community lifespan, niche expansion and the evolution of ... · 02/01/2020 · ecology, demography...

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Community lifespan, niche expansion and the evolution of interspecific cooperation

António M. M. Rodrigues1,2,*,§, Sylvie Estrela2,§, Sam P. Brown3,4

1. Department of Zoology, University of Cambridge, Downing Street, CB2 3EJ Cambridge, UK.

2. Department of Ecology & Evolutionary Biology, Yale University, New Haven, CT 06511,

USA.

3. School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA.

4. Center for Microbial Dynamics and Infection, Georgia Institute of Technology, Atlanta, GA,

USA.

* corresponding author, email: [email protected]

§ joint first authors

Article Type – Original Article.

Running Title – Demography and mutualism.

.CC-BY-NC-ND 4.0 International license(which was not certified by peer review) is the author/funder. It is made available under aThe copyright holder for this preprintthis version posted January 3, 2020. . https://doi.org/10.1101/2020.01.02.893321doi: bioRxiv preprint

https://doi.org/10.1101/2020.01.02.893321

http://creativecommons.org/licenses/by-nc-nd/4.0/

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Abstract – Natural selection favours individuals who maximise their own reproductive success

and that of their close relatives. From this perspective, cooperation that benefits individuals of a

different species represents an evolutionary conundrum. The theory of mutualism seeks to resolve

this puzzle, and it posits that there must be downstream benefits to cooperators that offset any

costs inherently associated with interspecific cooperation. Thus, individuals should only further

the survival and fecundity of their interspecific partners if this generates additional return

benefits, such as food, shelter or protection. A major challenge for the evolution of mutualism is

when the ecological niches of partner species overlap, as this creates a tension between the

benefits of exchanging services and the costs of competing for shared resources. Here we study

the extent to which niche expansion, in which cooperation augments the common pool of

resources, can resolve this problem. We find that niche expansion facilitates the evolution of

mutualism, especially when populations are at high densities. Further, we show that niche

expansion can promote the evolution of reproductive restraint, in which a focal species adaptively

sacrifices its own growth rate to increase the density of partner species. We interpret these results

in the context of microbial community interactions, which are often characterized by yield-

enhancing exchanges of nutrients, termed ‘cross-feeding’. Our findings suggest that yield-

enhancing mutualisms are more prevalent in stable habitats with a constant supply of resources,

where populations typically live at high densities, but such mutualisms are particularly vulnerable

to the emergence of cheats. In general, our findings highlight the need to integrate both temporal

and spatial dynamics in the analysis of mutualisms.

Keywords – demography, ecology, mutualism, cross-feeding, kin selection, spatial structure.


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Introduction

Multi-species communities are more than just an aggregate of individuals struggling for survival

in the face of antagonistic interactions. While competitive and exploitative interactions are most

common (e.g. Foster and Bell 2012), spectacular examples of interspecific mutualism enliven our

natural world (Leigh 2010). On the microbial scale, examples of costly investments in the growth

of a partner species have recently been described among microbes in the gut (Rakoff-Nahoum et

al. 2016) and among partner species engineered (Shou et al. 2007, Wintermute and Silver 2010,

Mee et al. 2014) and evolved in the lab (Harcombe 2010, Pande et al. 2014, Harcombe et al.

2018). These examples pose the question of whether costly microbial mutualisms are more

widespread and awaiting discovery. To approach this question, we ask what ecological conditions

are most likely to support these mutualistic investments?

Microbial cells release compounds into their environment that are then used by other members of

the community for survival and growth (McNally and Brown 2015, Estrela et al. 2019). In some

cases (termed cross-feeding or syntrophy), these exo-molecules are a waste product of an

individual’s metabolism that is advantageously co-opted by a partner species (Hillesland and

Stahl 2010, Estrela et al. 2012, LaSarre et al. 2017, Goldford et al. 2018), and as such, it comes at

no cost to the producer. More challenging for evolutionary theory is when the exchanged

compounds are not simple metabolic waste products but specifically designed costly secretions,

such as the secretion of nutrient-scavenging molecules (e.g. siderophores; D'Onofrio et al. 2010)

and digestive enzymes (e.g. glycoside hydrolase; Rakoff-Nahoum et al. 2016), or the production

of detoxifying enzymes (e.g. beta-lactamases; Yurtsev et al. 2016). In the majority of these cases,

the most parsimonious explanation is that the secreted factor serves to aid a conspecific (or even

the focal producer cell), posing little dilemma if the anticipated recipient likely carries a copy of

the gene coding for the trait. However, there are exceptions where the costly secreted factor

provides benefits that are targeted to another strain or species (Harcombe 2010, Pande et al. 2014,

Rakoff-Nahoum et al. 2016, Harcombe et al. 2018).

The interspecific exchange of costly secretions seems to be at odds with the Darwinian theory of

adaptation by natural selection, which posits that selfishness should be rife in the natural world


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(Hamilton 1964a, b, Price 1970). The resources that an individual could use for its own selfish

growth and survival are instead redirected to the production of exo-molecules that do not benefit

their producer directly. Therefore, the evolution of these costly traits requires special conditions

(Trivers 1971, Sachs et al. 2004, Foster and Wenseleers 2006, Leigh 2010). Mutualism theory

provides the primary framework for understanding the adaptive nature of interspecific costly

cooperation, where the general hypothesis is that the cost of interspecific cooperation must lead

to a return benefit to the cooperator that offsets a cooperator’s initial costly investment (Trivers

1971).

Mutualisms, however, can become unstable when cheats can reap the benefits of interspecific

cooperation without paying its costs. The stabilisation of mutualisms, therefore, requires the

existence of specific mechanisms such that the return benefits reward cooperators rather than free

riders. Three general stabilisation mechanisms have been proposed. First, partner fidelity occurs

whenever individuals form close-knit lifetime associations, and therefore any products of

cooperation are used up by partners, and not by selfish outsiders (Bull and Rice 1991, Sachs et al.

2004, Momeni et al. 2013). Second, partner choice enables cooperators to engage preferentially

with other cooperators and to ostracise free riders (Bull and Rice 1991, Simms and Taylor 2002,

Sachs et al. 2004, Regus et al. 2014). Finally, sanctions impose additional costs on cheats that

offset any of the benefits associated with cheating (West et al. 2002, Kiers et al. 2003, Jandér and

Herre 2010, Jandér et al. 2012, Regus et al. 2014).

Studies of microbial communities, however, have drawn attention to additional demographic

challenges in the understanding of the adaptive exchange of molecules that have not been the

focus of the general theory of mutualism (e.g. Foster and Bell 2012, Mitri and Foster 2013).

Microbial communities have complex life histories where exchanges of services or resources

occur while the community grows and depletes local resources, while it disperses and colonises

new patches, or while the community experiences environmental disturbances. This rich

ecological and demographic substrate provides the backdrop against which cooperative

exchanges unfold, mediating the fitness costs and benefits associated with cooperation, and

ultimately influencing the evolution of mutualism within microbial communities. For instance,

theory suggests that interspecific cooperation is more likely to evolve at intermediate densities


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when individuals can reap the benefit of interspecific cooperation while avoiding the costs of

interspecific competition (Bull and Harcombe 2009). This work, however, assumes a rate

mutualism in which interspecific partners exchange resources that only influence their growth

rates. Natural populations, by contrast, are often characterised by niche expansion in which

individuals profit from an enlarged resource pool created by their interspecific partners (Samuel

and Gordon 2006, Kolenbrander 2011, Ramsey et al. 2011, Goldford et al. 2018).

With a particular emphasis on cross-feeding interactions, here we study how different aspects of

ecology, demography and genetic structuring mediate the evolution of mutualistic interactions.

First, we focus on a rate mutualism and explore how the initial density of individuals, the lifespan

of communities, local competition and relatedness within species interact with each other to

mediate the evolution of mutualisms. Second, we extend our model to consider the possibility of

niche expansion where interspecific partners expand the common pool of resources locally

available. Specifically, we include cases in which niche expansion increases the local carrying

capacity, and we determine how this, in turn, mediates the evolution of mutualisms.

Model and Methodology

Eco-evolutionary dynamics

We assume a metapopulation where each patch is colonised by d0 individuals of the focal species

A, and by an equal number d0 of individuals of the partner species B. Interactions between the

two species influence their growth trajectories, which we model using standard logistic equations.

The intrinsic growth rate of species A is ϕA(z), where z is the amount of help a focal individual of

species A provides to individuals of species B. The intrinsic growth rate of the partner species B

is ϕB. Each individual of species A improves the growth rate of species B by an amount β(z).

Similarly, each individual of the partner species B improves the growth rate of the focal species A

by an amount α. There is density-dependent regulation in each patch, whose carrying capacity is

K. The population of our focal species is composed of a resident strain that expresses a phenotype

z, and of a mutant strain that expresses the phenotype x = z + δ, where δ is vanishingly small.

Thus, the mutant strain deviates only slightly from the resident strain in their level of investment


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in helping behaviours. The growth trajectories of each species, including the resident and mutant

strain of species A, is then given by

!̇ = $%& +((*),-((.),/

0-12 $1 − ,-,/-0

52 !, (1)

6̇ = $%7(8) +90

,-,/-12 $1 − ,-,/-0

52 6, and (2)

6̇: = $%7(;) +90

,-,/-12 $1 − ,-,/-0

52 6:, (3)

where: b is the density of the partner species B; a is the density of the resident strain of species A;

aH is the density of the mutant strain of species A; and < is a constant that mediates the growth

rates of each species. After the initial colonisation of a focal patch, each species grows during a

period of time τ, at which point there is competition for a new round of patch colonisation events.

Within each species, we assume that a proportion s of the competition occurs locally, while a

proportion 1 – s of the competition occurs globally, where s is the scale of competition (Frank

1998, Rodrigues and Gardner 2013). Individuals within each species compete for the d0 breeding

sites available to each species in each patch, and those who fail to obtain a breeding site die.

After this, the life-cycle of the community resumes (see Figure 1 for a schematic representation

of the life-cycle).

Fitness and stable strategies

We focus on helping that has a cost to the growth rate of individuals of species A and a benefit to

the growth rate of the partner species B. We assume that the growth rate ϕA(z) of species A is a

decreasing function of the investment in helping z. Thus, dϕA(z)/dz < 0. In addition, we assume

that the growth rate β(z) of species B is an increasing function of the investment in helping z.

Thus, dβ(z)/dz > 0 (see Figure S1 for a visual representation of the cost and benefit functions).

Our aim is to understand how much helping z should individuals of the focal species A allocate to

their partner species B. In other words, we want to determine the evolutionarily stable helping


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strategy z*, which is the strategy that cannot be beaten by an alternative strategy z* ± δ (Otto and

Day 2007).

To determine the stable strategy z* of a focal individual of our focal species A, we need to define

her reproductive success, which we denote by f(x,z), where the first argument x denotes the

helping strategy of the focal strain and the second argument z denotes the helping strategy of the

competing strain within the focal patch. We define the reproductive success of a focal individual

as the number of descendants she produces after one growth round after she first colonises a

patch, which is given by the final density of individuals in the local patch divided by the initial

density of individuals in the same focal patch. Thus, the reproductive success of a focal

individual that expresses the resident strategy is f(z,x) = a(τ)/(d0(1-p)), whilst the reproductive

success of a focal individual that expresses the alternative strategy is f(x,z) = aH(τ)/(d0p), where p

is the fraction of species A colonisers that are mutant individuals. A fraction s of the competition

is local, in which case the focal individual competes with both clones of herself and wild-type

individuals. The other fraction 1 – s of the competition is global, in which case the focal

individual competes with wild-type individuals only. Thus, the fitness of a focal individual

expressing the alternative strategy x = z + δ is given by

>(;, 8) = @(.,*)ABC@(.,*)-(DEC)@(*,.)F-(DEA)@(*,*)

. (4)

Note that the probability p is also the kin selection coefficient of relatedness r among individuals

of species A within the focal patch (i.e. r = p; Bulmer 1994). The coefficient of relatedness gives

the probability that an intraspecific social partner within a patch carries an identical allele relative

to the population average.

We assume that the alternative helping strategy has a vanishingly small phenotypic effect, and

therefore the selection gradient, denoted by S, is given by the slope of fitness on the phenotype

(Otto and Day 2007). Thus, we have

G(;, 8) = HI(.,*)H.

J.K*

. (5)


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An evolutionarily stable helping strategy z* is found when the selection gradient is null. That is,

when there is neither selection for slightly more investment in helping nor selection for slightly

less investment in helping, and therefore S(z*,z*) = 0 (Otto and Day 2007).

Analysis and Results

Here we study how the different genetic and demographic factors affect the optimal investment

into helping behaviour.

Community lifespan -- Let us focus on how the lifespan of the community, as given by τ,

influences optimal investment in helping effort. Consistent with earlier work (Bull and Harcombe

2009), we find that mutualism is favoured at intermediate values of the community lifespan,

while disfavoured when dispersal is early or late in the cycle of ecological development (Figure

2A). Interspecific cooperation slows down the initial growth rate of cooperators, and therefore, if

dispersal occurs at this early stage (i.e. during the early exponential phase of bacterial growth),

cooperation is not favoured by selection. On the other hand, interspecific competition is stronger

at high densities when resources are scarce (i.e. during the stationary phase), and therefore

cooperation is not favoured either when dispersal occurs at later stages of ecological

development. This effect arises because the carrying capacity is fixed, and therefore as we

approach the stationary phase the interaction between the two species becomes a zero-sum game.

Any increase in the density of one species necessarily leads to a decrease in the density of the

partner species. At intermediate community lifespans (i.e. during the exponential phase),

interspecific cooperation is highest because sufficient time has elapsed for cooperators to recover

from their initial slow growth and because interspecific competition is still weak. However, we

find that competition imposed by intraspecific cheats (low r) is an important factor mediating this

“window of opportunity” for interspecific cooperation, which can be drastically reduced when

relatedness falls below 0.5 (Figure 2A).

Abundance of colonisers -- Let us now study the impact of the initial number d0 of colonisers on

the evolution of cooperation. We find that cooperation is disfavoured as the initial number of


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colonisers increases (Figure 2B). As the initial density of colonisers increases, the amount of

competition for local resources also increases. Therefore, even during the early growth stages,

individuals are already suffering from intense competition for resources, which undermines the

evolution of cooperation. As in the previous section, we find that intraspecific cheats have a

strong impact on the evolution of interspecific cooperation, which can rapidly drop from full

helping (i.e. z* = 1) to no helping (i.e. z* = 0) as soon as relatedness falls below 0.5.

Scale of local competition -- We now turn the attention to the impact of local competition on the

evolution of cooperation. We find that as competition becomes more local (higher s), cooperation

is less likely to evolve (Figure 2C). Moreover, under intense local competition, cooperation

requires longer growth periods to evolve. Local competition, however, exerts less influence on

the optimal cooperative strategies when the dispersal stage occurs at high densities (higher τ).

This is because growth that occurs later in a community’s lifespan is strongly regulated by the

availability of local resources (i.e. density-dependent local regulation), and therefore regulation

of the population exerted through local competition becomes less important.

Mutualism and Niche Expansion

So far, we have assumed a rate mutualism in which there is a growth rate cost for helpers, and a

growth rate return benefit. This mirrors cases, for instance, of detoxification mutualisms where

microbial species protect each other from antibiotics through the production of resistance

enzymes that break down the antibiotics (e.g. beta-lactamases; Yurtsev et al. 2016). In many

other cases, microbes secrete or excrete products that can lead to the expansion of the resource

pool by providing access to novel substrates (see Figure 1B). Niche expansion can take various

forms, including: the production of metabolic waste by one species that opens a new niche for a

cross-feeding species (incidental cross-feeding; Hillesland and Stahl 2010, Estrela et al. 2012,

LaSarre et al. 2017, Goldford et al. 2018); the secretion of exomolecules that enhance nutrient

supply (e.g. extracellular enzymes and scavenging molecules; (e.g. D'Onofrio et al. 2010, Flint et

al. 2012, Rakoff-Nahoum et al. 2016); or the killing of competitors that opens up space for

growth and access to new resources (Yanni et al. 2019). Detoxification of environmental toxins


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can also lead to niche expansion, but it will often relieve growth inhibition as well. Here, we ask

what is the role of niche expansion on the evolution of cooperation?

To study this scenario, we extend our base model to include a unidirectional cross-feeding

relationship, impacting the yield of the community (see Figure 1B). Specifically, we now assume

that the carrying capacity of the community is K = Ki + KB, where Ki is the intrinsic carrying

capacity, and where KB is the component of the carrying capacity that depends on the density of

the partner species B. This is given by

L& = MLN0

O-0, (6)

where e is a carrying capacity elasticity factor due to the presence of the partner species B, and k

is a constant that determines how the carrying capacity increases with the density of the partner

species (e.g. Frank 2010). If we set elasticity to zero (i.e. e = 0), we recover the base model, in

which we have a rate mutualism with no niche expansion (i.e. K = KI, see Figure 3A and

equations (1)-(3)).

In the absence of elasticity (i.e. e = 0), an increase in density of the partner species has a

corresponding increase in the competition for resources to the focal cooperator and her relatives.

Under this scenario, the additional competition for local resources generated by the partner

species precludes the evolution of cooperation at high densities, as we have described above. If

the elasticity e is sufficiently high, however, the partner species provides additional resources that

expand the carrying capacity of the local patch. As a result, an increase in the density of the

partner species need not lead to an increase in the competition for the local resources. Under this

scenario, the additional resources provided by the partner species B offset the additional

competition for resources, and therefore cooperation is favoured at high densities, as shown in

Figure 3B (see also Figure 4, top row).

So far, we have considered a scenario in which interspecific interactions influence the rate and

the carrying capacity of each species simultaneously (i.e. α > 0, β0 > 0 and e > 0). As a result, we

are unable to precisely gauge what are the forces driving the evolution of the mutualism. To


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investigate this, we now consider a simpler scenario in which interspecific interactions do not

affect the growth rate of both the focal and the partner species (i.e. α = 0, β0 = 0), but the partner

species still promotes niche expansion via the production of additional resources (L&). Under this

scenario, we ask under what conditions natural selection favours the evolution of cooperation in

the focal species. As shown in Figure 4 (bottom row), while cooperation does not evolve at

intermediate densities, it does evolve at high densities. Unlike the previous scenario, here

cooperation from the focal species A does not involve the secretion of any exo-products. Instead,

cooperation takes the form of reproductive restraint in which individuals of the focal species A

are selected to consume resources (replicate) more slowly (e.g. Kerr et al. 2006) to promote the

growth of the partner species B. Slow growth has an initial cost for the focal species. However,

this initial cost is offset by the niche expansion that occurs later on in the community lifecycle

due to the additional individuals of the partner species B.

The evolution of reproductive restraint depends on the relative growth rate of the two interacting

species (Figure 4). This growth-rate dependent outcome occurs because reproductive restraint has

two contrasting effects on the fitness of the focal species. On the one hand, reproductive restraint

has a fitness cost for the focal species because they are in direct competition with the partner

species for limiting resources. On the other hand, reproductive restraint has a positive fitness

effect for the focal species because it increases the abundance of the partner species, which also

increases the carrying capacity of the local patch. When the baseline growth rate of the focal

species is too small, the costs of reproductive restraint offset its benefits, and therefore,

reproductive restraint does not evolve. If the baseline growth rate of the focal species is too high,

the fast-growing focal species suppresses the growth rate of the partner species, which suppresses

the benefits of cooperation at later ages of the community lifespan, and reproductive restraint is

less favoured (Figure 4, bottom row).

We now consider a scenario in which in addition to the partner species leading to niche

expansion, the focal species boosts the growth rate of the partner species (i.e. α = 0, β0 = 0.01).

Do we still observe the evolution of interspecific cooperation? Under such scenario, we find that

cooperation is less likely to evolve (Figure 4, third row). The cooperative behaviour of the focal

species reduces its own growth (restraint), but it also increases the growth of the partner species.


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As a result, the additional growth rate of the partner species imposes an additional cost on the

focal species. Overall, the benefits from niche expansion are not sufficient to offset the direct cost

of cooperation arising from consuming common resources more slowly and the indirect cost of

cooperation that arise from the additional competition imposed by the partner species.

Finally, let us now consider a scenario in which, in addition to niche expansion, the partner

species also provides a growth rate benefit to the focal species (i.e. α = 0.01, β0 = 0). As shown in

figure 4 (second row), we find that the focal species evolves reproductive restraint at high

densities, but not at intermediate or low densities. Here restraint increases the density of the

partner species, which in turn benefits the growth rate of the focal species, and also, the yield

when at high densities owing to niche expansion by the partner species.

Mutualism and Niche Overlap

So far, we have assumed that both species, A and B, compete for the same resources (represented

by the common carrying capacity K). However, in many cases the degree to which niches of

different species overlap varies. While in some cases species fiercely compete for common

resources, i.e. complete niche overlap, in others they compete for some but not all resources, i.e.

partial niche overlap, and yet in others they compete for very different resources, i.e. non-

overlapping niches. We therefore extended our model to study the effect of niche overlap

between species A and B on the evolution of mutualism. The degree to which species A and B

compete for resources – degree of niche overlap – is modelled by an interspecific competition

coefficient, denoted by γ, which varies from 1, i.e. complete niche overlap, to 0, i.e. non-

overlapping niches. This coefficient affects the density-dependent terms in equations (1-3), such

that they become: (1 – (γ(a + aH) + b) / K) in equation (1), which describes the growth trajectory

of species B; and (1 – ((a + aH) + γb) / K), in equations (2) and (3), which describes the growth

trajectories of species A. When there is complete niche overlap (γ = 1), we recover our initial

model. However, when niches do not overlap (γ = 0), the density-dependent term of species B

becomes 1 – b/K, and the density-dependent term of species A becomes 1 – (a + aH) / K.


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Given niche expansion by the partner species (KB > 0), relaxing competition for resources

between the focal and partner species disfavours the evolution of reproductive restraint, and

therefore yield-enhancing mutualisms are less likely to evolve (Figure 5 and Figure S2).

Moreover, in such cases, mutualism with dispersal at later stages of community growth is no

longer favoured when the degree of interspecific competition falls below 0.5 (Figure S2). This

negative effect of lower interspecific competition on mutualism is especially pronounced in cases

where the rate mutualism is turned-off (Figure S2, bottom row). Without niche expansion,

cooperation at high densities is disfavoured regardless of the niche overlap (Figure 5). This

suggests that interspecific cooperation in the form of reproductive restraint can only evolve when

there is both a high degree of niche overlap and niche expansion.

Discussion

In mutualistic interactions, individuals receive a benefit from their interspecific partners. In such

cases, individuals should care for the survival and growth of their interspecific partners to the

extent that this is associated with a higher probability of receiving the return benefit. In many

cases, however, there is at least some degree of niche overlap between species, which may lead to

interspecific competition for shared limiting resources, which, in turn, may have an adverse

impact on the evolution of mutualisms. Previous theory seeking to understand this problem has

shown that interspecific cooperation is more likely to evolve at intermediate densities (Bull and

Harcombe 2009). This outcome arises because at intermediate densities the return benefits from

interspecific cooperation are sufficiently high to outweigh the initial costs of cooperation and

because the intensity of density-dependent competition for resources is still comparatively low.

The conclusion that mutualism evolves at intermediate densities relies on the assumption of a rate

mutualism, in which individuals exchange resources that influence their growth rates.

Mutualisms among microbes, by contrast, are commonly yield-enhancing (Samuel and Gordon

2006, Kolenbrander 2011, Ramsey et al. 2011). We have shown that in such cases interspecific

cooperation can evolve even at high population densities, a condition that may be prevalent in

natural microbial populations (e.g. Rakoff-Nahoum et al. 2016). In line with our findings,

Rakoff-Nahoum et al. (2016) recently provided evidence of costly interspecific cooperation


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between Bacteroidales species that live at high densities in the human intestine. Specifically,

Bacteroides ovatus secretes digestive enzymes that break down inulin, the products of which are

then used by Bacteroides vulgatus, which, in turn, improves the fitness of B. ovatus. This study

provides a rare example of a costly yield mutualism in a natural ecosystem. Evidence for costly

mutualism between microbial species in a natural setting is still scarce, in part due to the

difficulty of measuring the costs and benefits associated with a specific trait in complex

environments such as the gut microbiota. Our study, however, suggests that rather than an

exception, costly yield mutualisms may be a prevalent form of cooperative exchanges in the

microbial world.

Understanding the nature of the costs and benefits accrued to individuals involved in interspecific

exchanges is crucial for explaining the diversity and stability of mutualisms in microbial

communities (e.g. Harcombe 2010, Rakoff-Nahoum et al. 2016, Harcombe et al. 2018). In rate

mutualisms, the return benefits materialise quicker than in yield mutualisms, and so rate

mutualisms are favoured at early stages of community growth (i.e. exponential phase of bacterial

growth) while yield mutualisms are favoured at later growth stages (i.e. late-exponential and

stationary phase). Given this difference in the rate of return of benefits, it is tempting to speculate

that environmental conditions can predict the type of mutualism that is more likely to evolve in a

given habitat. In general, we hypothesise that natural selection favours rate mutualisms in more

variable and transient environments so that individuals maximise the exploitation of the available

nutritional niches and minimise nutritional losses (e.g. due to resource washout). In contrast, in

more stable and durable environments, natural selection should favour yield-enhancing

mutualisms.

The evolution of interspecific cooperation also depends on the number of individuals who

colonise a patch. If the density of colonisers is initially high, then there is intense competition for

resources right from the beginning of colonisation, which narrows the window of opportunity

within which cooperation evolves. Mixed genotypes in a patch, either due to mixed patch

colonisation or due to mutations, may also disrupt cooperation, which may occur due to two

processes. Firstly, collective action at an early stage of the demographic dynamics is required to

produce enough benefits at intermediate stages, which can only happen if there is a sufficiently


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high number of cooperators during the early stages of community growth. Secondly, the benefits

provided by the partner species at intermediate densities come in the form of public goods, and

therefore all individuals of the focal species, both cooperators and cheats, benefit equally from

the help provided by the partner species. As a result, high relatedness within the focal species

ensures that the benefits of cooperation are directed towards cooperators, which prevents free-

riders from exploiting the products of cooperation.

We find that the evolution of cooperation in the form of reproductive restraint in the focal species

depends on the relative intrinsic growth rate of the two partner species. Reproductive restraint can

evolve if the intrinsic growth rate of the focal species is high enough so that its own growth is not

suppressed by the growth of its partner species at early stages of community development, but

also not too high so that the focal species does not suppress the growth of its partner species, and

consequently the benefits of cooperation that are accrued at later ages of the community lifespan.

Broadly related to this idea, it has been shown that both growth rate differences between species

and competition for a shared resource can affect the stability of cross-feeding interactions

(Hammarlund et al. 2019). Starting with a bidirectional obligate cross-feeding mutualism

between two species, Hammarlund et al. (2019) showed that when one partner becomes

independent, coexistence can only be maintained when the obligate partner is the faster growing

species but breaks down when the obligate partner is the slower grower. In our model,

interspecific cooperation evolves between two species that can grow independently. It would be

interesting to investigate whether restraint is more or less likely to evolve in systems where the

partner species depends on the focal species for growth.

Our findings, so far, assumed that the focal and partner species compete for the same limiting

resources, which is consistent with the idea of strong niche overlap. What happens if now they

compete less, or not at all, for the same resources – that is, if there is low or no niche overlap?

Previous work has suggested that low niche overlap and high relatedness can favour cooperation

between species (Mitri and Foster 2013). Here we find that interspecific cooperation, in the form

of reproductive restraint, is only favoured when interspecific competition is high, but not when

interspecific competition is low. In other words, interspecific competition selects for interspecific

cooperation. This effect occurs because without a shared limiting resource, the incentives for


https://doi.org/10.1101/2020.01.02.893321


16

reproductive restraint are eliminated. Indeed, prudence in resource consumption no longer

promotes the growth of the partner species and its associated yield-enhancing benefits, but it still

carries the costs associated with intraspecific cheats. We would expect, however, low niche

overlap to favour other forms of interspecific cooperation that directly impact the yield of partner

species.

We have assumed that cooperation is constitutively expressed. Under this scenario, rate

mutualisms are favoured at intermediate densities whilst yield mutualisms are favoured at high

densities. These contrasting selective pressures raise the hypothesis that natural selection favours

the density-dependent regulation of these cooperative traits. It is now well understood that

intraspecific microbial cooperation is commonly regulated in a density-dependent manner

(Xavier et al. 2011, Darch et al. 2012, Ghoul et al. 2016), often controlled by cell-cell signalling

mechanisms termed quorum sensing (Whiteley et al. 2017). Quorum sensing limits the

expression of multiple social traits to high-density environments, and limits the extent of

intraspecific social cheating by positive-feedback control of cooperative behaviour (Allen et al.

2016). Our results suggest that interspecific cooperation may also be regulated in a manner that

depends on total community density- for instance, through a mechanism akin to the interspecific

quorum sensing molecule, the autoinducer AI2, that allows bacteria to determine their overall

population density and regulate their behaviour accordingly (Xavier and Bassler 2005).

Specifically, we predict that rate-enhancing traits are more likely to be up-regulated during earlier

growth phases (low densities) but down-regulated during later growth phases (high density). By

contrast, we predict that yield-enhancing traits are down-regulated during earlier growth phases

but up-regulated during later growth phases and the stationary phase.

In this paper, we have not considered the co-evolutionary process between the two species and

we have assumed that the partner species remains in its ancestral form and expresses a constant

level of helping. Helping in the partner species is, however, also a trait under the action of natural

selection, and allowing for the coevolution of helping between the two species may have

important consequences for optimal levels of investment in cooperation (West et al. 2002).

Moreover, we have also assumed that the partner species is not able to discriminate between

cooperators and cheats in the focal species (Allen et al. 2016). For example, in the rhizobia-


https://doi.org/10.1101/2020.01.02.893321


17

legume symbiosis, the plant is able to punish bacterial groups that do not help, and this

mechanism has been shown to stabilise cooperation in this system (West et al. 2002). Also, here

we assume that the focal and partner species are both autonomous – the most likely starting point

of mutualisms. The production of costly leaky goods or services can, however, select for the

evolution of one-way metabolic dependencies to save on metabolic costs (Morris et al. 2012) and

ultimately interdependencies where microbes engage in the exchange of essential traits (Estrela et

al. 2016). Extending our model in these multiple directions provides an interesting avenue for

future studies.

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Figures

Figure 1. Model of the community lifecycle and interactions between species. We assume a

metapopulation model where each patch is colonized by d0 individuals of the focal species A and

of partner species B. Within each patch, species interact and grow until they disperse to a new

empty patch. The carrying capacity of the patch is K. Two mutualistic interaction scenarios are

illustrated: (A) a case of rate mutualism where the focal species A pays a cost on its own intrinsic

growth rate (ϕA(z)) to enhance the growth rate of its partner species B by β(z), and in return, gets

a growth rate benefit α from B. This is defined as a rate mutualism because interspecific

cooperation causes the two species to grow faster at intermediate stages of community

development (here KB = 0); (B) a case of yield mutualism in the form of reproductive restraint in

the focal species A and niche expansion by B. Here the focal species A grows more slowly, which

promotes the growth of the partner species B, and consequently increases the carrying capacity of

the local patch by KB (here α = β0 = 0). This is defined as a yield mutualism because interspecific

cooperation causes both species to reach a higher equilibrium density.

patch colonization initial abundance, d0

patch growth community lifespan, !

rate mutualism no niche expansion, KB = 0

yield mutualism with niche expansion, KB > 0

α

β(z)

ɸA(z) ɸBK+KB

dens

ity

� community lifespan, !

community lifespan, !

dens

ity

AB

Figure 1

ɸA(z) ɸBK+KB

patch colonization initial abundance, d0

patch growth community lifespan, !

focal species Apartner species B

expansion of K by species B

A

B

nutrients detox killing competitors

no helping (z = 0)

AB with helping (z > 0)

}

}

mutualism favoured

mutualism favoured

��

��

��

��


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22

Figure 2. Rate mutualisms are favoured at high levels of relatedness and when dispersal occurs at intermediate values of community lifespan. (A) The optimal investment in helping

(z*) as a function of community lifespan (τ) and relatedness (r). (B) The optimal investment in

helping (z*) as a function of the initial density of bacteria (d0) and relatedness (r). (C) The

optimal investment in helping (z*) as a function of the intensity of local competition (s) and

community lifespan (τ). Parameter values: ϕA,0 = 0.012, ϕB = 0.011, α = 0.01, e = 10-4, K = 1, and

(A) s = 0.5 and d0 = 0.01, (B) t = 100 and s = 0.5, (C) r = 0.5 and d0 = 0.01.

Figure 3. Niche expansion facilitates the evolution of mutualism at high densities. (A)

Carrying capacity as a function of the partner species B density for various levels of elasticity (e).

(B) Higher elasticity increases the window of opportunity within which cooperation is favoured

by natural selection (see Figure 2A for the no elasticity baseline scenario), and may even favour

cooperation at high densities. Parameter values: ϕA,0 = 0.012, ϕB = 0.011, e = 10-4, s = 0.5, k = 5,

α = 0.01, d0 = 0.01, and Ki = 1.

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

community lifespan, τ

relatedness,r

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

initial density, d0 (×10-1)

relatedness,r

1 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


scaleofcompetition,s

A B C

helping, z*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

K

rate mutualism

Figure 2

A B

e = 0

e = 10

0 2 4 6 8 1.00

2

4

6

8

10

species B density (b, ×103)

carryingcapacity

(K,×10

3 )

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

A B helping, z*

0.10.20.30.40.50.60.70.80.9

Figure 3

K+KB

rate + yield mutualism

A B


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23

Figure 4. Rate mutualisms increase the range of parameters under which mutualisms can evolve. Optimal investment in helping (z*) as a function of community lifespan (τ) for various

values of baseline growth rate (ϕA,0) and rate of benefits (α and β0) in the presence of niche

expansion. When there are cross-benefits (first row; α = 0.01, β0 = 0.01) mutualism evolves at

intermediate and high densities. When there are return benefits (second row; α = 0.01, β0 = 0)

mutualism evolves when communities are long-lived and is favoured by lower baseline growth

rate of the focal species. When only the partner species enjoys a rate benefit (third row; α = 0, β0

= 0.01), interspecies cooperation becomes unstable, and only evolves when the baseline growth

rate of the focal species A is sufficiently high. In the absence of rate benefits (fourth row; α = 0,

β0 = 0), cooperation in the form of reproductive restraint evolves at high densities only, and is

highest at intermediate value of baseline growth rate. Parameter values: ϕB = 0.011, e = 10-4, s =

0.5, k = 5, d0 = 0.01, and Ki = 1.


rela

tedn

ess,

r

baseline growth rate of focal species A, ɸA,0

0.020 0.010

Figure 3.

Figure 4.

e = 0

e = 10

0 2 4 6 8 1.00

2

4

6

8

10


carryingcapacity

(K,×10

3 )

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

A B helping, z*

0.10.20.30.40.50.60.70.80.9

!A = 0.020 !A = 0.018 !A = 0.016 !A = 0.014 !A = 0.012 !A = 0.010

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

cummunity lifespan, �

relatedness,r

�A = 0.20 �A = 0.18 �A=0.16�A = 0.14 �A = 0.12 �A = 0.10

�=0.00

�=0.00

�=0.01

�=0.01

�=0.00

�=0.01

�=0.00

�=0.01

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

community lifespan, �

relatedness,r

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

1 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0



A B C

helping, z*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.018 0.016 0.014 0.0121.0

0.61.0

0.61.0

0.61.0

0.61 4000 1 4000 1 4000 1 4000 1 4000 1 4000

Figure 4

K+KBA B

K+KBA B

K+KBA B

K+KBA B


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24

Figure 5. Non-overlapping niches disfavour the evolution of mutualism by reproductive restraint. Yield-enhancing mutualisms are sustained by reproductive restraint, which is only

favoured under high degree of niche overlap. Rate-enhancing mutualisms, however, evolve

regardless of the degree of niche overlap. Parameter values: α = 0.01, β0 = 0.01, ϕA,0 = 0.014, ϕB

= 0.011, e = 10-4, s = 0.5, k = 5, d0 = 0.01, and Ki = 1.

Figure 5

complete niche overlap

no niche overlap

no niche expansion(KB = 0)

with niche expansion(KB > 0)

Figure 3.

Figure 4.

e = 0

e = 10

0 2 4 6 8 1.00

2

4

6

8

10

species B density (b, ×103)carryingcapacity

(K,×10

3 )0 100 200 300 400

0.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

A B helping, z*

0.10.20.30.40.50.60.70.80.9

!A = 0.020 !A = 0.018 !A = 0.016 !A = 0.014 !A = 0.012 !A = 0.010

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0


relatedness,r

�A = 0.20 �A = 0.18 �A=0.16�A = 0.14 �A = 0.12 �A = 0.10

�=0.00

�=0.00

�=0.01

�=0.01

�=0.00

�=0.01

�=0.00

�=0.01

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

1 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0



A B C

helping, z*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9


rela

tedn

ess,

r

1.0

0.6

1.0

0.61 4000 1 4000

K+KBA B K+KBA B


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25

Supplementary Figures

Figure S1. (A) Growth rate cost for the focal species as a function of their investment in helping

(z). We assume ϕA(z) = ϕA,0 – φAz. (B) Growth rate benefit enjoyed by the partner species B as a

function of the investment in helping (z) by species A. We assume β(z) = β0z. Parameter values:

ϕA,0 = 0.012, φA = 0.001, β0 = 0.01.

A

0.0 0.2 0.4 0.6 0.8 1.08.0

8.2

8.4

8.6

8.8

9.0

helping, z

growthcostspeciesA(×10

-3) B

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

helping, z

growthbenefitspeciesB(×10

-2)


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Figure S2. Low niche overlap disfavours the evolution of mutualism by reproductive restraint. When there are rate-enhancing cross-benefits (first row; α = 0.01, β0 = 0.01), little

niche overlap (lower γ) selects against mutualism in long-lived communities but does not select

against mutualism in short- and intermediate-lived communities. In the absence of rate benefits

(second row; α = 0, β0 = 0), little niche overlap (lower γ) selects against mutualism in the form of

reproductive restraint. Parameter values: ϕA,0 = 0.014, ϕB = 0.011, e = 10-4, s = 0.5, k = 5, d0 =

0.01, and Ki = 1.

A B

A B

1.00 0.000.75 0.50 0.25

degree of niche overlap, "


rela

tedn

ess,

r

1.0

0.6

1 4000 1 4000 1 4000 1 4000 1 4000

1.0

0.6

Figure S2

Figure 3.

Figure 4.

e = 0

e = 10

0 2 4 6 8 1.00

2

4

6

8

10


carryingcapacity

(K,×10

3 )

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

A B helping, z*

0.10.20.30.40.50.60.70.80.9

!A = 0.020 !A = 0.018 !A = 0.016 !A = 0.014 !A = 0.012 !A = 0.010

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0

1 40000.6

1.0


relatedness,r

�A = 0.20 �A = 0.18 �A=0.16�A = 0.14 �A = 0.12 �A = 0.10

�=0.00

�=0.00

�=0.01

�=0.01

�=0.00

�=0.01

�=0.00

�=0.01

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0


relatedness,r

1 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0



A B C

helping, z*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

K+KB

K+KB


https://doi.org/10.1101/2020.01.02.893321


community lifespan, niche expansion and the evolution of ... · 02/01/2020 · ecology, demography...

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