For the nucleotide substitution model of Section 10.5, verify in general that the equilibrium distribution is A

For the nucleotide substitution model of Section 10.5, verify in general that the equilibrium distribution is

πA = (δ + κ) + δ(γ + λ)

(α + γ + + λ)(γ + δ + κ + λ)

πG = α(δ + κ) + κ(γ + λ)

(α + γ + + λ)(γ + δ + κ + λ)

πC = γ(δ + κ) + σ(γ + λ)

(β + δ + κ + σ)(γ + δ + κ + λ)

πT = λ(δ + κ) + β(γ + λ)

(β + δ + κ + σ)(γ + δ + κ + λ)

.