Application of ecological
models in entomology:
a view from Brazil
Wesley A. C. Godoy
University of São Paulo
"Luiz de Queiroz" College of Agriculture
Piracicaba, São Paulo, Brazil - [email protected]
Working with ecological models
in different places and areas
Medical and forensic entomology
Agricultural and forest entomology
University of São Paulo - ESALQ
“Luiz de Queiroz” College of Agriculture
Universidade Estadual Paulista
Overview
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly
species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
•
•
•
Ecological basis for modelling pests and natural enemies
Concept of economic injury level
A preliminary model combining host-parasitoid theory and IPM
Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass production
Population dynamics: a scenario involving
exotic and native blowfly species
Importance of blowflies
Larval therapy
Vector of diseases
Myiasis
Forensic
entomology
and finally, as an experimental model
to study population dynamics in laboratory
Life cycle of blowflies
Carrion
Modelling biology and ecology of flies
N t 1 
1
2
F ( Nt ) S ( Nt ) Nt
Fecundity
Survival
Prout & McChesney, 1985
Density dependence
N t 1 
1
2
F ( Nt ) S ( Nt ) Nt
F e
*
F*
 f Nt
S e
*
 s Nt
S*
f
s
N(t)
N(t)
Different values for fecundity and survival
produce different dynamics
2000
900
1800
800
1600
700
Population size
Population size
1400
1200
1000
800
600
500
Native blowfly species
400
600
300
400
Exotic blowfly species
200
0
0
10
20
30
Generations
40
200
50
60
100
0
50
100
150
Generations
200
250
300
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
•
•
•
Ecological basis for modelling pests and natural enemies
Concept of economic injury level
A preliminary model combining host-parasitoid theory and IPM
Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass production
Forensic applications
How can ecological models provide
useful information for forensic sciences?
Showing what factors govern
diversity and abundance
of insects
Three important ecological factors:
Diversity and abundance
of blowflies
Diversity and abundance
influence strength
of interactions
Interspecific and
trophic interactions
demographic parameters
depend on resources
available and
influence dynamic
behaviours
Psychoactive drugs or
medicines
and population dynamics
of blowflies
Influence of drugs on
demographic parameters
Comparing demographic parameters
influenced by drugs with the
Prout & McChesney model
1
N t 1  F ( N t ) S ( N t ) N t
2
F e
*
 f Nt
S e
*
 s Nt
1. Amphetamine (stimulant drug)
2. Phenobarbital (anticonvulsant, sedative
and hypnotic)
3. Methanol (organic solvent)
4. Oxycodone (analgesic)
Table 1. Exponential regression analysis of fecundity and survival for the control,
phenobarbital, methanol and amphetamine treatments
Control
Phenobarbital
Methanol
Amphetamine
F
S
F
S
F
S
F
S
Y intercepts
26.74
0.81
22.87
0.90
27.12
0.54
27.45
0.60
RC
0.0009
0.00163
0.0006
0.002
0.0009
0.001
0.0009
0.001
r2
0.66
0.80
0.54
0.90
0.65
0.90
0.61
0.89
ANOVA
445
40.60
264
94.64
414
80.59
345
81.53
P < 0.001; F = fecundity; S = survival; RC= Regression coefficient
Fecundity and survival influenced or not by drugs in C. albiceps
Control
Phenobarbital
Fecundity
Survival
Fecundity and survival influenced or not by drugs in C. albiceps
Methanol
Amphetamine
Fecundity
Survival
Table 1. Exponential regression analysis of fecundity and survival for the control,
phenobarbital, methanol and amphetamine treatments
Control
Without prey
Phenobarbital
Methanol
Amphetamine
F
S
F
S
F
S
F
S
Y intercepts
26.74
0.81
22.87
0.90
27.12
0.54
27.45
0.60
RC
0.0009
0.00163
0.0006
0.002
0.0009
0.001
0.0009
0.001
r2
0.66
0.80
0.54
0.90
0.65
0.90
0.61
0.89
ANOVA
445
40.60
264
94.64
414
80.59
345
81.53
P < 0.001; F = fecundity; S = survival; RC= Regression coefficient
Table 2. Exponential regression analysis of fecundity and survival in oxycodone,
phenobarbital, methanol and amphetamine treatments with the addition of C.
megacephala prey
Oxycodone
With prey
Methanol
Amphetamine
F
S
F
S
F
S
Y intercepts
29.15
0.87
23.34
0.57
28.14
0.77
RC
0.0008
0.002
0.0006
0.001
0.0009
0.001
r2
0.54
0.83
0.50
0.86
0.59
0.89
ANOVA
228
48.98
216
63.31
272
70.97
P < 0.001; F = fecundity; S = survival; RC= Regression coefficient
Fecundity and survival influenced or not by prey consumption
Without prey
With prey
Fecundity
Survival
Table 3. Percentage of predation of C. albiceps on C. megacephala without choice of
prey
Predation rate on C. megacephala
Time
Control
Phenobarbital
Oxycodone
Amphetamine
Methanol
30
27.5
52.5
12.5
12.5
47.15
60
17.5
8
20
7.5
12.5
90
7.5
8
32.5
12.5
5
120
7.5
2.5
7.5
17.5
15
150
2.5
7.5
12.5
2.5
5
180
5
2.5
5
17.5
0
Total
67.5
81
90
70
85
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
•
•
•
Ecological basis for modelling pests and natural enemies
Concept of economic injury level
A preliminary model combining host-parasitoid theory and IPM
Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass production
Intraguild predation
Predator
Prey
Intraguild predation
equations
Satiation intensity
Attack intensity
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
•
•
•
Ecological basis for modelling pests and natural enemies
Concept of economic injury level
A preliminary model combining host-parasitoid theory and IPM
Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass production
Tri trophic interactions investigated
IGP: Intraguild predation
Interactions investigated with experiments
IG-prey
survival
in presence
of IG
predator
IG-prey
survival
in absence
of IG
predator
IG-predator
survival
in absence
of IG
prey
IG-predator
survival
in presence
of IG
prey
IG - Intraguild
IG prey alone
IG prey and
parasitoid
IG predator,
prey and
parasitoid
IG predator
alone
IG predator and
parasitoid
IG predator and prey
Nomenclature for the ecological model
ne = time from oviposition to hatching = 1 day
nl1 = development time for 1st and 2nd larval instars
nl2 = development time for o 3rd Instar
nl = nl1 + nl2 = 4 days
np = pupal time = 4 days
na = adult time = 7 days
Species:
Chrysomya megacephala (PREY): 1
Chrysomya albiceps (PREDATOR): 2
Nasonia vitripennis (PARASITOID): W
Functions for the model
IGP by L2n on L1n
Cannibalism on L2n,
IGP (), cannibalism ()
and parasitism ()
f1 and f2 with values between 1 and 0.5
Parasitism
Number of pupae parasitized
=
Maximum number of pupae parasitized for 1 day
Model description
Age of fly
E, L,P ou A
Species
Egg
Larva
Pupa
Natural
mortality
IGP and
cannibalism
Following day
3rd Instar: beginning of
interactons between flies
Adult
Beginning of simulation
1st day
Pupae
Parasitism
Natural
mortality
Natural mortality
Interactions with parasitoids
Surviving pupae
reaches adult
phase
Oviposition by
flies
New life cycle
Parasitoid equation
Natural mortality
k = cycle length
h = sex ratio (eggs)
q = eggs per day
Days since the beginning of the experiment
Density of blowfly species long to generation
Prey + 1 parasitoid
Prey + 10 parasitoids
Initial population
Size = 300
Predator + 1 parasitoid
Predator + 10 parasitoids
Initial population
Size = 100
Gray bars = larvae and pupae of blowflies, White bars = dead individuals, Black lines = parasitoids
Only IG prey and predator
high IGP and low cannibalism
low IGP and low cannibalism
Prey: bars
Predator: black line
high IGP and high
cannibalism
low IGP and high cannibalism
IG prey, predator and parasitoids
Prey
Predator
high IGP and low cannibalism
low IGP and low cannibalism
high IGP and high cannibalism
parasitoid
low IGP and high cannibalism
parasitoid
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
Ecological basis for modelling pests and natural enemies
• Concept of economic injury level
• A preliminary model combining host-parasitoid theory and IPM
• Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass production
Starting from a host parasitoid model
with functional response type II
densityindependent
survival of
parasitoid
propagules at
generation
t
1200
1000
800
600
400
200
0
1
11
21
31
41
If N(t+1) < threshold (L)
If N(t+1)  threshold (L)
q1 = reduction of host population by other methods
q2 = parasitoid release rate
= number of released parasitoids
L = economic threshold
Tang & Cheke, 2008
Introducing integrated pest management (IPM)
strategies into the model
1200
1000
800
+
600
400
200
0
1
11
21
31
41
Population dynamics without IPM strategies
30
25
20
N,P
H
15
P
10
5
0
1
11
21
31
41
51
61
71
81
91
Population dynamics taking into account IPM strategies
25
20
L = 15
15
H
N,P
P
10
5
0
1
6
11
16
21
Tempo
26
31
36
Now including migration by using coupled lattice model
Diffusion type I
Host Density independent
Diffusion type II
Host Density dependent
H < Economic threshold: white; H  Economy threshold: gray; H  Injury level: black
with
IPM
without
IPM and
migration
with
IPM and
migration
Part I: blowflies as a study model to investigate intra and interspecific
interactions
•
•
•
•
Population dynamics: a scenario involving exotic and native blowfly species
Population dynamics applied to forensic entomology
Intraguild predation
Tri-trophic interactions
Part II: combining population theory with biological control and
integrated pest management (IPM)
•
•
Ecological basis for modelling pests and natural enemies
• Concept of economic injury level
• A preliminary model combining host-parasitoid theory and IPM
• Inserting spatial dimension into the system
Experiments focused on potential natural enemies for mass
production
Relationships between
pest and potential predators
Experiments to compare the best diet
for natural enemies
Experiments focused on potential natural enemies
for mass production
M=
Population dynamics of Podisus nigrispinus structured in life
stages maintained in artificial diet
N
Life cycle stages
Population dynamics of P. nigrispinus structured in life
stages maintained in Drosophila melanogaster
N
Life cycle stages
Population dynamics of P. nigrispinus structured in life
stages maintained in Chrysomya putoria
N
Life cycle stages
Current projects by graduate students
• Fennel and cotton with colored fibers intercropping,
pest and natural enemies (Master thesis)
• Trophic interactions between Spodoptera frugiperda (corn caterpillar) and natural
enemies (Master thesis)
• Trophic interactions between soybean bug and their parasitoids (phD thesis)
• Intraguild predation in Diaphorina citri and their natural enemies:
citrus and sorghum intercropping (phD thesis)
• Population dynamics of forest pest and natural enemies (phD thesis)
• Trophic interactions between predator stink bugs and crop pests (phD thesis)
• Functional response and predator prey dynamics in coccinelids and aphids (posdoc)
Thank you