# Population of Pets

Using mathematics to estimate pet populations has occurred for many years. The famous sequence of numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, , in which each new number is the sum of the previous two, was given as the answer to the following problem, stated by Leonardo Pisano Fibonacci in his Liber Abaci:

What is the number of pairs of rabbits at the beginning of each month if a single pair of newly born rabbits is put into an enclosure at the beginning of January and if each pair breeds a new pair at the beginning of the second month following birth and an additional pair at the beginning of each month thereafter?

The first twelve numbers of the Fibonacci series give the answer for the first year. The sum of these first twelve is 376. At least in these theoretical circumstances, one pair of rabbits results in close to 400 rabbits after 1 year.

However, the theoretical math of this problem does not represent the actual situation. It is true that a rabbit can have a litter about every 31 days, so that part of the problem is correct. However, rabbits must usually be from 3 to 6 months old before they start to breed successfully, so the problem, which gives them only 2 months from birth before they begin breeding, is not completely realistic.

## The Impact of Estimating Pet Populations

The mathematics of animal populations is a matter of interest to people in many fields. Those who work to rescue threatened and endangered species, such as the whooping crane, condors, and Kemp's Ridley turtles, among others, use population mathematics to assess their work and predict future levels of animal populations.

The mathematics of pet populations is of interest because of the effort to minimize the number of animals that must be euthanized (or put to sleep) in animal shelters all over the United States. One California county, Santa Clara, decided that its policies and procedures for population control of unwanted animals should be based on research, rather than on pure speculation. After conducting a study, it was determined that four times more cats than dogs were euthanized in the county's shelters. Citizens also learned that 86 percent of owned cats are already spayed or neutered. This revealed that their educational efforts emphasizing the importance of spaying or neutering pets had been effective. This is also true on a national scale: since the 1980s, there has been a tremendous drop in animal euthanasia.

The survey found that some cats had litters because the owners did not realize that cats can reproduce when they are as young as 6 months. In Santa Clara, unowned, or feral, cats made up a minimum of 46 percent of the known cat population. The report showed that 10 percent of all households in the county fed stray cats.

By gathering mathematical data, organizing and analyzing them, and using graphs and tables to report the findings as useful information, those who conducted this survey came up with a specific plan to address the goal of minimizing unwanted cats. The recommendations suggested a program of education, adoption, and TTVAR, which means Trap, Test, Vaccinate, Alter, and Release. The data support such a program and predict that it would be much more effective than a new set of harsh and unenforceable regulations.

Lucia McKay

## Bibliography

Ebert, Thomas A. Plant and Animal Populations: Methods in Demography. San Diego: Academic Press, 1998.

Garland, Trudi Hammel. Fascinating Fibonaccis: Mystery and Magic in Numbers. Palo Alto, CA: Dale Seymour Publications, 1987.

### Internet Resources

"Are Owned Cats Causing an Overpopulation Crisis?: A National Pet Alliance Report." Cat Fanciers. <http://www.fanciers.com/other-faqs/owned-cats.html>.

"Survey Report: Santa Clara County's Pet Population." Cat Fanciers. <http://www.fanciers.com/npa/santaclara.html>.

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