In-class Exercise #7 (Lab 7):

Analysis of Time Series Abundance Data

  In today’s lab we will be looking at the probability that abundance will decline beneath a specified level and the influence of environmental covariates on population growth.  In the first part, we will describe an approach called “Viable Population Monitoring” (Staples et al. 2005) which is a yearly prediction of the probability that within a given time frame the population abundance will decline below a specified level.  In the second part of this lab, we will describe how data from a time-series of abundance can be analyzed to investigate questions such as:  Is there evidence for density dependence?  What are the important environmental factors that cause population fluctuations? 

I. IN-CLASS EXERCISE: 

Objective 1:

If a series of abundance estimates is available for a population, then those data can be used to estimate the probability of reaching quasi-extinction thresholds (Braun 2005).  For the in-class exercise, we will use the program PopGrowthAnalysis written by Dr. Horne.  The analysis will be based on abundance data collected on the Hawaiian akepa.  The modeling procedure will utilize the Exponential Growth Model with Process Noise (EGPN) to estimate growth rates based on the abundance data.  After obtaining estimates of parameters, this model will be used to predict probability of persistence into the future.

Steps:

1)      Navigate to the S:\Courses\WLF448\PopulationData with Windows Explorer.  Copy and paste the 3 Excel spreadsheets there (AmRedstart.xls, AkepaForest.xls, and Coregonus.xls) onto your network drive or other media.  Note: The in-class exercise will use AkepaForest.xls for part A and Coregonus.xls for part B.  The problem set will utilize AmRedstart.xls and Coregonus.xls.  

2)       Open the program PopGrowthAnalysis Beta 1 located under Start - UI Software - Programs - Analytical. OR search for the program PopGrowthAnalysis.

3)      Select File, then open and navigate to the AkepaForest.xls data.  Under the “Select Excel Worksheet” dialogue highlight Sheet1.  This will automatically plot your time series abundance data (in this case density of akepa/ha) on the graph.  Note that this plot displays the data as continuous although the data are actually discrete.  

4)      Select the Analyses drop-down menu and choose Viable Population Monitoring. 

5)      Under the option “You will need to establish the following parameters:”,

       enter 0.35 for “1) the lower (or upper) threshold population size”,

      enter 20 for “2) The time in the future for which the probability of reaching the threshold applies”, and

      enter 5 for “3) The amount of time since the first observation to begin projecting the probability of reaching the threshold”. 

6)      Uncheck the box next to “EGSS (exponential growth with process variation and observation error)” and then click on the “Calculate VPM>>” tab. 

7)      The output displays the original data (black line) and the predicted probability of falling below the threshold within the specified time horizon (green line).  Ignore the red line for VPM (EGSS) as this is referring to the box unchecked in step 6 and was not included in the analysis.  The green line represents the probability of the akepa population going beneath 0.35 birds/ha (the quasi-extinction threshold) after 20 years, as each successive year of data is included in the model. 

8)      To save these results, select the Output drop-down menu and choose Save Text Output.  Save the output in your working directory (wherever the input file is saved) as AkepaForestOutput.txt.   

9)      Open the output text file saved in step 8. Scroll down to the section entitled Viable Population Monitoring (VPM) and examine the results (Note that mu(EGPN) = r).  Discuss why the estimate of mu(EGPN) changes through time.  What was the probability, based on abundance data up to 1996, that akepas would fall beneath 0.35 birds/ha in the next 20 years? 

Objective 2:

For the second part of the in-class exercise we will look to see if there is a correlation between any covariates and the observed population growth rate.  For this part of the in-class exercise we will analyze data collected by Eckmann et al. (1988) on common whitefish (Coregonus lavaretus) in Lake Constance.  For this exercise we will treat year class strength (YCS) as a measure of abundance. 

Steps:

1)      Open the Coregonus.xls file in Excel.  Scroll down to year 1983 and 1984 and note there are no data entered in the corresponding YCS column.  Copy and paste the entire worksheet into a new workbook.  Fill in the blank entries next to 1983 and 1984 with 1’s (blank entries in the abundance data will cause the program to crash).  Save the new workbook as Coregonus2.xls.  Be sure to save the new workbook as an Excel 97-2003 (*.xls) file.  The PopGrowthAnalysis Beta 1 program does not recognize *.xlsx files.  

2)      Restart the program PopGrowthAnalysis Beta 1, open the Coregonus2.xls file that you just created, and select Sheet1.  Make sure that Year is selected for the time period of interest (x-axis) and YCS is selected for abundance (y-axis).  Note that by highlighting a column header under the Sheet1 dialogue and selecting the “Apply current selection for time” or the “Apply current selection for abund.” the graph can be modified to examine other relationships among the data.   

3)       Select the Analyses drop-down menu and this time select Fit Growth Model(s). 

4)      Check the 4 models that have process noise exclusively:  Exponential growth with process noise (EGPE), Gompertz density dependent (GOMP), Ricker density dependent (RICK) and the Theta-logistic dependent (THET).  Click the “Next>>” tab. 

5)      A window titled “Bootstrapped Confidence Intervals for Density Dependent Models” will appear.  Keep a 95% confidence interval but change the number of Bootstrap replicates for calculating C.I. to 400.  Click the “OK” tab. 

6)      The graphical output should now include the estimated population growth models you selected (EGPE, GOMP, RICK, and THET). 

7)      Select the Output drop-down menu and choose “Save Text Output” as Coregonus2Output.txt in your working directory.   Close the “Analysis of Population Growth Using Time Series Data” program. 

8)      Open Coregonus2Output.txt and scroll down to the “Information Theoretic Model Selection”.  Note that the Ricker model has the lowest AIC score.  Beneath the “Model Selection Criteria” are the model parameters for each of the estimated models.  Note that that trend(mu) = r and process variance = sigma²).  Beneath the parameter estimates are the “Residuals” for each model.   

9)      Highlight the data under the “Residuals” section from the Ricker model and copy and paste the data into Sheet2 in Coregonus2.xls.  Rename Sheet2 to Ricker Residuals. 

10)  On Sheet1 copy the column of data entitled O2 (dissolved oxygen) and insert this column into the sheet name Ricker Residuals so that it appears to the left of the column titled Residuals.  Delete the row for year 1984 since there are no residuals for that year. 

11)  Make a scatterplot of Residuals against the environmental covariate of dissolved oxygen (O2).  To do this using Excel 2007, highlight the Residuals and 02 columns simultaneously (Columns E and F, respectively).  Under the Insert tab select Scatter, and the first icon that appears (“Scatter with only Markers”).  A graph should appear, entitled “Residuals”, with Residuals data plotted on the y-axis versus O2 data plotted on the x-axis. 

12)  On the graph, right-click the mouse on one of the plotted data points.  This should select all of the plotted data and open a dialogue box.  Select Add Trendline and the “Format Trendline” dialogue should open.  Under Trendline Options - Trend/Regression Type, select Linear and check the boxes next to Display Equation on chart and Display R-squared value on chart.  Click “Close”. 

13)  The R-squared value (0.1277) seems fairly low for what is often considered a major factor on fish survival.  What does this mean?  Consider the influence of time?  Could there be a lag effect between O2 levels and fish abundance?  How might these data and knowledge of fish ecology be used to develop a more conclusive link between population growth and environmental covariates?  You will explore these questions more in the problem set.  

II.  LITERATURE CITED

Braun, C., editor.  2005.  Techniques for wildlife investigations and management.  Sixth edition.  The Wildlife Society, Bethesda, Maryland, USA. 

Eckmann, R., U. Gaedke, and H. J. Wetzler.  1988.  Effects of climatic and density-dependent factors on year-class strength of Coregonus lavaretus in Lake Constance.  Canadian Journal of Fisheries and Aquatic Sciences 45:1088-1093. 

Staples, D. F., M. L. Taper, and B. B. Shepard.  2005.  Risk-based viable population monitoring.  Conservation Biology 6:1908-1916.

Revised: 04 October 2011