Behavioral Ecology Vol. 12 No. 5: 577-583
© 2001 International Society for Behavioral Ecology
Variable host quality, life-history invariants, and the reproductive strategy of a parasitoid wasp that produces single sex clutches
a Natural Environment Research Council Centre for Population Biology and Department of Biology, Imperial College, Ascot, Berkshire SL5 7PY, UK b Institute of Cell, Animal and Population Biology, University of Edinburgh, EH9 3JT, UK
Address correspondence to S.A. West, Institute of Cell, Animal and Population Biology, University of Edinburgh, King's Buildings, Edinburgh, EH9 3JT, UK. E-mail: stu.west{at}ed.ac.uk .
Received 31 January 2000; revised 13 October 2000; accepted 16 November 2000.
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ABSTRACT |
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The parasitic wasp Achrysocharoides zwoelferi (Hymenoptera, Eulophidae) produces clutches consisting of only one sex. Moreover, male clutch size is invariably one while female clutches are in the range one to four. We designed field experiments to determine the effect of host quality on clutch composition. We found that solitary male and solitary female clutches were reared from the same size mines, and that larger mines tended to produce gregarious female clutches. A higher proportion of male clutches were placed in older hosts, despite their large size. Variation in body size, both between and within clutches, was measured in order to test the predictions of models that take into account the constraint that clutch size is an integer trait, something of potential importance when absolute clutch size is low. Our data supported several predictions of these models, including the trade-off-invariant rule for optimal offspring size developed by Charnov and Downhower. However, while most invertebrate clutch size models assume equal resource share among members of the same clutch, we found an increase in inequality in larger clutches.
Key words: body size, clutch size, Hymenoptera, sex allocation, sex ratio, trade-off.
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INTRODUCTION |
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Clutch size and sex ratio are major components of the life history strategy of many animals and have been studied intensively, both theoretically and experimentally (Bulmer, 1994
;
Charnov, 1982;
Stearns, 1992;
West et al., 2000). Parasitoid
wasps have proved to be an extremely useful model system for testing ideas in
this area (Godfray, 1994).
This is chiefly because the decisions made by an ovipositing female on
encountering a host are intimately related to her fitness, and also because
parasitoids show a wide range of clutch size and sex ratio strategies
(parasitoid wasps are haplodiploid and offspring sex is determined by whether
the parent fertilizes the egg or not;
Godfray, 1994). While earlier
studies of parasitoids tended to be laboratory based, and concerned with
either clutch size or sex ratio, there has been an increasing move in recent
years to study both sex ratio and clutch size simultaneously, and to work with
wasps in the field (Driessen and Hemerik,
1992; West et al.,
1999).
This is the third in a series of articles concerned with the reproductive
strategies of wasps in the genus Achrysocharoides (Hymenoptera,
Chalcidoidea, Eulophidae) and in particular the species A. zwoelferi
Delucchi (West et al., 1996,
1999). We chose to work with
these wasps because of their varied and unusual oviposition strategies. All
species lay small clutches of eggs (1-4) in the larvae of leaf-mining
Lepidoptera, but the majority of species segregate males and females in
different hosts (Bryan, 1983).
In many of these species, including A. zwoelferi, the size of male
and female clutches differ with the former being invariably one while the
latter is generally one, two, or three. The obligate segregation of the sexes
is very unusual in parasitoid wasps (and other animals). We do not understand
why the sexes are segregated in many Achrysocharoides species, or why
in species such as A. zwoelferi the size of male clutches is always
one (see Discussion). Consequently, our previous work has considered this
phenomenon as a constraint, and focused on predicting and testing how the
oviposition behavior (sex ratio and clutch size) of these species should vary
depending on the extent to which a female's reproductive success is limited by
egg availability or host availability
(West et al., 1999). In this
article we are concerned with how a female's oviposition behavior depends on
host quality.
Host quality (especially size) has been shown to have an important effect
on both clutch size and sex ratio in parasitoid wasps. In species where more
than one wasp can develop per host (gregarious wasps), many studies have shown
that females are able to assess host size and lay more eggs on larger hosts
(reviewed in Godfray, 1994),
broadly as predicted by a number of theoretical models (Charnov and Skinner,
1984,
1985;
Iwasa et al., 1984;
Parker and Courtney, 1984;
Waage and Godfray, 1985). In
solitary species, where only a single wasp develops per host, females eggs are
often laid on large hosts and males on small hosts. A reason for this was
suggested by Charnov et al.
(1981) who noted that larger
hosts led to larger parasitoids and argued that females would gain more by
being large than males. Other more complicated interactions between host size,
clutch size, and sex ratio occur in situations where the optimal clutch size
depends on the sex ratio and vice versa
(Williams, 1979). In
particular, differences in competitiveness between the sexes can favor biased
sex ratios (Godfray, 1986),
and might even lead to the evolution of segregated clutches as occurs in many
Achrysocharoides species
(Pickering, 1980;
Rosenheim, 1993). Our first
aim in this article is to investigate the relationship between clutch
composition and host quality (size and age) using field manipulation
experiments with A. zwoelferi.
Most optimal clutch size models treat clutch size as a continuous variable,
even though only an integer number of eggs are laid. Where a fractional number
of eggs are predicted, most workers assume that natural selection will favor
the nearest integer clutch size. Recently, several workers have examined
models that explicitly deal with the complications that arise when a parent
divides up a certain amount of resources between a small, integer, clutch of
offspring (Charnov, 1997;
Charnov and Downhower, 1995;
Charnov et al., 1995;
Downhower and Charnov, 1998;
Ebert, 1994). Specifically,
Charnov et al. (1995;
Charnov and Downhower, 1995)
have argued that if offspring size (I) is a function of the amount of
resources each individual receives, then the ratio of the range of offspring
sizes found for clutches of i and j offspring (j =
i — 1) is the reciprocal of the ratio of clutch sizes. In
symbols:
 | (1) |
2, because Imin 1 depends on the minimum size of
viable offspring. Equivalently, the range in sizes of offspring is
proportional to the inverse of clutch size. The accuracy of this invariant
rule depends on a linear relationship between resources allocated to offspring
and the particular measure of offspring used (I); an equal division
of resources among offspring, and the precise form of the function
S(I) relating offspring size to fitness. Charnov and
Downhower (1995) demonstrated
the widespread applicability of Equation 1 by showing that Equation 1 was true
or nearly true for a wide range of functions, S(I), used in
the life history theory literature. We return to the reasons for, and general
applicability of this rule in the Discussion.
Our second aim in this article is to test both the predictions and
assumptions of the invariant rule of Charnov et al.
(1995), using the small integer
female clutches of A. zwoelferi. We examined whether resources were
distributed equally among young by seeing if individuals from the same clutch
differed more in size than randomly chosen individuals (from clutches of the
same size). We carried out a direct test of Equation 1 by exploring whether
the size range of adult wasps from different sized clutches was proportional
to the inverse of clutch size. However, statistical estimators of ranges tend
to converge only slowly with sample size, and so we also tested Equation 1 by
determining if the variance of offspring size decreased with increasing clutch
size. Finally, we observed how the average body size of offspring varied with
increasing clutch size. While Charnov and Downhower
(1995) predicted that this
should remain constant, Ebert
(1994) has shown that in some
circumstances it can decrease.
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METHODS |
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Study organism and site
A. zwoelferi is a small metallic wasp approximately 2 mm in length. It is oligophagous, attacking those species of Phyllonorycter (Lepidoptera, Gracillaridae) that mine the leaves of Salix spp. In our study site at Silwood Park (Berkshire, UK), the wasp is the commonest parasitoid attacking Phyllonorycter salicicolella (Sircom) on Salix cinerea L. and Salix caprea L. Females oviposit in first, second, or third instar Phyllonorycter larvae after first causing temporary paralysis (Bryan, 1980
). The final instar parasitoid larvae kill the host in its
fourth or fifth instar and pupate in the mine
(Bryan, 1983). Both host and
parasitoid have two generations a year with the peak wasp flight periods being
June and September. At this time, females can be collected searching the
leaves of Salix for hosts. Parasitoids overwinter as pupae in mines
within fallen leaves.
Mine size and clutch composition
The aim of the first experiment was to find out whether the proportion of
male and female clutches, and the size of female clutches, varied with host
size. Leaf mine area is used as a surrogate for host size which cannot be
measured directly. We collected mature mines of P. salicicolella at
Silwood Park during September 1994, and placed them individually in corked
glass tubes in an outside insectary. At the beginning of May 1995 we placed
nine large muslin sleeves over branches of individual S. cinerea
trees at Silwood Park. These sleeves prevent access by both moths and
parasitoids. We placed 10 individual moths that had emerged from the mines
collected in 1994 in each sleeve. Female moths lived for only a few days in
these sleeves, and so all mines produced are approximately of the same age.
After 3 weeks the mines had developed within the sleeves to a size at which
they could be parasitised by females of A. zwoelferi. At this point
we removed all the muslin sleeves simultaneously, labeling and measuring the
size (length x width, measured in mm2) of each mine. The
sleeves were replaced after 1 week to prevent further parasitoid attack, hence
minimizing the risk of superparasitism. The sleeves were placed on different
trees and are unlikely to have been visited by the same wasps. During July
1995 we picked all the mines that had completed development in the sleeves and
stored them in an outside insectary. The wasps and moths emerged from these
collections during August and September 1995, whereupon we recorded the number
and sex of any emerging A. zwoelferi.
Mine age and clutch composition
The aim of the second experiment was to find out whether the proportion of
male and female clutches, and the size of female clutches, varied with host
age. During May 1994 we located very small P. salicicolella mines, a
few days old, on S. cinerea trees at Silwood Park. We labeled these
mines and allocated them at random to one of three treatments (total sample
size = 300 mines). In the first treatment we left mines uncovered and exposed
to parasitism for the first week after they were discovered and subsequently
enclosed them in a small muslin envelope which prevented the entry of
parasitoids. We refer to these mines as young at the time of parasitism. In
the second treatment we enclosed the mines for the first and third weeks, and
left them uncovered for the second week to produce mines of medium age at the
time of oviposition. Similarly, in the third treatment we enclosed mines for 2
weeks and then left them uncovered for the third week of the experiment to
produce old mines at the time of oviposition. Mines were added to the three
treatments over a period of 30 days and consequently the day the mines were
exposed to parasitism (with 5 May defined as day 0) was included in the
analysis. After the third week all mines were left covered until the larvae
pupated, at which time the leaves were picked and placed in corked glass
tubes, and reared in an outside insectary. We recorded the number and sex of
any emerging A. zwoelferi.
Tests of the Charnov and Downhower invariant rule
We obtained data on the size range of A. zwoelferi developing in
different sized clutches from two sources: naturally occurring clutches
recorded in our previous study examining the relationship between fitness and
body size (West et al., 1996);
and clutches collected to provide the moths used in Experiment I (above). In
both cases we used hind tibia length as a measure of individual size (measured
in mm). The cube of hind tibia length (hereafter just called body size) was
used in all analyses as a measure of wasp volume.
Statistical analyses
We analyzed the data using generalized linear modeling techniques
(Crawley, 1993;
McCullagh and Nelder, 1983)
which are implemented in the GLIM statistical package. The sex of the clutch
was treated as a binary variable and analyzed using a logit link function.
Terms were removed from the full model by stepwise deletion
(Crawley, 1993), and whether
the removal of a term caused a significant increase in deviance was assessed
with a 
2 test. We analyzed the data on body size assuming
normally distributed errors, checking this assumption by standard tests on the
residuals, and testing for significance with F tests. Where the
appropriate replicate was the clutch developing in a single mine, we analyzed
the average size of an individual in order to avoid pseudoreplication
(Hurlbert, 1984).
To test whether resources are allocated equally among offspring, we calculated the average within-clutch variance for clutches of size two (the sample size for clutches of size three is too small for analysis). We then created a new data set of exactly the same size by randomly allocating individuals to clutches, and again calculated the average within-clutch variances. We repeated this randomization procedure 1000 times and asked whether our observed within-clutch variance was significantly different from that expected by chance.
We tested Charnov and Downhower's
(1995) invariant rule using
data on the mean body size of females for clutches of size one (n =
67), two (n = 60), and three (n = 35). This enabled us to
test Equation 1 for {i,j} = {2,1} and {3,2}. We estimated confidence
intervals for (Imax i — Imin
i) / (Imax j —
Imin j) by the bootstrap with 1000 resamples. A
problem with using range as a statistic is that the sample range converges
slowly from below on the true range with increasing sample size. To control
for this in calculating the ratio in Equation 1, we used the same sample size
in both the denominator and numerator (i.e., the smallest sample size of the
two, n = 60 for {i,j} = {2,1}, and n = 35 for
{i,j} = {3,2}). By this means we obtained estimates of the mean and
95% confidence intervals of the Charnov and Downhower ratio.
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RESULTS |
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Mine size and clutch composition
The 158 clutches of wasps that we reared in this experiment were of five different types: single male clutches, and female clutches containing clutches of one to four females. The numbers of each, and the average size of the mine at the time of oviposition, are shown in Figure 1. In analyses of the effect of mine size on clutch composition, we first controlled for differences in clutch size across the different experimental units (sleeve effects). We also tested the interaction terms between mine size and sleeve, but as none even approached significance they are not reported further below.
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Male clutches were recorded from smaller mines than female clutches
(2(1) = 7.41, p <.01, n = 158)
when female clutches of all sizes were included in the analysis, and there was
also a strong sleeve effect (2(8) = 40.59,
p <.001). However, as Figure
1 suggests, there was no difference in the size of mines that gave
rise to solitary male and solitary female clutches
(2(1) = 0.007, p >.1, n = 86;
controlling for a significant sleeve effect, 2(7) =
18.22, p <.05) and hence the difference between the sexes is due
to female clutches containing more than one wasp. Considering only female
clutches, larger clutches were produced on bigger mines
(F(1,83) = 5.57, p <.05,
r2 =.06; sleeve effect not significant,
F(7,76) = 0.43, p >.05) though the regression
explained only a relatively small fraction of the variation.
The average size of individuals emerging from different clutch types are shown in Table 1. Females were larger than males (F(1,109) = 9.41, p <.01) but neither male nor female size was influenced by mine size (F(1,49) = 2.62 and F(1,46) = 0.26, respectively). The effect of clutch size on body size was significant in females (F(1,47) = 12.88, p <.01; a factor we controlled for in the analysis above). Sleeve effects were significant for females but not males (F(6,47) = 29.51, p <.01 and F(6,44) = 0.26, respectively).
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Mine age and clutch composition
Of the 300 small mines included in this experiment, parasitoids emerged
from 40 (13%), a fraction that did not differ significantly among treatments
(2(2) = 0.77, NS).
Table 2 shows the proportion of
male clutches found in mines parasitized when young, medium-aged, or old. In a
statistical analysis using treatment and oviposition date as explanatory
variables, a significant interaction term was found
(2(2) = 6.56, p <.05). Inspection of
the data and step-wise deletion to obtain a minimum adequate model showed that
there was a significant bias towards male clutches in the young and old mines,
both absolutely (2(1) = 7.95, p <.005,
Table 2) and relative to the
medium-aged mines (2(1) = 8.40, p
<.005, Table 2); and that
oviposition date was only important for the medium-aged mines where later
clutches were significantly more likely to be male
(2(1) = 11.32, p <.001,
Table 2).
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Tests of the Charnov and Downhower invariant rule
Charnov and Downhower (1995)
assume that resources are equally divided among individuals within a clutch.
If this is true then the within-clutch variance in body size will be small,
and much lower than the overall variance in body size. Our randomization
procedure in which individuals were allocated at random to clutches (within
clutch size classes) allows the relative magnitude of the two variance
components to be assessed. The results for a clutch size of two, using data
collected by West et al.
(1996), are shown in
Figure 2. The average
within-clutch variance in body size (with variance in a clutch of two
calculated as (x1 —
x2)2/4 where x1 and
x2 are the two sizes) was 3.7 x 10-5 (95%
confidence limits ± 1.2 x 10-5, n = 34) which
is significantly lower than the value we obtained from our resampling
procedure (4.5 x 10-4, 95% confidence limits 2.7-6.6 x
10-4, p <.001,
Figure 2). Thus the
within-clutch component of variance in body size is very small compared to the
overall variance in body size for individuals emerging from a clutch of size
two, suggesting resources are shared relatively equally between individuals in
a clutch. We then tested whether resources were shared less equally in larger
clutches. The variance in body size within clutches was significantly greater
in clutches from which three wasps emerged compared with those giving rise to
just two insects (F(1,40) = 28.17, p <.01,
n = 42, Figure 3),
suggesting that resources were shared less equitably in larger clutches.
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In order to test the invariant rule of Charnov and Downhower's
(1995;
Charnov et al., 1995) invariant
rule (Equation 1) we examined the mean body size of females from different
sized clutches and calculated (Imax i —
Imin i) / (Imax j
— Imin j) with bootstrap confidence
intervals. We observed ratios of 0.759 (95% C.I.: 0.601, 0.954) and 0.503 (95%
C.I.: 0.358, 0.681) for {i,j} = {2,1} and {3,2} respectively. The 95%
C.I. for {i,j} = {3,2} includes the theoretical prediction of 0.67.
This pattern in ranges is also reflected by the observed variance in body
sizes: both data collected by West et al.
(1996; Bartlett's test,
2(3) = 19.69, p <.001, n =
106) and the mines collected as part of experiment I (Bartlett's test,
2(3) = 9.42, p <.025, n = 57)
showed that the variance in female body size decreased significantly with
clutch size (Table 1), as
predicted.
Finally, we tested the prediction that mean body size is unaffected by
clutch size. Both data from the mines collected by West et al.
(1996) (Spearman correlation
coefficient, (rs) =.18, p <.05, n =
106) and the mines collected as part of Experiment I (rs
=.90, p <.001, n = 57) showed that female body size was
negatively correlated with clutch size
(Table 1). In these analyses a
nonparametric test was used because the variance in body size changed
significantly with clutch size (see above).
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DISCUSSION |
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The parasitoid wasp A. zwoelferi lays clutches containing eggs of only one sex: males always develop alone in a clutch while female clutches consist of one to four eggs. We carried out experiments in the field to examine the influence of host quality on clutch composition. We found that a combination of host size and age influenced the wasp's oviposition strategy. In addition, we found that the variation in body size both between and within clutches supported the predictions and assumptions of a suite of clutch size models appropriate to organisms that lay only a few eggs per clutch (Charnov and Downhower, 1995
;
Charnov et al., 1995;
Ebert, 1994).
Solitary females were laid in the same size mines as solitary males
(Figure 1), but had larger body
sizes. The smaller size of males is probably a reflection of their faster
development time leading to less efficient use of host resources
(Bryan, 1983). The observation
that females were laid in the same size hosts as males contrasts with a large
number of previous studies where females were laid in larger hosts (though in
species where both sexes are solitary;
Godfray, 1994), presumably
because they gain a larger fitness benefit from increased body size
(Charnov et al., 1981). We have
not been able to test this assumption in A. zwoelferi because
although we have previously estimated the relationship between fitness and
size for females in the field (West et
al., 1996), we do not know where mating takes place, and so have
been unable to estimate this relationship for males.
The positive correlation between the clutch size of female clutches and
mine size is predicted by clutch size theory if larger mines provide more
resources for developing parasitoid larvae
(Godfray, 1987). This has been
shown to be the case for numerous parasitoid species, including several
koinobiont species, like A. zwoelferi, where the host continues to
grow after oviposition (Godfray,
1994; King, 1989).
Body size was not influenced by mine size, but in gregarious species where the
main effect of varying host size is to change the number of eggs laid by the
parent, the residual effect of host size on parasitoid size can be hard to
predict (Godfray, 1994).
In the mine age experiment we found that a greater proportion of females,
and therefore of larger clutches, were laid in medium-aged mines. A possible
explanation for this is that medium-aged mines represent the best quality host
for developing larvae. The age of a host can affect its quality through its
potential to grow and support parasitoid growth
(Kouame and Mackauer, 1991).
For example, parasitizing a young mine may cause it to die early and hence
yield less resources for larvae, while older mines may contain more
differentiated morphological structures which are harder for larvae to
metabolize (Strand, 1986).
Detailed studies are required to examine how parasitoid mortality and growth
rates vary with mine age; such studies would be extremely hard to carry out on
a species such as A. zwoelferi which so far has not successfully been
brought into laboratory culture.
The results of the mine size and mine age experiments have implications for
the interpretation of our previous work examining how the reproductive
strategy of a female should depend on the extent to which she is egg- or
host-limited (West et al.,
1999). Purely host-limited females are predicted to produce the
clutch size that maximizes the fitness return per clutch (termed the Lack
clutch size; Charnov and Skinner,
1984,
1985), and smaller clutch
sizes are predicted as females become more egg-limited. However, clutch sizes
above the Lack value were occasionally observed in the field (about 5% of the
time). The Lack clutch size (three) we predicted was based on a host of
average size. The results of this study suggest that the female wasp modulates
clutch size in response to host size, and so clutches of four or even higher
might be laid on exceptionally large hosts.
Numerous models for the evolution of clutch size, especially in
invertebrates, assume that resources are shared equally between the members of
a clutch. We found some support for this in clutches of size two, where
individuals were more similar in body size to other members of the same clutch
than expected by chance (Figure
2; see Charnov et al.,
1995, for a similar result in a fish). However, resources were
shared less equally in larger clutches
(Figure 3), a pattern that was
also found in a study on another parasitoid wasp, Laelius pedatus Say
(Hymenoptera: Bethylidae), by Mayhew (1997). Increased variability has a
complex effect on optimal clutch size, chiefly determined by the manner in
which fitness declines on either side of the optimum
(Godfray and Ives, 1988). If
the total fitness costs for laying a clutch size larger than the optimum are
less than the costs of laying a smaller than optimal clutch, increased
variation selects for higher clutch size and vice versa. For A.
zwoelferi (and the other species of wasp whose fitness has been measured
in the field), the penalties for the individual of being slightly smaller than
the optimum are greater than the advantages of being slightly bigger
(West et al., 1996),
suggesting that increased variability may select for lower clutch sizes,
though this effect is not likely to be big.
Our results largely support Charnov and Downhower's
(1995;
Charnov et al., 1995) invariant
rule. We found that the variance in body size between clutches decreased
significantly with clutch size (Table
1; see also Mayhew, 1997). Furthermore, our estimate of the
(Imax i — Imin
i) / (Imax j —
Imin j) ratio for {i,j} = {2,3} was not
significantly different from Charnov and Downhower's
(1995) theoretical prediction
of 0.67. In contrast, Mayhew
(1998), also working with
parasitoid wasps, found that the range of body sizes did not decrease as
predicted by this invariant rule. One important difference between the two
studies is that we examined a species that produces single sex clutches while
the species studied by Mayhew
(1998) had mixed sex clutches
where there may be different levels of optimum investment in sons and
daughters. Other possible factors that might contribute to the failure of the
invariant rule include: (1) the assumption that females are
host-limited—field studies on parasitoids suggest partial egg and host
limitation to be most common (Casas et al.,
2000; Driessen and Hemerik,
1992; Ellers et al.,
1998; West and Rivero,
2000; West et al.,
1999); (2) parent-offspring conflict over clutch size, and (3)
inequality of resource share that changes with clutch size (this study and
Mayhew, 1997).
Why exactly does the invariant rule
(Charnov and Downhower, 1995;
Charnov et al., 1995) work? In
their original paper they justify the rule by the observation that it works
remarkably well for a range of possible functions, S(I),
relating offspring size to fitness. We provide an intuitive argument for the
invariant rule using a "rule of thumb" approach, and then show why
this rule of thumb can be justified theoretically. Let total parental
resources be R so that investment per offspring in a clutch of
i eggs is I = R/i. The optimum investment per
offspring is given implicitly by I* =
S(I*) / S'
(I*) where the prime denotes a derivative
(Smith and Fretwell, 1974).
But what happens when R/i is not an integer? A rule of thumb might be
that as resources accumulate keep the current clutch size and share the extra
resources amongst your i offspring until you have
I* / 2 extra resources and then add another offspring, the
deficit this time being shared by i + 1 offspring (see also
Ricklefs, 1968). This means
that Imin i = I* —
I* / 2i and Imax i =
I* + I* / 2i (and similarly
Imin j and so on) and the Charnov and Downhower
(1995) rule follows
immediately. In fact, the rule follows if the switch point occurs for any
constant fraction of I*, as this means that the resource
spectrum, R, can be divided into intervals of equal length in which
clutch sizes of 2, 3... i, and so on, are produced and, as Charnov
and Downhower (1995) note, this
automatically leads to the rule.
But can this rule of thumb be justified? The precise point at which the
mother should switch from i to i+1 offspring depends on
S(I). In the appendix we show that if we approximate this
function by a second order Taylor expansion the switch point is not at 0.5
(expressed in units of I*) but at
. Clearly this is not equal to 0.5 and
independent of clutch size, as required for the invariant rule, but it is very
close: the switch point between 2 and 3 is at 0.45 and the expression quickly
asymptotes to 0.5 as i increases. Moreover, if the Imin
I, and so on, terms are calculated using these switch points
then the Charnov and Downhower
(1995) rule becomes
(j/i) C where C is a complicated
(dimensionless) function of i that is smaller than, but very near, 1.
For {i,j} = {3,2} (the worst case), C = 0.98. Thus, to
second order, an optimality argument predicts that the Charnov and Downhower
(1995) rule should never be
more than about 2% in error.
To conclude, this article extends our knowledge of A. zwoelferi, a
species that is of more than entomological interest because of its unusual
habit of segregating its offspring in single sex clutches, with solitary male
and gregarious female clutches. In previous papers we have shown that female
fitness increases with body size in the field, that the majority (>95%) of
clutches are equal to or less than the most productive clutch size, and that
if the wasp is host limited a simple Fisherian argument predicting equal
allocation of limiting resources to male and female function predicts a female
biased sex ratio (West et al.,
1996,
1999). Here we have found that
host quality also influences clutch composition, and have examined the
consequences of the wasp being constrained to produce a small, integer number
of eggs per clutch. However, all this work has been based on the assumption
that A. zwoelferi is constrained to produce segregated clutches, with
solitary males, and has not attempted to explain it. We see this as the next
challenge, and are currently addressing this problem by constructing a
molecular based phylogeny which will allow us to map the evolution of
reproductive strategies within Achrysocharoides and related
genera.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
|---|
Calculation of optimum switch point
Without loss of generality, measure resources in units such that the optimum allocation to offspring is 1. Where total resources (R) are non-integer, I < R < I + 1 where i is an integer, the question is whether to lay a clutch of i or i+1 offspring. Let R = i +
i where 0 < i < 1;
the question can be rephrased as whether the extra resources should be divided
such that all offspring receive an extra i/
i resources, or if one more offspring should be laid so that everyone
receives (1 — i) / (I + 1) less
resources than the optimum. If fitness as a function of resource share is
denoted by the function S(.), then at the switch point the fitness of
the two strategies should be the same:
 |
 |
 |
0. Solving explicitly for
i we obtain:
 |
 |
|
ACKNOWLEDGEMENTS |
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Funding was provided by Natural Environment Research Council (NERC) studentships (S.W. and K.F.) and a Biotechnology and Biological Sciences Research Council (BBSRC) Fellowship (S.W.).
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