### Population Growth Problem:

Rabbits were introduced to Australia in the 18th century and, lacking natural predators, their population exploded. A virus called myxoma was introduced in the 1950s, and caused a population crash, but the survivors have developed immunity and the population has rebounded.

This capability of living things to produce more of themselves than is absolutely necessary for replacement was first described by Thomas Malthus in his Essay on the Principle of Population in 1798, more than 60 years before Darwin would publish his Origin of Species.

Imagine that a male and female pet rabbit were released on an Australian farm in the 1700s, where there were abundant resources and no predators. A female can produce a new litter of 12 babies every month. Each litter will be assumed to have 50% male and 50% female rabbits. Rabbits reach reproductive maturity in 6 months, and can then start producing litters of 12 each. Given this starting information, calculate how many rabbits there will be a year later, by filling in the blanks in the table below. Use a calculator or a spreadsheet application to assist.

Important assumptions to remember in this example:

• No rabbits die from either predation or old age during the year of the study.
• All rabbits have enough to eat, and everything else they need to thrive.
• The sex ratio of litters is 50:50 male:female.
• Rabbits become fertile at 6 months of age.
• Litter size is a constant 12.
 Month Total Rabbits Fertile Females Litter Size Babies Female Babies Notes 1 2 1 12 12 6 2 14 1 12 12 6 Total Rabbits = 2 parents + 12 babies from month 1 3 26 12 Total Rabbits = 2 parents + 12 month 1 + 12 month 2 4 12 5 12 6 62 7 12 84 42 Fertile females = mom + 6 daughters from month 1 7 12 Fertile females = mom + 6 month 1 daughters + 6 month 2 daughters 8 12 9 12 10 830 31 12 372 186 11 12 12 12

Download the solution sheet in Excel. Have one member of your group review the solution and offer hints to the rest.

Questions:

1. If there were natural rabbit predators, would this kind of population growth be possible?
2. Under normal circumstances, why does a species spread out as its population grows?
3. If food resources became limited, what would happen?
4. Aren't there natural boom and bust cycles caused by food availability, annual weather patterns, etc?
5. Why is the number of fertile females the critical factor for population growth? Why don't males matter so much?
6. Why are introduced species more likely to disrupt the balance than native species?
7. Why are remote islands like Hawaii and Madagascar so sensitive to introduced species?
8. Describe a species that has been introduced to your region and has become a pest.
9. Describe a success story where people have introduced a biological control (a predator or disease) to contain an introduced pest.
10. Describe a situation where people have introduced a biological control to contain an introduced pest but it created a new problem.