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Table 2 Constraints on model parameters

From: A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Condition Limits on Uge Limits on γ Limits on pDZg Limits on fge
R oe R oo U ge ≤ (1 - γ) γγmax gewhere γ max g e = 1 1 + V g e V e MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFZoWzdaWgaaWcbaGagiyBa0MaeiyyaeMaeiiEaGNaem4zaCMaemyzaugabeaakiabg2da9maalaaabaGaeGymaedabaGaeGymaeJaey4kaSYaaSaaaeaacqWGwbGvdaWgaaWcbaGaem4zaCMaemyzaugabeaaaOqaaiabdAfawnaaBaaaleaacqWGLbqzaeqaaaaaaaaaaa@4011@   
R go R oo U g e ( 1 γ ) P A F g G P A F e E MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGvbqvdaWgaaWcbaGaem4zaCMaemyzaugabeaakiabgsMiJkabcIcaOiabigdaXiabgkHiTGGaciab=n7aNjabcMcaPmaalaaabaGaemiuaaLaemyqaeKaemOray0aa0baaSqaaiabdEgaNbqaaiabdEeahbaaaOqaaiabdcfaqjabdgeabjabdAeagnaaDaaaleaacqWGLbqzaeaacqWGfbqraaaaaaaa@438B@   p g D Z p g max D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyizImQaemiCaa3aa0baaSqaaiabdEgaNjGbc2gaTjabcggaHjabcIha4bqaaiabdseaejabdQfaAbaaaaa@3D07@ f g e 1 P A F e E MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaWgaaWcbaGaem4zaCMaemyzaugabeaakiabgsMiJoaalaaabaGaeGymaedabaGaemiuaaLaemyqaeKaemOray0aa0baaSqaaiabdwgaLbqaaiabdweafbaaaaaaaa@3972@
R ge R go U ge ≥ -γ γγ neg where γ n e g = 1 1 + V e V g e MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFZoWzdaWgaaWcbaGaemOBa4MaemyzauMaem4zaCgabeaakiabg2da9maalaaabaGaeGymaedabaGaeGymaeJaey4kaSYaaSaaaeaacqWGwbGvdaWgaaWcbaGaemyzaugabeaaaOqaaiabdAfawnaaBaaaleaacqWGNbWzcqWGLbqzaeqaaaaaaaaaaa@3D50@   
R ge R oe U g e ( 1 γ ) ε P A F g G ( 1 ε ) P A F e E MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGvbqvdaWgaaWcbaGaem4zaCMaemyzaugabeaakiabgwMiZkabgkHiTiabcIcaOiabigdaXiabgkHiTGGaciab=n7aNjabcMcaPmaalaaabaGae8xTduMaemiuaaLaemyqaeKaemOray0aa0baaSqaaiabdEgaNbqaaiabdEeahbaaaOqaaiabcIcaOiabigdaXiabgkHiTiab=v7aLjabcMcaPiabdcfaqjabdgeabjabdAeagnaaDaaaleaacqWGLbqzaeaacqWGfbqraaaaaaaa@4B5C@   p g D Z p g n e g D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyizImQaemiCaa3aa0baaSqaaiabdEgaNjabd6gaUjabdwgaLjabdEgaNbqaaiabdseaejabdQfaAbaaaaa@3CF0@ f g e ε ( 1 ε ) P A F e E MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaWgaaWcbaGaem4zaCMaemyzaugabeaakiabgwMiZkabgkHiTmaalaaabaacciGae8xTdugabaGaeiikaGIaeGymaeJaeyOeI0Iae8xTduMaeiykaKIaemiuaaLaemyqaeKaemOray0aa0baaSqaaiabdwgaLbqaaiabdweafbaaaaaaaa@405F@
R ge ≤ 1   γγmin gewhere γ min g e = 1 1 + F 1 2 ( V g / r t 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFZoWzdaWgaaWcbaGagiyBa0MaeiyAaKMaeiOBa4Maem4zaCMaemyzaugabeaakiabg2da9maalaaabaGaeGymaedabaGaeGymaeJaey4kaSYaaSaaaeaacqWGgbGrdaqhaaWcbaGaeGymaedabaGaeGOmaidaaaGcbaWaaSGbaeaacqGGOaakcqWGwbGvdaWgaaWcbaGaem4zaCgabeaaaOqaaiabdkhaYnaaDaaaleaacqWG0baDaeaacqaIYaGmaaGccqGGPaqkaaaaaaaaaaa@4503@   
R oo ≥ 0   γγ o where γ o = 1 1 + F 2 2 ( V g / r t 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFZoWzdaWgaaWcbaGaem4Ba8gabeaakiabg2da9maalaaabaGaeGymaedabaGaeGymaeJaey4kaSIaemOray0aa0baaSqaaiabikdaYaqaaiabikdaYaaakiabcIcaOmaalyaabaGaemOvay1aaSbaaSqaaiabdEgaNbqabaaakeaacqWGYbGCdaqhaaWcbaGaemiDaqhabaGaeGOmaidaaaaakiabcMcaPaaaaaa@3F90@