidemiological model
SIR model
Constant population size
(birth=death)
Ignore recovery
Rescale: µ = 1, N = 1
(time units of host lifespan)
I
S
disease−
mortality
(α)induced
mortality
(µ)
birth
R
infection (β)
recovery

19. Overview Emerging disease Seasonal disease Theory vs. data References
Epidemiological model
SIR model
Constant population size
(birth=death)
Ignore recovery
Rescale: µ = 1, N = 1
(time units of host lifespan)
I
S
disease−
mortality
(α)induced
mortality
(µ)
birth
R
infection (β)
recovery

20. Overview Emerging disease Seasonal disease Theory vs. data References
Epidemiological model
SIR model
Constant population size
(birth=death)
Ignore recovery
Rescale: µ = 1, N = 1
(time units of host lifespan)
I
S
disease−
mortality
(α)induced
mortality
(µ)
birth
R
infection (β)
recovery

21. Overview Emerging disease Seasonal disease Theory vs. data References
The model (2): evolutionary dynamics
Incorporate trait dynamics
Standard quantitative genetics model (Abrams, 2001):
Fitness depends on mean trait value (¯α)
and ecological context (proportion susceptible)
Constant additive genetic variance Vg
Trait evolves toward increased tness:
rate proportional to ∆tness/∆trait
Alternatives:
multi-strain, adaptive dynamics, PDEs, agent-based models ...

22. Overview Emerging disease Seasonal disease Theory vs. data References
The model (2): evolutionary dynamics
Incorporate trait dynamics
Standard quantitative genetics model (Abrams, 2001):
Fitness depends on mean trait value (¯α)
and ecological context (proportion susceptible)
Constant additive genetic variance Vg
Trait evolves toward increased tness:
rate proportional to ∆tness/∆trait
Alternatives:
multi-strain, adaptive dynamics, PDEs, agent-based models ...

23. Overview Emerging disease Seasonal disease Theory vs. data References
The model (2): evolutionary dynamics
Incorporate trait dynamics
Standard quantitative genetics model (Abrams, 2001):
Fitness depends on mean trait value (¯α)
and ecological context (proportion susceptible)
Constant additive genetic variance Vg
Trait evolves toward increased tness:
rate proportional to ∆tness/∆trait
Alternatives:
multi-strain, adaptive dynamics, PDEs, agent-based models ...

24. Overview Emerging disease Seasonal disease Theory vs. data References
The model (2): evolutionary dynamics
Incorporate trait dynamics
Standard quantitative genetics model (Abrams, 2001):
Fitness depends on mean trait value (¯α)
and ecological context (proportion susceptible)
Constant additive genetic variance Vg
Trait evolves toward increased tness:
rate proportional to ∆tness/∆trait
Alternatives:
multi-strain, adaptive dynamics, PDEs, agent-based models ...

25. Overview Emerging disease Seasonal disease Theory vs. data References
The model (2): evolutionary dynamics
Incorporate trait dynamics
Standard quantitative genetics model (Abrams, 2001):
Fitness depends on mean trait value (¯α)
and ecological context (proportion susceptible)
Constant additive genetic variance Vg
Trait evolves toward increased tness:
rate proportional to ∆tness/∆trait
Alternatives:
multi-strain, adaptive dynamics, PDEs, agent-based models ...

26. Overview Emerging disease Seasonal disease Theory vs. data References
Evolutionary dynamics, cont.
Virulence
Fitness(w)
frac inf=0.1

27. Overview Emerging disease Seasonal disease Theory vs. data References
Evolutionary dynamics, cont.
Virulence
Fitness(w)
frac inf=0.1
frac inf=0.3

28. Overview Emerging disease Seasonal disease Theory vs. data References
Power-law tradeo curves
Virulence
Transmission β(α) = cα1 γ
c = 2, γ = 2
c = 1, γ = 2
c = 1, γ = 3

29. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

30. Overview Emerging disease Seasonal disease Theory vs. data References
(Why) are emerging pathogens more virulent?
What might explain initially high, but rapidly decreasing, virulence
of emerging pathogens?
Pathogens with low virulence go unnoticed
Hosts less resistant to / tolerant of novel parasites
High transmission → frequent coinfection → selection for
virulence
Disease-induced drop in population density decreases selection
for virulence (Lenski and May, 1994)

31. Overview Emerging disease Seasonal disease Theory vs. data References
(Why) are emerging pathogens more virulent?
What might explain initially high, but rapidly decreasing, virulence
of emerging pathogens?
Pathogens with low virulence go unnoticed
Hosts less resistant to / tolerant of novel parasites
High transmission → frequent coinfection → selection for
virulence
Disease-induced drop in population density decreases selection
for virulence (Lenski and May, 1994)

32. Overview Emerging disease Seasonal disease Theory vs. data References
(Why) are emerging pathogens more virulent?
What might explain initially high, but rapidly decreasing, virulence
of emerging pathogens?
Pathogens with low virulence go unnoticed
Hosts less resistant to / tolerant of novel parasites
High transmission → frequent coinfection → selection for
virulence
Disease-induced drop in population density decreases selection
for virulence (Lenski and May, 1994)

33. Overview Emerging disease Seasonal disease Theory vs. data References
(Why) are emerging pathogens more virulent?
What might explain initially high, but rapidly decreasing, virulence
of emerging pathogens?
Pathogens with low virulence go unnoticed
Hosts less resistant to / tolerant of novel parasites
High transmission → frequent coinfection → selection for
virulence
Disease-induced drop in population density decreases selection
for virulence (Lenski and May, 1994)

34. Overview Emerging disease Seasonal disease Theory vs. data References
Transient virulence
Selection diers between the epidemic and endemic phases of an
outbreak (Frank, 1996; Day and Proulx, 2004)
endemic phase selection for per-generation ospring production:
maximize R0, βN/(α + µ)
epidemic phase selection for per-unit-time ospring production:
maximize r, βN − (α + µ)

35. Overview Emerging disease Seasonal disease Theory vs. data References
Transient virulence
Selection diers between the epidemic and endemic phases of an
outbreak (Frank, 1996; Day and Proulx, 2004)
endemic phase selection for per-generation ospring production:
maximize R0, βN/(α + µ)
epidemic phase selection for per-unit-time ospring production:
maximize r, βN − (α + µ)

36. Overview Emerging disease Seasonal disease Theory vs. data References
Transient virulence
Selection diers between the epidemic and endemic phases of an
outbreak (Frank, 1996; Day and Proulx, 2004)
endemic phase selection for per-generation ospring production:
maximize R0, βN/(α + µ)
epidemic phase selection for per-unit-time ospring production:
maximize r, βN − (α + µ)

37. Overview Emerging disease Seasonal disease Theory vs. data References
Transient emerging virulence
When a parasite previously in eco-evolutionary equilibrium
emerges in a new host population (at low density) it will show
a transient peak in virulence as it spreads
How big is the peak? Does it matter?

38. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

39. Overview Emerging disease Seasonal disease Theory vs. data References
Model parameters
Parameter
c Transmission
scale
γ Transmission
curvature
I(0) Initial
epidemic size
Vg Genetic variance
Alternative
R∗
0 Equilibrium R0
α∗ Equilibrium
virulence
1/N0 Inverse
population size

40. Overview Emerging disease Seasonal disease Theory vs. data References
Example
Time
Fractioninfective
0.00
0.05
0.10
0.15
0 10 20 30
Vg = 5, c = 3, I(0) = 0.001, γ = 2
(R0
*
= 1.5, α*
= 1, N = 1000)
1.0
1.2
1.4
1.6
1.8
2.0
α

41. Overview Emerging disease Seasonal disease Theory vs. data References
Response variables
Time
peak
time
peak height(α)

42. Overview Emerging disease Seasonal disease Theory vs. data References
Peak height
Equilibrium transmission (R0
*
)
Equilibriumvirulence(α*
)
1
10
100
1000
1.1 2 5 10 50
1.025
I(0) = 10−2
CVg=0.1
1.025
1.05
I(0) = 10−3
CVg=0.1
1.1 2 5 10 50
1.05
1.075
I(0) = 10−4
CVg=0.1
1.5
I(0) = 10−2
CVg=0.5
1.5
2.0
I(0) = 10−3
CVg=0.5
1
10
100
1000
1.5
2.0
I(0) = 10−4
CVg=0.5
1
10
100
1000
1.5
2.0
2.5
3.0
I(0) = 10−2CVg=1
1.1 2 5 10 50
1.5
2.0
2.5
3.0
3.5
I(0) = 10−3
CVg=1
1.5
2.0
2.5
3.0
3.5
4.0
I(0) = 10−4
CVg=1 1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5

43. Overview Emerging disease Seasonal disease Theory vs. data References
Estimates for emerging pathogens
Order of magnitude estimates for some emerging high-virulence
pathogens:
Pathogen R∗
0 α∗
Reference
SARS 3 640 Anderson et al. (2004)
HIV 1.43 6.36 Velasco-Hernandez et al. (2002)
West Nile 1.613.24 639 Wonham et al. (2004)
myxomatosis 3 5 Dwyer et al. (1990)

44. Overview Emerging disease Seasonal disease Theory vs. data References
Emerging pathogens: where are we?
CVg = 0.5, I(0) = 10−3 (middle panel):
R0
Equilibriumvirulence(α*
)
1
10
100
1000
1.1 2 5 10 50
1.5
2.0
SARS
HIV
WNV
MYXO
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5

45. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

46. Overview Emerging disease Seasonal disease Theory vs. data References
Overview
Mosquito-borne viral disease of rabbits
Benign in South American rabbits,
quickly fatal in European rabbits
Well characterized (Fenner et al., 1956; Dwyer et al., 1990)

47. Overview Emerging disease Seasonal disease Theory vs. data References
Myxomatosis tradeo curve
Scaled virulence
Totaltransmission
0 2 4 6 8 10 12
0.0
0.2
0.4
0.6
eq epi

48. Overview Emerging disease Seasonal disease Theory vs. data References
Estimating evolvability (Vg)
Key parameter: genetic variance in virulence (evolvability)
Despite case studies of rapid pathogen evolution:
myxomatosis (Dwyer et al., 1990)
syphilis (Knell, 2004)
serial passage experiments (Ebert, 1998)
Plasmodium chabaudi (Mackinnon and Read, 1999a)
we rarely have enough information to estimate Vg
Only (?) for myxomatosis do we know the variation in
virulence among circulating strains

49. Overview Emerging disease Seasonal disease Theory vs. data References
Estimating evolvability (Vg)
Key parameter: genetic variance in virulence (evolvability)
Despite case studies of rapid pathogen evolution:
myxomatosis (Dwyer et al., 1990)
syphilis (Knell, 2004)
serial passage experiments (Ebert, 1998)
Plasmodium chabaudi (Mackinnon and Read, 1999a)
we rarely have enough information to estimate Vg
Only (?) for myxomatosis do we know the variation in
virulence among circulating strains

50. Overview Emerging disease Seasonal disease Theory vs. data References
Estimating evolvability (Vg)
Key parameter: genetic variance in virulence (evolvability)
Despite case studies of rapid pathogen evolution:
myxomatosis (Dwyer et al., 1990)
syphilis (Knell, 2004)
serial passage experiments (Ebert, 1998)
Plasmodium chabaudi (Mackinnon and Read, 1999a)
we rarely have enough information to estimate Vg
Only (?) for myxomatosis do we know the variation in
virulence among circulating strains

51. Overview Emerging disease Seasonal disease Theory vs. data References
Myxomatosis grades vs. time
1950 1954 1956 1961 1965 1968 1972 1978
Proportion
0.0
0.2
0.4
0.6
0.8
1.0
Virulence grade
I II III IV V

52. Overview Emerging disease Seasonal disease Theory vs. data References
Myxomatosis variance vs. time
Date
Geneticvariance(Vg)
0
10
20
30
40
1950 1960 1970
Vg= 10
Vg= 2.5
Vg= 40

53. Overview Emerging disease Seasonal disease Theory vs. data References
Myxomatosis virulence dynamics: power-law tradeo
Date
Scaledvirulence
0
5
10
15
20
25
1950 1960 1970
h=2.5
h=10
h=40

54. Overview Emerging disease Seasonal disease Theory vs. data References
Myxomatosis virulence dynamics: realistic tradeo
Date
Scaledvirulence
0
5
10
15
20
25
1950 1960 1970
h=40
h=10
h=2.5

55. Overview Emerging disease Seasonal disease Theory vs. data References
Myxo virulence: equilibrium start, power-law tradeo
Date
Scaledvirulence
0
5
10
15
1950 1955
h=40
h=10
h=2.5

56. Overview Emerging disease Seasonal disease Theory vs. data References
Myxo virulence: equilibrium start, realistic tradeo
Date
Scaledvirulence
0
5
10
15
1950 1955
h=40
h=10
h=2.5

57. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

58. Overview Emerging disease Seasonal disease Theory vs. data References
Seasonality
Many pathogens uctuate annually
Host contact/aggregation patterns
Host (or vector) demography
Climatic eects on transmissibility
Fluctuating incidence = uctuating selection
Seasonal variation or latitudinal variation?

59. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

60. Overview Emerging disease Seasonal disease Theory vs. data References
Toy model
Basic Ross-MacDonald
vector-host model
Simple vector (mosquito)
demography
No host demography
Two pathogen strains
I disease−
mortality
(α)induced
S
I
infection (β)
recovery
S
R
host vector

61. Overview Emerging disease Seasonal disease Theory vs. data References
Case I: r1 r2, equal R0
0.000
0.025
0.050
0.075
0 25 50 75 100 125
time
density
variable
I1
I2
0.0
0.2
0.4
0 25 50 75 100 125
time
fractionofstrain1

62. Overview Emerging disease Seasonal disease Theory vs. data References
Case II: R0,1 R0,2, equal r
0.00
0.05
0.10
0.15
0.20
0 25 50 75 100 125
time
density
variable
I1
I2
0.5
0.6
0.7
0.8
0.9
1.0
0 25 50 75 100 125
time
fractionofstrain1

63. Overview Emerging disease Seasonal disease Theory vs. data References
Case III: R0,1 R0,2, r2 r1
0.00
0.05
0.10
0.15
0 25 50 75 100 125
time
density
variable
I1
I2
0.5
0.6
0.7
0.8
0.9
1.0
0 25 50 75 100 125
time
fractionofstrain1

64. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

65. Overview Emerging disease Seasonal disease Theory vs. data References
Titer vs infectiousness
q q q
q
q
q
q
q
q
q
q
q
q
q
q
q
0.0
0.2
0.4
0.6
4 6 8
titer
Transmissionprobability
source
q
q
q
q
Dohm
Tiawsirisup_2005_VBZD
Turell_altjmh
Turell_JME

66. Overview Emerging disease Seasonal disease Theory vs. data References
Titer curves (American crows)
1e−04
1e−02
1e+00
2 4 6 8
day
transmissionprobability
strain
BIRD1153
KEN
KENsub
NY99
P991
P991sub
TM171−03−pp5
TM173−03−pp1
TWN301

67. Overview Emerging disease Seasonal disease Theory vs. data References
Transmission vs clearance for WNV
BIRD1153
BIRD1461
NY99
TM171−03−pp5
BIRD1153
KEN
KENsub
NY99P991
TM171−03−pp5
TWN301
0.0
0.2
0.4
0.6
0.00 0.25 0.50 0.75 1.00
Clearance rate (1/infectious period)
Averagetransmissionrate
species
a
a
sparrow
amcrow

68. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

69. Overview Emerging disease Seasonal disease Theory vs. data References
Estimating tradeo curves
Usually assume a tradeo between virulence and transmission
Positive correlation virulence and transmissibility (or proxies)
known from many systems (Lipsitch and Moxon, 1997)
the shape of tradeo curves is largely unknown

70. Overview Emerging disease Seasonal disease Theory vs. data References
Malaria (Mackinnon and Read, 1999b; Paul et al., 2004)
q
q
qq
0 500 1000 1500
0
20
40
60
80
100
Scaled virulence
%mosquitoesinfected
Plasmodium gallinaceum
q
low−dose mixed
high−dose mixed
SL
Thai
q
q
q
q
qq
q
q
10 15 20 25
10
15
20
25
Maximum parasitemia
Overallinfection(%)
Plasmodium chabaudi

71. Overview Emerging disease Seasonal disease Theory vs. data References
Pasteuria ramosa (Jensen et al., 2006)
qqqqq
q
q
q
qq
q
q
q
qqq
qq
q
q
q
q
q
qq
qq
q
q
q
q
0 1 2 3 4 5
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Scaled virulence
Spores/day(×106
)
qqqqq
q
q
q
qq
q
q
q
qqq
qq
q
q
q
q
q
qq
qq
q
q
q
q

72. Overview Emerging disease Seasonal disease Theory vs. data References
HIV (Fraser et al., 2007)
0 10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
0.5
Transmissionrate
eq epi

73. Overview Emerging disease Seasonal disease Theory vs. data References
HIV dynamics (Shirre et al., 2011)

74. Overview Emerging disease Seasonal disease Theory vs. data References
Phage dynamics (Berngruber et al., 2013)

75. Overview Emerging disease Seasonal disease Theory vs. data References
What about space?
Theory: spatial structure
should select for decreased
virulence
Experiment: viscosity
decreases infectivity in
Plodia (Boots and Mealor,
2007)
Are we ready for space?

76. Overview Emerging disease Seasonal disease Theory vs. data References
Outline
1 Overview
The evolution of host-pathogen theory
Toy models
2 Transient virulence and emerging diseases
Overview
Toy model
Myxomatosis data
3 Transient virulence and seasonality
Overview
Toy model
WNV data
4 More on theory vs. data
Tradeo curves
Conclusions

77. Overview Emerging disease Seasonal disease Theory vs. data References
Conclusions
Eco-evolutionary dynamics of virulence are still plausible
(Alizon et al., 2009; Luo and Koelle, 2013)
Sensitive to genetic variance and shape of tradeo curve
Theory meets molecular biology:
mutations of large eect vs. quantitative variability

78. Overview Emerging disease Seasonal disease Theory vs. data References
Conclusions
Eco-evolutionary dynamics of virulence are still plausible
(Alizon et al., 2009; Luo and Koelle, 2013)
Sensitive to genetic variance and shape of tradeo curve
Theory meets molecular biology:
mutations of large eect vs. quantitative variability

79. Overview Emerging disease Seasonal disease Theory vs. data References
Crome (1997) on theory
When we regard theories as tight, real entities and devote
ourselves to their analysis, we can limit our horizons and,
worse, attempt to make the world t them. A lot of
ecological discussion is not about nature, but about
theories, generalizations, or models supposed to represent
nature . . .

80. Overview Emerging disease Seasonal disease Theory vs. data References
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