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Transcript of evolution of virulence: devil in the details
Overview Simple models HIV case study Conclusions References
Eco-evolutionary virulence of pathogens:the devil is (still) in the details
Ben Bolker, McMaster UniversityDepartments of Mathematics & Statistics and Biology
University of Tennessee
15 September 2016
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Acknowledgements
People Arjun Nanda and Dharmini Shah; Christophe Fraser;Daniel Park
Support NSF IRCEB grant 9977063; QSE3 IGERT; NSERCDiscovery grant
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Host-pathogen evolutionary biology
Why?Intellectual merit
Coevolutionary loopsCryptic effectsEco-evolutionary dynamics (Luo and Koelle, 2013)Lots of data (for humans)
Broader applicationsMedicalConservation and managementOutreach
Overview Simple models HIV case study Conclusions References
Host-pathogen evolutionary biology
Why?Intellectual merit
Coevolutionary loopsCryptic effectsEco-evolutionary dynamics (Luo and Koelle, 2013)Lots of data (for humans)
Broader applicationsMedicalConservation and managementOutreach
Overview Simple models HIV case study Conclusions References
Virulence: definitions
General public: badnessPlant biologists: infectivityEvolutionists: loss of host fitnessTheoreticians: rate of host mortality
Overview Simple models HIV case study Conclusions References
Evolution of virulence evolution theory
Classical avirulence theoryAnderson & May/Ewald virulence as an evolved (adaptive) trait.
Tradeoff theory, modes of transmission.post-Ewald mathematical models based on R0
Now tradeoff backlashwithin-host dynamics/multi-level modelseco-evolutionary dynamicshost effects: resistance vs tolerance vs virulence
Overview Simple models HIV case study Conclusions References
Evolution of virulence evolution theory
Classical avirulence theoryAnderson & May/Ewald virulence as an evolved (adaptive) trait.
Tradeoff theory, modes of transmission.post-Ewald mathematical models based on R0
Now tradeoff backlashwithin-host dynamics/multi-level modelseco-evolutionary dynamicshost effects: resistance vs tolerance vs virulence
Overview Simple models HIV case study Conclusions References
Evolution of virulence evolution theory
Classical avirulence theoryAnderson & May/Ewald virulence as an evolved (adaptive) trait.
Tradeoff theory, modes of transmission.post-Ewald mathematical models based on R0
Now tradeoff backlashwithin-host dynamics/multi-level modelseco-evolutionary dynamicshost effects: resistance vs tolerance vs virulence
Overview Simple models HIV case study Conclusions References
Evolution of virulence evolution theory
Classical avirulence theoryAnderson & May/Ewald virulence as an evolved (adaptive) trait.
Tradeoff theory, modes of transmission.post-Ewald mathematical models based on R0
Now tradeoff backlashwithin-host dynamics/multi-level modelseco-evolutionary dynamicshost effects: resistance vs tolerance vs virulence
Overview Simple models HIV case study Conclusions References
Basic tradeoff theory: assumptions
Homogeneous, non-evolving hostsNo super- or coinfectionHorizontal, direct transmissionTradeoff between rate of transmissionand length of infectious periodInfectious period ∝ 1/clearance rate
Overview Simple models HIV case study Conclusions References
Tradeoffs, R0, and r
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
Overview Simple models HIV case study Conclusions References
Tradeoffs, R0, and r
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
Overview Simple models HIV case study Conclusions References
Tradeoffs, R0, and r
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
●
●
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Epidemiological model
SIR model
Constant population size(birth=death)
Rescale: µ = 1, N = 1(time units of host lifespan)
I
S
disease−
mortality(α)induced
mortality(µ)
birth
R
infection (β)
recovery
Overview Simple models HIV case study Conclusions References
Epidemiological model
SIR model
Constant population size(birth=death)
Rescale: µ = 1, N = 1(time units of host lifespan)
I
S
disease−
mortality(α)induced
mortality(µ)
birth
R
infection (β)
recovery
Overview Simple models HIV case study Conclusions References
Epidemiological model
SIR model
Constant population size(birth=death)
Rescale: µ = 1, N = 1(time units of host lifespan)
I
S
disease−
mortality(α)induced
mortality(µ)
birth
R
infection (β)
recovery
Overview Simple models HIV case study Conclusions References
The model (2): evolutionary dynamics
Incorporate trait dynamicsStandard 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 fitness:rate proportional to ∆fitness/∆trait
Overview Simple models HIV case study Conclusions References
The model (2): evolutionary dynamics
Incorporate trait dynamicsStandard 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 fitness:rate proportional to ∆fitness/∆trait
Overview Simple models HIV case study Conclusions References
The model (2): evolutionary dynamics
Incorporate trait dynamicsStandard 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 fitness:rate proportional to ∆fitness/∆trait
Overview Simple models HIV case study Conclusions References
The model (2): evolutionary dynamics
Incorporate trait dynamicsStandard 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 fitness:rate proportional to ∆fitness/∆trait
Overview Simple models HIV case study Conclusions References
Evolutionary dynamics, cont.
Virulence
Fitn
ess
(w)
frac inf=0.1
Overview Simple models HIV case study Conclusions References
Evolutionary dynamics, cont.
Virulence
Fitn
ess
(w)
frac inf=0.1
frac inf=0.3
Overview Simple models HIV case study Conclusions References
Power-law tradeoff curves
Virulence
Tran
smis
sion
β(α) = cα1 γ
c = 2, γ = 2
c = 1, γ = 2
c = 1, γ = 3
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Transient virulence
Selection differs between theoutbreak phases(Frank, 1996; Day and Proulx,2004)
endemic phase selection forper-generation offspringproduction: maximize R0,βN/(α + µ)
epidemic phase selectionfor per-unit-time offspringproduction: maximize r ,βN − (α + µ)
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
●
●
Overview Simple models HIV case study Conclusions References
Transient virulence
Selection differs between theoutbreak phases(Frank, 1996; Day and Proulx,2004)
endemic phase selection forper-generation offspringproduction: maximize R0,βN/(α + µ)
epidemic phase selectionfor per-unit-time offspringproduction: maximize r ,βN − (α + µ)
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
●
●
Overview Simple models HIV case study Conclusions References
Transient virulence
Selection differs between theoutbreak phases(Frank, 1996; Day and Proulx,2004)
endemic phase selection forper-generation offspringproduction: maximize R0,βN/(α + µ)
epidemic phase selectionfor per-unit-time offspringproduction: maximize r ,βN − (α + µ)
Disease−induced mortality
Transmissionrate
µ 0 1 2 3 4 5
●
●
Overview Simple models HIV case study Conclusions References
Transient emerging virulence
When a parasite previously in eco-evolutionary equilibriumemerges in a new host population (at low density) it will showa transient peak in virulence as it spreads
How big is the peak? Does it matter?
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Model parameters
Parameterc Transmission
scaleγ Transmission
curvatureI (0) Initial
epidemic sizeVg Genetic variance
AlternativeR∗
0 Equilibrium R0
α∗ Equilibriumvirulence
1/N0 Inversepopulation size
Overview Simple models HIV case study Conclusions References
Example
Time
Fra
ctio
n in
fect
ive
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
Overview Simple models HIV case study Conclusions References
Response variables
Time
peaktime
peak height(α)
Overview Simple models HIV case study Conclusions References
Peak height
Equilibrium transmission (R0*)
Equ
ilibr
ium
viru
lenc
e (α
* )
1
10
100
1000
1.1 2 5 10 50
1.025
CV
g=
0.1
1.025
1.05
1.1 2 5 10 50
1.05
1.075
1.5
CV
g=
0.5
1.5
2.01
10
100
1000
1.5
2.01
10
100
1000
1.5
2.02.5
3.0
I(0) = 10−2 C
Vg
=1
1.1 2 5 10 50
1.5
2.0
2.53.0
3.5
I(0) = 10−3
1.52.0
2.53.0
3.5
4.0
I(0) = 10−4
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Overview Simple models HIV case study Conclusions References
Estimates for emerging pathogens
Order of magnitude estimates for some emerging high-virulencepathogens:
Pathogen R∗0 α∗ Reference
SARS 3 640 Anderson et al. (2004)West Nile 1.61–3.24 639 Wonham et al. (2004)
HIV 1.43 6.36 Velasco-Hernandez et al. (2002)myxomatosis 3 5 Dwyer et al. (1990)
Overview Simple models HIV case study Conclusions References
Emerging pathogens: where are we?
CVg = 0.5, I (0) = 10−3 (middle panel):
R0
Equ
ilibr
ium
viru
lenc
e (α
* )
1
10
100
1000
1.1 2 5 10 501.5
2.0
SARS
HIV
WNV
MYXO
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Overview Simple models HIV case study Conclusions References
Outline
1 OverviewThe evolution of host-pathogen theoryToy models
2 Transient virulence: simple modelsOverviewToy modelMyxomatosis model
3 Transient virulence: HIV case study
4 Conclusions
Overview Simple models HIV case study Conclusions References
Overview
Mosquito-borne viral disease of rabbitsBenign in South American rabbits,quickly fatal in European rabbitsWell characterized (Fenner et al., 1956; Dwyer et al., 1990)
Overview Simple models HIV case study Conclusions References
Myxomatosis tradeoff curve
Scaled virulence
Tota
ltra
nsm
ission
0 2 4 6 8 10 12
0.0
0.2
0.4
0.6
eq epi
Overview Simple models HIV case study Conclusions 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, 1999)
we can rarely estimate Vg reliably
Overview Simple models HIV case study Conclusions 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, 1999)
we can rarely estimate Vg reliably
Overview Simple models HIV case study Conclusions References
Myxomatosis grades over time (Fenner et al., 1956)
1950 1954 1956 1961 1965 1968 1972 1978
Proportion
0.0
0.2
0.4
0.6
0.8
1.0Virulence grade
I II III IV V
Overview Simple models HIV case study Conclusions References
Myxomatosis variance over time
Date
Gen
etic
varia
nce(
Vg)
0
10
20
30
40
1950 1960 1970
Vg= 10
Vg= 2.5
Vg= 40
Overview Simple models HIV case study Conclusions References
Myxomatosis virulence dynamics: power-law tradeoff
Date
Scal
edvi
rule
nce
0
5
10
15
20
25
1950 1960 1970
h=2.5
h=10
h=40
Overview Simple models HIV case study Conclusions References
Myxomatosis virulence dynamics: realistic tradeoff
Date
Scal
edvi
rule
nce
0
5
10
15
20
25
1950 1960 1970
h=40
h=10
h=2.5
Overview Simple models HIV case study Conclusions References
Myxo virulence: equilibrium start, power-law tradeoff
Date
Scal
edvi
rule
nce
0
5
10
15
1950 1955
h=40h=10h=2.5
Overview Simple models HIV case study Conclusions References
Myxo virulence: equilibrium start, realistic tradeoff
Date
Scal
edvi
rule
nce
0
5
10
15
1950 1955
h=40h=10h=2.5
Overview Simple models HIV case study Conclusions References
Simple models: conclusions
basic intuition about transient peak is correctrough estimates justify that eco-evo dynamics can matterdetails matter: shape of tradeoff curve, variance dynamics
Overview Simple models HIV case study Conclusions References
Phage dynamics (Berngruber et al., 2013)
Experimental evolution: phages started as endemic or epidemic
Overview Simple models HIV case study Conclusions References
HIV: background
Set-point viral load quantifies virus exploitation of host
Overview Simple models HIV case study Conclusions References
SPVL mediates a transmission/virulence tradeoff
transmission probability duration (years)
0.0
0.1
0.2
0.3
0
5
10
15
20
25
0.0 2.5 5.0 7.5 0.0 2.5 5.0 7.5log10 set-point viral load
Overview Simple models HIV case study Conclusions References
HIV tradeoff curve
0 10 20 30 40 50 60
0.0
0.1
0.2
0.3
0.4
0.5
Scaled virulence
Tran
smission
rate
eq epi
Overview Simple models HIV case study Conclusions References
SPVL dynamics
(Shirreff et al., 2011; Herbeck et al., 2014)
Overview Simple models HIV case study Conclusions References
Pair-formation dynamics (Champredon et al., 2013)
Overview Simple models HIV case study Conclusions References
Model structure
Six models:extra-pair contact [“epc”] ×instantaneous pair-formation [“instswitch”]“implicit” model: approx. (Shirreff et al., 2011)
random-mixing (no structure)Latin hypercube sampling over epidemic parameters(Champredon et al., 2013)
Overview Simple models HIV case study Conclusions References
SPVL trajectories
random pairform+epc pairform
instswitch+epc instswitch implicit
3
4
5
3
4
5
0 200 400 600 0 200 400 600 0 200 400 600
time (years)
popu
latio
n m
ean
set−
poin
t vira
l loa
d (lo
g 10)
Overview Simple models HIV case study Conclusions References
Univariate summaries
peak SPVL
peak time (years)
equilibriumSPVL
relativepeakSPVL
time
viru
slo
ad
Overview Simple models HIV case study Conclusions References
Results: univariate summaries
peak time peak SPVL
equilibrium SPVL relative peak
random
pairform+epc
pairform
instswitch+epc
instswitch
implicit
random
pairform+epc
pairform
instswitch+epc
instswitch
implicit
0 100 200 300 3.0 3.5 4.0 4.5 5.0
3 4 1.1 1.2 1.3 1.4 1.5value
Overview Simple models HIV case study Conclusions References
Bivariate summaries
peak
tim
epe
ak S
PV
Lre
lativ
e pe
ak
equilibrium SPVL peak time peak SPVL
0
100
200
300 ●
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Overview Simple models HIV case study Conclusions References
Conclusions
HIV: extra-pair contact washes out structural effectsmore complexity isn’t always better —need the right complexity(the modeling question)models purport to predict HIV evolution(Payne et al., 2014; Roberts et al., 2015; Herbeck et al., 2016):can we trust them?
Overview Simple models HIV case study Conclusions References
Crome (1997) on theory
Real research is best for toy problems, and toy research isoften all one can do on real problems . . . Never do toyresearch on toy problems, and recognize the extraordinarylimitations in attempting real research on real problems.. . .Recognize that someone might take your advice based onyour research. Try to estimate what the costs will be ifyou are wrong.
Overview Simple models HIV case study Conclusions References
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