Behavioral Ecology Vol. 12 No. 4: 490-495
© 2001 International Society for Behavioral Ecology
Effects of the temporal predictability and spatial clumping of food on the intensity of competitive aggression in the Zenaida dove
a Department of Biology, McGill University, 1205 Avenue Docteur Penfield, Montréal, Québec H3A 1B1, Canada b Department of Biology, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, Québec H3G 1M8, Canada
Address correspondence to J.W.A. Grant. E-mail: grant{at}vax2.concordia.ca .
Received 21 January 2000; revised 31 October 2000; accepted 12 November 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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The spatial and temporal clumping of food influence an animal's aggressiveness during competition. No studies, however, have investigated the effects of the temporal predictability of food and few studies have tested for interactions between the effects of two components of resource distribution on the rates of competitive aggression. We simultaneously manipulated the temporal predictability and the spatial clumping of food to test whether aggression increases as food becomes more predictable in time and more clumped in space. We tested these predictions using wild Zenaida doves (Zenaida aurita) in Barbados because previous work showed marked differences in social behavior between two populations, apparently related to differences in the distribution of food in space and time. There was a significant interaction between the effects of the temporal predictability and spatial clumping of food. As predicted, the rate of aggression increased as the temporal predictability of food increased, but only significantly in the spatially clumped condition. Similarly, as predicted, aggression increased as the spatial clumping of food increased, but only significantly in the temporally predictable condition. In addition, the per capita rate of aggression peaked at intermediate competitor densities in the spatially clumped condition. Differences in rates of aggression observed during experimental manipulations and between the two populations during baseline observations were generally consistent with predictions of resource defense theory.
Key words: aggression, economic defendability, feeding competition, spatial clumping, temporal predictability, Zenaida aurita.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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The study of competitive aggression (sensu Archer, 1988
) has traditionally
been approached from two theoretical perspectives
(Stamps and Krishnan, 1999).
Game theory models (e.g., Maynard-Smith,
1982; Parker,
1984) predict the form and outcome of contests based primarily on
asymmetries between competitors, whereas optimality models primarily predict
the occurrence of territoriality based on whether the net benefits of defense
are greater than the net benefits of a non-aggressive strategy; that is
whether the resource is economically defendable (sensu
Brown, 1964). The economic
defendability of a resource is thought to depend on competitor density and at
least five components of resource distribution in space and time (see Grant
1993,
1997;
Warner, 1980): resource
abundance (mean in an area over a particular time), spatial clumping (variance
in abundance over space), temporal clumping (variance in abundance over time),
spatial predictability (dependability of good sites over time, i.e., the
autocorrelation of resource abundance in space over time), and temporal
predictability (dependability of good times over space, i.e., the
autocorrelation of resource abundance in time over space)
(Davies and Houston, 1984;
Emlen and Oring, 1977;
Grant, 1993;
Myers et al., 1981;
Warner, 1980).
While territoriality has attracted much theoretical and empirical study
(Stamps, 1994), it is but one
form of interference competition, which also includes brief contests over a
single unit of resource, the guarding of ephemeral resource patches, and
dominance hierarchies (Archer,
1988). Nevertheless, resource defense theory, the loose body of
hypotheses concerning the occurrence of territoriality, also accurately
predicts the occurrence of competitive aggression at smaller spatial and
temporal scales. For instance, aggression while competing for ephemeral
resources increases as those resources become more clumped in space
(Grant and Guha, 1993;
Monaghan and Metcalfe, 1985;
Zahavi, 1971), dispersed in
time (Bryant and Grant, 1995;
Grant and Kramer, 1992), and
predictable in space (Grand and Grant,
1994), as predicted by resource defense theory
(Brown, 1964;
Davies and Houston, 1984;
Emlen and Oring, 1977;
Grant, 1993;
Myers et al., 1981;
Warner, 1980). The same
principles predict the strength of dominance hierarchies within groups (e.g.,
Isbell, 1991). Hence, the
concept of economic defendability, that was originally concerned only with the
occurrence of territoriality, can probably be broadened to a concept of the
economic use of aggression during competition.
While many studies have demonstrated the effects of the spatial and
temporal clumping of resources on the frequency of competitive aggression (see
references above), few studies have investigated the effects of the
predictability of resources in space and time. Dominant convict cichlids,
Cichlasoma nigrofasciatum, became more aggressive and monopolized a
greater share of the food when it was more predictable in space
(Grand and Grant, 1994).
However, the prediction (Warner,
1980) that aggression and monopolization of food increase as
resources become more dependable in time (e.g., daily or seasonally) has not
been tested.
Few studies have manipulated resource distribution in the field, while
monitoring the aggressive behavior of the competitors. Notable exceptions
showed that white wagtails (Motacilla alba alba;
Zahavi, 1971) and brown hares
(Lepus europaeus; Monaghan and
Metcalfe, 1985) shifted from scramble to contest competition as
their food was increasingly clumped in space (also see
Davies and Hartley, 1996;
Ims, 1988). Moreover, even
fewer studies have manipulated more than one component of resource
distribution at a time to test for interactions between these variables (but
see Robb and Grant, 1998). In
general, resource defense theory makes predictions about only one component of
resource distribution at a time and assumes no interactions between components
(but see Emlen and Oring,
1977). Hence, its predictions will only be applicable to the
multivariate distribution of resources in the wild if the main effects of each
component overwhelm any potential interactions between components.
Our study simultaneously manipulates the temporal predictability and
spatial clumping of food while monitoring the aggressive behavior of a
population of Zenaida doves (Zenaida aurita) on the island of
Barbados. We chose Zenaida doves as our test species because they show
striking intraspecific variation in aggressive behavior on Barbados. In most
areas, doves establish year-round feeding territories that are defended
against conspecifics. Territorial doves routinely use aggression to exclude
conspecifics from food, but often feed nonaggressively with other avian
species (Quiscalus lugubris, Columbina passerina, Molothrus
bonariensis, and Loxigilla noctis) in mixed aggregations
(Dolman et al., 1996;
Lefebvre et al., 1996). In
contrast, at the grain storage and transport facilities of the Deep Water
Harbour (DWH), Zenaida doves feed in large homospecific flocks with little
apparent aggression (Dolman et al.,
1996). We manipulated the distribution of artificial patches of
food at DWH to test the predictions that the frequency of aggression by doves
will increase as both the temporal predictability and spatial clumping of food
increase.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Study populations
Field observations were conducted at two study areas on the island of Barbados, separated by 9 km: (1) the grounds of the Bellairs Research Institute of McGill University and adjacent Folkestone Park, both in the parish of St. James (StJ); and (2) the Barbados Feeding Mills plant in Deep Water Harbour (DWH), in the parish of St. Michael. The StJ area included a public park and beach, hotel grounds, and the Bellairs research facilities. The study area featured extensive coastal woodland of predominantly casuarina, manchineel, mahogany, and coconut trees that provide the doves with roosting, nesting, and foraging sites (Bond, 1985
). The DWH is a landfill area that includes docking, grain
loading, milling, and storage facilities for a wide range of animal feeds and
grains (Dolman et al., 1996).
This 200 x 200 m area has been cleared of most of its arboreal
vegetation but frequently provides large, ephemeral patches of cereal and
legume spillage as a result of storage and transport operations. Feral pigeons
(Columba livia) are the most frequent heterospecific competitor of
doves at this study area, but are normally in much smaller numbers than Z.
aurita (Dolman et al.,
1996).
At StJ, doves defend year-round territories against intruding conspecifics
and forage most often alone or in monogamous pairs
(Lefebvre et al., 1996). In
contrast, Zenaida doves within DWH forage in large, homospecific flocks of up
to 120 birds, with little apparent aggression.
Premanipulation observations
Our study consisted of three phases: premanipulation observations at StJ
and DWH, an experimental phase in which the spatial clumping and temporal
predictability of food were manipulated at DWH, and postmanipulation
observations at DWH.
During the first 3 weeks of January, 40 adults were caught in walk-in
baited drop traps set throughout the StJ study area. Upon capture, birds were
fitted with individually colored plastic leg bands and immediately released at
their point of capture. Field observations (see below) were then conducted on
and around these areas of capture, using a time period and method identical to
the one used at DWH (see below). Over 90% of the tagged birds were resighted
during field observations. Birds were not individually tagged at DWH because
two banding programs (90 individuals by
Carlier and Lefebvre, 1997; 40
individuals in a pilot study for this experiment) showed low resighting rates
of banded doves over the time period required for our study (31% and 15%,
respectively).
Premanipulation data were collected by a single observer (JLG) on 30 days at StJ and 18 days at DWH over a 2-month period (February-March) throughout the day (i.e., 0800-1700 h) at both study areas.
Seven sites characterized by frequent spillage were selected for
observations around the DWH area. Observations were made only when spills were
present, otherwise no doves were present or foraging. One focal dove per
session was chosen haphazardly and the following foraging information was
recorded in 15-s intervals: (1) size of the foraging group to which the focal
bird belonged; (2) number of paces and pecks at the ground for food; and (3)
intraspecific aggression. Doves were considered part of the same foraging
group if they were separated by less than 5 m
(Lefebvre et al., 1996).
Foraging was defined by the occurrence of at least one peck at the ground per
minute. Only pecks specifically targeted towards food were counted, excluding
cases in which the dove was simply searching without ingesting, pecking for
grit, or using pecks at the ground in a ritualized threat display. A pace was
defined as one step. Ratios of pecks per pace were calculated to estimate
foraging rate at the time and place of observation. An aggressive act was
defined as a chase, fight, or threat display involving the focal bird and
another Zenaida dove within 5 m of the focal animal. Fights were defined as a
wing slap towards or on its opponent. Threat displays were characterized by
either the raising of a wing contra-lateral to the opponent or as threatening
pecks, which were ritualized beak swipes at the ground in the absence of food,
performed during a very characteristic parallel walk display of the two
opponents.
If the focal animal withdrew from the site, was lost track of, or did not peck once within a 1-min interval (unless it was engaged in aggressive displays), observations were discontinued and a new focal individual chosen haphazardly.
Manipulating the spatial clumping and temporal predictability of
food
We manipulated the distribution of food in space and time at six sites at
DWH. These sites were around and within the feeding mills plant, separated by
at least 10 m from one another and 15 m from one of the seven sites used for
premanipulation observations. We used a commercial mix of seed for caged
birds, obtained from Tropical Fish Pets, Bridgetown, Barbados. Spatial
clumping was manipulated by presenting 40 ml of seed in either an 8 x 8
cm area (clumped) or an 6 x 6 m area (dispersed). We had two levels of
temporal predictability: predictable, seed was presented at the same site at
1400 h for 14 consecutive days (after 7 days of training, see below); and
unpredictable, seed was presented at haphazard times each day, between 0800
and 1700 h, and on only 14 of 24 days (i.e., after 5 days of training, food
was presented on days 6, 7, 9, 10, 12, 14, 15, 19, 20, 22, 25, 26, 27, and
29).
The experimental manipulations were conducted over four time periods
(Table 1). Sites received the
predictable treatment during periods 1 and 3 and the unpredictable treatment
during periods 2 and 4, in a crossover design
(Wilkinson, 1990). Prior to
periods 1 and 3, food was presented in a clumped manner at 1400 h for 7 days
in a row to train the birds to expect a temporally predictable environment.
Data collection began on day 8 when three sites were randomly chosen to
receive the clumped treatment, and the remaining three sites received the
dispersed treatment. After 7 days of data collection, each site was switched
and received the alternate level of spatial clumping for another 7 days. Prior
to periods 2 and 4, sites received no food for 5 days in a row to train birds
that they were no longer in a temporally predictable environment. Data
collection began on day 6, when three sites were randomly chosen to receive
the clumped and dispersed treatments, respectively. Halfway through data
collection, each site received the alternate level of spatial clumping
(Table 1).
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Focal animal observations were made at each site when food was present. The order of observation among sites was randomly determined; food was present at only one site at a time. The median duration of a focal observation was 45 s (range = 30-240 s). Observations of pecking, pacing and intraspecific aggression were taken in the same manner as they were in the premanipulation phase, again using 15-s intervals. In addition, any aggression with heterospecifics, chiefly shiny cowbirds (M. bonariensis) and Carib grackles (Q. lugubris) was noted, as was the number of times the focal animal was chased. The median number of focal birds observed at a site per day was four (range = 1-10). Observations at a particular site were concluded when the seeds were eaten or the birds ceased foraging. The median duration of an observation at a particular site was 5 min (range = 0.5-10 min).
Postmanipulation observations
Following the completion of experimental manipulations, postmanipulation
data were collected at DWH every day for 7 days in the exact manner as during
the premanipulation phase. We used these data to test for any seasonal changes
in aggressive behavior. Our observations and experiments were conducted during
the dry season (Caribbean Meteorological
Institute, 1982), when reproduction is at its lowest
(Wiley, 1991). However,
opportunistic breeding occurred sporadically during our study.
Analysis
For each focal bird, the total number of aggressive acts was divided by the
length of time observed (minimum 30 s) to obtain a rate of aggression.
Differences among treatments at DWH were analyzed as a randomized complete
block design with sites as blocks and spatial clumping and temporal
predictability as the main effects. Because the same focal bird could be
observed on more than 1 day, we used the average competitor density (number of
doves within 5 m of the focal animal) and the average rate of aggression by
focal birds at a site over the 7 days of observations as an individual datum
for these analyses. When investigating the relationship between aggression and
competitor density, we recorded the average rate of aggression at a particular
density and site. For statistical tests, however, we used the mean rate of
aggression at a particular density and treatment across all sites as an
individual datum. The data met the assumptions required for parametric
analyses, so transformations were not required.
We used an eight-period crossover design
(Wilkinson, 1990) to test for
potential carryover effects of the treatment in the previous period on the
doves' behavior. We also used a repeated measures analysis of variance to test
for temporal trends in behavior over the 7 days of data collected for a
particular combination of temporal predictability and spatial clumping.
Because neither analysis detected any significant trends, we did not present
the results of these analyses; both are described by Goldberg
(1998).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Pre- and postmanipulation observations
The doves at DWH routinely fed in large groups of conspecifics (median number within 5 m = 8), at high rates (x ± SE pecks per pace = 2.43 ± 0.43), and exhibited low rates of intraspecific aggression (x ± SE acts/30 s = 0.41 ± 0.062). Escalated fighting accounted for only 8% of the aggressive interactions. In contrast, doves at StJ typically fed alone (median number of conspecifics within 5 m = 0), at low rates (x ± SE pecks per pace = 0.019 ± 0.002), but exhibited high rates of aggression (x ± SE acts/30 s = 1.08 ± 0.15). Escalated fighting accounted for 20% of all aggressive interactions. The behavior observed at StJ was typical for doves observed in other parts of Barbados (Dolman et al., 1996
;
Lefebvre et al., 1996). To test for seasonal differences in level of aggression, we compared the premanipulation data with those collected after the experiments were completed, 3 months later. Aggression rate did not differ between the pre- and postmanipulation observations at DWH (t = 1.31, df = 241, p =.19).
Manipulation of spatial clumping and temporal predictability
The number of competitors within 5 m of the focal bird was significantly
affected by the distribution of food. Competitor density was higher at
spatially dispersed than at spatially clumped patches
(Figure 1;
F1,39 = 26.87, p <.001). The effects of the
temporal predictability of food (F1,39 = 0.16, p
=.69), the interaction between the spatial clumping and the temporal
predictability of food (F1,39 = 0.04, p =.84),
and site (F1,39 = 1.05, p =.40) did not
significantly affect competitor density
(Figure 1).
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There was a significant interaction between the effects of the temporal predictability and the spatial clumping of food on the rate of aggression (Figure 2; F1, 39 = 8.79, p =.005). The increase in aggression when food changed from temporally unpredictable to temporally predictable was significant in the spatially clumped condition (Tukey's HSD post hoc test, p <.001), but not in the spatially dispersed condition (p =.96). Rates of aggression also tended to increase when food was spatially clumped; this increase was significant when food was temporally predictable (Tukey's HSD post hoc test, p <.001), but not when food was temporally unpredictable (p =.087). In spite of the significant interaction, all trends in aggression were consistent with the predictions of resource defense theory: that is, aggression increased as the spatial clumping of food increased and as the temporal predictability of food increased. Morever, as predicted, rates of aggression were highest when food was both clumped in space and predictable in time. Rate of aggression did not differ significantly among sites (F1,39 = 2.22, p =.072).
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Compared to the premanipulation data, aggression rate was significantly higher when food was either clumped in space or predictable in time (i.e., the 95% C.I. did not include the premanipulation mean). When food was both dispersed in space and unpredictable in time, the rate of aggression did not differ significantly from the premanipulation mean.
Aggression exhibited a "dome-shaped" relationship with competitor density only when food was both clumped in space and predictable in time (Figure 3a). A cubic function best described the change in aggression with competitor density (Y = 0.0130x3 - 0.344x2 + 2.318x - 0.702, r2 =.89, F3,11 = 30.22, p <.0001); the rate of aggression initially increased with increasing competitor density, peaked at a density of about five, and then declined before increasing slightly at high densities. The cubic term explained a significant amount of the variation in rate of aggression (F1,11 = 27.19, p =.00029), even after the linear and quadratic terms were included in the model. A cubic function also described the relationship when food was clumped and unpredictable (Figure 3b; Y = 0.00669x3 - 0.151x2 + 0.847x + 0.234, r2 =.70, F3,11 = 8.46, p =.0034). Unlike Figure 3a, however, there was a marked increase in aggression at high competitor density. In the dispersed and predictable treatment, aggression increased linearly with increasing competitor density (Figure 3c; r2 =.47, F1,13 = 11.58, p =.0047). However, there was no significant relationship between rate of aggression and competitor density in the dispersed and unpredictable treatments (Figure 3d).
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Chasing was the primary behavior used by doves when interfering with each
other at food patches (Figure
4). However, the type of behavior used differed significantly
among the four treatments (
26 = 42.0, p
<.001). These differences were largely due to relatively more fights and
fewer threats in the two predictable treatments than in the two unpredictable
treatments (21 = 13.97, p <.001; with
Yates's correction). A similar comparison between scattered versus clumped
treatments revealed no significant difference in the relative use of fights
versus threats (21 = 0.96, p =.76; with
Yates's correction).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Our study provides experimental evidence that an increase in the temporal predictability of food leads to an increase in competitive aggression, at least when food was also clumped in space. The doves apparently learned that a patch was temporally predictable during the 7 days of training, as no temporal trends in behavior were apparent during data collection (see Methods; Goldberg, 1998
). Two
mechanisms, that are not mutually exclusive, may explain the increase in
aggression at temporally predictable patches. Individual doves may become more
aggressive as they learn that a patch is predictable in time, in the hope of
monopolizing the patch in the future (see
Grant and Kramer, 1992).
Dominant convict cichlids also adjust their behavior as they became more
familiar with a spatially predictable environment
(Grand and Grant, 1994).
Alternatively, inherently more aggressive doves may have been attracted to
predictable patches, in which they were able to monopolize a large share of
the food. In such a truncated phenotype ESS (sensu
Milinski and Parker, 1991),
less competitive doves may simply avoid clumped, predictable patches when
dominants are present. Either mechanism involves learning and is consistent
with the finding that doves used escalated fighting more often at predictable
than unpredictable patches.
Our data also confirmed previous research showing increased aggression with
an increased spatial clumping of food
(Grant and Guha, 1993;
Monaghan and Metcalfe, 1985;
Zahavi, 1971). The lack of
temporal trends in behavior following a change in the spatial clumping of a
patch (see Methods section; Goldberg,
1998) suggest that doves can assess patch size with little or no
learning.
Resource defense theory primarily makes verbal, qualitative predictions
about how individual components of resource distribution affect the frequency
of aggression or territoriality. The significant interaction between the
temporal predictability and spatial clumping of food in this study and between
the spatial and temporal clumping of food in Robb and Grant (1988) underline
the need for quantitative, multivariate measures of resource distribution. Our
study suggests that Zenaida doves will not or cannot defend an ephemeral patch
of 36 m2, regardless of its predictability in time, where patches
of 0.0064 m2 are defendable at a variety of levels of temporal
predictability. Despite the interactions, all trends in aggression, whether
significant or not, were consistent with the univariate predictions from
resource defense theory (also see Robb and
Grant, 1998).
Competitor density was lower at smaller patches presumably because fewer
doves could participate in feeding due to crowding and the effect of
aggression. It was more surprising that temporal predictability had no effect
on competitor density. This result suggests that the doves were highly mobile
and readily joined patches discovered by others (see
Giraldeau and Beauchamp,
1999), even when those patches appeared unpredictably in time.
The variation in competitor density allowed us to test the prediction that
the rate of competitive aggression peaks at an intermediate competitor density
(see Grant et al., 2000). In
both spatially clumped treatments, aggression initially increased and peaked
at a competitor density of about 4-5 doves per 5m2. Interestingly,
rate of aggression decreased at competitor densities greater than five, but
then increased again at densities greater than 12. This bimodality, which is
not predicted by any current theory, suggests that two processes are at work.
We suspect that the high initial peak in aggression resulted from dominant
doves attempting to defend and monopolize the entire patch when the number of
intruders was relatively low (i.e., a short-term territory). As competitor
density continued to increase, defense of the patch may have become
increasingly uneconomical, so aggression decreased. The increase in aggression
at extremely high competitor densities may be caused by doves becoming
increasingly hawk-like (sensu
Maynard-Smith 1982) in the
face of increased crowding, as observed in other species of birds
(Morse, 1980) and predicted by
a game theory model of social foraging
(Sirot, 2000). Doves made no
attempt to defend the large patches in the dispersed treatment, so there was
no initial peak in aggression at low densities. If anything, rate of
aggression tended to increase monotonically with density, as predicted by
Sirot (2000). The challenge
for a unified theory of competitive aggression is to predict when animals
switch from trying to defend and monopolize an entire patch to using
aggression while sharing a patch with others. Patch size and competitor number
are likely key variables.
Of the six key environmental variables thought to influence economic
defendability (see Introduction; Grant,
1993; Warner,
1980), we manipulated temporal predictability and spatial
clumping, while controlling the abundance (always 40 ml of seed per patch),
spatial predictability (always the same sites), and temporal clumping (food
always presented once per patch per day) of food at experimental patches.
Competitor density was not controlled. The success of the manipulations at DWH
was probably partly due to the uniqueness of the site; the doves were used to
human activity and responding to ephemeral patches of food. Hence, they
readily discovered our experimental patches and responded to the manipulations
of food distribution. Similar manipulations at StJ had little effect on dove
behavior (Goldberg, 1998).
Virtually all patches were within a feeding territory and, hence, were
discovered and eaten only by the resident pair. In addition, presumably too
little food was added on too short a time scale to affect the permanent system
of territories at StJ (Goldberg,
1998). The switch between defending resource patches to
territories containing patches is a fundamental problem in behavioral ecology
and will likely be related to the distribution of patches in space and
time.
At DWH, the lower rate of aggression during baseline observations, compared to experimental conditions, was likely due to the ephemeral nature of patches resulting from anthropogenic spillage. The spilling of grain occurs unpredictably in space and time, delivering large amounts of grain in a spatially and temporally clumped manner that attracts many doves. In between spills, food was in low abundance. In contrast, during experiments food was always spatially predictable, at a moderate density, and attracted fewer doves.
Differences in behavior between the DWH and StJ populations may also be
related to the distribution of food. When food was available at DWH, feeding
rates were two orders of magnitude higher than at StJ (also see
Dolman et al., 1996).
Presumably, the high abundance of food in conjunction with the ephemeral
nature of the patches and high competitor density at DWH made the defense of
permanent feeding territories uneconomical. Taken together, our observations
on wild Zenaida doves show that the rates of aggression were influenced by
food distribution and competitor density in a manner largely consistent with
the predictions of resource defense theory.
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ACKNOWLEDGEMENTS |
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This research was financially supported by a Natural Sciences and Engineering Research Council (NSERC) postgraduate scholarship to J.L.G., an NSERC Research Grant to L.L., and a team grant from Fonds pour la Formation de Chercheurs et l'Aide à la Recherche (FCAR) to L.L. and J.W.A.G. We thank the Barbados Feed Company for permission to conduct research on their property, David Armstrong for help in the field, and David Westneat and two anonymous referees for comments on the manuscript.
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