Ecological Archives A025-091-A1

Fritzi S. Grevstad and Leonard B. Coop. 2015. The consequences of photoperiodism for organisms in new climates. Ecological Applications 25:15061517.

Appendix A. Method detail: phenological event and voltinism mapping.

Our approach to modelling phenology and voltinism combines two available data sets:

(1) Spatially interpolated 30-year average (NORMALS) of monthly maximum and minimum temperatures obtained from the PRISM group at Oregon State University (Daly et al. 2008). This spatial climate data set has a 30 sec or ca. 800 m grid cell resolution and covers of all of the lower 48 United States for each month of the year.

(2) Non-spatialized daily degree-days for > 15,000 public weather stations distributed throughout the United States (a combination of data distributed by Mesowest Utah,, and several Western state agricultural weather networks). These degree days were calculated using the Oregon State University Integrated Plant Protection Center’s U.S. Degree-Day Mapping Calculator (2014) which was developed by L. Coop and uses the single sine method to calculate degree days (Baskerville and Emin 1969).

Combining these two data sets allowed us to estimate degree days and corresponding phenology and voltinism with both high spatial resolution (800 m grid cell) and high temporal resolution (daily) as described below. GRASS-GIS software (Geographic Resources Analysis Support System--geographic information system) (Neteler and Mitasova 2008) and the Perl programming language (Wall et al. 2000) were used to program all map and site calculations.

Degree-Day Maps. Our model of temperature-dependent development involves lower and upper thresholds below and above which no development occurs. This non-linear relationship means that developmental degree-days cannot be calculated directly from time-averaged temperatures available in the PRISM data. Instead, we used the PRISM data to create approximate base maps of degree-day topography for each of the 12 months of the year and then corrected these layers using degree-days calculated from the daily weather station data. The base map approximations were calculated using the single triangle method (Sevacherian et al. 1977), which produces results similar to the single sine method but is simpler. These base map values were subtracted from degree-days calculated at the weather station locations and the inverse-distance-squared spatial-interpolations of the differences were added back to the base layer as a correction. This process is generally known as “climatologically aided interpolation” (Willmott and Robeson 1995; Hunter and Meentemeyer 2005) and was automated and placed online at the Integrated Plant Protection Center website beginning in 1998 (U.S. Degree-Day Mapping Calculator 2014). This correction process was used to (1) improve temporal resolution to daily, and (2) create maps for a specified year rather than relying on normals. For Galerucella calmariensis, we calculated a series of monthly degree-day maps for the years 2007 through 2013, using 10 °C and 37.8 °C lower and upper developmental thresholds. These were used for estimating the number of generations that are physically possible in an area if photoperiod response was optimal.

Phenological Event Maps. We define a phenological event map (PEM) as a map of the dates on which accumulating degree-days reach a value (target DD total) that corresponds with a phenological event for a poikilothermic organism. In the Galerucella example, the event of interest is the arrival of the photoperiod-sensitive stage (newly eclosed adult), the timing of which determines whether the organism enters diapause or reproduces (depending on the day length for that date and latitude). Other PEMs have been used to support monitoring and surveillance programs for selected invasive pest insects including the first flight of the European gypsy moth (Lymantria dispar dispar L.), and initial adult emergence of the emerald ash borer (Agrilus planipennis Fairmaire)(USDA-APHIS-PPQ-CPHST, unpublished).

We used several components of the degree-day mapping program infrastructure to also automate the creation of PEMs. First, normals-based base maps of the approximate date (day of year) of eclosion of the sensitive life stage were computed, and these were then corrected using day-of-year estimates from degree-day calculations using weather station (site) data. Base map construction used the following logic: 1) For a given target DD total (to reach the photoperiod sensitive life stage), if the total degree days in the month of January is greater (i.e., the event was reached sometime during the month), use bilinear interpolation to estimate the day-of-month that the total was reached. 2) Otherwise, subtract the January DD total from the target DD total and repeat step 1 for the month of February. 3) Repeat this process iteratively until all grid cells have reached the target DD total. 4) If the end of the year arrives before reaching the target DD total, assigned the grid cell a day-of-year value of 366 (367 for leap years) signifying that the event did not occur at that location in that year.

To make the corrections, the expected date of eclosion (same target DD total) was determined for each of the 15,000+ point locations. These values were subtracted from the base map values at each location and spatially interpolated with either 1/distance squared or regularized splines with tension algorithms, both available in GRASS GIS. This spatially interpolated difference layer was then added to the base map to make a corrected PEM. In the case of the G. calmariensis model, PEM’s were created and stored for the date of eclosion of the photo-sensitive teneral adult stage of each potential generation (F1, F2, F3 etc.).

Photoperiod Maps. For each PEM (each generation of the sensitive stage), a corresponding map layer was produced that contained the calculated photoperiods for the event date and latitude. We used the “CBM” formula (Forsythe et al. 1995) to calculate photoperiod for a case where the photophase includes 25% of the civil twilight period.

Voltinism Maps. The photoperiod maps were compared to the critical photoperiod for the sensitive teneral adult stage (at 497 DD10) to determine, for each grid cell, where additional generation(s) may be attempted (Table A1). For the regions where there were sufficient degree days for the F2 generation to develop, we repeated the assessment of photoperiod on the date when the F2 sensitive stage emerged (at 1020 DD10) to determine regions where a third generation is attempted, and again (where appropriate) for the date when the F3 sensitive stage emerged (1542 DD10).

Literature cited

Baskerville, G. L., and P. Emin. 1969. Rapid estimation of heat accumulation from maximum and minimum temperatures. Ecology 50:514–-517.

Daly, C., et al. 2008. Physiographically-sensitive mapping of temperature and precipitation across the conterminous United States. International Journal of Climatology 28:2031–-2064.

Forsythe W. C., E. J. Rykiel, R. S. Stahl, H. Wu, and R. M. Schoolfield. 1995. A model comparison for daylength as a function of latitude and day of year. Ecological Modelling 80:87–95.

Hunter, R. D., and R. K. Meentemeyer. 2005. Climatologically aided mapping of daily precipitation and temperature. Journal of Applied Meteorology 44:1501–1510.

Neteler, M., and H. Mitasova. 2008. Open Source GIS: A GRASS GIS Approach. Third Edition. Springer, New York, New York, USA. 406 pp.

Sevacherian, V., V. M. Stern, and A. J. Mueller. 1977. Heat accumulation for timing Lygus control measures in a safflower-cotton complex. Journal of Ecological Entomology 70:399–401.

U.S. Degree-Day Mapping Calculator. 2014. Version 4.5. Oregon State University Integrated Plant Protection Center. Updated September 2014 by Coop LB.

Wall, L., T. Christiansen, and J. Orwant. 2000. Programming Perl, Third edition. O'Reilly Media. New York, New York, USA

Willmott, C. J., and S. M. Robeson. 1995. Climatologically aided interpolation (CAI) of terrestrial air temperature. International Journal of Climatology15:221–229.

[Back to A025-091]