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ORIGINAL ARTICLE
doi:10.1111/evo.13563
The influence of ecological and geographic
limits on the evolution of species
distributions and diversity
Leonel Herrera-Alsina,1,2 Alex L. Pigot,1,3 Hanno Hildenbrandt,1and Rampal S. Etienne1
1Groningen Institute for Evolutionary Life Sciences, University of Groningen, Groningen 9700 CC, The Netherlands
2E-mail: leonelhalsina@gmail.com
3Centre for Biodiversity and Environment Research, Department of Genetics, Evolution and Environment, University
College London, London WC1E 6BT, United Kingdom
Received October 27, 2017
Accepted July 18, 2018
The role of ecological limits in regulating the distribution and diversification of species remains controversial. Although such limits
must ultimately arise from constraints on local species coexistence, this spatial context is missing from most macroevolutionary
models. Here, we develop a stochastic, spatially explicit model of species diversification to explore the phylogenetic and biogeo-
graphic patterns expected when local diversity is bounded. We show how local ecological limits, by regulating opportunities for
range expansion and thus rates of speciation and extinction, lead to temporal slowdowns in diversification and predictable differ-
ences in equilibrium diversity between regions. However, our models also show that even when regions have identical diversity
limits, the dynamics of diversification and total number of species supported at equilibrium can vary dramatically depending on
the relative size of geographic and local ecological niche space. Our model predicts that small regions with higher local ecological
limits support a higher standing diversity and more balanced phylogenetic trees than large geographic areas with more stringent
constraints on local coexistence. Our findings highlight how considering the spatial context of diversification can provide new
insights into the role of ecological limits in driving variation in biodiversity across space, time, and clades.
KEY WORDS: Diversity-dependence, geographic area, geographic range size, local carrying capacity, species diversification,
species saturation.
Two coexisting insect species in a pond in Palermo made G. E.
Hutchinson wonder about the limited size of this community in
stark contrast to the huge number of species on Earth (Hutchinson
1959). Ever since then, the notion that there are ecological and
geographical limits to the diversity of species found on Earth has
been a central tenet of ecology and evolution. For instance, in-
creases in diversity over geological time have often been linked to
the accessing of novel regions of geographic or ecological niche
space (Benton 2009), while differences in richness between clades
and regions are typically associated with differences in environ-
mental conditions or geographic area that are thought to limit the
total number of species that can be packed within a region (Ra-
bosky 2009; Ezard et al. 2011). However, it has also been argued
that such limits–if they even exist–do not impose an important
constraint on diversity, which instead may be largely controlled
by historical factors (Wiens 2011). According to this argument,
variation in diversity primarily involves nonequilibrium explana-
tions, including differences in the time available for diversifica-
tion, rates of colonization, speciation, or extinction (Ricklefs and
Bermingham 2001; Wiens and Donoghue 2004; Jetz and Fine
2012). Despite decades of interest, opinions regarding the rela-
tive importance of limits to diversity in driving macro-ecological
and evolutionary patterns remain divided (Harmon and Harrison
2015; Rabosky and Hurlbert 2015).
Resolving the debate about whether species richness is
bounded is challenging because present-day patterns of diver-
sity are the result of processes acting over a variety of spatial
and temporal scales, from the local ecological dynamics within
1
C2018 The Author(s). Evolution published by Wiley Periodicals, Inc. on behalf of The Society for the Study of Evolution.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, providedthe original
work is properly cited.
Evolution
L. HERRERA-ALSINA ET AL.
assemblages, to the processes of geographic range expansions
and speciation operating over thousands to millions of years. Ul-
timately, any limit to the total number of species that can be
packed within a region must arise through two primary routes.
First, at a local level, species diversity will be limited by the size
of available ecological niche space which places an upper bound
on the number of species that can coexist within an assemblage
(Macarthur 1965; Brown et al. 2001). Second, species occupy-
ing identical ecological niches may coexist at a regional scale, if
they occur in different geographic places (i.e., different assem-
blages) (Levins and Culver 1971; Atkinson and Shorrocks 1981;
Ruokolainen and Hanski 2016; Mehrparvar et al. 2017). Thus at
the level of entire regions, richness will be a function of both
the number of species that can be packed within a given assem-
blage (i.e., ecological niche space) and the number of assemblages
available for colonization (i.e., geographic space).
Tests of whether diversity is bounded typically rely on com-
parative approaches, examining how diversity varies across dif-
ferent regions, clades, and over evolutionary time (Cornell and
Lawton 1992; Cornell 2013; Pinto-S´
anchez et al. 2014). A key
prediction of bounded models of species diversity is that the rate
of species diversification should slow down over time as richness
approaches an ecological or geographic limit (Nee et al. 1994;
Phillimore and Price 2008; Etienne et al. 2012; Price et al. 2014).
In contrast, if diversity were unbounded, then richness is expected
to fluctuate randomly or increase exponentially over time (Alroy
et al. 2008). Many studies have attempted to test these predic-
tions by inferring the temporal dynamics of diversification from
the fossil record and from reconstructed phylogenies of extant
species (Stanley 1973; Alroy 2010; Ezard et al. 2011). However,
these patterns of species diversification may be difficult to inter-
pret for at least two key reasons. First, it has been argued that
even if local communities are saturated with species, regional
diversity may still increase over time if there are continued ge-
ographic opportunities for speciation and this outpaces rates of
regional extinction (Cornell 2013). Second, even if rates of diver-
sification slow down over time this need not necessarily imply
that local coexistence is limited by niche availability, because this
same pattern can also arise through other mechanisms (Moen and
Morlon 2014), including methodological artifacts (model mis-
specification, Revell et al. 2005; or incomplete sampling, Nee
et al. 1994; Pybus and Harvey 2000), temporal lags in the com-
pletion of speciation (Etienne and Rosindell 2012) or neutral geo-
graphic range dynamics (Pigot et al. 2010). Patterns of species di-
versification alone may therefore not provide enough information
to discriminate bounded versus unbounded models of diversity
(Cornell 2013).
A related problem is that most models of species diversi-
fication assume a direct link between the total species diversity
of a clade or region and the fundamental rates of speciation and
extinction. In reality, however, these rates are likely to respond to
regional richness indirectly through a chain of intermediate stages
in which geographical factors play a central role (Price 2008). In
particular, widespread species are more likely to give birth to
new species whereas small-ranged species are more likely to go
extinct by chance (Gaston 1998). As a result, sustained diversi-
fication requires that newly formed species are able to expand
their geographic ranges, thus avoiding extinction and providing
new opportunities for speciation. However, range expansion re-
quires species to colonize areas that often already contain other
species (Moreno et al. 2006; Ricklefs 2012). As the number of
species in local communities increases, resource and niche avail-
ability are expected to decline until further colonization is pre-
vented or at least strongly inhibited (Price et al. 2014). By con-
straining the opportunities for geographic range expansion, local
limits to diversity may therefore reduce rates of speciation and in-
crease rates of extinction, thus regulating overall regional diversity
(Rosenzweig 1975; Pigot et al. 2010). This chain of causation is
generally overlooked by current models of diversification, where
diversity-dependence is assumed to act globally and where it is
the richness of the entire clade that influences the speciation or
extinction rate of each individual lineage even though many of
these lineages will not be interacting (Xu and Etienne 2018). Un-
derstanding the macroevolutionary and macroecological patterns
expected in the presence or absence of limits to diversity there-
fore requires developing models that more explicitly account for
the key ecological and geographic mechanisms linking variation
in standing-diversity with rates of speciation and extinction over
time.
Here, we study how local ecological limits to coexistence and
regional geographic constraints influence the dynamics of species
diversification and geographic range evolution using a stochastic,
spatially explicit simulation model of speciation, colonization,
and local extinction. We model the spatial dynamics of diver-
sification on a two-dimensional gridded domain where each cell
represents a local assemblage and where the area of the region (A)
sets an upper bound on the number of populations or geographic
range size of each species. We model the effects of ecological
limits to coexistence, by assuming that only a limited number of
species (KL) can be packed within any given local assemblage,
so that once saturated no more species can colonize the assem-
blage until a resident species has become locally extinct. Thus,
we model ecological limits to the number of coexisting species
rather than limits to the number of individuals (e.g., Ranjard et al.
2018; Hurlbert and Stegen 2014a, b). We assume that species are
ecologically neutral in the sense that their constituent populations
are governed by identical rates of extinction, speciation, and colo-
nization (Economo and Keitt 2008; Etienne and Rosindell 2011).
In this model, the potential total diversity of the region (KR)is
determined by the number of assemblages in the region Aand the
2EVOLUTION 2018
DIVERSIFICATION AND LOCAL LIMITS
local ecological limit KLof each assemblage, which we assume
is uniform across space.
We first describe the general dynamics of this model, focus-
ing on the links between the saturation of local assemblages, the
dynamics of species geographic ranges and the diversification of
species at the regional scale. By examining how these dynamics
vary according to different parameter combinations we address
the following key questions. First, how do local ecological limits
to diversity KLand constraints on regional area Ainfluence both
the true and reconstructed temporal dynamics of species diver-
sification, and how are these effects modulated by relative rates
of speciation, extinction, and colonization? Second, do regional
area Aand local ecological limits KLhave equivalent effects on
the dynamics of species diversification or do they limit diver-
sity in fundamentally different ways? Finally, how do ecological
and geographic limits, influence other key dimensions of biodi-
versity, including species geographic range size, the relationship
between range size and species evolutionary age and the variation
in species richness across clades (i.e., phylogenetic tree balance)?
Methods
MODELING THE SPATIAL DYNAMICS OF
DIVERSITY-DEPENDENT DIVERSIFICATION
We constructed a continuous-time stochastic Markov model to de-
scribe the dynamics of speciation, extinction, and colonization on
a square gridded domain with hard boundaries. The grid contains
Acells and each cell can contain up to KLdifferent species. By in-
dependently varying Aand KLwe examine the effects of varying
both the total diversity limit of the entire region KRandalsothede-
gree to which this potential diversity is partitioned mainly across
(i.e., A>KL) or mainly within (i.e., A<KL) local assemblages.
The simulation starts with a single species occupying a single cell,
randomly chosen from within the domain. Species expansion is
modeled by selecting a population (i.e., a single cell from within a
species’ range) with probability rate γ, and then randomly select-
ing one of the four adjacent (in the cardinal directions) cells for
colonization. If the species is already locally present in this target
cell, then colonization has no effect. Furthermore, colonization is
prevented if the target cell is already saturated with species (i.e.,
local richness equals KL). In this way, local ecological limits act
by preventing the geographic expansion of species ranges (Price
2008). The extinction of populations (hereafter called local extinc-
tion) occurs with a per-population probability μand is modeled
by removing a randomly selected population. The stochastic pro-
cesses of colonization and local extinction give rise to changes in
both local diversity and the geographic range size of species over
time. Species extinction takes place when the last population of
a species becomes extinct. Speciation occurs at a per-capita rate
λand is modeled by randomly selecting a single population from
within the range of the species and labeling this as a new species.
Thus, at the time of speciation, sister species will initially have
nonoverlapping spatial distributions (i.e., allopatric or parapatric
speciation) (Pigot et al. 2010).
We used the Gillespie algorithm to sample the waiting times
between colonization, local extinction, and speciation events.
Specifically, the waiting time to the next event is determined
by randomly drawing a value from an exponential distribution
with a mean equal to the sum of the rates of the three events.
Which event occurs is then determined randomly according to
the relative summed rates of each event. Although per-population
rates of colonization, local extinction, and speciation are equiv-
alent across species, species will differ in their probability of
undergoing these events, due to differences in range size (i.e.,
number of populations). In particular, per species rates of colo-
nization, local extinction, and speciation will increase with species
geographic range size, while rates of colonization will also de-
pend on differences in the shape and placement of species ge-
ographic distributions which determine the chance of invading
a yet unoccupied cell. Simulations were terminated after Ttime
units or following the complete extinction of the clade. The sim-
ulation was programmed in C++ and the code is available at
https://doi.org/10.6084/m9.figshare.5437126.v2.
GEOGRAPHIC AND PHYLOGENETIC METRICS
At the end of the simulation, species range size was calculated as
the number of cells occupied by each species. From the record of
speciation and extinction events, we determined the age of each
species as the time since its origination (i.e., the identity of the par-
ent species is retained across speciation events). During each unit
time interval we calculated evolutionary turnover as the number
of species extinctions (i.e., all populations of a species become
extinct) divided by the number of speciation events (Weir and
Schluter 2007). This quantity is informative about (im)balance in
speciation-extinction dynamics across evolutionary history. We
quantified changes in net diversification rates over time using the
rstatistic (Pigot et al. 2010; Etienne and Rosindell 2012), which
is defined as the difference between the net diversification (loga-
rithm of the change in number of lineages having extant descen-
dants) of the second and first half of the simulation. While shifts
in diversification dynamics within each half are not accounted for
by r, this metric has many advantages that make it suitable for
our purpose. For instance, by varying the parameters in our model,
a wide range of species richness values would be expected and r
is robust to tree size differences. Moreover for those cases where
simulations have the same crown age, rprovides a fair compar-
ison across KLbecause calculating diversification rates (in each
half) will be done over the same time duration. We expect rto be
equal to zero for constant rates of diversification, while negative
values indicate a slowdown whereas positive values suggest an
EVOLUTION 2018 3
L. HERRERA-ALSINA ET AL.
Figure 1. Changes in regional (A) and local (B–E) species richness over time under a model with a local ecological limit to diversity (KL=
16) in a bounded region (A=256). Regional diversity initially increases rapidly but then asymptotes at a dynamic equilibrium (A). A single
ancestral species expands its geographic range and produces new daughter species (B), leading to an increase in both local and regional
richness (C). Local richness quickly saturates but ongoing allopatric speciation allows regional diversity to continue to increase but at a
progressively slower rate (D). Finally, a steady state in regional species richness is attained (E). Local extinctions reduce local diversity
and lead to the global extinction of species, resulting in a regional equilibrium that is lower than the theoretical maximum number of
species (KR=KL×A, dashed line) that can be packed within the region at saturation (i.e., each species comprises a single population).
We used the following rates: λ=0.08, γ=80, μ=1.
increase in diversification toward the present. By keeping track of
ancestor-descendent relationships, we reconstructed a phylogenic
tree for the extant species and recalculated rfor these lineages.
We also measured tree asymmetry with a normalized version of
Sackin’s index which in contrast to other commonly use metrics
allows direct comparison between trees of different sizes (Blum
and Francois 2005). Sackin’s index (S) can take both positive and
negative values,with higher values indicate greater imbalance and
a pure birth process generating trees with S=0.
EXPLORING DIVERSITY-DEPENDENT DYNAMICS
UNDER DIFFERENT BIOLOGICAL SCENARIOS
We conducted exploratory simulations to identify combinations
of region sizes A, local ecological limits KL, rates of speciation
λ, colonization γ, and local extinction μthat would ensure the
system reached equilibrium over the duration of the simulation
(T=35 time units) and did not result in a computationally un-
manageable number of species (maximum KR=384 000). We
defined equilibrium as the state of the system when regional rich-
ness is (dynamically) constant over time; in evolutionary terms,
equilibrium is reached when speciation equals extinction. We note
that the total duration of the simulation Tand limit to richness KR
specified in our simulations are arbitrary, and that the dynamics
described by our model are in theory relevant across phylogenetic
scales, from the global dynamics of large clades unfolding over
hundreds of millions of years, to the dynamics of small clades
taking place within a single region over only a few million years.
Because a short (long) duration of the simulation Tis equivalent
to specifying rapid (slow) rates of speciation, colonization, and
local extinction, we generally kept the duration of the simulation
Tfixed (Fig. 2).
We varied the parameter values used in our simulations to
explore a wide range of biological scenarios. First, while keeping
all other parameters fixed, we examined the effects of varying the
local ecological limit to diversity (KL=4, 12, 36, 1500). Because
the size of the region was fixed at A=256, this also had the effect
of varying the total regional limit to diversity (KR=1024, 3072,
9216, 384 000). In the case of KL=1500, local diversity never
approached this limit within the timeframe of the simulation, thus
approximating an unbounded model of diversity in which the limit
to regional diversity KRis essentially infinite. Second, to explore
the independent effects of both geographic and ecological-niche
space, we simultaneously varied the local ecological limit KL
and the area of the region A, while keeping the regional limit
to richness KRfixed. We explored a scenario where the local
ecological limit is low and the region is large (KL=1, A=4096),
a scenario where the local ecological limit is high but the region
is small (KL=256, A=16), and a scenario with intermediate
4EVOLUTION 2018
DIVERSIFICATION AND LOCAL LIMITS
Figure 2. The evolutionary dynamics of geographic range size and its dependence on the local ecological limit to coexistence (KL=4,
16, 32; columns) and clade age (i.e., the time since the beginning of the simulation; young =1, intermediate =7, old =35). Points in
each panel represent individual species from 100 replicate simulations, with darker colors indicating a higher density of points. Marginal
histograms show the frequency distribution of species age (top) and range size (right). Dotted lines show the mean range size under
each scenario. The area of the region (A=256), the per population speciation rate (λ=0.08), and colonization rate (γ=80) were held
constant across all scenarios while local extinction rate was either set to high (μ=1, top three rows) or zero (μ=0, bottom row). When
local extinction (μ)=0, the region becomes fully saturated with species so that each species has a range size of 1 cell at the time when
saturation is achieved (T=100).
values of KLand A(KL=16, A=256). A scenario with KL
=4096 and A=1, representing an extremely high ecological
limit in combination with the smallest regional area possible,
was not explored. We did not study this scenario because species
range size will be 1 and during a speciation event, the entire
population of a species would be selected to undergo speciation,
that is change of species identity. In other words, every speciation
event implies the extinction of the parental species, making the
local richness never higher than 1. Third, for these ecological
and geographical settings we examined different combinations of
speciation λ, colonization γ, and local extinction μ(See Table S1
for all parameter combinations explored).
Because colonization in our model is restricted to occur only
between spatially adjacent cells (i.e., local dispersal), range ex-
pansions, and diversification may be locally inhibited by the
boundary or the region or by the presence of locally saturated
communities, even before the entire region is filled with popu-
lations. To examine how these local effects may influence the
EVOLUTION 2018 5
L. HERRERA-ALSINA ET AL.
Figure 3. The effects of local (KL) ecological limits on the tem-
poral dynamics of species diversification. The change in species
diversification rate over time (r) is shown for both the full phy-
logeny (including extinct species, solid symbol) and the recon-
structed phylogeny (excluding extinct species, empty symbol) for
different local ecological limits (KL=1, 16, 256). Regional area is
varied (A=4096, 256, 16 cells) so that the regional limit to rich-
ness (KR) is kept fixed. In the case of KL=1500 the area is 256.
rindicates the relative diversification rate in the first and second
half of the simulation. When r<0, lineage accumulation slows
down whereas when r>0, lineage accumulation speeds up. The
mean (and 95% confidence interval) in expected ris shown for
100 replicate simulations.
expected dynamics we repeated our analysis allowing species to
colonize any available cell in the region (i.e., global dispersal)
rather than only those adjacent to already occupied populations.
For each combination of parameters, we performed 100 repli-
cate simulations. When KL=1500, clade diversity was extremely
large, greatly increasing the computation time. For this scenario,
we therefore conducted 50 replicate simulations.
Results
THE DYNAMICS OF DIVERSIFICATION AND RANGE
SIZE EVOLUTION UNDER ECOLOGICAL LIMITS
Starting from a single population, the ancestral species in our
simulation expands its range through the process of colonization.
Some of these populations become new species leading to an
increase in regional richness (Fig. 1A). In these early stages of
diversification, and so long as rates of colonization are faster than
rates of speciation, average species range size tends to increase
with species evolutionary age (Fig. 2, top panel). The increase in
species’ range sizes in a young clade leads to an initially accelerat-
ing rate of speciation and declining rate of extinction, and thus an
increasing rate of diversification over time. This transient increase
in diversification rate is most evident under simulations where lo-
cal ecological limits are extremely high (Fig. 3, KL=1500), and
thus where species assemblages remain far from saturation over
the duration of the simulation (final mean local richness across
cells =502, with the parameters of Fig. 3).
As species colonize assemblages local diversity increases
(Fig. 1B–E). When there are ecological limits to local diversity
KL, communities become saturated with species preventing fur-
ther colonization events. Because colonization is hindered, newly
formed species are unable to expand their distributions and thus
range sizes remain small long after speciation (Fig. 2). In addi-
tion, the geographic ranges of widespread species start to contract
because rates of per-population speciation and local extinction
now exceed rates of colonization (Fig. 2). Together, these pro-
cesses lead to a decline in species mean range size (Fig. 4), which
in turn leads to an increase in the per-species rate of extinction
and also a decline in the per-species rate of speciation. As a result,
rates of species diversification start to slow down (Fig. 3). Even-
tually, the clade reaches a dynamic equilibrium whereby rates
of speciation are balanced by rates of extinction and diversity
remains approximately constant over time (Fig. 1A). This equi-
librium in regional diversity is also reflected in approximately
constant levels of mean local richness and species geographic
range size.
In the presence of ecological limits to local diversity a strong
temporal slowdown in diversification rate is visible when using
the reconstructed diversification process, but this is considerably
weaker than the true diversification slowdown (Fig. 3). This is
because, as previous simulation studies have shown (Quental and
Marshall 2009; Liow et al. 2010), high or accelerating rates of
species extinction erode the signature of slowdowns in phyloge-
nies containing only extant lineages. Interestingly, for a constant
limit to regional diversity KR, the strength of the slowdown in the
reconstructed phylogeny depends on the relative values of KLand
regional area A(Figs. 3 and 4). In particular, when the limit to
local richness KLis reduced to a very low level (and thus Ais
large), evidence of a slowdown in the reconstructed rate of diver-
sification becomes weaker (KL=1: rmean =–0.46) compared
to a scenario with intermediate values of KLand A(KL=256: r
mean =–0.61) (Fig. 3). This is because low local limits to diversity
KLinhibit geographic range expansions, leading to faster rates of
species extinction, thus eroding the signature of a temporal slow-
down in diversification rate from the reconstructed tree. When r
is calculated using the full tree, the slowdown is similar in both
scenarios (rmean =–0.971 for KL=1andrmean =–1.004 for
KL=256).
PATTERNS OF REGIONAL SPECIES RICHNESS AT
EQUILIBRIUM
The regional richness attained at equilibrium depends on KL,A
and the relative rates of speciation, local extinction, and colo-
nization (Figs. 4 and 6). As expected larger values of KL,and
6EVOLUTION 2018
DIVERSIFICATION AND LOCAL LIMITS
Figure 4. The effect of differences in local ecological limits (KL=4, 16, 32) on regional species richness and geographic range size and
at different times in a clade’s history (young =1 my, intermediate =7my,old=35 my). The per population speciation rate (λ=0.08),
rate of colonization (γ=80), rate of local extinction (μ=1), and regional area (A=256) were the same across simulations. Results are
based on 100 replicate simulations per scenario.
thus regional diversity limit KR, lead to a higher regional rich-
ness at equilibrium (Fig. 4). This occurs because a higher KR
supports more species populations and thus, for a given level of
richness, faster rates of speciation and slower rates of species
extinction. For a given KR, lower per-population rates of speci-
ation λlead to a lower equilibrium regional richness (Fig. 6A)
compared to when per-population rates of speciation λare high
(Fig. 6B). Conversely, higher rates of local extinction μlead to a
lower equilibrium richness because of an increase in the rate of
species extinction (Fig. 6). Indeed, in the absence of local (and
thus species) extinction (μ=0), clades would eventually saturate
the region, whereby every assemblage contains KLspecies and
each species is present in only a single local assemblage, that
is all species have a range size of 1 (Fig. 2, bottom panel). In
contrast, when rates of local extinction μexceed zero, regional
diversity is maintained at a dynamic equilibrium lower than the
theoretical upper limit to diversity (Figs. 1 and 5). Unless rates
of colonization γare very low, variation in γhas relatively little
effect on regional richness (Fig. 6A and B). This is because, at
equilibrium, rates of colonization are limited by the rate at which
local sites become available following local extinction rather than
by the colonization rate γ.
In the absence of extinction, the region eventually becomes
saturated with species (i.e., KRspecies) and this upper limit to
diversity is the same regardless of the relative values of Aand KL
(KR=KL×A).However, when rates of local extinction are greater
than zero, we found that geographic area Aand local diversity
limits KLhave different effects on the accumulation of diversity
EVOLUTION 2018 7
L. HERRERA-ALSINA ET AL.
Figure 5. Temporal patterns in species richness, lineage accumulation, and evolutionary turnover (the ratio of extinction to speciation
rate) for different local ecological limits (KL=1, 16, 256) in combination with different regional area (A=4096, 256, 16 cells) thus
keeping the regional limit to richness (KR) fixed. The top row shows the regional species richness (gray line) and the number of lineages
in the reconstructed phylogeny over time (black line) along with their 95% confidence intervals (dashed lines) across 100 simulations.
The horizontal line represents the maximum potential number of species the region can hold (KR=KL×A). The bottom row shows the
dynamics of speciation and extinction over time. When evolutionary turnover equals 1 (dashed lines) rates of speciation and extinction
are identical. Values lower (greater) than 1 indicate when rates of speciation are greater (less) than extinction. Darker cells indicate a
higher concentration of observations. In each case, speciation rate (λ)=0.05, colonization rate (γ)=30, and local extinction (μ)=1.
and the regional richness attained at equilibrium. Specifically, it
takes longer to reach equilibrium (Fig. 4) but diversity attains a
higher level (Fig. 6A and B) when the geographic area of the
region Ais small but the local ecological limit KLis high, than
when the area of the region Ais large but the local ecological limit
KLis small. This difference in richness is robust to differences
in rates of speciation λand colonization γand strengthens with
higher rates of local extinction μ(Fig. 6). For instance, when the
rate of local extinction is low (μ=0.5), a small region with a high
local ecological limit (A=16, KL=256) has a regional richness
that is 1.3 times that of a large region with a low local ecological
limit (A=4096, KL=1), but when rates of local extinction
are high (μ=5) the difference in regional richness increases to
fivefold (Fig. 6B).
PATTERNS OF PHYLOGENETIC TREE IMBALANCE
We found that clades diversifying in regions with extremely high
local ecological limits (KL=1500, A=256), and which are
far from reaching local saturation, exhibit a similar level of phy-
logenetic tree imbalance to that expected under a Yule process
(Smean =–0.08). In contrast, when local ecological limits are
lower (i.e., impose greater constraints on diversification), the ex-
pected shape of phylogenetic trees varies greatly depending on
the relative size of the geographic region Aand local ecologi-
cal niche space KL, rates of speciation λ, local extinction μ,and
colonization γ(Fig. 6E and F). In particular, when the region
is large but local ecological limits are low (A=4096, KL=
1), phylogenetic trees are highly unbalanced. This arises because
newly formed species have small geographic ranges leading to
large asymmetries in range size and thus probabilities of speci-
ation and extinction (Fig. 2). By contrast, in small regions with
high local ecological limits, phylogenetic trees are more balanced
than expected under a pure birth process (A=16, KL=256).
This arises because a small geographic area constrains species to
have relatively small geographic ranges (Fig. 6C and D). Species
undergoing rapid speciation will thus exhibit large proportional
declines in range size, thus substantially decreasing the probabil-
ity of further speciation and increasing the chances of extinction.
This negative feedback on the diversification of rapidly speciat-
ing lineages leads to more balanced phylogenetic trees. Higher
rates of local extinction μand colonization γ, relative to rates of
speciation λ, lead to phylogenetic trees converging on the shape
expected under a pure birth process (Fig. 6E and F). This is be-
cause rapid extinction-colonization dynamics erode the signature
of past speciation history on geographic range size, thus equaliz-
ing probabilities of diversification across lineages.
THE PATTERNS AND TEMPORAL DYNAMICS OF
GEOGRAPHIC RANGE SIZE
For a given regional area A, and when the local ecological limit KL
is low, communities rapidly become saturated with species thus
inhibiting geographic range expansions. As a result, species retain
8EVOLUTION 2018
DIVERSIFICATION AND LOCAL LIMITS
Figure 6. Regional richness, range size, and tree imbalance (Sackin index) under different diversification scenarios. We explored scenarios
encompassing different combinations of local carrying capacity (KL) and regional area (A), rates of colonization (γ), local extinction (μ),
per population speciation (λ), and mode of dispersal. For each combination of parameters, a local dispersal model is assumed, except in
the cases marked with an “∗” that assumes a global model of dispersal. The duration of the simulation (T=35) and the potential regional
diversity limit (KR=4096) was held constant across all scenarios. Results are based on 100 replicate simulations per scenario. N.B the
scale of the y-axes differs between plots. In (E, F), tree imbalance according to Sackin’s index is plotted on a log-scale with the dashed
horizontal line indicating the expected level of tree imbalance under a Yule process (Sackin =0). Because Sackin’s index may take values
<0, we added a value of 2 to the index prior to log-transformation, that is log(Sackin +2).
EVOLUTION 2018 9
L. HERRERA-ALSINA ET AL.
a small geographic range for longer periods of time following
speciation. In contrast, when constraints on local richness are
relaxed (i.e., the local ecological limit KLis higher), there is
more time available for range expansion before local communities
become saturated leading to larger mean range sizes and a stronger
relationship between species age and range size (Fig. 2). This
effect of KLon species range size is, however, transient. When
richness reaches a regional equilibrium, mean geographic range
size becomes independent of the local KLand thus regional KR
limit to richness (Figure 4). This is because mean range size is
maintained at a dynamic equilibrium set by a balance between
rates of local extinction μand speciation λ, which act to reduce
range size, and the rate of colonization γ, which acts to increase
range size. Furthermore, for a given limit to regional diversity KR,
although clades occupying smaller regions (i.e., Ais low) exhibit
less variation in range size than clades occupying large regions
(i.e., Ais high), there is relatively little variation in mean range
size (Fig. 6C and D).
Although local extinction events reduce species’ range size,
we found that mean species range size actually increases with
the rate of local extinction μ(Fig. 6C and D). We argue that this
happens via two coupled mechanisms: first, when rates of local
extinction μare high, species with small geographic ranges are
more likely to become extinct. Second, the ecological space left
by extinct species becomes available to be colonized by large-
ranged species that implies further range expansion. Therefore
both the selective filtering of rare species and the expansion of
widespread species lead to an increase in mean range size among
the survivors. As expected, a higher speciation rate λleads to
smaller range sizes, but the rate of colonization γhad surprisingly
little effect on range size (Fig. 6C and D). Indeed, our simula-
tions also showed that the characteristics of clades at equilib-
rium are rather insensitive to whether dispersal is local or global
(Fig. 5). This is because once communities are saturated with
species, range expansions become limited by the rate at which
local extinctions open up opportunities for colonization rather
than the intrinsic rate of colonization per se. Thus, at equilibrium,
higher dispersal capacities either in the form of global dispersal or
higher colonization rate play a secondary role in range expansions
and the accumulation of diversity.
The shape of the range size frequency distribution at equi-
librium is strongly right skewed, with many small-ranged species
and only a few widespread species (Fig. 2). This pattern is gener-
ally evident regardless of the values of KL,λ,andγ.Incontrast,in
the absence of local extinction (μ=0), ongoing speciation leads
to a continuous decline in range size so that all species eventually
have a range size of 1. While a right skewed distribution with a
single mode predominates at equilibrium, a bimodal distribution
in range size may emerge early in the clade’s history (Fig. 2).
This is because early arising species rapidly expand their distri-
butions throughout the region but this subsequently inhibits the
expansion of later arising species. This bimodal pattern is, how-
ever, a transient phenomenon and as diversity reaches a steady
state, the range size distribution shifts to becoming increasingly
right-skewed with a single mode. This smoothing of the range size
distribution occurs because speciation and local extinction grad-
ually erode the range size of the most widespread species, while
rare species gradually expand their distributions as they invade
spaces in local communities left empty by local extinction.
Discussion
With a spatially explicit model of species diversification we ex-
plored the phylogenetic and geographic patterns expected when
regional limits to diversity arise from local limits to coexistence.
Most mathematical models of diversity-dependent diversification
(Rabosky and Lovette 2008; Etienne et al. 2012) assume a direct
connection between clade richness and rates of speciation and ex-
tinction. In contrast, in our model diversity-dependence in these
macroevolutionary parameters arises as an emergent property of
local limits to coexistence.
Our model shows that when local diversity is bounded, rates
of species diversification decline over time. This occurs because as
local assemblages become ecologically saturated, newly formed
species are unable to expand their distributions thus preventing
further rounds of speciation and increasing rates of extinction.
Eventually regional species diversity reaches a steady state in
which the number of species and their average geographic range
size fluctuate around an equilibrium set by the relative rates of
speciation and extinction.
Previous studies, using nonneutral models, have also shown
how diversity-dependence in rates of diversification can emerge
from local processes. For instance, in models of adaptation radi-
ation (Gavrilets and Vose 2005; Birand et al. 2012), an initially
high rate of diversification precedes a decrease in the rate of
speciation and an increase in the rate of extinction. Pontarp and
Wiens (2017) modeled species’ trait distributions as a function
of local resources, the utilization of which determines the local
species carrying capacity. In these nonneutral models high ecolog-
ical niche availability initially promotes high rates of ecological
speciation and thus an early burst in species diversification. Here,
we modeled ecological opportunity in a simpler way (simply as
the number of locally available niches), but our model neverthe-
less provides a number of novel insights into how geographic and
local ecological niche diversity regulates species radiations.
One intriguing result from our model relates to how the rel-
ative dimensions of geographic and ecological-niche space influ-
ence biodiversity. We found that small regions with high local
ecological limits are able to support more species at equilibrium
than large regions with low ecological limits, especially when
10 EVOLUTION 2018
DIVERSIFICATION AND LOCAL LIMITS
rates of stochastic population extinction are high. This result may
appear surprising because in our model the theoretical upper limit
to diversity–occurring when each species comprises only a single
population–is the same regardless of the relative dimensions of
geographic and ecological-niche space. The most likely explana-
tion for this finding is that a high local ecological limit within a
small geographic area maximizes the number of species that can
regionally coexist by favoring the geographic spread, and thus
persistence, of rare relative to widespread species. This arises be-
cause the area of the region ultimately constrains the maximum
number of populations that a species can attain, thus preventing
any single species from monopolizing the entire regional niche
space. In other words, when an opportunity for colonization be-
comes available through the local extinction of a resident species,
this opportunity can only be exploited by species absent from the
local community, which by definition will tend to be relatively
rare. In contrast, in a region where each locality contains only a
single niche (KL=1), species that are already widespread are
more likely to be available to exploit gaps left by recent extinc-
tions, so that rare species may rapidly drift to extinction. This
finding has a number of important implications. First, it suggests
that differences in the diversity of regions and clades may be more
strongly driven by differences in local ecological niche space than
regional area. Second, variation in diversity between clades or re-
gions may to a certain extent be uncoupled from variation in
overall diversity limits.
In addition to the effects on overall regional diversity, we
found that the relative size of geographic and local ecological
niche space also influenced the structure of diversity within re-
gions. In particular, we found that when local ecological limits
are low (low KL), diversity is distributed highly asymmetrically
across clades (i.e., phylogenetic trees are unbalanced). In a similar
scenario (low number of available niches mediated via competi-
tion). Gascuel et al. (2015) found that phylogenetic trees show
high imbalance and claimed that this is a trace of allopatric speci-
ation taking place early in the history of a clade. In our model, the
imbalance arises because newly formed species tend to be rare
leading to highly skewed range size distributions and thus asym-
metries in rates of speciation and extinction. In contrast, when lo-
cal niche diversity limits are high (high KL) and geographic limits
are small (small A), range expansion among widespread species
is constrained relative to that of newly formed species, leading to
more balanced phylogenetic trees. These results make the novel
prediction that patterns of phylogenetic tree shape should vary
predictably with local ecological niche diversity.
While our model shows that local limits to diversity must
eventually lead to a steady state in regional richness, these local
and regional dynamics may be partially decoupled. In particular,
even when all local communities are saturated with species, on-
going allopatric speciation and the increasing turnover of species
between assemblages can enable regional diversity to increase for
long periods of time before the system reaches a dynamic equi-
librium (Cornell 2013). An important implication of this result is
that even if there is evidence that local diversity is saturated, this
need not imply that the diversity of the entire region has reached a
carrying capacity. Equally, even when total clade diversity is still
increasing, this should not be taken as evidence that there are no
ecological limits to local diversity or that any such limits have yet
to be reached.
One of the more surprising results revealed by our analysis,
is that although imposing a limit to local species richness acts as a
constraint on range expansion, the average range size attained by
extant species is similar regardless of whether the local ecologi-
cal limit is high or low. This is counterintuitive because species
should more readily expand their distributions when local diver-
sity is less constrained. We found that early in the radiation and
when communities are far from saturated, this is indeed the case,
with higher ecological limits (high KL) enabling species to attain
large range sizes. However, rapid range expansion also leads to
faster rates of speciation and thus the accumulation of species with
small range sizes. These two processes balance one another so
that mean range size is independent of the local ecological limit.
Eventually, range sizes reach a dynamic equilibrium whereby in-
creases in range size due to colonization are balanced by decreases
in range size due to speciation and local extinction.
What determines the distribution of species range size has
long been the subject of debate; explanations are sought in dif-
ferences among species in niche breadth, environmental toler-
ances, or dispersal capacity (Tomasovich et al. 2015; Fenberg and
Rivadeneira 2017). The right-skewed distribution of range sizes
observed in empirical datasets (Hecnar 1999; De Troch et al.
2001; Pither 2003; Reed 2003) was recovered in our model re-
gardless of the strength of the local ecological limit or the other
key macroevolutionary parameters (e.g., rates of speciation). This
consistency in the shape of the range size frequency distribution
suggests that this distribution contains little information about the
underlying process structuring species distributions. There are a
few studies reporting a bimodal range size distribution (Gaston
et al. 1998; Mora and Robertson 2005; Scott et al. 2012). Scott
et al. (2012) suggest that this bimodal distribution is the result of
differential dispersal capacities among species. Our findings show
that such a distribution can also arise early in a clade’s history for
ecologically identical species with local limits to diversity. Under
this scenario, species arising early in the clade’s history are able
to spread throughout the entire region, attaining large range sizes.
In contrast, species that are formed later (when local communities
are saturated) can only expand their ranges when resident species
become locally extinct, leading to slow rates of range expansion
and a bimodal distribution in range size. However, our model also
shows that this bimodal distribution is a transient phenomenon.
EVOLUTION 2018 11
L. HERRERA-ALSINA ET AL.
Over time, speciation and local extinction events lead to a
decrease in the range size of the most widespread species, so that
the range size distributions becomes increasingly right-skewed
range with a single mode.
Conceptually, our model is strongly rooted in the existing
birth-death framework of macroevolution. First, as in existing
birth-death models, we assume that species (or more precisely in
our case species populations) are neutral in the sense that they are
governed by identical dynamics. Second, as in existing diversity-
dependent birth-death models, we assume that there is a limit to
the number of species that a clade can support, but in our case this
limit arises from a combination of both local ecological and spa-
tial constraints. On the one hand, the simplicity of this extension
to the existing birth-death framework represents a key strength of
our model, because it allows us to identify how simply consid-
ering space influences the expected dynamics of diversification.
On the other hand, the way we have modeled ecological and ge-
ographical limits to richness still represent a major abstraction of
reality. We therefore see room for much further refinement and
extension of our model. For instance, limits to coexistence could
be modeled as a result of individual level dynamics rather than at
the level of species (Chesson 2000; Hillerislambers et al. 2012).
Another obvious extension would be to incorporate a model of
trait evolution, so that traits determine the place of a species
within niche space. In this case, ecological constraints on coex-
istence could be modeled by making colonization/extinction a
positive/negative function of ecological dissimilarity (Jiang et al.
2010; Pigot and Etienne 2015). Finally, the interplay between
range evolution and diversification might be affected by the mode
of speciation. Our model assumes that new species are initially
rare, comprised of a single local population. However, other mod-
els of speciation, including vicariance driven by geographic bar-
riers, may enable new species to inherit a large range size from
their parent. This could produce different patterns of diversifi-
cation and range size evolution. For instance, more symmetrical
splitting of species ranges during speciation is expected to lead
to more balanced phylogenetic trees (Pigot et al. 2010), while
the drastic reduction in range size accompanying each speciation
event would potentially leading to a faster attainment of a regional
diversity equilibrium.
Conclusions
Here, we developed a spatially explicit model of diversity-
dependent diversification to explore the phylogenetic and bio-
geographic patterns expected when ecological limits to diversity
arise from local-scale species interactions. While our findings
demonstrate how local ecological limits lead to a predictable dy-
namic equilibrium in regional diversity and range size, they also
highlight that variation in regional richness can to a certain extent
be decoupled from variation in regional diversity limits, depend-
ing on the relative size of geographic and local ecological niche
space and the relative rates of speciation, extinction, and coloniza-
tion. Taken together, these findings provide an important bridge
for understanding how large- and small- scale processes inter-
act and further unite evolutionary and ecological mechanisms for
understanding patterns of species diversity.
AUTHOR CONTRIBUTIONS
R.S.E. and A.L.P. coordinated the study; H.H. codded the simulations;
L.H.-A. programmed and carried out the analysis; R.S.E., A.L.P., and
L.H.-A. wrote the article. All authors gave final approval for publication.
ACKNOWLEDGMENTS
This manuscript was enriched by constant discussions with members
of Theoretical and Evolutionary Community Ecology. L.H.-A. is sup-
ported by a grant from Consejo Nacional de Ciencia y Tecnologia (CVU
385304). R.S.E. thanks the Netherlands Organisation for Scientific Re-
search (NWO) for funding through a VICI grant. We are grateful to the
Editor and two anonymous reviewers for the suggestions made which
greatly improved the manuscript.
DATA ARCHIVING
The doi for our data is https://doi.org/10.6084/m9.figshare.5437126.v2.
CONFLICT OF INTERESTS
The authors have declared no conflict of interest.
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Associate Editor: F. Debarre
Handling Editor: M. Noor
Supporting Information
Additional supporting information may be found online in the Supporting Information section at the end of the article.
Tab l e S 1 . Parameter values explored in the simulations.
14 EVOLUTION 2018
