# LESSON 2 Carrying Capacity: What is a Viable Population? A Lesson on Numbers and Space

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1 Ï MATH LESSON 2 Carrying Capacity: What is a Viable Population? A Lesson on Numbers and Space Objectives: Students will: list at least 3 components which determine the carrying capacity of an area for a certain species. mathematically determine minimum range sizes for maintaining a theoretical minimum viable population for three to six animal species. Duration: One class period for Do You Have Enough Space for Those Animals? Carrying capacity as a population limiting factor. Location: classroom Background: The number of animals that can live in an area is determined by that area s carrying capacity. Carrying capacity may be seen as a type of dynamic equilibrium. It is typically expressed as the number of animals of a given type which can be supported by a given area. Carrying capacity is usually limited by some aspect of a species habitat requirements. These requirements include the quantity and quality of available food, water, shelter, space and the suitability of their arrangement. Natural and human causes both affect carrying capacity. Effects may be short or long term. Activity 1 focuses on inbreeding depression and why small populations generally are not viable ones. Activity 2 focuses on carrying capacity and the needs for large tracts of natural space for populations of animals to survive. Page 435

2 MATH Ï Activity 1: Do You Have Enough Space for Those Animals? Materials: maps of Wilderness areas or National Park areas. These can be local maps (within the state) or maps provided in the Í wilderness box. Maps should include topography. paper and pencil. student handouts population and area chart, discussion questions, pages Procedure: Have students: 1. Make copies of the student handout, page Study the range requirements for each species. 2. Calculate the minimum area required for each species. If time is limited, have them pick 3 of the listed species to work with. To do this, multiply each range value (the low value and the high value) for area needed by one individual by 50 to get the needed range for a population of 50 (25 breeding pairs). 3. Find three areas of open space on their maps which have enough acreage to support each of the species. Consider using the low end ranges first, then try to find areas that have enough space for the high end ranges. To do this, students may have to use the distance scale on the map and a conversion factor. 1 square mile = 640 acres Hint: if an area is one mile long and 1 mile wide, it contains 640 acres or 1 x 1 x 640 = 640 acres if an area is 1/2 mile long and 1/2 mile wide, it contains 1/2 x 1/2 x 640 = 1/4 x 640 = 640/4 = 160 acres if an area is 1/2 mile long and 1/4 mile wide, it contains 1/2 x 1/4 x 640= acres Students will then fill in the chart and answer the questions. Follow-up: Discuss the student answers in class. Have them compare their calculations with other students to determine their accuracy. As you reach the numbers section of each reading, have a student write the animal s name, the minimum viable population number, and the number of acres needed on the board. If it is easier, have a student read the passages and you write the numbers on the board. Page 436

3 Ï MATH Follow-up continued: After reading the passage(s), ask the students if they think they have enough animals for viable populations and if they have enough space in their chosen areas for a viable population. Have the students read or listen to either or both of these passages: Wild Hunters, Predators in Peril (the paragraphs concern Canada s population conservation goals) or Reserve Size and Populations Viability from The Wildlands Project. Reading: Wild Hunters Predators in Peril The basic principle behind calculating a minimum viable population (MVP) of a wildlife species is to determine a conservation bottom line. If we allow numbers to sink below that bottom line, we run the unacceptable risk of the species or population declining toward extinction. Calculating MVPs is a complicated and still-evolving field of population ecology. Such calculations, though they are the best guesses anyone can make for now, are fraught with uncertainty and assumptions that have been made in the absence of definitive scientific evidence. Nevertheless, the work of various researchers has helped the World Wildlife Fund make best guesses at MVPs for those large carnivores for which some information is known. Our MVP estimates are only for short-term population viability of top predators, in other words, for a 50 to 100 year time frame. Current genetic research suggests that, for long-term population viability, say for 1,000 years, ten times the number of animals and therefore ten times the amount of protected habitat, would be needed. Although these calculations are imprecise, they are the best possible to date, and they result in some pretty startling figures. For example, MVP calculations are 393 for grizzly bears, 148 for wolves, 78 for cougars, and 313 for wolverines. Using known information on the homerange or habitat requirements for these species, such MVPs translate into very large space requirements. Examples are in the order of 19,650 to 78,600 square kilometers (7,600 to 30,400 sq. miles) for a minimum viable population of grizzly bears, and between 26,650 and 59,990 square kilometers (10,300 and 22,000 sq. miles) for wolverines. The areas required for minimum viable populations of wolves and cougars are difficult to calculate because of the great variation in wolf and cougar densities occurring in different regions of Canada. Career Options: geneticist, wildlife biologist, range scientist References: Anderson, A.L., D. C. Bowden, D. M. Kattner The Puma on the Uncompahgre Plateau, Colorado. Colorado Division of Wildlife Technical Publication No. 40 CDOW, Fort Collins, Colorado. Benedict, A. D A Sierra Club Naturalist s Guide - The Southern Rockies. Sierra Club Books, San Francisco, California. Page 437

4 MATH Ï References continued: Hummel, M., S. Pettigrew, J. Murray Wild Hunters Predators In Peril. Roberts Rinehart Publishers, Niwot, Colorado. Noss, R. F. The Wildlands Project - Land Conservation Strategy. Wild Earth Special Issue Cenozoic Society, Inc. Canton, New York. p. 19. Project Wild, Secondary Activity Guide Carrying Capacity Western Regional Environmental Education Council, Project Wild, Salina Star Route, Boulder, Colorado. p Schmidt, K. J Conserving Greater Yellowstone A Teacher s Guide Northern Rockies, Conservation Cooperative, Jackson, Wyoming. Page 438

5 Ï MATH STUDENT HANDOUT Activity 1: Do You Have Enough Space for Those Animals? (copy front to back for one sheet, pages ) Information chart with range requirements for a number of species of mammals: grizzly bear From sq. miles depending on vegetation. They require substantial vegetation. wolverine From sq. miles, in general. Wolverines need all sizes of mammals to prey on and enough other large predators (wolves, lions, etc.) to kill large animals and leave carcasses which make up the wolverine s primary food source. bobcat 1-65 sq. miles depending on availability of prey adaptable to - all terrain. mountain lion sq. mi. (Colorado) depending on prey base (male ranges are larger that female ranges). lynx 6-19 sq. miles dense forest, northern areas - mature coniferous forests, need a population of small mammals to prey on. wolf 20 to 600 sq. miles - need year round supply of large ungulates (deer, elk, moose, bison) and denning cover. Procedure: 1. Study the range requirements for each species. 2. Calculate the minimum area required for each species. To do this, multiply each range value (the low value and the high value) of the area needed by one individual by 50 to get the needed range for a population of 50 (25 breeding pairs). Keep your calculations. 3. Find an area of open space on the maps for each species which has enough acreage to support 50 individuals of that species. Consider using the low end ranges first, then try to find areas that have enough space for the high end ranges. To do this, use the distance scale on the map and a conversion factor. 1 square mile = 640 acres Hint: if an area is one mile long and 1 mile wide, it contains 640 acres. This can be written in an equation to help you figure other areas: 1 x 1 x 640 = 640. If an area is 1/2 mile long and 1/2 mile wide, it contains 1/2 x 1/ 2 x 640 = 1/4 x 640 = 640/4 = 160 acres. If an area is 1/2 mile long and 1/ 4 mile wide, it contains 1/2 x 1/4 x 640= 1/8 x 640 = 640/8 = acres Page 439

6 MATH Ï STUDENT HANDOUT Activity 1: Do You Have Enough Space For Those Animals? Fill in the chart and answer the questions: Range Needs for 50 Individuals & Areas Where Each Species May be Found acreage needed for 25 pairs (50 animals) area chosen Grizzly bear Wolverine Bobcat Mountain lion Lynx Wolf After finding areas which are large enough in terms of acreage, study the terrain of the area you have chosen. Answer the following questions (on a separate piece of paper). 1. Is there enough suitable habitat for each species? Is there enough shelter, food, and water, or does the area need to be enlarged? 3. What will happen to your animal populations if there is a drought or fire? Can they move to an area of more water, or more food? 4. Can you enlarge the area without encroaching into human inhabited areas? 5. Are the areas you chose comprised of protected designated Wilderness or do they include national forest, state forest, national park, national wildlife refuges, or BLM land? What are the chances your reserves may be developed? 6. If you cannot enlarge the area, how many pairs of animals can the area support? Page 440

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