Living systems are hierarchically structured, whereby replicating components are grouped into reproducing collectives; URLanelles are grouped into cells; cells, into URLanisms; and URLanisms, into colonies. We consider how such hierarchically-structured replicator systems evolve along a continuum -- between cooperation and cheating. Cooperation is selected through competition among collectives, whereas cheating is selected through competition among replicating components within collectives . We determine how the evolution depends on the number of replicating components per collective (N) and the mutation rate of replicating components (m)  such that evolution becomes increasingly independent of m as s decreases (i.e., \alpha}\downarrow0 \downarrow0 . We demonstrate a scaling relation that holds when selection for cooperation exactly balances out selection for cheating: N \propto m^{-\alpha, where \alpha(>0)increases with selection strength. Increasing N or m drives the system towards a phase where cheating evolves, and the above scaling relation separates this phase from that where cooperation evolves. We develop a simple theory that can account for this scaling relation using moment evolution equations and clarify the limit of applicability of the theory using time-backward observation}  .
The evolution of altruism is a key step in major evolutionary transitions. Previous theoretical studies often assume that individuals adopt one of two possible strategies, altruism or selfishness. In reality, however, cooperative strategies are likely to constitute a continuum between selfishness and altruism. Here, we investigate how such continuous variation affects the evolution of altruism through multilevel selection. In our model, altruism is favoured by selection among groups, whereas selfishness is favoured by selection within groups . We determine how evolution depends on the number of replicators per group (N) , mutation rate (m) , and selection strength (s). We find that decreasing N or m promotes evolution toward altruism, and if this evolution is exactly balanced out by evolution towards selfishness, N and m satisfy a scaling relation N\,\propto\, m^{-\alpha such that evolution becomes increasingly independent of m as s decreases (i.e., \alpha}\downarrow0 as s\downarrow0) . , where \alpha(>0)increases with selection strength. Increasing N or m drives the system towards a phase where cheating evolves, and the above scaling relation separates this phase from that where cooperation evolves. We develop a simple theory that can account for this scaling relation using moment evolution equations and clarify the limit of applicability of the theory using time-backward observation} This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases. We show that this difference is caused by the assumption implicit in binary-trait models that mutation causes convergent evolution even in the absence of selection. Our study illustrates how considering quantitative variation can be important for understanding the evolution of altruism during major evolutionary transitions .
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Living systems are hierarchically structured, whereby replicating components are grouped into reproducing collectives; URLanelles are grouped into cells; cells, into URLanisms; and URLanisms, into colonies. We consider how such hierarchically-structured replicator systems evolve along a continuum -- between cooperation and cheating. Cooperation is selected through competition among collectives, whereas cheating is selected through competition among replicating components within collectives
The evolution of altruism is a key step in major evolutionary transitions. Previous theoretical studies often assume that individuals adopt one of two possible strategies, altruism or selfishness. In reality, however, cooperative strategies are likely to constitute a continuum between selfishness and altruism. Here, we investigate how such continuous variation affects the evolution of altruism through multilevel selection. In our model, altruism is favoured by selection among groups, whereas selfishness is favoured by selection within groups
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the
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replicating components per collective
replicators per group
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and the mutation rate of replicating components
, mutation rate
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, and selection strength (s). We find that decreasing N or m promotes evolution toward altruism, and if this evolution is exactly balanced out by evolution towards selfishness, N and m satisfy a scaling relation N\,\propto\, m^{-\alpha
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as s
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)
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We demonstrate a scaling relation that holds when selection for cooperation exactly balances out selection for cheating: N \propto m^{-\alpha
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This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases. We show that this difference is caused by the assumption implicit in binary-trait models that mutation causes convergent evolution even in the absence of selection. Our study illustrates how considering quantitative variation can be important for understanding the evolution of altruism during major evolutionary transitions