BioMath Home Range: Species’ Living Rooms Student Edition

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Home Range: Species’ Living Rooms Overview How do researchers determine the home range of a particular species? What is meant by a species’ home range? How does the home range of a species connect to its habitat? This unit explores how data is collected and analyzed to determine the home range of a number of species. Students use actual data for prairie dogs, black-footed ferrets, pronghorn antelopes. They determine the home range of these animals, including the size and breadth of the home range, and how one would create a buffer zone for the home range. Students are encouraged to draw conclusions as they compare their data to other student’s data. They consider the usability and the effectiveness of different tracking techniques.

Unit Goals and Objectives Goal: Understand the concept of home range and gain an appreciation for the uses of identifying a species’ home range. Objectives:  Analyze tracking data to determine the home range of one species.  Determine the area of the home range of that particular species.  Predict the human impact on home range.  Describe how a buffer can be used for conservation of a home range. Goal: Understand the determination of and uses for identifying locations using the Universal Transverse Mercator (UTM) geographic coordinate system. Objectives:  Determine latitude and longitude for a particular street address  Convert latitude and longitude into UTM coordinates using an on-line conversion program  Describe why UTM coordinates are preferable to minutes, degrees, seconds to describe latitude and longitude  Generate a list of locations at 2 distinct times in both UTM and latitude/longitude for the past seven days.  Define and be able to use the following terms: home range, territory, population density, latitude, longitude, Universal Transverse Mercator (UTM) system Goal: Use Data and geometric concepts to model home range of a species. Objectives:  Plot data from the list of locations at 2 distinct times for the past seven days on a graph  Determine the home range based on the data  Estimate, then calculate, the area of the home range for a variety of home range shapes. Shapes include regular polygons and irregular polygons.  Define and be able to use the following terms: patch, polygon, regular polygon, convex polygon (or convex hull), concave polygon

Home Range

Student 1

Goal: Collect data to determine home ranges. Objectives:  Describe three techniques for collecting data to determine home range data for organisms: radio telemetry, GPS tracking, mark & recapture.  Describe how sampling is used to reflect an entire population, but that there may be underlying assumptions that may not hold true for an entire population.  Plot the data points, determine the home range of the animal, and create a buffer.  Define and be able to use the following terms: buffer, uniform buffer, directional buffer, similar polygon Goal: Gain an appreciation for the differences of habitats and home ranges between two or more species. Objectives:  Compare and contrast the habitats and home ranges of various species.  Predict interactive relationships and feeding interactions between species (trophic levels).  Predict the animal for which the data was collected, as well as the tracking method used to obtain the data.

Home Range

Student 2

Lesson 1

Introduction to Home Range

We begin our study of home range by thinking about our own home range. How would you define and determine your home range? Your Space

ACTIVITY 1-1

Home Range, Territory and Density

Objective: Understand the concept of home range and identify characteristics of a home range. Materials: Handout: HR-H1 Home Range, Territory and Density Activity Worksheet 1. To get you thinking about how you would describe the meaning of home range, jot down your answers to the following questions. a. How much personal space do you need? b. Where do you go in a typical day? Week? Month? Year? c. How much space do you use in your daily life? Weekly life? Monthly life? Yearly life? d. What resources do you need to live? e. Where do you acquire those resources? (Or where do your family members go to acquire those resources for you?) f. Which of those resources can you live without for 1 day? 2 days? 3 days? A month? A year? g. Which resources do you share with your family members? What happens when they encroach on “your” territory? 2. Compare your answers with another student. How are your answers similar? Different? How much overlap do you have? What are the implications of this? 3. On your own, without looking at a dictionary or talking to another student, define the following: a. Home range b. Territory c. Population density 4. Compare your definitions with your partner and come up with improved definitions. As a class come up with agreed upon definitions.

Home Range

Student 3

5. Based on these definitions, address the following: a. Define your own home range: b. Define your territory: c. What is the population density of your home? d. What is the population density of the school? e. Which has a higher density: your home or your school? Latitude and Longitude Do you recall how to identify a location using latitude and longitude? When looking at a map, the latitude lines run horizontally (east and west) and the longitude lines run vertically (north and south). The latitude lines are parallel to each other and approximately 69 miles apart (with some variation due to not perfect shape of the earth. The longitude lines are about 69 miles apart when crossing the equator, but get closer and converge at the poles. The equator is considered 0 degrees latitude and the north and south poles are at 90 degrees latitude. The 0 degree longitude line goes through Greenwich, England and then are marked to 180 degrees east and west meeting in the Pacific Ocean forming the International Date Line. Locations are defined in terms of degrees, minutes and second latitude (North or South of the equator) and longitude (East or West of Greenwhich). You can use a computer to find the latitude & longitude for a particular street address. We have two possible ways. The first works well if we do not need a map to tell where the location is, while the second one provides a map in various forms for each location. - Converting Addresses to/from Latitude/Longitude in One Step. There are sites online that will convert an address to a latitude and longitude location. One site is http://stevemorse.org/jcal/latlon.php.[1] You can use a search engine to find other sites. - Google Maps. You can use Google Maps (http://maps.google.com/[2]) to map the address of interest and then click on “Link” in the upper right corner of the map. Scroll to the far right of the first line of the pop up box that begins with http://maps.google… and the latitude & longitude appear in the URL. If you have access to a computer try a few locations. For example, find the location for your home or your school or the closest movie theater. Universal Transverse Mercator (UTM) Have you heard of the Universal Transverse Mercator (UTM) geographic coordinate system? What do you think this might be?

Home Range

Student 4

The UTM provides a location system that represents the Earth’s three-dimensional surface in a relatively accurate two-dimensional display. The system allows identifying locations between 84 degrees North latitude and 80 degrees South latitude. Unlike latitude and longitude lines, the UTM grid consists of parallel horizontal and parallel vertical lines each 1000 meters apart. The Yellowstone National Park has established the Research Coordination Network (RCN). You can translate latitude and longitude location to UTM coordinates and vice versa. The RCN utilities and tools are found at: http://www.rcn.montana.edu/resources/tools/coordinates.aspx.[3] Now let’s convert the latitude & longitude for a particular street address to the Universal Transverse Mercator, UTMs for short, using RCN Utilities and Tools. Fill in the latitude & longitude under “degree decimal”. Then click on “Convert DD”. Scroll down, and the latitude and longitude will be converted into UTM’s in a particular zone. Record your data and be sure to include the Zone, and the Easting number and the Northing number. Universal Transverse Mercator (UTM) is a grid-based method of identifying locations on the Earth. Unlike the latitude and longitude method, it uses a series of 60 zones or projections rather than just one. So, a location is given by three features: Zone, Northing and Easting. The advantage of the UTM system is that the locations are given in meters thus making it simple to calculate distances between two points.

Source: http://en.wikipedia.org/wiki/File:Utm-zones.svg). This work is licensed under the Creative Commons Attribution 3.0 License.

Figure 1.1: UTM Zones For each UTM zone, the origins are calculated as follows: Northing values: For locations in the Northern hemisphere, all northing distances are measured from the equator (minimum northing value is 0, and a maximum of 9,328,000). For locations in the Southern hemisphere, all northing distances are measured as (10,000,000 – distance from the equator). The number, 10,000,000, was arbitrarily chosen simply to prevent there from being negative UTM values. Home Range

Student 5

Easting values: For each zone, the meridian (center location) is given a value of 500,000 meters. Locations to the west of center are measured as (500,000 – distance from center). Locations to the east of center are calculated as (500,000 + distance from center). Projection: The parabola shape of the UTM zones is a result of the projection of a globe onto a flat surface. See the following image for a simplified example of this type of projection.

Figure 1.2: Projection onto UTM Source: http://en.wikipedia.org/wiki/Transverse_Mercator_projection.

Figure 1.3: Finding Northing and Easting So the UTM Northing for points A and B is calculated as meters north of the equator. UTM Easting for point A = 500,000 – distance from zone meridian UTM Easting for point B = 500,000 + distance from zone meridian

Home Range

Student 6

Practice 1. Develop a chart, or use the one your teacher hands out, that indicates where you have been in the last week at 10AM and 6PM each day. Look up the latitude and longitude of each address and convert each to UTMs using the website given above. 2. What do you notice about the patterns of your travels during the week?

Lesson 2

Plotting Data To Determine Home Range

In order to determine home range, we plot location data on a UTM grid. We first convert the UTMs in meters to kilometers, for example 535136 easting is 535.136 km and 4981670 northing is 4981.670 km. These are still very large numbers to plot on a graph so we can convert them to 100’s of kilometers and plot 5.35 easting and 49.81 northing. Be sure to note the scale on your graph. The x-axis is easting and the y-axis is northing in 100’s of km. Each block on the graph is 400 km by 400km. The point for the example is shown below. In this example, all values are in zone 18. Northing 100 km

Easting 100 km

Figure 2.1: Example Graph of UTM Location

Home Range

Student 7

UTM Locations to Home Range

Northing UTM

Now let’s look at how we can use the points we graphed to determine our home range. The graph below is a set of points graphed on a grid that has 2000 by 2000 unit blocks. If you have studied scientific notation, note that the scale is in 105 units, so 4.72×105 is 472,000 meters. The dimension of one side of the block is .02×105 = 02000 = 2000 meters. The grid is only a portion in the upper right hand section of an actual graph.

Easting UTM

Figure 2.2: Example Of Graphed Locations Think of different ways you can enclose this set of points. One possibility is to use a circle or an elliptical shape as shown in the next picture. This elliptical shape contains each of the points and the area inside is called a patch that determines home range.

Figure 2.3: Elliptical Home Range Patch Home Range

Student 8

Questions for Discussion 1. Estimate the area of this patch. Compare your answer with your neighbors’ answers. How did you estimate the area? 2. Consider a rectangular patch like the one shown in Figure 2.4.

Figure 2.4: Rectangular Patch a. Estimate the area of this patch. b. How does it compare to the area of the elliptical patch? c. Could we have used a “better” rectangle? d. Is the rectangular patch any “better” than the elliptical one? e. Could we have used an irregular patch, perhaps composed of triangles and done any better? Polygons Recall that a polygon is a closed flat (2-dimensional) shape whose edges are formed by line segments. The rectangular patch is a polygon, but the elliptical patch is not a polygon. The following is an example of a polygon. It is called a regular polygon because all of its sides are equal and all of its angles are equal. This is a hexagon since it has six equal sides.

Home Range

Student 9

Figure 2.5: Regular Polygon Convex polygons have every interior angle less than 180 degrees as in the pentagon on the left in the figure below. Concave polygons have at least one interior angle greater than 180 degrees. The angle bigger than 180 degrees is shown in the polygon on the right below.

Figure 2.6: Concave vs. Convex Polygons Home ranges are created using convex polygons, sometimes called convex hulls. These shapes include all data points. Rarely, an outlier may be excluded. Since the elliptical patch in Figure 2.3 is a curve and therefore not a polygon, it cannot depict a home range. However, we can approximate any circular or elliptical patch with a polygon and then use it as a home range. The rectangle in Figure 2.4 takes our previous example of an elliptical patch and approximates it with a polygon.

Figure 2.7: A polygonal approximation of the elliptical patch in Figure 2.3 Home Range

Student 10

Techniques for Finding Area Some common formulas for area and perimeter: Rectangle: A = Area in units2 = length × width Triangle: Area = ½ base times height For example, calculate the area of the rectangle in Figure 2.4: Length appears to be 2 squares long = 2000 m × 2 = 4000 m long Width appears to be 1.5 squares wide = 2000 × 1.5 m = 3,000 m long A = 4,000 × 3,000 = 12,000,000 m2 Often one subdivides a region into triangles to compute the total area of an irregular polygon. For example, you can use the area formula for triangles to compute the total estimated area of the home range depicted in Figure 2.7. Try drawing a line on a 3x5 card equal to the length of a side of one square – the scale of the graph - and use this to measure off the lengths of the bases and altitudes of the triangle.

Figure 2.8: Quadrilateral Patch Divided Into Triangular Pieces Question for Discussion 3. Estimate the area of this polygonal patch and compare it to your previous estimates. Which area is smaller? We can also use this method to compute the area of a trapezoid, another type of quadrilateral with one pair of parallel sides. For example, a trapezoid could be considered to be a rectangle of base “b” and two right triangles with height “h.”

Home Range

Student 11

The area of a trapezoid with longer base “a” is the area of the left triangle with base “l,” plus the area of the rectangle with base “b,” plus the area of the right triangle with base “r.” A = ½lh + bh + ½ rh = ½ h(l +2b + r) = ½ h (a + b), or ½ the height times the sum of the bases. Note that a = l + b + r.

Activity 2-1 Home Range Plot Objective: Use data to determine and measure home range. Materials: Handout HR-H3: Home Range Plot Activity Worksheet 1. Using the data from your Lesson 1 practice (your own data), plot the points on graph paper. 2. Draw a convex polygon to enclose the points on the graph of your own home range. 3. Estimate or calculate the area of your home range. 4. Compare your home range with your partner and discuss why they are different. List at least three reasons for the differences. Practice 1. Complete the following chart using RCN Utilities and Tools: http://www.rcn.montana.edu/resources/tools/coordinates.aspx[3] latitude

longitude

49. 0490917 48.8384828 49.1828050 48.8436814

-109.9393864 -109.1967053 -110.2613850 -109.2389553

zone

Easting UTM

Northing UTM

12 12

441826 627755

5460000 5412266

2. Plot the points on a graph (grid) and find the home range determined by these data points using a rectangle, a triangle. Try another polygon. 3. President Garfield is said to have proved the Pythagorean Theorem using a trapezoid. Since the Pythagorean Theorem addresses right triangles we form a trapezoid using two copies of a right triangle (with sides a, b and c) and a third isosceles right triangle with equal sides of length c as shown in Figure 2.9.

Home Range

Student 12

Pythagorean Theorem: In a right triangle the sum of the squares of the legs of the triangle is equal to the square of the hypotenuse (a2 + b2 = c2).

Figure 2.9: Trapezoid Proof of the Pythagorean Theorem Show that this theorem is true by computing the area of the whole figure, first by using the area formula for a trapezoid, and secondly by adding up the area of the three right triangles.

Lesson 3

Determining Home Ranges For Specific Species

Home range is a concept that can be traced back to the 1943 publication Territoriality And Home Range Concepts As Applied To Mammals by W. H. Burt,[4] who constructed maps delineating the spatial extent or outside boundary of an animal's movement during the course of its everyday activities. Understanding the home range of a species helps to provide insight into what is needed for survival of the species. This is especially important when studying endangered or threatened species. Conservation efforts require an understanding of how much space is needed to save a species from extinction. Additionally, home range research can shed light on the requirements of a species as it is assumed that everything needed for survival is present within the home range boundaries. Home Range and Interrelationships of Species When more than one species have the same or overlapping home ranges, an interrelationship occurs. In this unit, we will look at a few specific species, located in the glaciated plains area of Montana, southern Canada and northern Wyoming. Since they are found in one locale, they offer good examples for you to understand the interrelationships of species. Pronghorn antelope, also called pronghorn or prong buck, (Antilocapra americana) is a species of ungulate mammals that are native to interior western and central North America. Photo by Yathin S Krishnappa (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

Figure 3.1: Pronghorn Antelope

Home Range

Student 13

The black-footed ferret (Mustela nigripes) is a small carnivorous endangered mammal in North America. They are nocturnal hunters that require a plentiful supply of prairie dogs for prey.

Photo by Ryan Hagerty, U.S. Fish and Wildlife Service [Public domain], via Wikimedia Commons

Figure 3.2: Black-Footed Ferret Prairies dogs (Cynomys sp.) are diurnal rodents in the prairies and plateaus of the American west. They live in burrows with complex social structures.

Photo by Wing-Chi Poon [CC-BY-SA-2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons

Figure 3.3: Prairie Dog The sage grouse (Centrocercus urophasianus) is a bird of the sagebrush plains in North America. They are an endangered species that feed on plants and insects.

By Pacific Southwest Region U.S. Fish and Wildlife Service from Sacramento, US (Greater Sage Grouse Uploaded by Snowmanradio) [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

Figure 3.4: Sage Grouse The Long-Billed Curlew (Numenius americanus) is a migratory bird that spends winters on the shores of California, Texas and Mexico. They spend from spring until late‐July in the Montana prairies to breed and nest. The curved bill of the Curlew is adapted to eating many species of invertebrates and some vertebrates, including shrimp and crabs from tidal mudflats and burrowing earthworms in fields. Their population has declined due to hunting and habitat destruction. In order to create effective conservation practices for this species, more data is needed regarding their home range. Figure 3.5: Long-Billed Curlew Photo by "Mike" Michael L. Baird [CC-BY-2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

Home Range

Student 14

The Sharp-Tailed grouse (Tympanuchus phasianellus) is a chicken-like bird of open prairies and parklands. The Sharptailed Grouse uses a wider variety of habitats than its close relatives the prairie-chickens. The sharp-tailed grouse lives in plant communities dominated by grasses and shrubs. They eat seeds, buds, berries, forbs (a non-grass-like plant with annual stems & tops), and leaves, also insects, especially grasshoppers, in summer. Adults have a relatively short tail with the two central feathers being square-tipped and somewhat longer than their lighter, outer tail feathers giving the bird its distinctive name. Figure 3.6: Sharp-Tailed Grouse Photo by Gerry from Fort St. John, BC, Canada (Sharp-tailed Grouse) [CC-BY-SA-2.0 (http://creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons

The American Bison (Bison bison) is the heaviest terrestrial animal in North America. Bison have a fairly simple diet. The bison's main food is grass. Bison also eat low-lying shrubbery. In the winter, bison forage in the snow looking for grass. If there is little grass available, bison have to resort to eating the twigs of the shrubs and plants. They generally live in small, separate bands and come together in very large herds in the summer mating season. Photo by Jack Dykinga [Public domain], via Wikimedia Commons

Figure 3.7: American Bison

ACTIVITY 3-1 What’s My Living Space? Objective: Use data to determine size of home range for a species. Materials: Handout HR-H4: What’s My Living Space? Activity Worksheet HomeRange_DataSet (provided by your teacher)[5] Use the data set that your teacher has provided to answer the following questions. 1. Guess the size of the home range for this data set before you plot the data points. (Think about the size of your personal home range and what you know about the species from the reading.) 2. Plot the points on a graph on a transparency for your species. 3. Draw a patch (convex polygon) that encloses all of the data points. This is the home range of your species. 4. Calculate the area of your home range.

Home Range

Student 15

5. Get into groups of organisms of the same species. Share the size of the home range for your organism. There are multiple sets of data for some species. Overlay all of one species to see the comparison. 6. As a group, a. list the minimum & maximum home ranges b. calculate the average home range for the species. 7. Share this information on the board. 8. Discuss whether it makes sense to average home range size over all species. Why or why not? 9. How does your estimate at the beginning compare to the actual home range size found? 10. Overlay small and large species data sets. Is there a difference? For which organisms, large or small, do you suspect there will be more of? 11. Overlay the prairie dog and the black footed ferret data. What do you notice? 12. Do you see the existence of corridors in any of the home ranges of your species? How can you tell? 13. What hypotheses would you like to test further? Certain aspects of Ethology, the study of animal behavior, play an important role in determining the home range of a species, especially when various tracking methods are used to locate the animals or birds. Some of the species we talked about in this section are nocturnal, they sleep during the day, and are awake at night, in contrast to humans who’s preferred sleep pattern is at night and they are awake during the day (diurnal). For example, the black-footed ferret is a nocturnal animal, making finding them hard during the day. To track them by sight, one needs to be awake during the night searching for them. Species, such as the curlew, live part of the year in the north and another part of the year in the south, and are considered migratory birds. Their home range will come in two parts with a corridor between them. The corridor is the flight area covered as they move from one patch to the other as the seasons change.

Home Range

Student 16

Questions for Discussion 1. Is there another species among the ones studied that is migratory? Which one? How do you know? 2. How would you determine the corridor for this species using the UTM data? 3. Populations of any species change over time. Four factors affect changes in population size: birth, death, immigration and emigration. Birth increases the population, and death decreases the population. Immigration is the movement of individuals INTO one population from another population, usually located somewhere else, and results in increasing population size. Emigration is the movement of individuals OUT of a population and would reduce the total population. It is important to keep these factors in mind when one is studying a particular population. How would each factor affect studying a population and determining its home range? Collecting Home Range Data There are methods used for collecting data points to determine home ranges: radio telemetry, GPS tracking, and mark & recapture (including leg banding). You can find additional information at internet sites such as Green Science, The Science blog of The Nature Conservancy found at http://blog.nature.org/science/2014/08/04/long-billed-curlewmigration-study-idaho-intermountain-bird-observatory/.[6]

Photograph by U.S. Fish and Wildlife Service [Public domain], via Wikimedia Commons

Figure 3.8: Radio telemetry Practice Your teacher will assign you to one of the three methods for collecting data points for determining home ranges:  Radio telemetry  GPS tracking  Mark & Recapture

Home Range

Student 17

1. Answer the following questions about your method and be prepared to discuss your answers in class tomorrow: a. What animal species would be ideal candidates for your tracking method? b. Are there species that wouldn’t work for your tracking method? Give examples and explain why it won’t work. c. Is your method “active” or “passive”? Why? d. Is your method expensive or cheap? Why?

2. Consider population size and the four factors – birth, death, immigration, and emigration – that contribute to population size. Data on births, deaths, immigration and emigration are given as rates. Suppose the birth rate is 4% per year. This means that the population is 4% larger next year than it was this year. If the population is 1000 this year then next year it will be 1000 + .04(1000) = 1000 + 40 = 1040. a. What will the population be in two years? b. Three years? 3. How would you calculate these rates (birth, death, immigration, emigration) using the three (3) tracking methods. How would you predict life expectancy & life history with radio collar or GPS? (Use the web if you need more information.)

Home Range

Student 18

Lesson 4

Tracking and the Relationships of Habitat and Home Range

Photograph by Menke Dave, U.S. Fish and Wildlife Service [Public domain], via Wikimedia Commons

Figure 4.1: Radio tracking device on a bear

ACTIVITY 4-1 Tracking Techniques Objective: Investigate and match tracking techniques to various species. Materials Handout HR-H5: Tracking Techniques Activity Worksheet 1. Complete a questionnaire for the tracking technique you investigated from Lesson 3 Practice. All members of your group should fill out a questionnaire. If some members investigated the same technique consolidate research onto one questionnaire per technique. 2. Which method requires the most monitoring? Why? 3. Which method is the most expensive? Why? *********************Tracking Questionnaire********************** Name of tracking method ___________________________________________ 1. Which animal species are ideal candidates for this tracking method? 2. Are there species that wouldn’t work for this tracking method? Give examples and explain why it won’t work. 3. Is this method “active” or “passive”? Why? 4. Is this method expensive or cheap? Why?

Home Range

Student 19

Habitat Overlay All living things-humans and other animals, and even plants-share some of the same basic needs. One of those needs is a home. But a home is more than just a house. Home is the place where plants and animals find food, water, shelter and space. The scientific name for this kind of home is habitat. All animals need some kind of shelter. People build houses, apartments, trailers and even houseboats, for shelter. Wild animals don't need that kind of home, but they do need some kind of shelter. They might use an underground den, or a bush, or build a nest in the crook of a tree. All animals, including humans, need food and water. There are people who plant gardens to provide some of the food they need, but most of us go to the grocery store to find food. Wild animals don't have that luxury. All of their food and water must be available within their home range territory. Unlike the grocery store, which can order more food when the shelves are bare, a wild animal's "store" only has so much food. Animals need enough space to find food and water for themselves and their young. The land where they live can only support so many animals. Carrying capacity is the term scientists use to describe the number of animals a certain portion of land can support. There are many different kinds of habitats. Some habitats are very small, while others are quite large. The animals that live in these different habitats have special characteristics, which enable them to survive under these special conditions. For example, the kangaroo rat lives in a desert habitat. There is very little water to drink in a desert, but that isn't a problem for the kangaroo rat. This special little animal is able to get all the water it needs to live from the seeds and grasses it eats. The polar bear has a thick layer of fat and special hollow hairs covering its body, which help to keep it warm in its arctic habitat. A kangaroo rat would freeze to death in this habitat, but polar bears do just fine. In fact, polar bear bodies are so well insulated that they have to be careful not to overheat! The ocean is another kind of habitat. There are many different kinds of marine animals living in the ocean. Starfish, dolphins, turtles, sea cucumbers, and hundreds of different kinds of fish live in an ocean habitat. All fish need to live in water, but not all fish can live in the ocean. If you take a fish from a fresh water stream or lake and put it in the ocean, it will die. Its body doesn't have the special adaptations needed to live in such a salty habitat. Not all animals are as specialized as a kangaroo rat or a polar bear or a sea turtle. But, all wild animals need a habitat, and, actually, so do you.

Home Range

Student 20

Figure 4.2: Example of a Habitat Map USGS. Work of the U.S. Government, public domain http://landcover.usgs.gov/glcc/research.php

Home Range

Student 21

Questions for Discussion 1. Revisit the each species listed in the table below and identify the habitat needs for each one. Species Bison Pronghorn Antelope Black-Footed Ferrets Prairie Dog Sage Grouse Curlews Sharp-Tailed Grouse

Habitat Requirements

Table 4.1: Habitat Chart 2. What is the relationship between a species’ habitat and its home range?

ACTIVITY 4-2 Mapping Out Home Ranges Objective: Use data to site a home range within appropriate habitat. Materials: Handout HR-H6: Mapping Out Home Ranges Activity Worksheet 1. What would we expect from putting a home range for a species onto a habitat map? Consider the data below for five animals. Species

Animal

Hardwood Forest

#1

Total Size Home Range (sq units) 25

#1

Grasslands Pine Forest

Water

0

20

4

1

#1

#2

25

0

22

3

0

#2

#1

16

12

1

3

0

#2

#2

16

16

0

0

0

#3

#1

72

0

44

28

0

Table 4.2: Species Home Range and Habitat a. In which habitat do you predominantly find each species? b. Indicate on the habitat map below, a possible home range for each animal in Table 4.2.

Home Range

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Habitat Map Legend: Green Hardwood Forest Red Grasslands Violet Pine Forest Blue Water Scale: Each block represents 1 square unit of area.



c. Are there any home ranges that overlap? Can you reposition the home ranges so they do not overlap? Can you reposition the home ranges so that they overlap more? 2. Again consider the relationship between the habitats and the home ranges. Are there any patterns and, if so, develop hypotheses for these patterns? Use the following questions to help you. a. Do you notice any predator-prey relationships? b. What does this say about the trophic level differences among the species considered? c. Is this reflected in the home range of these species? d. Is there any indication of human interference? e. What would human interference say about the habitat and the home range? f. Does an understanding of individual behaviors tell you anything about the entire population? Consider that when we are using tracking devices, we are tracking one animal at a time. g. What are the patterns and relationships between habitats and home ranges? Home Range

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Buffers What is a buffer? Would having a buffer help a species? There are two types of buffers – uniform and directional. A uniform buffer is a buffer of uniform size all around the home range. A directional buffer is a buffer that does not go all around the home range. The purpose of the buffer is to offer additional conducive habitat to the animal or specie’s home range.

Figure 4.4: A Home Range With a Uniform Buffer Directional buffers can be driven by habitat or availability. For example, a home range may abut a river and therefore cannot expand in that direction. In a man-made habitat, adjoining land may not be available. Figure 4.5 shows an example of a directional buffer in yellow.

Legend Red Yellow Blue Green

Home Range Buffer Unsuitable Habitat Suitable Habitat

Figure 4.5: Directional Buffer

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Similar Polygons, Home Ranges and Buffers Two polygons are similar if their corresponding sides are proportional and their corresponding angles are equal.

Rectangle A is 1 unit × 6 units

Rectangle B is 2 unit by 12 units

We can show that the two rectangles, A and B, are similar as follows. Sides: The ratio of the lengths is 6:12 and the ratio of the widths is 1:2. 6/12 = 1/2 so the sides are proportional. Angles: All of the angles in each rectangle are 90 degrees, so their corresponding angles are equal. Questions for Discussion 1. The following illustrates similar trapezoids although they do not initially look the same. Can you locate the corner corresponding to P in the other two trapezoids?

Figure 4.6: Similar Trapezoids 2. The rectangles, one inside the other in Figure 4.4 are similar rectangles, but the rectangles, one above the other in Figure 4.5, are not similar. Explain why. 3. What conclusion can you make about the resulting home range polygon when you add a uniform buffer? When you add a directional buffer? Practice 1. A 10% uniform buffer in all directions of a home range polygon creates a new home range polygon that is similar to the original polygon. a. Show this first with a rectangle. b. Show for a triangle. c. Show for any polygon. 2. Add a 10% uniform buffer to your home range polygon in Lesson 3. Compare the area of the home range with the buffer and without. Why might you want to create a uniform buffer for your animal (or bird)? Home Range

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3. Add a directional buffer to your home range polygon in Lesson 3. Compare the area of the polygon with and without the buffer added. Why might you want to create a directional buffer instead of a uniform buffer for you animal (or bird)?

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Lesson 5

Extensions

Extension 1 – Threats to Habitats The Glaciated Plains lie at the heart of Montana’s grasslands, spanning nearly three million acres. It is made up of two major areas – the Bitter Creek and the Comertown Prairie. The Bitter Creek is an expansive 1.5 million acres of grassland that encompasses Grassland National Park in Saskatchewan, as well as the largest potential grassland wilderness area in the United States. The landscape is nearly unbroken by roads and development and is host to many endangered grassland species. The Montana portion provides habitat that is vital during migration and winter months for species such as sage grouse and pronghorn antelope. Comertown Prairie, in the far northeastern corner of Montana, has a rolling landscape of native grasses and shallow “pothole” lakes formed years ago by the great continental glacier. This area is the largest unplowed stretch of prairie pothole ecosystem left in Montana. Each year millions of ducks, geese, and shorebirds migrate through the Great Plains to breed in the Comertown Prairie for its wetlands and grasslands. Energy development and conversion to farming lands (“sodbusting”) are threats to the Montana Northern Prairies. Sodbusting is the most serious threat as it destroys the balance between grasses, wildflowers, shrubs, and diverse microfauna. Approximately 500,000 acres of native grasslands were converted between 2002 and 2007 according to the US Department of Agriculture. Other threats include invasion by noxious plant and animal species, poor management of grazing and water, climate change, fire, and exotic diseases Requirement: Write a paper on the history and current status of this Glaciated Plains area. Choose one of the threats to this area (sodbusting, plant/animal invasion, management of grazing and water, climate change, fire or exotic diseases) and research its impact on the wild life of the area. Suggest policy and practice changes that would be advantageous to promote continued use of this area as a wildlife habitat. Extension 2 – Managing Disease Spread Managing disease spread through tracking and identification of home ranges. Use both the prairie dog and the grizzly bear as examples. The Northern Rocky Mountain Science Center conducts scientific research in support of natural resource management in the Northern Rocky Mountains of Wyoming, Montana and Idaho. NoRock scientists have been studying grizzly bear populations in the Greater Yellowstone ecosystem for over 30 years. Scientists have used radio collars to track grizzly bear movements, monitored habitats and key foods, and most recently have developed non-invasive hair snaring techniques to genetically identify individual bears. This work has been done under the guidance of the Interagency Grizzly Bear Committee (IGBC), which includes representatives from Wyoming, Montana, and Idaho, and various federal agencies. USGS scientists, in collaboration with Wyoming Game and Fish, have provided valuable scientific information in support of the recovery and delisting efforts undertaken by management agencies in the state of Wyoming. Science conducted by the interagency Grizzly Bear Study Team has provided the foundation for

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the current de-listing proposed for the Greater Yellowstone. New research techniques used by the IGBST include highly accurate Global Positioning System (GPS) collars that pinpoint a bear’s location many times a day, as well as the hair snares fashioned of barbed wire that collect small clumps of hair when bears rub against them, and DNA and nutritional analyses that determine the sex, identity, diet of each bear that left a hair sample and whether they have diseases. There has been an emergence, or resurgence, of parasites that move between livestock, wildlife, and/or humans, including grizzly bears. Almost 75% of all emerging human infectious diseases like Brucellosis and chronic wasting disease can spread between different species and many livestock disease issues are associated with repeated introductions from wildlife. References: http://www.nrmsc.usgs.gov/research/igbst-home.html[7] and http://www.nrmsc.usgs.gov/research/NCDEbeardna.htm[8] Requirements: Describe the process of using mathematics of finding one grizzly bear, which has been infected out of a group of 40 through various tracking devices and calculating simple probabilities. Use web to investigate the effect of prairie dog plague on the black-footed ferret population. Write up your finding in the form of a report to the Wildlife Commission. Extension 3 – Mark-Recapture to Estimate Population Basic method (more details in Activity below): Trap some animals, mark and release Repeat trapping and count captures of marked individuals and non-marked individuals Mark non-marked individuals, release all individuals Estimate population size based on proportion of recaptured marked individuals Background Information Closed populations. No individuals enter or leave the population between surveys. Characteristics of a closed population include dispersal barriers, philopatry (mating of organisms only within the population, no cross populations), large surveyed area, slow reproductive rate, slow death rate, and short time between surveys.

Figure 5.1: Closed Population

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Open populations. Individuals enter or leave the population between surveys. The arrows represent the individuals who entered or left the population between samples. The individual with the “sparkle” around it represents a birth.

Figure 5.2: Open Population

ACTIVITY 5-1 Mark-Recapture Simulation Using Beads Objective: Estimate total population Materials: (per group) clear marbles blue marbles 3 cups large enough to hold marbles Handout HR-H7: Mark-Recapture Simulation Using Beads Activity Worksheet Mark-Recapture Simulation – Using Lincoln-Petersen Method of Estimation 1. Put all of your clear marbles in a container or cup. This is your population cup. Put all your blue marbles in a second container or cup. Keep one container or cup empty. In your group write down a prediction of how many total clear marbles you have. In other words, estimate the size of your population. Prediction of number of clear beads initially in the cup; N =_______. 2. Variation in Sampling. a. One member of the group takes 12 marbles out of your population cup. Put these clear marbles in the empty cup and replace all of these clear marbles with blue marbles back in the population cup. Blue marbles are considered “marked” marbles. Mix thoroughly! Note this action is recorded in the first row of Table 5.1. b. Have another group member take a random sample (one handful) of your population. Record the number of clear and blue marbles in Table 5.1. Estimate the population.

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c. Repeat to sample the population five times, recording the sample and estimating the population after each sample. Total # marked # beads in Round beads in handful population (C) (M) 0 12 Initial round 1

12

2

12

3

12

4

12

5

12

Average

12

# clear beads

12

#blue beads # beads that get (R) marked

0

12

Population estimate (N)

N/A

Table 5.1: Data Recording Table 3. Look at your data in Table 5.1. a. What do you notice about the samples? b. Why are the samples different? c. What is your prediction about what percent of the population is blue? d. How did you estimate the population after each step? e. Compare your initial estimate of population with the estimates in Table 5.1. 4. Improving Estimates. a. Replace all of the marbles into their original containers (all clear in population cup; all blue in a second cup; a third cup empty). Again remove 12 clear marbles and replace them in the population cup with 12 blue marbles. This action is noted in the first row of Table 5.2. b. One group member takes another sample (one handful) of your population. c. Count the number of clear and blue marbles sampled, record the numbers in Table 5.2 and return the blue marbles back in the population cup. d. Put the clear marbles in the extra cup (with the previously discarded 12 clear marbles) and replace these clear marbles with blue marbles back in the population cup. Mix thoroughly! e. Estimate the total population. f. Repeat the sampling process, parts a-e, five more times.

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Round

Total # # beads that Population marked beads in # beads in # clear #blue beads get marked estimate (N) (R) population handful beads (M) (C)

Initial round 1 2 3 4 5

0

12

12

0

12

N/A

12

Average Table 5.2: Data Recording Table 5. Look at your data in Table 5.2. a. How did the estimates vary with additional mark-recapture samples? b. Would more sampling help your estimate? c. Compare your initial estimate of population with the estimates in Table 5.2. d. What happens if you get R = 0? (No recaptures). Do you throw that sample out? Do you count it in an average of recaptures? 6. How could your group better estimate the total number of beads in your population cup? Consider the following diagram.

Figure 5.1: Population Sampling

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N = Total Population (unknown; this is what will be estimated) M = Total # Marked C = # Captured in each survey R = # Recaptured organisms in that particular survey (M’s caught again)

Figure 5.2: Exploring Ratios

So using ratios: a. Use the formula N = MC/R and determine a population estimate for each row of data in Tables 5.1 and 5.2. b. Compare your initial population prediction to the new estimates of population size. c. Count the actual number of clear beads (initial population) and compare the estimates to the actual population size. d. What conditions might lead to Lincoln-Petersen giving you a bad estimate?

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Assessment – Home Range – Species’ Living Rooms 1. Draw a polygonal patch for the home range of the sage grouse depicted in the following portion of a map. Trace it on a grid and compute the area of the patch.

2. A researcher has given you the following data in UTMs for one animal or bird of the species considered in this module. Draw a graph and plot the data points on graph paper. Be sure to label both axis with the appropriate scale and what it represents. All data comes from zone 13. Easting 0278424 0278401 0278393 0278430 0278424 0278481 0278564 0278783 0278549 0279618 0279618 0278556 0278556 0278547 0278566 0278505 0278505

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Northing 5276178 5276160 5276134 5276030 5276001 5275913 5275792 5275721 5275910 5275510 5275510 5275991 5275991 5276092 5276248 5276295 5276295

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3. Draw a polygonal patch containing the points and find its area. Draw a uniform small buffer around the patch. Estimate or compute the area with the buffer added. 4. Guess which bird or animal that you studied corresponds to these data points. Give reasons for your answers. Talk about the habitat, and its predators or prey. 5. What type of tracking system was most likely used and what did the tracker have to consider in using the tracking system and recording the data?

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Glossary Buffer – an area around a home range that offers additional conducive habitat to the animal or specie’s home range. Carrying capacity – the largest number of individuals of a particular species that can survive over periods of time in a certain portion of land. Concave polygon – a polygon with at least one interior angle greater than 180 degrees. Convex hull –the smallest convex set of points that contains all data points of interest. Convex polygon – a polygon with every interior angle less than 180 degrees. Directional buffer – a buffer that does not go all around the home range area. Easting – one of three features that determine location on a UTM grid; the feature describing the east or west distance from the center meridian. Ethology – the study of animal behavior. GPS tracking – a method used for tracking members of a species using Global Positioning System (GPS) equipment. Habitat – an ecological or environmental area that is inhabited by a particular species of animal, plant, or other type of organism; the natural environment in which an organism lives, or the physical environment that surrounds a species population. Home range –the area in which members of a species live, travel and spend their time; an area that possesses the resources required for the species to survive. It is closely related to, but not identical with, the concept of "territory" which is the area that is actively defended. Latitude – is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. Lincoln-Peterson Method (of estimation) – a method of estimating population size that assumes the population is closed (no births or deaths) and is done with only two closely timed visits to a study area. Longitude – is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. Mark & recapture – a method of estimating a population by capturing, marking and releasing individual members of a species during a visit and then returning to the area to recapture a sample and estimate the population using proportions.

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Northing – one of three features that determine location on a UTM grid; the feature describing the north or south distance from the equator. Population density – the number of a particular organism in an area measure given as a ratio. Pythagorean theorem – If a and b represent the legs of a right triangle and c represents the hypotenuse of the right triangle then a2 + b2 = c2 Radio telemetry – the method of using radio waves from a distance to transmit information; in animal tracking this is done by attaching a radio transmitter to the animal. Regular polygon – a polygon with all sides and angles equal Similar polygons – polygons whose corresponding sides are proportional and corresponding angles are equal. Territory – an area inhabited and defended by an animal or group of animals. Uniform buffer – a buffer of uniform size all around the home range area. Universal Transverse Mercator (UTM) – a conformal projection (preserves shape) that represents the Earth’s three-dimensional surface in a relatively accurate two-dimensional display using a geographic coordinate system to provide location. The system allows identifying locations between 84 degrees North latitude and 80 degrees South latitude.

References [1] Morse, S.P. Converting addresses to/from latitude/longitude/altitude in one step. Found at http://stevemorse.org/jcal/latlon.php. [2] Google Maps. Found at http://maps.google.com. [3] Montana State University. Convert geographic units. Found at http://www.rcn.montana.edu/resources/tools/coordinates.aspx. [4] Burt, W. H. (1943). Territoriality and home range concepts as applied to mammals. Journal of Mammalogy. 24:346–352. [5] Home Range Data Set. Data for student activities provided by the following: Randy Matchett, Senior Wildlife Biologist for the United States Fish and Wildlife Service – CMR NWR in Lewistown, Montana for data and black-footed ferret pictures and the video included with the unit. David Jachowski, graduate student at the University of Missouri, for the ferret and prairie dog data. Paul Jones, Wildlife Biologist, and the Alberta Conservation Association in Lethridge, Alberta, Canada for the pronghorn antelope data and pictures. Barbara Jean Keller, graduate student at the University of Missouri and the Department of Fisheries and Wildlife for the bison data.

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Barbara Cozzens, Program Director, Northern Montana Prairies, The Nature Conservancy, for the curlew data and pictures. [6] The Nature Conservancy. (2014, August). Follow that curlew: Radio tracking a mysterious migration. Cool Green Science. Found at http://blog.nature.org/science/2014/08/04/long-billedcurlew-migration-study-idaho-intermountain-bird-observatory/. [7] U.S. Geological Survey. Northern Rocky Mountain Science Center. Interagency grizzly bear study team. Found at http://www.nrmsc.usgs.gov/research/igbst-home.htm. [8] U.S. Geological Survey. Northern Rocky Mountain Science Center. Northern divide grizzly bear project 2002-2008. Found at http://www.nrmsc.usgs.gov/research/NCDEbeardna.htm.

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