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Table 1 Salient features of the proposed model in terms of scaling of the number of domain classes, compared to the model of Gerstein and coworkers [8, 22]

From: Universal features in the genome-level evolution of protein domains

  K i p N p O MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacaWGWbWaaSbaaeaacaWGobaabeaaaeaacaWGWbWaaSbaaeaacaWGpbaabeaaaaaaaa@3414@ p N p O i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacaWGWbWaaSbaaeaacaWGobaabeaaaeaacaWGWbWaa0baaeaacaWGpbaabaGaamyAaaaaaaaaaa@3503@ F(n) F(j, n)/F(n)
CRPα = 0 ~ n ~ n-1 ~ n-1 ~ log (n) ~ θ j MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqefeKCPfgBaGabaiaa=5hajuaGdaWcaaqaaiabeI7aXbqaaiaadQgaaaaaaa@35F0@
CRPα > 0 ~ n ~ nα-1 ~ nα-1 ~ nα ~ j -(1+α)
Qian et al. ~ n p O MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqefeKCPfgBaGabaiaa=5hacaWGUbWaaWbaaSqabeaacaWGWbWaaSbaaeaacaWGpbaabeaaaaaaaa@35B7@ = R ~ n 1 p O MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8viVeY=Nipec8Eeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqefeKCPfgBaGabaiaa=5hacaWGUbWaaWbaaSqabeaacaaIXaGaeyOeI0IaamiCamaaBaaabaGaam4taaqabaaaaaaa@375F@ ~ n ~ j-(2+R)
  1. The first three columns indicate the resulting average population of a class K i , and the ratios of the probability to add a new class p N to the total and per-class probabilities of duplication, as a function of genome size n. These latter two quantities are asymptotically zero in the CRP, while they are constant or infinite in the model of Gerstein and coworkers. The last two columns indicate the resulting scaling of number of domain classes F(n) and fraction of classes with j domains F(j, n)/F(n). The results of the CRP agree qualitatively with observations 1-3 in the text.