Lab. 6. Phenology of Gypsy Moth FlightThe goal of this lab is to develop a model that can be used to predict the timing of the flight of gypsy moth males. Male moths numbers are monitored using pheromone traps. Pictures below show the trap and dead males removed from the trap.
Predicting the dates of male moth flight is important for selecting time when the traps should be placed and removed at various geographic locations.
1. Save file "phenol.txt", and open it from the Microsoft Excel. This file contains the following information:
1. Use data from Casagrande et al. (1987) on gypsy moth larval and pupal development (table below). Plot development rate vs. temperature and estimate the lower temperature threshold and degree-days separately for larval and pupal periods.
Table. Development time of gypsy moth males
Temperature Larval Pupal C development development ====================================== 13 93 - 18 55 27 20 44 18 25 30 16 28 28 12 30 27 12 ======================================2. Use the model of Johnson et al. (1983) for egg development: eggs start hatching after accumulating of 282 degree-days since January 1 (lower temperature threshold = 3 degrees C).
3. Build the model as follows. Put weather data from any station in the first 3 columns of a new worksheet: Julian day which is the day number since January 1, minimum temperature, and maximum temperature. The next column will be used for accumulating degree-days for the egg stage. Put zero in the upper cell (D2) of this column because initially no degree days have been accumulated. In the cell below (D3) put the following equation: =D2+0.5*(MAX(0,B2-3)+MAX(0,C2-3)). This equation implements the "rectangular method for accumulating degree days: it assumes that the minimum temperature (B2) has lasted for half day, and then the maximum temperature (C2) has lasted for another half day. Function MAX(0,B2-3) gives the effective temperature: if the temperature (B2) is greater than 3 (the lower temperature threshold) then the effective temperature = B2-3; if B2 < 3, then the effective temperature = 0 (because 0 is greater than B2-3).
4. In column E estimate degree-days for larvae. Degree-days for larvae start accumulating only when accumulated egg degree-days exceed 282 (model of Johnson et al. 1983). Thus, use the following equation for cell E3:=E2+(C2>282)*(effective temperature for larvae). The term (C2>282) equals 1 if C2 > 282, otherwise it equals 0. The equation for the effective temperature is the same as for the egg stage (write it yourself!). Use the lower temperature threshold for larval stage that you have estimated before (section 1).
5. In column F estimate degree-days for pupae. Degree-days for pupae start accumulating only when accumulated larval degree-days exceed the required amount of degree days which you have estimated before (section 1). You the equation similar to that in column E (write it yourself!). Use the lower temperature threshold for pupal stage that you have estimated before (section 1).
6. Adult males start emerging on the day when accumulated pupal degree-days exceed the amount required for pupal development, which you have estimated before (section 1). However, they continue emerging later for about 1 week. The model for egg phenology (Johnson et al. 1983) simulates the start of egg hatch, but many eggs hatch later than predicted by this model. Individuals that hatch later will have a delay in their development through all stages. This delay can be simulated by tracing the phenology of several cohorts that start their larval development at varying dates. However, we will use a simplified approach. We already found the date of the beginning of male moth flight. Now we will assume that emergence period is extended from this date till additional 150 degree-days are accumulated (for pupae). The cumulative proportion of emerged males, P, is estimated as P = (D - S)/150, where D = degree-days currently accumulated by pupae and S = degree required for the start of moth emergence. Also, P = 0 if D < S, and P = 1 if D > S+150. Combining all these conditions we get the equation that you need to put in cell G2: =MIN(150,MAX(0,F2-300))/150. Autofill it to the entire column.
7. The number of males caught in pheromone traps is assumed to be proportional to the density of males that are alive. We will assume that all males live for 10 days. Then the density of males that are alive is proportional to the difference between the cumulative proportion of emerged males, P(t), and the cumulative proportion of males emerged 10 days ago, P(t-10). Thus, estimate the value N(t) = P(t) - P(t-10) in column H.
8. Estimate the mean date (Julian day) of moth flight using the equation:
where N(t) was estimated in section 7. Use function SUMPRODUCT(array1, array2) to estimate the numerator. This function returns the sum of products of all elements of array1 and array2.
9. Estimate the mean moth flight date using weather data from all 6 weather stations. Estimate the regression of the date from elevation, latitude and longitude of these weather stations. Use this regression equation to predict the mean moth flight date at all trap locations.
10. Estimate the mean date of moth flight recorded by all traps (use the same equation for the mean; use the middle of the period between trap checks as t). Plot actual mean date of moth flight versus predicted. Use the diagonal line to check the accuracy of predictions. Does the model fit the data? Is there any bias in model predictions?
11. (Optional) How flight periods will change with global warming by 2 degrees?