Download Competition theory and the structure of ecological

Evolutionary Ecology, 1993, 7, 142-154
Competition theory and the structure of ecological
communities
F. A . H O P F t
Optical Sciences Center, University of Arizona, Tucson, AZ 85721, USA
T H O M A S J. V A L O N E and J A M E S H . B R O W N *
Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA
Summary
We develop a theory of competition based on two mechanisms that we call the cost of rarity (Mechanism R)
and the cost of commonness (Mechanism C). These reduce the rate of population increase only at high
densities (asexual organisms) or both at high and low densities (sexual species). The theory predicts that, in
certain circumstances, the number of coexisting species in any assemblage will be finite and that these
species will differ in their utilization of resources (and in associated morphological traits) more than
expected by chance. Specifically, it predicts such nonrandom assortment in assemblages of three or more
(i.e. multispecies) sexual species, especially in those communities where a few species are numerically
dominant, but not in two-species associations and not in asexual forms. Unlike other theories, however,
ours does not predict any specific value of morphological ratio or limiting similarity.
We develop procedures to assess the degree of numerical dominance in an assemblage, and then test the
predictions of the theory using data on morphological size ratios. The tests yield results that are consistent
with the theory. Our analysis of multispecies assemblages of granivorous rodents, bird-eating hawks, Anolis
and sexual Cnemidophoruslizards, show that in these assemblages very small ratios are observed less often
than expected by chance. Coexisting asexual Cnemidophoruslizards tend to be extremely similar in size.
Nesting sparrow and flycatcher assemblages exhibit low numerical dominance which we predict will inhibit
detection of regular assortment, and we find no regular pattern in these assemblages. Finally, we fail to
detect regular assortment in most two-species associations as expected. We examine several alternative
mechanisms that might account for morphological segregation among coexisting species but find little
evidence that they have been important.
Keywords: competition; body size ratio; statistical analysis; coexistence; community morphological assortment; limiting similarity; cost of rarity; cost of commonness; stochastic extinction; dominance; standardization
Introduction
Since Lack (1947) and Hutchinson (1959) called attention to the apparently n o n r a n d o m ratios of
morphological traits of ecologically similar, sympatric species, ecologists have speculated about
the effects of interspecific competition on community structure and coexistence. Since Gause's
(1934) principle of competitive exclusion had claimed that two species with identical requirements could not persist indefinitely in the same environment, ecologists began to ask how similar
t A rough draft of the manuscript was completed before F. A. Hopf's untimely death.
* To whom correspondence should be addressed.
0269-7653
© 1993 Chapman & Hall
Competition and c o m m u n i t y structure
143
two species could be and still coexist stably. MacArthur and Levins' (1967) theory of limiting
similarity attempted to provide a mathematical solution to this problem. Like many of the early
theories of pairwise species interaction, this one was soon shown to be too sensitive to its
mathematical assumptions to provide a robust answer to the problem (e.g. May and MacArthur,
1972; May, 1973, 1978; Stewart and Levin, 1973; Abrams, 1975, 1984; Armstrong and McGehee,
1980; Chesson and Warner, 1981; Turelli, 1981; Chesson, 1986). While theoretical studies have
explored the mathematics of competitive interactions without providing a general solution
(Abrams, 1983), empirical studies have continued to supply evidence that assemblages of
ecologically similar, coexisting species are often comprised of species that are more different
from each other in their body sizes or dimensions of trophic appendages than would be expected
by chance (e.g. Schoener, 1970, 1984; Brown, 1973; Grant and Abbott, 1980; Bowers and
Brown, 1982; Case, 1983; Brown and Bowers, 1985; Losos et al., 1987; Taper and Case, 1993a,b;
but see Simberloff and Boecklen, 1981; Simberloff, 1984). Thus, while the inductive proposition
that morphological differences reduce competition and promote coexistence has been supported,
we still lack a theoretical basis for predicting a priori the effects of competition on the
morphology of coexisting species.
In this paper, we develop a theory of competition that predicts when coexisting species should
differ from each other more than is expected by chance. We build on ideas about the
commonness and rarity of species introduced by MacArthur (1960), Preston (1962), and Williams
(1964). Our treatment is an extension of a theory developed by Hopf and Hopf (1985; see also
Hopf, 1990). These authors showed how a 'cost of rarity', that is a necessary consequence of
sexual reproduction, results in the clustering of individual organisms into discrete species that are
evenly dispersed along a resource axis, even when the resources themselves are distributed
continuously along this axis. Here we show how an additional 'cost of commonness' may
influence our ability to detect structure in ecological assemblages. We are concerned primarily
with the role of interspecific competition in producing larger than expected differences among
species in resource utilization or in related morphological traits, which we shall refer to as a
regular assortment pattern. We develop the concept of numerical dominance to provide an
operational measure of the magnitude of the cost of commonness within a community. This
allows us to predict the circumstances in which regular assortment patterns are most likely to be
observed.
Unlike earlier theories (e.g. MacArthur and Levins, 1967; May, 1973), our theory does not
predict any specific value of limiting similarity. Instead, we predict the situations in which the
differences between species in resource utilization or in related morphological traits will be larger
than expected by chance. We present a preliminary evaluation of the predictions by analysing the
ratios of morphological traits in assemblages of (i) asexual organisms, (ii) sexual organisms in
which a few species dominate the community numerically, and (iii) sexual organisms in which
abundances are relatively evenly distributed among species.
The theory
The theory developed here is an extension of the non-mathematical model of Bernstein et al.
(1986) and the formalization of Hopf and Hopf (1985). The latter is based on a generalized form
of MacArthur's (1972) model for multiple consumer species with overlapping requirements for
heterogeneous resources. Population growth of species i is described by Equation 1
dNi
T
= biai (Ni)fi(Ri)Ni - diNi
(1)
Hopf, Valone and Brown
144
where Ni is adult density and Ri is the set of resources used by competitor i for reproduction and
survival through the function 1], which is unity in the limit of abundant resources, ai(Ni) regulates
reproduction and mortality in a manner independent of competitors and is unity when no such
regulation occurs, bi is a coefficient such that the quantity bi ai(Ni) )~(Ri) is the rate of production
of new breeding individuals. We loosely refer to this as reproduction, but the process includes the
mortality of individuals that have not yet joined the adult breeding population, d i is the
coefficient describing the mortality of breeding individuals.
Equation 1 departs from most conventional models (e.g. Roughgarden, 1979), because of the
inclusion of parameter ai. We allow a i to be a function of Ni, so that population growth can be
limited at both high and low densities.
Our model is a more general formulation of MacArthur (1972), which uses a special case of
Equation 1 in which ai(Ni) = 1. When ai(Ni) = 1, and all species have the same b's, d's andf()'s,
but different Ris, the equilibrium number of species in the community equals the number of
resources (e.g. MacArthur, 1972; Levins, 1979). If we assume that the niche of each species
represents requirements for a unique combination of biotic and abiotic variables, so that the
niche can be defined in terms of location along axes of continuous variables, then the number of
niches potentially available can approach infinity. In such a scenario, Hopf and Hopf (1985) show
that as the total number of individuals of all species (Y~Ni) approaches infinity, the number of
species (S) in the community will also approach infinity. Hopf (1990) has verified that the specific
value of the limiting similarity derived by MacArthur and Levins (1967) is an artifact of the
special assumptions of their model (see also Abrams, 1983). In the kind of Malthusian system
represented in Equation 1, no specific values of niche separation can be derived for communities
where S = 3 or for any other value of S. While such a result seems biologically unrealistic, Hopf
and Hopf (1986) demonstrate it in a non-living competitive system.
The cost of rarity
Hopf and Hopf's (1985) solution to the problem of limitless proliferation in biological systems is
to assume that ai (Ni) is of the form sketched in Fig. 1. This function is roughly constant, but it
decreases at both low and high densities by the action of Mechanisms that we denote as R and C,
respectively. Mechanism R, the cost of rarity, and Mechanism C, the cost of commonness, have
the consequence of imposing lower and upper bounds, respectively, on the density, Ni, at
equilibrium. Hopf and Hopf (1985) show that Mechanism R robustly yields a finite number of
species, even when the number of potential n~ches approaches infinity.
What are costs of rarity? Sexual reproduction has many consequences that act, directly or
R
a(Ni)
I°
0
C
Ni
Figure 1. The relationship between regulation of reproduction and mortality, parameterized as ai (Ni), and
adult population density, Ni. The function decreases at low and high densities (shaded regions) due to
Mechanisms R (costs of rarity) and C (costs of commonness), respectively.
Competition and community structure
145
indirectly, as a cost of rarity (Bernstein et al., 1986). Indeed, all other Allee effects (Dennis,
1989), including population-specific mutualisms or obligate social interactions (e.g., flocking in
birds), impose a cost of rarity.
Thus, the theory predicts that communities of organisms subject to a cost of rarity (including all
sexual organisms) should be comprised of distinct species with differences in resource use that are
greater than expected by chance; i.e. these assemblages should exhibit an assortment pattern.
Hopf (1990) has shown, however, that in communities composed of only two species (species
pairs) the detectability of the assortment pattern depends strongly on species density. The
assortment pattern will be strong only when population densities of both species are low.
Detectability of an assortment pattern is not a problem when communities contain greater than
two species (Hopf, 1990).
Asexual organisms, on the other hand, have no cost of rarity. Thus assemblages of
parthenogens should behave like the non-living system in Hopf and Hopf (1986) and show no
robust pattern of assortment.
The cost of commonness
Mechanism C, the cost of commonness, imposes an upper bound on the density of a particular
species in a manner independent of interspecific competition. Examples of such a mechanism
include many kinds of density-dependent predator-prey, plant-herbivore, and host-pathogen
interactions (e.g. Janzen, 1970; Ricklefs and O'Rourke, 1975; Holt, 1984). If Mechanism C acts
strongly on an association, it can prevent the detection of an assortment pattern. To see this,
consider first an association at equilibrium in which a Mechanism R, but no Mechanism C, is
operating. Next, turn on a Mechanism C, and make it act strongly enough that population density
for each species is substantially reduced. As a result, fewer resources are consumed by the
existing species. The increased resource level allows another set of species, previously excluded
from the assemblage, to use the same range of resources and hence to invade the community. The
species that will survive and coexist will depend largely on the history of the sets. Whilst the
species within any one set may exhibit assortment rules relative to other members of the same set,
their properties of resource utilization will tend to be distributed at random with respect to
members of the other set. Hopf (1990) shows that if Mechanism C is strong enough to increase
the number of species by a factor of 1.5 - 2, then the resulting asssortment pattern will be difficult
to detect.
The only mechanism left to generate patterns in associations where C is strong is local (i.e.
within community) character adjustment. Our use of average morphologies to characterize entire
species over large regions largely prohibits testing for character adjustments. Thus, patterns we
can observe are restricted to assortment effects, and these are predicted to occur only if
Mechanism C is weak or absent.
Thus, while the theory does not require that we identify the specific factor C that may act on a
particular community, it will be important to determine the strength of Mechanism C in the
associations studied. All Cs should have the effect of reducing the density of the commoner
species relative to the density of the rarer ones (e.g. Glasser, 1979). To assess the strength of C on
a community, we define an association as having high numerical dominance if it contains a few
species that are very abundant and consistently present (core species of Hanski, 1982) and many
species that are rare and ephemeral (satellite species). Since C reduces numerical dominance, we
can assess the strength of C by measuring the relative abundances of species in the community.
Communities experiencing a strong C will exhibit low numerical dominance while those
experiencing a weak C will exhibit high numerical dominance.
146
Hopf, Valone and Brown
Preliminary evaluation of the theory
Measuring the cost of commonness
We measure the strength of a Mechanism C on a community by examining the relative
(fractional) abundances of each species. Assemblages that contain a few abundant and many rare
species are said to exhibit high numerical dominance. Assemblages in which most species are
relatively equally abundant are said to exhibit low dominance.
Numerical measures of dominance depend on the total number of species in the assemblage
(S). Most such measures can be said to be biased estimators, because the number of species
counted empirically is often less than the number, S, actually present (Pielou, 1977; Lloyd and
Ghelardi, 1965; Hopf and Brown, 1986). Sampling of few individuals at a site (small sample size)
will tend to underestimate S (Preston, 1962), and the magnitude of this bias will increase with
increased numerical dominance.
Therefore, when a sample of an assemblage appears to exhibit low dominance, we need to be
able to determine whether this is due to undersampling an assemblage with high dominance or to
true reduced dominance. To do this we follow the method of Hopf and Brown (1986) for
obtaining a quantitative measure of the relative abundances of species that is independent of the
total number of species in an assemblage. Their method can be used to calculate an Sindependent measure of dominance from the value of Simpson's (1949) diversity index.
Numerical dominance (D) is expressed as a score, that can range from 1 - 20, for each
community. Communities of low dominance (even distribution of abundances) will yield low
scores, communities of high dominance will give high scores, and communities with a random
distribution of abundances among species will give a uniform random distribution of Ds.
We illustrate the application of this method and the bias that can come from undersampling
using extensive census data that are available for breeding and wintering assemblages of North
American ducks (see Appendix 1). These are suitable for this purpose because there are censuses
of numerous sites during both nesting and wintering seasons, and some of these include very large
numbers of individuals so they should be relatively free of undersampling bias. In Fig. 2 we show
that when the samples include large numbers of individuals, scores for the winter assemblages
cluster tightly around 20, but those for the nesting communities are much more evenly
distributed. Samples of both nesting and wintering assemblages that contain few individuals gave
more evenly distributed scores. Note that the winter assemblages exhibited substantially higher
dominance than the nesting ones, and that the smaller samples, especially of the winter
assemblages, gave a more even distribution of D's than the larger samples. The winter
assemblages show that bias from undersampling can cause communities with high dominance to
appear to exhibit a much lower degree of dominance. Hopf and Brown (1986) demonstrated a
similar effect of undersampling bias by computer simulation, drawing at random small
subsamples from a community exhibiting high dominance.
Tests
Here we provide a brief, preliminary evaluation of the theory by comparing three different kinds
of assemblages;
(i) asexual species,
(ii) sexual species exhibiting low numerical dominance, and
(iii) sexual species exhibiting high numerical dominance.
We chose these three categories because in the first there is no cost of rarity (no Mechanism R);
in the second there is a Mechanism R, but a high cost of commonness (a strong Mechanism C);
Competition and community structure
147
30
b) Winter
25
8
'*6
o)
Nesting
2O
ts
I:: to
Illlllllllllollilllll
$
=,o
F~
S
c) Nesting Undersomple
I.)
= [I
d) Winter Undersample
S
,,,,n n
"6
gZ
,,r, . . . . . ,,nII01
I
rr)A
Z
i
I Ilol I
S
S
Figure 2. Distribution of scores from the evenness test applied to censuses of nesting and wintering ducks
containing different numbers of individuals per site: a) >300, b) >1000, c) < 100, d) 50200. The effect of
undersampling is illustrated by the much wider distribution of scores (and correspondingly reduced ability to
reject the null hypothesis) for the sites where few individuals were recorded, especially in winter.
and in the last there is a Mechanism R, but a weak Mechanism C. Therefore the theory predicts
that we should observe assortment patterns only in the last case.
Before comparing the theoretical predictions with data, it is necessary to determine the
strength of Mechanism C necessary to obscure the effects of competition on assortment patterns.
Our method of measuring numerical dominance provides a quantitative assessment of the
strength of Mechanism C, but the theory is not yet developed to the stage where we can predict
the level of numerical dominance required to observe regular assortment. We can, however,
make two qualitative predictions. First, regular assortment patterns should be observed only in
assemblages of ecologically similar sexual species (i.e. in the same guild) exhibiting high values
of D. Second, there should be a threshold relationship between the level of numerical dominance
and assortment. That is, all assemblages above some level of D should show an assortment
pattern while those below such level should not.
The theory predicts larger than expected differences in resource utilization among coexisting,
ecologically similar species. Resource utilization is rarely measured directly, but can be inferred
from body size or dimensions of other morphological traits (e.g. Lack, 1947; Hutchinson, 1959).
It is the ratios (or the differences in the logarithms) of morphological traits that most accurately
reflect differences in resource utilization, because the requirements for resources and the
morphological traits used in acquiring and processing resources are allometric functions of body
size (Peters, 1983; Calder, 1984).
The assessment of regular patterns of assortment is complex. There are many biological and
statistical issues involved in the selection of assemblages that are appropriate for analysis and in
the statistical methods that are appropriate for detecting nonrandom patterns of assortment. For
example, regular assortment patterns can be expressed and tested either as ratios that are more
even than expected by chance, or as the tendency of very small ratios to be observed less
Hopf, Valone and Brown
148
frequently than expected by chance. We address these issues elsewhere (Hopf et al., in
preparation). Here, for simplicity, we use the most rigorous of the methods that we have
developed in this preliminary assessment of the theory.
We have compiled from the literature data sets on the species composition of local
communities and on the relative abundances and morphologies of the species in seven guilds of
terrestrial vertebrates (for references and additional details see Appendix 2). These assemblages
include granivorous desert rodents, nesting sparrows, nesting flycatchers, bird-eating hawks,
Anolis lizards, sexual Cnemidophorus lizards, and assemblages of exclusively asexual (i.e.
parthenogenetic) Cnemidophorus lizards.
Our theory makes three predictions that can be evaluated using these data:
(i) the parthenogenetic assemblages should not show regular assortment patterns;
(ii) the two-species assemblages will often not exhibit detectable assortment;
(iii) when all sexual assemblages are ranked according to dominance, there should be some
value of dominance above which all assemblages exhibit regular assortment and below which all
assemblages do not exhibit detectable assortment.
Table 1 presents data on the average degree of dominance in these assemblages and the results
of the minimum ratio test, subdivided into two categories: two-species assemblages and
communities containing three or more species. The data are consistent with all of these
predictions. First, all assemblages of asexual Cnemidophorus tended to have significantly smaller
ratios than expected by chance. Second, of the other guilds, we failed to detect regular
assortment in all two species assemblages except in the hawks. And third, there was a significant
correlation between numerical dominance and tendency to avoid small ratios (Spearman rank
correlation, Rs = -0.77, p < 0.05). That is, significantly fewer than expected small ratios were
observed in multi-species assemblages of all guilds of sexual forms that had as high or higher
dominance than the rodents, while we failed to observe regular assortment patterns in the two
guilds of sexual animals that exhibited lower dominance than the rodents (Fig. 3).
Table 1. Numerical dominance (D) and the results from the test for the tendency to avoid
small ratios in the assemblages. Each assemblage is subdivided into two-species associations
(S = 2) and multispecies associations (S > 2). g is a quantitative measure of assortment
pattern (Hopf et al., in preparation). Negative g values indicate a tendency to avoid small
ratios
S=2
Assemblage
S>2
D
~
p<
2
p<
Cnemidophorus lizards
18.8
4.5
0.05
6.5
0.05
Sexual species
Nesting sparrows
Nesting flycatchers
Desert rodents
Anolis lizards
Cnemidophorus lizards
Hawks
15.0
15.6
18.4
19.0
19.1
20.0
-0.5
0
0.1
1.2
0
-2.5
NS
NS
NS
NS
NS
0.05
-0.4
1.0
-3.5
-2.1
-2.5
-4.6
Asexual species
NS
NS
0.01
0.02
0.05
0.001
Competition and community structure
149
2
i
I
V
-4
14
16
18
20
Dominance
Figure 3. Relationship between assortment pattern and level of dominance for the six sexually reproducing
assemblages analysed (see Table 1). All assemblages with a dominance score above 18 exhibit regular
assortment while the two assemblages with a dominance score below 16 exhibit random assortment.
Additional data from communities with dominance scores between 16 and 18 are required to determine
more precisely the critical level of dominance required to observe regular assortment.
Discussion
In our analysis of seven terrestrial vertebrate communities, we found that some exhibited strong
assortment patterns while others showed no evidence of such patterns. It is especially interesting
that, even within a taxon, we find assemblages that differ in the extent to which they exhibit
regular assortment patterns. For example, among lizards, Anolis and Cnemidophorus assemblages containing sexual species exhibited strong assortment, while entirely parthenogenetic
Cnemidophorus did not; and among birds, bird-eating hawks exhibited a pronounced pattern,
while breeding flycatchers did not. In general, these results corroborate those of the investigators
who obtained the original data (Schoener, 1970, 1984; Case, 1983).
This is not the first demonstration that some assemblages exhibit regular assortment patterns
while others do not (e.g. Simberloff and Boecklen, 1981; Bowers and Brown, 1982; Case, 1983;
Taper and Case, 1992, 1993). The special feature of the theory proposed above is that it predicts the
situations in which we should and should not expect to observe regular assortment patterns based
on just two parameters: the cost of rarity and the cost of commonness acting on an assemblage.
We are encouraged that the theory fared well in our preliminary tests. The limited data sets
that we analysed did not refute any of its predictions. We emphasize, however, the preliminary
nature of these results. All of our tests involved communities of terrestrial vertebrates. We see no
theoretical reason why the theory should not apply equally well to other kinds of assemblages
(e.g. terrestrial invertebrates and plants, and freshwater and marine organisms). There are,
suggestions in the literature, however, that populations of some of these organisms are less
regulated by resource availability and their community structure may reflect weaker or
insignificant influences of interspecific competition (Schoener, 1983). It remains to be seen
whether our methods for estimating the relative strengths of Mechanisms R and C will provide a
sufficient basis for predicting which of these assemblages will show assortment patterns.
To our knowledge, there are three alternative explanations that might impose a cost of rarity,
limit the number of species, and cause regular assortment patterns. First, Darwin (1859) in trying
to account for the absence of 'missing links' or individuals with attributes intermediate between
existing species, suggested that evolution proceeded most rapidly in large populations. Thus, he
reasoned that species comprising many individuals would become and remain superior competitors, eliminating any rare intermediate phenotypes that might arise. Second, spite, in which an
individual harms conspecific individuals without obtaining any benefit for itself, might be
150
Hopf, Valone and Brown
envisioned as an alternative to Allee effects as a possible Mechanism R. We know of no
compelling theoretical arguments or empirical data to suggest that either of these mechanisms is
important in natural communities. Third, May (1973, 1974) invoked stochastic demographic
extinction of rare species populations as a mechanism that might cause coexisting species to
exhibit regular assortment patterns. This suggestion has been explored mathematically by Turelli
(1981) and H o p f and H o p f (1985; see also Hopf, 1990). These studies concluded that stochastic
demographic extinction is unlikely to produce assortment patterns. Thus, Allee effects, which
include but are not restricted to costs of rarity due to sexual reproduction, remain the best
explanation for the discreteness of species and for the absence of Darwin's missing links.
Acknowledgements
We thank R. A. Pospahala for providing the duck census data listed in Appendix 1 and those
individuals listed in Appendix 2 for sharing their data and insights from the field. B. Dennis and
T. W. Schoener contributed valuable discussions during the development of these ideas. S. L.
Pimm, M. L. Taper, M. L. Rosenzweig and B. Dennis made helpful comments on the
manuscript. During the research and writing T. J. Valone was supported by a N S F - N A T O
Postdoctoral Fellowship and J. H. Brown was supported by NSF Grant BSR-8807792.
References
Abrams, P. A. (1975) Limiting similarity and the form of the competition coefficient. Theor. Popul. Biol. 8,
356-75.
Abrams, P. A. (1983) The theory of limiting similarity. Ann. Rev. Ecol. Syst. 14, 359-76.
Abrams, P. (1984) Variability in resource consumption rates and the coexistence of competing species.
Theor. Popul. Biol. 25, 106-24.
American Ornithologists' Union (1983) Check-list of North American Birds, 6th edition. American
Ornithologists' Union, Washington, DC, USA.
Armstrong, R. A. and McGehee, R. (1980) Competitive exclusion. Amer. Nat. 115, 151-70.
Bernstein, H. C., Byerly, H. C., Hopf, F. A. and Michod, R. E. (1986) Sex and the Emergence of Species.
J. Theor. Biol. 117,665-90.
Bowers, M. A. and Brown, J. H. (1982) Body size and coexistence of desert rodents: chance or community
structure? Ecology 63, 391-400.
Brown, J. H. (1973) Species diversity of seed-eating desert rodents in sand dune habitats. Ecology 54,77587.
Brown, J. H. and Bowers, M. A. (1985) Community organization in hummingbirds: relationships between
morphology and ecology. Auk. 102, 251~9.
Calder, W. A. (1984) Size, Function, and Life History. Harvard University Press, Cambridge, MA, USA.
Case, T. J. (1983) Sympatry and size similarity in Cnemidophorus, in Lizard Ecology (R. B. Huey, E. R.
Pinaka and T. W. Schoener, eds). pp. 297-325. Harvard University Press, Cambridge, MA, USA.
Chesson, P. L. (1986) Environmental variation and coexistence of species. In Community ecology
(J. Diamond and T. J. Case, eds). pp. 240-56. Harper and Row, NY, USA.
Chesson, P. L. and Warner, R. R. (1981) Environmental variability promotes coexistence in lottery
competitive systems. Amer. Natur. 117, 923-43.
Cuellar, O. (1979) On the ecology of coexistence in parthenogenic and bisexual lizards. Amer. Zool. 19,
773-86.
Darwin, C. (1859) On the Origin of Species. John Murray, London, UK.
Degenhardt, W. G. (1966) A method of counting some diurnal ground lizards of the genera Holbrookia and
Cnemidophorus with results from Big Bend National Park. Amer. Mid. Nat. 75, 61-100.
Degenhardt, W. G. (1974) A changing environment: documentation of lizards and plants over a decade. In
Competition and community structure
151
Transactions of the symposium on the biological resources of the Chihuahuan Desert region, United
States and Mexico (R. H. Waver and O. H. Riskind, eds). National Park Service No 3, Washington,
DC, USA.
Dennis, B. (1989) Allee effects: population growth, critical density, and the chance of extinction. Nat. Res.
Model. 3, 481-538.
Dunning Jr, J. B. (1984) Body weights of 686 species of North American birds. Western Bird Banding
Association. Monograph No. 1. Eldon, Cave Creek, AZ, USA.
Gause, G. F. (1934) The Struggle for Existence. Williams and Wikins, Baltimore, MA, USA.
Glasser, J. W. (1979) The role of predation in shaping and maintaining the structure of communities. Amer.
Natur. 113, 631-41.
Germano, D. J. and Hungerford, C. R. (1981) Reptile population changes with manipulation of Sonoran
desert scrub. Great Basin Nat. 41, 129-38.
Grant, P. R. and Abbott, I. (1980) Interspecific competition, island biogeography and null hypotheses.
Evolution 34, 332-41.
Hanski, I. (1982) Dynamics of regional distribution: the core and satellite species hypothesis. Oikos 38,210-21.
Heilbrun, L. H. (1982) The eighty-second Audubon christmas bird count. Amer. Birds 36, 369-778.
Heilbrun, L. H. (1983) The eighty-third Audubon christmas bird count. Amer. Birds 37, 369-806.
Holt, R. D. (1984) Spatial heterogeneity, indirect interactions, and the coexistence of prey species. Amer.
Nat. 124, 197-229.
Hopf, F. A. (1990) Darwin's dilemma of transitional forms: a comparison of a model with data. In
Organisational constraints on the dynamics of evolution (J. Maynard-Smith and G. Vida, eds)
pp. 357-72. University of Manchester Press, Manchester, UK.
Hopf, F. A. and Hopf, F. W. (1985) The role of the Allee effect in species packing. Theor. Pop. Biol. 27,
27-50.
Hopf, F. A. and Hopf, F. W. (1986) Darwinian evolution in physics and biology: the dilemma of missing
links. In Frontiers of non-equilibrium statistical physics (G. T. Moore and M. O. Scully, eds) pp. 41129. Plenum, NY, USA.
Hopf, F. A. and Brown, J. H. (1986) The bull's-eye method for examining randomness in ecological
communities. Ecology 67, 1139-55.
Hutchinson, G. E. (1959) Homage to Santa Rosalia, or Why are there so many kinds of animals? Amer.
Nat. 93, 137-45.
Janzen, D. H. (1970) Herbivores and the number of tree species in tropical forests. Am. Nat. 104, 501-28.
Lack, D. (1947) Darwin's Finches. Cambridge University Press, Cambridge, UK.
Levins, R. (1979) Coexistence in a variable environment. Amer. Nat. 114, 765-83.
Lloyd, M. and Ghelardi, R. J. (1965) A table for calculating the 'equitability' component of species
diversity. J. Animal Ecol. 33,217-25.
Losos, J. B., Naeem, S. and Colwell, R. K. (1987) Hutchinsonian ratios and statistical power. Evolution 43,
1820-6.
MacArthur, R. H. (1960) On the relative abundance of species. Amer. Nat. 94, 25-36.
MacArthur, R. H. (1972) Geographical Ecology. Harper and Row, NY, USA.
MacArthur, R. H. and Levins, R. (1967) Limiting similarity, convergence, and divergence of coexisting
species. Am. Nat. 101,377-85.
Martin, F. W., Pospahala, R. R. and Nichols, J. D. (1979) Assessment and population management of
North American migratory birds. In Environmental Biomonitoring, Assessment, Prediction, and
Management (J. Cairns, G. P. Patil and W. E. Waters, eds) pp. 187-240. International Cooperative
Publishing House, Fairfield, MA, USA.
May, R. M. (1973) Stability and Complexity it, Model Ecosystems. Princeton University Press, Princeton,
N J, USA.
May, R. M. (1974) On the theory of niche overlap. Theor. Popul. Biol. 5, 297-332.
May, R. Mo (1978) The dynamics and diversity of insect faunas. Sympos. Royal Entolmol. Soc. London 9,
188-204.
152
Hopf, Vatone and Brown
May, R. M. and MacArthur, R. H. (1972) Niche overlap as a function of environmental variability. Proc.
Nat. Acad. Sci., USA 69, 1109-13.
Pielou, E. C. (1977) Mathematical Ecology. J. Wiley & Sons, NY, USA.
Preston, F. W. (1962) The canonical distribution of commonness and rarity, Part I. Ecology 29, 185-215.
Ricklefs, R. E. and O'Rourke, K. (1975) Aspect diversity in moths: a temperate-tropical comparison.
Evolution 29, 313-24.
Roughgarden, J. (1979) Theory of Population Genetics and Evolutionary Ecology. MacMillan, NY, USA.
Schoener, T. W. (1970) Size patterns in West Indian Anolis lizards. II. Correlation with sizes of particular
sympatric species - displacement and convergence. Am. Nat. 104, 155-74.
Schoener, T. W. (1983) Field experiments on interspecific competition. Am. Nat. 122, 240-85.
Schoener, T. W. (1984) Size differences among sympatric, bird-eating hawks: a worldwide study. In
Ecological Communities: Conceptual issues and the Evidence (D. Strong, D. Simberloff, L. G. Abele
and A. B. Thistle, eds) pp. 254-81. Princeton University Press, Princeton, NJ, USA.
Simberloff, D. (1984) Properties of coexisting bird species in two archipelagos. In Ecological Communities:
conceptual issues and the evidence (D. Strong, D. Simberloff, L. G. Abele and A. B. Thistle, eds) pp.
234-53. Princeton University Press, Princeton, N J, USA.
Simberloff, D. and Boecklen, W. (1981) Santa Rosalia reconsidered: size ratios and competition. Evolution
35, 1206-28.
Simpson, E. H. (1949) Measurement of diversity. Nature 163, 688.
Stewart, F. M. and Levin, B. R. (1973) Partitioning of resources and the outcome of competition: a model
and some general considerations. Am. Nat. 107, 244-67.
Taper, M. L. and Case, T. J. (1992) Models of character displacement and the theoretical robustness of
taxon cycles. Evolution 46, 317-33.
Taper, M. L. and Case, T. J. (1993) Coevolution among competitors. Evol. Biol. (in press).
Turelli, M. (1981) Niche overlap and invasion of competitors in random environments. I. Models without
demographic stochasticity. J. Theor. Biol. 20, 1-56.
Walker, J. M. (1966) Morphology, habitat, and behavior of the teiid lizard, Cnemidophorus labial&. Copeia
4, 644-50.
Willet, T. and Van Velzen, A. C. (1984) The forty seventh breeding bird census. Amer. Birds 38, 64-129.
Williams, C. B. (1964) Patterns in the balance of nature. Academic Press, NY, USA.
Appendix 1
Winter duck data
Winter data were obtained from the A u d u b o n Christmas count (Heilbrun, 1982). Sites were
chosen in salt and freshwater areas and over all of North America. Sites were required to have at
least 1000 individual ducks, with at least 90 % identified to species. Sites were rejected if there
was any ambiguity of species present. We are interested in uniform habitats and chose sites that
often deliberately cross habitats. Most sites were chosen prior to examining data, based on the
authors' experience with the areas, in order to minimize the possibility of composite associations.
Sites chosen (numbers are as in Heilbrun, 1982): 2 , 1 9 0 , 2 4 4 , 2 5 6 , 2 9 7 , 3 5 9 , 4 2 0 , 4 5 6 , 5 4 0 , 5 4 7 ,
556, 675,682, 9 0 9 , 9 5 2 , 9 5 3 , 1038, 1065, 1066, 1128, 1178, 1211, 1229, 1275, 1283, 1339, 1362,
1370.
Nesting duck data
W e obtained the computer readout of the 1980 United States Fish and Wildlife Service ground
survey (that is used to calibrate aerial surveys) from R. A. Phosphahala. The ground surveys
cover an area that includes North and South Dakota, eastern Montana, southern Alberta,
Saskatchewan, and Manitoba (see Martin et al., 1979). All transects that recorded more than one
species were used. The sample sizes range up to 1000 individuals per transect. Prior to examining
Competition and community structure
153
data all species were accepted in the censuses. After examining the data, however, we discovered
that the nesting duck data lacked several species found in the winter data. Thus, we eliminated
those species from the winter data to determine this consequence but found no effect on
dominance structure.
Winter data with small sample sizes
The site list for small sample sizes was taken from Heilbrun (1983). A site was chosen if it
contained 50 to 200 individuals. Most of these sites are located in northern latitudes. No effort
was made to insure uniform habitat.
Site list: 11, 23, 32, 33, 35, 38, 40, 41, 42, 95,114, 167,220,226,252, 257,528,619,628,652,
853,961,963, 1182, 1161, 1173, 1168, 1209, 1321, 1449.
Appendix 2
For each group analysed we provide the source of the species lists and the morphological
character used.
Desert rodents
Obtained from Bowers and Brown (1982), all granivore data set. Their site list is contained in the
ESA Supplementary Publication Service Document No. 8103. They define the granivore guild,
and use averaged body masses obtained from the literature. This list excludes rarities (< 5% of
population) on sites. We use the species masses they provide.
Hawks
Obtained from Schoener (1984), group 2. Morphological data were obtained from Schoener
(1984), Appendix I. The character chosen was wing length, averaged over males and females.
The associations are inferred from overlap in geographic ranges rather than observed.
Nesting flycatchers
Assemblages include all species of the family Tyrannidae plus the genus Siales. The set with
Tyrannidae alone gives no difference in results. The silky flycatcher Phainopepla nitens is largely
frugiverous and was judged not to belong to this group. Our data are primarily from Willet and
Van Velzen (1984) and the morphological character was body mass.
Site list: 1, 2, 3, 5, 14, 15, 25, 27, 33, 46, 61, 63, 64, 65, 66, 71, 75, 77, 80, 81, 84, 86, 87, 90, 91,
93, 99, 111,113,120, 121,122, 123,124,125,131,135,136, 139,140, 141,143,145,148,170, 172,
178, 185, 187, 189, 193, 199, 204, 207, 208.
This survey, however, poorly represents the set of associations in North America insofar as it
includes only about half the species. We therefore supplemented the list with other data. We
asked various naturalists to provide personal records by choosing sites that best matched the size
of the censuses of the breeding bird survey. We obtained the following data: (Source-species list):
NAU-26, 29; DC, 37, 31; SM1-7, 8, 10, 15, 17, 29, 30, 33; SM2-6, 7, 10, 12, 15, 22, 29, 30; SM36, 7, 10, 11, 15, 22, 29, 30; SM4-6, 7, 10, 12, 15, 29, 30; SM5-7, 12, 22, 29, 30; SM6-6, 7, 11;
SM7-7, 11; SM8-12, 29; SM9-6, 7; SM10-7, 29; SMl1-14, 24, 26; SM12-7, 29, 32; SM13-7, 15,
29, 32; SM14-7, 15, 29; SM15-10, 11; SM16-15, 29; SM17-7, 15, 29, 30; SM18-7, 11, 29; SM196, 7, 10, 12, 29, 30; SM20-6, 7, 15, 29, 30; SM21-6, 7, 10, 15, 29, 30; SM22-7, 29, 30; SM23-6, 11;
SM24-7, 11, 15, 29; SM25-6, 7, 10, 17, 30; SM26-6, 10, 17, 30; SM27-15, 29, 30; FH1-2, 3.
Sources; DC site from D. Cooley personal records. SM sites from S. Mills censuses. FH site
from F. A. Hopf personal records. NAU site from Masters (1979).
154
Hopf, Valone and Brown
Numbers identify the following species: 2-Pitangus sulphuratus, 3-Tyrannus couchii, 6Tyrannus vertical&, 7-Tyrannus vociferans, 8-Tyrannus crassirostris, lO-Sayornis nigricans, 11Sayornis saya, 12-Pyrocephalus rubinus, 14-Contopus borealis, 15-Contopus sordidulus, 17Camptostoma imberbe, 22-Ernpidonax traillii, 24-Empidonax oberholseri, 26-Empidonax
wrightii, 29-Myiarchus cinerascens, 30-Myiarehus tyrannulus, 31-Myiarchus crinitus, 32Myiarchus tuberculifer, 33-Pachyramphus aglaiae, 37-Tyrannus dominicensis. (Note: all avian
names were taken from the American Ornithologists' Union 1983 Check-list).
Nesting sparrows
Associations include all species of the family Fringillidae and all species of the following genera:
Pheucticus, Cardinalis, Guiraca, Cyanocompsa, Passerina, Arremonops, Pipilo, Ammodramus,
Pooecetes, Passerculus, Melospiza, Chondestes, Amphispiza, Aimophila, Spizella, Junco, Zonotrichia, Passerella, Melospiza, Calcarius, Plectrophenax, Emberiza, Spiza, Calamospiza, Dolichonyx, Molothrus, and Passer. Data were obtained from Willet and Van Velzen (1984) and the
character used was body mass.
Site list: 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 24, 25, 26, 31, 34, 40, 41, 42,
43, 45, 46, 47, 50, 51, 52, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77,
78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 97, 99, 100, 101,102, 103, 104, 105,
106, 108, 110, 112, 113,117, 118, 120, 121,123,131,132, 134, 135,136, 137,138, 139, 140, 141,
143,146, 147, 148, 149, 150, 151,152, 153, 155,156, 157, 158, 159, 160, 161,165,166, 167,168,
169, 170, 171,172, 173,175,176, 178, 179, 180, 181,182, 183, 184, 185,186, 187, 188,189, 190,
191, 192, 193, 196, 197, 198, 210.
All avian species masses were taken from Dunning (1984). Note: Dunning averaged the masses
for Tyrannus couchii and T. melancholius which, at the time of publication, were still considered
subspecies. We used this mass for each. This change in species status has no impact on our
results.
Anolis lizards
Site list for trios and quartets obtained from Table 3 of Schoener (1970). We were not able to
deduce whether a pair of species found in multispecies assemblages also occur in isolation.
Therefore, from Table 1 we extracted all pairs not included in any of the trio or quartet
associations. We also constructed test sets in which some of the pairs were assumed to exist in
isolation and found that the likelihood of significant bias in the results is small. The
morphological characteer used was snout-vent length.
Sexual Cnemidophorus lizards
Data were obtained from both published work (Degenhardt, 1974: Tortilla; Degenhardt, 1966:
largest sample; Germano and Hungerford, 1981: three associations) and by personal communication of unpublished data of A. Price, O. Cuellar, H. Fitch, F. Turner and P. Medica.
Morphological character used was snout-vent length.
Asexual Cnemidophorus lizards
Data were obtained from Cuellar (1979). Five assemblages: San Antonio riparian, Elephant
butte riparian (and personal communication), Bosque riparian, San Ildefonso, and the assemblage on p. 780. Morphological character used was snout-vent length.
Snout-vent length measurements were taken from Case (1983). Morphological measurements
for species not treated in Case (1983) were obtained from Walker (1966) and by personal
communication with J. Wright.