Eco-evolutionary dynamics of clonal multicellular life cycles

  1. Vanessa Ress
  2. Arne Traulsen
  3. Yuriy Pichugin  Is a corresponding author
  1. Max Planck Institute for Evolutionary Biology, Germany
  2. Hamburg Center for Health Economics, University of Hamburg, Germany
  3. Department of Ecology and Evolutionary Biology, Princeton University, United States
6 figures, 2 tables and 1 additional file


Model of clonal life cycles.

(A) There are four processes occurring in the model: groups grow by cell division, which occurs with rates bi, groups spontaneously die with rates di, groups fragment immediately upon exceeding maturity size m (3 in this example), according to predefined fragmentation pattern κ (1 + 1 + 1 + 1 here), and groups of size i die due to the competition with groups of size j at rates Kij. (B) Together, group growth and fragmentation constitute a life cycle, in which initially small groups grow in size and eventually fragment, giving rise to more small groups. Colors represent group sizes: red, solitary cells; green, bicellular groups; blue, tricellular groups.

A single life cycle comes to a stationary state.

(A) For a unicellular life cycle 1+1, our model is equivalent to logistic growth. There, the number of solitary cells (red) approaches the carrying capacity from any initial state. (B, C) For multicellular life cycles (2 + 1 depicted), the population also approaches such a stationary state from any initial state. (B) shows the dynamics of solitary cells (red) and bicellular groups (green) with time. (C) shows the trajectories of the population composition, the dot marks the stationary state. (B) and (C) show the same dataset.

Competitive interactions can lead to the bistability between life cycles (A), a dominance of either of them (B,C), or their coexistence (D).

Each panel shows the evolutionary trajectories of populations with various initial abundances of the life cycles 1 + 1 and 2 + 1 (lines) and all final states (dots). In (A), colors indicate to which of two stationary states the trajectory converges. Birth and death rates are b=(1,0.5) and d=(0,0); they favor the unicellular life cycle 1 + 1 in the absence of competition. Simulations performed on each panel only differ in the competition matrix K shown in panels.

Evolution in a population with multiple competing life cycles.

(A) The schematics of the life cycles taking part in evolution. Groups colored according to the number of cells. (B) The frequencies of various classes of outcomes. A single life cycle (yellow) is the most common. Coexistence of life cycles (red) and bistability between them (blue) are less common. More complex composite configurations (gray) are also possible, but found rarely.

Constrained triplets demonstrate fewer patterns of pairwise invasion.

(A) For a combination of three life cycles, there are 223=64 pairwise invasion patterns possible. For the triplet κ(1)=5+3,κ(2)=4+4,κ(3)=4+2+2, the rates of all processes (bi,di,Ki,j) were randomly sampled from an exponential distribution with unit rate parameter. Then the pairwise invasion pattern was identified. All 64 possible patterns were observed in these simulations. (B) In a similar investigation for the triplet κ(C1)=2+2,κ(C2)=4+4,κ(M)=4+2+2, in which κ(C1) and κ(C2) constrain κ(M), only eight patterns were found; see the main text for a discussion.

There are only eight patterns of pairwise invasion in a constrained triplet of life cycles.

Four patterns are shown here and four more are symmetric to them. Blue lines are population dynamics trajectories with different initial composition of the population. Red points are final states. Black arrows show directions of invasion from rare. (A) In a hierarchical dominance, one of the constraining life cycles outcompetes the two others from any initial condition. (B) In a bistability situation, each of the two constraining life cycles is able to outcompete the third life cycle. Which of them will survive depends on the initial conditions. Trajectories converging to different stationary states are highlighted with different colors. (C) In a coexistence, all three life cycles survive to a stationary state. (D) In a non-hierarchical dominance, one of the constraining life cycles outcompetes another; however, in the abundance of the constrained life cycle, the dominance is reversed. The parameters used to produce these figures are presented in Appendix 5.


Table 1
Competitive interactions in a pair of life cycles can lead to the dominance of either life cycle, their coexistence, or bistability.
κ(1) cannot invade into κ(2)
κ(1) can invade into κ(2)
κ(2) cannot invade into κ(1)
Bistability between κ(1) and κ(2)Dominance of κ(1)
κ(2) cannot invade into κ(1)
Dominance of Coexistence of κ(1) and κ(2)
Table 2
Observation frequencies of different kinds of evolutionary outcomes in a population with multiple competing life cycles.
Single life cycle0.751
Coexistence ofTwo life cycles0.121
Three life cycles0.044
Four or more life cycles0.003
Multistability betweenTwo life cycles0.065
Three life cycles0.002
Four or more life cycles0
Composite configurationsBistability with a coexisting pair0.007
Other configurations0.007

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  1. Vanessa Ress
  2. Arne Traulsen
  3. Yuriy Pichugin
Eco-evolutionary dynamics of clonal multicellular life cycles
eLife 11:e78822.