Behavioral Ecology Vol. 11 No. 6: 670–675
Competitor-to-resource ratio, a general
formulation of operational sex ratio, as a
predictor of competitive aggression in
Japanese medaka (Pisces: Oryziidae)
James W. A. Grant, Chantal L. Gaboury, and Howard L. Levitt
Department of Biology, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Québec,
H3G 1M8, Canada
Operational sex ratio (OSR), the number of potentially mating males divided by the number of fertilizable females, plays a
central role in the theory of mating systems by predicting the intensity of intra-sexual competition and sexual selection. We
introduce a general version of OSR, competitor-to-resource ratio (CRR, the number of potential competitors divided by the
number of resource units), as a potential way of predicting the intensity of competition for any resource. We manipulated CRR
over a broad range (0.5–8) by varying both the number of competing male Japanese medaka fish (Oryzias latipes) and the
number of resources, either females or food items. We tested whether the rate of male–male aggression differed depending on
resource type and whether it increased monotonically or followed a dome-shaped relationship with increasing CRR. The patterns
of competitive aggression in relation to CRR did not differ significantly between resource types. In addition, the per capita rate
of aggression followed a dome-shaped curve; it was low when CRR was less than one, initially increased as CRR increased, was
highest at a CRR of about two, and then decreased when CRR was greater than two. However, competitor number, independent
of CRR, had a significant and negative effect on rate of aggression. We suggest that CRR is a valuable predictor of the rate of
competitive aggression and may be a useful concept for synthesizing ideas about resource competition and monopolization that
are currently dispersed in the separate bodies of literature on mating systems, social foraging and territoriality. Key words:
aggression, competitor-to-resource ratio, Japanese medaka, mating systems, operational sex ratio, Oryzias latipes, resource competition, territoriality. [Behav Ecol 11:670–675 (2000)]
S
eparate bodies of literature currently exist concerning the
competition for food (e.g., Giraldeau and Caraco, 2000)
and mates (e.g., Andersson, 1994). Although there are important differences between mates and other types of resources (see Stamps, 1994), the use of aggression during competition may be influenced by both the benefits and costs of defense, regardless of resource type (e.g., Brown, 1964; Emlen
and Oring, 1977; Huntingford and Turner, 1987). Hence, deliberate comparisons of how animals compete for food and
mates may help promote a general theory of resource competition and monopolization (e.g., Blanckenhorn et al., 1998;
Kokko et al., 1999).
The dispersion of resources in space and time plays a central role in whether resources are economically defendable
(Brown, 1964; Grant, 1993; Warner, 1980). Nevertheless, few
studies have provided strong links between the dispersion of
resources and quantitative measures of competitive interactions, perhaps because of the difficulty of measuring or manipulating the dispersion of resources in the wild (Davies,
1991; but see Davies and Hartley, 1996; Ims, 1988; Monaghan
and Metcalfe, 1985). Perhaps anticipating this difficulty for
mating systems, Emlen (1976) introduced the concept of operational sex ratio (OSR, hereafter defined as the number of
potentially mating males divided by the number of fertilizable
females in a population at one time) as an empirical predictor
of the intensity of intra-sexual competition and the resulting
Address correspondence to J. W. A. Grant. E-mail: grant@vax2.
concordia.ca.
Received 23 August 1999; revised 1 March 2000; accepted 15 May
2000.
2000 International Society for Behavioral Ecology
monopolization of mating opportunities (Emlen and Oring,
1977). OSR has two attractive characteristics: it is easier to
measure than the dispersion of resources or mates and it integrates the often complex ways that members of a breeding
population map on to the dispersion of resources, mates, and
predators in the wild. The recent recognition that OSR is also
directly influenced by sexual differences in potential reproductive rate (Clutton-Brock and Parker, 1992) has only increased the predictive power of OSR as part of a modern theory of mating systems (Kvarnemo and Ahnesjö, 1996; Reynolds, 1996).
OSR potentially predicts the form of intra-sexual competition. By definition, as OSR increases the relative scarcity of
females increases, so the intensity of competition by males for
access to females also increases (and vice versa for females).
Of more interest is the prediction that the frequency and intensity of male aggression (i.e., the interference component
of competition) will increase, while the frequency and intensity of female aggression will decrease, as OSR increases (see
Kvarnemo and Ahnesjö, 1996: Figure 2). Growing evidence
now supports this prediction for both males (Enders, 1993;
Grant et al., 1995; Kodric-Brown, 1988; Souroukis and Cade,
1993; Ward and FitzGerald, 1988) and females (Kvarnemo et
al., 1995). However, this directional prediction about how
OSR affects the rate of competitive aggression should only
hold for a narrow range of OSRs. At extremely high values of
OSR, resource defense theory predicts that aggression will become uneconomical as many males compete for each available female (Brown, 1964; Grant, 1993; Warner, 1980).
Hence, a dome-shaped relationship between the rate of competitive aggression and OSR is predicted.
The heuristic value of OSR is how it scales the abundance
Grant et al. • Competitor-to-resource ratio as a predictor of aggression
671
Table 1
Levels of competitor-to-resource ratio (CRR), the numbers of
competitors (males) and resources (females or shrimp), and
duration of trials for experiments 1 and 2
of one sex to the other. We suggest that a similar approach
may be useful in the foraging competition literature. Competitor-to-resource ratio (CRR, hereafter defined as the number of potentially competing individuals divided by the number of resource units in a patch at a time), a more general
formulation of OSR, might be a useful way to scale the abundance of competitors to resource units within a patch. Such
a general approach may aid in exploring similarities, or differences, between the competition for mates and other resources. At a larger spatial scale, the ideal free distribution
(Fretwell and Lucas, 1970) predicts that CRR will be equal
across patches (i.e., the input matching rule; Milinski and
Parker, 1991).
Our study has two primary objectives. First, we tested whether the rate of competitive aggression in relation to CRR differed either qualitatively or quantitatively depending on
whether males competed for mates or food. Second, we used
a broad range of CRR (0.5–8) to test whether the rate of competitive aggression increased monotonically with increasing
CRR or followed a dome-shaped relationship as predicted by
resource defense theory. We used Japanese medaka as our test
animal because males compete aggressively for access to females (Grant et al., 1995; Hamilton et al., 1969; Howard et
al., 1998) and both sexes compete aggressively for food (Bryant and Grant, 1995; Robb and Grant, 1998). Individuals shoal
and mate daily and synchronously at dawn (Grant et al., 1995;
Howard et al., 1998). Hence, OSR likely varies widely in nature, depending on the sex ratio of a shoal at a particular
time and place.
CRR
a
METHODS
No. of males
No. of females
Trial
per trial or
duration
shrimp every 30 s (min)
Manipulating CRR via resource number
0.5
4
8
0.67
4
6
1
4
4
1.33
4
3
2
4
2
4
4
1
2
2.5
4
5
8
16
Manipulating CRR via competitor number
2a
2
1
4
4
1
6
6
1
8
8
1
8
16
24
32
Manipulating competitor number independent of CRR
1
2
2
1
4
4
1
6
6
1
8
8
a
2
2
1
2
4
2
2
6
3
2
8
4
4
4
4
4
8
8
8
8
Because these trials were identical, the data were collected once
and used in both analyses.
General
The Japanese medaka were purchased from a biological supply company. Fish were kept in mixed-sex stock tanks (60 ⫻
30 ⫻ 30 cm) maintained at 30⬚C on a 13:11 day:night photoperiod (lights on at 0800 h). The tanks each contained dechlorinated Montréal tap water, approximately 40 fish, an undergravel filter, gravel to a depth of 3 cm, an aquarium heater
and were covered by a glass lid. The fish were fed to satiation
several times per day to promote egg production by females.
Experimental tanks were similar to stock tanks except the
top of each was covered by an aquarium light and a piece of
black Plexiglas. An 8 mm hole was drilled through the Plexiglas lid to allow the introduction of food via an eye dropper.
During experiments, we also established a tank containing 20
actively reproducing females. Females with eggs attached to
their abdomens (i.e., that had spawned earlier that day) were
transferred from the stock tanks to the female tank. To ensure
that these females continued reproducing, we introduced five
males into the female tank daily from 1130 to 1630 h.
Experiment 1: manipulating CRR via resource number
An experimental group comprised four males competing for
food or mates at six different levels of CRR (0.5, 0.67, 1, 1.33,
2, and 4) in a repeated-measures design. The food consisted
of 32 previously frozen (defrosted) brine shrimp (Artemia
sp.). To achieve the desired levels of CRR, eight, six, four,
three, two, or one shrimp, respectively, were dropped simultaneously into the tank every 30 s. Hence, as CRR increased,
the duration of the feeding trial also increased (Table 1). To
achieve the desired levels of CRR for mates, eight, six, four,
three, two, or one female were captured from the female tank
and transferred to the experimental tank. The duration of the
mating trials was matched to the duration of the feeding trial
for the same level of CRR. To ensure that CRR remained constant throughout a mating trial, females that had spawned
(those with a clutch of eggs attached to the abdomen) were
replaced by an unspawned individual from the female tank.
At least one female spawned in 59 out of 90 trials. Videotaping
began 30 s after the females were added to the tank at the
beginning of a trial, ceased during the replacement of
spawned females, and resumed 30 s after the replacement female was added.
A series of trials with each particular group of males lasted
6 days. On day one, four males were captured from a single
stock tank and transferred to an experimental tank. The objective of day one was to ensure that all males were feeding
comfortably in the tank; fish were fed once in the morning
and once in the afternoon. To cue the males that a trial was
about to begin, the air was shut off and the aquarium light
turned on. The 32 shrimp were added from above, suspended
in drops of water containing one to eight shrimp. A new drop
was added only after all the previous shrimp were eaten. Four
females were introduced after the morning feeding, but were
removed during the afternoon feeding and at night.
On days two and three, males were given experience with
the two extreme levels of CRR (i.e., 0.5 and 4). In the morning, the fish were subjected to one of the two levels, chosen
at random, first for mates then for food. The fish were then
exposed to the other level for mates. Trials involving mates
were always conducted between 0900–1130 h, because Japanese medaka typically spawn in the morning (Hamilton et al.,
1969; Howard et al., 1998). The other food treatment was
given 3–5.5 h after the first to ensure that fish were hungry.
On day four, we randomly selected two of the six levels of
CRR and repeated the general procedure of days two and
three. These trials were videotaped for later analysis. We repeated this procedure on days five and six, until each group
of males had received all levels of CRR once, for both food
and mates. At the end of day six, the four males were trans-
Behavioral Ecology Vol. 11 No. 6
672
air shut off and lights turned on), and (2) a wide range of
CRR for both food and mates. On day one, the males were
exposed to a CRR of one, by transferring the required number of females to the experimental tank for 8 min. Immediately following the removal of the females, the males were fed
the appropriate number of shrimp every 30 s to create a CRR
of one. Each feeding trial lasted as long as needed to ensure
that the group of males were given a total of eight shrimp/
male (Table 1). After the feeding trial, one female was added
to the experimental tank for 8 min to create the highest CRR
for that group size (Table 1). In the afternoon, the males were
fed one shrimp every 30 s (i.e., the highest CRR for that group
size) until a total of eight shrimp/male were delivered. On
day two, the procedure was repeated except males received
the highest level of CRR first. Day three was identical to day
one.
Data were collected on days four and five. On day four, the
groups received two randomly selected levels of CRR. The procedures were identical to training except females were removed after spawning and replaced by a new female, as in the
first experiment, and the trials were videotaped. For group
sizes four, six, and eight, the males received the final level of
CRR on the morning of day five. H.L.L. completed five replicates for group sizes two, four, and six and six replicates for
group size eight, between July and September 1997.
Data analysis
Figure 1
Per capita rate (mean ⫾ SE, n ⫽ 15) of (a) aggression when
competing for access to either mates or food for the first 2 min of
each trial, and (b) courtship by four male Japanese medaka in
relation to CRR.
ferred to a tank for used fish and were not used again. A total
of 15 groups of four males were used. Experiment 1 was conducted by C.L.G. from June to October 1995.
Experiment 2: manipulating CRR via competitor number and
competitor number independent of CRR
To extend the upper range of CRR, we also manipulated the
number of males (two, four, six, or eight) competing for food
or mates that arrived one at a time (i.e., CRR ⫽ two, four, six,
or eight) while monitoring the aggressive behavior of the
competitors (Table 1). In addition, we tested whether there
was an effect of competitor number, independent of CRR, on
the rate of competitive aggression by allowing groups of two,
four, six, or eight males to compete for food and mates at two
levels of CRR: one and two (Table 1). To minimize the number of fish used in experiment 2, the CRR manipulation trial
and the competitor number manipulation trials listed in Table
1 were conducted together as one experiment. For example,
a group size of four fish would receive a CRR of one, two, and
four in random order. Group size two received only two levels
of CRR, one and two, because the data for two males competing at a CRR of two were used in both analyses (see below).
Experimental tanks and general procedures were as described for experiment 1. On day one, males were selected
from a stock tank to form a group of two, four, six, or eight
and transferred to an experimental tank. During the first 3
days, each group of fish was trained to expect: (1) food and
mates to arrive shortly after the presentation of the cues (i.e.,
The behavior of interest was scored from the video recordings. The most common agonistic behavior was ‘‘chasing,’’ defined as a short unidirectional burst of increased swimming
directed at another individual (Grant et al., 1995). We did not
record the rare occasions when males chased females. In experiment 1, we also recorded the number of quick circles
(Hamilton et al., 1969), a courtship display characterized by
the male swimming in a distinct, rapid, circular movement
beside the female. This behavior either precedes another
quick circle or an attempt to spawn (Grant et al., 1995).
Because trial duration varied directly with level of CRR in
the first experiment, we tested for any temporal effects by
analyzing both the first 2 min of every trial and the complete
trial. Because both analyses gave very similar results, we present only the data for the first 2 min of each trial. In the
second experiment, we analyzed the first 4 min of each trial;
that is, we analyzed and presented data for the longest period
that was common to all treatments within an experiment (2
min for experiment 1 and 4 min for experiment 2). We used
a repeated measures analysis of variance (ANOVAR) to compare rates of aggression across levels of CRR within groups of
males in experiments 1 and 2. The Huynh-Feldt correction
was used for all tests of within-subjects effects because the assumption of compound symmetry was not always met (Potvin
et al., 1990). We used a two-way analysis of variance (ANOVA)
to analyze the effects of CRR via changes in competitor number. The use of the same data (two males at a CRR of two) in
two different analyses (see Table 1) is potentially problematic.
Because neither analysis was qualitatively changed by the inclusion of these data, we used the data in both analyses.
RESULTS
Effect of CRR via resource number
Level of CRR had a significant effect on the rate of male aggression independently of competitor number for both mates
(ANOVAR: F5,70 ⫽ 4.36, p ⫽ .002) and food (F5,70 ⫽ 2.70, p ⫽
.028). As expected, the rate of aggression was low when CRR
was less than one, initially increased as CRR increased, and
Grant et al. • Competitor-to-resource ratio as a predictor of aggression
673
Figure 2
Per capita rate of aggression (mean ⫾ SE, n ⫽ 5 or 6) of male
Japanese medaka in relation to CRR when competing for access to
either one female or one food item at a time.
then appeared to decrease when CRR was greater than 1.33
for food and two for mates (Figure 1a). When competing for
mates, the apparent decline in aggression at high levels of
CRR was supported by a significant linear (F1,14 ⫽ 16.78, p ⬍
.0001) and quadratic (F1,14 ⫽ 5.24, p ⫽ .038) contrast (Wilkinson, 1990). When competing for food, the apparent decline in aggression at high levels of CRR was supported by a
significant quadratic contrast (F1,14 ⫽ 11.98, p ⫽ .004).
When we included the effect of mates and food in a twoway ANOVAR, there was a significant effect of CRR on the
rate of competitive aggression (F5,140 ⫽ 8.15, p ⬍ .0001). However, the effect of resource type (i.e., mates vs. food) on rate
of aggression was not significant (F1,28 ⫽ 0.64, p ⫽ .43), nor
was the interaction between the effects of resource type and
CRR (F5,140 ⫽ 0.79, p ⫽ .56).
In contrast to the rate of aggression, the per capita rate of
courtship declined with increasing CRR (male-to-female ratio;
Figure 1b; F5,70 ⫽ 3.89, p ⫽ .004). This result was not surprising because the number of females in the tank decreased as
CRR increased. The rate of courtship per female, however,
increased slightly but significantly (F5,70 ⫽ 2.47, p ⫽ .041) as
CRR increased (Figure 1b).
Effect of CRR via competitor number
When competing for one resource unit at a time, the rate of
competitive aggression decreased as CRR increased (Figure 2;
ANOVA: F3,34 ⫽ 13.81, p ⬍ .0001). Although the rate of aggression tended to be higher for food than for mates, the
effect of resource type was not significant (F1,34 ⫽ 2.83, p ⫽
.10), nor was the interaction between resource type and CRR
(F3,34 ⫽ 0.48, p ⫽ .70).
Effect of competitor number independent of CRR
The rate of competitive aggression decreased with increasing
competitor number independent of CRR for values of CRR
equal to one and two (Figure 3; ANOVAR: F3,34 ⫽ 13.54, p ⬍
.0001). The effect of resource type was not significant (F1,34 ⫽
1.73, p ⫽ .20), nor was the interaction between number of
competitors and resource type (F3,34 ⫽ 0.10, p ⫽ .96).
For all group sizes and both resource types, the rate of aggression was higher for a CRR of two than for a CRR of one
(Figure 3; ANOVAR: F1,34 ⫽ 21.48, p ⬍ .0001). There was no
significant interaction between CRR and type of resource
Figure 3
Per capita rate of aggression (mean ⫾ SE, n ⫽ 5 or 6) in relation
to the number of male Japanese medaka when competing for either
(a) mates or (b) food, at two levels of CRR. Open triangles indicate
data that were also included in Figure 2.
(F1,34 ⫽ 0.59, p ⫽ .45) or between CRR and number of males
(F3,34 ⫽ 2.56, p ⫽ .071).
Comparison of experiments 1 and 2
To facilitate quantitative comparisons, the data for both experiments was plotted together in Figure 4. The most noticeable difference between the data sets was the higher rate of
aggression in experiment 1 compared to experiment 2. For
example, for a CRR of four (i.e., four males competing for a
single food item or mate at a time), the only treatment common to both experiments, the per capita rate of aggression
was 1.75 and 0.75 chases per min for experiments 1 and 2,
respectively. While not expected, this difference was probably
related to different observers scoring the behavior of different
fish in different years.
Despite these differences, the combined data (means for
treatments from Figures 1a and 2) were well described by a
single quadratic curve [log10 chases/male/min ⫽ 0.217 ⫹
0.657 log10 CRR ⫺ 1.771 (log10 CRR)2, r2 ⫽ .834, F2,17 ⫽ 42.78,
p ⬍ .00001], providing strong support for the dome-shaped
relation predicted by resource defense theory. The peak in
the quadratic curve was at a CRR of 1.53.
DISCUSSION
The quantitative patterns of aggression in relation to CRR
were remarkably similar regardless of whether males competed for access to females or food. Although a similar pattern
674
Figure 4
Comparison of per capita rate of aggression of male Japanese
medaka from experiments 1 and 2; both axes are logarithmically
transformed.
in aggression versus CRR was expected for both resource
types, the similarities in the absolute levels of aggression were
not necessarily expected, and were likely the result of the particular experimental conditions. Like previous studies that
have manipulated OSR (Enders, 1993; Grant et al., 1995; Kodric-Brown, 1988; Kvarnemo et al., 1995; Souroukis and Cade,
1993; Ward and FitzGerald, 1988), our data showed an increase in aggression as CRR increased from 0.5 to two. When
the resource was females and CRR was less than one, each
male courted a separate female, so the rate of courtship was
high and the rate of aggression was low. Aggression was presumably uneconomical because any time spent chasing other
males was time away from courting females or searching for
food. As CRR increased towards two, multiple males increasingly competed for the same female or food item, resulting
in higher per capita rates of aggression and lower per capita
rates of courtship. While male competition intensified, by definition, as CRR increased beyond two, the form of competition shifted from contest to scramble as reflected by the lower
rate of aggression. Once again, the use of aggression was presumably uneconomical because of the high cost or ineffectiveness of chasing away so many potential competitors. At low
and high levels of CRR, the behavior of male medaka is aptly
described by Nicholson’s (1954) original description of scramble competition: ‘‘the kind of competition exhibited by a
crowd of boys striving to secure broadcast sweets.’’
A decrease in aggression at high population densities has
been widely documented for fish defending territories in the
wild (e.g., Jones, 1983; Kawanabe, 1969; Warner and Hoffman, 1980) and the laboratory (e.g., Chapman and Kramer,
1996). Nonterritorial fish seem to take advantage of this effect
by intruding on territories in schools to gain access to food
(Barlow, 1974; Robertson et al., 1976).
Our data provided strong support for a dome-shaped relationship between rate of aggression and CRR. Emlen and Oring (1977: Figure 2) recognized that resource defense might
decline at extreme values of OSR, when females arrive asynchronously on the breeding ground. Nevertheless, Emlen and
Oring are often misquoted as predicting a monotonic increase
in aggression with ever-increasing OSR. Hence, any decline in
aggression with increasing OSR is often taken as a contradiction of their theory (e.g., Davis and Murie, 1985; Michener
and McLean, 1996; Tejedo, 1988). In all three cases, however,
aggression declined at extremely high values of OSR (12.3,
46.3, and 250, respectively), that would appear to fall on the
‘‘right-side’’ of our dome-shaped curve. These apparent ‘‘con-
Behavioral Ecology Vol. 11 No. 6
tradictions’’ emphasize the need for quantitative descriptions
of how OSR influences competitive aggression across a broad
range of OSRs and taxonomic groups.
The per capita rate of aggression was highest at a CRR of
about two when, on average, two males competed for each
female or food item. Two individuals competing for one resource unit is well described by animal contest theory (e.g.,
Parker, 1984). The hawk-dove model predicts that hawk will
be an ESS for a CRR of two if the value of the resource is
greater than the cost of injury (Parker, 1984). In general,
therefore, one might expect to see contest competition whenever CRR equals two and the resource is valuable. However,
there appear to be no models predicting the use of aggression
when three of more individuals are competing (i.e., an n-person game; Parker, 1984). The actual CRR where aggression is
most intense or frequent will likely vary and depend on the
value of the resource, the relative competitive abilities of the
contestants, and characteristics of the species, such as mobility
and degree of weaponry. For example, aggression by giant
danios (Danio aequipinnatus) defending a localized food
source peaked at the relatively high CRR of six (Chapman
and Kramer, 1996), presumably because the intruding zebrafish (D. rerio) were considerably smaller than the defender.
Like OSR, CRR is a ratio and suffers from the same statistical limitations of other ratio variables (Green, 1979; Sokal
and Rohlf, 1995). Perhaps the most serious problem is that
CRR is derived from two separate and important variables: the
numerator, number of competitors, and the denominator,
number of resource units. The effect of resource number and
competitor number are illustrated in Figures 1a and 2, respectively. However, the rate of aggression also decreased with
increasing competitor density independent of CRR. In contrast, population density had no independent effect of OSR
on competitive interactions in sand gobies, Pomatoschistus
minutus (Kvarnemo et al., 1995). Further study will be needed
to determine whether population density is simply used as a
cue to assess CRR or if the optimal level of aggression decreases with population density independent of CRR. The potential complications of disentangling the independent causal
effects of competitor density and CRR, however, should not
detract from the predictive power of CRR.
As with OSR, measuring CRR in the field will not always be
easy. While it is relatively straightforward to measure the number of eagles fighting for access to a salmon carcass or the
number of hermit crabs competing for an available shell, it is
less obvious how one would calculate the CRR of ungulates
grazing on a prairie. To paraphrase Emlen and Oring (1977),
while the practical problem of measuring CRR is important,
it is a separate issue that should not detract from its heuristic
value in understanding or predicting the degree of competitive aggression.
Our study suggests that CRR may have considerable heuristic value as a predictor of the form of animal competition,
regardless of resource type. Just as OSR is a better predictor
of the intensity of sexual selection than the overall population
sex ratio (Emlen and Oring, 1977), CRR should be a better
predictor of the intensity of competitive aggression than the
overall abundance of competitors and resources. For example,
the rate of aggression varied markedly among levels of CRR
in experiment 1, despite a constant overall abundance of competitors and food. When measured at a small spatial and temporal scale, CRR appears to be a useful predictor of the rate
of competitive aggression (also see Grant et al., 1995;
Lawrence, 1986). Perhaps the simplest way to estimate CRR is
to measure the average number of individuals competing for
each resource unit in a patch.
Just as OSR has been a valuable concept for structuring
thinking about mating systems and sexual selection, CRR may
Grant et al. • Competitor-to-resource ratio as a predictor of aggression
be a useful tool for synthesizing ideas about resource defense
and monopolization (e.g., see Blanckenhorn et al., 1998) that
are currently dispersed in the separate bodies of literature on
social foraging (e.g., Giraldeau and Caraco, 2000), mating systems and sexual selection (Emlen and Oring, 1977; Kvarnemo
and Ahnesjö, 1996; Reynolds, 1996), and territoriality and social systems (Brown, 1964; Lott, 1991). The ideal free distribution has already been used in this way to predict the distribution of individuals across patches, whether competing for
food, mates, or shelter (Milinski and Parker, 1991). While the
ideal free distribution predicts the CRR across patches, CRR
predicts the form of competition, and perhaps the degree of
resource monopolization, within a patch.
We thank Jason Praw and Stacey Robb for help in the laboratory, Mike
Bryant for initiating our medaka research, Wolf Blanckenhorn for
helpful discussion, and David Westneat and two anonymous reviewers
for insightful comments. This research was financially supported by a
Research Grant from NSERC to J.W.A.G.
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