Analogously to example 8.17 (page 369), consider a population with a maximal size of \(z=5\) individuals, which comprises at the beginning of its observation 3 individuals. Its birth and death probabilities with regard to a time unit are

\[\begin{aligned} & p_{0}=0, p_{1}=0.6, p_{2}=0.4, p_{3}=0.2, p_{4}=0.4, p_{5}=0 \\ & q_{0}=0, q_{1}=0.4, q_{2}=0.4, q_{3}=0.6, q_{4}=0.5, q_{5}=0.8 \end{aligned}\]

(1) What is the probability of extinction of this population?

(2) Determine its mean time to extinction.

Data from Example 8.17

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Example 8.17 Consider a population with a maximal size of z = 6 individuals and transition probabilities with regard to a unit time given by Table 8.3. Then, by (8.50), m(1) = + 1 P1 PIP2 9192 919293 + + P1P2 P5 919296 = 155. Table 8.3 shows the mean times to extinction m(1), m(2), ..., m(6). Condition (8.49) is satisfied.