1495
CONCEP TS & SYNTHESIS
EMPHASIZING NEW IDEAS TO STIMULATE RESEARCH IN ECOLOGY
Ecology,
80(5), 1999, pp. 1495–1504
q
1999 by the Ecological Society of America
TROPHIC RANK AND THE SPECIES–AREA RELATIONSHIP
R
OBERT
D. H
OLT
,
1,5
J
OHN
H. L
AWTON
,
2
G
ARY
A. P
OLIS
,
3,6
AND
N
EO
D. M
ARTINEZ
4
1
Natural History Museum, Department of Ecology and Evolutionary Biology, University of Kansas,
Lawrence, Kansas 66045 USA
2
NERC Centre for Population Biology, Imperial College at Silwood Park, Ascot, Berks SL5 7PY UK
3
Department of Biology, Vanderbilt University, Box 93B, Nashville, Tennessee 37235 USA
4
San Francisco State University, PO Box 855, Tiburon, California 94920 USA
Abstract.
The species–area relationship may be the strongest empirical generalization
in community ecology. We explore the effect of trophic rank upon the ‘‘strength’’ of the
species–area relationship, as measured by
z,
the slope of a log(species) vs. log(area) plot.
We present a simple model for communities closed to immigration, composed of ‘‘stacked
specialist’’ food chains (where each plant species supports a specialist herbivore, which in
turn sustains a specialist carnivore, etc.), that predicts
z
should increase with trophic rank;
the model brings out some of the spatial implications of sequential dependencies among
species. We discuss empirical examples in which the
z
values of taxa differing in trophic
rank were reported and lament the shortage of well-documented examples in the ecological
literature. Several examples fit the expected pattern, but others do not. We outline several
additional reasons why
z
values might increase with trophic rank, even for generalists. If
the qualitative assumptions of the model are relaxed, the predicted effect of trophic rank
on
z
should weaken or even be reversed. Trophic rank may not have a systematic effect
on the species–area relationship if (1) there are strong top-down interactions leading to
prey extinctions; (2) communities are open, with recurrent immigration, particularly at
higher trophic ranks; (3) consumers are facultative generalists, able to exist on a wide range
of resource species; or (4) systems are far from equilibrium. Our aim in this thought piece
is to stimulate community ecologists to link theoretical and empirical studies of food web
structure with analyses of spatial dynamics and landscape ecology, and to encourage em-
pirical studies of the species–area relationship focused on comparisons across taxa varying
in trophic rank.
Key words: distribution; generalist; island; patch; specialist; specialist vs. generalist food webs;
species–area; trophic rank and species–area relationship.
I
NTRODUCTION
The tendency for species richness to increase with
area (the ‘‘species–area relationship’’) is one of the
most robust empirical generalizations in ecology (May
1975, Rosenzweig 1995). Most studies of species–area
patterns have focused on particular taxa, guilds, or
functional groups, rather than broader comparisons
within entire communities. Yet, comparisons of spe-
cies–area relationships among taxa or functional
groups can highlight essential differences in their spa-
Manuscript received 5 September 1997; revised 8 June
1998; accepted 15 June 1998; final version received 13 July
1998.
5
E-mail: predator@kuhub.cc.ukans.edu
6
Current address: Department of Environmental Science
and Policy, 2132 Wickson Hall, University of California, Da-
vis, California 95616 USA.
tial dynamics and responses to spatial heterogeneity
(Kareiva 1994). For instance, biogeographic studies of
West Indies vertebrates reveal stronger species–area
relationships for nonflying mammals than for bats or
birds, consistent with the likely greater importance of
mobility for determining local community composition
in the latter groups (Wright 1981).
A familiar way to characterize the structure of entire
communities is to construct food webs, which are in-
terlinked chains of trophic interactions that define en-
ergy and material flows among species (Pimm 1982,
Cohen et al. 1990). An enormous amount of work has
been devoted to empirical and theoretical food web
analyses (e.g., Martinez 1991, Pimm et al. 1991, Ha-
vens 1993, Polis and Winemiller 1996), with a growing
interest in spatial aspects of food web ecology (e.g.,
Briand and Cohen 1987, Schoener 1989, Warren 1989,
1496 Ecology, Vol. 80, No. 5
ROBERT D. HOLT ET AL.
Concepts & Synthesis
Winemiller 1990, Martinez and Lawton 1995, Holt
1996
a
,
b
, Polis et al. 1996, 1997, Harte and Kinzig
1997). A simple descriptor of a species position in a
food web is its ‘‘trophic rank.’’ Our specific purpose
in this paper is to explore the proposition that trophic
rank may systematically influence the strength of the
species–area relationship. Our more general aim is to
highlight the importance of linking studies of food web
structure with spatial and landscape ecology.
There are various ways to define trophic rank (Yodzis
1989:209). For instance, if for each quantum of energy
consumed by an individual in a focal species, one were
to back-calculate the number of species through which
that quantum had passed before being consumed, the
‘‘trophic rank’’ of the species might be the average
length of all such energetic pathways. Ambiguities in
assignment of species to trophic ranks arise principally
because of trophic generalization (e.g., omnivores feed
at multiple levels). If food webs were comprised en-
tirely of specialists, with specialist carnivores consum-
ing specialist herbivores feeding on single plant spe-
cies, there would be no ambiguity in trophic rank as-
signment.
We first briefly review salient aspects of species–
area theory. We then present a simple model that pre-
dicts that the species–area relationship should be stron-
ger at higher trophic levels, when most consumers are
trophic specialists. Next, we sketch empirical examples
in which species–area relations were assessed for taxa
differing in trophic rank. The theoretical predictions
match some, but not all, patterns in these systems. In
the
Discussion,
we examine alternative reasons why
trophic rank might influence the species–area relation,
as well as factors obscuring such an influence. In par-
ticular, we argue that the effect of trophic rank on the
species–area relationship may often be weaker (or even
reversed) in webs characterized by trophic generalists.
AP
RE
´
CIS OF THE
S
PECIES
–A
REA
R
ELATIONSHIP
There are three basic kinds of species–area relation-
ships (Holt 1992, Rosenzweig 1995): (1) species rich-
ness vs. sample area in nested samples, within a defined
habitat or region (a ‘‘type-1’’ species–area relation-
ship); (2) total species richness vs. total area, among
habitats or regions differing in area (e.g., islands in an
archipelago; a ‘‘type-2’’ relationship); (3) local species
richness in a sample of defined size, among habitats or
regions differing in area (a ‘‘type-3’’ relationship).
Types 1 and 2 have received the most attention in the
literature (Rosenzweig 1995). Often, a power law
S
5
cA
z
, or, equivalently, log(
S
)
5
log(
c
)
1
z
log(
A
), pro-
vides a reasonable statistical summary for the increase
of species richness with area (Rosenzweig 1995),
where
S
is the number of species and
A
is area. The
quantity
z
describes the strength of the scaling of spe-
cies richness with area;
z
is independent of the units
used to measure area (Rosenzweig 1995:21).
There are three explanations for species–area rela-
tionships (Connor and McCoy 1979, Williamson 1981):
sampling, habitat heterogeneity, and colonization–ex-
tinction dynamics.
Sampling.
—Consider a type-1 species–area relation-
ship, for instance nested quadrats used to sample a plant
community. Very small quadrats necessarily contain
few individuals; at small spatial scales, an increase in
species richness with increasing quadrat size almost
surely reflects merely an increase in sample size (Ro-
senzweig 1995). Sampling effects may also explain
some type-2 relationships. Type-3 species–area rela-
tionships, however, automatically control for sample
area, and so are less prone to sampling effects (Holt
1992).
Habitat heterogeneity.
—For type-1 and type-2 spe-
cies–area relationships, habitat heterogeneity is likely
to increase with area (Williamson 1981, Rosenzweig
1995). This can influence species richness, because
large areas are likely to include habitats needed by
species with specialized habitat requirements.
Dynamics.
—Island (type-2) species–area relation-
ships (where each sample is a distinct island commu-
nity) typically have higher
z
values than do type-1 re-
lationships on nearby mainlands (e.g, MacArthur and
Wilson, 1967:10). This systematic difference between
island and mainland species–area relationships usually
reflects spatially mediated processes (Holt 1993, Ro-
senzweig 1995). For instance, local mainland com-
munities are likely to enjoy higher colonization and
lower extinction rates than comparable communities on
islands, and can be enriched via source–sink and me-
tapopulation dynamics (Holt 1993).
The relative importance of sampling, heterogeneity,
and colonization–extinction dynamics as explanations
for species–area relationship on islands and island an-
alogs (e.g., host plants) is still the subject of consid-
erable debate (e.g., Nilsson et al. 1988, Hart and Hor-
witz 1991). For the most part, we focus here on how
trophic rank might influence type-2 species–area re-
lationships among isolated ‘‘island’’ communities,
where one might expect to observe colonization–ex-
tinction dynamics for trophically linked species.
AL
IMITING
C
ASE
:T
IGHT
T
ROPHIC
S
PECIALIZATION
For simplicity, consider an idealized community
comprised of trophic specialists (in the
Discussion,
we
examine a broader range of scenarios). We analyze how
z
should vary with trophic rank, using a generalization
of the incidence function model of Holt (1993, 1996
a
).
The ‘‘mainland’’ community contains
m
food chains of
length
n,
i.e.,
m
plant species, each with its specialist
herbivore, each in turn with
its
specialist carnivore,
and so on. This trophic organization may describe some
assemblages composed of insects that are plant spe-
cialists and parasitoids that are herbivore specialists.
The mainland community of ‘‘stacked specialists’’ is
assumed to be the source pool for a set of islands. Label
each species in a food chain by trophic rank (i.e., spe-
July 1999 1497
TROPHIC RANK AND SPECIES–AREA RELATIONSHIPS
Concepts & Synthesis
cies 1 is the basal producer; species 2 is the herbivore,
etc.). In a snapshot of the system, a fraction
p
(
i
)of
islands (of given area, distance from source pool, etc.)
will contain species
i.
When plotted against variables
such as area,
p
(
i
) is the ‘‘incidence function’’ (Gilpin
and Diamond 1981, Hanski 1992).
Now, assume species
i
is absent unless its required
food resource, species
i
2
1, is present. This implies
nested distributions; species
i
2
1 may be present with-
out species
i.
Define the ‘‘conditional incidence func-
tion’’
p
(
i
z
i
2
1)
5
p
(
i
)/
p
(
i
2
1) as the conditional
probability that species
i
is present, given that its re-
quired food is present (Holt 1993). The basal species’
incidence is
p
(1), so the incidence of species
i
arises
from compounding conditional incidence functions, as
follows:
i
p
(
i
)
5
p
(1)
p
(
i
z
i
2
1). (1)
P
n
5
2
For simplicity, assume all rank
i
species have the same
conditional incidence function; all species of a given
rank thus have the same incidence function.
p
(
i
)isthe
probability that a given species of rank
i
is present on
an island, so the expected number of species of rank
i
on the island is
S
i
5
mp
(
i
), thus log(
S
i
)
5
log(
m
)
1
log(
p
(
i
)). The strength of the species–area relationship is
z
5
d
log(
S
)/
d
log(
A
)
5
d
log(
p
(
i
))/
d
log(
A
). (2)
ii
Now, further assume that basal incidence and the con-
ditional incidence function for each higher rank in-
crease with area (as often observed, Hanski, 1992). One
general reason to expect this arises from basic prop-
erties of small populations (Pimm 1991, Lawton 1995).
If the expected population density of species
i
is con-
stant, total population size scales linearly with island
area. Populations on small islands are likely to risk
extinction due to demographic and environmental sto-
chasticity, even if their required resources are present.
Formally, we assume that
]
p
(1)
]
p
(
i
z
i
2
1)
.
0, and
.
0(
i
.
1) (3)
]
log(
A
)
]
log(
A
)
where variables other than log(
A
) (e.g., distance to a
source) are assumed to be held constant. Taking the
logarithm of
p
(
i
)/
p
(
i
2
1), and differentiating with re-
spect to log(
A
), leads to
]
log[
p
(
i
)]
z
5
i
]
log(
A
)
1
]
p
(
i
z
i
2
1)
]
log[
p
(
i
2
1)]
51
(4)
p
(
i
z
i
2
1)
]
log(
A
)
]
log(
A
)
where the right-most term is
z
i
2
1
. If the conditional
incidence function increases with log(
A
), log[
p
(
i
)] in-
creases faster with log(
A
) than does log[
p
(
i
2
1)]. Thus,
species–area relationships should be stronger (i.e.
greater z) at higher trophic ranks.
Predicting that
z
increases with increasing trophic
rank emerges from the concatenation of three quali-
tative assumptions: (1) species at each level are trophic
specialists on a single species in the level below (a
‘‘stacked specialist’’ community organization); (2) spe-
cialist consumer populations do not persist in the ab-
sence of the resource population they require; (3) spe-
cies are not guaranteed to be present, even if their
required resources are, and a species’ presence be-
comes more likely on larger areas, given the presence
of the needed resource population. These three quali-
tative assumptions are consistent with a wide range of
dynamical possibilities (e.g., explicit colonization–ex-
tinction models for food chains with ‘‘bottom-up’’ con-
trol [Holt 1996
a
,
b
]). These assumptions do not require
a dynamic equilibrium between colonization and ex-
tinction; the predicted patterns may emerge, for in-
stance, in a community being assembled by coloniza-
tion (Drake 1990, Luh and Pimm 1993). Nor do they
require that consumer populations be less abundant
than resource populations. In the
Discussion
we explore
how violating these three assumptions alters the pre-
dicted effect of rank on the species–area relationship.
In particular, for reasons given later, trophic generalists
might often show different patterns than specialists.
(Though our focus is on the species–area relationship,
it should be noted that if conditional incidence declines
with distance from source areas, effects of distance on
species’ richness should also be stronger at higher tro-
phic rank in communities dominated by trophic spe-
cialists.)
E
XAMPLES
One purpose we have in presenting this conceptual
paper is to stimulate comparative empirical studies of
species–area relationships across taxa varying in tro-
phic rank. Though the ecological literature is replete
with species–area datasets (Connor and McCoy 1979),
few investigators have explicitly examined a range of
taxa, differing in trophic rank, simultaneously in a giv-
en archipelago or array of habitat patches (Spencer
1995). In our judgement, there are
no
reasonably com-
plete studies of the structure of whole food webs, re-
solved to the level of species, for islands varying in
size or distance from defined source pools. However,
there are tantalizing hints in the literature of systematic
differences among systems in the influence of trophic
rank upon
z.
In the following paragraphs, we draw to-
gether the salient conclusions of examples known to
us, which mostly deal with subwebs or incompletely
resolved webs. Rather than discuss any particular sys-
tem in great detail, we simply ask whether the reported
z
values (or related attributes) match the qualitative
pattern predicted by the above model. We should stress
that we take reported results at face value. A task for
future work will be to conduct more rigorous analyses
(once a wider range of suitable datasets are available)
with an eye towards the hypotheses presented here.
1) Itamies (1983) reported
z
values for plants and
1498 Ecology, Vol. 80, No. 5
ROBERT D. HOLT ET AL.
Concepts & Synthesis
Lepidoptera on Baltic islands. The values were reported
to differ strongly;
z
plants
5
0.362, and
z
leps
5
0.671.
Given that most of the Lepidoptera are specialists or
oligophages (Itamies 1983), these data are consistent
with our prediction that specialist consumers should
exhibit stronger species–area relationships than do their
resource populations.
2) Kruess and Tscharntke (1994) examined the dis-
tribution on experimental and natural red clover patch-
es of insect herbivores and specialist herbivores. Both
area (in natural meadows) and distance (in meadows
and experimental patches) exerted more pronounced
effects on species richness in parasitoids than on their
hosts, and the effects were in the predicted direction.
These patterns have persisted for the past four years
(T. Tscharntke,
personal communication
).
3) Glasser (1982) reanalyzed data from four islands
in the classic defaunation experiments of Simberloff
and Wilson (1969) and demonstrated a broad pattern
of sequential colonization in these arthropod commu-
nities, with herbivores colonizing prior to their pred-
ators and parasitoids. Though Glasser did not explicitly
make this point, herbivore species richness averaged
over the last three months of the experiment is rela-
tively uniform across mangrove islet sizes, whereas
there are markedly fewer total predator and parasitoid
species on the smaller islands. These data match the
prediction that species of higher rank have stronger
species–area relationships.
4) Schoener and Spiller (1995) used sticky traps to
examine insect communities of small Bahamian is-
lands. The fraction of captured insects comprised of
parasitoids declined with decreasing island area and
increasing distance from neighboring large islands.
This data set does not quite address species–area the-
ory, as it reports the fraction of total individuals, not
the fraction of the total species list comprised of par-
asitoids. Still, this finding is consistent with our the-
oretical expectations. Preliminary sorting by species
supports the conclusion that small and distant islands
are disproportionately poor in parasitoid species (T.
Schoener,
personal communication
).
5) Nilsson et al. (1988) and J. Bengtsson (
personal
communication
) report
z
values for a variety of taxa
occupying islands in Lake Malaren, Sweden. The taxa
and their respective
z
values are as follows: plants, 0.1;
snails, 0.156; carabids, 0.361; spiders, 0.228; and birds,
0.616. The pattern here may not be entirely consistent
with our theory (depending on the relative trophic rank
assignments of carabids and spiders), but at least the
basal trophic layers (plants and snails) have shallower
species–area relationships than do higher ranked spe-
cies (carabids, spiders, and birds).
6) Our prediction of an effect of trophic rank on the
species–area relationship rests on a lower level pre-
diction, namely that trophic rank, in part, predicts the
spatial incidence of species, independent of abundance.
Wright and Coleman (1993) provide supportive data.
These authors isolated nematode assemblages in soil
cores over a 16-mo period and monitored changes in
community composition and trophic structure. Many
extinctions occurred. Those species that persisted tend-
ed to be abundant initially, and of lower trophic rank,
than species going extinct. An analysis of covariance
showed that both abundance and trophic rank signifi-
cantly and independently contributed to survival; high-
er ranked species did not persist as long as lower ranked
species, even controlling for abundance effects.
7) Havens (1992) (and see Martinez [1993]) de-
scribed the pelagic food webs of 50 lakes in the Adi-
rondacks with 10–74 taxonomic species (mean
5
38
species). If lakes can be viewed as aquatic ‘‘islands,’’
these webs allow us to assess effects of trophic rank
on the species–area relationship. The webs are based
on species lists obtained via consistent sampling pro-
cedures performed in 1984 (e.g., epilimnion phyto-
plankton tows, vertical zooplankton tows, and fish traps
and nets). We assigned a rank to each consumer species
in the webs by calculating the mean length of all food
chains leading from basal resources to the consumer.
Basal resource species have rank one, while consumers
are given a rank equal to their mean chain length
(rounded off to the nearest integer) plus one. The log-
arithm of species richness at each rank was regressed
against the logarithm of surface area, leading to an
estimate of the
z
value for species of each rank and an
error term for the
z
value (the standard error of the
regression slope). Although there is a positive slope of
regression of
z
values vs. trophic rank, the slope is not
significantly different from zero. (N. D. Martinez,
un-
published analyses
). At best, then, Havens’ lake da-
tasets provide weakly corroborative evidence in favor
of the rank dependency theory. We suggest in the
Dis-
cussion
that the lack of fit to the theoretical prediction
may be due to widespread trophic generalism in pelagic
lake organisms.
8) Islands in the Gulf of California support plant
communities typical of Sonoran desert associations,
and, despite low and temporally variable productivity,
are surprisingly rich in species (Case and Cody 1983).
Ongoing studies by G. Polis and associates are docu-
menting distributional patterns of species at several
trophic levels (Due 1992, Polis and Hurd, 1995, 1996;
G. A. Polis,
unpublished data
), building on published
distributional data for reptiles (Case 1983), plants
(Cody et al. 1983), and birds (Cody 1985). Preliminary
analyses using data on islands ranging 0.001–1208 km
2
suggest a pattern contradicting the prediction of the
‘‘stacked specialist’’ model, with estimated
z
values as
follows: vascular plants, 0.424; scorpions, 0.162; land
mammals, 0.160; reptiles, 0.319; and land birds, 0.291
(G. Polis,
unpublished results
). The vertebrate taxa in
this study are trophically heterogeneous (e.g., ‘‘rep-
tiles’’ include a herbivore [chuckwalla] as well as car-
nivorous snakes and arthropodivorous lizards). None-
theless, quite clearly, the lowest trophic level (plants)
July 1999 1499
TROPHIC RANK AND SPECIES–AREA RELATIONSHIPS
Concepts & Synthesis
has a higher
z
value than many higher ranked consum-
ers.
9) A recent study by Spencer et al. (
in press
)of
invertebrate communities in temporary ponds in Israel
has shown that the proportion of predatory species in-
creases with pool surface area, implying that predators
in these communities have larger
z
values.
To summarize our impression of highlights of these
empirical studies, study number six suggests trophic
rank influences incidence, even independent of popu-
lation size. Studies one through five and nine all match
the qualitative predictions. Study number seven pro-
vides, at best, weak support for the theory, whereas
study number eight reveals a pattern in
z
values op-
posite to that predicted. In the
Discussion,
we present
some ideas as to the factors that may lead to such
differences among systems.
D
ISCUSSION
The incidence function model formalizes the quali-
tative notion that trophic specialization entails a com-
pounding of spatial effects: specialist taxa of high tro-
phic rank are constrained in their distribution by pro-
cesses that operate directly upon their own dynamics,
as well as by spatial constraints impinging on those
lower-ranking taxa upon which they depend. One con-
sequence of sequential trophic dependencies among
specialist species is that spatial effects compound in
the assembly of food chains. This implies that the spe-
cies–area relationship should become stronger (viz.,
higher
z
) at higher trophic levels.
However, other factors can lead to the same predicted
effect of trophic rank on
z
; hence, observing the pattern
need not support the above theory. Moreover, in many
reasonable circumstances the predicted effect should
not occur at all. Here, we first discuss alternative factors
that can lead to positive trophic effects on
z,
and then
examine the consequences of weakening the three qual-
itative assumptions of our model.
Alternative explanations for greater z at higher
trophic ranks
Energetics, trophic rank, and population size.
—The
usual dynamical explanation for the species–area re-
lation goes as follows: small area
⇒
low abundance
⇒
high extinction rates
⇒
low incidence on small ar-
eas. If population size systematically declines with in-
creasing trophic rank (say, for energetic reasons), high-
er ranked species should be more prone to extinction
on small islands (Schoener 1989), leading to stronger
species–area relationships at higher levels. This pre-
diction arises from the effect of trophic position on
population size and, hence, on extinction rates, an ef-
fect that may complement effects due to trophic spe-
cialization. The population size explanation should also
apply to many trophic generalists.
Sampling effects and trophic rank.
—As noted, sam-
pling effects can provide a simple explanation for spe-
cies–area relationships, particularly at small spatial
scales. The range of island sizes over which sample
size effects generate a species–area relationship should
tend to increase as average population density in the
focal taxa declines. If higher ranked taxa, on average,
have lower abundances than do lower ranked taxa, sam-
ple size effects should be evident over a wider range
of island sizes for higher ranked taxa, than for lower
ranked taxa, This may explain some observed effects
of trophic rank on
z
values. For instance, in Example
5, birds have the highest
z
and also likely have the
highest average trophic ranks among the taxa recorded.
However, in this case, high trophic rank is correlated
with low abundance, with few individuals per species
on each of these small islands. Because most of these
bird species settle afresh each breeding season, it is
plausible that sampling taxa of low abundance accounts
for the observed high
z
for birds on these islands (J.
Bengtsson,
personal communication
). The main effect
of trophic rank, here, is upon abundance and, thus, upon
the likelihood of sampling effects being pronounced in
small areas.
Ecological processes that weaken the effect of
trophic rank upon z
Violating any of the three qualitative assumptions
that underlay the incidence model can weaken or re-
verse the predicted effect of rank on
z.
Conditional incidence may decrease with area.
—We
assumed that the conditional incidence for species
i
increases with area. This seems reasonable but does
rest upon implicit assumptions about underlying spe-
cies interactions. In some plausible circumstances, con-
ditional incidence may decrease with area. Holt (1996
a
,
b
) analyzed explicit island biogeographic and meta-
population models of food chains, in which species’
incidence on islands or patches in a heterogeneous
landscape emerges from the dynamic interplay of
trophically driven colonizations and extinctions. One
conclusion was that larger
z
values at higher trophic
ranks are likely, if the food chain is ‘‘donor-controlled’’
(i.e., extinctions in level
i
are not driven by the presence
of higher trophic levels), or when weak top-down ef-
fects are present (i.e., predators increasing prey ex-
tinction).
However, if increasing area reduces rates of predator
extinctions for reasons other than prey depletion (e.g.,
small predator populations may be vulnerable to ex-
tinction due to inbreeding, or catastrophes, even with
abundant prey), prey populations may overall be more
prone to extinction on larger islands, because that is
where predators, on average, persist long enough to
potentially extirpate their resource species. In this case,
prey species richness can actually decline with increas-
ing island area, or have a flat relationship. Comparing
the species richness of intermediate consumers to their
own resources may paradoxically result in an inverted
relationship between trophic rank and
z,
because of