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ecological complexity 3 (2006) 148–159
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Evolution of body size, range size, and food composition
in a predator–prey metapopulation
C. Hui *, M.A. McGeoch
Spatial, Physiological and Conservation Ecology Group, Department of Entomology, University of Stellenbosch,
Private Bag X1, Matieland 7602, South Africa
article info
abstract
Article history:
Relationships among body size, range size, and food composition are central to community
Received 25 August 2005
ecology. Utilizing a simple framework of allopatric speciation, a stochastic, cellular auto-
Received in revised form
maton model of predator–prey metapopulations in one- and two-dimensional patchy net-
12 December 2005
works are constructed. In the model, ecological processes, such as local extinction,
Accepted 30 December 2005
recolonization, and predation, and evolutionary processes, such as mutation, influence
Published on line 12 May 2006
the average body size or morphological value of a local population in a patch. Accumulating
morphological divergence between local populations incurs allopatric speciation. Results of
Keywords:
the model, highly correlated with some experimental data (795 species totally in China:
Allopatric speciation
Tetrigoidea 139 species, Fringillidae 453 species, and Serpentes 203 species), show that
Dietary niche breadth
distribution of body size is right-skewed and multimodal. The right-skewed distribution
Metacommunity
arises from the proportionality assumption and multimodality is a result of adjacent
Skewness
colonization. Predation (the increase of tropic level) can decrease the skewness and increase
Distribution
the number of modes in the distribution. Distributions of range size and food composition
Tropic level
are also right-skewed. Species with small range size like to aggregate in space surrounding
by widespread species, forming a fountain of allopatric speciation. Furthermore, two rough
rules from these distributions about the proportion of prey numbers to predator numbers
and food composition are represented, showing that the proportion is about 2.3 and the
number of prey species in food is 4.3 with about 47% similar between neighboring predator
species. Additionally, the relationship between range size and body size is triangular,
implying that widespread species has medium body size and large or small species is
always spatially restricted. Relationship between body size and food composition is also
triangular and indicates that extreme body size, largest or smallest, is always accompanied
with stenophagic, while species with medium body size can be either euryphagic or
stenophagic.
# 2006 Elsevier B.V. All rights reserved.
1.
Introduction
The evolution of life history characters is central to both
ecological and evolutionary research. These characters range
from body size and longevity, describing the organism itself
(Brown, 1995; Gaston and Blackburn, 2000; Makarieva et al.,
2004a, 2005a), to spatial distribution and food composition,
indicating the relationship with its environment (McGeoch
and Gaston, 2002; Hui et al., 2004). Traditional and classical
approaches to life history evolution involve optimization
under constraints and trade-offs (Roff, 1992; Stearns, 1992;
Charnov, 1993; Kozlowski and Weiner, 1997). The realm of
* Corresponding author. Tel.: +27 21 808 4775; fax: +27 21 808 4807.
E-mail addresses: [email protected] (C. Hui), [email protected] (M.A. McGeoch).
1476-945X/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecocom.2005.12.003
ecological complexity 3 (2006) 148–159
most studies of life history theory encompasses a single, large,
undisturbed, and spatially homogeneous population.
Recently, owing to global rates of habitat destruction and
fragmentation, as well as progress in computing techniques,
spatial modelling, and analysis (Tilman and Kareiva, 1997), e.g.
the dynamic complexity of metapopulations (Hui and Li, 2003),
has become a key instrument in ecological research and
biological conservation (Hanski, 1998). For example, using a
spatial modeling approach, Hui and Li (2004) found a new
equilibrium of the spatiotemporal population dynamics
resulting in a ‘‘circumscription’’ distribution which cannot
appear under the mean-field assumption (that is a single wellmixed population). Olivieri and Gouyon (1997) illustrated how
disequilibrium and the spatial structure characteristic of
metapopulations might significantly affect the evolution of
life history traits, a phenomenon they called ‘‘the metapopulation effect’’. Populations in spatially structured habitats may
generate an ‘‘ecological imprint’’, on the environment that
leads to environmental heterogeneity and the distribution
segregation of different species, and even an oscillation
dynamics in community (Hui et al., 2004), which brings about
the maintenance of polymorphism in natural population (Yue
et al., 2004). All these studies show that spatial factors are
essential to ecological patterns. However, studies of life
history evolution in a metapopulation context remain rare
compared to the explosion of metapopulation demographic
studies (see review in Ronce and Olivieri, 2004). In this paper,
spatial factors are introduced into a life history evolution
model that reveals some spatial and scaling patterns of life
history characters.
Body size is one of the most important quantitative traits
under evolutionary scrutiny, because it is strongly correlated
with many physiological and fitness characters, and exhibits
prominent general evolutionary and allometric patterns in
many organisms (Blanckenhorn et al., 1999; Brown et al., 2004;
Li et al., 2004; Makarieva et al., 2005a). Because the allometric
scaling relationship between body size and metabolic rate
(Huxley, 1932; Kleiber, 1932; Savage et al., 2004; Chown et al.,
2004; West et al., 1999; Brown et al., 2004; Li et al., 2004), body
size and allometry has become the focus in recently ecological
and physiological debate. Within species, body size, determined by allometry and life history constraints (Kozlowski
and Weiner, 1997; Charnov, 2002), can affect heritability
(Leibowitz et al., 1995), niche breadth (Shine et al., 1998),
spatial structure (Ward et al., 2002), and mating success (Jones
and Purvis, 1997). Interspecific pattern of body size presents a
rough rule (S L2, where S is the number of species and L the
characteristic linear dimension) for animals on the land (May,
1978), and in the sea (Fenchel, 1993), except for the less
knowledge about smaller organisms (L < 0.01 m). The ecological or evolutionary origins of this rule may result from future
studies on allometric scaling relationships (Enquist et al., 1998;
West et al., 1999; Gillooly et al., 2001; Makarieva et al., 2004b,
2005b,c,d,e) and branching vascular structure (Banavar et al.,
1999; West et al., 1999; Makarieva et al., 2006). Compared with
the above taxonomic rule, observations in a community
always show a lumpy distribution of body size (Holling, 1992).
This universal lumpy distribution may result from discontinuous texture of landscape (Raffaelli et al., 2000), and this
landscape structure can result from many self-organizing
149
ecosystem processes such as fire, storm and water, and
biological process (McNaughton et al., 1988; Naiman, 1988).
Evidences reinforce the point that discontinuities in the
geometry of vegetated landscape impose discontinuities on
the morphology of animals (Morton, 1990). However, species
richness and body size distribution in different tropic levels
have been little investigated and compared.
Several recent studies have modeled the joint dynamics
of speciation, extinction, and colonization in a spatially
explicit framework using phenomenological descriptions of
speciation (Bramson et al., 1996; Durrett and Levin, 1996;
Hubbell, 2001). Although these earlier approaches are
heuristically very useful for the process of diversification
in metapopulations and for providing a basis for additional
numerical and analytical work, the phenomenological
treatment of speciation they employ is not satisfactory
(Gavrilets, 2004). In the point speciation model each new
species starts with exactly one individual (Bramson et al.,
1996; Durrett and Levin, 1996). In the random fission model,
the new species gets a random proportion of individuals of
the ancestral species (Hubbell, 2001). However, these studies
do not consider underlying genetics and simply postulate
that a new species with a certain number of individuals
emerges with a certain probability out of the ancestral
species. However, excluding processes such as polyploidy
and major chromosomal changes, speciation does not occur
instantaneously (Gavrilets, 2004).
In the model presented here, the speciation process is
based on a simple model of allopatric speciation (Gavrilets
et al., 2000), which is closely related to several previous
studies (Orr and Orr, 1996; Gavrilets, 1999). Allopatric
speciation is the origin of two or more species resulting from
divergent evolution of populations that are geographically
isolated from one another. Speciation through reproductive
isolation that is a consequence of incompatibilities between
different genes and traits (Gavrilets, 2004) is utilized in most
existing studies, which firstly expressed by Bateson (1909),
Dobzhansky (1937), and Muller (1942). Growing experimental
evidence supports this definition (Wu and Palopoli, 1994; Orr,
1995; Wu, 2001). By the metaphor of adaptive landscapes
(Wright, 1932), populations diverge genetically along the
‘ridge’ of highly fit genotypes and become reproductively
isolated species when they come to be on opposite sides of a
‘hole’ in a ‘holey’ adaptive landscape (Gavrilets, 1997;
Gavrilets and Gravner, 1997). Therefore, quantitative characteristics, such as body size, determined by multi-locus
genes evolve gradually and the morphological distance
between two adult individuals is, to some extent, a reflection
of the inner genetic differences, and can incur reproductive
isolation if a threshold value is exceeded.
Paleontologists have adopted the related morphological
species concept, in which species are discerned by phenotypic
differences (Benton and Pearson, 2001). The morphological
species concept is that a species is defined by being sufficiently
morphologically distinct from all others. The definition can
include multivariate tests of the statistical distance between
species centroids in relation to intraspecific variation about
the centroids (Sneath and Sokal, 1973). It is assumed that,
although morphological differentiation need not form part of
reproductive isolation, populations will nonetheless diverge
150
ecological complexity 3 (2006) 148–159
genetically, and this will be reflected rapidly enough in the
divergence of phenotypes that the point of splitting and
detectable morphological differentiation effectively coincide.
This might be true given that the finest geological timescales
are generally in the order of hundreds or thousands of years
(Benton and Pearson, 2001). The assumption that morphologically recognized species in the fossil record correspond to
biological species is an essential underpinning of palaeontological studies of speciation (Benton and Pearson, 2001).
Genetic and morphological differentiation need not coincide,
but there is extensive evidence for such a coincidence at the
temporal and spatial scales used in studies of fossils
(Ereshevsky, 1992; Roth, 1992; Coyne, 1992).
Here, we will simulate allopatric speciation in a metapopulation framework. This speciation is a consequence of
accumulating morphological distance, e.g. body size differences. Ecological processes, such as local extinction, recolonization, and predation, as well as evolutionary processes,
such as mutation, can affect this allopatric speciation as well
as the frequency distribution of the life history characteristic
in a patchy environment. For simplicity, we will call this
quantitative character decided by multi-loci genes as body size
in this paper. What patterns of these life history characters
generated in a metapopulation structure and how predation
and local space-competition (extinction–recolonization process) affects these life history patterns will be discussed. As
the corollaries of the results, relationships among body size,
range size, and dietary niche breath, i.e. food composition will
also be discussed. Further, results from empirical data (795
species totally: Tetrigoidea 139 species, Fringillidae 453 species
and Serpentes 203 species) are compared with the theoretical
results of the model.
2.
Models
In 1968, Levins indicated that both the spatial and temporal
organization of the environment might significantly affect the
extent to which a population would rely on genetic polymorphism (Levins, 1968). Furthermore, Levins (1969) defined a
metapopulation as a population consisting of many local
populations or demes. Due to aggregated distributions of
individuals (Weiher and Keddy, 1999), any species is, to some
extent, a metapopulation influenced by ecological processes
(such as local extinction and recolonization) and microevolutionary processes (such as selection and gene flow)
(Hui and Yue, 2005). In a metapopulation, all local populations
have a substantial probability of extinction, and hence longterm persistence of the species can only occur at the regional
or metapopulation level (Hanski, 1998). The stochastic cellular
automaton model (SCAM) here is based on the metapopulation framework.
Here, we assume the phenotypic differences (such as the
differences in body size) are a reflection of genetic differences,
which will lead to reproductive isolation beyond a certain
threshold. This assumption is consistent with the Bateson–
Dobzhansky–Muller Model (Bateson, 1909; Dobzhansky, 1937;
Muller, 1942; also see Gavrilets, 2004) and the shift from the
two-dimensional rugged adaptive landscape (Wright, 1932) to
the high-dimensional holey adaptive landscape that are
extensive nearly neutral networks (Gavrilets and Gravner,
1997; Gavrilets, 1997; Reidys, 1997; Reidys et al., 1997).
SCAM is constructed to investigate distributions and
relationships mentioned above. The model will be run in a
one-dimensional stepping-stone habitat (SCAM-1d) with n
patches and in a two-dimensional patchy network (SCAM-2d)
with n n patches. Periodic boundary condition that patches
are located in a circle or a spherical surface is adopted to
exclude the boundary effect. The ‘‘body size’’ of an individual
can be measured by a morphological value, and hence every
local population has its average morphological value. The
morphological variation within populations is neglected
(Gavrilets et al., 2000) since we only concentrate on evolutionary events and neglect the ecological ones (such as how a
particular body size predominates in the local population).
In each patch, there is a local prey population and a local
predator population, with average morphological values
m1(i) and m2(i), respectively, where i indicates the location of
each patches. The average morphological values can be
altered by mutation and metapopulation processes. Because
most speciation events involve gradual or relatively smallscale changes (Strickberger, 2000), we assume that body size
can only change from mk(i) to (1 b)mk(i) with probability u
at each time step, where b is a parameter of mutation
intensity. This assumption implies that the absolute
morphological change of a large species by mutation will
be larger than that of a small species (i.e. an elephant that is
1 m larger than the average becomes a new species, while a
Fig. 1 – A schematic illustration of ecological speciation. (a) Punctuated speciation. (b) Classic phyletic gradualism speciation.
A species located in a one-dimensional eight patches (bottom) is separated to two species (up with white and gray
background) if the morphological difference between two local populations is larger than two. Numbers in square indicate
the morphological value of local population in the patch, and numbers nearby the arrow is the average morphological
values of different species.
ecological complexity 3 (2006) 148–159
Table 1 – Algorithm of the simulation procedure in SCAM
Step 1
‘‘Lock-and-key’’ relationship of body size between
prey and predator
If jm2 ðiÞ H m1 ðiÞj B, extinction rates
are e1 + d for prey and e2 for predator, else if
extinction rates are e1 for prey and e2 + d for predator.
Step 2
Metapopulation processes
If the prey extinct, choose a prey in the neighborhood
re-colonize the patch (and hence the new prey have
the same body size as the neighbor). The same
process for the predator.
Step 3
Mutation processes
If the prey mutate (mutation rate: u), m1(i) =
(1 W b)m1(i), else if m1(i) = m1(i). The similar process
for the predator.
Step 4
Allopatric speciation processes
If patch j is a neighbor of patch i and d1 ði; jÞ > b Dðm1 ðiÞþ
m1 ð jÞÞ=2, there forms a reproductive isolation between the
prey populations in these two patches and the populations
belong to two different species according to the concept of
allopatric speciation. The same process for the predator.
Step 5
Go to step 1.
151
mouse just needs 1 cm larger to be a new species), which is
analogous to the assumption of the model STEVE (Cumming
and Havlicek, 2002). The gradual morphological change in
speciation events is consistent with the concept of ecological speciation (Schluter, 2001; Hey, 2001). Ecological
speciation might come about indirectly as a consequence
of natural selection on morphological, physiological or
behavioral traits, or it might include direct selection on
pre-mating isolation (Schluter, 2001). This gradual morphological change in the sub-populations does not mean the
gradual morphological change in speciation, but a combination between the classic phyletic gradualism model and the
punctuated equilibrium model (Simpson, 1944; Eldredge,
1971; Eldredge and Gould, 1972; Benton and Pearson, 2001).
As shown in Fig. 1, the gradual morphological change in
local populations can lead to the punctuated speciation
(Fig. 1a) and the classic phyletic gradualism speciation
(Fig. 1b), which depends on the variability of the morphological values within the metapopulation.
Evidences have shown that there is a ‘lock-and-key’
relationship between the body size of prey and that of
Fig. 2 – Spatial structure of species border and body size in two-dimensional habitat after 2000 generations. (a) and (b) are
species borders of prey and predator, respectively. Black curves indicate that the two adjacent populations are
reproductively isolated. (c) and (d) are spatial structure of body sizes for prey and predator, respectively. Darkness
represents the relatively morphological values of body size. Parameter values are n = 100, u = 0.05, b = 0.05, e1 = 0.1, e2 = 0.1,
D = 5, d = 0.1, s = 0.5, H = 50, and B = 1.
152
ecological complexity 3 (2006) 148–159
predator (Morand et al., 2000). The relationship between mean
prey size (Wprey) and predator size (Wpred), in kilograms, for
mammals and birds of prey (large-prey eaters) and for lizards,
amphibians, seabirds, and insectivorous birds (small-prey
eaters) is consist with a positive power relationship (for
1:18
small-prey eaters, Wprey ¼ 0:0018Wpred
, R2 = 0.75; for large-prey
2
1:16
eaters, Wprey ¼ 0:109Wpred , R = 0.74; for raptorial birds,
0:93
1:26
; for codfish, Wprey ¼ 0:0035Wpred
) (A.
Wprey ¼ 0:179Wpred
Vézina, unpublished; Schoener, 1968; Ware, 1980; see also
Peters, 1983). Hence, we assume that a predator population can
only feed on prey populations with corresponding body sizes,
jm2 ðiÞ H m1 ðiÞj B, where H is a constant depicting body
size differences between prey and predator, and B indicates the
body size range of available prey (e.g. if m2(i) = 100, H = 50, and
B = 1, the body sizes of available prey are m1(i) = 49, 50, and 51).
Because predation can profoundly affect the metapopulation
processes (Taylor, 1991), the local extinction rates of prey and
predator are e1 + d and e2, respectively, if the predator can find
the available prey, and are e1 and e2 + s, respectively, if not.
After extinction, individuals from one of the adjacent nonextinct populations can colonize the empty patch immediately
(Durrett and Levin, 1996).
Let the morphological difference between patch i and
patch j is dk(i, j), where k is either 1 for prey or 2 for predator.
This morphological difference represents genetic divergence
between these populations and can result in reproductive
isolation between these populations if it exceeds a threshold, dk ði; jÞ > b Dðmk ðiÞ þ mk ð jÞÞ=2, where D is the mutation
steps needing for species separation. It implies that largebody populations need more morphological differences for
diversification than small ones, although the mutation steps
are the same. This speciation pattern is coincident with the
speciation mechanism in a holey adaptive landscape
(Gavrilets et al., 1998), which shows that speciation is an
inevitable consequence of genetic divergence (Orr, 1995).
According to the above rules, we can construct the SCAM
(see Table 1 for the simulation procedure), a cellular
automaton, which is one of the most prevalent approaches
in spatial ecology (Tilman and Kareiva, 1997; Hui, 2004; Hui
et al., 2005; Li et al., 2005).
3.
Results
The spatial structures of distribution border and body size of
species are presented in Fig. 2, by SCAM-2d. Populations
surrounded by closed species border are a new species in
terms of allopatric speciation. We noticed that speciation
always occur clustered, which implies that new species are
always spatial restricted (small range size) and the spatially
restricted species are clustered in space; moreover, the
species richness of prey is larger than that of predator
(Fig. 2(a) and (b)). The spatial structure of body size is a mosaic,
and the fountain of speciation is the region that the
morphological values intensively change between patches
(i.e. the region of drastically fluctuation of gray-level in
Fig. 2(c) and (d)). The fountain of speciation is consistent with
the region that spatially restricted species distribute, which
has important corollary in discussion. Because SCAM-2d is
very time-costing, we only use it to describe the spatial
Fig. 3 – Evolutionary dynamics of species border. (a) Border
dynamics of prey species. (b) Border dynamics of predator
species. Parameter values are the same as in Fig. 2.
structure of allopatric speciation. More theoretical analysis
will be based on the SCAM-1d.
Using SCAM-1d, evolutionary dynamics can be presented
(Fig. 3). Firstly, species borders of prey are more stable than
those of predator, which means that species with high
trophic level is more vulnerable to environmental changes,
such as local extinction and species invasion, than species
with low trophic level, which is accordance with the
experiences of biological conservation (Taylor, 1991). Secondly, ecosystem needs a coalescence phase, about 500
generations, to construct its structure. According to Gavrilets’ estimation (Gavrilets et al., 2000), the coalescence phase
is about T D/u. This result indicates that reconstructed
artificial ecosystem can hardly generate stable structure and
ecological complexity 3 (2006) 148–159
produce normal ecosystem service within short duration,
which challenges the optimism in biological conservation.
Thirdly, morphological values or body sizes are clumpy
distributed in space even though the habitat is homogeneous. This clumpy pattern is a consequence of local
colonization and the coarseness or lumpiness of body-size
distribution is even amplified in higher trophic. Colonization
between neighboring patches is the key to maintain the
lumpy pattern and discrete distribution of body size in
metapopulation communities.
4.
153
Discussion
4.1.
Distributions of body size, range size and food
composition
Real-world data on body size are abundant, since it is the
most fundamental measure of species. According to the data
from Fauna Sinica (Li et al., 1982; Liang and Zheng, 1998), we
show the body size distributions of grasshoppers (Tetrigoidea,
139 species) and finches (Fringillidae, 453 species) of China
Fig. 4 – Distributions of body size, range size, and food composition of prey and predator. (A) and (B) are body-length
distributions of Tetrigoidea and Fringillidae in China (data from Li et al., 1982; Liang and Zheng, 1998). (C) and (D) are body
size distributions of prey and predator. (E) and (F) are range size distributions of prey and predator. (G) is the distribution of
food composition of predator. Simulated data are obtained by SCAM-1d, sampling every 100 generations from 4000 to 5000
generations. Parameter values are the same as in Fig. 2 except n = 400 and u = 0.02.
154
ecological complexity 3 (2006) 148–159
(Fig. 4A and B). Simulated distributions of prey and predator
are also presented for comparison (Fig. 4C and D). Simulated
results, highly consistent to the results from taxonomy, imply
that distributions of body size are right-skewed and multimodal both for prey and predator. The effect of predation, or
tropic level, is a weakener of skewness and an amplifier of
lumpiness. This right-skewed distribution in our work is a
consequence of the proportional assumption that a genetic
mutation can lead to more morphological variation in the
organism of large body size than that in small one, and hence
large organisms have a larger speciation threshold for
morphological diversification. Right-skewed distribution of
body size turns to normalized distribution without the
proportional assumption. Therefore, this assumption, a
certain result of allometric scaling relationships (Kozlowski
and Weiner, 1997; Enquist et al., 1998), may be a kernel for
pattern formation in communities, which needs additional
experimental attestations.
May (1978, 2001) indicated that the species-body size
distribution could be described by a rough rule S L2
(L > 0.01 m). What are the ecological or evolutionary origins
of this rough rule, which holds true over four or more orders-ofmagnitude in characteristic lengths of animals on land, and
roughly similarly in the sea (Fenchel, 1993)? To what extent and
why is the breakdown in this rule at small sizes real, and to what
extent may it be a consequence of less knowledge about smaller
things (May, 2001)? In Fig. 4, we analyzed the distribution of the
right tail (from modal body size to maximal size) by the power–
function regression and found that the relationships do not fit
this rough rule very well (for Tetrigoidae in Fig. 4A, S L6.58,
R2 = 0.74; for Fringillidae in Fig. 4B, S L8.1, R2 = 0.59; for the
prey in Fig. 4C, S L4.97, R2 = 0.73; for the predator in Fig. 4D,
S L3.98, R2 = 0.39). First, these relationships are consistent
with the negative power equations; yet, the exponents in these
equations are significantly different from the one in May’s
formula. Second, the coefficient of determination R2 decreases
with the tropic level, which indicates the uncertainty of the
community structure in high tropic level.
Kozlowski and Gawelcyk (2002) presented an excellent
review about why body size distribution is skewed to the right.
They indicated that skewness of body size distribution is
influenced by geographic scale and explained by macroevolutionary models, the fractal character of the environment, or
body size optimization (Kozlowski and Gawelcyk, 2002). For a
broad range, distributions in a class are usually right-skewed;
for a narrower scale, distributions remain right-skewed or
become symmetric or even close to uniform (Kozlowski and
Gawelcyk, 2002). Roy et al. (2000) analyzed the body size
distribution of the north-eastern Pacific marine bivalves along
a latitudinal gradient at the provincial level and found that the
modal sizes and shapes of these distributions are invariant.
They further indicated that the modal size is an evolutionary
attractor over geological time (Roy et al., 2000). Yet, Knouft
(2004) studied the regional communities of North American
freshwater fishes and suggested that there is a negative
correlation between latitude and regional community size
distribution skewness, with size distributions becoming leftskewed at high latitudes. The reason of the commonness of
right-skewed distribution of body size in a regional community is still not clear.
Three mechanisms were presented to explain this character of body size distribution. First, the fractal nature of
environment will straightforwardly leads to the right skewed
distribution (Morse et al., 1985; see a review by Gaston and
Blackburn, 2000). Yet, as Kozlowski and Gawelcyk (2002)
indicated, the most serious problem is that the smallest sizeclass should always be most numerous, and this is never or
almost never the case. Second, small-biased speciation and
large-biased extinction can also lead to right skewness
(McKinney, 1990; Maurer et al., 1992). Third, there might be
an optimal body size, which will form the modal in the
distributions (Brown et al., 1993; Charnov, 1993; Perrin and
Sibly, 1993; Kozlowski, 1996; Chown and Gaston, 1997). Results
here suggested that (1) the assumption of proportional
morphological change to body size and (2) tropic level in
community are also two important factors to the skewness of
body size distribution.
On the other hand, although textural discontinuity indeed
generates lumpiness in distribution of body size (Holling, 1992;
Cumming and Havlicek, 2002), it can also come from adjacent
colonization even in homogenous patchy habitat, which can
be amplified by trophic levels. Additionally, the top species
(the largest species in body size) of prey is larger than the one
of predator. This interesting result has been reported in
dinosaurs by Burness et al. (2001), which show that the body
size of the top species decreased in the sequence: ectothermic
herbivore > endothermic herbivore > ectothermic carnivore > endothermic carnivore.
Distributions of range size and food composition are also
right-skewed in linear scale (Fig. 4E–G). Right-skewed distribution of range size has been reported in many real
experiments (Gaston, 1994, 1996; also called occupancy
frequency distribution in McGeoch and Gaston, 2002). While,
there are also numerous evidences showing that the distribution of range size is hollow, i.e. bimodal (Blackburn et al., 1997;
Tokeshi, 1992). In contrast to the unimodal, right-skewed
distribution that is the norm for geographic range-size
distributions, at finer scales bimodal and uniform occupancy
distributions are not uncommon (Tokeshi, 1992), and at least
eight forms of occupancy distribution have been distinguished
in empirical studies (McGeoch and Gaston, 2002). Numerous
mechanisms, such as sampling artefactual effects include
sampling characteristics and biological mechanisms include
organism niche-based and metapopulation models, have been
proposed to give rise to range-size distributions of different
shapes (see review in McGeoch and Gaston, 2002). An increase
in sample number may bring about a reduction in the number
of species in the core class, i.e. a change from bimodal to a
unimodal (satellite-mode) occupancy distribution (Gotelli and
Simberloff, 1987; Brown, 1995; Guo et al., 2000). The distribution will also change from bimodal to unimodal with the
sample extent changing from local scales to geographic and
continental scales (Brown, 1984; Gaston, 1998). Additionally,
sampling coverage, intensity, and temporal factors also affects
the shape of occupancy distributions (McGeoch and Gaston,
2002). Our results show that skewness of the range size
distribution of prey is smaller than that of predator, which
implies that there are relatively fewer widespread species in
high trophic level. The distribution curves of range size vary
from lognormal to hollow with the increase of trophic level. It
ecological complexity 3 (2006) 148–159
is the trophic level that determines the types of range size
distribution, either right-skewed or hollow (bimodal).
Many works have focused on the species–area relationship (Bell, 2001; He and Legender, 2002), which can also be
depicted by using different patch number in our model.
However, we interests in the proportion of prey species
number to predator species number, p, which is an important
index to describe food–web structure. A rough result in
simulation is that the species richness of prey and predator
vibrate around equilibriums after coalescence phase. By all
50 possible combinations of parameters of SCAM-1d, we
found that p 1:25 expð4bDÞ. It strongly suggests that this
result could be obtained from basic considerations of
diffusion process in the metapopulation. For example,
parameter D in the power of the exponent corresponds to
the number of steps needed to drive the morphological
difference to the level of divergence between two species.
Coefficient exp(4b) can be interpreted as the mean increment
of species numbers per step. With the increase of the
morphological difference threshold to incur reproductive
isolation, species richness will decrease more rapidly with
the tropic level. This result is insensitive to the mutation rate
and the colonization–extinction rate, which means that it is
an attractive equilibrium of community structure. Note that
bD is the proportion of morphological difference for species
diversification to average morphological values, which varies
from 0% to 25% presumably. Therefore, the typical values of p
vary from 1.25 to 3.40, which is accordance with the classical
experiment in Florida Keys (Simberloff and Wilson, 1969;
p = 1.53) and the data of Tetrigoidea and Fringillidae from
155
Fauna Sinica (Li et al., 1982; Liang and Zheng, 1998; p = 2.12).
Further, it has been strongly argued that each plant or animal
species in a food web typically is connected (eating or being
eaten) with only three to five other species (May, 2001).
Raymond et al. (2001) studied 18,223 individual lizards of 127
species and found that the dietary niche breadth in the whole
world is from 1 to 10.45, with the mean 4.58 and the standard
deviation 2.3. This rough rule, which reveals the proportion
of stenophagic species to euryphagic ones, can be obtained
from the SCAM-1d. The average number of species in food
composition distribution is 4.3, which varies typically from 1
to 7. Therefore, we obtain a typical ecosystem pattern:
species number of prey is about 2.3-times (average of p
values) greater than that of predator, and each predator
species feeds on 4.3 prey species, which means that two
predator species have 53% different foods.
4.2.
Relationships among body size, range size, and
food composition
Gaston and Blackburn (1996) and Blackburn et al. (1997)
indicated that the relationship between body size and range
size is triangular, which implies that large species always has
large range and small species can be either widespread or
spatially restricted. Note this triangular relationship between
body size and range size as ‘‘ ’’ (breadth is range size, and
height is body size). In general, range size is an increasing
function of body size, or at least the minimum range size of
species in a body size class increases with the mean body size
of that class (Gaston, 1994). Species tend to fall within a
Fig. 5 – (a) Relationships among body size, range size, and food composition of predator. (b) Relationship between body
length and range size of Serpentes in China (~, male; *, female). Range size is measured by the number of county or region
in China, where the snake is found. Data from Fauna Sinica (Zhao et al., 1998). Data are obtained by SCAM-1d with similar
parameters as in Fig. 4.
156
ecological complexity 3 (2006) 148–159
roughly triangular region of range size–body size space, with
species with small range sizes tending to have small body
sizes (Gaston, 1994). Some studies indicated that there are no
significant correlations between range size and body size
(Juliano, 1983); others even found a negative interaction
between range size and body size, such as for North American
Peromyscus (Glazier, 1980). The explanations of this vague
correlation are based on energetic constraints (Damuth, 1987;
Maurer and Brown, 1988; Root, 1991), but still inadequate
(Lawton, 1991; Nee et al., 1991; Gaston, 1994).
Using SCAM-1d, we reveal that the relationship is indeed
triangular, but with different form, " (Fig. 5(a)). This result
implies that species with medium body size, not large one, is
widespread, and the largest or the smallest species is always
spatially restricted in an evolutionary lineage. Our deduction
is validated by the relationship of Serpentes in China,
including five families and 203 species (Fig. 5(b); data from
Zhao et al., 1998). The most widespread snake in China,
Rhabdophis tigrinus, inhabited in 207 counties, has a medium
body length about 751 mm for male and 900 for female. The
largest serpent Ophiophagus hannah, with 3906 mm on domestic record, just inhabits in 39 counties, and the smallest snake
Ramphotyphlops braminus, with only 100 mm body length in
general, inhabits in 27 counties. The average body lengths of
the most spatially restricted snake, inhabited in only one
county, vary from 125 to 2686 mm.
The relationship between body size and food composition
also presents triangular-like (Fig. 5(c)). This result implies that
species with medium body size could be either stenophagic or
euryphagic. Largest or smallest species always has restricted
dietary niche breadth. Brändle et al. (2002) have also
discussed the relationship between body size and food
composition (called dietary niche breadth in their work).
They suggested that range size of species in Eastern Germany
did not correlate with dietary niche breadth. Although body
size has no correlation with food composition in their work,
we found that the data points in the plane of body size and
dietary niche breadth indeed distribute triangularly (Fig. 1(c)
in Brändle et al., 2002; also see Brändle and Brandl, 2001).
Therefore, the relationship between body size and food
composition, in spite of no linear correlation, is also ‘‘"’’-like
triangular.
The most obvious result is that food composition is positive
correlated with range size (Fig. 5(d)). Widespread predator
species, i.e. euryoecious species, always have larger morphological variability within species than the stenoecious one, and
hence can be euryphagic with wider dietary niche breadth.
Therefore, in the fountain of speciation (Fig. 2(a) and (b)), the
stenoecious always lead to stenophagic with narrow dietary
niche breadth, which also means that stenophagic species are
likely aggregated spatially restricted in habitats surrounding
by euryoecious species with wide dietary niche breadth.
4.3.
Muller, 1942; also see Kauffman, 1993), in which reproductive
isolation is a consequence of ‘‘incompatibilities’’ between
different genes and traits. In this model, the populations are
not required to cross any adaptive valleys to evolve reproductive isolation, as they simply follow a ridge of high fitness
values (Kauffman, 1993; Gavrilets, 1999). This model is to
response to the improbability of high fitness ridge in a twodimensional rugged adaptive landscape (Wright, 1932). Analyses have shown that the properties of the three-dimensional
adaptive landscape implicit in Wright’s metaphor are a rather
poor indicator when describing genetic systems with thousands of loci (Gavrilets and Gravner, 1997; Gavrilets, 1997). A
prominent feature of adaptive landscapes of very high
dimensionality is extensive nearly neutral network (Gavrilets,
2004). Connected networks of genotypes with very similar
fitnesses that expand throughout the genotype space (Gavrilets and Gravner, 1997; Gavrilets, 1997; Reidys, 1997; Reidys
et al., 1997). Existing data on the genetics of reproductive
isolation support this assumption that typically there are
many different loci underlying reproductive isolation (Wu and
Palopoli, 1994; Naveira and Masida, 1998; Wu, 2001). This
founding makes the assumption in this paper appropriate that
reproductive isolation and ordinary phenotypic differences
tend to go hand-in-hand (Orr, 2001).
Speciation in spatially structured networks has been
studied. Bramson et al. (1996) and Durrett and Levin (1996)
considered the individual based model in a two-dimensional
networks. Their model has similar extinction–recolonization
process as in this model. The difference is that their model is
a point speciation model that new species starts from a
mutation in one individual, which seems like not true,
because there are numerous loci involved in the speciation
event (Gavrilets, 1997). Hubbell (2001) also studied the
evolutionary dynamics in a metacommunity (that is, a
community consisting of many local populations with
different competitive species). The speciation in his ‘‘random fission model’’ is also a probable event (Hubbell, 2001).
In fact, the speciation in their models is a particular situation
here that when D = 1. From Fig. 1, we can see that the
speciation adopted here consists of the phyletic gradualism
speciation and the punctuated equilibrium speciation.
Classic palaeontological studies adopts the phyletic gradualism speciation (Ereshevsky, 1992; Roth, 1992; Coyne, 1992);
yet theoretical ecologists like to choose the punctuated
speciation (Eldredge, 1971; Eldredge and Gould, 1972), which
is also adopted in the studies of community structure
(Bramson et al., 1996; Durrett and Levin, 1996; Barraclough
and Vogler, 2000; Hoelzer, 2001; Hubbell, 2001). Moreover, up
to now, there is no other paper studying the coevolution of
predator and prey in a metapopulation framework. The
model here opens the door to study the evolutionary
dynamics of predator–prey in metapopulations.
Speciation in metapopulations
5.
Here, we have build the stochastic cellular automaton based
on allopatric speciation, predator–prey process and extinction–recolonization process in metapopulation framework.
The theoretical foundation of this model is the Bateson–
Dobzhansky–Muller Model (Bateson, 1909; Dobzhansky, 1937;
Conclusion
In conclusion, predation can profoundly affect speciation
dynamics and community patterns. Skewness and lumpiness
of distributions are changing with tropic level. Metapopulation
processes, especially adjacent recolonization, can deeply
ecological complexity 3 (2006) 148–159
influence the spatial structure of community and allopatric
speciation. Although there are no obviously linear relationships between body size and range size, and between body size
and food composition, these relationships are in fact ‘‘"’’-like
triangular. Only dietary niche breadth is positive correlated
with distribution range. Therefore, predation and colonization
are the most important factors influencing the community
patterns, which can be depicted soundly by body size, range
size, and food composition. The particular spatial model used
here has properties that are likely to exemplify a broad of
models, and the assumptions of model are made largely on the
basis of analytical convenience. This pregnant model can
amplify the effects of spatial factors and interspecific interactions on dynamics, distribution and competition, and reveal
the mechanisms underlying distinctly. In realistic ecosystem,
this model needs specializing, and the substitution of
ecological and evolutionary processes comprising more
factors for the simply assumption here is inevitable.
Acknowledgments
We are very grateful to S. Gavrilets, J. Kozlowski, Z. Li, B.
Laniewski, B.L. Li, and anonymous reviewers for their
helpful comments, and F. Zhang and X.Z. Han for the data
collection from Fauna Sinica. This work was partially
supported as a fellowship for C.H. by the National Research
Foundation of South Africa (GUN2053618) and the University
of Stellenbosch.
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