The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation , here, is a persistent behavioural pattern of individual entities pooling and sharing resources. Examples are: individual cells forming multicellular systems whose various parts pool and share nutrients; pack animals pooling and sharing prey; families firms, or modern nation states pooling and sharing financial resources. In these examples, each atomistic decision, at a point in time, of the better-off entity to cooperate poses a puzzle: the better-off entity will book an immediate net loss -- why should it cooperate? For each example, specific explanations have been put forward. Here we point out a very general mechanism -- a sufficient null model -- whereby cooperation can evolve. The mechanism is based the following insight : natural growth processes tend to be multiplicative . In multiplicative growth, ergodicity is broken in such a way that fluctuations have a net-negative effect on the time-average growth rate , although they have no effect on the growth rate of the ensemble average. Pooling and sharing resources reduces fluctuations, which leaves ensemble averages unchanged but -- contrary to common perception -- increases the time-average growth rate for each cooperator .
Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness gain in a cooperative transaction which, through reciprocity or relatedness, finds its way back from recipient to donor. We seek the source of this fitness gain. Our analysis rests on the insight that evolutionary processes are typically multiplicative and noisy. Fluctuations have a net negative effect on the long-time growth rate of resources but no effect on the growth rate of their expectation value. This is an example of non-ergodicity. By reducing the amplitude of fluctuations, pooling and sharing increases the long-time growth rate for cooperating entities, meaning that cooperators outgrow similar non-cooperators. We identify this increase in growth rate as the net fitness gain, consistent with the concept of geometric mean fitness in the biological literature. This constitutes a fundamental mechanism for the evolution of cooperation. Its minimal assumptions make it a candidate explanation of cooperation in settings too simple for other fitness gains, such as emergent function and specialization, to be probable. One such example is the transition from single cells to early multicellular life .
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The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation , here,
Cooperation
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behavioural pattern of individual
behavioral pattern of
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Examples are: individual cells forming multicellular systems whose various parts pool and share nutrients; pack animals pooling and sharing prey; families firms, or modern nation states pooling and sharing financial resources. In these examples, each atomistic decision, at a point in time, of the better-off entity to cooperate poses a puzzle: the better-off entity will book an immediate net loss -- why should it cooperate? For each example, specific explanations have been put forward. Here we point out a very general mechanism -- a sufficient null model -- whereby cooperation can evolve. The mechanism is based the following insight : natural growth processes tend to be multiplicative . In multiplicative growth, ergodicity is broken in such a way that fluctuations have a net-negative
Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness gain in a cooperative transaction which, through reciprocity or relatedness, finds its way back from recipient to donor. We seek the source of this fitness gain. Our analysis rests on the insight that evolutionary processes are typically multiplicative and noisy. Fluctuations have a net negative
R
time-average growth rate , although they have
long-time growth rate of resources but
R
the ensemble average. Pooling and sharing resources reduces fluctuations, which leaves ensemble averages unchanged but -- contrary to common perception -- increases the time-average
their expectation value. This is an example of non-ergodicity. By reducing the amplitude of fluctuations, pooling and sharing increases the long-time
R
each cooperator
cooperating entities, meaning that cooperators outgrow similar non-cooperators. We identify this increase in growth rate as the net fitness gain, consistent with the concept of geometric mean fitness in the biological literature. This constitutes a fundamental mechanism for the evolution of cooperation. Its minimal assumptions make it a candidate explanation of cooperation in settings too simple for other fitness gains, such as emergent function and specialization, to be probable. One such example is the transition from single cells to early multicellular life