Populations Lab
LAB #3, PART I: ESTIMATING POPULATION SIZE
OBJECTIVE: To estimate population sizes and dynamics, you will be able to:
1. Compare and contrast methods of estimating population size (CLO #1)
2. Explain and use simple mathematical models of population dynamics (CLO #2)
3. Synthesize your research with the primary literature in ecology (CLO #3)
BACKGROUND INFORMATION:
Estimating the size of populations of organisms is a central problem in field ecology. It is one of the most basic pieces of information we can collect and is an important start for other ecological studies and conservation and management efforts. There are several ways to evaluate organism count (pop. size) or density (count/area), which are two means of characterizing populations
Sometimes, it is sufficient to evaluate organism relative abundance (relative representation of a species in a particular location). In that case, an ecologist can use indices. Indices are anything that can be correlated to the number of organisms in a given habitat (e. g., feces pellets, browsed branches, tracks, plant cover, etc.).
When population size is necessary, population estimates can be developed with a number of sampling and mathematical methods. Since it is rarely feasible to count an entire population, ecologists count a portion of the population and then estimate the total population size using mathematical functions. This can be done a number of ways, but in this exercise we will use two of the most common: density methods and mark-recapture methods.
Density method: In this method, ecologists will count the number of individuals in a prescribed area and then scale this measurement up to estimate the whole population size. Transect methods, in which an ecologist traverses a transect and counts individuals at specific locations along the line, are commonly used for plants and occasionally for animals.
Density methods require a few key assumptions:
1. The population is confined to a specific area
2. Individuals are readily detectable
3. Count areas are extensive relative to area occupied by population
Using these assumptions, ecologists use various models to calculate population size. In this lab, you will use a simple Seber (1973) model:
where N = the population estimate, N0 = the average number of organisms found in a plot. And p = the ratio of the individual plot area to total area (e.g. 25 cm2/820 cm2). Once you have calculated No, use the equation above to calculate N.
Confidence intervals provide a measure of the precision of our estimate (population size, N, in this case). A 95% confidence interval is a range of values that is thought to contain the true population size 95% of the time…that is, if you repeat your sampling and confidence interval calculation 100 times, the confidence intervals will capture the true value 95 of those times. To calculate the 95% confidence interval we can simply calculate the upper and lower confidence limits for N0 and then use those values in the equation above to calculate the upper and lower values of our population estimate, N. Follow these instructions:
1. Calculate your value for No by taking the average of the number of individuals in each plot (3 plots for your group, 9 plots for the class). For example, in the image below the average, No=10.33.
2. Calculate the standard deviation (s) of the three values from your plots (or 9 values for the class). You can do this in excel by using the function =STDEV.S(data cell range). (see image on right). In the example, s= 2.52
3. Divide the standard deviation by the square root of your sample size, n (i.e. n=3 for your group data, n=9 for the class data). This gives the standard error of the mean (SE). In the example,
4. Use the table below to find the t-value (t.05 highlighted in yellow) for the correct degrees of freedom (df). df is the sample size minus one (i.e. df=2 for your group data, 8 for the class). In the example, t.05= 4.30.
5. Use the equation below to calculate the upper and lower estimates of No. These values fall above and below the No you calculated earlier.
In the example, this is or an upper value of 17.99 and a lower value of 2.68
6. Use those two values (we can call them No-upper and No-lower) with the equation to calculate the upper and lower limits of the population size estimate (i.e. Nupper and Nlower). In the example, this is
7. What does this mean? You estimate of population size is N, as originally calculated with No, and you are 95% confident that the true value of N falls between Nupper and Nlower (i.e. Nlower < N < Nupper). For the example this means that 88.0<N<590.
8. When you graph your data in a bar graph, the height of the bar should be your estimate of N. Then, format your 95% confidence interval bars to the difference between N and Nupper (or Nlower). Display these CI bars above and below your estimate of N.
For the example, the estimate of , therefore the length of the 95% confidence interval bars should be 589.9-338.9=251. See the example graph below. Don’t forget to add an informative captions…and your graph should also include a bar for the entire class data set (n=9).
Mark-recapture method: In this method an ecologist captures animals, marks and releases them, and then repeats the process at a later time. The ratio of marked to unmarked animals during later capturing events can be used to estimate the size of the population.
The mark-recapture method requires a few key assumptions:
1. The population is closed
2. The marks are not lost or overlooked
3. All animals are equally likely to be caught.
Using these assumptions, ecologists use the Lincoln-Peterson model to calculate population size. In this lab, you will use a simplified version of the model:
where is the estimate of population size, M is the number of animals marked and released during the first session, C is the number of animals captured during the second session, and R is the number of recaptures in the second session. This equation can be rearranged to solve for .
There are a number of ways to calculate confidence intervals, depending on the R/C ratio. We will use a simple binomial confidence interval that is estimated with the help of Figure 2.2. This estimate assumes that the ratio of R/C is > 0.1.
1. Calculate using the equation above.
2. Calculate R/C and find this value on the X-axis (sample proportion) of the graph.
3. Look vertically from that point to the first (lowest) contour line that most closely matches your recapture sample size “C”, then follow horizontally to the Y-axis (population proportion). This is the lower 95% confidence limit of R/C.
4. Repeat this procedure but look vertically to the second contour line with sample size “C” to find the upper confidence limit of R/C.
5. Convert these R/C confidence limits to limits for the population size by plugging the reciprocal of the confidence limit value into the population estimate equation. (e.g. if your estimate from the Y-axis is R/C = 0.4, then this is placed as a reciprocal in the following equation.)
6. Perform this calculation for the upper and lower 95% confidence limits of the population size estimate.
7. In your graph, format the height of the bar to be at and the length of the 95% confidence interval bars to be the difference between and the upper (or lower) 95% confidence limits, similarly to what you did in your first graph. Be sure to include your group data and the class data on the graph.
Equipment: Handout, notebook, pencil, aquarium, plastic beakers, dry erase markers, paint pens
In-lab Methods:
Read through this handout so you know what you’re going to do. You may work in groups, but every student is responsible for their own report.
You will be working in groups with one person capturing, one marking, and one recording data.
Density plot estimate:
1. On the under-side of your aquarium, use a dry-erase marker to draw a transect line down the middle of the tank in the long direction. Measure the total length of the transect in cm.
2. Produce a list of random numbers between 0 and 5 cm less than the total length.
3. Use the list of random numbers to place three 5-cm x5-cm quadrat plots (25 cm2) along the transect, beginning on the left side of the transect and alternating sides for each plot. The random number identifies the beginningof the quadrat (e.g. the number 2 would indicate a plot from 2-7 cm along the transect). Draw the 3 plots on the underside of the aquarium with a dry-erase marker.
4. Add your “organisms” by dropping them haphazardly into the upright aquarium.
5. Count all of the individuals you observe in each of the three 25-cm2 plots and record your data. Also make a note about how the “organisms” are distributed across the entire population distribution.
6. Measure and record the inside dimensions of the aquarium (i.e. total population distribution area), then calculate N and the standard deviation for your data. Write your raw data on the white board to share with the class.
7. Combine the entire class dataset and calculate N and the standard deviation for the whole class.
Mark-recapture estimate:
1. Sample: Trap “organisms” by sweeping your trap through the aquarium once and placing your trapped individuals into a container. Repeat until you have trapped 50 individuals (M).
2. Mark each “organism” using the paint pen.
3. Return the “organisms” to the aquarium and haphazardly mix the population.
4. Repeat the sampling process until you have captured another 50 individuals (C). Then record how many of those individuals are marked (R).
8. Calculate and 95% confidence intervals for your group’s data and write the raw data on the white board to share with the class.
9. Calculate and 95% confidence intervals for the class’s data as a single combined dataset.
Census:
1. Remove the “organisms” from the terrarium and count them all while returning them to another container.
2. Record the true population size. Write this on the whiteboard and calculate a total class population size
Questions to answer (due next Friday)
1. Provide your data as tables, including the raw data, calculated estimate of population size, and upper and lower 95% confidence intervals. Also report your results in a single figure for all estimates (bar chart with 95% confidence intervals for all estimates, i.e. your group data and the entire class data for each of the two methods of estimating population size).
2. Why are indices not useful for estimating population sizes, but only for relative comparisons?
3. Evaluate your estimated population sizes in comparison to the actual population size. Which method of estimation was more accurate? What assumptions, if any, were violated for each method? How could you improve your estimate?
4. Why do ecologists estimate population size? When would an ecologist want to use a density estimate versus a mark-recapture estimate? (Think about organisms, habitats, types of questions…)
5. What would happen to your density estimate if:
a. the area observed was 50% smaller?
b. some individuals (e.g., females) were harder to detect?
c. individuals were attracted to sampling areas?
d. sampling areas were not randomly located?
Provide mathematical explanations for why each would occur, making sure to think about both estimates and confidence intervals.
6. What would happen to your mark-recapture estimate if:
a. several of the animals died or migrated out of the area between captures?
b. the marks were not properly observed?
c. handling the animals killed them after you had released it back into the wild?
d. some individuals had a higher probability of being caught than other individuals?
Provide mathematical explanations for why each would occur, making sure to think about both estimates and confidence intervals.
Consult your textbook, reputable parts of the web, and the primary literature to put your results in context. Please cite all outside sources!251.0 251.0 338.9333333333333
Group data (n=3)
Estimated population size
BIO317 page 1
