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Table 6 Summary of Model 1A: Evolution of competitive ability with fixed policing = a = ai = aij

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 - z(1 - a.))(1 - ca.) (1 - z(1 - a.))(1 - ca.)
Δq within groups (Δqw) p q z a ( 1 a . ) ( p 2 z 1 H S + 2 p q + 1 2 z 2 H S + q 2 z 3 H S 3 ( 1 a ) 2 ) / ( 2 w ¯ F S ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@654D@ p q z a ( 1 a . ) ( p 2 z 2 F S + 2 p q z 4 F S + q 2 z 4 F S + a 1 ) / ( 2 w ¯ F S ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@5EE9@
Δq between groups (Δqb) -pqza.(1 - a.)(1 - a . c)/(4 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG3bWDgaqeaaaa@2E3B@ HS ) -pqza.(1 - a.)(1 - a . c)/(2 w ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG3bWDgaqeaaaa@2E3B@ FS )
Δq total (Δqt) p q z a ( 1 a . ) ( p 2 z 1 H S + 2 p q + 1 2 z 2 H S + q 2 z 3 H S + a ( 3 + c ) 2 2 ) / ( 2 w ¯ H S ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6779@ p q z a ( 1 a . ) ( p 2 z 2 F S + 2 p q z 4 F S + q 2 z 5 F S + a ( 1 + c ) 2 ) / ( 2 w ¯ F S ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6397@