Behavioral Ecology Vol. 11 No. 4: 429-436
© 2000 International Society for Behavioral Ecology
Energetic dynamics and anuran breeding phenology : insights from a dynamic game
Department of Zoology, Center for Dynamic Modeling, University of Florida, 223 Bartram Hall, PO Box 118525, Gainesville, FL 32611-8525, USA
Address correspondence to S. J. McCauley, 830 N. University, Department of Biology, University of Michigan, Ann Arbor, MI 48109, USA. E-mail : mccaule{at}umich.edu .
Received 24 August 1998; revised 22 October 1999; accepted 20 January 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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We designed a dynamic optimization model to examine anuran-breeding phenologies. We evaluated the fitness consequences for males adopting one of four alternative strategies : calling, satelliting, foraging, or hiding. Various factors potentially influence male behavior, including energy reserves, predation risk, cost of calling, probability of finding food, distribution of male energy states in the population, and probability of surviving to another breeding season. We manipulated these parameters to determine how strongly each affects breeding phenology and chorus structure. Manipulating parameters related to the energetic costs and benefits of individual decisions, we generated the three basic patterns of anuran breeding phenology : explosive, continuous, and prolonged breeding with episodic chorusing. Increasing the probability of successful foraging caused a shift from an explosive pattern to a prolonged, episodic chorusing pattern. Decreasing the calling cost resulted in continuous chorusing. Our model predicted that satelliting will be a rare strategy adopted by individuals with relatively low energy reserves. Additionally, individuals adopting the satellite strategy should alternate among satelliting, foraging, and calling as their energy reserves fluctuate. Our results suggest that energetic costs of reproduction and resource limitation may be crucial factors influencing the phenology of anuran chorusing. We propose that under varying conditions of resource availability, male decisions are the consequence of two strategies : a starvation minimization strategy and an energy-state maximization strategy.
Key words: alternative mating strategies, anuran breeding, breeding phenology, chorusing, dynamic optimization modeling, leks.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Temporal patterns of anuran breeding activity are highly variable between and occasionally within species. This level of variation makes anurans an especially suitable system for testing hypotheses about ecological and evolutionary forces affecting reproductive strategies. Anuran breeding seasons can be generally classified as either explosive or prolonged. Although the length of the breeding season actually represents a continuum, those animals that breed for 1-14 days are generally considered explosive breeders, whereas prolonged breeders may breed anywhere from 1 month to throughout the entire year (Wells, 1977
). Whereas
explosive breeding seasons typically consist of continuous calling, prolonged
seasons often involve a series of synchronous calling bouts alternated with
periods of relative quiescence (Donnelly
and Guyer, 1994 ; Green,
1990 ; Tejedo,
1992 ; Wagner and Sullivan,
1992). However, a few species of prolonged breeders have
continuous chorusing throughout their entire breeding season. Continuous
chorusers include species in which individual male participation is also
continuous (Given, 1988) and
species in which individual males have abbreviated chorus tenures within a
continuous season (Bevier,
1997a ; Murphy,
1994). Although these species have similar seasonal breeding
phenologies, the differences in individual male behavior suggest that the
factors influencing the development of continuous chorusing may vary between
species. Understanding this variation will help us explore the general
mechanisms important in structuring reproductive strategies.
Anuran breeding patterns have received significant theoretical and
empirical attention, and several hypotheses have been proposed to explain the
existence of prolonged and explosive breeders both within and among species.
For many explosive breeders, the length of the breeding season may be limited
by environmental conditions and the availability of suitable breeding sites
(Sullivan, 1982b ;
Wells, 1977). Empirical and
theoretical work also suggests that explosive breeding may be the result of
increased predation pressure on a population
(Lucas et al., 1996 ;
Woodward and Mitchell, 1990),
or it may serve to decrease egg and tadpole cannibalism by conspecifics
(Petranka and Thomas, 1995).
Finally, empirical evidence suggests a trade-off between the level of energy
investment in calling on a single night and explosive or continuous chorusing
patterns (Bevier, 1997a).
Several hypotheses have been proposed to explain the episodic bouts of
calling by prolonged breeders. For example, calling periods may be associated
with specific environmental conditions, such as rainfall
(Green, 1990). In other
species, hormonal cycles produce episodic breeding activity
(Obert, 1977). In addition,
because calling is typically considered energetically expensive (reviewed in
Pough et al., 1992 ;
Taigen and Wells, 1985 ;
Taigen et al., 1985 ;
Wells and Taigen, 1989), males
may periodically cease calling to conserve energy
(Grafe, 1997 ;
Grafe et al., 1992 ;
Schwartz et al., 1995). The
relative importance of these factors may differ between species or
populations.
We constructed a dynamic optimization model to explore the selection pressures that may have been important in the evolution of existing reproductive strategies. It is difficult to manipulate breeding phenologies experimentally or to obtain historical information on factors that contributed to the evolution of these reproductive strategies. Modeling these conditions allowed us to explore outcomes of multiple ecological and social forces and how they interact to produce a species' or a population's breeding phenology. Our model assumed an environment in which all days were equally suitable for breeding in order to evaluate explicitly whether energetic constraints could generate episodic or explosive calling bouts under environmentally favorable conditions.
In addition to variation in temporal chorusing patterns, we were interested
in factors affecting male behavior within the chorus. Within choruses in which
females have the opportunity for mate choice, males may adopt one of two
alternative mating behaviors. Callers maintain territories and vocalize to
attract females. Other males act as satellites : they remain silent and wait
near callers, and then attempt to mate with females approaching the caller.
The mating success of callers usually exceeds that of satellites, with callers
obtaining up to 92% of the matings in some cases
(Krupa, 1989). Although some
females mate indiscriminately with both satellites and callers, other females
avoid the mating attempts of satellites
(Howard, 1988 ;
Krupa, 1989 ;
Sullivan, 1983).
There is significant inter- and intraspecific variation in the extent to
which males adopt calling and satelliting. Callers have greater mating success
than satellites, but they also face greater costs : calling is energetically
expensive and may attract predators. Males have been observed switching
between the two behaviors within the same breeding season or even in the same
night (Krupa, 1989 ;
Perrill et al., 1982 ;
Sullivan, 1983,
1989). In some populations,
callers are larger than satellites
(Fairchild, 1984 ;
Gerhardt et al., 1987 ;
Sullivan, 1983). In other
populations, there is no size difference
(Lance and Wells, 1993 ;
Sullivan, 1989). These results
suggest that in some populations a male's success for a given behavioral
strategy may depend on his size or energy reserves. The frequency of
satellites may also be positively correlated with the density of callers
(Krupa, 1989 ;
Sullivan, 1982a). However,
some anuran breeding aggregations consist solely of calling males
(Cherry, 1993 ;
Sullivan, 1982b).
We developed a model focused primarily on factors potentially influencing
anuran breeding phenology given the basic breeding system. We were able to
compare our results with those of an earlier model of anuran breeding behavior
(Lucas et al., 1996). However,
we reduced the number of factors involved, and thus we also evaluated the
level of complexity necessary to generate observed anuran breeding phenologies
in those species where weather does not limit the breeding season. We also
explored how predation risk and foraging success affect the structure of the
breeding season. A variety of other factors, including the distribution of
initial male states, the length of the breeding season, and the probability of
a lone male obtaining a mate, were also manipulated to evaluate the
sensitivity of our model.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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We used a dynamic optimization approach to model the sequence of decisions an animal must make to maximize expected lifetime reproductive success. With each decision, the state of the animal is altered, influencing the choices it makes in the future. Dynamic optimization predicts time-specific optimal decisions for each level of a state variable, X, at a given time, t. The model is solved by iterating backward through time, evaluating the fitness outcome of each alternative action given the current state and assuming subsequent behavior maximizes fitness. The result is a matrix of optimal decisions for each X(t). Furthermore, we can use this matrix to describe the trajectory from time 0 to T (the time horizon) for an individual starting at any particular state (Mangel and Clark, 1988
).
We incorporated a game component using the approach outlined by Houston and
McNamara (1987). Their
"playing the field" formulation consists of solving a simple
dynamic optimization model and then using forward iteration to predict the
population distribution of states and behavior given the optimal
state-dependent decision matrix from the model. The population distribution of
states and behavior then determines the benefits and/or costs associated with
alternative behavior, and the simple dynamic optimization model is rerun with
these new parameter values. An evolutionarily stable strategy (ESS) is
established if after several iterations, the new mutant strategy is equivalent
to the population strategy, so that no alternative strategy can successfully
invade the population's strategy (see also
Arak, 1988 ;
Maynard-Smith, 1982).
The simple dynamic optimization model
We assumed that male frogs adopt one of four tactics, indexed as
i, specified by Lucas et al.
(1996) : (1) hide, (2) forage,
(3) satellite, or (4) call. In the basic model, each time interval,
t, corresponds to one night in a potential breeding season of 14
nights (T = 14). Energy reserves serve as the state variable,
X(t), and take 1 of 16 levels. These levels were arbitrarily
designated 1-16. In the basic model, our starting population consisted of an
even distribution of males across states. We assumed that individuals died if
X(t) < 1. In the final time period, expected future
reproductive success (
, which represented a small probability of
surviving to breed in a second season) was a function of state at that time,
T :
 | (1) |
Each tactic is associated with a unique combination of costs and payoffs
(Table 1). We assumed predation
risk to be lowest in frogs that hide, higher in those that forage or
satellite, and highest in callers. Only foragers could increase their energy
reserves, receiving a net increase of 1 energy unit with a probability,
f, of 0.4. In addition, only satellites and callers could mate. A
lone caller had a fixed probability, 0.005, of mating in any time interval. In
the absence of callers, satellites had no probability of mating. As the number
of calling males increased, the mating success of each caller was :
 | (2) |
; Wagner and Sullivan,
1992). This relationship was adapted from Lucas et al.
(1996). However, our model
differed from theirs by not explicitly considering the effects of age and
weather and by incorporating energy state as a variable that could directly
influence caller mating success (e.g., Equations 2 and 4). The addition of
energy-state-dependent caller mating success was justified, as female
preference for long calls or high calling rates, calling patterns that require
increased energy expenditures by males
(Bevier, 1997b ;
Taigen and Wells, 1985), has
been demonstrated in several species
(Gerhardt, 1991 ;
Pass-more et al., 1992 ;
Sullivan, 1983). A logical
extension of this result is that males with higher energy states may be able
to produce calls that are more attractive to females. Satellites intercepted
females, and so increases in the number of satellites decreased each caller's
probability of mating (Figure
1). We assumed that the probability of a satellite mating was :
 | (3) |
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In the initial run of the model, mating success for callers was calculated
as a linear function of the male's energy state, X(t), using the
equation :
 | (4) |
The generalized form of the dynamic programming equation, which maximizes
expected lifetime reproductive success from time t forward given that
X(t) = x, is :
 | (5) |
 | (6) |
 | (7) |
 | (8) |
The dynamic game
We used a game approach to explore male behavior in the model. This
approach assumes an initial distribution of male states and assumes that all
males adopt the optimal state- and time-specific behavior. Based on the
optimal behaviors, we calculated the state transition probabilities between
time interval t and time interval t + 1. The product of the
current distribution of states and the appropriate transition matrix describes
the subsequent distribution of states. Thus, we described population
distributions of states for all time intervals. Parameters that are influenced
by the population were recalculated given the time-specific population
distributions, and the original model was rerun with these new parameters. The
output at the end of each iteration described the "mutant"
strategy with the greatest fitness. The model then assumes that the entire
population adopts this strategy and recalculates the population distributions.
This procedure was continued until the best mutant strategy was equivalent to
the population strategy (Houston and
McNamara, 1987 ; St. Mary,
1997). For our model, this convergence generally occurred after
approximately 10 iterations.
Parameter and sensitivity analysis
Manipulations of parameters were performed with two goals in mind : to
investigate the effect of varying particular parameters on the outcome of the
model, and to test the robustness of the model. An additional purpose of this
model was to compare the results of our manipulations to those of the Lucas et
al. (1996) model, which also
used a dynamic-optimization approach to explore chorusing behavior in anurans.
Consequently, we adapted some of their model's structure in creating our
model, differing primarily at those points where we wanted to direct our
investigations. One of the crucial differences between the models is how they
address the role of energetics in determining optimal strategies and temporal
chorusing patterns. Both models considered how varying the cost of calling can
affect chorusing patterns and optimal tactics, assuming that varying calling
cost may reflect either differences in physiological costs of calling or in
the ability of callers to recoup some of these costs by foraging during the
day. However, our model also considered how the environmental resource base of
a habitat might affect breeding behavior by varying the probability that a
forager will be successful.
We altered the following parameters to explore their effects on optimal
strategies : predation risk, scall ; foraging success,
f and y ; the terminal fitness function, , and the cost
of calling, ccall. To evaluate the impact of predation on
the model's predictions, caller survivorship was varied from 0.99 to 0.81 in
decrements of 0.02. At the low end, these levels of withinchorus mortality
approximate field estimates (Murphy, 1994). We explored the importance of
foraging using two different manipulations. First, the yield from foraging was
varied in integer values from 2 to 15 energy units, and second, the
probability of obtaining food was varied from 0.1 to 1.0 (in increments of
0.1). The effect of the terminal fitness function was examined by setting
terminal fitness to 0, 0.05, 0.1, 0.25, and 0.5 times the terminal state,
K(T). Finally, the cost of calling was incorporated into the model as
a constant, ccall = 2, which was later decreased such that
ccall = chide.
Several manipulations were also performed to test the robustness of the
model's predictions. First, a lone caller's probability of finding a mate was
set to either 0.05 or 0.1. The effect of the breeding season length was
examined by varying the number of available nights from 14 to 21. Finally, the
initial distribution of caller states was established as a normal curve with
mean = 8 and five different variances, SD = 1.2, 2.0, 2.4, 2.6, and 2.8. These
variances fall within a moderate to high range of within-population variation
relative to field measurements of male energy reserves, assessed with glycogen
or fat-body levels (MacNally,
1981 ; Wells and Bevier,
1997). We also ran the model using an initial distribution of
states with mean = 12 and SD = 2.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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By manipulating relatively few parameters (specifically, the probability of finding food and the cost of calling), the model was able to generate all three basic phenology patterns : explosive breeding, prolonged breeding with episodic chorusing, and prolonged breeding with continual chorusing (i.e., explosive). Sensitivity analyses suggested that the qualitative patterns obtained by these manipulations were not affected by changes in other parameters.
Predictions using the initial parameter values
Using the default parameter values, the model predicted a highly
synchronized and restricted pattern of chorusing. Males of nearly all states
called on nights 2-5 (Figure
2A), resulting in a high proportion of the male population calling
on each of those nights (Figure
2B). Males with high initial energy reserves tended to call
continuously, depleting their reserves, whereas males with lower reserves
tended to alternate between calling, satelliting, and foraging. When males
with initially high energy states called for a number of nights and depleted
their reserves, they too entered this alternating pattern. Thus, despite our
assumption that the environment was conducive to breeding over the entire time
frame, chorusing was explosive and occurred only over a few consecutive
nights. Males primarily foraged the remainder of nights.
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Manipulations of the parameter values
Our goal in manipulating parameters was to explore the circumstances under
which explosive versus more extended patterns of reproductive activity were
obtained. We also examined patterns of satelliting and calling for comparison
to the model of Lucas et al.
(1996). We manipulated
predation risk (scall), as well as the probability of
finding food when foraging (f), the terminal fitness (), and the
probability of attracting a mate in the absence of other calling males. For
the purpose of characterizing the predicted patterns of chorusing more fully,
we expanded the time horizon (T) for these manipulations to 21
nights. This change had no effect on the chorusing pattern predicted with the
default parameter values (compare Figures
2B and 3A).
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Changes in predation risk to callers had little effect on the pattern of calling. Over the range of survival probabilities (scall = 0.81-0.99 ; the latter representing decreased survivorship of callers), the predicted pattern of chorusing remained explosive. Increased predation risk to callers constricted the breeding period (4 nights when scall = 0.99, 2 nights when scall = 0.81). When terminal fitness was also increased, predation risks on the order of 0.81 resulted in the suspension of breeding entirely. The occurrence of the satelliting tactic was likewise unaffected. Under all predation regimes, satellites occurred most frequently in the lowest energy state classes (x = 2 and 3 generally, but occasionally values of x as high as 8). This result remained unchanged from the default model predictions (Figure 2A). Thus, predation risk can influence breeding patterns to a certain extent ; however, in the context of our model, it was not sufficient to explain the variation in explosive versus protracted breeding or the frequency of satellites.
The probability of finding food, on the other hand, was a critical
parameter in shifting between predicted patterns of explosive and protracted
breeding. When the probability of finding food was <0.6, explosive breeding
occurred (Figure 3A). However,
with higher probabilities of finding food, chorusing occurred in repeated
bouts over the course of the potential breeding season
(Figure 3B). These patterns
held as the potential breeding season was extended (note T = 21 for
Figure 3). The optimal state-
and time-specific decision for f < 0.6 included satellites in
essentially the same pattern as the default model
(Figures 2A and
3A). However, when f
0.6, satellites were rare, occurring only in the last few nights of the
potential breeding season and only at the lowest energy state participating in
the chorus (i.e., states 2-5, depending on the precise value of f).
Interestingly, the yield attained if food is found (y), did not
affect the breeding phenology and only marginally affected the pattern of
satelliting. We varied the foraging yield from 2 to 15 energy units ; when
yield was 8 energy units, satelliting no longer appeared in the optimal
decision set. Thus, breeding phenologies are predicted to be more explosive
and satellites more common as food limitation increases.
Although we varied several other parameters, cost of calling was the only other parameter that significantly affected breeding phenology. Specifically, for a fixed value of the probability of finding food (f), lower costs of calling (i.e., ccall = chide) increased the duration of chorusing bouts (compare Figure 3 with Figure 4). Even when the probability of finding food was low, the predicted pattern of calling was continuous and more extended (compare Figures 2B and 3 with Figure 4A-C). With no cost of calling, the model predicted continuous chorusing for 12 nights, regardless of the length of the potential breeding season. When the potential breeding season was extended (T = 21) and the probability of finding food was high, chorusing again became episodic (Figure 4D). Our interpretation of these results is that the chorusing generally continues until energy reserves are exhausted. Thus, as the number of energy states increases and the cost of calling is reduced, the number of nights calling may be extended. However, if the breeding season is sufficiently long and the probability of finding food is high, males alternate synchronously between calling and foraging. Furthermore, when there is no additional energetic cost of calling, satelliting disappears entirely from the optimal decision set, as would be expected.
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Variation in the initial distribution of male states in the population had relatively little effect on breeding phenology. Generally speaking, with a mean male energy state of 8 in the population, as the standard deviation about that mean decreased, the number of nights chorusing declined (e.g., with SD = 2.0 chorusing was reduced to 2 nights). Conversely, increased variation in male states increased the number of nights on which chorusing occurred, but did not change the qualitative results. This effect was more pronounced when predation risk to callers increased.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Male strategies
Previous models have examined alternative male mating tactics in anurans (Lucas and Howard, 1995
;
Lucas et al., 1996 ;
Waltz, 1982). The model by
Lucas et al. (1996) explicitly
considered energy state in determining the optimal strategy. It predicted that
age and energy state of males participating in the chorus, density-dependent
factors, and weather influence mating strategy. Our findings largely support
these hypotheses, although our model is not as complex. Both models found that
increasing the cost of calling caused males to switch from calling to
satelliting and that individuals foraged as their probability of surviving to
another breeding season increased. Additionally, when the terminal fitness
function equaled zero, satelliting was dropped from the behavioral repertoire.
Lucas et al. (1996) also found
that first-year males did not chorus as often and were more likely to become
satellites than second-year males. Together, these results suggest that the
probability of an individual surviving to another breeding period is a
significant determinant of his mating strategy. Specifically, energetic
constraints may determine male strategies not because males become incapable
of calling but because calling may decrease lifetime reproductive success by
decreasing the probability of an individual surviving to another season.
Breeding phenology
The primary goal of our model was to evaluate what factors affect anuran
breeding phenology. By manipulating only a few parameters related to the
energetics of calling males, our model was able to produce all breeding
patterns observed in anuran reproduction : explosive, synchronized breeding
periods as well as extended breeding periods with either continuous or
intermittent calling.
In our model, the temporal patterns of reproduction remained relatively
stable in response to manipulations of several parameters initially expected
to affect breeding phenology. Varying the probability of surviving to
subsequent seasons had little impact except at extreme levels. When the
probability of surviving was high, reproduction was foregone entirely.
Conversely, when there was no probability of surviving, the length of the
breeding season increased, although it did not occupy all available nights.
The Lucas et al. (1996) model
found that either a high probability of a satellite successfully intercepting
a female or a high risk of predation for callers produced explosive breeding.
This was not found in our model. Although low caller survivorship did condense
the breeding period by a few days, it did not result in explosive chorusing.
Low caller survivorship in our model either produced shorter calling periods
within a prolonged episodic season or reduced the length of an explosive
season, depending on the phenology generated by other factors in the model. In
addition, extremely high caller survivorship, equivalent to that experienced
by foragers or satellites, did not prolong the breeding season.
In contrast, significant qualitative changes in the predicted breeding
phenology of our model were associated with varying the probability of
successful foraging. At low probabilities of finding food (< 0.5), all
reproductive activity was confined to a single, explosive period with most of
the population participating as either callers or satellites. In contrast,
when the probability of finding food was relatively high (f = 0.6),
the breeding season expanded and consisted of multiple chorusing bouts
punctuated by foraging periods, a pattern similar to many prolonged breeders
(Donnelly and Guyer, 1994 ;
Green, 1990 ;
Sullivan, 1992 ;
Tejedo, 1992). These results
suggest that when resources are limited or patchy, other extrinsic factors may
not be necessary for explosive breeding to occur.
Reducing the cost of calling to that of hiding also influenced the temporal
pattern of reproduction. With a low cost of calling, populations with both
high and low probabilities of successful foraging bred synchronously in a
single, continuous chorus. The duration of this chorus (12 days) was
considerably longer than the chorus generated when the cost of calling was
greater (4 days ; Figure 4).
When the potential breeding season was expanded and the probability of
successful foraging was low, the chorus duration remained 12 days. This
precise chorus length may be a function of the magnitude of the maintenance
cost relative to the range of potential energy states in our model.
Nonetheless, these results reflect the qualitative effects of varying the cost
of calling. Bevier's (1997a)
work examining chorus tenure and calling rate in two species of hylids,
Scinax rubra and Scinax boulengeri, supports our findings.
Scinax rubra has a higher call rate, calls for more hours per night,
and presumably has a higher calling cost than S. boulengeri.
Accordingly, S. boulengeri breeds continuously and has much longer
chorus tenures than S. rubra. However, it is also important to note
that in our model, when the potential breeding season was expanded and the
probability of finding food was high, chorusing was episodic and punctuated by
foraging activity despite a low calling cost. This suggests that variation in
resource availability may shape breeding phenologies regardless of the
energetic cost of calling.
Our model suggests that it is the probability of finding food that
determines chorusing pattern rather than energetic constraints produced by low
but reliable foraging yields. Increasing the potential yield to half that of
the highest possible energy state lengthens the breeding season slightly but
does not affect the patterns of explosive breeding at low probabilities of
finding food and prolonged episodic breeding at higher probabilities of
finding food. Murphy's (1994,
1999) studies of the
determinants of chorus tenure in a prolonged-breeding frog, Hyla
gratiosa, support our findings. He found that males that were fed as they
left a chorus returned sooner and stayed in the chorus longer than unfed
males. The amount fed, however, did not significantly affect the timing of
their return or their subsequent chorus tenure. Patterns of resource
distribution may therefore have a greater affect on breeding phenology than
absolute resource abundance. An unpredictable and patchy distribution of
resources may produce an explosive phenology even when prey, once captured,
are highly energetically profitable.
These results suggest two nonexclusive hypotheses about the role of
resource availability in determining the breeding phenology of anuran
populations : a starvation minimization strategy and an energy-state
maximization strategy. In resource-limited or patchy environments, the
probability of starvation increases, and foraging becomes increasingly
significant in determining the lifetime fitness of an iteroparous organism.
Thus, individuals have to forage more to decrease the probability of
starvation. The starvation minimization strategy is to restrict reproduction
to a few days in the potential breeding season when the presence of other
callers increases the probability of reproductive success, and then to spend
the remainder of the potential breeding season foraging. In contrast, if the
probability of a forager increasing its energy state is high and energy state
is positively related to reproductive success, the optimal behavior may be the
energy-state maximization strategy in which calling is interspersed with
foraging. There is considerable evidence that this occurs in some prolonged
breeders as males move in and out of the chorus throughout the season
(Krupa, 1989 ;
Murphy, 1994 ; Sullivan,
1982b,
1992). Under these conditions,
foraging itself is a reproductive activity (Abrams,
1983,
1991).
Our model does not consider the physiological adaptations anurans may
possess to fuel calling under conditions of low resource availability. For
example, wood frogs (Rana sylvatica) and spring peepers
(Psuedacris crucifer) frequently inhabit the same ponds. Both begin
calling in the spring at similar times ; however, wood frogs are explosive, 3-
to 5-day breeders, whereas spring peepers breed for up to 2 months
(Wells, 1977). It appears that
these frogs face a seasonal gradient in resource availability with resources
limited at the outset of the season (Wells
and Bevier, 1997). Spring peepers have substantial lipid reserves
that allow them to pass through the period of limited resources and extend
their breeding season as resources increase. In contrast, wood frogs do not
have lipid reserves and may breed explosively because of constraints imposed
by the interactions of physiology, calling energetics, and a resource-limited
environment (Wells and Bevier,
1997). This example highlights the need to consider not only the
interactions between resource availability and breeding phenology, but also
the adaptations species possess to overcome resource constraints.
Few data exist that would allow us to test the hypothesis that explosive
breeding is more prevalent in resource-limited or unpredictable, patchy
environments. Some anuran species, including Bufo woodhousii and
Bufo americanus, include both explosive and prolonged breeding
populations (Fairchild, 1984 ;
Howard, 1988 ; Sullivan,
1989,
1992). Such species provide an
excellent opportunity for examining the hypotheses developed here.
Additionally, both explosive and prolonged breeders inhabit some permanent
habitats. Comparisons of the degree of resource specialization, foraging
efficiency, competitive ability, and seasonal variations in resource abundance
for these species would allow a critical assessment of the hypothesis that
breeding phenology is related primarily to resource availability.
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ACKNOWLEDGEMENTS |
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This project was the product of a course offered by the Department of Zoology, University of Florida. We thank L.L. Kellogg for his work on the early development of this model. The Department of Zoology provided us access to computer facilities that made this work possible. We thank D. Brazeau, S.D. Peacor, E.E. Werner, and an anonymous reviewer for helpful comments and criticisms. This is the first contribution from the Center for Dynamic Modeling in the Department of Zoology.
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