Lab. 6. Phenology of Gypsy Moth Flight

   The 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.

   [trap.gif] [males.gif]

   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 "[1]phenol.txt", and open it from the Microsoft Excel. This file
   contains the following information:
     * Moth catches in pheromone traps located in Virginia, West Virginia, and North
       Carolina in 1996. Traps were checked twice a week and moths were removed from
       the trap each time.
     * Geographic coordinated of traps: longitude and latitude in decimal degrees,
       and elevation at trap location.
     * Minimum and maximum daily temperature at 6 weather stations in Virginia, West
       Virginia, and North Carolina in 1996.
     * Geographic coordinated of weather stations: longitude and latitude in decimal
       degrees, and elevation.

   You need to build the model of gypsy moth flight from literature data and
   validate it using the given data set. The lab include the following steps: build
   the model; simulate the dates of gypsy moth flight that are expected at locations
   of weather stations; using the regression of moth flight dates vs. elevation,
   latitude, and longitude predict moth flight at trap locations; compare actual and
   predicted moth flight dates.

   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:

                                     [eqmean.gif]

   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?

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     ____________________________________________________________________________

   [5]Alexei Sharov 12/4/98

References

   1. http://alexei.nfshost.com/PopEcol/lab6/phenol.txt
   2. http://alexei.nfshost.com/PopEcol/lab5/lab5.html
   3. http://alexei.nfshost.com/PopEcol/popecol.html
   4. http://alexei.nfshost.com/PopEcol/lab7/lab7.html
   5. http://alexei.nfshost.com/~sharov/alexei.html