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Table 3 Summary of Model 1A: Evolution of competitive ability with no policing. With no policing, a = ai. = aij = 0.

From: The evolution of competition and policing: opposing selection within and among groups

  Half sib Full sib
Mean fitness ( w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG3bWDgaqeaaaa@2E3B@ ) 1 - (z0 + 2qz a ) 1 - (z0 + 2qz a )
Δq within groups (Δqw) p q z a ( p 2 z 1 H S + 2 p q + 1 2 z 2 H S + q 2 z 3 H S 3 2 ) / 2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@56D0@ p q z a ( p 2 z 2 F S + 2 p q z 4 F S + q 2 z 5 F S 1 ) / 2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCcqWGXbqCcqWG6bGEdaWgaaWcbaGaemyyaegabeaakmaabmaabaWaaSaaaeaacqWGWbaCdaahaaWcbeqaaiabikdaYaaaaOqaaiabdQha6naaBaaaleaacqaIYaGmcqWGgbGrcqWGtbWuaeqaaaaakiabgUcaRmaalaaabaGaeGOmaiJaemiCaaNaemyCaehabaGaemOEaO3aaSbaaSqaaiabisda0iabdAeagjabdofatbqabaaaaOGaey4kaSYaaSaaaeaacqWGXbqCdaahaaWcbeqaaiabikdaYaaaaOqaaiabdQha6naaBaaaleaacqaI1aqncqWGgbGrcqWGtbWuaeqaaaaakiabgkHiTiabigdaXaGaayjkaiaawMcaaiabc+caViabikdaYiqbdEha3zaaraaaaa@52F0@
Δq between groups (Δqb) -pqz a /4 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG3bWDgaqeaaaa@2E3B@ -pqz a /2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG3bWDgaqeaaaa@2E3B@
Δq total (Δqt) p q z a ( p 2 z 1 H S + 2 p q + 1 2 z 2 H S + q 2 z 3 H S 2 ) / 2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@55CA@ p q z a ( p 2 z 2 F S + 2 p q z 4 F S + q 2 z 5 F S 2 ) / 2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCcqWGXbqCcqWG6bGEdaWgaaWcbaGaemyyaegabeaakmaabmaabaWaaSaaaeaacqWGWbaCdaahaaWcbeqaaiabikdaYaaaaOqaaiabdQha6naaBaaaleaacqaIYaGmcqWGgbGrcqWGtbWuaeqaaaaakiabgUcaRmaalaaabaGaeGOmaiJaemiCaaNaemyCaehabaGaemOEaO3aaSbaaSqaaiabisda0iabdAeagjabdofatbqabaaaaOGaey4kaSYaaSaaaeaacqWGXbqCdaahaaWcbeqaaiabikdaYaaaaOqaaiabdQha6naaBaaaleaacqaI1aqncqWGgbGrcqWGtbWuaeqaaaaakiabgkHiTiabikdaYaGaayjkaiaawMcaaiabc+caViabikdaYiqbdEha3zaaraaaaa@52F2@