To find constant, we perform summation over equation (A 9):Combining (A 10) and (A 11) yieldsThen,is given byTherefore,Now using (A 9), we obtain the extinction probability To calculate b n, we use equation (A 7) f n n − ( λ + ϕ ) b n = − ϕ b n − 1 − λ b n + 1.
To proceed further, we substitute (A 3) into (A 2): ( s n + λ + ϕ ) ( f n − s b n ) = ϕ ( f n − 1 − s b n − 1 ) + λ ( f n + 1 − s b n + 1 ).