We employ genetic programming to model the release kinetics of a pheromone dispenser used to combat pests in an ecofriendly manner, by means of mating disruption

1. Modeling pheromone
dispensers using genetic
programming
Eva Alfaro-Cid, Anna Esparcia-Alcázar,
Pilar Moya, Beatriu Femenia-Ferrer,
Ken Sharman, J.J. Merelo

2. Contents
• Objetive
• Introduction: mating disruption
• Problem description
• Strongly typed genetic programming
• Modeling results
• Conclusions and future work

3. Objetives
• Modeling the pheromone release kinetics of an
experimental dispenser developed in the Centro
de Ecología Química Agrícola (CEQA) of the
Universidad Politécnica de Valencia.
• To validate the hypothesis (which is based on
experimental results) that the performance of the
CEQA dispenser is independent of the
atmospheric conditions, as opposed to the most
widely used commercial dispenser, Isomate
CPlus.)

4. Mating disruption technique
• Mating disruption by sexual confusion is an
agricultural technique that intends to substitute
the use of insecticides for pest control.
• Sexual confusion is achieved by the diffusion of
large amounts of sexual pheromone, so that the
males are confused and mating is disrupted.
How? → using pheromone dispensers
•)

5. Pheromone dispensers
•The Centro de Ecología Química Agrícola
(CEQA) of the Universidad Politécnica de
Valencia has developed biodegradable
dispensers which work effectively during
the whole flight period of the pest.

6. A few figures
• 1 kg of pheromone costs 1000 €
• 1 dispenser takes 200 mg of pheromone
→ i.e. 1 dispenser costs 20 cents (+ manufacturing)
• In 1 Ha there must be 500 or 1000
dispensers (depending on the pest)
– i.e cost is 100 or 200 € per Ha (+ handwork)
On the other hand,
• Spraying with a classical pesticide costs
20-30 €/Ha

7. Problem description
• Let the residual r be the percentage of product that has
not been released into the atmosphere
• For a given dispenser, find a function r (∙), so that
r = r ( t, T, H )
where:
t = time
T = temperature
H = humidity
r ≈ r (t)
Our hypothesis is that for the CEQA dispenser

8. Available data
Residual available data
120
100
Residual (%)
CPlus 2005
80
CPlus 2006
60
CEQA 2005
40
CEQA 2006
20
0
1 16 31 46 61 76 91 106 121 136 151 166
Day
Year 2005 15 data of dispenser CEQA
13 data of dispenser Isomate CPlus
Year 2006 7 data of both

9. Genetic programming
Algorithm Strongly typed GP, generational with elitism (0.1 %).
Inicialization Ramped half and half
Selection Tournament selection for all genetic operators
Genetic operators Replacement, crossover and mutation
Tree internal nodes are selected with a probability of 0.9,
terminals are selected with a probability of 0.1 and the root
cannot be selected as crossover or mutation point. The
resulting trees are accepted in the population only if their
length is smaller than 18.
Termination criterion 51 generations (including the initial generation)
Parameters Population size, popSize = 2000
Tournament size, tSize = 7
Mutation rate, pM = 0.1
Crossover rate, pC = 0.8
Replacement rate, pR = 0.1
Number of runs, n = 10

10. Strongly typed genetic
programming
4 types of variables were considered :
• temperature
• humidity
• time
• real value
Cost function: Mean Squared Error (MSE)
(rcalculated - rmeasured)2
MSE = 1/n * n

11. Genetic programming:
Functions and terminals
Available atmospheric data (daily):
maximum temperature and mean temperature,
maximum humidity and mean humidity.
Data obtained through the Xarxa Agrometeorològica de Catalunya.
Temperature and humidity values until 9 days prior to the residual
measurement were considered, i.e.
T0 is the temperature the day the residual was measured
Tn is the temperature n days before, n = 1..9
Terminal sets:
• { mean temperature, mean humidity, time, }
• { maximum temperature, maximum humidity, time, }
• { time, }
Function set: { +, -, *, /, exp, log}

12. Results - CEQA
Year 2006
Year 2005
Mean T 120 120
100 100
Residual (%)
Residual (%)
and H 80
80
60
60
values 40
40
20
20
0
0
1 21 41 61 81 101 121 141 161
1 21 41 61 81 101 121 141 161
Day
Day
Year 2006
Year 2005
120 120
Maximum 100 100
Residual (%)
Residual (%)
80 80
T and H 60 60
values 40 40
20 20
0 0
1 21 41 61 81 101 121 141 161 1 21 41 61 81 101 121 141 161
Day Day
Year 2006
Year 2005
120 120
100 100
Residual (%)
Residual (%)
Only time 80 80
60 60
40 40
20 20
0 0
1 21 41 61 81 101 121 141 161 1 21 41 61 81 101 121 141 161
Day Day

13. Results - CEQA

14. Results - CEQA
Time as the only variable:
2
t t t
r ( t ) 96 . 03 0 . 23 t log
79 . 47 t 70 . 77 t log( t ) 679 . 29 4t

15. Results – Isomate CPlus
Year 2006
Year 2005
Mean T 120 120
100 100
and H
Residual (%)
Residual (%)
80
80
60
60
values 40
40
20
20
0
0
1 21 41 61 81 101
1 21 41 61 81 101 121
Day
Day
Year 2006
Year 2005
120 120
Maximum 100 100
Residual (%)
Residual (%)
80
80
T and H 60
60
40
40
values 20
20
0
0
1 21 41 61 81 101
1 21 41 61 81 101 121
Day
Day
Year 2006
Year 2005
120 120
100 100
Only time
Residual (%)
Residual (%)
80 80
60 60
40 40
20 20
0 0
1 21 41 61 81 101 121 1 21 41 61 81 101 121
Day Day

16. Results – Isomate CPlus

17. Results – Isomate CPlus
Time as the only variable:
74 . 32 81 . 36 1 . 29 t N
r (t ) 76 . 46 0 . 23 t log t 93 . 95 log t
t log 81 . 46 1 . 29 t D
5642 . 08
N
log log t 0 . 77 t 15 . 67 0 . 02 t 1 . 47 log t 71 . 6 74 . 93 log log t t 83 . 38
71 . 6 79 . 8 log 2 log t
D
56 . 67
log log t 74 . 93 74 . 93 log t t 83 . 38
t

18. Results – Isomate CPlus
Maximum temperature, humidity and time as variables:
271 . 53
4
6 . 64 10 exp
t t
r (t ) 92 . 29 log
1 . 42 T 9 T 7 t log T 0 T1 t T1 L
271 . 53 179 . 87
2
exp 1 . 32 10 exp
t t
L log log
2
T0 T1 t 271 . 53 T1 t
2
T 7 t log T 2 t log 83 . 3 t log log exp
T1 t H 9 exp 271 . 53 t 43 . 93 T 7

19. Conclusions
• Genetic programming has proven to be capable of finding functions
that fit well the performance of both dispensers.
• For the CEQA dispenser the fitting of the functions is better when
the only variable under consideration is time. Although this is not a
conclusive proof of the independence of the pheromone residual
from the atmospheric conditions, it can be considered as an
evidence in that sense.
• The statistical test performed on the results obtained with the data of
CPlus dispenser reveals that there is a significant difference
between the results obtained using maximum values of temperature
and humidity and the rest. This confirms prior experimental evidence
that the atmospheric conditions have a big influence in the
performance of these dispensers.

20. Future work
Long term
• Modeling the release of pheromone in the environment.
– Great economic interest → it would allow the optimisation of the
placement of dispensers in the plot, hence minimising the
number of dispensers needed to guarantee an efficient pest
control.
Short term
• Inclusion of the gradient of temperature as a terminal for the GP
algorithm, as it may be the case that the dispensers are more
sensitive to sharp changes of temperature than to the temperature
itself.

21. Thanks!
aesparcia@iti.upv.es