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Table 1 Useful transformations for computing expectations and bounds for the rate of Muller's ratchet in diploids.

From: Quantifying the threat of extinction from Muller's ratchet in the diploid Amazon molly (Poecilia formosa)

Genome type Recessive Co-dominant Dominant
  (h = 0) (h = 0.5) (h = 1)
(1) asexual haploid U s d m s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4Camhaaaaa@3359@ U s d m s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4Camhaaaaa@3359@ U s d m s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4Camhaaaaa@3359@
(2) asexual diploid Core-Genome-Model Equal-Contribution-Model Every-Allele-Needed-Model
  (extreme forms are unrealistic) (useful first order approximation) (most unrealistic)
  Stage 1   Stage 1
  (MA is easy, may be harmless):   (MA is hard, may be impossible):
  2 U s d m s h 0 s h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4CamNaemiAaGgaaOGaeyOKH4Acfa4aaSaaaeaacqaIWaamaeaacqWGZbWCcqWGObaAaaaaaa@3BEF@ 2 U s d m s h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4CamNaemiAaGgaaaaa@35A4@ 2 U s d m s h > > 0 s h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaem4CamNaemiAaGgaaOGaeyOKH4Acfa4aaSaaaeaacqGH+aGpcqGH+aGpcqaIWaamaeaacqWGZbWCcqWGObaAaaaaaa@3E4D@
  Stage 2   Stage 2
  (MA is harder, may be impossible):   (MA is easier, may be still hard):
  0 s ( 1 h ) < 2 U s d m s ( 1 h ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIWaamaeaacqWGZbWCdaqadaqaaiabigdaXiabgkHiTiabdIgaObGaayjkaiaawMcaaaaakiabgkziUMqbaoaalaaabaGaeyipaWJaeGOmaiJaemyvau1aaSbaaeaacqWGZbWCcqWGKbazcqWGTbqBaeqaaaqaaiabdohaZnaabmaabaGaeGymaeJaeyOeI0IaemiAaGgacaGLOaGaayzkaaaaaaaa@43BF@   0 s ( 1 h ) < < 2 U s d m s ( 1 h ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIWaamaeaacqWGZbWCdaqadaqaaiabigdaXiabgkHiTiabdIgaObGaayjkaiaawMcaaaaakiabgkziUMqbaoaalaaabaGaeyipaWJaeyipaWJaeGOmaiJaemyvau1aaSbaaeaacqWGZbWCcqWGKbazcqWGTbqBaeqaaaqaaiabdohaZnaabmaabaGaeGymaeJaeyOeI0IaemiAaGgacaGLOaGaayzkaaaaaaaa@44C3@
(3) asexual diploid with mitotic recombination intermediate between genome type (2) and (4) intermediate between genome type (2) and (4) intermediate between genome type (2) and (4)
(4) automictic selfing diploid with free recombination 2 U s d m 2 s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaeGOmaiJaem4Camhaaaaa@353D@ 2 U s d m / 2 s ( 1 + s h ) ( 1 s h ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSGbaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaeGOmaiJaem4Cam3aaSaaaeaadaqadaqaaiabigdaXiabgUcaRiabdohaZjabdIgaObGaayjkaiaawMcaaaqaamaabmaabaGaeGymaeJaeyOeI0Iaem4CamNaemiAaGgacaGLOaGaayzkaaaaaaaaaaa@41A4@ 2 U s d m / 2 s ( 1 + s ) ( 1 s ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSGbaeaacqaIYaGmcqWGvbqvdaWgaaqaaiabdohaZjabdsgaKjabd2gaTbqabaaabaGaeGOmaiJaem4Cam3aaSaaaeaadaqadaqaaiabigdaXiabgUcaRiabdohaZbGaayjkaiaawMcaaaqaamaabmaabaGaeGymaeJaeyOeI0Iaem4CamhacaGLOaGaayzkaaaaaaaaaaa@3EF2@
  1. The table gives the variables in the exponent of N 0 = N e e U s d m / s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOta40aaSbaaSqaaiabicdaWaqabaGccqGH9aqpcqWGobGtdaWgaaWcbaGaemyzaugabeaakiabgwSixlabdwgaLnaaCaaaleqabaGaeyOeI0YaaSGbaeaacqWGvbqvdaWgaaadbaGaem4CamNaemizaqMaemyBa0gabeaaaSqaaiabdohaZbaaaaaaaa@3D9C@ , where N0 is the number of individuals in the population that are in the 'best class' (has the highest fitness) in mutation-selection balance. Here we propose that Muller's ratchet in a given genome type can be approximated by using predictions for Muller's ratchet in a haploid asexual genome and applying the scaling given here. U sdm = slightly deleterious mutation rate/haploid genome, s = homozygous selection coefficient, h = dominance coefficient, sh = heterozygous selection coefficient, where in this table positive s denote harmful mutations. The two stages for asexual diploids denote the fixation of the first and second deleterious mutation that can occur at a diploid locus. For individual stages, arrows indicate the change of U sdm /s with increasing mutation accumulation (= MA). '<' or '>' indicate that mutation rates will remain below or above the indicated level, respectably.