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Pathogen Virulence:
Evolutionary ecology
Outline: 29 Jan 15
• Functionally Dependent Life-History Traits:
Virulence Important Example
• Pathogen Traits Evolve via Strain Competition
• Spatially Structured Transmission
Dispersal Limitation Reduces Virulence
1
Virulence
Property of Host-Parasite Interaction
Parasite Generation Time Much Shorter
Virulence: Parasite’s “Strategy” for Exploiting Host
Virulence Evolution Affects Correlated
Demographic Traits
Functional Dependence = Pleiotropic Interaction
2
Increased Parasite
Virulence
Faster Consumption of Host Resources 
(1) Pathogen Reproductive Rate Increases
(2a) Host’s Mortality Rate Increases
or
(2b) Rate of Clearance by Immune System Increases
or
(2c) Host Reproduction Decreases
3
Virulence Trade-Off
Antagonistic Pleiotropy
Pathogen Increases Propagule Production
(Hence, Infection Transmission) Rate
Duration of Infectious Period Decreases
Evidence Reviewed
4
How Does Virulence Evolve?
Pathogen-Stain Competition
2 Phenotypes Differ in Virulence (Resident, Mutant)
Compete Between (and) Within Hosts
3 Modes of Strain Competition
5
Pathogen-Strain
Competition
1. Cross-Reactive Immunity
Competition Strictly Between-Host Scale
Flu strains
2. Coinfection: Two Strains Exploit Same Host Individual
Compete Both Within & Between-Host
3. Superinfection: More Virulent Strain Excludes Other
Compete Both Within & Between-Host
6
Strain Competition
Important
Ecological Generality
Cross-Reactive Immunity
Example of
Pre-emptive Competition
Two Species (Strains),
Same Niche
(Allstadt et al. 2009)
7
Strain Competition
Important
Ecological Generality
Coinfection: Example of
Scramble Competition =
Exploitative Competition
Two Species Interact Indirectly
Through Exploitation of
Same Limiting Resource
From
quizlet.com
8
Strain Competition
Important
Ecological Generality
Superinfection: Example of
Interference Competition
Two Species Interact Directly
Aggressive Exploitation of
Same Limiting Resource
quizlet.com
9
Strain Competition:
Adaptive Dynamics
Host-Pathogen Dynamics
Exert Selection Pressure on Competing Strains
Mutant-Resident Competition
Competitive Exclusion; Alter Parameters of Dynamics
Evolutionarily Stable Strategy (ESS) Resists Invasion
Adaptive Dynamics: Interplay of Ecology, Evolution
10
Strain Competition:
Adaptive Dynamics
“Solve” Strain Competition for a Preemptive Case
General: ESS Virulence Graphically
Virulence Evolution in a Second Preemptive Case
Pathogen with Free-Living Stage
e.g., Bacteriophage
Superinfection, Vary Pathogen Dispersal Distance
Impact on ESS Virulence
11
Cross-reactive Immunity
One Strain per Infected Host Individual
Strain Competition: Between-Host Scale Only
Ecology: Preemptive Competition
12
Host Preemption
Assume Homogeneous Mixing Host Population
“Optimally Virulent” Strain, Max R0
Equivalently
Minimizes Equilibrium Density Susceptible Hosts
No Strain Coexistence (Pure ESS)
Recall: Same Niche
13
Host Preemption
Homogeneous Mixing, No Recovery
Transmission-Infectious Period Trade-off
() Transmission Efficiency, Direct Contact
() Virulence, Extra Infected-Host Mortality
 Host Exploitation Strategy: d/d > 0
14
Natural Selection:
Optimize 
Invasion Dynamics (Conceptual Core)
Can Rare Mutant  Invade Resident * at
ecological (dynamic) equilibrium?
This case: ESS does Max R0( )
: Background Host Mortality
S: Susceptible Density
15
Natural Selection:
Optimize 
SI Transmission
Plus Host Birth, Death
Resident Pathogen’s Dynamics Sets Resource
Availability (Susceptible Density) for Mutant
Strain of Pathogen
Can Mutant find enough hosts to grow when rare?
16
Natural Selection:
Optimize 
b Per-capitum Birth
 Transmission Rate (Mass Action)
 Non-Disease Mortality (All)
( + ) Infective Mortality
: Virulence > 0
No Recovery from Infection
17
Dynamics of Epidemic
𝑑𝑆𝑡
𝑑𝑡
𝑑𝐼𝑡
= 𝑏 𝑆𝑡 + 𝐼𝑡 − 𝛽 𝑆𝑡 𝐼𝑡 − 𝜇 𝑆𝑡
=
𝛽
𝑆
𝐼
−
𝜇
+
𝛼
𝐼
𝑡
𝑡
𝑡
𝑑𝑡
Birth, Infection Transmission, Death
18
Analysis
𝑅0 : New Cases/Case When Invading
Pathogen Rare
Epidemiology: Invade All-Susceptible Population
Evolutionary Ecology: Invade Host-Resident Strain
at Endemic Equilibrium
19
Natural Selection:
Optimize 
Transmission Rate: Infections/Time = 𝛽 𝑆𝑟𝑒𝑠
Transmission Duration: Time = 𝜇 + 𝛼 −1
Transmission Ends at Host Death
𝑅0 =
𝛽 𝑆𝑟𝑒𝑠
𝜇+ 𝛼
20
𝑅0 (𝑀𝑢𝑡𝑎𝑛𝑡, 𝑅𝑒𝑠𝑖𝑑𝑒𝑛𝑡) =
Mutant Invades: 𝑆𝑟𝑒𝑠 >
𝛽𝑚 𝑆𝑟𝑒𝑠
𝜇+ 𝛼𝑚
𝜇 + 𝛼𝑚
𝛽𝑚
Recall: 𝜕𝛼 𝜕𝛽 > 0 among strains
Note:
𝜕𝑅0
𝜕𝜇
< 0; Background Mortality & Virulence
21
Natural Selection:
Optimize 
  
R0   
S
    
Endemic Equilibriu m, R  *   1
Rare Invader  ;
Advances if R0  ,  *   1
22
Natural Selection:
Optimize 
  
R0  ,   
S  * 
    
*
 * Sets Susceptible Density for Invader
23
Natural Selection:
Optimize 
von Baalen & Sabelis (1995, Am Nat)
24
Natural Selection:
Optimize 
1. ESS Virulence Maximizes R0 (for any Susceptible
Density)
2. ESS Virulence Minimizes Susceptible Density
Too Few Susceptible Hosts for Mutant Invasion
3. Greater Background Mortality   Greater Virulence
25
Natural Selection:
Optimize 
4. ESS May Exhibit Intermediate Virulence
Under Host Preemption; Natural Diversity
5. No Strain-Coexistence Possible
Under Well-mixed, Preemptive Competition
26
Preemptive Host Competition
Pathogen with Free-Living Stage
Life History:
Alternates Intra-Host Environment, External Environment
Bacteria/Viruses, Including Bacteriophage
“Curse of the pharaoh”
Persistent free-living stage costly; Requires conversion of large
amount of host resources; Pathogens with persistent free-living
stage likely virulent
27
Host-Pathogen Dynamics
S(t) Susceptible Density
I(t) Infectious Density
P(t) Free-living Stage
(Virions, Spores)
r Host Reproduction
c Host Self-Regulation
 Transmission (Adsorption)
 Mortality; Includes Virulence
𝜃= 𝜇+ 𝜈
 FLP Shed Rate
 FLP Burst Size
 FLP Decay Rate: Focus
28
Host-Pathogen Dynamics
Equilibria
Endemic Equilibrium
(Extinction Unstable)
Disease Free: (𝑟 𝑐 , 0, 0)
29
Local Stability: FLP Persistence = 1
𝜉
30
ESS Virulence: Pathogen Strain Competition
Preemptive Competition: ESS Minimizes S*
Positive Equilibrium Density of Susceptibles
Traits: Functionally Dependent
Altering Virulence: Antagonistic Pleiotropy
31
ESS Virulence: Pathogen Strain Competition
Curse of the Pharaoh: Increased persistence of FLP
(reduced ) demands more host resources,
and virulence () increases.
Equivalently: 𝜕𝜈 𝜕𝜉 < 0
Functional Constraint: 𝜈 𝜉 = 𝑏𝜈 𝜉 − 𝜎 ; 𝑏𝜈 , 𝜎 > 0
32
Functional Constraint: Virulence(Decay Rate)
33
Minimize S*
Suppose Shed Rate = 0; Burst Size > 0
Lytic Virus, Bacteriophage
Then 𝑆 ∗ =
𝜉
𝛼𝛽
= Decay/(Adsorption x Burst size)
ESS Reduces  and Increases Virulence
Virulent and Persistent
34
Minimize S*
Suppose Shed Rate > 0; Burst Size = 0
Animal Virus; Bacterial, Fungal Infection
Then 𝑆 ∗ = 𝜉 𝜇 + 𝜈 𝜉
𝛼𝛾
For 𝜎 < 1: Strain Competition Reduces Decay Rate
Virulent and Persistent
For 𝜎 > 1: Competition Favors Intermediate Virulence
𝜈 ^ = 𝜇 𝑏𝜈 𝜎 − 1 −1 ; Curse Broken
35
Shed Rate > 0 and Burst Size > 0
36
Preemptive Host Competition
Strain Minimizing Equilibrium Density of
Susceptibles Should be ESS
No Coexistence of Different Levels of Virulence
(Not True for Coinfection and Superinfection)
Curse of the Pharaoh Oversimplifies
Strain Competition
Caraco annd Wang (2008) J Theor Biol 250:569-579
37
Homogeneous Mixing Host Population
Assumed in Dynamics
Full Mixing: Hosts Highly Mobile over
Timescale of Expected Lifespan
Might Preclude Terrestrial Plants, Territorial
Animals, etc.: “Viscous Populations”
38
Contact Structure, Van Baalen (2000)
39
Pathogen: Dispersal Limitation
Contact Structures: Constrain Opportunities for
Pathogen to Generate New Infections
Ecology: Dispersal Limitation, Neighborhood Interactions
Ecological Implications:
Epidemic Invasion, Endemic Infection Levels
Evolutionary Implications:
(Including) Virulence
40
Pathogen: Dispersal Limitation
Contact Structure: (L x L) Lattice
Each Site: One of 4 Elementary States
Local Neighborhood: All Ecological Interactions
•
•
Opportunities for Host Reproduction (Open Sites)
Sources of Infection
41
SPATIAL SUPERINFECTION
42
SPATIAL SUPERINFECTION
Virulent Can Displace “Avirulent” Strain
Interference Competition
Discrete-Time Dynamics
Transmission (Virulence); No Recovery
Key: Superinfection (Virulence Difference)
Within & Between-Host Competition
Neighborhood Size: 8, 48
43
Develop Concepts
1. Mean-Field Analysis: Homogeneous Mixing
2. Pair Approximation: Local Correlation
3. Simulate Full Stochastic Spatial Model:
Large-Scale Correlated Fluctuations,
Strong Clustering Possible
44
Develop Theory:
Deduce Predictions
Pairwise Invasion Analyses: Adaptive Dynamics
Resident Strain at Ecological Equilibrium
Can Invading Strain (Mutant) Advance?
Assumed Time Scales
Convergence Stability; Evolutionary Stability
45
SPATIAL
SUPERINFECTION
Dynamics: Local Transition Probabilities
Stochastic Spatial Model
How do local interactions produce ensemble
effects (population, community scales)?
Model/Theory: Caraco et al. (2006)
Theoretical Population Biology 69:367-384
46
Mean-Field Results
Pairwise Invasion
Homogeneous Mixing
Evolution to
Criticality
Coexistence:
Niche Difference
47
Mean-Field Results
Pairwise Invasion
Homogeneous Mixing
Coexistence:
Niche Difference
CompetitionColonization
Trade-Off
48
Spatial Model Results
Increased Virulence
Decreased Infection
Increased Clustering
Pair Correlation Model OK
49
Adaptive dynamics
spatial process
Pair Approximation
Convergent Stable
Evolutionarily Stable
(Local ESS)
Virulence Constrained
By Contact Structure
50
Adaptive dynamics
spatial process
Simulation
Max Virulence
Lower
Local ESS Reduced
51
Adaptive dynamics
spatial process
Weaker Competitive
Asymmetry Via
Superinfection
Reduce ESS
Reduce Coexistence
52
predict
1. Spatial Structure Constrains Maximal Virulence
Capable of Dynamic Persistence, Through
Extinction of Highly Virulent Strains
2. Spatial Structure Reduces Evolutionarily Stable
Level of Virulence
3. Larger Neighborhood Relaxes Constraint,
Dynamic Penalty of Clustering Attenuated
53
predict
4. Spatial Structure Promotes Coexistence:
Extended Transmission/Low Virulence,
Poor Interference Competitor/Good Colonizer
and
Attenuated Transmission/High Virulence,
Advantage of Superinfection/Poor Colonizer
5. Coexistence Increases with Neighborhood Size
6. Comp. Asymmetry Increases Coexistence
54
Contemporary Questions
Virulence in Pathogens with Both Contact and
Environmental Transmission
Avian Flu: Contacts; Virus Persists In Drinking Water
Hyperparasites & Hypovirulence
Vertical Transmission
Sterilizing vs Killing Pathogens
55
Contemporary Questions
Vector-Borne More Virulent Than Direct Contact (?)
FLP: “Curse of the Pharaoh”
Conditions for More Virulence
Infective Dose: Remarkable Variation
Ecological Consequences
Strain Competition?
56
Contemporary Questions
Within-Host Dynamics
Parasite, Specific Immune Cell Densities
Affects Between-Host Transmission
Population Dynamics
Host-Pathogen Coevolution
Transmission Resistance, Tolerance
Virulence, Optimal Immune Response
57
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