Coevolution of
Economic and Ecological Systems
An Application to Agricultural Pesticide Resistance
Joëlle Noailly
CPB Netherlands Bureau for Economic Policy Analysis
EMAEE 2007
Manchester, 17-19 May
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Introduction
Objective & Motivation
Build a model of coevolution
economic activities ⇐⇒ biological evolution of species
ex: fishing technologies ⇐⇒ evolution of fish species (Policansky, 1993)
HERE: Application to pesticide resistance management
ex: pesticide use ⇐⇒ genetic resistance of pests (Munro, 1997)
Biological evolution: Modeling borrowed from biology describes how
changes in gene frequences relate to population dynamics
Economic evolution: More realistic description of agent’s behavior.
Economic activities as adapting response (not optimizing)
bounded rationality
population of heterogenous agents
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Model
3 types of interactions
We consider a population of agents
harvesting a crop subject to a pest.
3 evolutions:
1
the larger the pest population, the lower
economic revenues
2
the more pesticide use by economic agents,
the lower the fitness of susceptible genes
→ selects for resistant genes
3
the more resistant genes, the higher the
pest population
,→ In turn: pest population affects pesticide
strategies by agents.
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Coevolution of Economic and Ecological Systems
EMAEE ’07
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Model
Economic evolution
Evolution of economic activities
Set Up
Population of m agents harvesting a crop
2 types of pesticide strategies: INTENSIVE (xI ) or BIOLOGICAL (xB )
s.t. xI > xB and c (xI ) > c (xB )
Individual profits: πj (N ) = V (N , xj ) − c (xj )
J = I , B,
N = size of pest population s.t. V 0 (N ) < 0
Economic evolution [social learning]
Agents are boundedly rational: they imitate the strategy that yields
above-average profits
Evolution of economic strategies is given by a Replicator Dynamics
equation (π̄ = average profits, s=share of agents using intensive strategy).
ṡ = s(πI (N ) − π̄ (N ))
⇒ Economic evolution is affected by the size of the pest population
ṡ = f (s, N )
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Model
Genetic evolution
Selection of resistant genes
Modeling borrowed from population genetics in evolutionary biology
2 types of genes:
susceptible genes A are in fraction p
resistant genes a are in fraction 1 − p
Fitness of genes is WA and Wa respectively. Average fitness is W̄ (p)
The more pesticide use, the lower the fitness of susceptible genes:
WA (s) = WA − m(sxI + (1 − s)xB ) and also thus average fitness W̄ (p , s ).
Share of susceptible genes grows if fitness is above average:
ṗ = p
WA (s)
W̄ (p, s)
−1
⇒ Fitness of susceptible genes is affected by the share s of agents using the
intensive strategy
ṗ = g (p, s)
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
5 / 11
Model
Pest population dynamics
Dynamics of the pest population
Pest population dynamics grow with average fitness
Ṅ = N (W̄ (p) − 1)
The more pesticide use, the lower the average fitness
Evolution of pest population dynamics is now
Ṅ = N (W̄ (p, s) − 1)
⇒ Pest population dynamics is affected by the fraction of susceptible genes
and the level of pesticide use
Ṅ = h(N , p, s)
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Model
Coevolutionary system
The Coevolutionary System
Ultimately we want to solve the following system of differential equations:

ṡ = s(πI (N ) − π̄ (N )) = f (s, N )




WA (s)
ṗ = p
− 1 = g (p, s)
W̄ (p, s)




Ṅ = N (W̄ (p, s) − 1) = h(N , p, s)
(1)
(2)
(3)
Coevolution:
1
Economic evolution 7→ size of pest population
2
Fitness of resistant genes 7→ economic evolution
3
Pest population size 7→ genetic evolution + (indirectly) economic evolution
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Coevolution of Economic and Ecological Systems
EMAEE ’07
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Dynamics
Example of dynamics
Coevolution of N, p and s
1
Pesticides are efficient in killing
pests, so s grows and N falls.
2
As s gets large, resistance is created
and p falls. Eventually, pesticides are
inefficient and the pest population
recovers so N grows.
3
As N grows large due to resistance,
large pesticide use becomes too
costly (and inefficient), so s falls.
4
Only when pesticide use gets again
very low, can genes become
susceptible again.
with N0 = K , p0 = 0.8, and s0 = 0.25
⇒ Here the system converges to the
steady state: large pest population,
no resistance, all agents using xB
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Steady states
Steady states
Solving the coevolutionary system analytically gives 10 steady states.
We perform numerical simulations to track global stability properties: only
2 steady states appear to be globally stable:
1
no resistance, all agents use low levels of pesticide, N is large
2
full resistance, all agents use high levels of pesticide, N is large
Degenerate.
Rare. Only 7% of the runs.
Complex. Initial conditons irregularly scattered
Time-lags. Convergence occurs because all agents have switched to high levels of
pesticides before enough resistance is created. The system is then locked-in.
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Coevolution of Economic and Ecological Systems
EMAEE ’07
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Steady states
Speed, Time scale and Cycles
1
Speed. Depends on specific functional forms
Biological evolution characterized by rapid accelerations
Economic evolution modeled as gradual process
2
Time scale. Economic and ecological evolution take place on same
time-scale
Evidence from biology shows that pests can develop full resistance very
fast (ex: flies within a year).
Model can be easily extended to decouple both time-scales.
3
Cycles. Depending on initial conditions, different cycling trajectories can
occur before convergence
Certain trajectories may be economically more desirable than others.
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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Conclusions and Policy implications
Conclusions and Policy implications
1
New modeling framework: economy-environment coevolution
Bounded rationality in front of environmental change (characterized by
long-term uncertainty)
Heterogeneous agents
2
More work needed to understand complexity of coevolution models (role
of speed, time-lags, irreversibities).
3
Challenge for policymakers
Understand role of ecological dynamics and ecological thresholds
Dynamics similar to management practices based on rotation of pesticides,
but here rotation is the result of micro-interactions between agents
Role of policy is to frame the micro-interactions (by influencing central
parameters)
Joëlle Noailly (CPB)
Coevolution of Economic and Ecological Systems
EMAEE ’07
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