19.21 The Asian stochastic beetle. We can use simulation to examine the fate of populations of living creatures. Consider the Asian stochastic beetle. Females of this insect have the following pattern of reproduction:
• 20% of females die without female offspring, 30% have one female offspring, and 50% have two female offspring.
• Different females reproduce independently.
What will happen to the population of Asian stochastic beetles: will they increase rapidly, barely hold their own, or die out? It’s enough to look at the female beetles, as long as there are some males around.
(a) Assign digits to simulate the offspring of one female beetle.
(b) Make a tree diagram for the female descendants of one beetle through three generations. The second generation, for example, can have 0, 1, or 2 females. If it has 0, we stop. Otherwise, we simulate the offspring of each second-generation female. What are the possible numbers of beetles after three generations?
(c) Use line 105 of Table A to simulate the offspring of five beetles to the third generation. How many descendants does each have after three generations? Does it appear that the beetle population will grow?