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.
A 4 Rearranging terms yields − s 2 b n n + s ( f n n − b n ( λ + ϕ ) ) + ( λ + ϕ ) f n = ϕ f n − 1 + λ f n + 1 − s ( ϕ b n − 1 + λ b n + 1 ).