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Table 9 Summary of Model 2: Evolution of policing effort with fixed levels of competition = z.

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

  Half sib Full sib
Among-family variance in policing (σ2a_AF) tua a 2/2 tua a 2
Mean fitness (W) (1 - c a ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqeaaaa@2E0F@ )(1 - z(1 - a ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqeaaaa@2E0F@ )) - czσ2 a_AF_HS (1 - c a ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqeaaaa@2E0F@ )(1 - z(1 - a ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGHbqygaqeaaaa@2E0F@ )) - czσ2 a_AF_FS
Δu within groups (Δuw) a a c t u 4 w ¯ H S ( 3 z ( 3 ( 2 a ¯ + a 2 H S ) ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabgkHiTiabdggaHnaaBaaaleaacqWGHbqyaeqaaOGaem4yamMaemiDaqNaemyDauhabaGaeGinaqJafm4DaCNbaebadaWgaaWcbaGaemisaGKaem4uamfabeaaaaGcdaqadaqaaiabiodaZiabgkHiTiabdQha6naabmaabaGaeG4mamJaeyOeI0YaaeWaaeaacqaIYaGmcuWGHbqygaqeaiabgUcaRiabdggaHnaaBaaaleaacqaIYaGmcqWGibascqWGtbWuaeqaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaacaGLOaGaayzkaaaaaa@4B77@ a a c t u 2 w ¯ F S ( 1 z ( 1 ( a ¯ + a 4 F S ) / 2 ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabgkHiTiabdggaHnaaBaaaleaacqWGHbqyaeqaaOGaem4yamMaemiDaqNaemyDauhabaGaeGOmaiJafm4DaCNbaebadaWgaaWcbaGaemOrayKaem4uamfabeaaaaGcdaqadaqaaiabigdaXiabgkHiTiabdQha6naabmaabaGaeGymaeJaeyOeI0YaaeWaaeaacuWGHbqygaqeaiabgUcaRiabdggaHnaaBaaaleaacqaI0aancqWGgbGrcqWGtbWuaeqaaaGccaGLOaGaayzkaaGaei4la8IaeGOmaidacaGLOaGaayzkaaaacaGLOaGaayzkaaaaaa@4C4D@
Δu between groups (Δub) a a t u 4 w ¯ H S ( c + z ( 1 + c ( 1 ( a ¯ + a 2 H S ) ) ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdggaHnaaBaaaleaacqWGHbqyaeqaaOGaemiDaqNaemyDauhabaGaeGinaqJafm4DaCNbaebadaWgaaWcbaGaemisaGKaem4uamfabeaaaaGcdaqadaqaaiabgkHiTiabdogaJjabgUcaRiabdQha6naabmaabaGaeGymaeJaey4kaSIaem4yam2aaeWaaeaacqaIXaqmcqGHsisldaqadaqaaiqbdggaHzaaraGaey4kaSIaemyyae2aaSbaaSqaaiabikdaYiabdIeaijabdofatbqabaaakiaawIcacaGLPaaaaiaawIcacaGLPaaaaiaawIcacaGLPaaaaiaawIcacaGLPaaaaaa@4E2C@ a a t u 2 w ¯ F S ( c + z ( 1 + c ( 1 ( a ¯ + a 2 H S ) ) ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaWcaaqaaiabdggaHjabdggaHjabdsha0jabdwha1bqaaiabikdaYiqbdEha3zaaraWaaSbaaSqaaiabdAeagjabdofatbqabaaaaOWaaeWaaeaacqGHsislcqWGJbWycqGHRaWkcqWG6bGEdaqadaqaaiabigdaXiabgUcaRiabdogaJnaabmaabaGaeGymaeJaeyOeI0YaaeWaaeaacuWGHbqygaqeaiabgUcaRiabdggaHnaaBaaaleaacqaIYaGmcqWGibascqWGtbWuaeqaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaacaGLOaGaayzkaaaacaGLOaGaayzkaaaaaa@4DEE@
Δu total (Δut) a a t u ( c + z ( 1 4 + c ( 1 ( 3 a ¯ 4 + a 2 H S 2 ) ) ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGHbqydaWgaaWcbaGaemyyaegabeaakiabdsha0jabdwha1naabmaabaGaeyOeI0Iaem4yamMaey4kaSIaemOEaO3aaeWaaeaadaWcaaqaaiabigdaXaqaaiabisda0aaacqGHRaWkcqWGJbWydaqadaqaaiabigdaXiabgkHiTmaabmaabaWaaSaaaeaacqaIZaWmcuWGHbqygaqeaaqaaiabisda0aaacqGHRaWkdaWcaaqaaiabdggaHnaaBaaaleaacqaIYaGmcqWGibascqWGtbWuaeqaaaGcbaGaeGOmaidaaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaaa@4D1B@ a a t u ( c + z ( 1 2 + c ( 1 ( a ¯ 2 + a 2 H S ) ) ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGHbqydaWgaaWcbaGaemyyaegabeaakiabdsha0jabdwha1naabmaabaGaeyOeI0Iaem4yamMaey4kaSIaemOEaO3aaeWaaeaadaWcaaqaaiabigdaXaqaaiabikdaYaaacqGHRaWkcqWGJbWydaqadaqaaiabigdaXiabgkHiTmaabmaabaWaaSaaaeaacuWGHbqygaqeaaqaaiabikdaYaaacqGHRaWkcqWGHbqydaWgaaWcbaGaeGOmaiJaemisaGKaem4uamfabeaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaGaayjkaiaawMcaaaaa@4B1D@