Cronin and Strong (1993a, b) examined the oviposition behavior of Anagarus delicatus Dozier (Hymenoptera: Mymaridae), an egg parasitoid of the leafhopper Prokelisia marginate Van Duzee (Homoptera: Delphacidae). They reported oviposition rates that were lower than predicted if the rate of egg-laying was maximized. Cronin and Strong (1993a) considered, and subsequently rejected, several “rules of thumb” (Stephens and Krebs 1986) as explanations for the observed patterns of patch departure. They observed that hosts on leaves experience density-independent mortality due to leaf senescence. Based on that, they advanced the hypothesis that submaximal oviposition rates in A. delicatus are best explained as risk-spreading by the parasitoid. (That is, by laying a small number of eggs on many leaves, the parasitoid increases the probability that some of her offspring will survive; Cronin and Strong 1993a.) An alternative hypothesis (Rosenheim and Mangel 1994) suggests that by distributing the eggs among several leaves, A. delicatus avoids self-superparasitism. Here, we take a somewhat different approach than those provided above to explain an additional observation of Cronin and Strong (1993a): female wasps rejected most of the hosts that they had probed. In so doing, we argue that rate maximization was an inappropriate prediction for A. delicatus, and in light of the life history parameters of this species, egg limitation is more suitable. Furthermore, egg limitation, when combined with one of the proposed explanations for the distribution of eggs, can explain the high rejection level of potential hosts

Bouskila, Amos

Robertson, Ian C.

Robinson, Michael E.

Roitberg, Bernard D.

Tenhumberg, Brigitte

Tyre, Andrew J

vanRanden, Ed

English

UNL | Libraries

University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Faculty Publications in the Biological Sciences Papers in the Biological Sciences 
1995 
Submaximal Oviposition Rates in a Mymarid Parasitoid: 
Choosiness Should Not Be Ignored 
Amos Bouskila 
Ben Gurion University of the Negev 
Ian C. Robertson 
Simon Fraser University 
Michael E. Robinson 
Simon Fraser University 
Bernard D. Roitberg 
Simon Fraser University 
Brigitte Tenhumberg 
University of Nebraska - Lincoln, btenhumberg2@unl.edu 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/bioscifacpub 
 Part of the Life Sciences Commons 
Bouskila, Amos; Robertson, Ian C.; Robinson, Michael E.; Roitberg, Bernard D.; Tenhumberg, Brigitte; Tyre, 
Andrew J.; and vanRanden, Ed, "Submaximal Oviposition Rates in a Mymarid Parasitoid: Choosiness 
Should Not Be Ignored" (1995). Faculty Publications in the Biological Sciences. 207. 
https://digitalcommons.unl.edu/bioscifacpub/207 
This Article is brought to you for free and open access by the Papers in the Biological Sciences at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications in the 
Biological Sciences by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Authors 
Amos Bouskila, Ian C. Robertson, Michael E. Robinson, Bernard D. Roitberg, Brigitte Tenhumberg, Andrew 
J. Tyre, and Ed vanRanden 
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
bioscifacpub/207 
C ronin and Strong (1993a, b) examined the ovipo-sition behavior of Anagarus delicatus Dozier (Hy-
menoptera: Mymaridae), an egg parasitoid of the leaf-
hopper Prokelisia marginate Van Duzee (Homoptera: 
Delphacidae). They reported oviposition rates that were 
lower than predicted if the rate of egg-laying was maxi-
mized. Cronin and Strong (1993a) considered, and sub-
sequently rejected, several “rules of thumb” (Stephens 
and Krebs 1986) as explanations for the observed pat-
terns of patch departure. They observed that hosts on 
leaves experience density-independent mortality due 
to leaf senescence. Based on that, they advanced the hy-
pothesis that submaximal oviposition rates in A. delica-
tus are best explained as risk-spreading by the parasit-
oid. (That is, by laying a small number of eggs on many 
leaves, the parasitoid increases the probability that 
some of her offspring will survive; Cronin and Strong 
1993a.) An alternative hypothesis (Rosenheim and Man-
gel 1994) suggests that by distributing the eggs among 
several leaves, A. delicatus avoids self-superparasitism. 
Here, we take a somewhat different approach than those 
provided above to explain an additional observation of 
Cronin and Strong (1993a): female wasps rejected most 
of the hosts that they had probed. In so doing, we argue 
that rate maximization was an inappropriate prediction 
for A. delicatus, and in light of the life history parameters 
of this species, egg limitation is more suitable. Further-
more, egg limitation, when combined with one of the 
proposed explanations for the distribution of eggs, can 
explain the high rejection level of potential hosts. 
Cronin and Strong found that A. delicatus has a lim-
ited egg load, ranging between 21 and 45 eggs (X‾ = 
33.3, Cronin and Strong 1990a: Table 1). They also ob-
served that A. delicatus lives for up to 2 d and, in captiv-
ity, can oviposit 95% of its entire egg load in 8 h. More-
over, 6% of 200 field-caught females had laid all of their 
eggs (as evidenced by empty ovarioles, Cronin 1991), 
suggesting that a large proportion of wasps would de-
plete their ovarioles by the end of their lifetime. We sug-
gest that these animals appear to be egg-limited rather 
than time-limited. Because animals should only rate-
maximize when limited by time, rate-maximization is 
unlikely to be appropriate for A. delicatus. Cronin and 
Strong (1993a) dismissed egg limitation because wasps 
left patches before depleting their egg supply. Although 
we agree that egg limitation does not explain the low 
number of eggs laid per patch, egg limitation predicts 
selectivity of hosts (e.g., Mangel and Roitberg 1989). In-
deed, A. delicatus appears to be very selective because it 
probes ≈50% of potential hosts with its ovipositor (Cro-
nin and Strong 1993b), but accepts only 8.4% (6 of 71 on 
average; Cronin and Strong 1993a). 
Although Cronin and Strong acknowledge that A. 
delicatus may be choosy, they seem to dismiss selectivity 
by suggesting that all leafhopper eggs are suitable hosts. 
This was based on high parasitoid survival to the sec-
ond instar, even when 20 wasps were induced to par-
asitize up to 90% of hosts in a patch (average number 
of hosts per patch was 131). Their suggestion ignores 
the possibility that variation in host quality could affect 
components of fitness other than survival to the second 
instar. If all hosts were acceptable, and if risk-spreading 
was the main cause of selection operating on patch de-
parture behavior, as Cronin and Strong (1993a) imply, 
two predictions could be made: (a) wasps should ovi-
posit some fixed number of hosts per patch (determined 
Published in Ecology 76:6 (1995), pp. 1990-1993. 
Copyright © 1995 by the Ecological Society of America. Used by permission.
Submitted August 11, 1994; revised January 17, 1995; accepted January 19, 1995. 
Submaximal Oviposition Rates in a Mymarid Parasitoid: 
Choosiness Should Not Be Ignored 
Amos Bouskila,1,2 Ian C. Robertson,1 Michael E. Robinson,1 Bernard D. Roitberg,1  
Brigitte Tenhumberg,1 Andrew J. Tyre,1 and Ed vanRanden1 
1. Behavioural Ecology Research Group, Department of Biological Sciences,  
Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6. 
2. Present address: Department of Life Sciences,  
Ben Gurion University of the Negev, 84105 Beer Sheva, Israel. 
1990
Sub max i ma l Ov i pO Si ti O n Rate S i n a my ma R i d pa R a S i tO i d   1991
by the costs and benefits of moving between patches), 
and (b) wasps should not reject hosts after probing 
them. Only the first prediction was confirmed. More-
over, if life expectancy of ovipositing females declines 
over time, spending time probing hosts in a patch will 
be costly, and ovipositing the optimal number of eggs 
should be done as rapidly as possible. Host probing and 
rejection is only predicted if (a) variation in host qual-
ity exists, and if wasps are egg-limited to a degree that 
makes choosiness adaptive, or (b) “apparent” rejection 
occurs when wasps probe but are unable to complete 
oviposition because they fail to contact the host, contact 
host tissue unsuitable for oviposition, or some other ran-
dom mechanism. Although Cronin and Strong (1993a, 
1993b) observed that the wasps are apparently unable to 
detect previous parasitisms, it is possible that wasps can 
detect variation in host quality in spite of their inability 
to detect previous parasitisms. 
The number of hosts parasitized by A. delicatus is in-
dependent of the number of hosts per patch (Stiling and 
Strong 1982, Cronin and Strong 1990b, 1993a). In order 
to explain selectivity given the density independence of 
parasitization, we suggest a simple “rule of thumb” that 
may be employed by an ovipositing female: within a 
patch, use the quality of the last few hosts probed to up-
date the estimate of patch quality (similar to the sliding 
“memory window” of Li et al. 1993). Based on the esti-
mate of patch quality and on the number of remaining 
eggs, determine the rejection threshold, and attack the 
next host above that threshold. The process is repeated 
until the optimal number of eggs to lay within a patch 
is reached. This optimal number must be determined 
by another process, such as risk-spreading (Cronin and 
Strong 1993a). Our hypothesis requires that choosiness 
is adaptive. 
To illustrate the point, we developed a simple state 
variable model of parasitoid foraging on hosts of vari-
ous qualities. As we do not seek to explain patch-leav-
ing behavior, we make the simplifying assumption that 
wasps lay all their eggs on a single patch. There are 11 
different host qualities, and the mean host quality in 
a patch is referred to as the patch quality. All patches 
have the same variance in host quality. Expected fitness 
is discounted by a small constant risk of death at each 
time unit. The first part of the model computes the opti-
mal host rejection threshold for each combination of the 
two state variables, eggload and time, for a particular 
patch quality. The optimal behavior for each combina-
tion of state variables is computed by calculating the ex-
pected fitness of each possible host rejection threshold, 
and selecting the threshold that has the highest expected 
fitness. This is repeated for each different patch quality, 
creating a decision matrix (see Table 1) for each possi-
ble distribution of hosts (by backward induction, Man-
gel and Clark 1988). Our estimate of expected fitness for 
a particular time, eggload, and patch quality is:
 F(p, e, t, T) 
                                                                                        th–1
                 { F(p, e, t+1, T )· (1 – m) · ∑ f (p, type)   }= MAXth      max type                             type= 1                     + ∑ f (p, type)· [v(type)                              
                               type=th      + (1 – m)· F(p, e – 1, t + 1, T )]
where p is patch quality, e is eggload, t is the current 
time step, T is the end of a wasp’s life, m is the probabil-
ity of mortality in a single time step, “type” is the host 
type, “max type” is the highest quality host type, “th” 
is the host rejection threshold. “v(type)” is the value of a 
host type to the parasitoid, and can be interpreted as the 
probability of an offspring surviving to adulthood on 
that host. “f(p, type)” is the frequency of type in a patch 
of quality p. The operator MAXth represents maximiz-
Table 1. Acceptance thresholds (minimum host quality that will be accepted) for selected conditions (rows) and eggloads (col-
umns), and a single time period (t = 1). The first three rows are derived from a single run of the model, and show the effect of ex-
pected host distribution. Good hosts are more common in higher number worlds. The last six rows represent different runs, and 
show the effects of altering model parameter values (in world 3). “m” is mortality per time unit; increase in the variable “l” in-
creases absolute differences in host value. 
Acceptance threshold
Conditions                             Eggloads range from lowest (e = 1, left side) to highest (e = 31, right side) 
World 1 6 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 
World 3 8 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 
World 5 9 9 9 8 8 8 8 8 8 8 8 7 7 7 7 7 
m × 0.5 8 8 7 7 7 7 7 7 7 7 6 6 6 6 6 6 
m × 1.5 8 7 7 6 6 6 6 6 6 6 6 5 5 5 5 5 
m × 2.0 7 7 7 6 6 6 6 6 6 7 7 7 7 7 7 7 
l= 10 7 7 7 6 6 6 6 6 6 6 6 6 6 5 5 5 
l = 20 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 
l = 40 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6
1992 bO u S k i la et al. i n Ec ol og y  76 (1995) 
ing the equation over all possible values of th. The sec-
ond part of the model simulates the behavior of individ-
ual wasps that encounter hosts stochastically. At each 
time unit the wasps use recent encounters with hosts to 
form an estimate of patch quality according to our “rule 
of thumb,” and then parasitize or reject hosts based on 
the threshold drawn from the decision matrix for the es-
timated patch quality. 
We can make three generalizations if we follow the 
host rejection thresholds of individual wasps through-
out their simulated lifetimes (Figure 1). First, the host 
rejection threshold of an individual tends to increase 
with time. This occurs because wasps become more se-
lective about which hosts they accept as their eggload 
declines. Second, hosts that were rejected at one point 
in time may be accepted later because the host rejection 
threshold decreases when, occasionally, wasps encoun-
ter several low-quality hosts in succession and thus as-
sess their habitat as poor. This accounts for Cronin and 
Strong’s (1993a) observation that wasps sometimes ovi-
posited in eggs that had been probed and rejected pre-
viously. Third, wasps tend to lay all of their eggs in a 
shorter period of time in patches of higher quality. 
We used the model to simulate several “experi-
ments” to further test the “rule of thumb.” In the first 
experiment, from 1 to 10 wasps oviposited simultane-
ously in a patch until each wasp had laid 6 eggs, and the 
percentage of the total number of hosts parasitized was 
recorded. In an additional experiment, 20 wasps were 
placed on a patch and forced to oviposit their entire egg-
load (32 eggs). These experiments mimic experimental 
procedures used by Cronin and Strong (1993a: Figure 4). 
The results of our experiments (Figure 2) are consistent 
with Cronin and Strong’s results. The percentage of par-
asitized hosts increased with the number of wasps in a 
patch, reaching 68–93% when 20 wasps foraged simulta-
neously. Variation among different quality patches was 
large when 20 wasps foraged simultaneously, whereas 
variation among different quality patches for 1–10 
wasps was small. Cronin and Strong used the results of 
their experiment to suggest that all hosts were accept-
able to wasps. However, the model demonstrates that 
even if there are differences in quality among hosts, and 
wasps are choosy, the majority of hosts will be parasit-
ized if the wasps are not given any other choices. 
It is possible that rejection of hosts is not an adap-
tive behavior, but rather an apparent rejection caused 
by the wasp missing a host or contacting host tissue un-
suitable for oviposition. In our second experiment we 
compared the fitness of wasps that followed the “rule of 
thumb” with the fitness of wasps that accepted and re-
jected hosts on a random basis, regardless of host qual-
ity. Such a protocol allowed us to determine if the “rule 
of thumb” is more adaptive than a random choice null 
model. The experiment showed that random choice re-
sults in lower fitness than the “rule of thumb.” In a high-
quality patch (mean host quality = 8) the fitness of ran-
domly choosing females was 17.80 ± 0.01 (mean ± 1 Se, n 
= 1000), whereas selective females had a mean fitness of 
18.44 ± 0.01 (n = 1000). In a low-quality patch (mean host 
Figure 1. Host rejection thresholds of individual wasps as a 
function of time. 
Figure 2. Percentage of hosts parasitized as a function of the 
number of wasps simultaneously present on a patch. The dot-
ted lines represent minimum and maximum percentage para-
sitism estimated from data in Cronin and Strong (1993a: Fig-
ure 4). 
Sub max i ma l Ov i pO Si ti O n Rate S i n a my ma R i d pa R a S i tO i d   1993
quality = 4), randomly choosing females had a mean fit-
ness of 10.54 ± 0.01 (n = 1000), whereas selective females 
had a mean fitness of 12.71 ± 0.01 (n = 1000). Therefore, 
the “rule of thumb” yields an improvement in fitness 
over a random null model. 
Although the model cannot eliminate the possibility 
that wasps are rejecting hosts randomly, we can sug-
gest an experiment that would distinguish between 
the “rule of thumb” and the random rejection hy-
pothesis. Present a sequence of wasps with the same 
patch of eggs. Each wasp is allowed to lay 6 eggs, and 
is then removed from the patch. Parasitized eggs are 
also removed. If wasps are rejecting hosts randomly, 
then their fitness would not depend on their posi-
tion in the sequence, because the distribution of host 
qualities would not decline steadily with time. How-
ever, if wasps are using our “rule of thumb,” we ex-
pect their fitness to decline with their position in the 
sequence because wasps earlier in the sequence pref-
erentially remove the highest quality hosts. Fitness 
of females can be estimated by measuring survival of 
offspring to adulthood. When we simulate this experi-
ment with our model, the fitness of wasps early in the 
sequence was nearly constant, with the last wasps ex-
periencing a sharp reduction in fitness. This decline in 
fitness occurred earlier and was sharper for wasps in 
lower quality patches. In summary, we have suggested 
a “rule of thumb” for host acceptance decisions when 
there is variation in host quality and when average 
host quality in the patch is estimated from experience. 
A dynamic state variable model was used to formalize 
the predictions made from this “rule of thumb.” Our 
model is very general and is applicable to any wasp 
species (e.g., Leptopilina heterotoma, Roitberg et al. 1992) 
wherein host acceptance is determined by the afore-
mentioned parameters, but it can account for the pat-
terns of host rejection observed by Cronin and Strong 
(1993b). 
Acknowledgments — We thank J. T. Cronin, M. Mangel, and 
J. A. Rosenheim for stimulating discussions and D. Cohen, D. 
Strong, and anonymous reviewers for Ecology for suggestions 
on the manuscript. This work was supported by a Natural Sci-
ences and Engineering Research Council of Canada Research 
Grant to B. D. Roitberg. 
Literature Cited 
Cronin, J. T. 1991. Parasitoid foraging behavior and the 
stabilization of host-parasitoid populations. Disser-
tation. Florida State University, Tallahassee, Florida, 
USA. 
Cronin, J. T., and D. R. Strong. 1990a. Biology of Anagrus 
delicatus (Hymenoptera: Mymaridae), an egg para-
sitoid of Prokelisia marginate (Homoptera: Delphaci-
dae). Annals of the Entomological Society of Amer-
ica 83:846-854. 
Cronin, J. T., and D. R. Strong. 1990b. Density indepen-
dent parasitism among host patches by Anagrus del-
icatus (Hymenoptera: Mymaridae): Experimental 
manipulation of hosts. Journal of Animal Ecology 
59:1019-1026. 
Cronin, J. T., and D. R. Strong. 1993a. Substantially sub-
maximal oviposition rates by a mymarid egg parasit-
oid in the laboratory and field. Ecology 74:1813-1825. 
Cronin, J. T., and D. R. Strong. 1993b. Superparasit-
ism and mutual interference in the egg parasitoid 
Anagrus delicatus (Hymenoptera: Mymaridae). Eco-
logical Entomology 18: 293-302. 
Li, C., B. D. Roitberg, and M. Mackauer. 1993. Patch res-
idence time and parasitism of Aphelinus asychis: A 
simulation model. Ecological Modelling 69:227-241. 
Mangel, M., and C. W. Clark. 1988. Dynamic modeling in 
behavioral ecology. Princeton University Press, Prince-
ton, New Jersey, USA. 
Mangel, M., and B. D. Roitberg. 1989. Dynamic informa-
tion and host acceptance by a tephritid fruit fly. Eco-
logical Entomology 14:181-189. 
Roitberg, B. M. Mangel, R. Lalonde, C. Roitberg, J. van 
Alphen, and L. Vet. 1992. Seasonal dynamic shifts in 
patch exploitation by parasitic wasps. Behavioral Ecol-
ogy 3:156-165. 
Rosenheim, J. A., and M. Mangel. 1994. Patch leaving 
rules for parasitoids with imperfect host discrimina-
tion. Ecological Entomology 19:374-380. 
Stephens, D. W., and J. R. Krebs. 1986. Foraging theory. 
Princeton University Press, Princeton, New Jersey, 
USA. 
Stiling, P. D., and D. R. Strong. (1982) Egg density and 
the intensity of parasitism in Prokelisia marginate (Ho-
moptera: Delphacidae). Ecology 63:1630-1635. 


Submaximal Oviposition Rates in a Mymarid Parasitoid:
Choosiness Should Not Be Ignored

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications in the Biological Sciences Papers in the Biological Sciences 1995 Submaximal Oviposition Rates in a Mymarid Parasitoid: Choosiness Should Not Be Ignored Amos Bouskila Ben Gurion University of the Negev Ian C. Robertson Simon Fraser University Michael E. Robinson Simon Fraser University Bernard D. Roitberg Simon Fraser University Brigitte Tenhumberg University of Nebraska - Lincoln, btenhumberg2@unl.edu See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/bioscifacpub  Part of the Life Sciences Commons Bouskila, Amos; Robertson, Ian C.; Robinson, Michael E.; Roitberg, Bernard D.; Tenhumberg, Brigitte; Tyre, Andrew J.; and vanRanden, Ed, "Submaximal Oviposition Rates in a Mymarid Parasitoid: Choosiness Should Not Be Ignored" (1995). Faculty Publications in the Biological Sciences. 207. https://digitalcommons.unl.edu/bioscifacpub/207 This Article is brought to you for free and open access by the Papers in the Biological Sciences at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications in the Biological Sciences by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors Amos Bouskila, Ian C. Robertson, Michael E. Robinson, Bernard D. Roitberg, Brigitte Tenhumberg, Andrew J. Tyre, and Ed vanRanden This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/bioscifacpub/207 C ronin and Strong (1993a, b) examined the ovipo-sition behavior of Anagarus delicatus Dozier (Hy-menoptera: Mymaridae), an egg parasitoid of the leaf-hopper Prokelisia marginate Van Duzee (Homoptera: Delphacidae). They reported oviposition rates that were lower than predicted if the rate of egg-laying was maxi-mized. Cronin and Strong (1993a) considered, and sub-sequently rejected, several “rules of thumb” (Stephens and Krebs 1986) as explanations for the observed pat-terns of patch departure. They observed that hosts on leaves experience density-independent mortality due to leaf senescence. Based on that, they advanced the hy-pothesis that submaximal oviposition rates in A. delica-tus are best explained as risk-spreading by the parasit-oid. (That is, by laying a small number of eggs on many leaves, the parasitoid increases the probability that some of her offspring will survive; Cronin and Strong 1993a.) An alternative hypothesis (Rosenheim and Man-gel 1994) suggests that by distributing the eggs among several leaves, A. delicatus avoids self-superparasitism. Here, we take a somewhat different approach than those provided above to explain an additional observation of Cronin and Strong (1993a): female wasps rejected most of the hosts that they had probed. In so doing, we argue that rate maximization was an inappropriate prediction for A. delicatus, and in light of the life history parameters of this species, egg limitation is more suitable. Further-more, egg limitation, when combined with one of the proposed explanations for the distribution of eggs, can explain the high rejection level of potential hosts. Cronin and Strong found that A. delicatus has a lim-ited egg load, ranging between 21 and 45 eggs (X‾ = 33.3, Cronin and Strong 1990a: Table 1). They also ob-served that A. delicatus lives for up to 2 d and, in captiv-ity, can oviposit 95% of its entire egg load in 8 h. More-over, 6% of 200 field-caught females had laid all of their eggs (as evidenced by empty ovarioles, Cronin 1991), suggesting that a large proportion of wasps would de-plete their ovarioles by the end of their lifetime. We sug-gest that these animals appear to be egg-limited rather than time-limited. Because animals should only rate-maximize when limited by time, rate-maximization is unlikely to be appropriate for A. delicatus. Cronin and Strong (1993a) dismissed egg limitation because wasps left patches before depleting their egg supply. Although we agree that egg limitation does not explain the low number of eggs laid per patch, egg limitation predicts selectivity of hosts (e.g., Mangel and Roitberg 1989). In-deed, A. delicatus appears to be very selective because it probes ≈50% of potential hosts with its ovipositor (Cro-nin and Strong 1993b), but accepts only 8.4% (6 of 71 on average; Cronin and Strong 1993a). Although Cronin and Strong acknowledge that A. delicatus may be choosy, they seem to dismiss selectivity by suggesting that all leafhopper eggs are suitable hosts. This was based on high parasitoid survival to the sec-ond instar, even when 20 wasps were induced to par-asitize up to 90% of hosts in a patch (average number of hosts per patch was 131). Their suggestion ignores the possibility that variation in host quality could affect components of fitness other than survival to the second instar. If all hosts were acceptable, and if risk-spreading was the main cause of selection operating on patch de-parture behavior, as Cronin and Strong (1993a) imply, two predictions could be made: (a) wasps should ovi-posit some fixed number of hosts per patch (determined Published in Ecology 76:6 (1995), pp. 1990-1993. Copyright © 1995 by the Ecological Society of America. Used by permission.Submitted August 11, 1994; revised January 17, 1995; accepted January 19, 1995. Submaximal Oviposition Rates in a Mymarid Parasitoid: Choosiness Should Not Be Ignored Amos Bouskila,1,2 Ian C. Robertson,1 Michael E. Robinson,1 Bernard D. Roitberg,1  Brigitte Tenhumberg,1 Andrew J. Tyre,1 and Ed vanRanden1 1. Behavioural Ecology Research Group, Department of Biological Sciences,  Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6. 2. Present address: Department of Life Sciences,  Ben Gurion University of the Negev, 84105 Beer Sheva, Israel. 1990Sub max i ma l Ov i pO Si ti O n Rate S i n a my ma R i d pa R a S i tO i d   1991by the costs and benefits of moving between patches), and (b) wasps should not reject hosts after probing them. Only the first prediction was confirmed. More-over, if life expectancy of ovipositing females declines over time, spending time probing hosts in a patch will be costly, and ovipositing the optimal number of eggs should be done as rapidly as possible. Host probing and rejection is only predicted if (a) variation in host qual-ity exists, and if wasps are egg-limited to a degree that makes choosiness adaptive, or (b) “apparent” rejection occurs when wasps probe but are unable to complete oviposition because they fail to contact the host, contact host tissue unsuitable for oviposition, or some other ran-dom mechanism. Although Cronin and Strong (1993a, 1993b) observed that the wasps are apparently unable to detect previous parasitisms, it is possible that wasps can detect variation in host quality in spite of their inability to detect previous parasitisms. The number of hosts parasitized by A. delicatus is in-dependent of the number of hosts per patch (Stiling and Strong 1982, Cronin and Strong 1990b, 1993a). In order to explain selectivity given the density independence of parasitization, we suggest a simple “rule of thumb” that may be employed by an ovipositing female: within a patch, use the quality of the last few hosts probed to up-date the estimate of patch quality (similar to the sliding “memory window” of Li et al. 1993). Based on the esti-mate of patch quality and on the number of remaining eggs, determine the rejection threshold, and attack the next host above that threshold. The process is repeated until the optimal number of eggs to lay within a patch is reached. This optimal number must be determined by another process, such as risk-spreading (Cronin and Strong 1993a). Our hypothesis requires that choosiness is adaptive. To illustrate the point, we developed a simple state variable model of parasitoid foraging on hosts of vari-ous qualities. As we do not seek to explain patch-leav-ing behavior, we make the simplifying assumption that wasps lay all their eggs on a single patch. There are 11 different host qualities, and the mean host quality in a patch is referred to as the patch quality. All patches have the same variance in host quality. Expected fitness is discounted by a small constant risk of death at each time unit. The first part of the model computes the opti-mal host rejection threshold for each combination of the two state variables, eggload and time, for a particular patch quality. The optimal behavior for each combina-tion of state variables is computed by calculating the ex-pected fitness of each possible host rejection threshold, and selecting the threshold that has the highest expected fitness. This is repeated for each different patch quality, creating a decision matrix (see Table 1) for each possi-ble distribution of hosts (by backward induction, Man-gel and Clark 1988). Our estimate of expected fitness for a particular time, eggload, and patch quality is: F(p, e, t, T)                                                                                         th–1                 { F(p, e, t+1, T )· (1 – m) · ∑ f (p, type)   }= MAXth      max type                             type= 1                     + ∑ f (p, type)· [v(type)                                                             type=th      + (1 – m)· F(p, e – 1, t + 1, T )]where p is patch quality, e is eggload, t is the current time step, T is the end of a wasp’s life, m is the probabil-ity of mortality in a single time step, “type” is the host type, “max type” is the highest quality host type, “th” is the host rejection threshold. “v(type)” is the value of a host type to the parasitoid, and can be interpreted as the probability of an offspring surviving to adulthood on that host. “f(p, type)” is the frequency of type in a patch of quality p. The operator MAXth represents maximiz-Table 1. Acceptance thresholds (minimum host quality that will be accepted) for selected conditions (rows) and eggloads (col-umns), and a single time period (t = 1). The first three rows are derived from a single run of the model, and show the effect of ex-pected host distribution. Good hosts are more common in higher number worlds. The last six rows represent different runs, and show the effects of altering model parameter values (in world 3). “m” is mortality per time unit; increase in the variable “l” in-creases absolute differences in host value. Acceptance thresholdConditions                             Eggloads range from lowest (e = 1, left side) to highest (e = 31, right side) World 1 6 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 World 3 8 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 World 5 9 9 9 8 8 8 8 8 8 8 8 7 7 7 7 7 m × 0.5 8 8 7 7 7 7 7 7 7 7 6 6 6 6 6 6 m × 1.5 8 7 7 6 6 6 6 6 6 6 6 5 5 5 5 5 m × 2.0 7 7 7 6 6 6 6 6 6 7 7 7 7 7 7 7 l= 10 7 7 7 6 6 6 6 6 6 6 6 6 6 5 5 5 l = 20 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 l = 40 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 61992 bO u S k i la et al. i n Ec ol og y  76 (1995) ing the equation over all possible values of th. The sec-ond part of the model simulates the behavior of individ-ual wasps that encounter hosts stochastically. At each time unit the wasps use recent encounters with hosts to form an estimate of patch quality according to our “rule of thumb,” and then parasitize or reject hosts based on the threshold drawn from the decision matrix for the es-timated patch quality. We can make three generalizations if we follow the host rejection thresholds of individual wasps through-out their simulated lifetimes (Figure 1). First, the host rejection threshold of an individual tends to increase with time. This occurs because wasps become more se-lective about which hosts they accept as their eggload declines. Second, hosts that were rejected at one point in time may be accepted later because the host rejection threshold decreases when, occasionally, wasps encoun-ter several low-quality hosts in succession and thus as-sess their habitat as poor. This accounts for Cronin and Strong’s (1993a) observation that wasps sometimes ovi-posited in eggs that had been probed and rejected pre-viously. Third, wasps tend to lay all of their eggs in a shorter period of time in patches of higher quality. We used the model to simulate several “experi-ments” to further test the “rule of thumb.” In the first experiment, from 1 to 10 wasps oviposited simultane-ously in a patch until each wasp had laid 6 eggs, and the percentage of the total number of hosts parasitized was recorded. In an additional experiment, 20 wasps were placed on a patch and forced to oviposit their entire egg-load (32 eggs). These experiments mimic experimental procedures used by Cronin and Strong (1993a: Figure 4). The results of our experiments (Figure 2) are consistent with Cronin and Strong’s results. The percentage of par-asitized hosts increased with the number of wasps in a patch, reaching 68–93% when 20 wasps foraged simulta-neously. Variation among different quality patches was large when 20 wasps foraged simultaneously, whereas variation among different quality patches for 1–10 wasps was small. Cronin and Strong used the results of their experiment to suggest that all hosts were accept-able to wasps. However, the model demonstrates that even if there are differences in quality among hosts, and wasps are choosy, the majority of hosts will be parasit-ized if the wasps are not given any other choices. It is possible that rejection of hosts is not an adap-tive behavior, but rather an apparent rejection caused by the wasp missing a host or contacting host tissue un-suitable for oviposition. In our second experiment we compared the fitness of wasps that followed the “rule of thumb” with the fitness of wasps that accepted and re-jected hosts on a random basis, regardless of host qual-ity. Such a protocol allowed us to determine if the “rule of thumb” is more adaptive than a random choice null model. The experiment showed that random choice re-sults in lower fitness than the “rule of thumb.” In a high-quality patch (mean host quality = 8) the fitness of ran-domly choosing females was 17.80 ± 0.01 (mean ± 1 Se, n = 1000), whereas selective females had a mean fitness of 18.44 ± 0.01 (n = 1000). In a low-quality patch (mean host Figure 1. Host rejection thresholds of individual wasps as a function of time. Figure 2. Percentage of hosts parasitized as a function of the number of wasps simultaneously present on a patch. The dot-ted lines represent minimum and maximum percentage para-sitism estimated from data in Cronin and Strong (1993a: Fig-ure 4). Sub max i ma l Ov i pO Si ti O n Rate S i n a my ma R i d pa R a S i tO i d   1993quality = 4), randomly choosing females had a mean fit-ness of 10.54 ± 0.01 (n = 1000), whereas selective females had a mean fitness of 12.71 ± 0.01 (n = 1000). Therefore, the “rule of thumb” yields an improvement in fitness over a random null model. Although the model cannot eliminate the possibility that wasps are rejecting hosts randomly, we can sug-gest an experiment that would distinguish between the “rule of thumb” and the random rejection hy-pothesis. Present a sequence of wasps with the same patch of eggs. Each wasp is allowed to lay 6 eggs, and is then removed from the patch. Parasitized eggs are also removed. If wasps are rejecting hosts randomly, then their fitness would not depend on their posi-tion in the sequence, because the distribution of host qualities would not decline steadily with time. How-ever, if wasps are using our “rule of thumb,” we ex-pect their fitness to decline with their position in the sequence because wasps earlier in the sequence pref-erentially remove the highest quality hosts. Fitness of females can be estimated by measuring survival of offspring to adulthood. When we simulate this experi-ment with our model, the fitness of wasps early in the sequence was nearly constant, with the last wasps ex-periencing a sharp reduction in fitness. This decline in fitness occurred earlier and was sharper for wasps in lower quality patches. In summary, we have suggested a “rule of thumb” for host acceptance decisions when there is variation in host quality and when average host quality in the patch is estimated from experience. A dynamic state variable model was used to formalize the predictions made from this “rule of thumb.” Our model is very general and is applicable to any wasp species (e.g., Leptopilina heterotoma, Roitberg et al. 1992) wherein host acceptance is determined by the afore-mentioned parameters, but it can account for the pat-terns of host rejection observed by Cronin and Strong (1993b). Acknowledgments — We thank J. T. Cronin, M. Mangel, and J. A. Rosenheim for stimulating discussions and D. Cohen, D. Strong, and anonymous reviewers for Ecology for suggestions on the manuscript. This work was supported by a Natural Sci-ences and Engineering Research Council of Canada Research Grant to B. D. Roitberg. Literature Cited Cronin, J. T. 1991. Parasitoid foraging behavior and the stabilization of host-parasitoid populations. Disser-tation. Florida State University, Tallahassee, Florida, USA. Cronin, J. T., and D. R. Strong. 1990a. Biology of Anagrus delicatus (Hymenoptera: Mymaridae), an egg para-sitoid of Prokelisia marginate (Homoptera: Delphaci-dae). Annals of the Entomological Society of Amer-ica 83:846-854. Cronin, J. T., and D. R. Strong. 1990b. Density indepen-dent parasitism among host patches by Anagrus del-icatus (Hymenoptera: Mymaridae): Experimental manipulation of hosts. Journal of Animal Ecology 59:1019-1026. Cronin, J. T., and D. R. Strong. 1993a. Substantially sub-maximal oviposition rates by a mymarid egg parasit-oid in the laboratory and field. Ecology 74:1813-1825. Cronin, J. T., and D. R. Strong. 1993b. Superparasit-ism and mutual interference in the egg parasitoid Anagrus delicatus (Hymenoptera: Mymaridae). Eco-logical Entomology 18: 293-302. Li, C., B. D. Roitberg, and M. Mackauer. 1993. Patch res-idence time and parasitism of Aphelinus asychis: A simulation model. Ecological Modelling 69:227-241. Mangel, M., and C. W. Clark. 1988. Dynamic modeling in behavioral ecology. Princeton University Press, Prince-ton, New Jersey, USA. Mangel, M., and B. D. Roitberg. 1989. Dynamic informa-tion and host acceptance by a tephritid fruit fly. Eco-logical Entomology 14:181-189. Roitberg, B. M. Mangel, R. Lalonde, C. Roitberg, J. van Alphen, and L. Vet. 1992. Seasonal dynamic shifts in patch exploitation by parasitic wasps. Behavioral Ecol-ogy 3:156-165. Rosenheim, J. A., and M. Mangel. 1994. Patch leaving rules for parasitoids with imperfect host discrimina-tion. Ecological Entomology 19:374-380. Stephens, D. W., and J. R. Krebs. 1986. Foraging theory. Princeton University Press, Princeton, New Jersey, USA. Stiling, P. D., and D. R. Strong. (1982) Egg density and the intensity of parasitism in Prokelisia marginate (Ho-moptera: Delphacidae). Ecology 63:1630-1635. 

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Submaximal Oviposition Rates in a Mymarid Parasitoid: Choosiness Should Not Be Ignored

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