Download Stable coexistence of ecologically identical species: conspecific

Journal of Animal Ecology 2016, 85, 638–647
doi: 10.1111/1365-2656.12490
Stable coexistence of ecologically identical species:
conspecific aggregation via reproductive interference
Lasse Ruokolainen* and Ilkka Hanski
Department of Biosciences, University of Helsinki, Viikinkaari 1, PO.Box 65, FIN-00014 Helsinki, Finland
Summary
1. Stable coexistence of ecologically identical species is not possible according to the established ecological theory. Many coexistence mechanisms have been proposed, but they all
involve some form of ecological differentiation among the competing species.
2. The aggregation model of coexistence would predict coexistence of identical species if there
would be a mechanism that generates spatially aggregated distributions that are not completely correlated among the species. Our aim is to demonstrate that continued dispersal, triggered by reproductive interference between ecologically identical species, is such a mechanism.
This study has been motivated by species using ephemeral patchy resources, such as decomposing fruits, fungal sporophores, carrion, and dung.
3. We analyse an individual-based model with sexual reproduction, in which the progeny
develops in ephemeral resource patches and the new generation disperses to a new set of
patches. We assume spatially restricted dispersal, that patches differ in detectability, and that
unmated females continue dispersal.
4. In the model, reproductive interference (males spend some time searching for and/or
attempting to mate with heterospecific females) reduces the mating rate of females, especially
in the less common species, which leads to increased dispersal and reduces spatial correlation
in species’ distributions.
5. For a wide range of parameter values, coexisting species show a systematic difference in
their relative abundances due to two opposing forces: (1) uncommon species have reduced
growth rate (Allee effect), which decreases abundance; (2) an abundance difference between
the species reduces interspecific spatial correlation, which in turn reduces interspecific competition and allows the rarer species to persist at low density.
6. Our results demonstrate a new mechanism for coexistence that is not based on ecological
differentiation between species.
Key-words: aggregation model, competition, dispersal, mate search, patchy habitat
Introduction
Under which conditions two or more species competing
for limiting resources are able to coexist in the same community is a fundamental question in population and community ecology (Hutchinson 1959; May 1973). A classic
result supported by a wealth of theory (Chesson 2000)
and empirical work (e.g. Gause 1934; Silvertown 2004)
maintains that stable coexistence is possible only if species
differ sufficiently in their ecology (Chesson 2000). The
most obvious ecological differences that facilitate coexistence include niche differences in resource use. However,
*Correspondence author: E-mail: [email protected]
there are also other mechanisms that may allow coexistence, such as temporal niche shifts (species using the
same resource at different times), differences in species’
functional responses to a common limiting factor, and
dissimilar responses to environmental fluctuations (Chesson 2000). Many coexistence mechanisms that assume
ecological differences among species are only manifested
in spatially structured communities (Amarasekare 2003).
For instance, coexistence can be mediated via competition–colonization trade-off (e.g. Lehman & Tilman 1997),
spatial heterogeneity in competitive hierarchy (e.g. Mouquet & Loreau 2003) and differences in species’ dispersal
patterns (Amarasekare 2009; Bode, Bode & Armsworth
2011). The hallmark of stable coexistence is that species
have positive expected growth rate when rare. Stable
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society
Spatial coexistence of identical species
coexistence should be distinguished from transient, albeit
possibly long-lasting, coexistence of identical species,
whose relative abundances exhibit a random walk until
only one species remains (Hubbell 2001).
In general, coexistence among competitors requires that
intraspecific competition is stronger than interspecific
competition (Chesson 2000). In spatially structured populations, this can happen if the spatial distributions of the
species are not completely correlated. In the 1980s, several
researchers realized that small-scale spatial aggregation of
individuals influences the outcome of competition (Atkinson & Shorrocks 1981; Hanski 1981, 1983; Shorrocks
et al. 1984; Ives & May 1985; Ives 1988). Intraspecific
spatial aggregation increases the strength of intraspecific
competition, because more individuals experience high
level of competition in high-density areas than low level
of competition in low-density areas. If the spatial distributions of competing species are not completely correlated,
the level of intraspecific competition may thereby become
greater than the level of interspecific competition. This
amplification of intraspecific competition has to occur at
the scale of regional populations over the full generational
cycle for the effect on coexistence to be realized, and the
aggregation of individuals should not be proportional to
their density in the landscape (Chesson 2012).
Some authors went as far as claiming that the ‘aggregation model’ could explain the coexistence of competitors
without any ecological differences between species (Atkinson & Shorrocks 1981; Shorrocks et al. 1984; Silvertown
& Law 1987), but as pointed out by Chesson (1991), the
more or less independent spatial distributions of competing species require some mechanism – identical species
would converge to identical spatial distributions and
aggregation would not therefore alter the balance between
intraspecific and interspecific competition. Notice, however, that interspecific differences among the species that
reduce spatial covariance in their distributions may have
nothing to do with resource use, and hence stably coexisting species can be identical in their resource requirements
– as long as there is some mechanism that prevents the
convergence of their spatial distributions. Notice also that
spatially aggregated distributions of individuals that are
not related to local resource abundance are not generally
adaptive – it would typically pay for individuals in highdensity patches to move to low-density patches – but in
reality there are constraints preventing individuals from
reaching the ideal free distribution (e.g. Jackson, Humphries & Ruxton 2004; Abrams & Ruokolainen 2011).
In theory, conspecific aggregation may allow ecologically identical species to coexist only if individuals
respond dissimilarly, in one way or another, to conspecifics and heterospecifics, without compromising the
premise that they are, in every respect, identical. This is
what Chesson (1991) referred to by some ‘social factors’
being needed for stable coexistence of identical species in
the aggregation model. One such mechanism was
639
described by Zhang, Lin & Hanski (2004). They assumed
that species reproduce in discrete resource patches, such
as fig wasps in figs, and that mating occurs after eclosion
but before dispersal. In this situation, if only one or a few
females of a particular species have laid eggs in a resource
patch, the mating in the next generation occurs entirely (if
there is only one ovipositing female), or largely, among
siblings (with several ovipositing females), and it would
pay for the female to produce a female-biased sex ratio
among her offspring to reduce competition among the
brothers for mates (local mate competition). If females
are able to adjust sex ratio at the time-scale of a few generations, an uncommon species would have a more
female-biased sex ratio than a common species, which
would increase the growth rate of the former and lead to
stable coexistence; each species tends to increase when
rare (Zhang, Lin & Hanski 2004).
Here, we describe another and more general mechanism
that may lead to stable coexistence of ecologically identical species. This mechanism relies on individual mating
behaviour, resulting in reproductive interference between
species. We start from the observation that two general
reasons for movements in sexually reproducing species are
searching for mates and foraging for resources. Consider
a species breeding on a patchy resource, such as drosophilids breeding in decaying fruits (Sevenster & van Alphen
1996) and carrion and dung-inhabiting flies and beetles
(Hanski 1980, 1987a; Ives 1991), in which newly eclosed
individuals disperse before mating (unlike in fig wasps).
Assume that dispersing individuals are attracted by olfactory cues to a new set of resource patches, in which they
mate and reproduce. The resource patches differ in terms
of how detectable (attractive) they are, due to various
environmental factors. Crucially, we then assume that,
following a period of dispersal and mating in the resource
patches, females that remain unmated continue dispersal,
while mated females settle down and start reproducing.
Thus, we assume that individual movement decisions are
affected by mating, which has been documented for many
species (Bellamy & Byrne 2001; Fauvergue, Lo Genco &
Lo Pinto 2008). In the present study, we show that this
mechanism, prolonged dispersal until mated, combined
with some level of interspecific courting or mating
attempts, may reduce correlation in the spatial distributions of the competing species sufficiently to allow ecologically identical species to stably coexist in the same
metacommunity. Importantly, both components are
required for coexistence; reproductive interference alone is
not sufficient, and continued dispersal needs to be
engaged in response to high abundance of heterospecifics.
In addition, we show that under a range of conditions
coexisting species show, unexpectedly, persistent differences in their relative abundances across the region. Systematic abundance differences between species have
previously been demonstrated only for models with demographic differences between the species.
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
640 L. Ruokolainen & I. Hanski
Model
We assume an individual-based model, in which species
with discrete generations breed in discrete, ephemeral
resource patches that last for one generation only. Once
the life cycle in a particular generation has been completed, the old resource patches disappear and new ones
become available. The model is motivated by insects such
as drosophilids, blowflies and dung beetles and flies,
which lay their eggs in decomposing fruits, carcasses and
dung pats. Comparable dynamics occur in other species
using other types of resources with spatially aggregated
distribution of individuals, for which our model can be
considered as a rough approximation.
Assume a set of n patches in each generation, randomly
located within a unit square area. Each patch is characterized by its spatial location (coordinates xi, yi) and ‘attractiveness’ (detectability) Ai. Attractiveness Ai influences the
likelihood that dispersing individuals are drawn to the
patch (below), and it depends on exposure and other features of microtopography as well as on the current environmental conditions, such as the direction and strength of
wind, which influence the diffusion of olfactory cues used
by dispersing individuals to locate the resource patches. We
assume that all patches have the same carrying capacity K,
which influences population regulation (below). This
assumption reduces stochasticity in the simulations, but
does not have a qualitative effect on the results. Patch
attractiveness A is assumed to be log-normally distributed,
A ~ exp[N(lA, rA)], with parameters lA and rA setting the
mean and the standard deviation respectively.
Each generation begins by mated females of each species reproducing in the patch in which they are located
following dispersal, with a per-capita fecundity b. Hence,
the total number of offspring produced per female in species j in patch i is N0 ij = bNij. Each offspring has equal
probability of being a male or a female. The offspring
compete for the resources in the patch, such that the
pooled number of fully developed individuals in patch i is
restricted, on average, to the carrying capacity. That is, if
ΣjN0 ij > Ki, the probability of individual survival is given
by Psurv = Ki / ΣjN0 ij. If ΣjN0 ij ≤ Ki, all individuals survive,
Psurv = 1.
Following the development of the offspring in patch i,
all of them, comprising the next generation, disperse to a
set of n newly appeared resource patches with different
coordinates and attractiveness values. The probability of
an individual arriving at patch k (Pik
disp ) depends on the
distance between patch k and the natal patch i (dik) as
well as the attractiveness of patch k (Ak), such that:
expðddik ÞAk
s:
m¼1 expðddim ÞAm
Pik
disp ¼ Pn
eqn 1
The numerator gives the dispersal propensity to patch
k, which is scaled by the summed propensity over all
patches, assuring that RPik
disp ¼ 1. Here, s is a constant
probability of surviving the episode of dispersal and d is
the scale of dispersal (average dispersal distance is given
by 1/d in the exponential dispersal kernel).
Following dispersal, individuals search for mates, which
takes place randomly within each resource patch.
Thereby, a female of species j encounters a male of either
species with probability Pjenc , defined as:
Pjenc ¼ 1 expðEC EH Þ;
eqn 2a
where the exponential term gives the expected proportion
of females that do not encounter any males, and EC and
EH indicate conspecific and heterospecific encounter
propensities:
EC ¼
aC MC
1 þ hðaC FC þ aH FH Þ
eqn 2b
EH ¼
aH MH
:
1 þ hðaH FC þ aC FH Þ
eqn 2c
Individuals of conspecific and heterospecific males (MC
and MH) are encountered with rates aC and aH, respectively, and each encounter is associated with a ‘handling’
time h. Thus, mate search time by males is reduced by the
handling time associated with encounters with both conspecific (FC) and heterospecific (FH) female individuals.
The parameters aC and aH reflect a combination of male
and female traits involved in the search process. If there
are no differences between the species in this respect,
aC = aH. Otherwise we assume that there are some chemical or morphological cues that help individuals in species
recognition and hence aC > aH. Note that Eqn. (2)
imposes an Allee effect – population growth is reduced at
low density – the strength of which depends on the
parameters h and aC. The Allee effect arises when many
females fail to mate due to strong interspecific mating
interference. When only one species is present, strong saturation of males (due to high h and/or aC) can lead to
perpetuating mating failure (Allee effect), especially when
local carrying capacities are low. In Eqn. (2b,c),
heterospecific females reduce mating rate because males
waste time in searching and courting them, unless aH = 0.
Similarly, heterospecific males reduce mating rate by
reducing the number of females that are available for
mating at any point in time (i.e. not courted by a
heterospecific male).
In Eqn. (2b,c), the encounter propensity between conspecific males and females is reduced by the handling time
of individual encounters. Thus, the availability of conspecific males depends on the abundance of both conspecific and heterospecific females. The actual encounter
probability also needs to take into consideration not only
the reduced availability of males but also the fact that
females are occupied in male–female encounters. This is
taken into account here in Eqn. (2a), which gives the
probability that a female encounters any male. To obtain
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
Spatial coexistence of identical species
the probability that a female encounters and consecutively
mates with a conspecific male, Eqn. (2a) is modified by
multiplying Penc with the probability that an encountered
male is conspecific:
Pjmate ¼ Pjenc
EC
;
EC þ EH
eqn 3
where the probability of encounter with a conspecific
male is given by the proportion EC/(EC + EH), which
takes into account the availability of different males to
the females.
In the special case of h = 0, female encounter probability becomes Penc = 1 – exp(–aCMC – aHMH), where the
exponential term decreases much faster with increasing
male abundances than when h > 0. This means that Penc
approaches 1 when h goes to zero. In turn, female mating
probability approaches Pmate = aCMC/(aCMC + aHMH).
Reproductive interference still operates, as the presence of
heterospecifics reduces mating probability via the aHMH
term, and this reduction becomes more prominent with
increasing asymmetry in species abundances, which
leads to a strong tendency for a rare species to continue
dispersing.
The final, and crucial, assumption of the model is the
possibility of multiple episodes of dispersal within each
generation. Following the initial round of dispersal from
natal patches to the new ones, females that have not
become mated during the discrete time interval considered
in Eqn. (2) perform another round of dispersal among the
new patches. Increasing the number of possible dispersal
episodes above two had little qualitative effect on the
results, and hence we report results for two dispersal episodes only. We assume that males continue dispersal with
probability 1 – Pmate, and thus more males disperse from
a patch from which a large fraction of conspecific females
dispersed because they remained unmated. In other
words, males tend to follow the dispersal behaviour of
females. Importantly, we assume that environmental conditions change between each episode of dispersal, such
that the Ai values are redrawn anew from the same distribution as for the first episode of dispersal. We also vary
the variance of Ai (rA) to make sure our conclusions are
not sensitive to this assumption.
In model analysis, we assume that there are two species with identical demographic parameters b and s. We
start by considering the case where the species do not
differ in terms of resource use and competitive ability,
but they do differ in some trait that affects their dispersal
behaviour as reflected by the values of patch attractiveness A. That is, the species are not ecologically identical.
We denote the between-species correlation in the patch
attractiveness values by qA, which defines how similarly
the species respond to variation in patch attractiveness
(Ruokolainen & Fowler 2008; Ruokolainen 2013). We
calculate the attractiveness of patch i for species j at
time t as
3
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
ð1
q
u
þ
x
Þq
j;t
t
A A
6
7
Aij ðtÞ ¼ exp4rA qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ lA 5;
1
1 þ ð1 qA ÞqA
641
2
eqn 4
where φt and xj,t are standard normal random deviates. φt
is common to the two species, while xj,t are species
specific. Equation (4) generates a series of attractiveness
values for each patch and each species, such that the
patch-specific attractiveness values are correlated between
species, given by the correlation coefficient qA.
Simulations are initiated by placing 10 individuals of
each species in each resource patch with probability 05.
The dynamics are simulated for 2000 time steps, of which
the first 1000 steps are discarded as a transient.
Results
interspecific differences in foraging
behaviour
We start by considering situations where resource patches
attract different species in a dissimilar manner, when there
is only one dispersal episode. We thus assume that while
the species do not differ in their resource use and competitive abilities, they differ in some trait that affects their dispersal behaviour. When the correlation in the patch
attractiveness values is low, the species coexist at similar
regional abundances due to spatially segregated distributions (Fig. 1a,b). Increasing the value of qA from zero does
not affect coexistence until it is abruptly lost at an intermediate value of qA (Fig. 1a). At higher values of qA, the spatial distributions of the two species tend to converge,
which leads to competitive exclusion of one of the species
(Fig. 1a,b). This result demonstrates that reproductive
interference alone does not facilitate species coexistence.
ecologically identical species
Here, we assume that qA = 1, in other words the two species respond identically to the environment (have the same
patch attractiveness values) and are hence identical in
every respect. This means that the species identity of an
individual does not affect its probability of local survival
nor dispersal to a given patch from another patch. Under
these assumptions, coexistence is possible only if there is
sufficient segregation in the spatial distributions of the
species. The main result from the analyses below is that
coexistence is possible if males are attracted by and/or
search for heterospecific females at least to some extent
(aH > 0) and some time is thereby wasted (Fig. 2). When
there are no interactions between the adults of the two
species (aH = 0), or when individuals do not differentiate
between conspecifics and heterospecifics (aC = aH), coexistence is not possible and one of the species goes extinct
(Fig. 2a). However, as noted above, if coexistence is
observed, it arises due to the effect of continued dispersal.
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
642 L. Ruokolainen & I. Hanski
Fig. 1. Differences in patch attractiveness as experienced by different species allow coexistence of otherwise similar competitors. (a) The
effect of the correlation in patch attractiveness between two species (qA) on their long-term regional abundances. The y-axis shows the
mean population size across patches averaged across time. (b) Sample time series for qA = 02 (above) and for qA = 06 (below). The yaxis shows the mean population size across patches. The colour indicates the rank order of species in each simulation: red = more
abundant species, blue = less abundant species. Parameters: n = 20, K = 200, lA = 3, rA = 1, b = 10, d = 1, s = 1, h = 005, aC = 1 and
aH = 02. Only one dispersal episode was assumed.
Fig. 2. Examples of typical model outcomes: (a) only one of two
identical species survives (aH = aC = 1), (b) species coexist with
similar long-term regional abundances (aH = 02) and (c) species
coexist with a persistent asymmetry in regional population sizes
(aH = 06). Red and blue indicate species with higher and lower
long-term abundance respectively. The value on the left axis (grey
line) gives the mean number of mated females in each species,
while the value on the right axis gives the degree of spatial correlation between the species. Constant parameters: n = 20, K = 200,
lA = 3, rA = 1, qA = 1, b = 10, d = 1, s = 1, aC = 1, h = 01, and
the number of dispersal episodes = 2.
Courting heterospecific females leads to a reduction in
the mating rate of especially the locally less common
species, and as unmated females continue dispersal,
spatial correlation in the abundances of the two species
(i.e. the correlation between abundances across patches)
is reduced and the likelihood of coexistence is increased.
In the long run, the two species may be regionally
equally common (Fig. 2b), but when the reproductive
interference is strong, a persistent abundance difference
between the two species can emerge (Fig. 2c). The
asymmetry is due to two opposing forces. First,
the rarer the less common species is, the smaller interspecific spatial correlation is and hence the weaker interspecific competition is. Second, the common species
reduces the mating success of the rare species, while the
rare species has no comparable effect on the common
species.
Coexistence is not possible when aH is either very small
or very large, approaching aC (Fig. 3). When aH is small,
there is not enough reproductive interference to repel a
species away from the patches where the other species is
numerically dominant and hence the spatial distributions
of the two species converge. On the other hand, if aH is
close to aC, female mating probability critically depends
on the relative abundances of conspecific and heterospecific males. In this case, a reduction in male abundance
reduces mating rate, which further reduces abundance
and quickly leads to extinction (Fig. 2a). Moreover, coexistence is not possible when mating rate becomes saturated by large handling time (Fig. 3). When h is large,
females of the less common species have low probability
of mating after the first episode of dispersal; they continue
dispersal, but mating rate is low also after the second episode of dispersal because of large h. The less common
species then suffers a low growth rate, which is not sufficiently compensated for by reduced correlation in the spatial distributions of the species. The species coexist at
similar long-term densities when aH is intermediate and h
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
Spatial coexistence of identical species
is small (Fig. 3), such that the species affect each other’s
mating success over a broad range of abundances.
Finally, we reiterate that in the model coexistence and
competitive exclusion depend on density-dependent mating success and associated prolonged dispersal. If this
component of the model is eliminated by assuming, e.g., a
constant mating probability independent of male density,
say Pmate = 05, species’ relative abundances exhibit a random walk until only one species remains, which may take
Fig. 3. (a) Heterospecific mate search rate (aH) and handling
time (h) interact in affecting coexistence of identical species. Here,
aH is varied, while keeping aC constant (aC = 1). The colour scale
indicates the relative abundance of the less abundant species.
Constant parameters: n = 20, K = 200, lA = 3, rA = 1, qA = 1,
b = 10, d = 1 and s = 1, and the number of dispersal
episodes = 2.
643
a long time in a large population. In contrast, when mating success is density dependent, extinction, when it
occurs, happens rapidly.
sensitivity to parameter values
The structure of the landscape does not have major qualitative effects on the results, beyond that stochastic extinction of the regionally rarer species is more likely from
small landscapes (small number of resource patches, n)
with small local carrying capacity (Fig. 4a). Increasing the
size of the landscape reduces the role of demographic
stochasticity and makes it more likely that there is a systematic difference in the abundances of the two species
(Fig. 4b). Individual fecundity (b) has no qualitative effect
on the results, although naturally with very low fecundity
no species will persist (not shown). In the above analyses,
we assumed that there is no cost to dispersal (s = 1). For
a wide range of parameter values, assuming a dispersal
cost does not have a qualitative effect on the results, but
when survival during dispersal becomes low, coexistence
becomes impossible due to an Allee effect in the rare species with high overall dispersal rate (Fig. 4c). We have
also assumed that the species are identical, including symmetric interspecific mating interference. If this is not the
case, for instance, because one species is more strongly
attracted to heterospecifics than the other, asymmetry in
regional abundances increases and eventually, when asymmetry in mating interference is strong, one species goes
extinct (Fig. 4d).
Coexistence is not possible if variation in patch attractiveness (rA) is very large (Fig. 5), in which case most
individuals are attracted to a small number of resource
Fig. 4. Sensitivity of simulation results to
model parameters. (a) Local carrying
capacity (K), (b) landscape size (n), (c) dispersal survival (s) and (d) asymmetry in
mating interference between the species.
Notice that increasing asymmetry in
heterospecific search rates first leads to
asymmetric abundances of the two species,
but eventually leads to the exclusion of
one of the species. Here, the heterospecific
mating rate against species 1 is constant
aH1 = 05, while that against species 2
(aH2) is varied. Constant parameters:
n = 20, K = 200, rA = 1, qA = 1, b = 10,
h = = 01, aC = 1, aH = 02, d = 1, s = 1,
and the number of dispersal episodes = 2.
Red and blue stand for the more
abundant and less abundant species
respectively.
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
644 L. Ruokolainen & I. Hanski
Fig. 5. Spatial variation in patch attractiveness and average dispersal distance interact in affecting species coexistence. The colour scale indicates the relative abundance of the less abundant
species. Constant parameters: n = 20, K = 200, qA = 1, b = 10,
h = 01, aC = 1, aH = 025, s = 1, and the number of dispersal
episodes = 2.
patches. On the other hand, variation in patch attractiveness interacts with the spatial scale of dispersal (d), such
that more localized dispersal promotes coexistence, and in
the extreme case, coexistence is possible even when there
is no spatial variation in patch attractiveness (Fig. 5).
With long dispersal distances, rA has to be greater than a
threshold value for coexistence, below which the spatial
distributions convergence. In the example in Fig. 5, asymmetric coexistence is possible only for intermediate values
of rA.
Discussion
The present results demonstrate that coexistence of ecologically identical species is possible in the aggregation
model, if individuals can continue dispersing in response
to individual abundances. Here, we assume that this arises
due to reproductive interference, meaning here that males
court for and/or attempt to mate with heterospecific
females. Reproductive interference reduces the mating
probability, and if unmated females continue dispersal
and patch attractiveness values change in time, the spatial
distributions of the competing species become, to some
extent, uncorrelated, which facilitates coexistence. Our
model also makes the unexpected prediction that stably
coexisting identical species may exhibit a persistent difference in their regional abundances, which has been previously associated with ecological differentiation between
species. Abundance differences arise in the model due to
the opposing effects of an Allee effect in reproduction
and a dynamic relationship between species abundances
and spatial covariance. Below, we discuss the mechanisms
underlying these results in greater detail and consider
these results in the light of previous theory and empirical
data.
Stable coexistence in our model is based on three
assumptions. First, we assume that there is variation in
the detectability of the resource patches by dispersing
individuals, which promotes spatially aggregated distributions. This assumption is expected to be widely applicable;
this is the main explanation for spatially aggregated distributions in, e.g., carrion flies (Hanski 1987a; Ives 1988,
1991), fruit flies (Sevenster & van Alphen 1996; Takahashi
2006), fungivorous flies (Hanski 1987b) and dung beetles
(Hanski & Cambefort 1991). Conspecific aggregation can
also arise due to aggregation pheromones (Takahashi
2006), as in some fruit flies (e.g. Hedlund et al. 1996), but
in this case, there are interspecific differences in longrange pheromones. Alternatively, spatial variation in
detectability is not necessary for coexistence if dispersal is
strongly localized (Fig. 5). In this case, local abundances
become, to some extent, uncoupled from abundances at
the landscape level, and hence different species can
numerically dominate in different resource patches.
Secondly, we assume that the movement behaviour of
females is affected by their mating status, which has been
observed in experimental studies (e.g. Fauvergue, Lo
Genco & Lo Pinto 2008; Wenninger, Stelinski & Hall
2009). Male dispersal was assumed to reflect the mating
success and mating-status related dispersal of females.
Thirdly, we assume that the detectability of resource
patches varies in time, which makes it more likely that
individuals dispersing from patches with low conspecific,
but high heterospecific, density end up in patches with
low density of heterospecifics. Such variation is likely
whenever detectability depends on the prevailing weather
conditions, which may change rapidly. For example, carrion flies use olfactory cues to locate carcasses (Hammack
et al. 1987), and olfactory cues also play an important
role in the foraging behaviour of fruit flies (Gaudry,
Nagel & Wilson 2012). It is reasonable to assume that
environmental conditions, such as moisture, temperature,
exposure to sunlight, and the strength and direction of
wind, will all affect the quality and quantity of the substances emitted from the resource patches and how the
odours diffuse into the environment. We assume, for simplicity, that there is no spatio-temporal autocorrelation in
patch attractiveness.
Our model predicts coexistence of identical species, but
also that identical species can exhibit a persistent difference in their regional abundances, which arises under a
broad range of conditions. This is counter-intuitive, as the
general expectation is that the relative abundances of ecologically identical species undergo a random walk until all
but one species are extinct (e.g. Hubbell 2001; Chave
2004). While systematic abundance differences are interpreted to reflect differences in species’ demographic
parameters, there is little doubt that the dynamics of most
ecological communities are influenced by a combination
of niche-related and neutral processes (Chesson 2000; Leibold & McPeek 2006; Ruokolainen et al. 2009). In the
present model, there is no need for niche or other
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
Spatial coexistence of identical species
biological differences among the species. Instead, the
asymmetry in regional abundances is maintained by two
opposing forces: an Allee effect in reproduction (and the
cost of dispersal) tends to decrease the relative abundance
of the less common species. In turn, when the species has
become rare, interspecific spatial covariance becomes
small, which reduces interspecific competition and protects the rare species from global extinction. Increased dispersal with decreasing local abundance in our model is
somewhat reminiscent of the competition–colonization
trade-off (Lehman & Tilman 1997), where an inferior
competitor with higher dispersal rate can colonize patches
not occupied by the superior competitor. Here, there are
no interspecific differences in species’ competitive abilities
nor in their dispersal capacities, but nonetheless the less
common species persists because it disperses more, triggered by reproductive interference from the common species.
Coexistence of many seemingly similar species is well
documented for insect communities breeding in discrete
ephemeral resources, such as carrion, dung and decomposing fruits, in which resource competition is often fierce
(Beaver 1977; Ives 1991; Sevenster & van Alphen 1996;
Zhang, Lin & Hanski 2004). Moreover, coexistence of
similar species on these resources as inferred from observational studies has been supported by experiments (Hanski 1987c; Kouki & Hanski 1995). Studies on fruit-feeding
drosophilids (Atkinson & Shorrocks 1981) and carrion
flies (Hanski 1981) originally stimulated the aggregation
model of coexistence, which predicts that species using the
same resource may coexist if they have, to some extent,
independently aggregated spatial distributions, amplifying
the level of intraspecific over the level of interspecific competition (Sevenster 1996; Chesson 2000; Hartley & Shorrocks 2002). The key biological question in this context is
which mechanisms may reduce spatial correlation in the
distributions of competing species.
The most likely mechanisms include differences in species’ foraging and movement behaviours (see, e.g. Shorrocks et al. 1984; Ives & May 1985; Chesson 1991).
Coexistence of otherwise identical species is possible if
they have sufficiently dissimilar probabilities of detecting
resource patches (Fig. 1). For instance, patch attractiveness may depend on temperature, and the activity of different species may be dissimilarly affected by temperature;
or the species may be attracted to specific metabolites
produced by bacteria in the resource patches (Ives 1991).
These mechanisms are analogous to coexistence via temporal niche differentiation in non-spatial models; competitors that respond dissimilarly to environmental
fluctuations can coexist (Chesson 2000). A different mechanism was described by M’Gonigle et al. (2012), who
showed that sexual selection in a heterogeneous landscape, combined with a cost associated with female mate
search, can promote coexistence of ecologically equivalent
species by generating persistent single-species spatial clusters. This mechanism requires the presence of fixed envi-
645
ronmental heterogeneity, which ‘freezes’ the spatial
patterns (M’Gonigle et al. 2012), without which species’
relative abundances would drift and ultimately only one
species would remain. Another mechanism related to sexual reproduction was described by Zhang, Lin & Hanski
(2004), who showed that sex-ratio adjustment due to local
mate competition may provide the necessary rare species
advantage that may lead to stable coexistence (see Introduction).
Here, we have described another coexistence mechanism
for sexually reproducing species, which does not require
any differences in the biology of the species, no fixed spatial variation in resource distribution, nor any sex-ratio
adjustment. Instead, this mechanism relies on interspecific
reproductive interference (Gr€
oning & Hochkirch 2008)
combined with mating-status dependent movement behaviour (Bellamy & Byrne 2001; Fauvergue, Lo Genco &
Lo Pinto 2008). Coexistence arises when unmated females
move away from high density of heterospecifics to
increase their chances of mating. Combined with spatiotemporal variation in patch attractiveness or highly localized dispersal, such movement behaviour generates a rare
species advantage – positive growth rate when the species
is rare (a general criterion for invasibility) – due to
reduced spatial covariance between the competing species.
This is an example of mechanisms leading to growth-density covariance (Chesson 2000; Amarasekare 2003): the
average per-capita growth rate of an invading species is
elevated due to reproduction in areas with low interspecific competition. In our case, the rare species experiences
reduced interspecific competition because individuals frequently redisperse following a change in the attractiveness
of the resource patches, and hence these individuals disperse to resource patches independently of the distribution
of the common species among the patches.
Frequency-dependent reproductive interference is common especially among closely related species (Gr€
oning &
Hochkirch 2008), and it can be as important as resource
competition in affecting coexistence (Kishi, Nishida &
Tsubaki 2009). We have modelled reproductive interference as time wasted in heterospecific mating attempts.
This is supported by empirical findings, suggesting that
the time females spend being courted by heterospecific
males can reduce the mating success of females of the species in the local minority (Friberg, Leimar & Wiklund
2013). Other forms of reproductive interference include
signal jamming and hybridization (Gr€
oning & Hochkirch
2008). In nature, reproductive interference is often asymmetric (e.g. Hochkirch, Gr€
oning & B€
ucker 2007) due to,
e.g., differences in body size between the species. For
instance, males may prefer to court larger heterospecific
females as observed in groundhoppers (Hochkirch, Deppermann & Gr€
oning 2006). While we have assumed symmetric interference, increasingly asymmetric interspecific
interference would increase the asymmetry in species’
regional abundances and eventually leads to the exclusion
of one species (Fig. 4d).
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
646 L. Ruokolainen & I. Hanski
Observational and experimental studies have indicated
that reproductive interference can lead to spatial segregation, sexual displacement and resource partitioning
(Gr€
oning & Hochkirch 2008; Kishi & Tsubaki 2014). In
line with these results, previous theoretical models have
concluded that reproductive interference hampers coexistence (e.g. Kishi & Nakazawa 2013). This is due to a positive feedback between increasingly asymmetric relative
abundances of the species and reduced fecundity of the
less abundant species; it is disadvantageous to be the less
abundant species (Kishi & Tsubaki 2014). In contrast, in
our spatial model, reproductive interference promotes
regional coexistence under a broad range of conditions.
In this case, although reproductive interference leads to
rare species disadvantage locally, this can be reversed to
rare species advantage at the regional level. Landscapelevel coexistence can also arise for other reasons, whenever low conspecific density triggers prolonged dispersal.
Recently, Nishida, Takakura & Iwao (2015) have reported
that identical species with reproductive interference can
coexist with highly segregated spatial distributions, which
they call parapatric coexistence (see also Ribeiro & Spielman 1986). Their result is contingent on highly localized
dispersal: adults emigrate from their natal patch to a randomly selected neighbouring patch or remain in the natal
patch. We have shown that when dispersal is not localized, interference alone is not sufficient to allow regional
coexistence, which in our model depends on the possibility
of unmated females to continue dispersal. Nonetheless, in
agreement with Nishida, Takakura & Iwao (2015),
increasingly localized dispersal increases the possibility for
symmetric coexistence also in our model.
We call species identical even if there is a difference in
the mate search parameter a for conspecifics and heterospecifics. If there is no such difference, the two species
cannot coexist in this model (Fig. 3). Clearly, there must
be some pre-zygotic or post-zygotic differences between
two sexually reproducing species, otherwise they would
merge into one species. Increasing aH reduces mating
probability and thus increases the likelihood of continued
dispersal of non-mated females, especially in the locally
less abundant species. Increasing the search rate for heterospecifics (aH) decreases asymmetry in species’ abundances, while increasing the search rate for conspecifics
(aC) has the opposite effect.
One caveat to our results concerns the evolution of dispersal in the kinds of situations we have modelled. We
assume that females perform only one episode of dispersal
unless they fail to mate. Individuals might perform several
episodes of dispersal, and individuals located in high-density patches might have elevated rate of dispersal to avoid
resource competition. If mated females continue dispersal
in response to crowding, the exclusion of all but one species becomes more likely when their sensitivity to crowding increases. This happens because in this case, the
spatial distributions of different species converge and
thereby the rare species advantage is lost. However, the
fact that carrion and dung-inhabiting flies and beetles
(Hanski 1987b) and drosophilids breeding in decomposing
fruits (Shorrocks et al. 1984) exhibit highly aggregated
spatial distributions suggests that there are severe constraints that prevent individuals from achieving anything
even resembling the ideal free distribution. One factor
that penalizes prolonged dispersal is strong priority effect:
the progeny of the first individuals to oviposit have an
advantage in scramble competition (Hanski 1987b,c). Furthermore, the presence of conspecifics may be used as a
cue of favourable habitat, as has been documented for a
wide variety of animals (Bowler & Benton 2005). Including these additional features into the model, including the
evolution of dispersal, remains a task for further studies.
Acknowledgements
We thank Peter Chesson, Tony Ives, Tanjona Ramiadantsoa, Helene Weigang and Da-Yong Zhang for comments on early versions of the manuscript.
This research was supported by the Academy of Finland (grants 255350 and
250444 to IH and 13579 to LR). We declare no conflicts of interest.
Data accessibility
The code used to generate the simulation results is given in the
Appendix S1.
References
Abrams, P.A. & Ruokolainen, L. (2011) How does adaptive consumer
movement affect population dynamics in consumer–resource metacommunities with homogeneous patches? Journal of Theoretical Biology,
277, 99–110.
Amarasekare, P. (2003) Competitive coexistence in spatially structured
environments: a synthesis. Ecology Letters, 6, 1109–1122.
Amarasekare, P. (2009) Effect of non-random dispersal strategies on spatial coexistence mechanisms. The Journal of Animal Ecology, 79, 282–
293.
Atkinson, W.D. & Shorrocks, B. (1981) Competition on a divided and ephemeral resource: a simulation model. Journal of Animal Ecology, 50, 461–471.
Beaver, R.A. (1977) Non-equilibrium “Island” communities: diptera breeding in dead snails. The Journal of Animal Ecology, 46, 783.
Bellamy, D.E. & Byrne, D.N. (2001) Effects of gender and mating status
on self-directed dispersal by the whitefly parasitoid Eretmocerus eremicus. Ecological Entomology, 26, 571–577.
Bode, M., Bode, L. & Armsworth, P.R. (2011) Different dispersal abilities
allow reef fish to coexist. Proceedings of the National Academy of
Sciences of the United States of America, 108, 16317–16321.
Bowler, D.E. & Benton, T.G. (2005) Causes and consequences of animal
dispersal strategies: relating individual behaviour to spatial dynamics.
Biological Reviews, 80, 205–225.
Chave, J. (2004) Neutral theory and community ecology. Ecology Letters,
7, 241–253.
Chesson, P. (1991) A need for niches? Trends in Ecology & Evolution, 6,
26–28.
Chesson, P. (2000) Mechanisms of maintenance of species diversity.
Annual Review of Ecology and Systematics, 31, 343–366.
Chesson, P. (2012) Scale transition theory: its aims, motivations and predictions. Ecological Complexity, 10, 52–68.
Fauvergue, X., Lo Genco, A. & Lo Pinto, M. (2008) Virgins in the wild:
mating status affects the behavior of a parasitoid foraging in the field.
Oecologia, 156, 913–920.
Friberg, M., Leimar, O. & Wiklund, C. (2013) Heterospecific courtship,
minority effects and niche separation between cryptic butterfly species.
Journal of Evolutionary Biology, 26, 971–979.
Gaudry, Q., Nagel, K.I. & Wilson, R.I. (2012) Smelling on the fly: sensory
cues and strategies for olfactory navigation in Drosophila. Current Opinion in Neurobiology, 22, 216–222.
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647
Spatial coexistence of identical species
Gause, G.F. (1934) Experimental analysis of Vito Volterra’s mathematical
theory of the struggle for existence. Science, 79, 16–17.
Gr€
oning, J. & Hochkirch, A. (2008) Reproductive interference between
animal species. The Quarterly Review of Biology, 83, 257–282.
Hammack, L., Bromel, M., Duh, F.M. & Gassner, G. (1987) Reproductive factors affecting responses of the screwworm fly, Cochliomyia
hominivorax (Diptera: Calliphoridae), to an attractant of bacterial origin. Annals of the Entomological Society of America, 80, 775–780.
Hanski, I. (1980) Spatial patterns and movements in coprophagous beetles.
Oikos, 34, 293–310.
Hanski, I. (1981) Coexistence of competitors in patchy environment with
and without predation. Oikos, 37, 306–312.
Hanski, I. (1983) Distributional ecology and abundance of dung and carrion-feeding beetles (Scarabaeidae) in tropical rain forests in Sarawak,
Borneo. Acta Zoologica Fennica, 167, 1–45.
Hanski, I. (1987a) Carrion fly community dynamics: patchiness, seasonality and coexistence. Ecological Entomology, 12, 257–266.
Hanski, I. (1987b) Nutritional ecology of dung- and carrion-feeding
insects. Nutritional Ecology of Insects, Mites, Spiders, and Related Invertebrates (eds F. Slansky Jr & J.G. Rodriques), pp. 873–884. John Wiley
and Sons, New York, NY, USA.
Hanski, I. (1987c) Colonisation of ephemeral habitats. Colonization, Succession and Stability (eds A.J. Gray, M.J. Crawley & P.J. Edwards), pp.
155–185. Blackwell, Oxford, UK.
Hanski, I. & Cambefort, Y. (1991) Dung Beetle Ecology. Princeton
University Press, Princeton, NJ, USA.
Hartley, S. & Shorrocks, B. (2002) A general framework for the aggregation model of coexistence. Journal of Animal Ecology, 71, 651–662.
Hedlund, K., Bartelt, R.J., Dicke, M. & Vet, L.E.M. (1996) Aggregation
pheromones of Drosophila immigrans, D. phalerata, and D. subobscura.
Journal of Chemical Ecology, 22, 1835–1844.
Hochkirch, A., Deppermann, J. & Gr€
oning, J. (2006) Visual communication behaviour as a mechanism behind reproductive interference in three
pygmy grasshoppers (genus Tetrix, Tetrigidae, Orthoptera). Journal of
Insect Behavior, 19, 559–571.
Hochkirch, A., Gr€
oning, J. & B€
ucker, A. (2007) Sympatry with the devil:
reproductive interference could hamper species coexistence. Journal of
Animal Ecology, 76, 633–642.
Hubbell, S.P. (2001) The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Press, Princeton, NJ, USA.
Hutchinson, G.E. (1959) Homage to Santa Rosalia or why are there so
many kinds of animals? The American Naturalist, 93, 145–159.
Ives, A.R. (1988) Aggregation and the coexistence of competitors. Annales
Zoologici Fennici, 25, 75–88.
Ives, A.R. (1991) Aggregation and coexistence in a carrion fly community.
Ecological Monographs, 61, 75–94.
Ives, A.R. & May, R.M. (1985) Competition within and between species
in a patchy environment: relations between microscopic and macroscopic models. Journal of Theoretical Biology, 115, 65–92.
Jackson, A.L., Humphries, S. & Ruxton, G.D. (2004) Resolving the departures of observed results from the ideal free distribution with simple
random movements. Journal of Animal Ecology, 73, 612–622.
Kishi, S. & Nakazawa, T. (2013) Analysis of species coexistence comediated by resource competition and reproductive interference. Population Ecology, 55, 305–313.
Kishi, S., Nishida, T. & Tsubaki, Y. (2009) Reproductive interference
determines persistence and exclusion in species interactions. Journal of
Animal Ecology, 78, 1043–1049.
Kishi, S. & Tsubaki, Y. (2014) Avoidance of reproductive interference
causes resource partitioning in bean beetle females. Population Ecology,
56, 73–80.
Kouki, J. & Hanski, I. (1995) Population aggregation facilitates coexistence of many competing carrion fly species. Oikos, 72, 223–227.
647
Lehman, C.L. & Tilman, D. (1997) Competition in spatial habitats. Spatial Ecology, Monograph in Population Biology (eds Tilman D. & Kareiva P.), pp. 185–203. Princeton University Press, Princeton, NJ, USA.
Leibold, M.A. & McPeek, M.A. (2006) Coexistence of the niche and neutral perspectives in community ecology. Ecology, 87, 1399–1410.
May, R.M. (1973) Stability and Complexity in Model Ecosystems.
M’Gonigle, L.K., Mazzucco, R., Otto, S.P. & Dieckmann, U. (2012) Sexual selection enables long-term coexistence despite ecological equivalence. Nature, 484, 506–509.
Mouquet, N. & Loreau, M. (2003) Community patterns in source-sink
metacommunities. The American Naturalist, 162, 544–557.
Nishida, T., Takakura, K. & Iwao, K. (2015) Host specialization by reproductive interference between closely related herbivorous insects. Population Ecology, 57, 273–281.
Ribeiro, J.M.C. & Spielman, A. (1986) The satyr effect: a model
predicting parapatry and species extinction. American Naturalist, 128,
513–528.
Ruokolainen, L. (2013) Spatio-temporal environmental correlation and
population variability in simple metacommunities. PLoS ONE, 8,
e72325.
Ruokolainen, L. & Fowler, M.S. (2008) Community extinction patterns in
coloured environments. Proceedings of the Royal Society B: Biological
Sciences, 275, 1775–1783.
Ruokolainen, L., Ranta, E., Kaitala, V. & Fowler, M.S. (2009) When can
we distinguish between neutral and non-neutral processes in community
dynamics under ecological drift? Ecology Letters, 12, 909–919.
Sevenster, J.G. (1996) Aggregation and coexistence. I. Theory and analysis. Journal of Animal Ecology, 65, 297–307.
Sevenster, J.G. & van Alphen, J.J.M. (1996) Aggregation and coexistence.
II. A neotropical Drosophila community. Journal of Animal Ecology, 65,
308–324.
Shorrocks, B., Rosewell, J., Edwards, K. & Atkinson, W. (1984) Interspecific competition is not a major organizing force in many insect communities. Nature, 310, 310–312.
Silvertown, J. (2004) Plant coexistence and the niche. Trends in Ecology &
Evolution, 19, 605–611.
Silvertown, J. & Law, R. (1987) Do plants need niches? Some recent developments in plant community ecology. Trends in Ecology & Evolution, 2,
24–26.
Takahashi, K.H. (2006) Spatial aggregation and association in different
resource-patch distributions: experimental analysis with Drosophila.
Journal of Animal Ecology, 75, 266–273.
Wenninger, E.J., Stelinski, L.L. & Hall, D.G. (2009) Roles of olfactory
cues, visual cues, and mating status in orientation of Diaphorina citri
Kuwayama (Hemiptera: Psyllidae) to four different host plants. Environmental Entomology, 38, 225–234.
Zhang, D.-Y., Lin, K. & Hanski, I. (2004) Coexistence of cryptic species.
Ecology Letters, 7, 165–169.
Received 12 August 2015; accepted 4 January 2016
Handling Editor: Jean-Michel Gaillard
Supporting Information
Additional Supporting Information may be found in the online version
of this article.
Appendix S1. Programming code for simulating the model, implemented in R.
© 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647