Behavioral Ecology Vol. 11 No. 6: 670-675
© 2000 International Society for Behavioral Ecology
Competitor-to-resource ratio, a general formulation of operational sex ratio, as a predictor of competitive aggression in Japanese medaka (Pisces: Oryziidae)
Department of Biology, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Québec, H3G 1M8, Canada
Address correspondence to J. W. A. Grant. E-mail: grant{at}vax2.concordia.ca .
Received 23 August 1999; revised 1 March 2000; accepted 15 May 2000.
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ABSTRACT |
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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.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Separate 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 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.
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The heuristic value of OSR is how it scales the abundance 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.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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General
The Japanese medaka were purchased from a biological supply company. Fish were kept in mixed-sex stock tanks (60 x 30 x 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.
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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
transferred 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., 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
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.
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RESULTS |
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Effect of CRR via resource number
Level of CRR had a significant effect on the rate of male aggression independently of competitor number of 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 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).
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When we included the effect of mates and food in a two-way 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).
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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 (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.
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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.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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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 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
"contradictions" 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 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.
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ACKNOWLEDGEMENTS |
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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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