Ecological Archives A015-067-A1

Rick D. Scherer, Erin Muths, Barry R. Noon, and Paul Stephen Corn. 2005. An evaluation of weather and disease as causes of decline in two populations of boreal toads. Ecological Applications 15:2150–2160.

Appendix A. Descriptions of each weather variable, information on the weather stations and the methods used to derive estimates of weather conditions at Kettle Tarn (KT) and Lost Lake (LL), and a complete list of the weather models in the candidate set.

 

Description of the variables used in weather models

Brief descriptions of each of the weather variables evaluated in this study are shown below (Table A1). The ecological rationale for the inclusion of each variable is described in the paper (see Specification of Models with Weather Variables in the main article).

TABLE A1. Descriptions of the climatic covariates evaluated in the analysis of survival rates.

Variable Name

Variable Description

T-min. coldest 7 days

Mean daily minimum temperature over coldest 7-day period between December 1 and last day in February

Hibernation mean T-min.

Mean daily minimum temperature from December 1 to last day in February

Snowpack

Snow-water equivalent (SWE) at the beginning of January

Snowpack 1st day

SWE temporally closest to the first day of the coldest 7-day period

1st day sustained snow

Day of the year that a persistent snowpack developed

Hibernation 12 precipitation

Cumulative precipitation in the 12 months preceding the start of the hibernation period (November 1)

Hibernation 32 precipitation

Cumulative precipitation in the 32 months preceding the start of the hibernation period (November 1)

Growing 12 precipitation

Cumulative precipitation in the 12 months preceding the start of the growing season (June 1)

Growing 32 precipitation

Cumulative precipitation in the 32 months preceding the start of the growing season (June 1)

T-max. warmest 7 days

Mean daily maximum temperature over warmest 7-day period between June 1 and September 30

Growing mean T-max.

Mean daily maximum temperature from June 1 to August 31

Growing mean T-avg.

Mean daily average temperature from June 1 to August 31

Growing season length

The number of days between last spring killing frost and first fall killing frost

 

Use of weather stations for weather data

Weather data from nearby weather stations were used to evaluate the relationship between weather variation and observed declines in boreal toads at KT and LL (Table A2). Distance from the toad populations and elevation primarily determined which weather station data would be used to represent conditions at the two study sites. However, distance from the Continental Divide was used to determine whether data from the Bear Lake weather station would be applied to KT or LL. Most precipitation in the Rocky Mountains of Colorado comes from storms that move across the state from the west. Generally, locations that are higher in elevation and nearer the Continental Divide receive more precipitation from these storms (Pielke et al. 2003). Upslope storms (those that generally move from east to west) contribute relatively little precipitation and tend to deposit more precipitation at lower elevations farther from the divide. The weather station at Bear Lake is at an elevation intermediate to KT and LL. Because it is relatively near the Continental Divide and slightly nearer to LL, data from the Bear Lake weather station were applied to LL (Table A2).

TABLE A2. The weather station data that were used to represent KT and LL for each weather covariate. Distances of the Hourglass Reservoir and Copeland Lake weather stations from Kettle Tarn are approximately 13 and 30 km. Distances of the Willow Park, Bear Lake, Deadman Hill, and University Camp weather stations are approximately 15, 22, 35, and 53 km from Lost Lake.

Site

Climatic Covariate

Weather Station(s) Used

Kettle Tarn

Mean temperature covariates

Copeland Lake, Hourglass Reservoir

 

T-min. coldest 7 days

Copeland Lake

 

T-max. warmest 7 days

Copeland Lake

 

Snowpack covariates

Copeland Lake

 

Precipitation covariates§

Hourglass Reservoir

 

Growing season length

Copeland Lake

Lost Lake

Mean temperature covariates

Bear Lake, Deadman Hill, University Camp and Willow Park

 

T-min. coldest 7 days

Willow Park

 

T-max. warmest 7 days

Willow Park

 

Snowpack covariates

Willow Park

 

Precipitation covariates§

Willow Park

 

Growing season length

Willow Park

Includes the following covariates: Hibernation mean T-min., Growing mean T-max., and Growing mean T-avg..

Includes the following covariates: Snowpack, Snowpack 1st day, and 1st day persistent snowpack.

§ Includes the following covariates: Hibernation 12 precipitation, Hibernation 32 precipitation, Growing 12 precipitation, and Growing 32 precipitation.

 

Development of Climatic Covariates of Survival Rate

Mean temperature variables - The process used to estimate mean daily minimum temperature over the hibernation period (i.e., Hibernation mean T-min.; Table A1) is the same as that used to estimate Growing mean T-max. and Growing mean T-avg. (Table A1).

The mean daily minimum temperature from the first day of December to the end of February was derived for each weather station from the winter of 1991–1992 to the winter of 2000–2001. Then, the difference between the mean daily minimum temperature in the winter of year i and year i + 1 was calculated for each weather station and for all years. The inverse distance-squared method (Isaaks and Srivastava 1989) was used to derive a weighted-mean, between-year difference in daily minimum temperature across the two stations representing KT and the four stations representing LL (Table A2). The preceding steps resulted in estimates of the difference in mean daily minimum temperature in year i + 1 relative to year i at both sites. Starting values were needed to generate absolute annual estimates of mean daily minimum temperature. These were derived by calculating the average mean daily minimum temperature in 1991 across the weather stations used to represent each site (Table A2).

High variation in the between-year differences in temperature across the weather stations selected to represent each site would suggest high uncertainty in the derived temperature estimates. To evaluate the degree to which the temperature variables from different weather stations were correlated over time, we computed correlation coefficients for three temperature variables: (1) mean daily minimum temperature from December 1 to the last day in February, (2) mean daily maximum temperature from June 1 to August 31, and (3) mean daily average temperature from June 1 to August 31. Correlation coefficients averaged 0.89 (range = 0.77 to 0.96) for the four weather stations selected to represent LL. Correlation coefficients averaged 0.83 (range = 0.68 to 0.86) for the two weather stations selected to represent KT.

T-min coldest 7 days and T-max warmest 7 days - To document the occurrence of extreme temperatures that may cause mortality in boreal toads, we derived estimates of the mean minimum daily temperature over the 7 coldest days of the hibernation period (T-min coldest 7 days; Table 1) and the mean maximum daily temperature over the 7 warmest days of the growing season (T-max warmest 7 days). To derive estimates of T-min coldest 7 days, we calculated 7-day moving averages of mean minimum daily temperature between December 1 and the last day in February. The lowest of these values was used to identify the coldest 7-day period for that year. We applied the same process to the months of the growing season (June 1 to September 30) to derive estimates of T-max warmest 7 days.

Snowpack, Snowpack 1st day, and 1st day sustained snow - Three variables were developed as measures of the snow depth in each hibernation period. Snow-water-equivalent (SWE), a measure of the water content in the overlying snowpack, at the beginning of January of each year was used to represent snow depth. All else being equal, a year with high SWE would be expected to have a deeper snowpack than a year with low SWE, though characteristics of the snow affect the relationship. The use of SWE at the beginning of January as a covariate did not account for the possibility that a period of cold temperatures prior to January might reduce survival rates. To account for this possibility, the measure of SWE closest to the first day of the coldest 7-day period in each winter was also used as a covariate. Finally, cold air temperatures prior to the establishment of a persistent snowpack could kill hibernating boreal toads. The third covariate used daily SWE data to determine the day of the year that a persistent snowpack developed. Without an insulating layer of snow, hibernating toads may have a higher probability of being exposed to fatal air temperatures the longer it takes a persistent snowpack to develop. Daily SWE data were examined beginning in October for non-zero values. If a non-zero value was observed, subsequent days were searched to see if the snowpack remained. A persistent snowpack was assumed if a non-zero value of SWE was registered into the following spring.

Hibernation 12 precipitation and Hibernation 32 precipitation - The cumulative amount of precipitation in the months preceding hibernation in a given year was used as a covariate. The beginning of the hibernation period was set at November 1 for every year. Monthly precipitation measurements over the 12 months prior to November 1 were summed for each year. Monthly precipitation measurements from the 32 months prior to hibernation were summed to derive a second covariate. Precipitation over thirty-two months was used because it allowed for the possibility that xeric conditions take longer than 12 months to develop. It was not possible to incorporate longer time periods, because earlier precipitation data were not available.

Growing 12 precipitation and Growing 32 precipitation - The cumulative amount of precipitation in the months prior to the growing season was used to reflect the amount of available water. The beginning of the growing season was set at June 1. For each year, monthly precipitation measurements over the 12 and 32 months prior to June 1 were summed.

Growing season length - The Natural Resources Conservation Service considers temperatures at or below -4.44° C sufficient to produce a killing frost (http://www.wcc.nrcs.usda.gov). The number of days between the last day that the temperature dropped to -4.44° C or below in the spring and the first day the temperature dropped to or below that level in the fall was determined and used as a measure of the length of the growing season in each year.

The candidate set of weather models

Each of the climatic covariates was incorporated into one or more mathematical models. A complete list of the climate models of  is available below (Table A3). Additive and interactive effects between variables in a model are represented by the ‘+’ and ‘*’ in model descriptions.

TABLE A3. Models in the candidate set that represent hypothesized relationships between weather variables and annual apparent survival rates.

Weather Hypotheses

Variable(s)

Linear Model

Annual apparent survival is related to minimum daily temperature over the hibernation period

T-min. coldest 7 days

 = b0 + b1(T-min. coldest 7 daysi)

Annual apparent survival is related to minimum daily temperature over the hibernation period

Hibernation mean T-min.

 = b0 + b1(Hibernation mean T-mini)

Annual apparent survival is related to depth of snow over the hibernation period

Snowpack

 = b0 + b1(Snowpacki)

Annual apparent survival is related to depth of snow over the hibernation period

Snowpack 1st day

 = b0 + b1(Snowpack 1st dayi)

Annual apparent survival is related to depth of snow over the hibernation period

1st day sustained snow

 = b0 + b1(1st day sustained snowi)

Annual apparent survival is related to minimum daily temperature plus depth of snow over the hibernation period

T-min. coldest 7 days; Snowpack 1st day

 = b0 + b1(T-min. coldest 7 daysi) + b2(Snowpack 1st dayi)

Annual apparent survival is related to minimum daily temperature plus depth of snow over the hibernation period

Hibernation mean T-min.; Snowpack

 = b0 + b1(Hibernation mean T-mini) + b2(Snowpacki)

Effect of minimum daily temperature over the hibernation period on annual apparent survival depends on the depth of snow

T-min. coldest 7 days; Snowpack 1st day

 = b0 + b1(T-min. coldest 7 daysi) + b2(Snowpack 1st dayi) + b3(T-min. coldest 7 daysi * Snowpack 1st dayi)

Effect of minimum daily temperature over the hibernation period on annual apparent survival depends on the depth of snow

Hibernation mean T-min.; Snowpack

 = b0 + b1(Hibernation mean t-mini) + b2(Snowpacki) + b3(Hibernation mean T-mini * Snowpacki)

Annual apparent survival is related to the amount of precipitation over the months preceding the hibernation period

Hibernation 12 precipitation

 = b0 + b1(Hibernation 12 precipitationi)

Annual apparent survival is related to the amount of precipitation over the months preceding the hibernation period

Hibernation 32 precipitation

 = b0 + b1(Hibernation 32   precipitationi)

Effect of minimum daily temperature over the hibernation period on annual apparent survival depends on the amount of precipitation over the months preceding hibernation

Hibernation mean T-min.; Hibernation 12 precipitation

 = b0 + b1(Hibernation mean T-mini) + b2(Hibernation 12 precipitationi) + b3(Hibernation mean T-mini * Hibernation 12 precipitationi)

Effect of minimum daily temperature over the hibernation period on annual apparent survival depends on the amount of precipitation over the months preceding hibernation

Hibernation mean T-min.; Hibernation 32 precipitation

 = b0 + b1(Hibernation mean T-mini) + b2(Hibernation 32 precipitationi) + b3(Hibernation mean T-mini * Hibernation 32 precipitationi)

Annual apparent survival is related to minimum daily temperature plus depth of snow over the hibernation period plus the amount of precipitation over the months preceding the hibernation period

Hibernation mean T-min.; Snowpack; Hibernation 12 precipitation

 = b0 + b1(Hibernation mean T-mini) + b2(Snowpacki) + b3(Hibernation 12 precipitationi)

Annual apparent survival is related to minimum daily temperature plus depth of snow over the hibernation period plus the amount of precipitation over the months the preceding hibernation period

Hibernation mean T-min.; Snowpack; Hibernation 32 precipitation

 = b0 + b1(Hibernation mean T-mini) + b2(Snowpacki) + b3(Hibernation 32 precipitationi)

Annual apparent survival is related to maximum daily temperature over the growing season

T-max. warmest 7 days

 = b0 + b1(T-max. warmest 7 daysi)

Annual apparent survival is related to maximum daily temperature over the growing season

Growing mean T-max.

 = b0 + b1(Growing mean T-mini)

Annual apparent survival is related to average daily temperature over the growing season

Growing mean T-avg.

 = b0 + b1(Growing mean T-avgi)

Annual apparent survival is related to the amount of precipitation over the months preceding the growing season

Growing 12 precipitation

 = b0 + b1(Growing 12 precipitationi)

Annual apparent survival is related to the amount of precipitation over the months preceding the growing season

Growing 32 precipitation

 = b0 + b1(Growing 32 precipitationi)

Annual apparent survival is related to maximum daily temperature over the growing season plus the amount of precipitation over the months preceding the growing season

Growing mean T-max.; Growing 12 precipitation

 = b0 + b1(Growing mean T-maxi) + b2(Growing 12 precipitationi)

Annual apparent survival is related to maximum daily temperature over the growing season plus the amount of precipitation over the months preceding the growing season

Growing mean T-max.; Growing 32 precipitation

 = b0 + b1(Growing mean T-maxi) + b2(Growing 32 precipitationi)

Annual apparent survival is related to maximum daily temperature over the growing season plus the amount of precipitation over the months preceding the growing season

T-max. warmest 7 days; Growing 12 precipitation

 = b0 + b1(T-max. warmest 7 daysi) + b2(Growing 12 precipitationi)

Annual apparent survival is related to maximum daily temperature over the growing season plus the amount of precipitation over the months preceding the growing season

T-max. warmest 7 days; Growing 32 precipitation

 = b0 + b1(T-max. warmest 7 daysi) + b2(Growing 32 precipitationi)

Effect of the amount of precipitation over the months preceding the growing season on annual apparent survival depends on maximum daily temperature over the growing season

Growing mean T-max.; Growing 12 precipitation

 = b0 + b1(Growing mean t-maxi) + b2(Growing 12 precipitationi) + b3(Growing mean T-maxi * Growing 12 precipitationi)

Effect of the amount of precipitation over the months preceding the growing season on annual apparent survival depends on maximum daily temperature over the growing season

Growing mean T-max.; Growing 32 precipitation

 = b0 + b1(Growing mean T-maxi) + b2(Growing 32 precipitationi) + b3(Growing mean T-maxi * Growing 32 precipitationi)

Annual apparent survival is related to growing season length

Growing season length

 = b0 + b1(Growing season lengthi)

 

LITERATURE CITED

Isaaks, E. H., and R. M. Srivastava. 1989. Applied geostatistics. Oxford University Press, New York, New York, USA.

Pielke, R. A., Sr., N. Doesken, and O. Bliss. 2003. Climate of Colorado. Climatology Report 60. Department of Atmospheric Sciences, Colorado State University, Colorado, USA .



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