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A Model of the Oviposition Behavior of
Copidosoma koehleri Parasitoid Wasps
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
June 22, 2010
Abstract
Copidosoma parasitoid wasps play an
important role in controlling agricultural
pests. This paper describes a complex
discrete time model for the mating,
oviposition, host and egg development
of these wasps. The model was used to
obtain optimal strategies for uninformed
wasps and to test these strategies both
in a statistical and evolutionary way.
Furthermore experimental data provided
by Ben Gurion University was used to
obtain estimates of parameters for partly
informed wasps. These parameters were
then tested for different properties using
the model. The results show that the
strategy estimated from the experimental
data is superior to the uninformed strat-
egy.
Key words. Wasps, simulation, para-
sites, sex choice
1 Introduction
Copidosoma koehleri are small parasitoid wasps
which lay their eggs into larvae of the potato tuber
moth Phthorimaea operculella. We will therefore
refer to these larvae as hosts. The female wasps
have the special ability to choose the sex of each
egg they lay, given they have been fertilized. A
virgin wasp can only lay male eggs. When a wasp
lays an egg into a host a number of wasps (clones)
will develop inside the host while consuming and
eventually killing it. The wasps commonly lay
more than one egg into one host (super parasitism)
which yields to competition within the host [3]. In
order to give the female eggs an advantage they ad-
ditionally develop a soldier larvae which protects
the offspring by feeding on other eggs. Hosts that
contain too many eggs will die prematurely before
the wasps fully develop and no wasps will survive.
Experiments indicate that there is a fraction of
wasps mating inside the host, given it contains
males and females [5]. Copidosoma koehleri
wasps are successfully used as a biological control
agent for the potato tuber moth in potato fields and
in potato storage facilities since the moths are an
agricultural pest in warm countries.
The objective of this paper is to describe a
probabilistic model of the oviposition behavior and
egg development of Copidosoma koehleri wasps.
The model allows long term simulations with
thousands of wasps with different strategies and
monitoring of output values over multiple simula-
tions. Therefore different set-ups (strategies and
model parameters) can be analyzed for stability or
dominance of specific strategies.
A central issue when modeling the behavior
of the wasps is the amount of information about a
host that a wasp can access using its senses. There
are three levels of information a wasp can access.
An uninformed wasp has no information about
eggs that have previously been laid into a host. A
partly informed wasp can sense the relatedness
of eggs within a host. A fully informed wasp can
also sense the sex of the eggs. First experiments
indicated that if wasps do not notice whether a host
can still feed additional eggs, premature host death
becomes very common and the wasp population
will eventually be extincted. Therefore we will
refer to a wasp with only that single bit of infor-
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
mation as an uninformed wasp. Unfortunately,
the question, what information a wasp can access,
can hardly be answered by practical experiments.
Therefore all possible levels of information will be
included into the model.
2 Assumptions
In order to make it possible to implement the
model in an effective way, a number of assump-
tions have been made. According to observations
generations do not overlap [2]. This implies that
each generation starts with a number of parasitized
and non-parasitized hosts. A certain fraction of
wasps mate within the host so there will be a
fraction of non virgin wasps directly after disper-
sal. Furthermore the lifespan of a female wasp
is defined as the number of eggs it can lay, while
the lifespan of a male is defined as the number of
females it can fertilize. The life span parameter
refers to the life span of the females and is assumed
to be equal for every wasp. A wasp is assumed to
be able to visit a specific number of hosts before
making a choice where to lay an egg. This number
is set by the Host sample size parameter.
3 The Model
The Model has been split into three sub models,
each modeling an intuitive part (see Figure 1). The
main model is the environment model which con-
tains lists of wasps and hosts and uses both the
wasp and the host sub-models for the related sub-
processes.
3.1 Environment model
The purpose of the environment model is to
store information about the hosts and wasps that
are currently being simulated. Furthermore it
models the lifespan and reproduction of hosts and
the lifespan, mating and traveling of the wasps.
The initial number of hosts is specified by the
Host count parameter. Depending on the host
reproduction parameter hosts can either die from
parasites, while the survivors reproduce at a certain
rate, or refresh for each generation, such that at the
beginning of each generation a certain number of
hosts is available. The virility parameters define
the number of females a male wasp can fertilize
on average. This takes into account that virgin’s
sons are generally less virile then non-virgin’s. In
Figure 1: Model layout.
order to model the traveling of the wasps and the
spatial distribution of hosts the host sample size
parameter is used to set the number of hosts a wasp
visits before deciding if and where to lay an egg.
3.2 Host model
Since hosts may die prematurely when they
contain too many eggs, the host model includes
both egg and host development. In order to model
the possibility of premature host death, a limit for
the number of wasps that can disperse out of a host
has to be defined as the parameter host limit. For
sufficient modeling of the competition between
eggs inside the host, a number of parameters, the
survival distributions are used. For the default
values for these parameters data from field experi-
ments was used [3]. These distributions define the
number of dispersing wasps for each egg and for
each possible configuration of eggs in a host as a
matrix of normal distributions (see Figure 2). The
parameter ratio mating before dispersal defines
the ratio of females that disperse as non virgin, on
condition that the host contained male eggs as well.
3.3 Wasp model
To model the host choice of the wasps, each type
of host (hosts differ by the eggs they carry) is
given an host attractiveness value. Furthermore
(v. June 22, 2010, p.2)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
Brood type Female Male
Unrel. fem. µ = 30
σ = 10
Rel. fem. µ = 45.8
σ = 10.9
Unrel. male µ = 24
σ = 10
Rel. male µ = 32.7
σ = 10.99
Unrel. mix. µ = 36 µ = 10
σ = 10 σ = 1
Rel. mix. µ = 45.8 µ = 32.7
σ = 10.9 σ = 10.99
Figure 2: Example of a survival table. Each cell
contains parameters of a normal distribution for the
given case.
the parameter egg count influence determines how
much attractiveness a host loses by carrying eggs.
As a model for the oviposition behavior a matrix
of Bernoulli distributions, the oviposition matrix
(see Figure 3), is used.
Sex of eggs
Relation Male Female Mixed
Empty 0.2
Related 0.4 0.4 0.4
Unrelated 0.5 0.5 0.5
Mixed 0.3 0.3 0.3
Figure 3: Example of an oviposition matrix. Each
cell contains the probability for laying a male egg
into the given host type.
3.4 Parameters
There are two types of parameters in the model.
The main parameters mainly affect the environ-
ment model and these are equal for all wasps in the
simulation. The strategic parameters on the other
hand, correspond to properties of the wasps and
these can be different for every wasp. The model
can be initialized with specific numbers of wasps
following different strategies.
3.5 Implementation
To be able to implement the model to be executed
by a computer, all processes have to be described
mathematically. The probability of a wasp losing
its virginity within a time step is calculated using
the formula:
p
f
=
P
n
k=1
u
k
lv
,
where n is the number of males in the population,
u
k
is the virility of wasp k, l is the life span of
individual wasps and v is the number of virgins in
the population.
In order to create a probability distribution for
a sample of hosts the attractiveness value for each
host is calculated and the result is normalized to a
sum of 1.
a(h, w) =
A(T
h
,v
w
)
1+ie
h
,
where a(h, w) is the attractiveness of host h to
wasp w, A(T
h
, v
w
) is the host attractiveness of
host type T
h
given that the virginity of wasp w is
v
w
, i is the egg count influence parameter and e
h
is the number of eggs in host h.
3.6 Statistical counters
The model contains a series of statistical counters
to record specific values during a simulation.
Each value is recorded for the entire population
and for each of the used strategies. To follow
the development of the wasp population, the
population size and the number of male and female
wasps are recorded. The counters for male, female
and mixed broods record information about which
brood types appear in the simulation. A brood
is a number of wasps emerging from one host.
Furthermore the number of male and female eggs
are recorded. Environmental values are the number
of empty hosts, the size of the host population and
the number of premature host deaths.
4 Optimal strategies for
uninformed wasps
A large number of experiments has been conducted
using the simulation. The aim of these experiments
was to determine optimal values for the parameters
of an uninformed wasp. An uninformed wasp is
unable to tell the sex and relatedness of eggs that
were previously laid into a host. Experiments
showed that wasps that cannot tell whether a host
can feed any more eggs, are unable to survive. This
is due to the fact that hosts containing too many
eggs die prematurely. Therefore we assume hosts
to get more unattractive with a higher number of
(v. June 22, 2010, p.3)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
eggs inside.
The host attractiveness and sex choice parameters
of the model have been set to equal values for
each host type, so that the wasps are uninformed.
The population is initialized with 1000 female
wasps with a virgin ratio of 5 percent. Experiments
indicated that the number of hosts scales the size
of the population linearly.
Since these starting conditions do not match a
realistic wasp population an initial number of gen-
erations is discarded until the simulations reaches
a steady state, where the output is independent of
the starting conditions. Experiments showed that
discarding a constant number of 20 generations
is usually sufficient. In order to obtain a large
number of samples, 200 generations have been
simulated for each case.
An important measure for the performance of a
strategy is the stability of the population over a
large number of generations. The variance of the
numbers of male and female wasps and of the pop-
ulation size are used to quantify this. Simulations
in marginal cases showed partly stability where
the population is stable at some time intervals and
unstable in others (see Figure 4).
0 20 40 60 80 100
0
1000
2000
3000
4000
5000
6000
7000
8000
Generation
Number of wasps
Wasps
population
male wasps
female wasps
Figure 4: Plot of partly stable output.
4.1 Sex choice
Since wasps do not have information about the
types of eggs in the host, the sex choice parame-
ter comes down to a single value between 0 and 1.
Where 1 means only laying male eggs. The range
of this parameter has been covered with 100 repli-
cations of the model. The results indicate a clear
disadvantage of a strong preference for laying fe-
male eggs. This can be explained by virginity of
the wasps. A generation of wasps that (nearly) al-
ways lays female eggs will have a lack of males in
the followinggeneration. Thereforethenewfemale
wasps will not (entirely) get fertilized and therefore
be unable to follow their strategy to lay preferably
female eggs. This will cause high instability since
every second generation will have a lot of males,
while the other generations have a lot of females.
The results of the simulations are illustrated in Fig-
ure 6. The local minimum at 0.33 can be explained
as an artifact caused by partly stability.
4.2 Superparasitism
The egg lay threshold parameter determines the
amount of superparasitism in the simulation. Fig-
ure 5 shows the influence of the parameter on the
number of eggs a host receives on average. Exper-
iments have been conducted to obtain information
about the influence of the parameter on the popu-
lation. The experiments showed that the parameter
mainly influences the size of the populationand has
only little influence on stability. The output of the
simulations is illustrated in Figure 7 where a max-
imum in population at a egg lay threshold value
of 0.3 occurs. This indicates that it is best to lay 2
eggs into each host.
0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Egglay threshold e
Average number of eggs per host n
Influence of the egglay threshold
with host attractiveness 0.5 and egg count influence 0.3
0.5/(1+0.3*n)=e
Figure 5: Influence of egg lay threshold parameter
on superparsitism.
4.3 Life span
Since a wasp population quickly outnumbers the
host population a life span of just 1 egg seems
to be sufficient to utilize all hosts. A number
of experiments with different life spans and
stable values for the other parameters confirmed
this hypothesis. On the other hand when using
unstable values for the sex choice parameter the
experiments showed that it is possible to stabilize
these strategies by increasing the life span of the
wasps. This is illustrated in Figure 8. The local
(v. June 22, 2010, p.4)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
minimum in the variances at a life span of 22 can
be explained as an artifact due to partly stability.
4.4 Optimality testing
An optimal strategy should maximize the popula-
tion size and minimize the variance. Since only
a little ratio of male wasps is required to fertilize
the females, another objective is to maximize the
number of females. According to the performed
experiments, a sex choice of 0.6, an egg lay
threshold of 0.3 and a life span of 20 eggs seem to
be optimal. To test this hypothesis this strategy was
compared pairwise to a number of other strategies
using a paired-t test [1]. In order to obtain data
100 simulations with each 100 generations for
100 hosts have been performed for each strategy.
The first 20 generations are again discarded. Each
strategy is then compared to the strategy defined
above by means of stability, number of females
and population size. As a measure of stability, the
sum of the variances of the population and of the
male and the female wasps, is used. The higher
the variance the more instable the strategy. Since
the variance is dependent on the population size
we scale it by dividing by the population size. The
data of the hypothesis strategy is then compared
to the output of each of the other strategies by
creating a paired-t confidence interval for the
difference of the strategies and see with what
confidence the hypothesis strategy is better.
Table 1 shows that the hypothesis strategy is
more stable than the other strategies and mostly
produces more females and larger populations.
The strategies with a higher sex choice value, so
with a stronger preference for male eggs, result in
larger populations but, as to be expected, in lower
numbers of females.
A second approach is to simulate a population
of the hypothesis strategy and try to invade it with a
small number of wasps following a different strat-
egy. If a strategy cannot be invaded by other strate-
gies, the strategy is referred to as evolutionary sta-
ble [4].
In order to test these properties, a simulation is ini-
tialized with a population of 1000 wasps of one
strategy and 10 invading wasps following a differ-
ent strategy. For each pair of strategies 20 simula-
tions of 100 generations with 100 hosts have been
performed.
Table 2 shows the results of these experiments.
s e l Mean difference ϕ
0.2 0.3 20 ¯p = 867.03 > 0.99
¯
f = −4 31.49
< 0.01
¯v = −10 .68 > 0.99
0.5 0.2 25 ¯p = 4232.4 > 0.99
¯
f = 16 47.8
> 0.99
¯v = −19 .74 > 0.99
0.5 0.3 10 ¯p = 159.23 > 0.99
¯
f = −6 52.89
< 0.01
¯v = −4.3 1 > 0.99
0.5 0.3 20 ¯p = 54.20 > 0.99
¯
f = −3 14.09
< 0.01
¯v = −0.1 9 > 0.99
0.5 0.3 25 ¯p = 918.48 > 0.99
¯
f = 32 6.95
> 0.99
¯v = −1.5 2 > 0.99
0.5 0.4 25 ¯p = 2063.2 > 0.99
¯
f = 10 66.4
> 0.99
¯v = −11 .31 > 0.99
0.7 0.3 20 ¯p = −64.20 < 0.01
¯
f = 36 6.40
> 0.99
¯v = 0.16 0.2
0.9 0.3 20 ¯p = −254.94 < 0.01
¯
f = 15 06.6
> 0.99
¯v = 2.91 < 0.01
In this table
s
is the sex choice,
e
is the egg
lay threshold,
l
is the life span,
¯p
is the mean
difference in population size,
¯
f
is the normalized
mean difference in in number of females,
¯v
is the
normalized mean difference in variance and
ϕ
is
the confidence for the hypothesis strategy being
better than the tested one by means of higher
population or lower variance.
Table 1: Optimality of hypothesis strategy.
(v. June 22, 2010, p.5)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
0 10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
3.5
x 10
4
Probability of laying a male egg in %
Stability depending on sexchoice for uninformed wasps
male wasp mean
male wasp variance
female wasp mean
female wasp variance
population mean
population variance
Figure 6: Sexchoice output.
0.15 0.20 0.25 0.30 0.35 0.40 0.45
0
1000
2000
3000
4000
5000
6000
7000
Egglay threshold
Stability depending on egglay threshold for uninformed wasps with sexchoice 0.5
Male wasp mean
Male wasp variance
Female wasp mean
Female wasp variance
Population mean
Population variance
Figure 7: Egg lay threshold output.
0 5 10 15 20 25 30 35 40
0
1000
2000
3000
4000
5000
6000
7000
Lifespan of a wasp
Stability depending on life span for uninformed wasps with sexchoice 0.15
Male wasp mean
Male wasp variance
Female wasp mean
Female wasp variance
Population mean
Population variance
Figure 8: Life span output.
(v. June 22, 2010, p.6)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
s
p
e
p
s
i
e
i
n
i
0.1 0.3 0.6 0.3 0
0.1 0.3 0.2 0.3 0
0.2 0.3 0.1 0.3 6
0.5 0.3 0.1 0.3 15
0.6 0.3 0.1 0.3 14
0.6 0.3 0.8 0.3 0
0.6 0.3 0.6 0.25 20
0.6 0.3 0.6 0.35 0
0.6 0.35 0.6 0.3 0
0.7 0.3 0.6 0.3 8
0.8 0.3 0.6 0.3 10
In this table
s
p
is the sex choice of the main
population,
e
p
the egg lay threshold of the main
population and
s
i
,
e
i
are the same parameters for
the invading wasps.
n
i
is the number of times the
invasion was successful within the
20
performed
simulations.
Table 2: Successful invasions of strategies.
It showsthat although the hypothesisstrategy is op-
timal from a statistical perspectiveit does not seem
to be evolutionary stable since it can be invaded by
a number of strategies either laying more eggs or
having a stronger preference for females.
5 Optimal strategies for partly
informed wasps
A wasp that can sense eggs inside a host and
determine its relation to the eggs is referred to
as a partly informed wasp. In order to describe
a sex choice strategy for a partly informed wasp
four values between 0 and 1 are required. Each
value stands for the average sex choice for one
of the four host types. Furthermore four host
attractiveness values for each of the host types are
required.
At Ben Gurion University a number of exper-
iments with real wasps have been conducted in
order to gain information about the sex choice
behavior. Wasps have been put together with hosts
and were allowed to lay a controlled number of
eggs. After the eggs developed, it was checked
whether it was an all female, an all male or a mixed
brood.
The results of these experiments are shown in
Table 3. The first row, vms, refers to an experiment
where a virgin wasp lays one egg into one host,
male female mixed
vms 10 4 2
vmd 5 1 6
mms 4 7 2
mmd 3 7 3
Table 3: Brood sizes that resultedfromexperiments
with real wasps.
male female
vms 26 6
vmd 16 7
mms 10 16
mmd 9 17
Table 4: Estimated number of eggs within the hosts
from experiments with real wasps.
is then mated and lays another egg into the same
host. The second row, vmd, shows the brood sizes
that resulted from a virgin wasp laying an egg into
one host and another mated wasp laying another
egg into the same host. The third row, mms, gives
the results for a mated wasp laying two eggs into
one host and the last row, mmd, shows the results
of two different mated wasps laying two eggs into
one host.
Table 4 shows estimations of the number of
eggs in the real experiments shown in Table 3.
Since we cannot estimate host attractiveness val-
ues from these experiments we focus on the four
sex choice parameters. From the results ranges for
each of the four sex choice values were estimated.
In case of an empty host the wasps seem to pre-
fer laying female eggs since the number of female
eggs is higher for the last two experiments. Since in
case of the second experiment more females were
produced than in the first case there seems to be a
preference for females given a non self parasitized
host. For self parasitized hosts there seems to be
a preference for males. Unfortunately we cannot
make any assumptions about the mixed parasitized
host type, since no more than 2 eggs were laid into
one host in the experiments.
In order to estimatethe benefit of using the extra in-
formation, a number of strategies has been created
that match the experimental data. These strategies
are listed in Table 5.
These strategies were now statistically tested
against the optimal uninformed sex choice strategy
of laying a male egg in 6 0% of the cases. For each
of the strategies 100 simulations with 100 gener-
(v. June 22, 2010, p.7)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
S s
e
s
s
s
n
s
m
h
1
0.2 0.66 0.33 0.5
h
2
0.2 0.66 0.2 0.5
h
3
0.0 1.0 0.0 0.0
h
4
0.0 1.0 0.0 0.5
In this table
s
e
is the sex choice given an empty
host,
s
s
given a self parasitized host,
s
n
, given a
non self parasitized host and
s
m
is the sex choice
given a mixed parasitized host (contains both
related and unrelated eggs).
Table 5: Hypothesis strategies for partly informed
wasps.
ations with each 100 hosts have been performed
similar as in Section 4.4. The results of the tests
are shown in Table 6.
The
¯
f values show that each of the hy-
pothesized partly informed strategies produces
significantly higher numbers of females. At the
same time the populations are smaller and the
variance is slightly increased. Since the variances
are still low, all four strategies can be viewed as
superior to the uninformed strategies. The highest
number of females was observed at the third
strategy h
3
.
In order to check for evolutionary stability
of the strategies, more experiments have been
performed to test whether the partly informed
strategies can invade or can be invaded by the
uninformed strategy. These experiments clearly
show that none of the hypothesized partly informed
strategies can be invaded by the uninformed strat-
egy. Also all of the partly informed strategies
manage to invade an uninformed wasp population.
These results are listed in Table 7.
6 Concluding remarks
This paper describes a discrete time model for the
oviposition behavior of Copidosoma koehleri para-
sitoid wasps. The possible levelsof information are
included into the model. Furthermore we showed
that the model can be used to find and test strategies
for different properties. We performeda large num-
ber of simulations to determine optimal strategies
for uninformed wasps. Then we performed statis-
tical tests to confirm our hypothesis. Furthermore
we performed simulations with wasps of different
strategies and tested for evolutionary stability.
s
e
s
s
s
n
s
m
Mean diff. ϕ
0.2 0.66 0.33 0.5 ¯p = −138.12 < 0.01
¯
f = 85 4.55
> 0.99
¯v = 0.81 < 0.01
0.2 0.66 0.2 0.5 ¯p = − 190.26 < 0.01
¯
f = 10 32.6
> 0.99
¯v = 1.13 < 0.01
0.0 1.0 0.0 0.0 ¯p = −264.56 < 0.01
¯
f = 13 73.2
> 0.99
¯v = 2.24 < 0.01
0.0 1.0 0.0 0.5 ¯p = −268.73 < 0.01
¯
f = 13 67.6
> 0.99
¯v = 2.19 < 0.01
In this table
s
e
is the sex choice given an empty
host,
s
s
given a self parasitized host,
s
n
, given a
non self parasitized host and
s
m
is the sex choice
given a mixed parasitized host.
¯p
,
¯
f
and
¯v
are
the mean differences for population, females and
variance respectively.
ϕ
is the probability of the
strategy being better than the optimal uniformed
strategy in the respective category.
Table 6: Test of the hypothesized partly informed
strategies against the optimal uninformed strategy.
S
p
S
i
n
i
S
u
h
1
9
S
u
h
2
8
S
u
h
3
9
S
u
h
4
11
h
1
S
u
0
h
2
S
u
0
h
3
S
u
0
h
4
S
u
0
In this table S
p
is the strategy of the population and
S
i
is the strategy of the invaders. n
i
is the number
of successful invasions. S
u
is the uniformed
strategy.
Table 7: Successful invasions of partly and unin-
formed wasps.
(v. June 22, 2010, p.8)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
Data from experiments with real wasps has been
provided by University of Haifa. We used this data
to obtain estimates for the sex choice parameters
for partly informed wasps. Both statistical and evo-
lutionary stability experiments showed that these
estimates are superior to the uninformed strategy.
In order to obtain more detailed information about
optimal strategies and evolutionary stability, larger
numbers of simulations should be performed. For
example 2
k
-factorial design [1] can be used to ob-
tain better approximationsfor the parameters of the
model. Due to the high number of simulations re-
quired to do so, this was not possible within the
time frame of this paper.
We thank Dr. Tamar Keasar from University
of Haifa for providing accurate information and
helpful discussion.
References
[1] Averill M. Law, W. David Kelton (1991).
Simulation Modeling and Analysis
. 4th
edition edition.
[2] Michal Segoli, Ally R. Harari
Amos Bouskila, Tamar Keasar (2009a).
Limited kin discrimination abilities
mediate tolerance toward relatives in
polyembryonic parasitoid wasps.
Be-
havioral Ecology
, Vol. 20, No. 6, pp.
1262–1267.
[3] Michal Segoli, Amos Bouskilaa
Tamar Keasar, Ally R. Hararia (2009b).
Brood size in a polyembryonic parasitoid
wasp is affected by relatedness among
competing larvae.
Behavioral Ecology
,
Vol. 20, No. 4, pp. 761–767.
[4] Smith, John Maynard (1982).
Evolution
and the theory of games
. University of
Cambridge.
[5] Tamar Keasar, Roi Barak Shimon Stein-
berg David Giron Michael R. Strand Amos
Bouskila Ally R. Harari, Michal Segoli
(2006). Costs and consequences of super-
parasitism in the polyembryonicparasitoid
copidosoma koehleri.
Ecological Ento-
mology
, Vol. 31, pp. 277–283.
(v. June 22, 2010, p.9)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
Appendix A: Parameters
Main parameters
Generations Number of generations
to simulate.
Lifespan Lifespan of a wasp
in number of eggs it can lay.
Host count Number of hosts
at initialization.
Host limit Number of wasps one
host can feed on average.
Host refresh Toggles whether hosts
refresh for each generation.
Host- Rate of reproduction
reproduction of surviving hosts,
if hosts do not refresh.
Strategic parameters
Wasp count Number of wasps
at initialization.
Sex ration Ratio of males
at initialization.
Virgin ratio Ratio of virgins
at initialization.
Egg count Influence of number of
influence eggs on host
attractiveness.
Egg lay Attractiveness Threshold
threshold for laying eggs.
Virgin’s son Virility of a son
virility of a virgin.
Non virgin’s Virility of a son
son virility of a non virgin.
Host sample Number of hosts a
size wasp visits before laying
an egg.
Ratio mating Ratio of wasps
before mating within the host.
dispersal
Virgin host Attractiveness for each
attractiveness host type for virgins.
Non virgin host Attractiveness for each
attractiveness host type for non virgins.
Oviposition Probability of laying
matrix a male egg for each host
type (see Figure 6).
Survival Mean and standard deviation
matrix for each gender for each
brood type (see Figure 2).
Appendix B: Flowcharts
Figure 9: Wasp flowchart.
Figure 10: Host flowchart.
(v. June 22, 2010, p.10)
Max B¨ugler
Supervisor: Frank Thuijsman, Maastricht University
External advisor: Tamar Keasar, University of Haifa
Figure 11: Environmentflowchart. ”Lay eggs” cor-
responds to Figure 9, ”Develop eggs” corresponds
to Figure 10
(v. June 22, 2010, p.11)
