^{*}

Conceived and designed the experiments: NT PH. Performed the experiments: NT. Analyzed the data: NT PH. Contributed reagents/materials/analysis tools: NT. Wrote the paper: NT PH.

The authors have declared that no competing interests exist.

Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities.

The origin of life has ever been attracting scientific inquiries. The RNA world hypothesis suggests that, before the evolution of DNA and protein, primordial life was based on RNA-like molecules both for information storage and chemical catalysis. In the simplest form, an RNA world consists of RNA molecules that can catalyze the replication of their own copies. Thus, an interesting question is whether a system of RNA-like replicators can increase its complexity through Darwinian evolution and approach the modern form of life. It is, however, known that simple natural selection acting on individual replicators is insufficient to account for the evolution of complexity due to the evolution of parasite-like templates. Two solutions have been suggested: compartmentalization of replicators by membranes (i.e., protocells) and spatial self-organization of a replicator population. Here, we make a direct comparison of the two suggestions by computer simulations. Our results show that the two suggestions can lead to unanticipated and contrasting consequences in the long-term evolution of replicating molecules. The results also imply a novel advantage in the spatial self-organization for the evolution of complexity in RNA-like replicator systems.

Consideration of selection acting on multiple levels of biotic organization is important for understanding of biological evolution in general

The RNA-like replicator system is considered one of the simplest chemical systems that can undergo Darwinian evolution in a self-sustained manner

The importance of multilevel selection in prebiotic evolution is based on two problems that arise in the evolution of replicator systems. Firstly, there is a fundamental problem about the accumulation of information in exponentially growing replicators. That is, the maximal length of sequence patterns that can be maintained under the mutation-selection process in a single replicator quasi-species is severely limited by high mutation rates, which are supposed in primordial replication processes based on RNA molecules

Generally speaking, spatial population structure can be classified according to whether it is implicit or explicit: Implicit population structure arises from the birth-death-migration process of individuals themselves, whereas explicit population structure is imposed to a population by some external boundaries (of course, the external factors can depend on the activity of individuals). In the context of prebiotic evolution, both kinds of population structure have been investigated: (i) spatial self-organization of populations in a diffusion-limited, surface-bound replicator system as implicit structure

In a previous study, we constructed a computational model that can simulate a surface-bound replicator system and compartmentalized replicator system in a unified framework. We therewith investigated the two different types of spatial population structure—explicit versus implicit—with respect to their influence on the macroscopic stability of different evolving replicator systems

Our model of a compartmentalized replicator system consists of two planes of stochastic cellular automata (CA), where one simulates replicator-level processes, and the other simulates vesicle-level processes. The compartmentalized replicator model (compartment model in short) can be converted to the surface-bound replicator model (surface model) simply by removing the vesicle plane. (See

The replicator model investigated here consists of two types of molecules: replicase and parasite. The replicase can catalyze replication of other molecules, whereas the parasite cannot. The parasite switches between two conformations, viz. folded state and template state. When a parasite is in the folded state, it can facilitate the growth of the vesicle in which it resides (explained later), but cannot be replicated by the replicase; when in the template state, it can be replicated, but cannot facilitate the vesicle growth. We assume the conformation switching is so fast that it is always in equilibrium (see also

is complex association/dissociation and replication. We assume that the sum of the rate constants of association/dissociation is fixed and, without loss of generality, set it to 1.

is decay, and it is assumed that its rate is invariant. Each molecule forming a complex also decays independently, which can be considered the decay of

is the reaction that facilitates the vesicle growth as explained in Section “Vesicle Model”.

The consideration of complex formation is to take into account the fact that replication takes finite amount of time, during which the replicase cannot be replicated. Complex formation thus considerably disadvantages the replicase over the parasite (see

The replicator dynamics was modeled in the framework of stochastic cellular automata (CA). The model consists of a two-dimensional grid of

To investigate the evolution of replicators, we introduced “mutations” in

Vesicle-level processes were modeled by using the so-called Cellular Potts Model (CPM)

We implemented a two-dimensional CPM of

Importantly, our compartmentalized replicator model ignores the transport process across vesicle boundaries and the resource for the target volume growth. This simplification is to avoid introducing an extra constraint for survival that is not considered by the replicator model per se (cf. the surface model), which allows us to directly compare spatial self-organization and compartmentalization with respect to their effects on the replicator dynamics. Also notable is that vesicle-level selection is nearly at optimal efficiency, for a difference in

This section is organized in seven parts. Firstly, we explain that the replicator system without spatial population structure is evolutionarily unstable. Secondly, we show that the two models with different spatial population structure—i.e. the surface model and compartment model—allow the evolutionary stability of the replicator system. Moreover, they display an emergent long-term evolutionary trend which is inconceivable in a well-mixed system. To understand these results, in the third and forth section, we analyze each model separately. In the fifth section, we compare the findings from the two models and delineate the similarities and differences between them. In the sixth section, we turn our attention to the condition under which the two models display the macroscopic stability.

The dynamics of the replicator system without population sturcutre can be considered the point of reference for the dynamics with population structure. A simple ordinary differential equation (ODE) model was constructed that describes the well-mixed system of one replicase and one parasite species according to Reaction 1:

We study the behavior of Eqn. 2 as a function of

Colored lines represent the stable attractor of each population as a function of

In summary, the well-mixed replicator system is evolutionarily unstable, so that some sort of spatial population structure is necessary for the feasibility of the evolving interacting replicator system (see

In this section, we examine the evolutionary dynamics of the replicator system with the two types of spatial population structure, viz. compartmentalization and spatial self-organization. We will examine whether the replicator system can survive despite the evolution of parasites and what kind of evolutionary dynamics the system will display.

The surface model and compartment model were initialized by inoculating the system with small populations of the replicase and parasite of an equal size.

To obtain the visual image of our models, snapshots of the simulations are shown in

The long-term behavior of the simulations is depicted as the evolutionary trajectories of the population average of

The lines represent the average value of

To understand these results, we next delve into each model.

To understand how the compartmentalization enables the stable coexistence of the replicase and parasite, we followed the evolutionary dynamics of the internal replicator system of each vesicle. For simplicity, we analyzed a case in which

The dynamics of

As we saw previously, selection on the microscopic level (individual replicators) favors the evolution of stronger parasitism (greater

In the earlier section, we saw that

To separate these two kinds of variations (i.e. target volume and the stability of the coexistence), we modified the model such that the target volume is set to a constant value as long as a vesicle contains at least one parasite molecule. This modification deletes the variation related to the target volume, so that the vesicle-level selection now operates solely on the stability of the coexistence between the replicase and parasite in internal replicator systems, which determines the longevity of vesicles. The evolutionary dynamics of the modified compartment model was investigated in the same manner as in the original model. As

Interestingly, the result also shows that the modified compartment model displayed an evolutionary trend that is opposite to that of the original model (

Our next aim is to understand the link between the longevity of vesicles, the stability of the coexistence in internal replicator systems and the values of

The measurement of the death rate was done through the simulation where the expansion/shrinkage and division of vesicles were forbidden. The volume of vesicles were set to 420, which is approximately the average volume during the evolution simulation of the original vesicle model. A vesicle is considered dead if it contains no molecules or contains only replicase molecules (the frequency of the latter increases as

Interestingly, the result shows an apparent contradiction: the smallest death rate is obtained if

The figure shows a sharp transition in the long-term evolutionary trend in the modified compartment model, where the target volume is fixed, as a function of the mutation rate (solid lines with filled circles). The survival of the flattest happens for greater mutation rates as explained in the main text, whereas the survival of the fittest happens for smaller mutation rates. Such a transition does not occur in the original compartment model (dashed line) because the selection pressure arising from the functionality of the folded state of the parasite (to increase the target volume) is independent of the mutation rate. For the sake of computational speed,

Having established the phenomenological explanation, we next seek for more mechanistic understanding of the relationship between the vesicle death rate and the values of

Interestingly,

In this section, we show that the population dynamics of traveling waves exhibit the property of multiplication, variation and inheritance, and therby it ensures the macroscopic stability of the replicator system. Moreover, we analyze what kind of selection pressure exists among waves, which turns out to be qualitatively different from the vesicle-level selection that arises by default.

As we did in the compartment model, we followed the dynamics of individual traveling waves to uncover the “life history” of waves. For simplicity, we took a case in which

The figure shows consecutive snapshots of a simulation with fixed

Firstly, an individual wave changes its characteristics, as it travels, such that the parasite in the wave back evolves to decrease

Secondly, new waves are generated mostly from the waves that consist of weaker parasites, i.e., those with greater values of

Thirdly, the parasites of a new wave descend from a small sub-population of the parasites of the wave that has generated the new wave. This is simply because of diffusion being finite and parasites replicating locally.

Finally, there is diversity in the population of parasites within a single wave (notice the color variation within each wave). This can be explained by finite diffusivity and stochasticity, which reduce the effect of local competition among parasites (cf.

The last three points respectively allow selection, inheritance and variation in traveling waves. The resulting evolutionary dynamics of traveling waves counteract the evolution of too strong parasitism, and thereby, allow the macroscopic stability of the replicator system. Needless to say, the parallelism with the compartment model is striking.

Additionally, we note that the wave-level selection does not favor an unlimited weakening of parasites. This is because traveling waves generated by weaker parasites have smaller empty space in between, so that stronger parasites can “permeate” through the regions inhabited by too weak parasites and out-compete them (

We have seen above that the surface model differs from the compartment model in an important aspect. Namely, a mesoscopic entity in the surface model (i.e. a traveling wave) can persist for a far longer time than that of the compartment model (i.e. a vesicle). This difference implies a shift in the focus of the selection, in that the wave-level selection tends to increase the fecundity of the wave rather than its longevity in contrast to the default vesicle-level selection (cf.

The evolutionary dynamics of the surface model are depicted from various aspects in

To understand the factors influencing the fecundity of waves, we again analyzed the qualitative behavior of Eqn. 2. From

Therefore we next analyzed the transient behavior of Eqn. 2 for the parameters chosen from the evolutionary trajectory (

Having identified the link between the wave generation in the surface model and the transient behavior of the well-mixed replicator system, we can now intuitively understand the relationship between the wave generation and the parameters

• The two multilevel selection models are quite similar in how they achieve the macroscopic stability of the replicator system: the evolutionary dynamics on the microscopic entities (i.e. replicators) are counteracted by the evolutionary dynamics on the mesoscopic entities (i.e. vesicles or traveling waves).

- In the compartment models, the vesicle-level selection operates on the variability in internal replicator systems generated by the stochastic evolutionary dynamics of replicators.

- In the surface model, selection operates on the level of traveling waves, which have the feature of multiplication, variation and inheritance.

• However, the two types of mesoscopic entities differ in their stability in isolation.

- In the compartment model, a vesicle is an externally imposed mesoscopic entity (explicit multilevel selection), and it is less persistent.

- In the surface model, a traveling wave pattern is a self-organized mesoscopic entity (implicit multilevel selection), and it is thus more persistent than a vesicle (if it is too unstable, it would not self-organize).

• The difference in the stability of mesoscopic entities results in the difference in the focus of mesoscopic selection.

- The vesicle-level selection, by default, operates for the longevity of vesicles due to its greater instability.

- The wave-level selection operates for the fecundity of waves (i.e. the generation of new traveling waves).

• Because multilevel selection keeps the evolution of too severe parasitism at bay, parasites have a trade-off situation between

These strategies gain selective differences through the interactions between the dynamics of microscopic entities and those of mesoscopic entities. This produces a novel trend in the long-term evolution of the replicator system, which can differ between the two multilevel selection models.

- In the compartment models, the death rate of vesicles depends on the stability of the coexistence between the replicase and parasite in the internal replicator system. If the coexistence is deterministically stable, strengthening the deterministic flow of the internal replicator dynamics is favored. If the coexistence is deterministically unstable, weakening the deterministic flow is favored.

The evolutionary dynamics of internal replicator systems are fast when the mutation rate of replicators is high and the population size of internal replicator systems is large. In this case, the coexistence is likely to be deterministically unstable; therefore, weakening the deterministic flow of the replicator dynamics (i.e. Strategy A) is favored. (Similarly, if the internal replicator evolutionary dynamics are slow, Strategy B is favored.)

However, this default direction of the vesicle-level selection can be overruled by an additional selection pressure arising from the (predefined) functionality of the folded state to facilitate the vesicle growth.

- In the surface model, the establishment of new waves depends on the (transient) growth of a population consisting of a small number of replicases and parasites. Therefore, Strategy B is favored.

In this section, we compare the surface model and the compartment model with respect to how the macroscopic stability responds to the change of either the diffusion rate (

Firstly, we investigated what might be called the “ecological” stability of the system, i.e. the range of

Secondly, we investigated the “evolutionary” stability of the system, i.e. the maximal tolerable value of

For simplicity,

These results indicate that there are two different aspects in the macroscopic stability of replicator systems. One is the range of rate constants for which a system displays the macroscopic stability—“ecological stability”. The other is the degree of perturbation to rate constants (i.e. mutation in the sense used here) for which a system displays the macroscopic stability—“evolutionary stability”. Interestingly, these two aspects do not necessarily correspond to one another. Consequently, the two models showing different degrees of ecological stability can show similar degrees of evolutionary stability.

However, as we saw above, the survival area of the surface model is far more sensitive to

To summarize, the macroscopic stability of the interacting replicator system has two different aspects: ecological stability and evolutionary stability. In the surface model, decreasing

The current study compared two multilevel selection models of replicator systems that had identical microscopic entities, but had qualitatively different mesoscopic entities. Despite the difference in the mesoscopic entities, we found that the two models were quite similar in how they achieved the macroscopic stability of the replicator system. Moreover, we also discovered an emergent trade-off situation in microscopic entities, which arose due to the multilevel selection (we note that a similar trade-off situation was previously discovered by van Ballegooijen and Boerlijst

The surface model showed that the parasite, through long-term evolution, increased the time it spent in the state in which it could not function as template, despite the fact that no functionality was predefined for this state. Since the folding of an RNA molecule is likely to reduce the template activity, this result can be interpreted as the implication that in the diffusion-limited surface-bound system the parasite can evolve stable folding “for free”, i.e. without any specific functionality in the folding. The evolution of stable folding might be used as substrate for the further evolution of new functionality. Hence, the current study revealed a novel advantage of spatial self-organization for the evolution of complexity in RNA-like replicator systems.

In the compartment model, we found a simple relationship between the persistency (i.e. longevity) of a vesicle and the dynamical property of the replicator system inside the vesicle. That is, if the evolutionary dynamics of internal replicator systems are fast, the coexistence of the replicase and parasite in internal replicator systems is deterministically unstable; hence, weakening the deterministic flow of the internal replicator dynamics would increase the longevity of vesicles. Similarly, if the evolutionary dynamics of internal replicator systems are slow, the internal replicator coexistence is deterministically stable; hence, strengthening the deterministic flow of the internal replicator dynamics would increase the longevity of vesicles. This point seems to be generally relevant in compartmentalized interacting replicator systems (i.e. the systems where replicases catalyze the replication of templates).

The crucial difference between this study and our previous study

We add that we deliberately avoided making a quantitative comparison between the models with respect to the area of the survival region in the parameter space and the maximum tolerable mutation rate for the following reasons. Firstly, the models have qualitatively different kinds of selection pressure because of the functionality of the folded state of parasites. Secondly, the result of a quantitative comparison depends on the parameters (e.g. one model can have a greater or smaller value of

We should also mention an important simplification made in the current models; i.e., mutations of replicators were restricted to the perturbation of the two parameters of parasites. Other types of mutation processes can have significant impacts on the eco-evolutionary dynamics of replicator systems. The diversity in the replicase population

Finally, let us comment on an interesting difference between the modern cell and the protocell conceived in this study (i.e. the vesicle containing replicators). The difference lies in the concept of genotype, which, we commonly assume in evolutionary biology, is a static state of an individual. Such an assumption can be justified for a modern cell because of the small rate of somatic mutation relative to the lifetime of the cell. However, it is clearly invalid for the protocell in the current study because the internal replicator system—of which population composition can be considered as the “genome” of the protocell—greatly changes its state over time comparable to the lifetime of a vesicle (

There are ongoing efforts to synthesize chemical systems that can undergo self-sustained Darwinian evolution in the laboratory. In particular, Szostak

Traditionally, multilevel selection has been investigated in the context of altruism-egoism dichotomy. In this context, models are constructed by defining the traits (or strategies) of individuals directly with respect to its fitness contributions at different levels of biological organizations either through a priori conception or through inference from observation as such (e.g.

This file consists of the following sections: (1) additional notes to the main text; (2) the extension of Equation 2 with two parasite species; (3) the details of the replicator CA model; (4) the details of Cellular Potts Model (CPM) and coupling between CPM and the replicator CA model; (5) Behavior of the surface model for greater diffusion rates (Figures S3 and S4).

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Survival region in the parameter surface of _{L}_{V}_{T}_{T}_{V}_{V}_{V}_{L}_{V}_{L}

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Maximum mutation rate (_{l}^{max}) for the modified compartment model. _{l}^{max} is plotted as a function of the threshold volume for division (_{T}_{T}_{l}^{max} are similar to those from the original compartment model with _{V}

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Compartment model dynamics. A movie of an early part of an evolution simulation with the compartment model. The parameters were the same as in _{L}_{L}_{L}

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Surface model dynamics. A movie of an early part of the evolution simulation with the surface model depicted in

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Life history of traveling waves. A movie of the simulation depicted in

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Competition between parasites. A movie of a competition experiment with the surface model. The movie shows that there is stabilizing selection on the strength of parasitism (the value of _{L}_{L}

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High diffusion case in the surface model. A movie of a simulation with the surface model for a greater diffusion rate (

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The authors thank two anonymous referees for their suggestions to the manuscript. NT thanks D. van der Post for extensive discussion on multilevel selection in general and on the manuscript.