مدل‌های سیر فرگشتی دی‌ان‌ای

${\displaystyle P(t+\tau )=P(t)P(\tau )}$

${\displaystyle \mathbf{P}(t)=(p_A(t),p_G(t),p_C(t),p_T(t){)}^T}$

${\displaystyle \mathcal{E}=\{A,G,C,T\}}$

${\displaystyle {\mu }_x=\sum _{y\ne x}{\mu }_{xy}}$

${\displaystyle p_A(t+\mathrm{\Delta }t)=p_A(t)-p_A(t){\mu }_A\mathrm{\Delta }t+\sum _{x\ne A}{p}_x(t){\mu }_{xA}\mathrm{\Delta }t}$

${\displaystyle \mathbf{P}(t+\mathrm{\Delta }t)=\mathbf{P}(t)+Q\mathbf{P}(t)\mathrm{\Delta }t}$

${\displaystyle {\mathbf{P}}^{\prime }(t)=Q\mathbf{P}(t)}$

${\displaystyle P(t)=\exp (Qt)}$

${\displaystyle \mathbf{P}(t)=P(t)\mathbf{P}(0)=\exp (Qt)\mathbf{P}(0).}$

${\displaystyle Q\mathbf{\Pi }=Q\mathbf{P}(t)=\frac{d\mathbf{P}(t)}{dt}=0.}$

${\displaystyle s_{xy}=s_{yx}}$

${\displaystyle \beta =1/\left(-\sum _i{\pi }_i{\mu }_{ii}\right)}$

${\displaystyle {\displaystyle \nu =\frac{3}{4}t\mu =(\frac{\mu }{4}+\frac{\mu }{4}+\frac{\mu }{4})t}}$

${\displaystyle \hat{d}=-\frac{3}{4}\ln (1-\frac{4}{3}p)=\hat{\nu }}$

${\displaystyle {\displaystyle K=-\frac{1}{2}\ln ((1-2p-q)\sqrt{1-2q})}}$

${\displaystyle \beta =1/(1-{\pi }_A^2-{\pi }_C^2-{\pi }_G^2-{\pi }_T^2)}$

${\displaystyle \beta =\frac{1}{2({\pi }_A+{\pi }_G)({\pi }_C+{\pi }_T)+2\kappa [({\pi }_A{\pi }_G)+({\pi }_C{\pi }_T)]}}$

${\displaystyle P_{AA}(\nu ,\kappa ,\pi )=\left[{\pi }_A\left({\pi }_A+{\pi }_G+({\pi }_C+{\pi }_T)e^{-\beta \nu }\right)+{\pi }_G{e}^{-(1+({\pi }_A+{\pi }_G)(\kappa -1.0))\beta \nu }\right]/({\pi }_A+{\pi }_G)}$

${\displaystyle P_{AC}(\nu ,\kappa ,\pi )={\pi }_C\left(1.0-e^{-\beta \nu }\right)}$

${\displaystyle P_{AG}(\nu ,\kappa ,\pi )=\left[{\pi }_G\left({\pi }_A+{\pi }_G+({\pi }_C+{\pi }_T)e^{-\beta \nu }\right)-{\pi }_G{e}^{-(1+({\pi }_A+{\pi }_G)(\kappa -1.0))\beta \nu }\right]/\left({\pi }_A+{\pi }_G\right)}$

${\displaystyle P_{AT}(\nu ,\kappa ,\pi )={\pi }_T\left(1.0-e^{-\beta \nu }\right)}$

${\displaystyle {\pi }_G={\pi }_C=\frac{{\pi }_{GC}}{2}}$

${\displaystyle {\pi }_A={\pi }_T=\frac{(1-{\pi }_{GC})}{2}}$

${\displaystyle d=-h\ln (1-\frac{p}{h}-q)-\frac{1}{2}(1-h)\ln (1-2q)}$

${\displaystyle \begin{array}{r}\alpha =r(T\to C)=r(C\to T)\\ \beta =r(T\to A)=r(A\to T)\\ \gamma =r(T\to G)=r(G\to T)\\ \delta =r(C\to A)=r(A\to C)\\ ϵ=r(C\to G)=r(G\to C)\\ \eta =r(A\to G)=r(G\to A)\end{array}}$

${\displaystyle \frac{n^2-n}{2}+n-1=\frac{1}{2}{n}^2+\frac{1}{2}n-1.}$