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Ordering structured populations in multiplayer cooperation games.

Peña J, Wu B, Traulsen A - J R Soc Interface (2016)

Bottom Line: Spatial structure greatly affects the evolution of cooperation.If population structure S1 is greater than population structure S1 in the containment or the volume order, then S1 can be considered a stronger promoter of cooperation.Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.

View Article: PubMed Central - PubMed

Affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany pena@evolbio.mpg.de.

No MeSH data available.


Related in: MedlinePlus

Comparability in the containment order. The structure coefficients  and  cross exactly once, implying that  and  are comparable in the containment order. Moreover,  crosses  from below; hence  is greater than  in the containment order  Likewise,  Contrastingly, the structure coefficients  and  cross exactly twice, implying that  and  are incomparable in the containment order  i.e. neither  nor  For such cases, the volume order provides an alternative way to order these structures. Here,  is a group splitting model with m = 10 groups of maximum size n = 6 and rare probability of splitting (),  is a cycle of size N = 60 and  is a group splitting model with m = 6, n = 10 and
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RSIF20150881F2: Comparability in the containment order. The structure coefficients and cross exactly once, implying that and are comparable in the containment order. Moreover, crosses from below; hence is greater than in the containment order Likewise, Contrastingly, the structure coefficients and cross exactly twice, implying that and are incomparable in the containment order i.e. neither nor For such cases, the volume order provides an alternative way to order these structures. Here, is a group splitting model with m = 10 groups of maximum size n = 6 and rare probability of splitting (), is a cycle of size N = 60 and is a group splitting model with m = 6, n = 10 and

Mentions: It can happen that neither is entirely contained in nor is entirely contained in In these cases, and are incomparable in the containment order (i.e. neither nor hold) and we write We show in Proposition 2 in the electronic supplementary material that a sufficient condition leading to such incomparability is that the sequences and cross twice (figure 2). In this case, there exist both a subset of cooperation games favoured under but not under and a subset of cooperation games favoured under but not under Figure 2.


Ordering structured populations in multiplayer cooperation games.

Peña J, Wu B, Traulsen A - J R Soc Interface (2016)

Comparability in the containment order. The structure coefficients  and  cross exactly once, implying that  and  are comparable in the containment order. Moreover,  crosses  from below; hence  is greater than  in the containment order  Likewise,  Contrastingly, the structure coefficients  and  cross exactly twice, implying that  and  are incomparable in the containment order  i.e. neither  nor  For such cases, the volume order provides an alternative way to order these structures. Here,  is a group splitting model with m = 10 groups of maximum size n = 6 and rare probability of splitting (),  is a cycle of size N = 60 and  is a group splitting model with m = 6, n = 10 and
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759793&req=5

RSIF20150881F2: Comparability in the containment order. The structure coefficients and cross exactly once, implying that and are comparable in the containment order. Moreover, crosses from below; hence is greater than in the containment order Likewise, Contrastingly, the structure coefficients and cross exactly twice, implying that and are incomparable in the containment order i.e. neither nor For such cases, the volume order provides an alternative way to order these structures. Here, is a group splitting model with m = 10 groups of maximum size n = 6 and rare probability of splitting (), is a cycle of size N = 60 and is a group splitting model with m = 6, n = 10 and
Mentions: It can happen that neither is entirely contained in nor is entirely contained in In these cases, and are incomparable in the containment order (i.e. neither nor hold) and we write We show in Proposition 2 in the electronic supplementary material that a sufficient condition leading to such incomparability is that the sequences and cross twice (figure 2). In this case, there exist both a subset of cooperation games favoured under but not under and a subset of cooperation games favoured under but not under Figure 2.

Bottom Line: Spatial structure greatly affects the evolution of cooperation.If population structure S1 is greater than population structure S1 in the containment or the volume order, then S1 can be considered a stronger promoter of cooperation.Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.

View Article: PubMed Central - PubMed

Affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany pena@evolbio.mpg.de.

No MeSH data available.


Related in: MedlinePlus