Obligate symbiosis evolved from free-living individuals most likely via the intermediate stage of facultative symbiosis. However, why should facultative symbionts, who can live independently but also benefit from their partners if these are available, give up this best of both worlds? Using the adaptive dynamics approach, we analyse a simple model, focusing on one partner of the symbiosis, to gain more insight into the selective forces that make individuals forgo the ability to reproduce in the free-living state. Our results suggest that, similar to the parasitism-mutualism continuum, the free-living way of life and obligate symbiosis are two extremes of a continuum of the ability to reproduce independently of a partner. More importantly, facultative symbiosis should be the rule as for many parameter combinations completely giving up independent reproduction or adopting a pure free-living strategy is not so easy. We also show that if host encounter comes at a cost, individuals that put more effort into increasing the chances to meet with their partners are more likely to give up the ability to reproduce independently. Finally, our model does not specify the ecological interactions between hosts and symbionts but we discuss briefly how the ecological nature of an interaction can influence the transition from facultative to obligate symbiosis.
Obligate symbiosis evolved from free-living individuals most likely via the intermediate stage of facultative symbiosis. However, why should facultative symbionts, who can live independently but also benefit from their partners if these are available, give up this best of both worlds? Using the adaptive dynamics approach, we analyse a simple model, focusing on one partner of the symbiosis, to gain more insight into the selective forces that make individuals forgo the ability to reproduce in the free-living state. Our results suggest that, similar to the parasitism-mutualism continuum, the free-living way of life and obligate symbiosis are two extremes of a continuum of the ability to reproduce independently of a partner. More importantly, facultative symbiosis should be the rule as for many parameter combinations completely giving up independent reproduction or adopting a pure free-living strategy is not so easy. We also show that if host encounter comes at a cost, individuals that put more effort into increasing the chances to meet with their partners are more likely to give up the ability to reproduce independently. Finally, our model does not specify the ecological interactions between hosts and symbionts but we discuss briefly how the ecological nature of an interaction can influence the transition from facultative to obligate symbiosis.
Many ecological interactions involve prolonged and intimate contact between two or more individuals, a phenomenon called symbiosis that may involve both mutualism and parasitism [1]. Since symbiosis was identified as a potential for evolutionary innovation [2-6], the conditions that favour it and its subsequent evolutionary outcomes have received much attention. Studies include the evolution of organelles from symbiotic relationships [7, 8], the maintenance of mutualism [9-14], the evolution of virulence [8, 15–20], and the transition along the parasitism-mutualism continuum (theoretical work: [21-25], empirical work: [26-29]).The interaction in symbiosis, whether it is parasitism or mutualism, is conventionally classified as obligate or facultative. Obligate symbiosis suggests that at least one of the partners cannot complete its lifecycle on its own while facultative symbiosis suggests that partners do not necessarily require one another to survive and/or reproduce. Moreover, this need for association may be asymmetric for the partners, that is, one partner may need the other but not necessarily vice versa, for instance, parasites may need hosts to complete their lifecycles but hosts definitely do better on their own. In mutualistic relationships, the assignment of ‘host’ and ‘symbiont’ is often arbitrary; and in many cases, the roles of host and symbiont are interchangeable. It is therefore important to specify which partner in an association the facultative and obligate relationship is referred to. In this article, we focus on the evolution of the dependency of only one partner, the symbiont, on the other partner, the host.Obligate symbionts have to evolve from free-living individuals, regardless of whether they are parasites or mutualists, because if there were no free-living individuals to begin with, there would be no ingredients for associations. If this process occurs due to, for instance, an event of engulfment of the symbiont by the host, followed by purely vertical transmissions of the symbionts to maintain the population then obligate symbionts may evolve directly from free-living organisms. However, many symbionts have to experience external environment before encountering new hosts, and facultative symbiosis is much likely an intermediate step leading toward obligate symbiosis. From an adaptationist point of view, the evolutionary transition to obligate symbiosis presents an evolutionary riddle since a facultative symbiont always has the option to live autonomously without a host, so why give that up?Indeed, facultative symbioses persist in many cases: among the parasites, for instance, Cholera pathogens, causing widespread epidemics, maintain a capacity for independent reproduction [30]. And among the more mutualistic interactions, many soil organisms that engage in cooperative interactions with plants can reproduce independently of their plant partners [31]. However, many times in evolutionary history, lineages have given up the capacity of independent reproduction, at least in nature [32]. The question of whether a given symbiont is obligate thus boils down to whether they are able to reproduce on their own, in absence of any potential host. This forces us to take the entire lifecycle of the species into account, which often is outside of the knowledge accessible by experiments. Our work, therefore, will be useful for both future theoretical and experimental studies.The question of why facultative symbiosis can become obligate is similar to why generalists may give up the ability to exploit some resources and become specialists, but there are subtle differences too. Rueffler et al. [33] showed that evolutionary consequences changed when density dependence and different evolving life-history traits were taken into account. In generalist-specialist models, very often the ecological dynamics of the two resources are simple and their interactions with the consumer are symmetric. Thus, the trade-off often assumes a single trait that affects consumption such that consumption efficiency of one resource directly affects consumption efficiency of the other because the trait has equivalent performances in the two resources. For instance, big beaks are more efficient in cracking big seeds and small beaks are more sophisticated to open small seeds but birds have but one beak.In contrast, host-symbiont interactions and external resource-symbiont interactions are typically asymmetric, hence, a trait that contributes to the former may not play the equivalent role in the latter or even any role at all. Trade-offs then may be among different traits. More importantly, the symbiont influences its host not only via its direct effects in the association but also through the dynamics of both unoccupied hosts and associations while, in contrast, the interactions between consumers and resources are often short, and the dynamics of such short associations have been considered irrelevant. For these reasons, the evolution of facultative-obligate symbiosis need to be treated separately from the evolution of specialist-generalist.Theoretical studies that address the evolutionary transition toward obligate symbiosis are rare, but even there, this aspect is not the main focus. Frank [34] only focused on the evolution of cooperation, hence only mutualistic interactions were taken into account. Law and Diekmann [7] considered parasitism but only evolution of vertical transmission was taken into account; horizontal transmission where symbionts have to experience the external environment was ignored. Van Baalen and Jansen [25], in an analysis of the mutualism-parasitism continuum, pointed out that members of associations are unlikely to give up their ‘evolutionary sovereignty’ as this requires their interests to be completely aligned, which they claim cannot occur whenever any of the partners has part of its lifecycle outside of the association. However, they did not consider trade-offs that linked traits expressed in the free and the associated states.In this article, we attempt to fill in the gaps left by those studies. We will study the conditions under which evolutionary transitions to obligate symbiosis are favoured or disfavoured, assuming that there is a constraint on adaptations to the associations. We first unravel different fitness components for different lifestyles of a symbiont, then work out conditions whether the symbiont forgoes its independent reproduction or retains the capacity to reproduce when alone. A complete loss of independent reproduction is equivalent to obligate symbiosis, whereas nonzero independent reproduction suggests facultative symbioses with different levels of independent reproduction. Purely free-living organisms do not form associations with the hosts even though they are available.To our knowledge, our study is the first to address the question of how facultative symbiotic relationships may become obligate. We therefore aim for a simple model that demonstrates the fundamental selective forces acting on this fundamental evolutionary transition. In order to do so, it is important to make some simplifications, for instance, we will leave out the host dynamics and consider the traits of the host as given. In this way, we can focus on the evolutionary dynamics of the symbiont and the types of constraints that might favour the evolution toward giving up independent reproduction. If even without the eco-evolutionary dynamics of the hosts, transitions toward obligate symbiosis are possible then host-symbiont interactions, such as host dynamics, types of ecological interactions, and so on, may not play a key role in such transitions. On the contrary, if transition to obligate symbiosis can only occur under limited conditions, then host coevolution may be essential. Furthermore, based on our simple model, we may obtain an idea of to what extent other factors may play a role in determining the evolutionary outcomes.
The ecological dynamics
We focus on a population whose members can be either in a free-living state () or associated with a host () (Fig 1). It should be noted that we only consider long-term interactions such as lichen, insects and symbiotic bacteria, and so on, instead of the short-term interactions such as plant-pollinators or cleaning mutualisms. The free-living individuals produce free-living progeny at a rate ρ while they die at a rate μ. At a rate β, free-living individuals encounter hosts and form associations. Individuals in associations produce free-living progeny at a rate τ, they die at a rate ν. Bound individuals also reproduce together with their hosts at a rate σ; this is essentially the vertical transmission.
Fig 1
Schematic representation of the model.
For the hosts we have to make a number of additional assumptions. We can assume, of course, that hosts have no appreciable dynamics of their own relative to the symbionts’ dynamics, which sets vertical transmission automatically to zero. Alternatively we can impart various forms of population dynamics to the host. In the latter case, the symbionts may have various effects on host dynamics as well as induce vertical transmission. As in this study we aim to focus on the evolutionary pressures on the symbionts, we assume that the total host population size is a constant number N, and we will only consider host dynamics in a future study. Finally, we assume that if a host dies, its symbiont dies with it. In other words, dead hosts do not release free symbionts.This gives us the dynamics of a mutant symbiont strain
where and stand for the equilibrium densities of the resident system (free-living residents, and free hosts, respectively) (S1 Appendix shows detailed calculation of feasible equilibrium). indicates density dependent mortality with intensity c. We will also assume that ν > σ so that the population of associations will not grow without bounds because of high vertical transmission.
A trade-off between reproduction and host encounter
In principle, mutation can affect any life history character, but we specifically consider mutations in the reproduction rates (ρ, τ) and the host encounter rate (β) for two reasons: first, the most straightforward indication for obligate symbiosis is the forfeit of the reproduction in the free-living state; second, the encounter rate indicates the success rate of the formation of associations, and one can observe in nature diverse strategies of symbionts to encounter their hosts [35-38]. The values of the reproduction rate and the host encounter rate would therefore be good indicators of facultative and obligate symbiosis.This set of assumptions effectively assumes that there is a trade-off between reproduction and host encounter. If x represents an investment in reproduction, we can assume that
while
where the primes indicate the derivative with respect to x. The conditions above imply that if an individual spends its energy on increasing host encounter rate, its reproduction will reduce. Furthermore, being in association boosts bound reproduction so that
There could be other effects on survival and vertical transmission but for simplicity we will not consider these here, hence the only differences among strains is the three phenotypic parameters.
Invasion analysis
A mutant, with dynamics (1), that adopts a different strategy than the resident is able to spread, replace the resident and become a new resident if its reproduction ratio R0 is greater than one. We obtain the expression of R0 using the next-generation method [39] (see S2 Appendix for detail). The invasion condition means that on average, a mutant individual is replaced by more than one mutant offspring, and it can be written as
where
is the overall decay rate of free-living individuals (so that represents the expected duration of the free-living state). The expected duration of the free-living state of the mutant depends on the population density of the resident , which itself depends on the strategy that the resident invest in its reproduction x.There are two fitness contributions at the free-living state, independent reproduction,
and through host encounter,
Note that the contribution through host encounter depends on the availability of the unoccupied hosts, , and the expected duration of an association 1/(ν − σ). Condition (5) also suggests that without any trade-off, mutants that keep investing in both independent and bound reproduction ρ(x), τ(x) will always be able to invade, suggesting that evolution of facultative symbionts that can reproduce independently in the absent of hosts is the only evolutionary end.
Evolutionarily stable strategy
The loop where a new mutant emerges, spreads and replaces the resident then becomes a new resident will stop if there exists a resident population adopting a strategy x* such that mutants with other strategies cannot invade. This strategy is called the evolutionarily stable strategy (ESS) [40, 41]. When the resident population adopts the ESS, the selection gradient dR0(x, x)/dx vanishes, which implies that the ESS x* satisfies
Our assumption that investing in host encounter rate comes at a cost on reproduction (condition 2, 3 and 4) implies that and . Condition (9) is only satisfied if . This means that mutants with higher investment in reproduction than the ESS resident undergo negative effects in their associated lifestyle, which strongly depends on how much cost is induced on their bound reproduction by investing on the host encounter rate (this is represented by dβ/dτ = β′(x)/τ′(x), where the primes indicate the derivatives with respect to the energy investment x).To simplify the analysis, we assume that the symbiont makes the same investment in reproduction regardless of whether it is inside the host or in the external environment, i.e. τ′(x) = ρ′(x). This is not an unreasonable assumption, the difference between the bound reproduction and the independent reproduction may be due to how the symbiont exploits the host but not in how it invests in reproduction. But the mechanism underlying host exploitation is not within the scope of this model. Now, the existence of an ESS and its exact value depend on the magnitude of β′(x)/ρ′(x) (Fig 2) [42, 43].
Fig 2
Relationship between β and ρ, which is derived from the assumption that increasing the investment x in independent reproduction ρ(x) leads to a reduction in host encounter rate β(x).
Host encounter rate and independent reproduction are functions of the investment such that β(x) = β/(αx + 1); ρ(x) = ωx/(δx + 1). Depending on the parameters, the resulting trade-off can be convex (A) α = 0.7, δ = 1.3 or concave (B) α = 3.1, δ = 1.3. A convex trade-off curve indicates that investing in host encounter rate does not reduce much reproduction rate, whereas a concave trade-off curve indicates the reverse.
Relationship between β and ρ, which is derived from the assumption that increasing the investment x in independent reproduction ρ(x) leads to a reduction in host encounter rate β(x).
Host encounter rate and independent reproduction are functions of the investment such that β(x) = β/(αx + 1); ρ(x) = ωx/(δx + 1). Depending on the parameters, the resulting trade-off can be convex (A) α = 0.7, δ = 1.3 or concave (B) α = 3.1, δ = 1.3. A convex trade-off curve indicates that investing in host encounter rate does not reduce much reproduction rate, whereas a concave trade-off curve indicates the reverse.Condition (9) of a zero selection gradient can be converted into the condition for the intersection of the trade-off curve between host encounter rate and reproduction, and the invasion boundary (Fig 3), which leads to
where . The left-hand side represents the trade-off curve between independent reproduction and host encounter rate (Fig 2 and solid lines in Fig 3). The right-hand side represents the invasion boundary of a resident (dashed lines in Fig 3) which indicates the area in which mutants can invade the resident (we showed that this expression is in fact the slope of the invasion boundary in S3 Appendix). Residents that invest differently in reproduction may have different invasion boundaries, and condition (10) suggests that the ESS has to be the tangent point of the trade-off curve and the invasion boundary (closed circles in Fig 3) because at this point, at least locally, the invasion area contains no possible mutant. Rewriting the selection gradient in this way is convenient because we can disentangle the effect of the trade-off from the ecological feedback on the value of the ESS.
Fig 3
Invasion boundaries as a function of different levels of resident investment in the independent reproduction rate are represented by dashed lines.
Open circles indicate the values of the traits of the residents. Shaded areas are invasion areas. Trade-off is assumed as in Fig 2. Free host population is , where N is the total number of hosts. ESS value is the tangent point (closed circle) between the invasion boundary and the convex trade-off curve (A) and concave trade-off curve (B). Parameter values: b = 3, ν = 3, c = 2, σ = 0, μ0 = 3, β = 5, ω = 6.5, N = 100, (A) α = 0.7, δ = 1.3, (B) α = 3.1, δ = 1.3.
Invasion boundaries as a function of different levels of resident investment in the independent reproduction rate are represented by dashed lines.
Open circles indicate the values of the traits of the residents. Shaded areas are invasion areas. Trade-off is assumed as in Fig 2. Free host population is , where N is the total number of hosts. ESS value is the tangent point (closed circle) between the invasion boundary and the convex trade-off curve (A) and concave trade-off curve (B). Parameter values: b = 3, ν = 3, c = 2, σ = 0, μ0 = 3, β = 5, ω = 6.5, N = 100, (A) α = 0.7, δ = 1.3, (B) α = 3.1, δ = 1.3.Depending on the conditions, the ESS can be obligate symbiosis, facultative symbiosis, or completely free-living organisms. A larger value of β′(x)/ρ′(x) may lead to an ESS of smaller independent reproduction. In other words, if investing in host encounter comes at a high cost, symbionts may evolve to forgo their independent reproduction, because the amount of energy left to invest in its reproduction is too small. However, a high cost of investment in host encounter does not always mean an increase in host dependency because the ESS value also depends on the ecological feedback, such as the abundance of free hosts.Given a fixed cost of investment in the host encounter rate, i.e. fixed value of β′(x)/ρ′(x), if all else being equal, strategies that result in a high bound reproduction value (i.e. high value of τ(x)) will lead to higher dependency of the symbiont on the host. There are several ways to obtain a high bound reproduction value, one of which is exploiting resources from the hosts (Fig 4). Thus, starting with a population of facultative symbiont, the higher the benefits inside the association obtained by exploiting the hosts, the more the symbiont is willing to forgo its independent reproduction and becomes more dependent on the host (Figs 4 and 5).
Fig 4
Effect of the compound benefit (B = b − ν + σ) on the ESSs in the case of a concave trade-off curve (black line) under the assumption that the bound reproduction is τ(x) = ρ(x) + b, where b is the bonus reproduction by exploiting the host.
Trade-off and host population are as in Fig 3. Dashed lines are the invasion boundaries that separate shaded areas in which mutants can invade and blank areas in which mutants cannot. Black points indicate the ESS values that are corresponded with different values of B. Other parameters: c = 2, N = 100, μ0 = 3, ω = 6.5, β = 5, α = 3.1, δ = 1.3, σ = 0.
Fig 5
Effect of the compound benefit B and density of the total host population N on the transition from fully retaining independent reproduction (ρ = ρ) to completely forgoing independent reproduction (ρ = 0) under cases with no vertical transmission (σ = 0).
Trade-off is as in Fig 3. A) Convex trade-off curve where α = 0.7, δ = 1.3, B) concave trade-off curve where α = 3.1, δ = 1.3. The dashed line corresponds to the case when the symbionts gain no benefit (b = 0). The thick lines separate the three regions: pure free-living (dark blue), obligate symbiosis (dark red) and faculative symbiosis with varying degrees of independent reproduction.
Effect of the compound benefit (B = b − ν + σ) on the ESSs in the case of a concave trade-off curve (black line) under the assumption that the bound reproduction is τ(x) = ρ(x) + b, where b is the bonus reproduction by exploiting the host.
Trade-off and host population are as in Fig 3. Dashed lines are the invasion boundaries that separate shaded areas in which mutants can invade and blank areas in which mutants cannot. Black points indicate the ESS values that are corresponded with different values of B. Other parameters: c = 2, N = 100, μ0 = 3, ω = 6.5, β = 5, α = 3.1, δ = 1.3, σ = 0.
Effect of the compound benefit B and density of the total host population N on the transition from fully retaining independent reproduction (ρ = ρ) to completely forgoing independent reproduction (ρ = 0) under cases with no vertical transmission (σ = 0).
Trade-off is as in Fig 3. A) Convex trade-off curve where α = 0.7, δ = 1.3, B) concave trade-off curve where α = 3.1, δ = 1.3. The dashed line corresponds to the case when the symbionts gain no benefit (b = 0). The thick lines separate the three regions: pure free-living (dark blue), obligate symbiosis (dark red) and faculative symbiosis with varying degrees of independent reproduction.However, an ESS of fully obligate symbiosis is not inevitable, if not often difficult to reach. It is only possible if the zero independent reproduction is the ESS, or the strategy x* such that ρ(x*) = 0 satisfies
Condition (11) suggests that obligate symbiosis is an ESS only if the bound reproduction τ(x) is sufficiently large, which indicates that the benefits that the symbionts gain from the host must be high enough (Red area in Fig 5). If the resident of obligate symbionts do not reproduce sufficiently via the hosts, mutants that invest more in the independent reproduction will be able to invade (Fig 6).
Fig 6
Different invasion boundaries (dashed lines) of the residents with zero independent reproduction and different values of the reproduction bonus b, assuming that τ(x) = ρ(x) + b.
Trade-off and other conditions are similar to Fig 3. The higher the bonus reproduction, the less negative the slope of the invasion boundary compared with the slope of the trade-off curve (black line). A) Concave trade-off α = 3.1, δ = 1.3. B) convex trade-off α = 0.7, δ = 1.3. Other parameter values N = 10, c = 2, σ = 0, ν = 3, μ0 = 3, β = 5, ω = 6.5.
Different invasion boundaries (dashed lines) of the residents with zero independent reproduction and different values of the reproduction bonus b, assuming that τ(x) = ρ(x) + b.
Trade-off and other conditions are similar to Fig 3. The higher the bonus reproduction, the less negative the slope of the invasion boundary compared with the slope of the trade-off curve (black line). A) Concave trade-off α = 3.1, δ = 1.3. B) convex trade-off α = 0.7, δ = 1.3. Other parameter values N = 10, c = 2, σ = 0, ν = 3, μ0 = 3, β = 5, ω = 6.5.At the other end, returning to fully free-living organisms is no less easier, which will only happen when
with β(x*) = 0. Condition (12) suggests that if reproducing via the association is small, especially much smaller than the mortality in the associations (i.e. τ(x) ≪ ν) then there is no point in investing in this lifestyle, and becoming free-living can be an evolutionarily stable point (Dark blue area below the dashed line in Fig 5B). Returning to the fully free-living lifestyle may be possible even if the symbionts see benefits in the associated lifestyle, i.e. sufficiently large τ(x), but only when hosts are extremely scarce, because only when can condition (13) be satisfied (Fig 7 and dark blue area above the dashed line in Fig 5B).
Fig 7
Different invasion boundaries (dashed lines) of the residents with zero host encounter rate in the environment of different total number of hosts N.
The lower the density of the total host population, the more negative the slope of the invasion boundary (dashed lines) compared with the slope of the trade-off curve (black line). A) Concave trade-off α = 3.1, δ = 1.3. B) convex trade-off α = 0.7, δ = 1.3. The blue lines are the invasion boundaries that respectively corresponds to different values of density of total host population N. Other parameter values b = 1, c = 2, σ = 0, ν = 3, μ0 = 3, β = 5, ω = 6.5.
Different invasion boundaries (dashed lines) of the residents with zero host encounter rate in the environment of different total number of hosts N.
The lower the density of the total host population, the more negative the slope of the invasion boundary (dashed lines) compared with the slope of the trade-off curve (black line). A) Concave trade-off α = 3.1, δ = 1.3. B) convex trade-off α = 0.7, δ = 1.3. The blue lines are the invasion boundaries that respectively corresponds to different values of density of total host population N. Other parameter values b = 1, c = 2, σ = 0, ν = 3, μ0 = 3, β = 5, ω = 6.5.Our analysis suggests that intermediate strategies of independent reproduction are common evolutionary ends, suggesting that facultative symbiosis should be common. The only way for full symbiosis requires a high reproduction value inside the association, which could be obtains by high exploitation from the hosts, and this in itself very likely depends on host co-evolution. How exactly does the symbionts exploit the hosts deserves a separate and more thorough study, and will not be dealt with here. Even so, we will briefly discuss possibilities how a symbiont could increase its bound reproduction.
Uncoupling free and bound reproduction on the difficult evolution toward obligate symbiosis
One of the important condition for an ESS of obligate symbiosis is that the symbiont has to gain sufficient bound reproduction τ(x). There are many way in which a symbiont can increase this value, and one of the simplifying assumptions we made for the numerical analysis example is that the rate of reproduction of associated symbionts is the same as that of free-living individuals plus a bonus they receive from their partner τ(x) = ρ(x) + b. Our assertion that obligate symbionts give up free reproduction thus implies that the rate of reproduction of symbionts is fully determined by the host. This could of course be the actuality in many full-blown obligate symbioses. For instance, the replication rate of mitochondria is tightly controlled by their host’s nucleus [44]. However, this cannot be the full picture. Many parasites, that are full-blown obligate symbionts, strongly resist the efforts of their hosts to curb their reproduction. Therefore, our assumption of identical reproduction rates and a fixed bonus is not justified in many cases.The first possibility is that symbionts reproduce differently in different environments (so that τ(x) ≠ ρ(x) + b for a given x). This could be either due to differential resource densities or that the individuals are able to detect that they are in different environments and respond to it. Evidence that symbionts behave differently inside and outside of hosts has been documented [31, 45]. A consequence of this relaxation is that ρ′(x) = τ′(x) no longer holds, therefore dτ/dρ is no longer a constant, which greatly simplified our analysis.A more in-depth analysis of the consequences of decoupling the reproduction rates ρ(x) and τ(x) will be published elsewhere, but suffice it here to state that it does not affect our conclusion that constrains performances in the free state and in the associated state are central to our understanding of what governs the evolutionary transition to obligate symbiosis.A second, equally interesting possibility is that the benefits are somehow dependent on the symbionts’ investment in reproduction. This is reflected in numerous cases where mutualistic symbionts trade some of their resources with their partners. Then, b, the bonus reproduction gained from the exploiting the host, is no longer a constant but depend on x. Moreover, this involves consideration of how the host responds to the symbiont, and thus of coevolution. This falls outside of the scope of this article. However, it is easy to see that if b depends positively on x it will most likely raise the invasion boundary and thus select for increased values of the encounter rate β generally.
Discussion
The term symbiosis was introduced in the late 1870s after several studies on lichens had shown that an individual lichen consists of individuals of more than one species [6]. Symbiosis was then considered as a source of evolutionary innovation ([6] and [46] and their references). Symbiosis of prokaryotic cells is suggested to result in eukaryotic cells [3], which is considered one of the major evolutionary transition by Maynard Smith and Szathmary [47], and this is only one extreme case of obligate symbiosis in which obligate dependency is required from both partners. Examples of obligate and facultative symbioses are ubiquitous, with different levels of dependency from both partners. Yet, how obligate symbioses may evolve out of facultative ones is not well-understood, thus studying this intriguing transition process may give insights and guide for future studies.Our study shows that it is useful to consider facultative and obligate symbiosis not as discrete traits but as part of a continuum where the key trait is the capacity of independent reproduction, that is, the capacity of the symbiont to reproduce without the host. The continuum of the independent reproduction implies that there are varying degrees of dependency in facultative symbiosis (this has been realised also in [48]), and only symbionts that completely give up their independent reproduction should be considered obligate symbionts.Our model suggests that, if encountering hosts comes at a price of reproduction, gaining benefits from the symbiotic lifestyle will select for more investment in host searching and loss of independent reproduction. Moreover, the higher the price, the less likely facultative symbiosis will be an evolutionary outcome, much the same as generalists are not necessarily favoured when the generalist-specialist trade-off curve is concave [49-52]. However, our model shows that even with a high cost of reproduction, a complete loss of independent reproduction is not guaranteed unless benefits from being in association are sufficient. This is because we assume that a symbiont invests in its free reproduction the same way that it does in its bound reproduction; what eventually keeps the symbiont in the association is the reproduction bonus that it receives from its host, which is assumed to be a constant amount in the scope of our model.There may be two reasons that the symbionts invest the same in reproduction regardless of whether it is free-living or associated with its host. First, the symbiont is not sensitive enough to perceive the differences between the external and the host environment. Second, the two environments are so similar that the symbiont does not need to respond differently. For either reason, obligate symbiosis is unlikely to evolve. In contrast, if the symbiont behaves differently in the host environment than in the external environment, regardless of whether this difference is a result of active response from the symbiont or it is simply due to strong intrinsic dissimilarities of the two environments, then obligate symbiosis may be a possible outcome.Ecological feedback on the density of free hosts may also make the full transition toward obligate symbiosis difficult. As we did not take into account host dynamics, higher benefits also imply higher density of associations, which leads to a lower density of free hosts. Therefore if an increase of benefits from the association cannot compensate for the reduction in the number of free hosts, obligate symbiosis will not be an evolutionarily outcome. Even if we relax the assumption of host dynamics, ecological feedback can take place in the competition between associations and free hosts, and similar results can be obtained.The evolution of a pure free-living lifestyle may not be easy either as passive formation of associations may be difficult to avoid. While we do not have evidence for whether or not it is easy to gain some benefits in the associations, it is certainly difficult to have no interaction at all with other species that may serve as potential hosts. Our model thus suggests that facultative symbiosis should be common but how then do we explain the many examples of obligate symbioses?First, many symbioses may be less obligate than they seem. In fact, partners in many symbioses that appear to be obligate in nature can nevertheless often been shown to be able to grow and reproduce outside the associations in laboratories [53-55]. Second, in many cases partners in profitable symbioses do need to make a significant effort to meet a suitable host. Our model also suggests that symbionts that have to make a bigger effort to find hosts are more likely to sacrifice all their independent reproduction while those that depend more on random encounter are more likely to retain some independent reproduction. There are examples indicating that such a pattern occurs in nature.Bacterial pathogens such as Bacillus cereus and Bacillus anthracis both form endospores as a protection strategy against destruction of gastric acid and harsh environmental conditions. This strategy is suggested to facilitate the transmission of the parasites. B. anthracis is a well-known obligate pathogen that cannot reproduce outside hosts [56] while B. cereus is present in the external environment under both spore and vegetative forms but proliferation seems rare [57, 58] (only one experimental study showed that the bacteria can germinate and grow in a soil mimicking condition [59]). According to our model, they can be placed at the obligate symbiotic end.On the other hand, many other bacterial pathogens such as Salmonella spp., Listeria monocytogenes, and Vibrio cholerae enter a stationary phase and depend on dose to overcome the gastric acid [30, 60, 61]. It is not unlikely that this strategy is less costly than forming spores because spores are often assumed to resist more extreme conditions for a longer period of time than a stationary phase does. Interestingly, Salmonella, L. monocytogenes, and V. cholerae have been shown to retain the ability to reproduce in the external environment [30, 62, 63], or equivalently, they are more likely at the freeliving-facultative symbiotic end.Another class of the effect of transmission costs is provided by mutualistic symbioses. Rhizobia and Arbuscular Mycorrhizas (AM) are symbionts that form nodules in plant roots; the former are bacteria that do not form spores while the latter are fungi that reproduce via sporulation. Both Rhizobia and AM encounter hosts randomly and establish the symbiotic relationship via complex molecular signals [31]. Intuitively, AM may increase the chance to encounter with their hosts by forming spores that can withstand harsh environmental conditions, whereas Rhizobia may die when the host is scarce and the environment is unfavourable. When environmental conditions are appropriate, Rhizobia are found as free-living bacteria in soil while AM may pay too high a price for sporulation that they cannot reproduce without the host plant even in laboratories.However, transmission costs may not explain everything. For instance, the parasitic bacterium Campylobacter jejuni survives through gastric acid without forming spores and its successful transmission is dose dependent, thus it is expected that C. jejuni is capable of independent reproduction. Yet, C. jejuni is extremely fragile and seems unable to reproduce in the external environment [64]. In a similar fashion, bacteria of the genus Shigella seem able to survive but not to reproduce in the external environment [65]. They do not form spores yet are more efficient than E. coli or Samonella in withstanding gastric acid owing to their sophisticated mechanisms of acidic resistance [66].That C. jejuni and Shigella cannot reproduce without hosts may simply imply that the benefit from the association is sufficient for the organisms to give up all the independent reproduction, or that spore forming is not the only costly aspect of host encounter. For instance, Ectomycorrhizas (ECM), fungi that form symbioses with plant roots, do form spores; they are not found to reproduce without host in the environment but can be cultured in vitro. The main difference between AM and ECM is that AM penetrate the root cells whereas EM do not [67]. If all else is equal, that is, if the cost to produce molecular signals and penetrating the epidermis is similar between the two types of mycorrhizas then it is possible that the intracellular colonization of AM is more costly than the extracellular establishment of ECM.These examples show that it is necessary to better quantify the costs of host encounter and independent reproduction if we want to understand the conditions that favour obligate symbiosis. The relationship between host encounter and independent reproduction may provide guidance for studies of symbionts whose lifecycles are not well understood.One of the limitations in our model is that it overlooks the ecological interactions between hosts and symbionts, as it assumes that the total host density is fixed. These interactions are nevertheless likely to have strong effects on the evolution of both the hosts and the symbionts [68-70], and are expected to affect the level of independent reproduction. Van Baalen and Jansen [25] showed that mutualistic associations may select for partners to forgo independent reproduction because mutualism increases the alignment of interest. Future work adding the effect of ecological interactions will shed more light on the evolutionary transitions of the freeliving-obligate continuum. For instance, are obligate mutualistic symbioses more likely to evolve than obligate parasites or not?We proposed a simple model, thus the mathematical results are straightforward and intuitive, yet interesting biological interpretations can be inferred from it. More importantly, it will give useful insights into possible evolutionary outcomes should more complicated models be built upon. In a future study, we will study the effects of additional mechanisms which are know to be important, such as incorporating host dynamics, considering more general trade-off, taking into account ecological interactions and so on.
Bifurcation analysis of the ecological equilibrium.
(TIF)Click here for additional data file.
Stability of the resident population equilibrium.
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Next generation method.
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Conditions for intermediate evolutionarily stable strategy (ESS).
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Effect of the reproduction bonus b on the associated population at equilibrium.
(PDF)Click here for additional data file.(NB)Click here for additional data file.(NB)Click here for additional data file.7 Nov 2019PONE-D-19-25560On the difficult evolutionary transition from free-living lifestyle to obligate symbiosisPLOS ONEDear Mrs Nguyen,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.The reviewer, who is expert in evolutionary conflicts of interest, found difficulty following many of the arguments, and their relationship to the biology. Therefore please attempt to clarify these in response to the reviewers comments, as far as possible.We would appreciate receiving your revised manuscript by Dec 22 2019 11:59PM. 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Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: Partly**********2. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #1: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: No**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)Reviewer #1: In this paper, the authors analyze and describe a model of the evolution of the transition from free-living to obligate symbiosis. Unfortunately I found the paper hard to follow and at a certain point I just got lost. I would be happy to review the article again if it can be substantially clarified.Abstract: I’m confused by the first two sentences. First sentence: Who has suggested this? Endosymbiosis of e.g. mitochondria is often hypothesized to have resulted from a predator-prey scenario, in which case it would not have evolved from what we normally think of as facultative symbiosis. Second sentence: Would e.g. protomitochondria, once engulfed, have the choice of living independently? I feel as though there is one obvious way in which individuals would “give up” the ability to live freely: the organisms which enter into certain symbioses outcompete those which do not, there are payoffs for closer and closer association (e.g. removal of conflict, better exchange of resources), and over time natural selection acts to remove those stretches of DNA which encode for free living, which are no longer needed and hence are a selective burden. So is this really a riddle? (line 15)line 2: “contact”?27–98: This may be a matter of taste, but I feel that a lot of this material going over existing models probably belongs in the discussion. I found it hard to work out from the introduction what the main message of the paper is.39: This paper is just by Frank, not Frank and colleagues.48: “sacrifices”81: “complete”100–104: There are lots of different kinds of symbiosis in the world and I think it would help to bring in some concrete examples here to clarify what you are modelling. Does this model apply only to endo/ectosymbiosis? Does it also apply to mutualisms like plant-pollinator and cleaner symbioses? I think it’s more about ecto/endosymbiosis, focusing on the symbiont rather than the host, but because the introduction was quite sweeping—e.g. citing in lines 4–9 previous work that looks very broadly at e.g. mutualisms like cleaner-client and plant-pollinator—it’s hard to grasp what’s being modelled here. Also, the parameter sigma needs to be explained here: when an A makes another A at rate sigma, is the new A associated with the same host as its parent or a new one?105–112: So this model cannot analyze vertical transmission? If we are indeed focusing on endo/ectosymbioses, isn’t vertical transmission a rather important part of the evolution of obligate symbioses?117–118: Does this assumption reduce the generality of your model? Why was this assumption used to prevent the population of associations from growing without bound, instead of e.g. a saturating growth function?136–205: These sections need to be substantially clarified. Moreover, I feel that statements like 167-169 and 190-192, which restate results as statements about geometry, are not helpful. I would appreciate these results being explained in more biological terms. I mostly gave up on the results section at this point.361–364: Unclear what this sentence means.409–411: The fact that Trichinella can be induced to grow on intestinal epithelial cells in a lab has no bearing on how “obligate” its symbiosis is in nature. Particularly as the intestine forms part of its natural habitat. What matters is what happens in nature.414: “sacrifice”Figures, generally: Please provide labels A and B on all the plots, and please left-align, don’t right-align these labels. I have never seen this done before and it’s very confusing. All the plots should have informative axis titles like Fig. 5 so they can more easily stand alone.Fig. 2: From the caption and figure alone, it’s unclear whether this trade-off is a result or an assumption. Obviously this is stated in the text, but it just doesn't help comprehension to have this much ambiguity.I’m sorry I couldn’t be more helpful on this occasion.Best wishes,Nick DaviesLondon School of Hygiene and Tropical Medicine**********6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? 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Please note that Supporting Information files do not need this step.30 Dec 2019Dear Nick Davies,Thank you for reviewing our manuscript. You will find below our response to each point that you raised. We hope that they sufficiently clarify your questions.# Abstract: Im confused by the first two sentences. First sentence: Who has suggested this? Endosymbiosis of e.g. mitochondria is often hypothesized to have resulted from a predator-prey scenario, in which case it would not have evolved from what we normally think of as facultative symbiosis. Second sentence: Would e.g. protomitochondria, once engulfed, have the choice of living independently? I feel as though there is one obvious way in which individuals would give up the ability to live freely: the organisms which enter into certain symbioses outcompete those which do not, there are payoffs for closer and closer association (e.g. removal of conflict, better exchange of resources), and over time natural selection acts to remove those stretches of DNA which encode for free living, which are no longer needed and hence are a selective burden. So is this really a riddle? (line 15)Response: The idea that obligate symbiosis evolves from facultative symbiosis is our extension of Poulin’s idea in his book: ”Evolutionary Ecology of Parasites” [1]. Here, he suggested that obligate parasites may evolve from facultative parasites if the contact between the parasite and the host is frequent enough [1, Chapter 2]. We argue that the type of ecological interactions may not play a key role in this evolutionary transition, that is, obligate symbiosis may evolve from facultative symbiosis, regardless of whether the interaction is parasitism or mutualism.We agree that for many symbiotic systems, the associations may have resulted from prey-predator interactions, and if the engulfed symbionts are then maintained purely by vertical transmission with the host then it is obvious that obligate symbiosis can evolve directly from free-living organisms. However, the prey-predator interaction at the level of microorganisms may completely be different from the interaction at the level of macroorganisms. For instance, a deer is surely dead and cannot escape after being consumed by a tiger, but a bacteria that are engulfed inside a host may escape. In fact, some hydra strains form association with algae by engulfing the algae, but the algae symbionts have been shown to be able to escape from the hydra hosts and enter the external environment ([2]). We argue that the mode of acquiring the symbionts is not that important, and symbiosis formed via engulfing is no different from symbiosis formed via other modes such as rhizobia entering the plant through forming nodules in the roots, or Vibrio fisherie entering the bobtail squid in the specialised light organ. Therefore, we find that conventional facultative symbiosis still holds even when it is formed via prey-predator interaction.In the example that you raised, when protomitochondria were engulfed, it does not follow by being trapped inside their bacterial hosts forever and could only vertically transmit with the hosts and benefit from the hosts. If for any reason, the protomitochondria can escape from the host, they have to deal with the external environment, such as harsh environment, intra and interspecific competition, then they should be better off retaining the ability of independent reproduction, thus, evolving toward obligate symbiosis may not seem so obvious.Below is our modified paragraph. It can be found in line 22-32 in the revision text file.” Obligate symbionts have to evolve from free-living individuals, regard- less of whether they are parasites or mutualists, because if there were no free-living individuals to begin with, there would be no ingredients for associations. If this process occurs due to, for instance, an event of engulfment of the symbiont by the host, followed by purely vertical transmissions of the symbionts to maintain the population then obligate symbionts may evolve directly from free-living organisms. However, many symbionts have to experience external environment before encountering new hosts, and facultative symbiosis is much likely an intermediate step leading toward obligate symbiosis. ”# line 2: contact?Response: This has been corrected in line 2#27-98: This may be a matter of taste, but I feel that a lot of this material going over existing models probably belongs in the discussion. I found it hard to work out from the introduction what the main message of the paper is.Response: We slightly modified the structure of the introduction, and shorten the explanation of existing models. Below is our modified paragraph. It can be found in line 64-74.”Theoretical studies that address the evolutionary transition toward ob- ligate symbiosis are rare, but even there, this aspect is not the main focus. Frank [34] only focused on the evolution of cooperation, hence only mutualistic interactions were taken into account. Law & Dieckmann [7] considered parasitism but only evolution of vertical transmission was taken into account; horizontal transmission where symbionts have to experience the external environment was ignored. Van Baalen & Jansen [25], in an analysis of the mutualism-parasitism continuum, pointed out that members of associations are unlikely to give up their evolutionary sovereignty’ as this requires their interests to be completely aligned, which they claim cannot occur whenever any of the partners has part of its lifecycle outside of the association. How- ever, van Baalen & Jansen [25] did not consider trade-offs that linked traits expressed in the free and the associated states.”# 39: This paper is just by Frank, not Frank and colleagues.Response: This has been corrected in line 65.# 48: sacrificesResponse: This part has been removed# 81: completeResponse: This has been corrected in line 80# 100 - 104: There are lots of different kinds of symbiosis in the world and I think it would help to bring in some concrete examples here to clarify what you are modelling. Does this model apply only to endo/ectosymbiosis? Does it also apply to mutualisms like plant-pollinator and cleaner symbioses? I think its more about ecto/endosymbiosis, focusing on the symbiont rather than the host, but because the introduction was quite sweeping e.g. citing in lines 49 previous work that looks very broadly at e.g. mutualisms like cleaner- client and plant-pollinatorits hard to grasp whats being modelled here. Also, the parameter sigma needs to be explained here: when an A makes another A at rate sigma, is the new A associated with the same host as its parent or a new one?Response: First, we affirm that our model only applies to endo/ectosymbiosis, such as algae-fungi in lichen, aphid-Buchnera, Rhizobia-legume, and so on, but not to the relationships like plant-pollinator.Furthermore, we completely agree with the reviewer that the definitionof symbiosis is rather ambiguous. When symbioses were discovered in the late 19th centuries, de Bary defined symbiosis as ”the living together of unlike named organisms”. According to this definition, symbiosis includes both parasitism, mutualism, and associations of all level of partner dependency, from endo/ectosymbiosis, such as lichen, and insects-bacteria to short term symbiosis such as cleaner-client and plant-pollinator. However, it is not very clear whether de Bary did want to include associations such as plant- pollinator or cleaning symbiosis. Zook [3] did mention this ambiguity and redefined symbiosis, that is ”Symbiosis is the acquisition of an organism(s) by another unlike organism(s), and through subsequent long-term integration, new structures and metabolism(s) emerge”. The symbiotic system that we modelled is closer system defined by Zook [3], that is, it includes only endo/ectosymbiosis.Furthermore, the parameter σ, vertical transmission is only relevant in the context of endo/ectorsymbiosis. When an association (A) makes another A, the symbiont reproduces with the host, that is the new A is the association of a new symbiont and new host.It is important to note that in terms of the type of interactions, we still follow de Bary’s definition, that is we consider both parasitism and mutual- ism, even though the type of interactions cannot be taken to account in this model because we considered a fixed number of hosts for simplification.We also add our affirmation when explaining the model schematic, which can be found in line 100-102.” It should be noted that we only consider long-term interactions such as lichen, insects and symbiotic bacteria, and so on, instead of the short-term interactions such as plant-pollinators or cleaning mutualisms. ”# 105 - 112: So this model cannot analyze vertical transmission? If we are indeed focusing on endo/ectosymbioses, isnt vertical transmission a rather important part of the evolution of obligate symbioses?Response: We agree with the reviewer that vertical transmission may play an important part in the evolutionary transition toward obligate symbioses and it would be best if we could consider both types of transmissions. However, for various reasons, we focus on horizontal transmission instead of vertical transmission. First, in nature, there are many examples of obligate symbioses with mixed modes of transmission [4]; in fact, many obligate parasites are only horizontally transmitted (it should be noted that we only consider symbionts with simple life cycle, that is symbionts with only one host). Secondly, early in the evolutionary transition from facultative to ob- ligate symbiosis, vertical transmission is likely to be rare as it may require specific adaptations [5]. Therefore, considering the evolution of both types of transmission will make our model much more complicated while we are aiming for a simple model as a start to understand this transition.# 117 - 118: Does this assumption reduce the generality of your model? Why was this assumption used to prevent the population of associations from growing without bound, instead of e.g. a saturating growth function?Response: We do not think that the assumption that the vertical transmission is smaller than the bound mortality rate (σ < ν) will reduce the generality of our model because as we responded in the question above, vertical transmission is very likely rare and only happens by chance in the early evolutionary transition. Examples of exclusive vertical transmission that are observed in nature are mostly systems that are already obligate symbioses, and we cannot be sure whether vertical transmission leads to obligate symbiosis or is it because obligate symbiosis (with horizontal transmission) promotes the evolution of vertical transmission.The assumption that σ < ν is to prevent the population of A from growing exponentially when the host encounter rate β evolves toward 0. This is the case of completely free-living population because even when there are free-living symbionts and hosts around, the symbionts will not encounter and establish inside the host and form association. If the mutant of zero β is created through horizontal transmission then nothing will happen but if it is created via vertical transmission, then the population of association A will grow exponentially. A saturating growth function require at least quadratic function with regard to the association population, and will prevent analytical results of the equilibrium.# 136 - 205: These sections need to be substantially clarified. Moreover, I feel that statements like 167-169 and 190-192, which restate results as statements about geometry, are not helpful. I would appreciate these results being explained in more biological terms. I mostly gave up on the results section at this point.Response: The entire section of model analysis and result have been modified in line 140-234.# 361 - 364: Unclear what this sentence means.Response: Below are the modified sentences. They can also be found in line 271-280”The term symbiosis was introduced in the late 1870s after several studies on lichens had shown that an individual lichen consists of individuals of more than one species [6]. Symbiosis was then considered as a source of evolutionary innovation ([6] and [42] and their references). Symbiosis of prokaryotic cells is suggested to result in eukaryotic cells [3], which is considered one of the major evolutionary transition by Maynard Smith and Szathmary [43], and this is only one extreme case of obligate symbiosis in which obligate dependency is required from both partners. Examples of obligate and facultative symbioses are ubiquitous, with different levels of dependency from both partner. Yet, how obligate symbioses may evolve out of facultative ones is not well-understood, thus studying this intriguing transition process may give insights and guide for future studies. ”# 409 - 411: The fact that Trichinella can be induced to grow on intestinal epithelial cells in a lab has no bearing on how obligate its symbiosis is in nature. Particularly as the intestine forms part of its natural habitat. What matters is what happens in nature.Response: Meerovitch et al 1965 successfully cultured Trichinella Spiralis in axenic environment. The basal medium used inactivated normal rabbit serum and 25 % chick embryo extract [6].# 414: sacrificeResponse: This has been fixed in line 328# Figures, generally: Please provide labels A and B on all the plots, and please left-align, dont right-align these labels. I have never seen this done before and its very confusing. All the plots should have informative axis titles like Fig. 5 so they can more easily stand alone.Response: The figures have been modified accordingly.# Fig. 2: From the caption and figure alone, its unclear whether this trade-off is a result or an assumption. Obviously this is stated in the text, but it just doesn’t help comprehension to have this much ambiguity.Response: The caption has been modified accordingly.References1. Poulin, R. Evolutionary Ecology of Parasites 2nd ed. (Princeton Univerity Press, 2006).2. Miyokawa, R. Y. et al. Horizontal transmission of symbiotic green algae between hydra strains. Arch. Am. Art J. 235, 113–122. (2018).3. Zook, D. in Reticul. Evol. Symbiogenesis, Lateral Gene Transf. Hybrid. Infect. Hered. 41–80 (2015).4. Russell, S. L., Corbett-Detig, R. B. & Cavanaugh, C. M. Mixed trans- mission modes and dynamic genome evolution in an obligate animal- bacterial symbiosis. ISME J. 11, 1359–1371 (June 2017).5. Bright, M. & Bulgheresi, S. A complex journey: transmission of microbial symbionts. Nat. Rev. Microbiol. 8, 218–230 (2010).6. Meerovitch, E. Studies on the in Vitro Axenic Development of Trichinella Spiralis. Ii. Can. J. Zool. 43, 81–85 (1965).Submitted filename: response_to_reviewer.pdfClick here for additional data file.30 Mar 2020PONE-D-19-25560R1On the difficult evolutionary transition from free-living lifestyle to obligate symbiosisPLOS ONEDear Mrs Nguyen,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.==============================Thanks for your careful work on this and responding to the prior reviews. The current reviewer has some minor comments that I would like for you to attend to before publication. The article will not need to go out for review again, but there is no way in the PLOS system to allow you to modify the article if we push it straight to accepted.==============================We would appreciate receiving your revised manuscript by May 14 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocolsPlease include the following items when submitting your revised manuscript:A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.A marked-up copy of your manuscript that highlights changes made to the original version. 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Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #2: Yes**********5. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #2: Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)Reviewer #2: The authors investigate the evolution of obligate symbiosis when symbionts can exist on a continuum between completely free-living, facultative, and obligate. They model a trade-off between host encounter and reproduction, so that symbionts that are best at finding a host reproduce least, and may even require their host's help in order to reproduce at all. Interestingly, while symbionts in the model can be vertically transmitted, vertical transmission is both independent of obligacy and not sufficient to maintain a symbiont population. Instead, both facultative and obligate symbionts produce free-living progeny while in symbiosis.This is an interesting model that seems applicable to many symbioses. The model of obligate symbionts that are not purely vertically transmitted seems like a great way to separate the evolution of obligacy from the evolution of transmission mode.I only have some minor comments.The authors mentioned in the supplement that they didn't determine the stability of the positive equilibrium when the trivial equilibrium was unstable. It would be nice add to the supplement some information about the stability of that equilibrium for a few parameter combinations, just as reassurance that nothing strange is going on for some reasonable parameter values.Fig. 1 appears to be missing.Lines 82-83: Since symbionts can always reproduce inside the host in this model, it might be better to say that free-living organisms are distinct from facultative symbionts because they are unable to enter into a symbiotic relationship (beta = 0).Lines 109-110: I found this a bit vague. Would it be possible to add that the host population size is kept constant at N?Fig 6 caption: "Black points indicate the ESS values that are corresponded with different values of B." I couldn't find any black points. Does this possibly refer to the colors in the plots?Line 254: Is "condition (x)" supposed to have a number in place of x?Lines 263-265: I think this should be "Then, b is no longer a constant but depends on x. As this involves consideration of how the host responds to the symbiont, and thus of coevolution..."Line 301-303: I don't understand this sentence. Does it mean that x will be the same in both cases or that b will become 0?Supplement: mu here is mu_0 in the main text.**********7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #2: No[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.12 May 2020Dear reviewer,Thank you very much for reviewing our manuscripts. You will find below our response to each point that you raised, and we hope that it will clarify your questions.\\# The authors mentioned in the supplement that they didn't determine the stability of the positive equilibrium when the trivial equilibrium was unstable. It would be nice add to the supplement some information about the stability of that equilibrium for a few parameter combinations, just as reassurance that nothing strange is going on for some reasonable parameter values.Response: Indeed, we did not consider the stability of the equilibrium in the first submission. To show that this is not so important in our simple model, and that there is no strange behaviour of the equilibrium, we added in the supplementary document the bifurcation analysis of the equilibrium with respect to the independent reproduction rate $\\rho$ and the mortality rate of the association $\\nu$. It shows that if the reproduction is not sufficient or if the mortality rate is too high then the trivial equilibrium is stable, whereas in the reverse conditions, there are two stable non zero equilibrium, of which only one is positive and is feasible for the analysis.\\# Fig. 1 appears to be missing.Response: We changed the order of the figures when we edited the manuscript and some erroneous references escape our attention. Thank you for pointing this out. We corrected the error.\\# Lines 82-83: Since symbionts can always reproduce inside the host in this model, it might be better to say that free-living organisms are distinct from facultative symbionts because they are unable to enter into a symbiotic relationship (beta = 0).Response: We agree with the reviewer for this clarification and modified the phrase as followed. It is in line 80-83 in the revision manuscript."A complete loss of independent reproduction is equivalent to obligate symbiosis, whereas nonzero independent reproduction suggests facultative symbioses with different levels of independent reproduction. Purely free-living organisms do not form associations with the hosts even though they are available."\\# Lines 109-110: I found this a bit vague. Would it be possible to add that the host population size is kept constant at N?Response: We added the clarification in line 114-116 in the revision manuscript. Followed is the modified phrase."As in this study we aim to focus on the evolutionary pressures on the symbionts, we assume that the total host population size is a constant number $N$, and we will only consider host dynamics in a future study."\\# Fig 6 caption: "Black points indicate the ESS values that are corresponded with different values of B." I couldn't find any black points. Does this possibly refer to the colors in the plots?Response: This is an error that we made during the revision of our manuscript. This phrase should be in the caption of Figure 4, and we corrected this mistake.\\# Line 254: Is "condition (x)" supposed to have a number in place of x?Response: This is again an error that we failed to notice. Thank you for pointing this out. We changed the phrase into"A consequence of this relaxation is that $\\rho'(x) = \\tau'(x)$ no longer holds, therefore $d \\tau/d \\rho$ is no longer a constant, which greatly simplified our analysis."This is modified in line 255 in the main text.\\# Lines 263-265: I think this should be "Then, b is no longer a constant but depends on x. As this involves consideration of how the host responds to the symbiont, and thus of coevolution..."Response: We modified the phrase as followed. We hope that this will clarify what we meant."Then, b, the bonus reproduction gained from the exploiting the host, is no longer a constant but depend on x. Moreover, this involves consideration of how the host responds to the symbiont, and thus of coevolution. This falls outside of the scope of this article."It can be found in line 265-268 in the main text.\\# Line 301-303: I don't understand this sentence. Does it mean that x will be the same in both cases or that b will become 0?Response: We modified the paragraph so that our message is clearer. We basically meant that if the symbiont invests the same in independent reproduction and bound reproduction, i.e. $\\rho'(x) = \\tau'(x)$, evolution toward obligate symbiosis may be more difficult than if it invests differently in the two reproduction rats, i.e. $\\rho'(x) \\neq \\tau'(x)$. In the latter case, the evolution of losing independent reproduction may be favoured depending on the specific assumption of $\\rho'(x)$ and $\\tau'(x)$.The following modified paragraph can be found in line 297-306 in the main text."This is because we assume that a symbiont invests in its free reproduction the same way that it does in its bound reproduction; what eventually keeps the symbiont in the association is the reproduction bonus that it receives from its host, which is assumed to be a constant amount in the scope of our model.There may be two reasons that the symbionts invest the same in reproduction regardless of whether it is free-living or associated with its host. First, the symbiont is not sensitive enough to perceive the differences between the external and the host environment. Second, the two environments are so similar that the symbiont does not need to respond differently. For either reason, obligate symbiosis is unlikely to evolve."\\# Supplement: $\\mu$ here is $\\mu_0$ in the main text.Response: We thank the reviewer for pointing this out. We changed the mathematical annotations in the supplementery document so that it matches those in the main text.Submitted filename: Response_to_reviewers.pdfClick here for additional data file.24 Jun 2020On the difficult evolutionary transition from the free-living lifestyle to obligate symbiosisPONE-D-19-25560R2Dear Dr. Nguyen,We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.Thank you for completing these changes. The addition of the stability analysis is a nice touch. I would like to apologize for the delay in processing your re-submission, it is entirely due to me being caught up with other responsibilities and I apologize for the long wait.An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.Kind regards,Stephen R ProulxAcademic EditorPLOS ONEAdditional Editor Comments (optional):Reviewers' comments:6 Jul 2020PONE-D-19-25560R2On the difficult evolutionary transition from the free-living lifestyle to obligate symbiosisDear Dr. Nguyen:I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.If we can help with anything else, please email us at plosone@plos.org.Thank you for submitting your work to PLOS ONE and supporting open access.Kind regards,PLOS ONE Editorial Office Staffon behalf ofDr. Stephen R ProulxAcademic EditorPLOS ONE
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