BIOS 3010: ECOLOGY

Dr Stephen Malcolm

Laboratory 9: Density dependence

Please analyze the attached data for density dependence as described below

Introduction:

George Varley and his colleagues at Oxford University in England wanted to find out what caused population fluctuations in the winter moth, Operophtera brumata, feeding on oak trees, Quercus robur, in Wytham Woods near Oxford. They censused oak trees as shown in Figure 7.1 (from Varley et al., 1973) in order to count the numbers in different life history stages and create a life table. The moth is reproductively active in early winter (hence its name) with males flying actively in November to find large, wingless females as they climb the trunks of oak trees. The females are basically large egg sacks and the winged males mate with them as they climb the trees to lay their eggs on twigs that will carry the new leaves the following spring. These leaves are the larval food.

Data Observations:

Observations by George Varley and his colleagues found that there were 4.39 live adult females/m2 climbing the trees in November and that each female laid 150 eggs on the bark of oak trees. In spring, there were 96.4 full-grown larvae/m2 and that of these, 6.2/m2 were killed by a fly parasitoid, 2.6/m2 were killed by other parasites, and 4.6/m2 were infected and killed by a microsporidian parasite. From these numbers they determined how many pupae were formed. It was easy to see that 13.4/m2 of the pupae were killed by a parasitic wasp, but it was not easy to measure how many were eaten by predators. So predator mortality was estimated from the information gathered. Finally, 7.5 adult females/m2 were found climbing the trees in the following November.

From these data, Varley and his colleagues produced the life table shown in Table 7.2 (also from Varley et al., 1973). The research team then went on to collect a further 19 years of data, and these data shown below provide the basis for your exercise in detecting density-dependent mortality factors.

Using the following data, we would like you to determine which mortality factors show the strongest density-dependent regulation of population size (from Varley et al., 1973, Table F) (Data are in this linked spreadsheet).

Year

stage	k	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
	k1	1.59	0.56	1.14	1.33	0.24	1.16	0.83	0.48	0.83	1.15	1.21	0.91	1.09	0.85	0.66	0.52	1.42	1.20	1.19
Log. larvae		2.05	2.07	1.74	1.26	2.20	1.89	1.98	2.44	2.28	1.76	1.33	0.88	1.13	1.61	2.12	2.43	1.71	0.99	1.00
	k2	0.11	0.01	0.003	0.01	0.004	0.003	0.03	0.02	0.07	0.10	0.02	---	0.02	---	0.005	0.03	0.04	0.01	---
	k3	0.04	0.02	0.06	0.02	0.03	0.03	0.01	0.01	0.02	0.04	0.06	0.06	0.06	0.04	0.01	0.01	0.005	0.03	0.01
	k4	0.05	0.03	0.05	0.04	0.06	0.04	0.02	0.05	0.04	0.02	0.03	0.04	0.03	0.01	0.01	0.01	0.02	---	0.03
	k5	0.69	0.77	0.75	0.34	0.73	0.65	0.47	0.79	0.82	0.66	0.72	0.22	0.24	0.40	0.74	0.87	0.86	0.50	0.48
	k6	0.29	0.10	0.03	0.16	0.07	0.09	0.28	0.20	0.16	0.15	0.45	0.08	0.06	0.12	0.14	0.13	0.33	---	---

Note: In the linked data sheet, estimates of the missing data have been added to make it easier for you to use Excel (it is important to note that Excel is not a reliable program to use for data analysis – we use it because it is readily available and illustrates the methods we are emphasizing).

To do this we would like you to do the following:

(1) Enter the data vertically as shown in the attached Excel sheet (do not enter zero for missing data points) and calculate K_total values for each year (sum each k_x value).

(2) Draw a graph using the graph wizard of each k_x-value and K_total (y-axis) plotted against time (year) on the x-axis. Which k_x values do you think are most responsible for overall mortality?

(3) Using the “Tools” menu select “data analysis” and then “regression” and use linear regressions to regress each k_x value as the dependent variable against K_total values as the independent variable across all 19 years. This will give you 6 separate analyses.

For each analysis do the following once you have selected “regression”:

Input Y: enter the range for your kx values (including the column title) e.g. $B$1:$B$20 (the $ just means that you have fixed that cell and it won’t change - this is the range of data from cell B1 to cell B20 in the B column and rows 1 to 20).

Input X: e.g. $H$1:$H$20 (if K_total is in column H).

Check the labels box: (this indicates that you have included the column headings)

Output options: indicate where you want the regression analysis to be placed (e.g. if you enter A23 the analysis will start at cell A23 in the top left hand corner)

Residuals: check the “line fit plots” option (this will automatically plot a graph of the data and the regression as a series of predicted points).

This analysis will tell you which mortality factors have a significant density dependent association with total mortality. From the summary output you need the R square value, and from the ANOVA table you need the F and significance of F values (these tell you whether the regression was significant - any significance value less than 0.05 is significant (very low probability (less than 5%) that they are the same), and lastly you need the coefficients for the intercept on the y-axis and the slope (b) which is the coefficient under the intercept (its P-value will be the same as the ANOVA “Significance F” value.

For each of these 6 regressions, make a summary table that gives the comparison (e.g. k₁ against K_total), then the R², intercept, regression coefficient (slope or b), F, and Significance F (P-value).

(4) In the same way as for (3) above, plot each k_x value against the logarithm of the density of the stage on which the mortality acted. To do this you will need to calculate these densities using the log larvae data. For example, k₁ was the mortality that acted on the eggs and so the actual density was (log larvae + k₁) Similarly you should appreciate that k₂ acted on log larvae, but k₃ acted on (log larvae - k₂), and k₄ acted on (log larvae-(k₂+k₃)), etc.

When you have completed these regressions, make a summary table as in (3) of the regression statistics.

(5) Using the two tables from (3) and (4) write up your conclusions about what mortality factors (k_x) were responsible for density dependent mortality and density-dependent regulation of this population of winter moths.

References:

Varley, G.C., G.R. Gradwell, and M.P. Hassell. 1973. Insect Population Ecology. An analytical approach. Black Scientific Publications, Oxford, 212 pages.