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  1. Evaluation Summary:

    This manuscript models the evolution of simple multicellular life cycles using evolutionary game theory. The authors discuss natural selection between different life cycles by modeling growth, fragmentation, and interactions between propagules, discovering conditions for selection of a single life cycle or coexistence of multiple ones. Overall, the model is biologically intuitive, the results are rigorous, and the implications for the evolution of multicellularity are interesting.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

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  2. Reviewer #1 (Public Review):

    In the current manuscript, the authors developed a general framework to study the evolution of multicellular life cycles and the investigated evolutionary advantage of certain life cycles and multicellular structures over other ones. Simple multicellular life cycles are comprised of growth of the propagule into a colony and its fragmentation to give rise to new propagule. For the evolution of multicellularity, a multicellular trait is not only identified by the genotype of individuals inside each propagule but also the life cycle it is programmed for growth and fragmentation. There is not a single fitness value but a set of fitness values, each assigned to one stage of life-cycle growth before fragmentation. The question is how natural selection chooses one life cycle over the other one. In other words how a robust life cycle is evolved from random fragmentation processes. Previous theoretical approaches mainly considered overall growth rate as a measure of advantage for a life cycle.

    This work is based on an extension of the several previous works of Pichugin and Traulsen on the subject. It introduces interaction between different stages of life cycle, as well as interaction between two traits, identified with differences in life cycle patterns. For brevity and focus on life cycle patterns, possible intra-propagule genotypic heterogeneity is ignored. (This has been addressed by same authors and others in past works.) A deterministic system of ordinary differential equations is set to describe the growth and competition of different life cycle stages. Abundance of each life cycle stage is the dynamical quantity and the dynamics is reminiscent of a general replicator equation for a complex multicellular structure. The interaction terms is identified by a kernel matrix, K_ij, which is effectively fitness payoff for a group of size i when encountered with a group of size j. Interaction terms introduces effective elevation in death rates. They focus on two main scenarios, 1) a killer kernel where the kernel is only a function of and 2) a victim kernel where is only a function of. In some cases authors considered more general cases including arbitrary (random-valued).

    Authors first considered the dynamics of a single life-cycles where the interaction between populations at different stages of life cycles changes the growth dynamics. They observe that the general dynamics and steady states are governed by overall growth rate of the whole lief-cycle as has been observed in the absence of group-group interactions. They suggest the modified steady states while there is no qualitative changes from no-interaction (diagonal kernel or constant-selection) case.

    The second part of the work focuses of competition between two and multiple life cycles in the presence of the group-group interactions. The authors considered invasion of one rare multicellular life cycle into another resident multi-cellular life cycle. They also consider competition between multiple life cycles. They discussed the condition for ESS in this scenario. Four interaction schemes including killer and victim kernels are discussed for some examples of fragmentation. Furthermore, competition of multiple life cycle is discussed. In particular a three life cycle competition is discussed using similar kernel interactions which now resemble a rock-paper-scissor type payoff in some cases.

    I believe the modeling framework to address competition and natural selection between life cycles in the same framework that introduces interaction between different stages of a same life cycle is a great step forward in modeling evolution of simple multicellularity, The results are very clear and I think further analysis of the model introduced in this work can have a strong impact on our understanding of the evolution of multicellular life cycles.

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  3. Reviewer #2 (Public Review):

    The authors investigate the impact of group interactions and the invasion of groups of cells with a different life cycle on the evolution of multicellular cell groups. The authors consider that each group of cells can contain a different number of cells. The authors were particularly interested in understanding how cell groups evolve when there is competition between different groups considering that each cell group can divide to increase the number of cells in each group, die, fragment into different groups of cells, and that there can be an invasion from rare mutant cells that change the patterns of fragmentation. The evolution of the fragmentation patterns are of particular interest in this paper since fragmentation determines the life cycle of a group of cells. To model the invasion between groups, the authors develop a mathematical model which considers that "invader" cells in a particular life cycle could enter a population of many groups of cells with a defined life cycle. The "invader" cell group can change the life cycle of the population or can die and the group conserves its previous life cycle. First, the authors find that the type of competition between the groups determines the growth of the number of groups with a different number of cells when invasions are not taken into account. Then, the authors analyze the impact of invasions and find that the type of competition between groups and the initial conditions determines the final abundance of the fragmentation patterns and can lead to only observing one particular fragmentation pattern, a bi-stability situation where the initial conditions determine which fragmentation pattern will only be observed in the long term and the coexistence of multiple fragmentation patterns.

    This is a very interesting paper with a strong mathematical foundation. This is a useful contribution to understand the long-term equilibrium of the evolution of life cycles in cells. The claims and conclusions are well backed up by the analysis conducted.

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  4. Reviewer #3 (Public Review):

    In their previous work, the authors studied the problem of clonal life cycles evolution. Here they extended the previous work by developing a model that describes such evolution under the presence of competition between groups. The model is studied using a combination of analytical methods and numerical simulations. The results obtained are more biologically justifiable than those obtained in the linear model that neglects competition between groups.


    - As is known from previous work, in a linear model (when the competition is absent), a typical outcome is an exponential growth in the number of groups of some life cycle, which can be considered as a natural limitation of the model. Obviously, this limitation is removed in the presented paper.

    - The authors provide analytical results for some special cases of the model and compare them with those obtained in the absence of competition. In the general case of the model, when analytical progress is impossible, the authors provide the results of extensive numerical simulations. All these results allow the authors to build a clear picture of the process under study.

    - The authors study the evolutionary stability of various life cycles. Specifically, it was shown that only binary fragmentation life cycles can be evolutionary stable strategies. This result holds in the linear model as well. In contrast to the linear model, more complex dynamics can be observed in the general case (like the existence of several evolutionary stable strategies).

    Overall, in my opinion, the model significantly contributes to our understanding of the evolution of clonal life cycles. Moreover, it illuminates to what extent are adequate the results of simple linear models in describing the processes under consideration.

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