Dynamically adapting parasite virulence to combat coevolutionary disengagement

John Cartlidge: ALife XI, Winchester, UK 1

Research AssociateComputing, Engineering & Physical SciencesUniversity of Central Lancashire, UK

Email: [email protected]

Dr John Cartlidge

5th August 2008

Dynamically adapting parasite virulence to combat coevolutionary disengagement

John Cartlidge: ALife XI, Winchester, UK 25th August 2008

Synopsis

Disengagement in coevolutionary systems Review Reduced Virulence (RV) Analysis of RV in Counting Ones domain Present Dynamic Virulence (DV), a novel

method for adapting Virulence online Summary/Conclusions


Disengagement

Competitive Coevolutionary Systems Relative fitness assessment through self-play Fitness varies as opponents vary in ability

Relativity leads to Disengagement Occurs when one population gets the “upper hand” Can’t discriminate individuals no selection pressure

Occurs when competitors are badly matched Suits of armour and nuclear weapons There must be no outright winner


Reduced Virulence (RV) Cartlidge, J. & Bullock, S. (2002, 2004) Reward competitors that sometimes lose

0

0.25

0.5

0.75

1

0 0.25 0.5 0.75 1

Score, x

Fit

nes

s, f

(x,v

)

10.750.5

RV Fitness Transform f(x,v) = 2x ∕ v – x2∕ v2

virulence: 0.5 ≤ v ≤ 1.0relative score: x


RV: An illustrative Example

Selection only. No mutation. Linear fitness ranking Population B has an innovation (20) not found in A Trade-off between engagement and innovation loss

V = 1 (standard) V = 0.75 V = 0.5

Selection drives pop B to 20 causing disengagement

Pop B drops genotype 20 and remains engaged at 19

Lots of innovation loss as populations move to 12


Symmetry

Mutation introduces genetic novelty Symmetric system with unbiased mutation profile

Populations have equal chance of +/– mutation Neither population has an advantage


Asymmetry Here population B has a favourable mutation bias

A finds it harder to discover +ve/beneficial genetic innovations

Disengagement is exacerbated by asymmetry In genetic representations, genotype-phenotype mappings, genetic

operators, interaction rules, location in genotype space, etc.


Couting Ones

Watson & Pollack, GECCO 2001 Two populations of binary strings Goal: evolve as many 1s as possible Asymmetrical bias controlled by varying

mutation bias of one population (parasites) When is it best to reduce virulence?


Virulence ‘Sweet-Spot’

Low bias requires high virulence for both populations As bias increases, want progressively lower parasite V

Par

asit

e vi

rule

nce

Host virulence

Parasite Bias / Asymmetry0.5 0.6 0.7 0.8 0.9 1.0

Maximums

Engagement

‘Sweet-Spot’


Choosing RV Value

Problem: How do we know a priori what the asymmetry

is likely to be? Is asymmetry is likely to remain fixed?

Solution:Adapt virulence dynamically during runtime


Dynamic Virulence (DV)

Reinforcement learning approach: Value(t+1) Value(t) + LearningRate [Target(t) – Value(t)]

Each generation, t, update virulence, Vt ∆Vt = ρ(1 − Xt ∕φ)

(1) Xt: Mean relative score of population at time t φ: Target mean relative score of population ρ: Acceleration (rate of change of virulence)

Μt = μΜt-1 + (1−μ)∆Vt (2) μ: Momentum, Μ0 = V0

if μ = 0, then t, Μt = ∆Vt no momentum if μ = 1, then t, Μt = V0 fixed virulence

Vt+1 = Vt+Μt (3) 0 ≤ φ, ρ, μ ≤ 1


Evolving φ, ρ, μ

Acceleration Rate, ρ

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Momentum, μ

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Target Fitness, φ

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30 runs. Mean value of parameter in population each generation. Bias fixed for each evaluation

Momentum, μ

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15 runs. Mean value of parameter in population each generation. Bias varying during each evaluation

Acceleration Rate, ρ

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DV Performance Performance of DV in the Counting Ones domain DV Parameters: φ = 0.56; ρ = 0.0125; μ = 0.3

180/180 successful runs. 31/135,000 disengaged generations Compare with maximum virulence

79/180 successful runs. 68,900 disengaged generations

Successful runs using fixed virulence (total 180 runs)

0.5 0.6 0.7 0.8 0.9 1.0Parasite Bias / Asymmetry

0.5 0.6 0.7 0.8 0.9 1.0

Parasite Bias / Asymmetry

Fixed VirulenceFixed Virulence Dynamic Virulence


DV in Action


Lessons for epidemiology?

Can we use DV for modelling virulence in natural systems? Can we translate ideas of RV to the natural world for

control of infectious diseases? Rather than attack parasites and encourage an arms-race, creating

‘super-bugs’, can we take a reduced virulence approach? E.g.: ‘Scientists create GM mosquitoes to fight malaria and save

thousands of lives’ (Guardian 2005) ‘Plan to breed and sterilize millions of male insects’ Project ‘almost ready for testing in wild’


Summary / Conclusions

Disengagement is problematic and is exacerbated by asymmetry

Reducing virulence helps to promote engagement As asymmetry increases, virulence should fall Its hard to know a priori what virulence level to set DV is able to adapt virulence during evolution to find the

best value DV has been shown to vastly outperform fixed virulence

(and standard virulence) in the Counting Ones domain


Further Reading

Cartlidge & Bullock (2002) CEC, p.1420, IEEE Press Cartlidge & Bullock (2003) ECAL, p.299, Springer Verlag Cartlidge & Bullock (2004) Evolutionary Comp., 12, p.193 Cartlidge (2004) PhD Thesis, University of Leeds

Dr John Cartlidge, Research Associate University of Central Lancashire

[email protected]

Documents

Dynamically adapting parasite virulence to combat coevolutionary disengagement