AMER. ZOOL., 24:407-418 (1984)
Male Reproductive Tactics in an Explosive
Breeding Toad Population1
LINCOLN FAIRCHILD
Department of Zoology, The Ohio State University,
Columbus, Ohio 43210
SYNOPSIS. American toad (Bufo amencanus) males use one of two different reproductive
tactics. Some males are stationary and call. Others are silent and mobile. Based on field
studies, I developed a computer program that simulates the behavior of females and males
to determine the probability of mating success of males engaging the different tactics and
the factors that effect male reproductive success.
Field studies indicate that non-calling males can be successful. Non-calling males were
more numerous and smaller than calling males. Population size changed greatly both
between and within nights. Contact rates for non-calling males were greater than those
for calling males.
The results of the preliminary simulations indicate that male mating success is a function
of the population size and the operational sex ratio. In small populations, contact rate has
no effect on male success. The effect of contact rate on male success has not been tested
in large populations. In large populations, mating success is also a function of the ratio
of calling to non-calling males. Generally, in small populations (n < 20) calling males are
more successful than non-calling males. In large populations (n > 40) the success of noncalling males is equal to or greater than the success of calling males.
alternatives, then the typical strategy must
also
cost more. In some cases, the payoffs
Observations that alternative reproducnot be equal. Animals employing an
may
tive tactics occur in a diversity of taxa have
stimulated the question: "How can differ- alternative to the typical strategy may be
ent strategies be maintained in a popula- merely "making the best of a bad situation?" Rubenstein (1980) argued that, if tion" (Maynard Smith, 1979). This possione tactic was more successful than bility still suggests that the benefits accrued
another, the "losing" tactic would be even- from the alternative are less than those
tually lost. He argued that two reproduc- obtained from employment of the typical
tive tactics can be maintained only if each tactic.
Despite the problems of transferring
is equally successful in terms of the payoffs,
i.e., benefits gained less the costs expended. model functions to the real world, models
In a general mathematical model, he ana- are very useful. Models often represent the
lyzed the various conditions that would lead only reasonable approach to assessing the
to equal payoffs and hence polymorphism effects of variables, which are often unconin reproductive behavior. More recently, trollable in the field. Therefore, I have
Waltz (1982) approached the same ques- developed a computer program that simtion and developed a graphical model based ulates alternative reproductive tactics. The
similarly on the law of diminishing returns. question I address in this report is: "How
Both of these models were based on the does the relative mating success of males
assumption that a dominant or typical employing the different reproductive tacstrategy has potentially greater benefits tics change as simple demographic condiassociated with it than any alternatives. If tions vary?"
My approach differs in two significant
the payoffs are equal, and if the typical
strategy produces greater benefits than ways from previous modelling efforts. First,
I make no assumptions about the costs or
the benefits of employing different reproductive tactics. Indeed, my objective is to
1
From the Symposium on Alternative Reproductive determine the benefits to the employers of
Tactics presented at the Annual Meeting of the Amerthe various tactics. Second, the model is
ican Society of Zoologists, 27-30 December 1982, at
totally mechanistic. By that I mean that I
Louisville, Kentucky.
INTRODUCTION
407
408
TABLE 1.
LINCOLN FAIRCHILD
Breeding population sizes of American toads.
Males
Date
Calling
Noncalling
%
Total
calling
plexed
pairs
24 April
0
0
0
0
0
0
13
I
14
0
25 April
0
4
31
0
26 April
27
0
0
0
0
0
28 April
0
0
1
1
0
29 April
0
0
0
0
0
30 April
0
0
5
5
0
1 May
4
0
0
0
4
2 May
0
0
—
—
—
3 May
12
113
22
4 May
10.6
79
26
94
20
130
10
5 May
13
47
70
10
6 May
18.6
5
14
19
0
7 May
26.3
1
25
3
4
0
8 May
0
0
0
0
0
9 May
The pond was not checked on 27 April. On 3 May,
the pond was checked but not searched.
TABLE 2.
Male population size variation on 4 May.
Time
Calling
Noncalling
Total
57c calling
2130
2230
2300
9
12
11
40
52
70
49
64
81
18.4
18.8
13.6
Only males on the eastern side of the pond were
counted. Most males in the pond were located in this
small region of the pond. Males in amplexus were not
included.
FIELD STUDIES
In order to construct a realistic model,
field studies were conducted on a population of American toads breeding in a small,
man-made pond in Westerville, Ohio. I
surveyed the pond prior to the 1982 breeding season. I checked the pond all nights
except one from 24 April through 13 May.
Each night, I plotted on a pond map the
have simulated the observed behavior of position of each located individual, noting
individuals employing different tactics its sex, whether it was calling or silent, and
rather than cost/benefit functions of the whether it was stationary or moving at the
behavior. Because the actual behavior is time.
modelled, the simulations must be and are
The 1982 breeding season was characbased on an actual system observed in the teristically short (Table 1). Males and
field. Therefore, the results of the simu- females arrived at the pond about the same
lations may be restricted to the particular time. As pairs were found in amplexus prior
system observed in the field.
to any calling activity at the pond, it is clear
American toads (Bufo americanus) were that non-calling males can successfully gain
selected as a model system. They are explo- access to females. Calling activity did not
sive breeders, and within a population, two begin until ten nights after males were first
distinct reproductive tactics are employed found at the pond. Males called for five
(Wells, 1977a; Gatz, 1981a). American consecutive nights. Approximately 95% of
toads are intriguing because mate selection all matings occurred during the first three
studies of this species have not produced nights of calling activity. Even on these
consistent results. For example, in many three nights, most males did not call. In
other anuran species, male mating success fact, on any given night during the breedis directly related to male body size (Wilbur ing season of 25 April-8 May, no more
et al., 1978; Howard, 1978; Ryan, 1980; than 27% of the males present called. After
Gatz, 1981*; Fairchild, 1981; Woodward, the 8th of May, only one male was seen at
1982). Although Gatz (1981a) found mated the pond.
American toad males larger on average
The number of males present at the pond
than unmated males, Kruse (1981) found changed between nights and during each
no difference in the sizes of mated and night. For example, on the 4th of May
unmated males, and Licht (1976) sug- which was one of the more active nights,
gested that American toad matings were the number of males present along the
size-assortative. Although some of these eastern shore, where most breeding activstudies may suffer from small sample sizes ity occurred, increased by 65% within l'/2
or insufficient analyses, any trend in male hr (Table 2). The increase was due primating success with respect to male body marily to an influx of non-calling males.
size is not obvious.
The number of calling males rose slightly
TOAD REPRODUCTIVE TACTICS
over the first hour but then did not increase
despite the substantial increase in non-calling males.
These findings are similar to those of the
previous year. In 1981, the breeding
aggregation was largest on the night of 28
April. There were 294 males, of which only
24 or 8.1% called. As these toads do not
remain in the pond during the day, the
number of toads at the pond must have
changed considerably as they entered and
left the pond during the night.
The pond was not uniformly occupied
by individuals. Landscape topography and
physical barriers afforded only four major
entry points to the pond (Fig. 1). One was
on the eastern shore. A second was associated with a stream flowing into the northeast corner of the pond. A third was associated with the drainage stream exiting the
western shore. The fourth was located at
the southern tip of the pond. During the
first four nights toads were found at the
pond, 76% of all individuals were found
near these four entry sites. Prior to the 4th
of May, only 21% of all individuals were
located along the eastern shore. However,
from the 4th of May on, when most mating
occurred, 85% of all individuals were
located on or off the eastern shore. This
shore represents about 30% of the entire
shoreline around the pond. All located
amplexed pairs on the nights when most
matings occurred were also found along
the eastern shore. Figure 1 shows the net
movement of individuals based on their
distributions over time.
When active, two behaviorally distinct
male classes can be identified: calling and
non-calling males. Calling males are practically stationary, but non-calling males are
very mobile. Calling males were usually
located in the water near the shoreline.
Non-calling males usually swam offshore.
Both types of males initiated contact with
other individuals. Contacts with other
males were usually brief, but occasionally
they escalated into aggressive "wrestling"
as described for other species (Davies and
Halliday, 1979).
Calling males were spaced apart and
rarely encountered one another. On occasion, calling males would leave their calling
409
FIG. 1. Net toad movement in pond. The shoreline
was divided into ten equal intervals indicated by solid
triangles (A) protruding into the pond. Numbers are
the differences in percents of individuals found before
and after 4 May when the breeding population
increased substantially. Arrows indicate movement
patterns. The size of the arrow indicates relative magnitude. Cross hatched areas are buildings.
sites and attack a nearby, passing silent
male. The outcome of these encounters
was very predictable. The silent male would
move off, and the calling male would return
to its calling site and resume calling. Calling males also occasionally initiated contact
with nearby females. Usually, however,
sexual contact was initiated by the female.
In either case, the male would attempt to
mount the female.
Non-calling males initiated contacts with
females and both types of males. The outcomes of observed contacts initiated by noncalling males appeared to depend upon the
type of individual contacted. If the contacted individual was another silent male,
both males swam rapidly away, although
not necessarily in opposite directions. If
the contacted individual was a calling male,
usually the silent male moved off after contact, and the calling male resumed calling.
Sometimes, however, the calling male left
410
LINCOLN FAIRCHILD
s
4
CALLING
-
3
co
Ul
->
<
e
-
1
1
u.
o
K
Ul
CD
5
z
SILENT
I «
2
1
56 08 6 0 6 2 84 66 6 8 7 0 72
SIZE
74 76
(SIL- mm.)
FIG. 2. Male body sizes. All males were measured to
the nearest 0.1 mm with vernier calipers, but are
grouped in 2 mm size classes for illustrative purposes.
The mean size of calling males is 68.99 ± 4.2 mm
SIL(n = 16). Non-calling male mean size was 64.63 ±
3.00 mm SIL (n = 15). SIL = snout-to-ischium length.
1.55 contacts/minute whereas for calling
males it was only 0.43 ± 0.48 contacts/
minute. These contact rates must be
adjusted to reflect opportunity. Offshore
silent males can be approached by individuals in any direction. Calling males, however, have only about half the contact
opportunity, as approaching individuals
come from the pond and not the shore.
However, even if the contact rates of calling males were doubled to reflect the difference in opportunity, non-calling male
contact rates would still be about three
times greater.
Non-calling males may avoid contact with
calling males. As only males call, a calling
male advertises its sex to both females and
non-calling males. Additionally, calling
males tend to be larger than non-calling
males (Student's Mest: / ( 2 9 ) =3.31, P<
0.005, Fig. 2). Because of the difference in
size, however, any contact made by a noncalling male with a calling male that escalates to a physical contest is likely to be
more costly to the non-calling male.
T H E MODEL
and relocated along the shore before
resuming calling. When the calling male
left, the silent male usually remained at the
contact site for a short while before moving
again. If the contacted individual was a
female, the silent male mounted her and
was carried off by her. Finally, if a silent
male contacted a pair in amplexus, he would
occasionally contest the success of the
mounted male. Females can and do solicit
male-male competition as do sea lion
females (Cox and LeBoeuf, 1977) by
remaining in the chorus area where unattached males may contest the mounted male
with some success (Davies and Halliday,
1977, 1979). I have observed upwards of
four males on the back of a single female.
Based on observations of individual males
for 3-5 min periods, it appears that the
rates at which calling and non-calling males
encounter other individuals are different.
Non-calling males encountered other males
at a much greater rate than calling males
did (Student's /-test: /(36) = 4.99, P < 0.001).
The mean contact rate ± one standard
deviation for non-calling males was 2.58 ±
The computer program is long and due
to space constraints cannot be listed here.
I will gladly send the program listing to
anyone who requests it. Because the listing
cannot be included, I describe the salient
features of its operation.
A denned number of calling males were
displayed linearly across the top of a video
screen. A defined number of non-calling
males were displayed in a two-dimensional
array below the calling males. A defined
number of females were displayed linearly
across the bottom of the video screen. The
position of individuals in their respective
arrays was randomly determined.
By varying the number of calling males,
the number of non-calling males, and the
number of females present, I ran simulations in which the operational sex ratio was
0.5, 0.375, and 0.25. The operational sex
ratio is the number of females divided by
the total number of males. To simplify and
standardize the calculation of mating success, the number of females always equalled
the number of calling males. This identity
meant that the ratio of calling to non-call-
411
TOAD REPRODUCTIVE TACTICS
NC d1 SEARCH
360° FOR
NEAR NEIGHBOR
? SEARCH
FOR NEAR
MOVE TOWARD
NEAR C <f
MOVE TOWARD
NEAR NEIGHBOR
SEARCH
FRONT 180°
FOR NEAR
NEIGHBOR
NO
DISPERSE
BOTH NOW
ATTRACTIVE
Fie. 3. Simulation algorithm. NC = non-calling male. C = calling male. See text for further explanation.
ing males varied with the operational sex
ratio. The number of non-calling males was
always equal to or greater than the number
of calling males as was the case in the field
(Table 1). The ratios of calling to non-calling males were 1/3, 3/5, and 1/1 for the
sex ratios 0.25, 0.375, and 0.5 respectively.
For each operational sex ratio, the number
of individuals in the population was varied
by adding individuals to each class such
that the ratio of calling to non-calling males
remained constant for all runs.
There were basically four components
to the simulation (Fig. 3): searching, moving, contact, and interaction.
At the beginning of each turn, silent
males searched for the nearest non-interactive individual within the denned detection distance. The detection distance was
constant. The distance silent males could
detect females was denned as one less unit
of distance than silent males could detect
other silent males. Females in the field
occasionally dove and swam underwater.
Males were never observed to do so unless
carried by a female. I assumed that surface
males could not detect submerged females.
As a silent male moved during a turn, the
search was further restricted to only those
animals in front of the male within a 180
degree arc whose chord was perpendicular
to the plane of movement. This restriction
simply meant that a moving male could not
see individuals behind him. The search
pattern by females was similar but simpler.
They only searched for the closest, noninteracting calling male. This search pattern took into account the fact that male
calls are known attractants to females
(Martof and Thompson, 1958; Blair, 1968;
Sullivan, 1982).
Silent males and females then moved one
space toward the nearest detected individual. If a silent and a calling male were equidistant from another silent male, the moving silent male would always approach the
412
LINCOLN FAIRCHILD
0.6
I
-
0.3
I
CO
<n
o
0,4
II
I
[
-
CO
[
•
0.3
T
T
1
£
1
i
_
I
T
T
T
O
1
1
o-l
0.1
-
MOVES
PER
1-0
0.2
i
1
i
i
TURN
FIG. 4. Effect of moves/turn on male mating success.
The average contact time is directly related to M/T.
Solid circles (•) = calling males. Open circles (O) =
non-calling males. Bars indicate ±1 SE of the mean
of 30 runs. Operational sex ratio = 0.25. In each case,
there were 3 calling and 9 non-calling males.
other silent male. This procedure was based
on the finding that contact rates for silent
males were greater than those for calling
males. If n o near neighbor had been
detected, the silent male would move
towards the nearest, non-interactive calling male. If there were no non-interactive
calling males, then the silent male or the
female, as the case may be, moved in a
random direction. In moving, females
would not land on another female, silent
male, or interacting individual. Silent males
would land on anything except interactive
individuals. The number of moves per turn
for males and females was identical. There
was no reason to assume that males move
at different rates than females.
There were four possible types of contact resulting from movement. Silent males
could initiate contact with other silent
males, calling males, or females. Females
could initiate contact only with calling
males.
Contact constituted interaction and was
maintained for the duration of the turn
regardless of when in the turn it was made.
All interacting individuals became unattractive for the duration of the interaction
and were ignored by searching individuals.
Two types of contact, i.e., female-calling
male and silent male-female, were permanent, representing success by calling and
silent males respectively. The other two
interactive types, i.e., silent-silent male and
silent-calling male, were resolved at the end
of the turn. For silent-silent male contacts,
both males dispersed a defined constant
distance to locations randomly determined. Since silent-calling male contacts
only occurred at the edge of the screen,
where calling males were linearly arrayed,
the possible displacement sites were defined
as the screen side, i.e., the pond. Seventyfive percent of the time, silent males dispersed, and calling males did not, as seemed
to be the case in natural populations. The
other 25% of the time calling males dispersed laterally to the left or right a randomly determined number of spaces up to
a maximum equal to the defined displacement distance. When calling males dispersed, silent males did not. These procedures were based on the observations that
most of the time silent males not calling
males dispersed after contact.
Simulation continued until all females
had been contacted. At the end of the simulation, the number and percent of each
type of male that contacted a female were
calculated. For each defined case, i.e., operational sex ratio and number of total individuals, a total of 30 runs were made. The
average proportions of calling and noncalling males that obtained a female were
calculated and reported as the probability
of mating success.
SIMULATION RESULTS
The probabilities of calling and non-calling males gaining access to females are
functions of the total number of males
present, the operational sex ratio, and the
relative number of non-calling males to
calling males. Increasing the movement
413
TOAD REPRODUCTIVE TACTICS
J-' x
\-
../I
T,
.'I
NUMBER OF MALES
NUMBER OF
MALES
NUMBER OF MALES
FIG 5 Effect of population size on male mating success. A) operational sex ratio = 0.5. B) operational sex
ratio = 0.375. C) operational sex ratio = 0.25. Solid circles (•) and solid curves = calling males. Open circles
(O) and broken curves = non-calling males. Vertical bars = ± 1 SE of the mean of 30 runs. Horizontal dashed
line = probability of any male's mating success if all males used the same tactic.
speed has no effect on male reproductive
success in small populations (Fig. 4). This
assumes that males and females move at
the same rate. Of course, if males and
females moved at different speeds, then
male success would be affected. If males
moved faster than females, silent male success would increase. If females moved faster
than silent males, calling male success would
increase. Since contact was maintained for
the duration of the turn, increasing the
number of moves per turn also increases
the average contact time and hence reduces
the contact rate. When the operational sex
ratio is 0.25, contact rate has no effect on
male success in small populations (Fig. 4).
As the number of males increases, the
probability of calling males gaining access
to females decreases, but that of non-calling males increases. When the operational
sex ratio is 0.5, the probabilities of calling
and non-calling male successes converge
on 0.5 (Fig. 5A). The curves for calling and
non-calling males' success are symmetrical
because there were an equal number of
calling and non-calling males. The point of
equal success is reached when there are
about 35-40 males present. At all other
operational sex ratios, the functions of noncalling and calling male successes intersect.
The point of equal success, or equilibrium,
is achieved when fewer males are present.
When the operational sex ratio is 0.375,
the equilibrium occurs when about 26 males
are present (Fig. 5B). The equilibrium is
reached when 24 males are present when
the operational sex ratio is 0.25 (Fig. 5C).
Asymmetry of these curves is due to the
surplus of non-calling males, as is usually
the case in the field (Table 1). The lower
the operational sex ratio is, the more rapidly calling male success will decline as population size increases. Similarly, the higher
the operational sex ratio is, the more rapidly non-calling male success will increase
as population size increases. Consequently,
the plot of the population size at which
equilibrium of the two strategies occurs as
a function of the operational sex ratio (Fig.
6) is fairly flat over a wide range of operational sex ratios less than or equal to 0.5.
The equilibrium points for the two male
414
LINCOLN FAIRCHILD
of the equilibrium point is fairly flat over
a wide range of operational sex ratios (Fig.
6), operational sex ratios may not be very
40 important in the males' "decision" to call
or not. For example, if the population consisted of less than about 22 males, all males
ALL SILENT
30
should call. But if the population size was
greater than about 26 males, no male
should call. These absolute numbers of
•
20
/
males apply only to the simulations and
cannot necessarily be used for field data.
ALL CALL
Undoubtedly, density, not male population
10
size per se, is the important parameter.
/
However, in simulations, since the video
/
1
1
screen area is fixed, male density is directly
I
I
1
related to the number of males present. It
O.I
0.2
0.3
0.4
0.8
could be argued that males are not able to
OPERATIONAL SEX RATIO
assess density very well. Consequently, some
FIG. 6. Effect of the operational sex ratio on tactics males may fail to switch from calling to
equilibrium. The solid circles (•) represent calculated non-calling. This argument, however, ultior measured equilibria from simulations. Dashed lines mately fails, because given a great enough
indicate estimated equilibria. Below the curve, calling
male success is greater than non-calling male success. change in density, all males should still
Above the curve, non-calling male success is greater. switch strategies. What should be expected
if this argument were true is that a transition period of mixed strategies would exist
tactics at operational sex ratios of 0.25 and as density changed.
0.375 and, therefore also 0.125, occur at
The reason non-calling males exist at low
very nearly the same population size. The densities is probably related to the availposition of the equilibrium points shifts ability of calling sites. Once the available
rapidly for operational sex ratios above calling sites are filled, no further increase
0.375 and presumably below 0.125. The in the number of calling males will be
curve of equilibrium points for operational observed. Even if all locations are equally
sex ratios greater than 0.5 should be the suitable for calling, there are still likely to
mirror image of the function for opera- be a limited number of calling males. Felltional sex ratios below 0.5.
ers (1979), for example, showed that varWhen the population size is large (n > ious hylid males space themselves out. The
40) and when the operational sex ratio is distance between males was acoustically
low (O.S.R. < 0.25), calling male success mediated. Consequently, a given length of
is much lower than non-calling male suc- shoreline can support only a limited numcess (Fig. 5C). In fact, calling male success ber of calling males.
is substantially lower than would be preAt high densities, when theoretically no
dicted by chance alone if all males used the male should call, some males may persist
same tactic. As the operational sex ratio in calling due to the effects of the ratio of
approaches 0.5, the difference in mating non-calling to calling males on male sucsuccess between calling and non-calling cess. As calling males become rarer, calling
males in large populations decreases.
male reproductive success increases (Fig.
Given these results, it is hard to under- 7). This is due to the fact that the few
stand how polymorphism in male behavior females that make it through the array of
could be maintained in a population. At silent males have fewer calling males from
low densities or small population sizes, all which to choose. So the average probabilmales should call, and at high densities no ity of calling male success increases. Simimale should call. Because the relationship larly, because there are more non-calling
of the operational sex ratio to the position males, their average probability of success
so
1
*
415
TOAD REPRODUCTIVE TACTICS
decreases slightly. Consequently, the equilibrium point shifts to the right as the percent of calling males decreases. The "rare
male" tactic does not work for non-calling
males given that females are not attracted
to them.
0.5
«0.4
0.3
DISCUSSION
As found in this study, calling males are
typically larger on average than non-calling males (Davies and Halliday, 1978;
Howard, 1978; Perrill et al., 1978; Gatz,
1981a). The reproductive tactics of males
of different sizes are likely to reflect differences in potential mating success. Large
males that may be either attractive to
females or the likely winners of competitive interactions with other males should
advertise their status. In most anuran
species, advertisement may be accomplished by vocalizations. The calls of the
common European toad, Bufo bufo, for
example, are related to the caller's size,
and the calls of large males inhibit the
approach of smaller males (Davies and Halliday, 1978). In other species, the sounds
of large males are more attractive to
females than the calls of smaller males
(Ryan, 1980; Fairchild, 1981). However,
small males that have neither an attractive
phenotype to females nor the competitive
ability to control resources attractive to
females, may adopt different reproductive
tactics.
Adopting the reproductive tactics of
large males may be costly for small males.
Competition is likely to increase due to the
increased numbers of potential competitors. Because small males are more likely
to lose in competition with larger males,
small males will disproportionately pay the
cost of increased competition. By adopting
alternative tactics, small males may reduce
competition and the associated costs.
Theoretically, small males have another
option. They could delay reproduction to
maximize growth and, hence, later potential reproductive success. Greater reproductive success in the future, however, is
at best uncertain, whereas the present loss
of reproductive success due to delayed
reproduction is guaranteed.
The above arguments are predicated on
o
z
<
0.2
I-
0 -I
I
10
%
15
MALES
20
25
CALLING
FIG. 7. Effect of the proportion of calling males on
mating success. Solid circles (•) and solid curve = calling males. Open circles (O) and broken curve = noncalling males. Vertical bars = ± 1 SE of the mean of
30 runs. Operational sex ratio = 0.25. Total number
of males in all cases = 36.
the assumption that females are either
attracted to large males or to resources
controlled by large males. In some cases,
the assumption is met. For example, Howard (1978) showed that large male bullfrogs, Rana catesbeiana, aggressively
defended large territories in which females
would eventually deposit their eggs. Large,
territorial males mated with more females
than did smaller non-territorial males. The
same may be the case for other ranids that
are also territorial (Wells, 19776).
To accommodate territoriality in the
model I have presented, all we have to do
is add in another factor, namely territory
size. As territory sizes increase, the numbers of surrounding non-calling males
would be spread over a wider area, hence,
density would decrease. The effect of territories, therefore, would be to shift the
point at which both reproductive tactics
were equally successful to the right or to
higher population sizes. The larger the
average territory size was, the greater the
shift would be.
If females preferentially selected large
males and were able to accurately discriminate among available males, the model may
416
LINCOLN FAIRCHILD
not apply. However, as Wells (1977a)
pointed out, in explosive breeding conditions, females may not have the opportunity to exercise whatever preferences they
may have. The longer a female takes to
make her selection, the greater the chances
are that she will be intercepted by a male
not of her choosing.
Throughout I have assumed that once a
female is contacted by a male, both are
effectively removed from the population
and that contact is synonymous with mating success. Davies and Halliday (1977,
1978) reported, however, that large males
can and do displace smaller males in
amplexus, and I have also observed such
attempts in the field. Amplexus is not, however, always contested. Even when
amplexus is contested, the success rate of
displacement attempts may be low (Gatz,
198 li>). Low success rate may be attributed
to the fact that the mounted male has a
decided advantage. The mounted male
grasping the female tightly around her
pectoral girdle has a substrate, i.e., the
female, against which to act whereas swimming males can achieve little leverage. On
one occasion during my field study, four
males were found wrapped around a single
female sitting on shore. I carefully picked
up this ball of toads and released them offshore in deep water. All males were
attached when released. But as males tried
to change position, they fell off the female
and were unable to regain a purchase on
either the female or the remaining
mounted males. The female swam back to
the shore and was immediately mounted
by additional males successfully. Undoubtedly some displacement attempts are successful. Consequently, the model underestimates large or calling male success and
overestimates small or non-calling male
success. Thus the equilibrium point will
shift to the right, i.e., to higher densities,
by a factor related to the frequency and
success rate of displacement attempts.
The problem with all models comes in
the comparison with the "real world." In
this case, the critical question is: "At what
densities will the equilibrium of the two
tactics occur in natural populations?" The
predicted equilibria may occur at densities
or population sizes that greatly exceed
those commonly found in the field.
Although the simulated equilibria occurred
when between 20 and 35 males were present, 200 males could have been entered
into the male array without initial contact
with one another. So the equilibria were
established at relatively low densities or
small population sizes. In fact, natural population sizes on active nights (Table 1) were
2-6 times greater than the predicted population sizes at equilibrium in the simulation studies.
Nonetheless the common field observation is that calling males are more successful than non-calling males (Fellers, 1979;
Howard, 1978; Gatz, 19816). Sullivan
(1982), however, showed that non-calling
Great Plains toad (Bufo cognatus) males were
almost as successful in obtaining females as
calling males were. He noted that calling
males were more likely to retain contacted
females than were non-calling males. Perrill et al. (1978) also found that in green
treefrogs, Hyla cinerea, calling and noncalling males were equally successful in
obtaining females. Unfortunately, no data
on population size for the field data were
presented. Additionally, whenever one can
show that different sized males employ different reproductive tactics and that matings are random with respect to male body
size, one has obtained strong evidence that
the different reproductive tactics are
equally successful, and therefore, an equilibrium exists.
Finally, there are some cases where the
model clearly does not apply. Fellers (1975,
1979), for example, found that calling and
non-calling males existed in the population
of several hylid species. The non-calling
males, however, were positioned nearby
calling males, and both types of males were
more or less stationary. Fellers argued that
calling sites were limited and that non-calling males were more likely to take over
vacated calling sites of successful calling
males than to intercept incoming females.
Once a non-calling male took over a calling
site, the male would call and thereby attract
a female. This situation is qualitatively different from what I have described and simulated for American toads. The success of
417
TOAD REPRODUCTIVE TACTICS
non-calling American toad males is dependent on their mobility and on their interactions primarily with calling males. Their
mobility allows them to chase and intercept
females. Interactions with calling males
disrupt calling activity and sometimes result
in the relocation of the calling male. Both
make it more difficult for females to locate
attractive calling males. The harder it is
for a female to find a calling male, the
longer it will take her. The longer it takes
a female to find a calling male, the more
likely she is to be intercepted by a noncalling male.
In summary, American toad males
employ one of two distinct reproductive
tactics. Some are stationary and call. Others are mobile and do not call. Simulations
indicate that when the operational sex ratio
is less than 0.5, which is typically the case
in natural populations, calling males are
more successful than non-calling males
in gaining access to females when the population size is small. Non-calling males may
exist in small populations due to limited
availability of calling sites. In large populations, however, non-calling males are
more successful than calling males. Even
in large populations, however, a rare calling male will still be successful. Consequently, some males may persist in calling.
Given the naturally occurring changes in
explosive breeding population sizes, these
results can explain polymorphism in male
reproductive behavior. In addition, noncalling males tend to be smaller than calling males. Thus the reproductive tactic that
an individual male employs is a function of
its developmental stage or age. As Rubenstein (1980) pointed out, this also can
explain the existence of alternative reproductive tactics in a population.
ACKNOWLEDGMENTS
This research was supported in part by
an Ohio State University Small Grant. I
gratefully appreciate and acknowledge the
field assistance of G. Thornhill, L. Thornhill, J. Kammer, andj. England. I benefited
greatly from discussions with J. F. Downhower, and I am indebted to A. S. Gaunt,
J. F. Downhower, S. Austad, and R. D.
Howard for their valuable comments and
criticisms of this manuscript. Any errors
that remain are my own.
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