Ecological diversification in sexual and asexual lineages

Abstract

The presence or absence of sex can have a strong influence on the processes whereby species arise. Yet, the mechanistic underpinnings of this influence are poorly understood. To gain insights into the mechanisms whereby the reproductive mode may influence ecological diversification, we investigate how natural selection, genetic mixing, and the reproductive mode interact and how this interaction affects the evolutionary dynamics of diversifying lineages. To do so, we analyze models of ecological diversification for sexual and asexual lineages, in which diversification is driven by intraspecific resource competition. We find that the reproductive mode strongly influences the diversification rate and, thus, the ensuing diversity of a lineage. Our results reveal that ecologically-based selection is stronger in asexual lineages because asexual organisms have a higher reproductive potential than sexual ones. This promotes faster diversification in asexual lineages. However, a small amount of genetic mixing accelerates the trait expansion process in sexual lineages, overturning the effect of ecologically-based selection alone and enabling a faster niche occupancy than asexual lineages. As a consequence, sexual lineages can occupy more ecological niches, eventually resulting in higher diversity. This suggests that sexual reproduction may be widespread among species because it increases the rate of diversification.

Full text

Ecological diversication in sexual
and asexual lineages
P. Catalina Chaparro-Pedraza1,2,3,4, Gregory Roth5 & Carlos J. Melián1,3,6
The presence or absence of sex can have a strong inuence on the processes whereby species arise.
Yet, the mechanistic underpinnings of this inuence are poorly understood. To gain insights into the
mechanisms whereby the reproductive mode may inuence ecological diversication, we investigate
how natural selection, genetic mixing, and the reproductive mode interact and how this interaction
aects the evolutionary dynamics of diversifying lineages. To do so, we analyze models of ecological
diversication for sexual and asexual lineages, in which diversication is driven by intraspecic
resource competition. We nd that the reproductive mode strongly inuences the diversication rate
and, thus, the ensuing diversity of a lineage. Our results reveal that ecologically-based selection is
stronger in asexual lineages because asexual organisms have a higher reproductive potential than
sexual ones. This promotes faster diversication in asexual lineages. However, a small amount of
genetic mixing accelerates the trait expansion process in sexual lineages, overturning the eect of
ecologically-based selection alone and enabling a faster niche occupancy than asexual lineages. As
a consequence, sexual lineages can occupy more ecological niches, eventually resulting in higher
diversity. This suggests that sexual reproduction may be widespread among species because it
increases the rate of diversication.
Ecological diversication is the process whereby new species emerge as a consequence of ecologically-based
disruptive selection1. is process has produced diverse adaptive radiations, including the Lake Victoria cichlid
shes2,3 the Lake Baikal amphipods radiation4, and the subalpine lakes whitesh radiations5. To understand
the origin of biodiversity, it is therefore fundamental to gain insights into the factors inuencing ecological
diversication. One of these factors may be the presence or absence of sex6.
A wide variety of ecological interactions can induce selection regimes leading to ecological diversication7,8.
Arguably, the most studied is intraspecic competition, which can induce disruptive selection in the presence of
ecological opportunity9,10, i.e. the availability of relatively unexploited ecological niches11–13. Under disruptive
selection, intermediate phenotypes have a tness disadvantage compared with more extreme phenotypes,
causing phenotypic diversication12,14,15. is results in speciation in asexual populations due to the lack of
genetic mixing. However, in sexual populations, for speciation to occur, barriers to gene ow must evolve
between clusters of individuals with divergent phenotypes (e.g. assortative mating)1,12,16.
e reproductive mode can additionally inuence ecological diversication in multiple manners: On one
hand, sexual reproduction can increase rates of adaptation and evolution due to genetic mixing17–20, the process
whereby the genetic material between individuals is reshued. is may result in higher rates of diversication.
On the other hand, an asexual population will have twice the reproductive potential of a sexual population (i.e.
the twofold cost of sex due to the production of males, as outlined by Maynard–Smith)21 . It can therefore quickly
reach a higher population density. With higher population density, competition for resources can be stronger
in an asexual population, resulting in stronger ecologically-based disruptive selection driving diversication.
Hence, to understand how the reproductive mode inuences ecological diversication, it is fundamental to gain
insights into the interaction between the reproductive mode, natural selection, and genetic mixing.
Previous research examining the eect of the reproductive mode on diversication has not investigated this
interaction. For example, Melian et al.22 examined how the reproductive mode inuences diversication in a
model of neutral evolutionary change, thus neglecting natural selection. Other studies have attempted to explain
how clusters may emerge under alternative reproductive modes neglecting the dierences in reproductive
potential inherent to the reproductive modes23–25 (i.e. the twofold cost of sex), which may alter the strength of
natural selection and thus diversication. eory that mechanistically link ecological and microevolutionary
1Department of Fish Ecology and Evolution, Swiss Federal Institute of Aquatic Science and Technology (EAWAG),
Kastanienbaum, Switzerland. 2Department Systems Analysis, Integrated Assessment and Modelling, Swiss Federal
Institute of Aquatic Science and Technology (EAWAG), Dübendorf, Switzerland. 3Inst. of Ecology and Evolution,
University of Bern, Bern, Switzerland. 4Swiss Institute of Bioinformatics, Lausanne, Switzerland. 5Friedrich Miescher
Institute for Biomedical Research, Basel, Switzerland. 6Inst. de Física Interdisciplinar y Sistemas Complejos IFISC
(CSIC-UIB), Palma de Mallorca, Spain. email: Catalina.Chaparro@eawag.ch
OPEN
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processes with diversication patterns is needed to understand how the interaction between the reproductive
mode, natural selection and genetic mixing inuences ecological diversication.
Here we address this question by analyzing models of ecological diversication driven by intraspecic
resource competition. Following the large body of theory in adaptive dynamics7,11,12,26, we model the eco-
evolutionary dynamics of a diversifying lineage, which initiates with a founder population colonizing an
environment with a variety of unexploited food resources. rough an adaptive process, the lineage diversies
to occupy the available niches. We use a model that was formulated for asexual lineages27, and a modied variant
for sexual lineages to compare the diversication process between the lineages with the alternative reproductive
modes, and examine the eect of natural selection and genetic mixing on their evolutionary dynamics. e
only ecological dierence between the sexual and asexual lineage lies on the fact that asexual females produce
only females (i.e., all individuals can produce ospring), whereas sexual females produce females and males
with equal probability (i.e. primary sex ratio is 1:1, and only females can produce ospring). erefore, sexual
and asexual females produce the same number of total ospring if they have identical feeding niche trait and
experience the same environment. However, because asexuals do not produce male ospring, they produce
exactly twice as many female ospring as the sexuals. In some organisms, the cost of producing males need not
be this high, e.g., if the sex ratio is biased towards females or if males provide parental care28. Our assumption is
therefore one of the least favorable for the sexual populations.
Methods
We formulate diversication models for sexual and asexual lineages that dier only in the mode of reproduction,
whereas environmental conditions (i.e. food resource availability) and ecological demographic rates (i.e. resource
use, mortality) are set equal. en, we use analytical techniques, numerical simulations and individual-based
models to examine the eect of natural selection and genetic mixing on diversication.
Model assumptions
e environment: food resources
We consider
n
food resources to exist prior to arrival of the diversifying lineage (preexisting resources,
i=1,...,n
) with density
Ri
. In the absence of consumers, resource density dynamics follow semi-chemostat
dynamics
dR
i
dt =
ρ
(
R
imax −
R
i)
, where
ρ
and
Rimax
are the renewal rate and the carrying capacity of the
ith
resource, respectively (but we evaluate the robustness of our results when resource density dynamics follow
logistic growth, i.e.
dR
i
dt =
ρR
i(1 −
R
i
/R
imax)
, see SI1). is representation of resource dynamics is more
stabilizing, and more realistic when the resource has a ‘size refuge’, than the logistic growth dynamics29,30. Such
resources with ‘size refuge’ are common in nature; for example, for zooplanktivourous sh, the zooplankton
community growing into the size range at which they become vulnerable to sh predation. e total productivity
is the sum of the product of the carrying capacities and the renewal rate of the resources,
P=
ρ
∑
i
Rimax. We
assume that, for each resource, there exists an optimal trait value
θi
to consume it. For the sake of simplicity, these
optimal traits are assumed to be ordered along a one-dimensional ecological trait space (i.e.
θ1<θ
2<...<θ
n)
and equally distant from one another by a distance
D
(Fig.1).
Individual food resource use and demographic rates
We describe the interaction between consumer individuals and their food resources using a classic Lotka-Volterra
predator–prey model. In the model, individuals are characterized by the feeding niche trait
η
determining
resource use, which can take any value. e attack rate of an individual with trait
η
on the resource
i
,
ai(η)
,
equals the maximum attack rate
A
when its feeding niche trait
η
equals
θi
, and decreases in a Gaussian manner
as
η
moves away from
θi
, i.e.,
a
i
(
η
)=
A
exp [−(
η
−
θi
)2
/
(2
τ
2)]
, where
τ
determines the width of the
Gaussian function (Fig.1). is implies that there exists a tradeo to feed on the alternative food resources, such
that specialization on one food resource goes at the expense of specialization on the others31. Such tradeos have
been generally observed in heterotrophic organisms, including bacteria32, insects33, and vertebrates34,35. Each
individual feeds at a rate
ai(η)Ri
on the
ith
resource, and thus depletes it at this rate (individual food intake
thus follows a functional response Type I; see SI1 for functional response Type II). Reproducing individuals
convert food into ospring with an eciency
ε
. Additionally, individuals die at a rate
δ
(mortality is independent
of the food intake; see SI1 for food-dependent mortality).
Eco-evolutionary models
Based on the assumptions described above, we formulate alternative eco-evolutionary models for lineages
with sexual and asexual reproduction and use two modeling approaches to analyze them: adaptive dynamics
and individual-based models. Adaptive dynamics provides analytical tools to investigate the eco-evolutionary
feedback between population dynamics and phenotypic evolution through natural selection11,12. We use these
tools to investigate the eect of natural selection alone on diversication. However, adaptive dynamics does not
allow for the description of explicit genetic dynamics. erefore, to investigate the combined eect of natural
selection and genetic mixing, we formulate individual-based, genetically explicit models of lineages with sexual
and asexual reproduction.
Modelling the eect of natural selection in the absence of genetic mixing using adaptive dynamics
We use adaptive dynamics to analytically investigate phenotypic evolution driven only by ecologically-based
natural selection. Adaptive dynamics assumes that ecological and evolutionary timescales are suciently
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separated, so that the system reaches the ecological equilibrium before the next phenotypic change occurs (we
relax this assumption in the individual-based model, see next section).
We rst formulate the ecological dynamics of a sexual and an asexual lineage. In the sexual lineage, only
females reproduce, producing females and males with equal probability, i.e. primary sex ratio is 1:1. Assuming
that mating is assortative and thus occurs only among individuals of the same ecomorph (the evolution of
Fig. 1. Individual food resource use in the model. Our model considers the existence of multiple niches, or
rather the resources that form them, prior to the arrival of an ancestral population. To consume each resource,
there exists an optimal feeding niche trait 9. Organisms dier in an ecological character, i.e. the feeding niche
trait (e.g. the maximum gape in sh or reptiles, or the bill size in birds, which determines the size of the food
particules that they can ingest). e coloured gaussian curves describe how the attack rate on the i-th resource,
ai(n), varies with the feeding niche trait n and the degree of specialization required to successfully feed on the
resources . An organism with a small feeding niche trait, e.g. n1 (exemplied by the grey sh) has an attack
rate on resource 1 and on resouce 2 indicated by the grey arrows; and its attack rate on other resources is
nearly zero. Whereas an organism with a large feeding niche trait, e.g. n2 (exemplied by the black sh) feeds
mostly on resource 4 and on resource 5 with attack rates indicated by the black arrows; its attack rate on other
resources is nearly zero.
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assortative mating is considered in the next section), we model the ecological dynamics of the sexual lineage
considering emerging ecomorphs (
k=1,...,l
) with feeding niche trait
ηk
, female density
Fk
and male
density
Mk
according to:
dFk
dt =1
2ε
n
∑
i=1
ai(ηk)RiFk−δF
k
dMk
dt =
1
2ε
n
∑
i=1
ai(ηk)RiFk−δMk
,
(1)
In contrast, in the asexual lineage, all individuals are clonally reproducing individuals. erefore, the ecological
dynamics of the lineage can be modeled considering
m
emerging ecomorphs (
j=1,...,m
) that dier in their
feeding niche trait
ηj
. e individual density
Nj
of each ecomorph follows:
dNj
dt =
(
ε
n
∑
i=1
ai(ηj)Ri−δ
)
Nj
,
(2)
e ecological dynamics of the food resources are given by
dRi
dt =ρ(Rimax −Ri)−
(
l
∑
k=1
ai(ηk)Ri(Fk+Mk)
)
(3)
in the case of the sexual lineage, and by
dRi
dt =ρ(Rimax −Ri)−
(
m
∑
j=1
ai(ηj)RiNj
)
(4)
in the case of the asexual lineage.
Based on the ecological dynamics, we then apply adaptive dynamics techniques36–38 to study the evolution
of the feeding niche trait. Using the lifetime reproductive output,
L
, as a proxy for tness (the derivation of an
analytical expression of
L
is in SI2), trait change in the sexual lineage is given by:
dηk
dt =σs
∂L
(
ηk′,η
)
∂ηk
′ηk′=ηk
,
(5)
where ∂L
(
ηk′,η
)
∂ηk
′ηk′=ηk
is the selection gradient and
σs
is a constant scaling the evolutionary timescale.
Similarly, the trait changes in the asexual lineage at a rate:
dηj
dt =σa
∂L
(
ηj′,η
)
∂ηj
′
η
j′=
η
j
,
(6)
where
σa
is the constant scaling the evolutionary timescale. Diversication, and thus the emergence of a new
ecomorph, occurs through a process of evolutionary branching when directional selection halts, i.e. when
∂L
(
ηk′,η
)
∂ηk
′ηk′=ηk
=0
or ∂L
(
ηj′,η
)
∂ηj′

η
j′
=η
j
=0
, if the trait value at this point corresponds to a minimum
of the tness landscape36,37. us, the curvature of the tness landscape can be used to determine whether a
diversication event occurs. e analytical expressions for the selection gradient and the curvature of the tness
landscape are in SI2.
To analyze the eect of natural selection on diversication, we rst analytically identify the conditions
that enable diversication in an asexual and a sexual population (see SI3) using analytical expressions for
the population and food resource densities (see SI4, exemplied by simulation in Fig.2). en, when these
conditions are satised, we address two questions: 1) do alternative reproductive modes have an eect on the
strength of natural selection (measured by the magnitude of the selection gradient)? and 2) how does such
an eect impact the rate of evolution in lineages with sexual and asexual reproduction? To address the rst
question, we analytically compare the selection gradient of two populations diering in their reproductive mode,
when each colonizes an environment with two dierent food resources (see SI5 and Fig.3A and B). To address
the second question, we perform numerical simulations to examine the eect of the reproductive mode on the
evolutionary rate of lineages expanding over the trait space to occupy multiple niches (Fig.3C). To perform these
simulations, the evolutionary dynamics are calculated using Eqs.5 and 6, and a constant σa = σs = 10−6 that scales
the evolutionary time. Because this constant is used to scale equally the evolutionary time of both sexual and
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asexual populations, results presented in Fig.3C for the lineages with dierent reproductive modes dier only in
the selection gradient and, thus, in the strength of natural selection.
Modelling the eect of natural selection in the presence of genetic mixing using individual-based models
We are interested in understanding how diversication in sexual lineages is inuenced by genetic mixing, the
process whereby male and female genetic material is shued (Fig.4). To do so, we implement genetically explicit
individual-based models (IBM) based on the birth, death, and feeding processes as well as the environment
described in the Section “Model assumptions” (details are in SI6). In IBM, individual consumers are discrete
entities; hence, birth and death occur as discrete, stochastic events. Because genetic mixing occurs between
sexually reproducing individuals, the evolution of barriers to gene ow is required besides ecologically-based
disruptive selection for speciation to occur in sexual populations1,16. Following a long tradition in speciation
theory, we allow the evolution of such barriers through the evolution of assortative mating12,16. Hereaer, we
refer to sexually reproducing individuals as males and females, and to asexually reproducing individuals as
clonal individuals. We use an additive diploid multi-locus genetic trait architecture. Each individual is assigned
a genotype that determines its phenotype. More precisely, individuals are assigned a set of E-locus (10 loci) that
determines their feeding niche trait, such that the sum of all alleles in the E-locus set equals the trait. Alleles
of the E-locus set can take any value, and so do the feeding niche trait. Sexually reproducing individuals are
assigned an A-locus set (5 loci) that determines the mating trait
ω
, such that the value of the trait equals the
average of the allele values, which can be -1 and 116. Assuming that mating depends on female preference only,
the alleles in the A-locus set are expressed only in females: females carrying an intermediate mating trait mate
randomly (
ω=0
); females with a negative
ω
mate disassortatively, and females carrying a positive
ω
mate
assortatively. Assortability is based on the feeding niche trait and is described by a self-matching mate-choice
function16. Reproductive isolation is calculated using the method of Sobel and Chen39. Ospring produced
through sexual reproduction inherit parental alleles at each locus independently; in other words, we assume
full recombination among all loci. To examine the eect of genetic mixing on the evolutionary rate of a sexual
lineage, we vary the contribution of paternal alleles to the ospring’s genes. We do so by assuming that ospring
receive in each locus one allele from the father and one from the mother with probability,
p
, or both alleles from
the mother with probability,
(1 −p)
. When
p=1
, ospring inherits one maternal and one paternal allele in
each locus, meaning that the contribution of each parent is 50% (
p=1
is used in all gures presenting IBM
results, except in Fig.5 where it varies). When
p=0
, ospring inherits only maternal alleles, therefore the
contribution of males to ospring is 0%. While biologically unrealistic, the latter scenario represents the case
in which natural selection and mutation are the only drivers of evolution. is scenario allows to test whether
the results obtained with the adaptive dynamics model are robust to the relaxation of assumptions inherent to
that approach, e.g. the separation of ecological and evolutionary timescales, and innite population size. In the
asexual lineage, we assume clonal apomictic reproduction, therefore ospring inherit the total maternal genetic
material (without recombination). Mutation probability is 0.001 per allele. When a mutation occurs, the value of
the ospring allele is drawn from a normal distribution with a mean equal to the parental value and a standard
deviation of
σ
= 0.01. To quantify the emergence of novel phenotypes (Fig.4D), we divide the feeding niche
trait space into bins of width
σ
. A novel phenotype is dened as the rst phenotype that emerges within a bin
throughout the simulation.
A modied version of the IBM explained above is used to explore how the absence of the cost of male
production aects our results (see SI6). All models are implemented in MATLAB. Initialization of the IBM can
be found in SI6. Table S2 in SI6 summarizes the parameters introduced above. Visualization of results from
replicated simulations (e.g. Figure5) were performed using the package ggplot in R. Model implementation code
is available in zenodo.
Robustness analysis
We examine whether our results are robust to assumptions regarding the food resource dynamics, the functional
response Type, a density-independent mortality rate (see SI1 for details), as well as the mutation rate and
the number of loci of the feeding niche trait (see SI6 for details). Additionally, we investigate the stability of
the attractor of the sexual lineage when the degree of specialization required to successfully feed on the food
resources is low (see SI7).
Results
Conditions that enable diversication in an asexual and a sexual population
Diversication driven by intraspecic resource competition is caused by frequency-dependent selection. Under
frequency-dependent selection, whether a trait confers a tness advantage depends on the traits of the other
organisms. Hence, as evolution unfolds the tness landscape changes. In this context, adaptive evolution can drive
phenotypic traits toward a local minimum of the tness landscape11,12. At this point, intermediate phenotypes
have a tness disadvantage compared with more extreme phenotypes, and thus selection is disruptive, enabling
diversication. In a previous work, Chaparro et al.27 derived the conditions for diversication for asexual
populations. Here we extend the analysis to the conditions for sexual populations (see analytical derivation in
SI3). Two conditions need to be satised for diversication to occur in a population colonizing an environment
with two dierent food resources:
Condition 1 (condition for mutual invasibility according to Geritz et al.11): e mean phenotype of the popu-
lation at an evolutionary equilibrium must be a local tness minimum. Both an asexual and a sexual population
satisfy this condition when (see ref27 and eq. SI3.9 in SI3):
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D>2τ.
(7)
erefore, when the distance between the optimal trait values to feed on preexisting resources
D
is too small
relative to the degree of diet specialization
τ
, disruptive selection does not occur. is is because a suciently
strong tradeo between feeding on the alternative food resources is needed to induce disruptive selection26,40.
Otherwise, the generalist strategy, corresponding to the evolutionary equilibrium in between the optima to feed
on the resources, is a tness maximum and thus selection is stabilizing.
Condition 2 (condition for convergence stability according to Geritz et al.11): is evolutionary equilibrium
where the population experiences disruptive selection is an attractor of the evolutionary dynamics, i.e., adaptive
evolution can drive a population toward this evolutionary equilibrium. is condition is satised when
P>
δρD
2
4τ
2
εA
eD
2
8τ2 (8)
in a population with asexual reproduction27, and when
P>
δρD
2
2τ
2
εA
eD
2
8τ2 (9)
in a population with sexual reproduction (see eq. SI3.25 in SI3). is implies that, for both sexual and asexual
populations, there exists a threshold of minimum productivity of the environment
P
that, given other
environmental and demographic parameters (
ε,A,ρ,δ,τ,D
), enables the trait to be attracted to the point where
selection becomes disruptive. If the productivity of the environment is lower than this threshold, evolution
drives the trait value to one of the optima to feed on the resources corresponding to a local maximum of the
tness landscape, where selection is stabilizing41,42. is threshold is higher for a sexual population, meaning
that a higher productivity, specically twice as higher, is required for diversication in a sexual population than
in an asexual population experiencing the very same conditions.
Diversication in asexual lineages is less restricted than in sexual lineages, because in asexual populations
it can occur at a relatively low level of productivity that is not sucient to enable diversication in sexual
populations. is is the consequence of the reduced reproductive potential of sexual populations. In a sexual
population only females, which are only half of the population, have the potential to produce ospring,
whereas in an asexual population all individuals can reproduce. Due to the lower reproductive potential, a
sexual population has a lower density (Fig.2, proof in SI4). Indeed, if the reproductive potential of the asexual
Fig. 2. Ecological dynamics of a sexual and an asexual population A sexual population (red line) reaches
a lower density than an asexual population (blue solid line) experiencing the same ecological conditions
(analytical proof in SI4), and the same density than an asexual population with a half of the eciency
to convert food into ospring (blue dashed line). e ecological dynamics are calculated assuming a
(nonevolving) trait value of 1.4, and using Eqs.1 and 3 for the sexual population and Eqs.2 and 4 for the
asexual population. e population encounters two food resources (optimal traits to feed on the resources:
6 = 1 and 6 = 2). e carrying capacity of each food resource is equal to 5g/L. At the beginning of the
simulation, the food densities equal the carying capacity (F(t0) = 5g/L) and the population density is very low,
0.1 ind/L, mimicking a colonization event of an environment with vacant niches. Under these conditions,
the population quickly grows overshooting its own carrying capacity. Latter, it decreases an stabilizes at its
ecological equilibrium. Other parameter values as in Table S1.
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population is halved, by for example halving the eciency to produce ospring, the population density of an
asexual population equals that of a sexual population (blue dashed line vs red line in Fig.2). As a consequence
of this dierence in population density—which does not depend on the type of growth used to describe the food
resource dynamics (Figure S1)—, under the very same ecological conditions, competition is stronger among
individuals in an asexual than in a sexual population. Because competition is the driver of diversication in
Fig. 3. e eect of natural selection alone on diversication. (A) Natural selection is stronger in asexual
than in sexual populations (proof in SI5), in other words, the magnitude of the selection gradient is always
larger in an asexual than in a sexual population experiencing the same ecological conditions. (B) Stronger
natural selection drives the trait to the value where selection is disruptive faster in an asexual than in a sexual
population. (C) As a result, in a habitat with multiple niches, an asexual lineage diversies to occupy all niches
faster than a sexual lineage (evolutionary dynamics of both lineages can be found in gure S2). In A and B, a
population encounters two food resources (optimal traits to feed on the resources: 91 = 1 and 92 = 2). In A, the
selection gradient is calculated using Eq. SI2.3 and SI2.7 for the sexual and asexual population, respectively.
In B, the evolutionary trajectory is calculated using Eq.5 and Eq.6 for the sexual and asexual population,
respectively. In C, the ancestral population encounters ten food resources. In all panels, the carrying capacity of
each food resource is equal to 5g/L. Other parameter values as in Table S1.
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our model, stronger competition enables diversication at a lower level of habitat productivity in an asexual
population than in a sexual population.
Natural selection drives diversication faster in asexually reproducing lineages in the
absence of genetic mixing
Our study of the selection gradient of an asexual and a sexual population colonizing an environment with two
dierent food resources reveals that natural selection is always stronger in the asexual population (Fig.3A, proof
in SI5). is is because, under the same ecological conditions, an asexual population has a higher density than
a sexual population. Higher density leads to stronger competition among individuals in an asexual population,
causing stronger natural selection. As a result, if the evolutionary rate is driven only by natural selection,
evolution drives the feeding trait of an asexual population to the value where selection is disruptive faster than
it drives the trait of a sexual population (Fig.3B). In scenarios with several niches, natural selection therefore
causes an asexual lineage to diversify and occupy the available niches faster than a sexual lineage (Fig.3C). A
further analysis reveals that competition is stronger in an asexual than in a sexual population when considering,
not only the birth, but also the mortality rate to be dependent on the feeding rate (Figure S3). In conclusion,
when natural selection is the only driver of evolution, the diversication process is faster in an asexual lineage
than in a sexual lineage.
Natural selection drives diversication faster in sexually reproducing lineages in the presence
of genetic mixing
We next consider the combined eect of genetic mixing and natural selection. Individual-based simulations of
lineages with dierent reproductive modes indicate that the expansion over the trait space of both sexual and
asexual lineages occurs through sequential diversication. In both lineages, the ancestral population evolves
towards the trait value in between the optimum to feed on resource 1 and the optimum to feed on resource 2 (in
between
θ1
and
θ2
in Fig.4A and B). At this point, the population experiences disruptive selection and undergoes
a diversication event. Aer diversication, the traits of the two resulting ecomorphs diverge. One of the
ecomorphs evolves towards the trait value that is optimal to feed on resource 1, whereas the other evolves towards
the trait value in between the optima to feed on resources 2 and 3. e rst ecomorph is now at a local maximum
Fig. 4. Example simulations of an asexual and a sexual lineage. (A) An asexual and (B) a sexual lineage
expands over the trait space through serial diversication events in which one population is split into two. (C)
In the asexual lineage, more mutations arise as a consequence of a larger population size. (D) During the trait
expansion, the rate at which novel phenotypes arise is higher in the sexual lineage. Ticks in the vertical axis in
A and B show the trait values corresponding to the optima to feed on food resources. Trait distribution shown
in A and B correspond to every 100 time steps in the simulation. Plots in C and D show the moving average
of number of individuals, mutations, and novel phenotypes calculated over a sliding window of 50 data points
(that is 5000 time steps, since there are 100 time steps between 2 data points). Total productivity is 3g/L*(unit
of time)−1 and the degree of specialization required to successfully attack a food resource, , is 1/4. Other
parameter values as in Tables S1 and S2.
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in the tness landscape; no further diversication can occur. e second ecomorph, in contrast, experiences
disruptive selection again, resulting in a new diversication event. is alternation between adaptation through
directional selection and diversication through disruptive selection is repeated until all preexisting resources
are fully utilized. As a result, both lineages have the same level of diversity (i.e. the lineages diversify into the
same number of ecomorphs as the number of existing niches). In the sexual lineage, assortative mating evolves
early during the trait expansion, maintaining a high level of reproductive isolation (0.98, corresponding to a 1%
probability of gene ow) between the emerging ecomorphs during the diversication process (Figure S4).
e simulations also reveal that diversication occurs much faster in the sexual lineage, opposite to what
we observed when natural selection acts in the absence of genetic mixing. e sexual lineage rapidly diversies
and lls up all available niches in less than half of the time that the asexual lineage takes to do so (Fig. 4B;
this faster expansion of a sexual lineage occurs independently of the functional response type for individual
food intake, see Figure S5A). e faster trait expansion of sexual lineages is mostly explained by the higher
rate at which novel phenotypes are generated (Fig.4D), which occurs despite fewer mutations taking place
due to the smaller population size (Fig.4C). In fact, when the emergence of novel phenotypes is not required
for the trait expansion because standing phenotypic variation is high, an asexual lineage can occupy available
niches faster than a sexual lineage (Figure S5B). As a consequence of the accelerated diversication process
in sexual lineages, an environment colonized by a sexual and an asexual lineage with the same history will
be dominated by phenotypic clusters with sexual reproduction due to the capacity of the sexual lineage to ll
up niches faster (Figure S6). In the face of disturbances, the faster niche occupancy enables a sexual lineage
to rapidly replace extinct ecologically specialized clusters with novel clusters emerging through diversication
(Figure S7). As a result, sexual lineages can readily recover their pre-disturbance diversity, or even increase it, by
further expanding over the trait space, occupying vacant niches le by extinct asexual ecomorphs.
e degree of specialization required to successfully feed on the food resources can aect the diversication
process and ensuing diversity in a sexual lineage. When this degree is high (
τ
is small, e.g., 1/4), trait expansion
and diversication occur simultaneously (Fig.4B). In contrast, when this degree is low (
τ
is large, e.g., 1/3), the
expansion over the trait space occurs rst, while diversication occurs much later (gure S8). A single sexual
population resembling a hybrid swarm rapidly expands over the trait space. Only aer all niches have been fully
utilized, discrete clusters emerge gradually (between time 500,000 and time 1,000,000 in gure S8B), some are
specialists (their mean trait is approximately equal to some optimum) and others are generalists (their mean trait
is approximately equal to the intermediate value between two optima). By the end of the simulation, the level of
reproductive isolation between these clusters is 0.9 (probability of gene ow is 5%). At the end of the simulation,
the lineage has a larger diversity due to the coexistence of specialists and generalists. Further analyses suggest
that this state in which specialists and generalists coexist is stable (see S17).
Fig. 5. e eect of genetic mixing on the trait expansion process. e expansion over the trait space occurs
faster in a sexual lineage with genetic mixing than in an asexual lineage, even when the level of genetic mixing
is low. Mean (black dots) and SD (black lines) in each violin plot correspond to 100 replicate simulations. Total
productivity is 0.5g/L*(unit of time)−1 and the degree of specialization required to successfully attack a food
resource, , is 1/3. Other parameter values as in Tables S1 and S2. Parameter values as in Tables S1 and S2.
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A small amount of genetic mixing is sucient to overturn the eect of natural selection
alone
To further assess the contribution of genetic mixing to the trait expansion and diversication process, we ran
individual-based simulations of the sexual lineage varying the level of genetic mixing. Without genetic mixing, a
sexual lineage takes a very long time to ll up available niches, almost double of the time that an asexual lineage
takes to do so (Fig.5). Because in the absence of genetic mixing, the main force driving evolution is natural
selection, this result supports our nding, from adaptive dynamics models, that natural selection alone promotes
faster diversication in asexually reproducing lineages. is shows that this result also holds when ecological
and evolutionary dynamics take place in the same timescale. Conversely, with a small amount of genetic mixing,
the time required for the sexual lineage to occupy all available niches is signicantly reduced. is reduction in
time required to ll in all available niches as a consequence of increasing genetic mixing behaves in a nonlinear
manner: small increases in male contribution to ospring’s genetic material have a larger impact when genetic
mixing is low (red violins at the le in Fig.5) than when it is high (violins at the right). Even relatively low genetic
mixing can speed up the trait expansion process in a sexual lineage to enable a faster niche occupancy than that
of an asexual lineage.
Discussion
Our results reveal that the reproductive mode substantially aects ecological diversication. We show that sexual
reproduction leads to faster diversication. Similarly, Melian et al.22 found that sexual reproduction increased
speciation rates in a neutral model. However, in that study, lineages with sexual reproduction had lower species
richness because extinction rates exceeded speciation rates. Our simulations show that sexual populations are
smaller than asexual populations (Fig.4C), which increases their extinction risk. However, the higher risk of
extinction can be balanced by a faster ecological diversication (Figure S7). erefore, our ndings provide
support for the emergence of more specious lineages associated to sexual reproduction. In line with these
ndings, a recent phylogenetic analysis showed that lineages with sexual reproduction have accelerated rates
of diversication (relative to asexual lineages), and that patterns of species richness are strongly related to these
dierences in diversication rates6. is statistically based analysis therefore supports our ndings that sexual
reproduction is associated with faster diversication and higher species richness.
Going a step further, we investigate how natural selection and genetic mixing inuence ecological
diversication in lineages with sexual and asexual reproduction. We nd diversication to occur in asexual
populations under less restrictive scenarios (SI3) and natural selection to be stronger during the diversication
process in asexual lineages (Fig.3, proof in SI5). Both ndings are the consequence of the paradox of sex
described by Maynard–Smith17,21; he acknowledged that sexual reproduction has an immediate cost relative to
asexual reproduction because sexual females invest half their reproductive resources into males that, in turn,
invest minimally into each ospring sired. Because asexuality is exactly twice as ecient at converting resources
into ospring, intraspecic competition is stronger in an asexual population. Competition drives natural
selection, therefore the twofold cost of sex due to male production translates into weaker selective pressures
in sexual populations that can hinder diversication, for example, when resource productivity is low, and slow
down the diversication process. We provide evidence that genetic mixing can overturn the eect of selection
alone, speeding up the trait expansion process in sexual lineages (Fig.4). Despite weaker selective pressures, trait
expansion is, therefore, faster in sexual than in asexual lineages because genetic mixing among sexual individuals
enables a faster emergence of novel phenotypes (this result is robust to variation in mutation rate and the number
of loci encoding the feeding niche trait, see Figure S9). is eect is complementary to the observations that sex
speeds adaptation by allowing natural selection to more eciently bring together mutations that confer a tness
advantage43–47.
An alternative scenario of diversication in a sexual lineage may occur in the absence of the cost of male
production. For instance, hermaphroditic species produce sperm and eggs in the same individual48. In this
case, all individuals can produce ospring, which will cause the strength of intraspecic competition and,
consequently, natural selection to be similar to the strength observed in asexual populations. However, because
genetic mixing occurs, strong natural selection results in an ever faster trait expansion process than in sexually
reproducing lineages with the cost of male production (Fig. S10). Yet, hermaphroditic species may incur other
costs of sex28,49 that may weaken natural selection, slowing down the diversication process. Future research
should investigate how other costs of sex aect ecological diversication in sexual and asexual lineages.
Our results show a strong nonlinear eect of genetic mixing. A small amount of genetic mixing in sexual
organisms is needed to accelerate the trait expansion of a lineage beyond the speed of an analogous lineage
of asexual organisms (Fig.5). Furthermore, increases in genetic mixing when its level is already high do not
have a signicant eect on the speed of the trait expansion. A similar nonlinear eect of genetic mixing has
been observed when organisms occasionally engage in sex, such as in species with facultative sex. In these
species, the evolutionary rate can be nearly as fast when the frequency of sex is low than when it occurs in every
reproductive event50–52. By reducing the frequency of sex and thus the rate of male production, these species
receive the benets of sex while paying a lower cost than the twofold cost of sex. In our model, sex is obligate and
females produce daughters and sons in equal proportion. An extension of our model implementing facultative
sex might increase the eciency at converting resources into ospring (relative to a population with obligate
sex). is could strengthen natural selection and thus speed up diversication. Hence, a lineage with facultative
sex could have a faster diversication rate than an obligate sexual lineage. eory has suggested that facultative
reproductive strategies should be more successful than obligate sexual or asexual strategies for adaptation
(microevolution)50–52. Our ndings suggest that this may be the case as well for diversication (macroevolution).
In the asexual lineage, we model reproduction through apomixis, i.e., ospring inherit the total maternal
genetic material without recombination. is reproductive system is common in many bacteria and fungi
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but also in some animals, such as aphids and snails53,54. ere are also organisms that reproduce asexually via
automixis, which involves meiosis and recombination without fertilization. In this case, genes are reshued
within an individual to produce ospring that may be genetically diverse28,55. Such a reproductive system is
present in several animal taxa, including arthropods, nematodes, mollusks, and vertebrates55. Despite the lack of
genetic mixing among individuals, automictic populations may have higher genetic variability than apomictic
populations but lower heterozygosity55. Hence, a lineage with automictic reproduction may diversify faster than
a lineage with apomictic reproduction if the trait expansion process does not hinge primarily on heterozygote
advantage, as is the case of our model with additive genetic trait architecture. Further research will be required
to determine whether and how much automixis can speed up diversication in an asexual lineage.
Similar to classic models of ecological diversication16,56, in our model, gene ow between phenotypically
divergent clusters of sexual organisms is reduced by the evolution of assortative mating based on the ecological
character, in our case, the feeding niche trait. ere is growing evidence of the existence of characters that inuence
both mating patterns and ecological tness in a variety of taxa, including plants, vertebrates, and invertebrates57.
erefore, assortative mating mechanisms like the one modeled here may be common, particularly when their
associated costs are low. Gene ow through assortative mating is, however, not completely halted in our model
(the probability of gene ow ranges between 1 and 5% depending on the degree of specialization required to
successfully feed on the food resources). Recurrent gene ow among ecologically diverse species is common in
the wild58, and according to recent research, it can play a major role in promoting diversication3.
Our ndings may shed light on the paradox of sex, oen stated as: why a larger number of eukaryotic
species reproduce sexually relative to those that reproduce asexually despite the costs of sex? Most research
addressing this problem has focused on identifying multiple mechanisms that enable the maintenance of sex
within populations18,51,59–77. However, dierences in diversication rate may also contribute to the relative
richness of species with each reproductive mode. Our results suggest that sexual reproduction may also be
widespread among species because it increased rates of diversication. Our results place the well-known long-
term benets of sex43–47 in a macroevolutionary context that can help explain broad diversity patterns associated
to each reproductive mode. Yet, future work is required to link them to the short-term benets of sex that
enable the sexual individuals to avoid being outcompeted by asexual ones. e integration of the well-known
mechanisms for the maintenance of sex within populations with ecological diversication might further explain
the widespread occurrence of sexual reproduction. We show how such integration can be done using models
that link macroevolutionary patterns to microevolutionary and ecological processes.
Data availability
No new data were collected and used for this study. e code implemented for this study will be available aer
acceptance in a zenodo repository, the accession number will be provided in the nal submission. For revision
purposes, we provide the code to the reviewers via the submission system in the le CodeModels.zip.
Received: 28 March 2024; Accepted: 28 November 2024
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Scientic Reports | (2024) 14:30369 12
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Acknowledgements
We thank Jukka Jukela, Hanna ten Brink and Hanna Kokko for valuable discussions and helpful comments on
an earlier version of this paper.
Author contributions
CCP conceived the idea. CCP and GR analyzed the model. CCP led the writing of the manuscript, and CM and
GR critically revised and contributed to later versions. All authors gave nal approval of the manuscript to be
published.
Declarations
Competing interests
e authors declare no competing interests.
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