Behavioral Ecology Vol. 13 No. 5: 705-712
© 2002 International Society for Behavioral Ecology
A state-based model of sperm allocation in a group-breeding salamander
Department of Biological Sciences, 1392 Lilly Hall, Purdue University, West Lafayette, IN 47907, USA
Address correspondence to W.E. Harris. E-mail: eharris{at}bilbo.bio.purdue.edu.
Received 13 November 2000; revised 1 February 2002; accepted 17 February 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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We developed a dynamic program of optimal sperm allocation for group-breeding species. Using the small-mouthed salamander, Ambystoma texanum, as a model organism, we considered how spermatophore deposition is affected by sperm reserves, male and female number in breeding aggregations, and time during the breeding season. Parameters for part of the model were based on field data of breeding-pond arrival times for both sexes and on laboratory spermatophore deposition data. Our model included simulations of three different seasonal patterns of female arrival rate: decreasing (as in A. texanum), increasing, and uniform. General predictions are (1) Increased male competitor numbers at breeding aggregations should cause a reduction in spermatophore allocation. (2) Increased female numbers at breeding aggregations should increase spermatophore allocation. (3) The effect of current sperm reserve levels on sperm allocation depends on the seasonal distribution of the mean number of females per male during the breeding season: (3a) If relative female availability decreases over time, males with low sperm reserves should limit allocation early in the season but should deposit maximal sperm loads late in the season; (3b) if female availability increases over time, males with low sperm loads should limit allocation throughout the entire breeding season; and (3c) if female availability is constant, sperm reserves are predicted to have little effect on spermatophore allocation tactics. We discuss model predictions in the context of current sperm allocation theory.
Key words: Ambystoma texanum, dynamic programming, ejaculate evolution, group breeders, mate competition, mating system, salamanders, sexual selection, sperm allocation, sperm competition.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Sperm competition occurs when gametes from more than one male compete to fertilize a female's ova (Parker, 1970
). The form and intensity of sperm competition may depend on
factors such as characteristics of the female reproductive tract and
sperm-storage organ anatomy, male sperm density or total ejaculate volume, and
the propensity for multiple mating by both males and females
(Birkhead and Parker, 1997;
Parker,
1990a,b,
1998). Consequently, a variety
of morphological, physiological, and behavioral adaptations have evolved in
both sexes (Birkhead and Møller,
1992,
1998;
Birkhead and Parker, 1997;
Parker, 1984;
Smith, 1984).
Although sperm are generally small compared to ova, ejaculates in some
species may contain so many sperm (or accessory materials) that male
reproductive success is limited by their production
(Dewsbury, 1982). Empirical
studies in a variety of taxa suggest that males do become sperm depleted
(e.g., fish: Nakatsuru and Kramer,
1982; Warner,
1997; insects: Gage and Cook,
1994; amphibians: Arnold,
1976; Smith-Gill and Berven,
1980; Verrell,
1986; mammals: Dewsbury,
1981). Also, sperm expenditure may be costly because the energetic
expenditure of producing sperm may limit the energy spent searching for mates
(Birkhead and Parker, 1997;
Parker, 1982). Due to these
constraints, males may be expected to economize when allocating sperm to
ejaculates (Parker, 1998).
Two recent game theory models have been proposed that focus on sperm
allocation strategies: Risk models apply to species in which sperm competition
is rare and in which males risk the chance that they compete with another
single male for reproductive access to ova
(Parker et al., 1997);
intensity models apply to species in which sperm competition is common, but
numbers (intensity) of competitors vary among breeding opportunities
(Parker et al., 1996). Under
the assumptions of the risk model (i.e., rare sperm competition), males are
predicted to produce larger ejaculates as the risk of sperm competition
increases. In addition, if sperm competition between two males does occur and
one male has a lower expected reproductive payoff than the other (e.g.,
because of sperm precedence), the disadvantaged male is predicted to allocate
relatively more sperm per ejaculate than the male with the higher expected
payoff (Parker et al.,
1997).
The intensity model of sperm competition
(Parker, 1998;
Parker et al., 1996) yields
different predictions than the risk model. Males are predicted to ejaculate a
small amount of sperm when there are no competitors (i.e., just enough to
fertilize ova), a relatively large amount of sperm when there is one
competitor, and a monotonically decreasing amount of sperm as the number of
competitors increases. The reason for this result is that, as the number of
competitors increases, the reproductive payoff expected from each unit of
sperm because since there are more males competing for the ova (i.e., as
occurs as the number of players increases in a lottery). The predictions
assume that males can assess the number of competitors and that paternity for
a given male is proportional to the sperm he allocates relative to the total
amount of sperm competing for access to ova.
Neither the risk nor intensity game theory models consider all potentially
important components of the fitness consequences of sperm utilization. For
example, the optimal allocation of sperm may depend on the specific sequence
of mating opportunities experienced by the male in species where males mate
multiply and sperm supply is limited
(Galvani and Johnstone, 1998).
The optimal sperm allocation decision at each mating may also depend on
several factors other than competition intensity, such as female quality or
future mate availability (e.g., Gage,
1998; Gage and Barnard,
1996; Shapiro et al.,
1994; Weddell,
1992). For example, larger sperm expenditures may be predicted if
environmental conditions correlate with a reduction in future female
availability or if risk of sperm competition is higher for more reproductively
valuable females (e.g., Gage,
1998; Gage and Barnard,
1996; Shapiro et al.,
1994). These additional factors generate conditions where the
payoff to sperm allocation changes dynamically with the reproductive state
(e.g., sperm reserves) of the male and with time. These issues are addressed
best using dynamic optimization (Mangel
and Clark, 1988).
Galvani and Johnstone
(1998) used dynamic
programming to model sperm allocation based on female quality and probability
of obtaining future mates. They explicitly modeled a finite, depleting supply
of sperm for males encountering sequential mating opportunities. The situation
they modeled is analogous to the sperm competition risk models of Parker et
al. (1997), while
incorporating sperm depletion and mate choice. An important assumption of the
Galvani and Johnstone (1998)
model was that female availability and the level of sperm competition does not
vary over time. Their model predicted that males should allocate fewer sperm
when future mating opportunities are uncertain. Also, they found that sperm
allocation should interact with female quality and female mate choice. That
is, males were predicted to allocate fewer sperm to high-quality females due
to a risk of future sperm competition or sperm rejection. We extend these
previous models and focus our model on sperm allocation in a group
breeder.
Here we present a dynamic optimization model of sperm allocation for
Ambystoma texanum, the small-mouthed salamander, that incorporates
the effects of sperm depletion as well as variation in the mean number of
females per male through time (i.e., operational sex ratio [OSR]; after
Emlen and Oring, 1977).
Pond-breeding urodeles, such as A. texanum, exhibit postnuptial
gametogenesis, such that males begin a breeding season with a full complement
of sperm and do not replenish their supply until after the breeding season
ends (Plummer, 1977;
Verrell et al., 1986). This
property makes the economics of sperm allocation critical to male reproductive
success in this species. Our model differs from that of Galvani and Johnstone
(1998) in that it is
constructed for group breeders (and thus is analogous to sperm competition
intensity models; Parker et al.,
1996) and incorporates competition intensity and different
distributions of the OSR during the breeding season. Seasonal variation in
mate availability is apparent in A. texanum (see below) and may be
characteristic of many species.
Our model explicitly considers sperm supply at each mating opportunity when
predicting the optimal sperm allocation decision. This approach is different
from that of Parker (1998). In
Parker's model, energy allocated to sperm is traded off against energy spent
searching for mates. Thus, total sperm allocated to ejaculates (which
determines paternity in the context of sperm competition) is traded off
against the number of mates a male can obtain. An advantage of our approach
(and that of Galvani and Johnstone,
1998) is that we can examine the time-dependent effect that
variation in sperm supply may have on sperm allocation (as a result of
variation in body size or condition among males for example). Below we first
present field data and laboratory experiments that provide an empirical basis
for several components of the model. We then develop the model and describe
predictions derived from it.
Methods
Study organism
Most ambystomatid salamanders, such as A. texanum, exhibit a
short, intense breeding season in early spring
(Krenz and Sever, 1995;
Petranka, 1998). A.
texanum at our observation pond bred in temporally and spatially discrete
aggregations (
1 m or less in diameter) in vernal ponds that contained
multiple males and at least one female. The bulk of the breeding season lasts
about 30 days (Figure 1; Harris
and Lucas, personal observations). Based on laboratory observations, the
number of spermatophores each male deposits in an aggregation is variable
(mean = 45.6, SD = 15.7, range = 22-85; n = 18 males), and males may
participate in multiple aggregations during a breeding season. These results
are similar to A. texanum spermatophore depositions observed by
McWilliams (1992) in similar
experiments (mean = 73.8, SD = 31.4, range = 23-128; n = 21 males).
In our model we assume spermatophore deposition rates intermediate to these
values (i.e., 60 spermatophores per male per breeding aggregation).
Aggregations last for approximately 2 h with spermatophores deposited during a
shorter period of 0.5-1.5 h (McWilliams,
1992). A. texanum exhibit little courtship behavior
compared to other salamanders (e.g.,
Arnold, 1976). Instead, males
deposit spermatophores on the substrate and females pick up these
spermatophores with their cloaca later. Thus, females mediate male—male
competition through the uptake of spermatophores.
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Dynamic program
We modeled spermatophore allocation decisions in A. texanum using
a state-based dynamic program (Galvani and
Johnstone, 1998; Mangel and
Clark, 1988), with state defined as the number of spermatophores a
male has available at any time during the breeding season. We assume that a
focal salamander chooses how many spermatophores to deposit and that these
decisions maximize reproductive success over the course of a single
reproductive season. Reproductive success, in turn, is determined by the
number of reproductively active females available to the focal male and by
competition with other males for access to the females' eggs. Similar to
Galvani and Johnstone (1998),
we assume that survival rates are not affected by the decision to enter a
breeding aggregation and that there is no fitness carryover from one breeding
season to the next. Under these assumptions, maximization of reproductive
success over the course of a single season is a realistic measure of
fitness.
We divided the breeding season into 10 discrete time intervals, each about
3 days in length. We assume that a male may participate in at most a single
breeding aggregation in any given time interval. Males enter the breeding
season with a finite and non-renewable quantity of spermatophores. The state
variable, X(t), denotes the number of spermatophore units a
male has remaining to deposit at the beginning of time period t. We
assume all spermatophores contain equal amounts of sperm. We assume that males
begin the breeding season with a maximum of 250 spermatophores. Because males
do not deposit spermatophores in the absence of females (Harris and Lucas,
personal observation), we assume that D(t) = 0 [where
D(t) = the number of spermatophore units deposited during
time period t] when no females are present. If females are present,
we model males as choosing to deposit between 0 and 100 spermatophores (in
increments of 10), with the constraint that the male cannot deposit more
spermatophores than he currently has stored at time t:
 | (1) |
).
We model breeding aggregation size by assuming that the number of females
and males at a given aggregation can be approximated with a truncated Poisson
distribution (Pielou, 1969).
The mean encounter rates of females and males are denoted by
f and m, respectively. Male mean
encounter rate was modeled using estimates of the OSR through the breeding
season. Three different distributions were modeled: decreasing, increasing,
and uniform (Figure 2). The
decreasing distribution approximates the pattern of the number of breeding
females per male observed in A. texanum during the breeding season
(Figure 1), and in our model is
generated by a reduction throughout the breeding season in male arrival rate
at individual breeding aggregations. The increasing distribution simulates the
opposite pattern of OSR, a pattern found in species such as A.
talpoideum (Krenz and Sever,
1995; Verrel and Krenz, 1998). The uniform distribution
approximates a constant, low degree of mate availability (1 female per 10
males) such as may occur in species with longer breeding seasons. Because
aggregations likely form around individual sexually receptive females, we
assume the average encounter rate of females per time unit is one over the
entire breeding season (i.e., f = 1 for all simulations).
The tails of the distributions were truncated when the probability of
occurrence of the largest class was < .0001. Thus, the maximum number of
males modeled was 45 for the decreasing and increasing distributions and 30
for the uniform distribution; the maximum number of females used was 9 for all
distributions.
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The number of clutches fertilized during the breeding season measures focal male fitness. The increment in this value for time t will be denoted by W(d, x, f, m, t) when d spermatophore units are deposited and spermatophore state X(t) = x in an aggregation consisting of f females and m males. Thus, the number of spermatophore units expended is the decision variable that will be determined at each state, time, and combination of males and females at the current breeding aggregation.
We assume that females take in sperm from spermatophores at random with
respect to the male that produced them; as a result, the number of selected
spermatophores of a particular male depends only on the proportion of the
total spermatophores that he deposits in a breeding aggregation. We also
assume that each male competitor deposits 60 spermatophores. The number of
spermatophores deposited by the focal male is denoted by d, and
Cm(t) is the number deposited by competing males.
Thus the total current number of spermatophore units selected by females at
time t belonging to the focal male is:
 | (2) |
 | (3) |
x is the change in state resulting from the
current decision, and therefore x + x is the expected
state at time t + 1; Dfm*(t +
1, x + x) represents the optimal spermatophore
allocation decision at time t + 1 (this is a function of the number
of males, m, and females, f, and state, x +
x, at time t + 1), and
WF(Dfm*(t + 1,
x + x), x + x,t + 1)
represents the future reproductive success at time t + 1. The optimal
decision at time t, Dfm*(t,x), can be
solved by maximizing the sum of Equations 2 and 3.
Forward simulation
The dynamic program generates a decision matrix that provides information
about the optimal decision at each combination of state and time, but it does
not provide information about the net results of this decision-making process.
For this we use a forward simulation of the decision matrix
(Mangel and Clark, 1988). A
forward simulation generates conditional probability distributions for each
state variable under consideration in the dynamic program. These may be viewed
as predictions about the distribution of decisions or distributions of states
resulting from decisions made by a population of salamanders.
To initiate the forward simulation at the beginning of the breeding season,
the probability distribution of states must be seeded with initial values
across all states. Thus, P(x, t, f, m) is the probability of
the focal male having x sperm reserves at time t in an
aggregation with f females and m males. For our simulation,
we simulated mean male spermatophore complement at two different starting
complements of spermatophores: 250 (full) and 125 (half). By varying the
starting complement of spermatophores, we attempted to model the effects of
variation in spermatophore supply on sperm allocation decisions (see below).
For the simulation, males start with either complement of spermatophores at
time 0 and the breeding season starts at time 1 (i.e., f = m
= 0 at time 0):
 | (4) |
Mating trials
To obtain data on sperm allocation characteristics in A. texanum,
W.E.H. collected adults during spring breeding migrations in 1998 using a
drift fence of aluminum flashing and pitfall traps. The population is located
in Tippecanoe County, Indiana, USA, near Purdue University. Field data were
used to estimate population sizes and OSR. All animals collected were returned
to the lab, measured, weighed, and stored at 4°C until used in breeding
trials (usually within 24 h).
Breeding trials were conducted in 40-l aquaria containing about 10 cm of well water chilled to 4°C. Males and females were added to the tanks in one of the following sex ratios 1 F:1 M, 3 F:1 M, and 1 F:3 M. In multi-male trials, male salamanders were marked for individual identification by attaching a small piece of colored flagging to their heads using cyanoacrylic glue. Tags did not appear to affect male behavior and were usually shed with skin within 24 h. Spermatophore depositions were recorded for each male. In single-male trials, spermatophores were counted after courtship and deposition; in multi-male trials, mating was audiotaped to record observations of mating behavior and spermatophore deposition.
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RESULTS |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Sperm reserves and seasonal OSR patterns
Dynamic program predictions are summarized in Table 1. Seasonal patterns in the OSR should strongly affect the relationship among sperm reserves, time during the breeding season, and sperm allocation. If the OSR decreases over the course of the season, males are predicted to deposit the maximum number of spermatophores possible if they have high sperm reserves and when many females are present in an aggregation (Figure 3a). As sperm reserve level declines, so too does the number of spermatophores males are predicted to deposit. Near the middle of the breeding season, males are predicted to deposit the maximum number of spermatophores possible (i.e., constrained only by sperm supply or physiological limits), regardless of how many females are present. Similar to predictions of Parker (1998
), males should be more
conservative with sperm allocation as competition intensity increases.
Competition intensity has a moderate influence on male allocation decisions
when the OSR decreases through the breeding season.
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If the OSR increases during the breeding season, males with low reserves are predicted to limit sperm allocation under conditions of high competition for females (low female number and high male number at a breeding aggregation). In contrast, unless there are very few females, males with high reserves are predicted to deposit a maximal number of spermatophores. Surprisingly, the time during the breeding season has little effect on spermatophore allocation in this case (Figure 3b).
When the OSR is uniform throughout the breeding season, spermatophore reserve level and time during the breeding season have only a weak effect on spermatophore allocation (Figure 3c). Males' allocation decisions are usually constrained physiologically and become conservative with sperm allocation only when the number of females is low and number of competitors is high in an aggregation. Surprisingly, when mate availability is constant, competition intensity is predicted to have a relatively minor effect on optimal sperm allocation.
Population profiles from forward simulations
Forward simulations predict different temporal patterns of mean
sperm-reserve state depending on the temporal pattern of the OSR. Sperm
reserves are predicted to decline relatively rapidly during the breeding
season for a species with a decreasing OSR
(Figure 4a). When males begin
the breeding season with few expendable spermatophores (small males compared
to large males), their mean sperm reserve state is predicted to be lower at
all times than it is for males beginning with more spermatophores. Also, mean
sperm reserve state decreases more slowly for small males than for large
males. In contrast, sperm reserves are predicted to decline linearly for large
males when OSR is uniform and decline relatively slowly for large males when
mean OSR increases during the breeding season
(Figure 4a).
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Temporal patterns of variability in sperm reserve level also differ depending on the seasonal pattern of female availability during the breeding season (Figure 4b). In general, variance is a unimodal function of time in season. The location of the peak of this function depends on the pattern of the OSR during the breeding season and therefore the opportunity to expend spermatophores; an early peak in sperm reserve variability characterizes environments with decreasing female availability, and a late peak characterizes environments with increasing female availability. The basis of this pattern is straightforward: males that deposit spermatophores early in the season (i.e., with decreasing female availability) will show a more rapid decline in spermatophore reserves compared to males that delay spermatophore deposition. Males that deposit spermatophores earlier will also show an earlier environment-induced increase in variance in spermatophore reserves because spermatophore production is partially dependent on stochastic variation in the number of males and females found in any given breeding aggregation. Males faced with decreasing access to females are predicted to deposit virtually all of their sperm by the end of the season (Figure 4a), causing a concomitant end of season reduction in the population sperm-reserve variance (Figure 4b). With increasing female availability during the breeding season, males are predicted to delay deposition of spermatophores early in the season, causing a shift in the peak population variance in spermatophore reserves to later in the season. The result of this delay in spermatophore deposition is that some males will fail to deposit all of their spermatophore stores by the end of the season because they are unable to find females (whose arrival is assumed to be a Poisson process) before the season ends. Also, when initial male sperm reserve is low (small males), the corresponding variance is small across the breeding season relative to large males (shown for decreasing OSR males; Figure 4b).
Mating trials
For small-mouthed salamanders, the number of spermatophores deposited was
correlated with male body weight across all three sex ratio treatments
(R2 = .35; p < .03; n = 18;
Figure 5). When treatments were
analyzed separately, however, the correlation was only significant in the high
competition (1 F:3 M) trials (R2 = .74; p <
.03; n = 6). Assuming that body weight is related to sperm stores
(see Discussion), the positive correlation for this trial supports a key
prediction of the dynamic program (Table
1): Males with lower sperm reserves should be more conservative in
sperm allocation when competition intensity is high. We found no significant
effect of sex ratio on average spermatophore production
(F2,15 = 1.45; p = .27; ANOVA;
Figure 6). However, the power
of this test was low (1 - ß = 0.25, for 
= 0.05; effect size = 15
spermatophores), and more data are required to elucidate the pattern of sperm
allocation in response to competition intensity and sex ratio for A.
texanum.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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The results from our model suggest that sperm reserves and time during the breeding season, as well as the temporal OSR pattern, should strongly influence decisions for sperm allocation in group breeders. The reason for this is that mate availability affects future reproductive payoffs expected by males and thus should affect allocation of sperm as a limiting commodity. We also show that the relative importance of sperm competition intensity for optimal sperm allocation is sensitive to the particular pattern of mate availability. This result is intuitive, yet most current models assume that mate availability is constant through time and focus on sperm competition intensity as the main factor affecting sperm allocation decisions. These effects will be most important for species in which these factors are likely to interact, such as species containing males that mate multiply during a short breeding season (e.g., pond-breeding salamanders: Verrell, 1989
; insects with
short adult phases: Engelman,
1970; ground-squirrels:
Schwagmeyer and Parker, 1987;
red-winged blackbirds: Westneat et al.,
1998), although sperm depletion appears to be a common phenomenon
in many taxa (Dewsbury,
1982).
In general, males should be more conservative with sperm expenditure early
in the breeding season compared to late in the season, especially when the
intensity of competition for a given mating is high and expected reproductive
payoff is low. The basis for this prediction is the trade-off between current
and expected future reproductive success. Early in the season future
reproductive success is a large component of fitness, and thus male sperm
allocation should be positively correlated with current expected reproductive
success. Late in the breeding season future reproductive success is
negligible; thus large sperm expenditures on present mating opportunities is
predicted. This is similar to predictions of Galvani and Johnstone
(1998) for conditions when
sperm competition is rare. These results underscore the importance of
evaluating time-based solutions to sperm-allocation decisions.
Our model explicitly considers the effect of sperm supply on sperm
allocation for individual mating events. Forward simulation results indicate
that initial sperm supply has a relatively strong effect on sperm reserve
level during the breeding season and consequently will influence predicted
sperm allocation decisions. Males with lower sperm reserves are generally
predicted to deposit fewer spermatophores in a given set of competitive
states. Our breeding trial results support this prediction: We found a
positive relationship between male mass and the number of spermatophores
deposited across breeding trials (Figure
5). The relationship between male body size and testis size in
salamanders has been documented (Verrell
et al., 1986); thus it is likely that larger males begin the
breeding season with larger sperm stores.
To interpret these results for different species, one must consider the
temporal pattern of sperm depletion and mating opportunity in males. That is,
multiple mating opportunities (resulting in depletion of immediate sperm
reserves) must occur during the period of time required for a male to
replenish sperm supplies. In pond-breeding salamanders (such as A.
texanum) sperm are depleted during a short breeding season and not
replenished until after the breeding season has ended
(Verrell, 1989). Thus, the
relevant time course for sperm depletion is the breeding season itself, during
which males mate multiply and no new sperm are produced.
Results presented here provide a framework to construct predictions
regarding sperm allocation in group breeders and compliment the models of
Parker et al. (1996). Both the
dynamic program and the game theory models make similar sperm allocation
predictions when female availability is uniform through time: Males should
become more conservative with sperm allocation as the number of competitors
increases at a given breeding aggregation. In this case, the effects of sperm
reserve level and time during the season, which we considered in our dynamic
program, are relatively weak. These predictions suggest that both dynamic
programming and game theory approaches generate robust and potentially
complementary insight into this problem when mean females per male is
temporally uniform. However, when female availability changes through
time, males are predicted to allocate much less sperm when their sperm
reserves are low. In contrast, a strong time effect is only evident when
female availability decreases during the course of the breeding season. In
this case males are predicted to allocate much more sperm per mating later in
the breeding season. Empirical studies of sperm allocation are lacking for
group breeders (Parker, 1998),
and therefore more data are needed to determine the importance of factors such
as sperm reserves and mate availability to sperm allocation.
Fundamentally, sperm allocation in group-breeders is a dynamic game. Sperm
allocation tactics in such systems have game aspects in that the payoffs to
males are likely to be frequency-dependent (as discussed in
Parker et al., 1996). Sperm
allocation is dynamic because both environmental conditions and sperm supply
may change stochastically over the course of the breeding season, and these
shifting conditions should be incorporated into a male's sequential allocation
of resources (sensu Alonzo and Warner,
2000; Lucas et al.,
1996). Thus, we see both our dynamic programming model and that of
Galvani and Johnstone (1998)
as necessary steps toward a more complete tool set for asking questions about
evolution of sperm allocation strategies.
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ACKNOWLEDGEMENTS |
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We thank Richard D. Howard for many editorial suggestions and whose encouragement and support made this research possible. We thank the following people for assistance in the field and in the laboratory: Trent Apple, Jason Larsen, Krista Larson, Tara Perez, Erin Smythe, and Robin Wilburn. This research was supported by National Science Foundation dissertation improvement grant 0078744, a grant from the Purdue Research Foundation, and by the Alton A. Lindsey Ecology Fellowship. The experiments were conducted under Purdue Animal Care and Use Committee approval HAR-192.
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