Author’s Accepted Manuscript Extreme operative temperatures are better descriptors of the thermal environment than mean temperatures Agustín Camacho, Miguel Trefaut Rodrigues, Carlos Arturo Navas www.elsevier.com/locate/jtherbio
PII: DOI: Reference:
S0306-4565(15)00025-X http://dx.doi.org/10.1016/j.jtherbio.2015.02.007 TB1616
To appear in: Journal of Thermal Biology Received date: 13 November 2014 Revised date: 13 February 2015 Accepted date: 13 February 2015 Cite this article as: Agustín Camacho, Miguel Trefaut Rodrigues and Carlos Arturo Navas, Extreme operative temperatures are better descriptors of the thermal environment than mean temperatures, Journal of Thermal Biology, http://dx.doi.org/10.1016/j.jtherbio.2015.02.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Extreme operative temperatures are better descriptors of the thermal environment than mean temperatures.
Agustín Camachoa, *, Miguel Trefaut Rodriguesa and Carlos Arturo Navasb . a
Laboratório de Herpetologia, Departamento de Zoologia, Instituto de
Biociências, Universidade de São Paulo,Caixa Postal 11.461, CEP 05508-090, São Paulo, SP, Brazil.São Paulo - SP, CEP 05508-090, Brazil. b
Laboratório de Ecofisiologia e Fisiologia Evolutiva, Departamento de
Fisiologia, Instituto de Biociências, Universidade de São Paulo, Caixa Postal 11.461, CEP 05508-090, São Paulo, SP, Brazil. *Corresponding
author:
[email protected]
Tel:
551130917570.
E-mail
address:
2 Abstract In ecological studies of thermal biology the thermal environment is most frequently described using the mean or other measures of central tendency in environmental temperatures. However, this procedure may hide biologically relevant thermal variation for ectotherms, potentially misleading interpretations. Extremes of operative temperatures (EOT) can help with this problem by bracketing the thermal environment of focal animals. Within this paper, we quantify how mean operative temperatures relate to the range of simultaneously available operative temperatures (a measure of error). We also show how EOT: 1) detect more thermal differences among microsites than measures of central tendency, like the mean OT, 2) allow inferring on microsite use by ectothermic animals, and 3) clarify the relationships between field operative temperatures and temperatures measured at weather stations (WS). To do that, we explored operative temperatures measured at four sites of the Brazilian Caatingas and their correspondent nearest weather stations. We found that the daily mean OT can hide temperature ranges of 41°C simultaneously available at our study sites. In addition, EOT detected more thermal differences among microsites than central quantiles. We also show how EOT allow inferring about microsite use of ectothermic animals in a given site. Finally, the daily maximum temperature and the daily temperature range measured at WSs predicted well the minimum available field OT at localities many kilometers away. Based on our results, we recommend the use of EOT, instead of mean OT, in thermal ecology studies. Keywords: quantile analysis, semiarid environments, climate change, thermal ecology.
3 1. Introduction The most used parameter to describe the thermal environment of focal organisms is the mean of environmental temperatures (e.g. the mean of temperatures measured at relevant microsites or at Weather stations (WSs), during any given period, Hillman, 1969; Asplund 1974; Sinervo et al., 2011, reviewed in Graae et al., 2012). This is problematic because microsites with similar mean temperatures may reach temperature extremes that overwhelm the thermal tolerance of the organisms under study (e.g. Fig. 1). Thus, mean temperatures potentially hide relevant thermal variation that may be responsible for the processes which thermal ecologists study. The thermal environment of a specific organism is best represented by the distribution of its operative temperatures (OT). OT represent the temperatures that a body may attain in its natural environment (Porter et al., 1973; Stevenson, 1985; Bakken, 1989; Hertz et al., 1993; Seebacher and Shine, 2003; Bakken and Angilletta, 2013). They can be obtained from temperature sensors installed in models that imitate key biophysical characteristics of the organism’s body (e.g. size and color, Geiger, 1950; Porter, 1973; Christian et al., 1984; Hertz et al., 1993, Helmuth and Hofman, 2001, Seebacher and Shine, 2003; Bakken and Angilletta, 2014). OT can also be deduced from biophysical and mathematical principles (Porter et al., 1973; Kearney and Porter 2004, Denny et al., 2006). Other authors have described the thermal environment of ectotherms locally, using thermal images (Chapperon et al., 2011) or using the worldclim database (e.g. Worldclim, Hijmans et al., 2005), which consists in an interpolation of WS data (e.g. Deutsch et al., 2008; Clusella-Trullas et al., 2011). In a different case, the body
4 temperatures of non basking lizards have been estimated from air temperatures measured at the nearest WS (Huey et al., 2009). Nevertheless, how WS data relates to OT is a highly relevant topic because WS are often far-away from where focal organisms live (Geiger, 1950) and can misrepresent the thermal environment of these organisms (e.g. Buckley et al., 2013). Recently, several authors have called for studies aiming to enhance our understanding of this problem (Suggit et al., 2011; Graae et al., 2012; Navas et al., 2013). We argue that the Extremes of Operative Temperatures (EOT) can solve problems derived from using mean temperatures. EOT are referred here as any maximum or minimum of OT measured at a single microsite or across several ones, along any period of time relevant for a study. Such extreme values can be analyzed as quantiles of data distributions, an approach that is gaining recognition in ecology, climatology, and ecophysiology (Cade et al., 1999; Cade and Noon 2003; Marengo et al., 2009; Huey et al 2009; Clusella-Trullas et al., 2011; and Kingsolver et al., 2013). EOT present several utilities. For example, they inform on which microhabitats provide thermal refuges for a given ectotherm, they can also show how WS temperatures relate to operative temperatures in the field. The biological interpretation of EOT is simple: organisms can only occupy microsites experiencing EOT within their tolerated range of temperatures (e.g. Porter et al., 1973; Kearney et al., 2009; Suggit et al., 2011; Teixeira et al., 2013). If the most buffered of available microsites for a population of organisms surpasses the organisms’ tolerated range of temperatures, then the population will necessarily experience thermal stress (e.g. Huey et al., 2009; Kingsolver et al., 2013). Despite their simplicity, EOT are still not as well examined as other parameters used for study
5 thermoregulation. Examples of these other parameters are the extent of thermoregulation (Hertz et al., 1993), null models of temperature distribution (Christian et al., 2006), or the daily amount of time precluding thermoregulation (Sinervo et al., 2010). To instigate researchers to consider carefully the use of mean temperatures in future studies, we quantify how much mean OT misrepresent available OT for organisms in a tropical semiarid region. After that, we test whether EOT are more sensitive to thermal differences among microsites than mean OT. Finally, we show how descriptors of EOT allow to: 1) infer on the spatial distribution of a theoretical ectotherm; 2) understand the relationship between WS data and field OT.
2. Material and methods 2.1.
Temperature sampling
Our database of OT comes from four localities in the Brazilian Caatinga, a tropical semiarid biome. Three localities are situated at Bahia state: Alagoado (9º20'14''S, 41º22'22''W, 400 m a.s.l., sampled during 6 days in February 2010); Vacaria, (10°40'38.22"S, 42°37'46.30"W, 450 m a.s.l, sampled during 3 days in September 2011); and Gameleira de Assuruá (11°18'2.86"S, 42°39'27.74"W, 880 m a.s.l, sampled during 9 days in September 2010). We sampled one additional site at Pernambuco state: Catimbau (8°35'29.23"S, 37°14'44.32"W, 760 m, a.s.l., during 6 days in February 2010). The obtained database contains temperatures measured during the dry and wet seasons, along a large segment of the altitudinal range of the Caatinga biome. Vegetation at our study sites
6 typically consisted of small bushes (typically less than 5 m diameter) or scattered small trees lower than 5 m, separated by sand banks. Within each sampling site, we recorded OT at 6 microsites per day using 3 “Logbox A” data loggers (error ± 1 ºC), each one carrying two registering sensors. These microsites consisted of three different depths under vegetation (surface, 5 and 10 cm depth) and three in the exposed sand (surface, 5 and 10 cm depth). Within each site, we repositioned sensors daily to avoid systematic effects of local nuances (i.e. a branch shading the logger always at the same hour). Each day, data loggers were deployed to record temperatures at 10 min intervals during 24h. The measurement sensor was inside a hollow cylindrical cap, with its single opening sealed by the sensor. The cap, made of shiny aluminium color, is not painted and measures 3.5 cm long and 0.3 cm wide (weight = 0.5 g). The physical properties of operative temperature models need to be adequated to each question and small and hollow metallic tubes with very low heat capacity have been used to estimate operative temperatures of small lizards and insects” (Bakken 1992). The probes of our dataloggers have been validated for very small lizards of diverse colors and body shapes (Camacho et al. 2014). We sampled 21 days, three to nine days for each site (13975 measurements in total). This dataset cannot fully describe the thermal dynamics of microsites within the caatingas, but is enough for the methodological questions addressed herein and constitutes a sample size comparable to previous approaches (Porter et al., 1973, Bakken and Angilletta, 2014). The local weather during the sampling period was daily categorized as clear (no or few clouds), cloudy (totally or almost totally overcast), or rainy. Due to the rarity and unpredictability of rainfall in the Brazilian Caatinga (Streilein, 1982), the
7 influence of rain could only be estimated from two days, one at Alagoado and another at Catimbau. We also obtained a WS dataset of air temperatures measured hourly and during the same periods at the nearest WSs from our field localities. These WSs belong to Brazil’s national meteorological service (INMET), which uses the “Stevenson screen” and measures temperatures at 1.5~2 m above the ground. The utilized WS were always within 150 m in altitude and at less than 100 km from their respective localities, common for studies that estimate OT through WS data (e.g. Sinervo et al., 2010, 2011; Clusella-Trullas et al., 2011). The nearest WS for the sampling localities listed above, respectively, were: Petrolina (at 80 km from Alagoado), Barra (at 70 km from Vacaria), Irecê (at 84 km from Gameleira) and Garanhuns (at 85 km from Catimbau). In total, we obtained 534 air temperature measurements from those WSs. 2.2 Analyses All our analyses can be reproduced using the supporting file 2 and the dataset
used
for
this
study.
The
dataset
is
stored
at
github:
(https://github.com/AgustinCamacho/temperature-datasetjot/blob/b640a4d1e37ff20585742b7c8846849cebdd11de/temperature.csv).
Comparison of mean OT and EOT To show how the daily mean OT hides thermal variation, we regressed the daily mean OT on the daily maximum OT range. The latter parameter represents the maximum daily error for behavioral thermoregulation options. It is calculated as the maximum difference between OT simultaneously measured each day.
8 Secondly, we tested whether extreme percentiles of OT (i.e. EOT) predict intermicrosite differences in OT better than central quantiles. Central quantiles represent central tendency of the measured temperatures and thus would have analog behavior to the mean. We examined this prediction calculating 100 percentiles for the data loggers’ temperature dataset. For each percentile, we calculated the F-value of an ANOVA model with OT as dependent variable and two categorical factors relevant for microsite description: type of vegetation (covered and exposed) and depth (surface, -10cm, and -5cm). The obtained Fvalue represents the magnitude of the differences in temperatures among microsites and it was calculated by fitting each model by permutation (R package “lmPerm”, Wheeler, 2010). Next, we recoded the percentiles so that they ranged from the most central (i.e. percentile 50 = rank 1) to the most extreme (first and last percentile = rank 50). Finally, F-values were regressed against the percentile ranks. By definition of the F-value, percentiles leading to greater F-values will necessarily better detect differences among microsites. Demonstrations of the use of EOT Herein, we first exemplify how knowing the distribution of EOT across different microsites and at the nearest WS helps understanding the local distribution of an ectotherm. To show this, we compared the daily minimum and maximum OT measured at the local microsites and the respective nearest WSs. We did this using an honest multiple comparison procedure, based on mixed linear models that fitted, separately, either the daily minimum or maximum OT (Hothorn et al., 2008). Our argument is that an ectotherm will avoid places in which EOT reach harmful levels. Thus, to infer on the effects of temperature on an ectotherm’s local distribution it is only necessary to compare the obtained
9 EOT and the animal’s thermal tolerance. For this example, we assumed that our sensors represent the OT of an imaginary lizard. The thermal tolerance of an ectotherm can be given by its critical maximum temperature (CTMAX), a temperature that immediately leads to immobility and then death (Cowles and Bogert, 1944). For this example, we used 46°C, the mean CTMAX of 10 species of small lizards with similar characteristics to our loggers and that inhabit the study sites (Camacho et al. 2014). In a second example, we determine the predictive power of WS over EOT. To do that, we fitted four ANCOVA models in which local EOT (dependent variables) were represented by different descriptors derived from WS. These were: the daily maximum, the daily minimum, the highest daily maximum OT and the lowest daily maximum (i.e. the warmest microsite available at the coldest moment of the day). We modeled each dependent variable using WS derived factors, a local weather factor (categorical with three levels: sunny, cloudy, rainy) and a random factor (sampling site). WS derived factors were the daily maximum temperature (Tamax) and the daily temperature range (TaR). These factors have shown significant predictive power in previous global studies on thermal challenges for ectothermic animals (e.g. Huey et al., 2009; Clusella-Trullas et al., 2011). In this case, we assessed the predictive power of WS factors over EOT looking at changes in model fit derived from excluding those factors from the model. We evaluated model’s fits comparing their respective values of Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) (Wang and Liu, 2006). All model comparisons are summarized within the supporting file 1 (tables S hereafter), and were generated using the script in the supporting file 2.
10 Control of temporal autocorrelation during analyses. Temperature data are often temporally autocorrelated due to temporal variation of the factors acting on temperatures (e.g. along a given sampling trip or during a day) and also due to measuring repeatedly at the same place (e.g. sensors being shaded at the same time of the day). In our first test, correcting for temporal autocorrelation was unnecessary because the ranked percentiles and F-values regressed do not keep the temporal structure of the original temperatures. In all the subsequent tests, we used linear mixed models (R package “lme4”, Bates et al., 2012), in which “site” was included as a random factor controlling temporal autocorrelations of measurements across sites. Finally, temporal autocorrelation at the within day scale was controlled by calculating variables on a daily basis. None of the models fitted herein showed visual signs of temporal autocorrelation in the residuals.
3. Results Comparison of mean OT and EOT The daily mean of OT significantly explained the daily error (ΔAIC= 21.82 and ΔBIC= 20.68 compared to a model without mean OT, table S1). The maximum daily error reached maximum values of 41°C, error of 25°C were already present for daily mean OT of 26°C (Fig.2B). Thus, at our study sites, higher daily mean OT leads to a very high loss of information about the range of available OT. Extreme quantiles led to higher F-values than central quantiles (R2= 0.4904, F-statistic: 16.82, DF: 97, p
PII: DOI: Reference:
S0306-4565(15)00025-X http://dx.doi.org/10.1016/j.jtherbio.2015.02.007 TB1616
To appear in: Journal of Thermal Biology Received date: 13 November 2014 Revised date: 13 February 2015 Accepted date: 13 February 2015 Cite this article as: Agustín Camacho, Miguel Trefaut Rodrigues and Carlos Arturo Navas, Extreme operative temperatures are better descriptors of the thermal environment than mean temperatures, Journal of Thermal Biology, http://dx.doi.org/10.1016/j.jtherbio.2015.02.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Extreme operative temperatures are better descriptors of the thermal environment than mean temperatures.
Agustín Camachoa, *, Miguel Trefaut Rodriguesa and Carlos Arturo Navasb . a
Laboratório de Herpetologia, Departamento de Zoologia, Instituto de
Biociências, Universidade de São Paulo,Caixa Postal 11.461, CEP 05508-090, São Paulo, SP, Brazil.São Paulo - SP, CEP 05508-090, Brazil. b
Laboratório de Ecofisiologia e Fisiologia Evolutiva, Departamento de
Fisiologia, Instituto de Biociências, Universidade de São Paulo, Caixa Postal 11.461, CEP 05508-090, São Paulo, SP, Brazil. *Corresponding
author:
[email protected]
Tel:
551130917570.
address:
2 Abstract In ecological studies of thermal biology the thermal environment is most frequently described using the mean or other measures of central tendency in environmental temperatures. However, this procedure may hide biologically relevant thermal variation for ectotherms, potentially misleading interpretations. Extremes of operative temperatures (EOT) can help with this problem by bracketing the thermal environment of focal animals. Within this paper, we quantify how mean operative temperatures relate to the range of simultaneously available operative temperatures (a measure of error). We also show how EOT: 1) detect more thermal differences among microsites than measures of central tendency, like the mean OT, 2) allow inferring on microsite use by ectothermic animals, and 3) clarify the relationships between field operative temperatures and temperatures measured at weather stations (WS). To do that, we explored operative temperatures measured at four sites of the Brazilian Caatingas and their correspondent nearest weather stations. We found that the daily mean OT can hide temperature ranges of 41°C simultaneously available at our study sites. In addition, EOT detected more thermal differences among microsites than central quantiles. We also show how EOT allow inferring about microsite use of ectothermic animals in a given site. Finally, the daily maximum temperature and the daily temperature range measured at WSs predicted well the minimum available field OT at localities many kilometers away. Based on our results, we recommend the use of EOT, instead of mean OT, in thermal ecology studies. Keywords: quantile analysis, semiarid environments, climate change, thermal ecology.
3 1. Introduction The most used parameter to describe the thermal environment of focal organisms is the mean of environmental temperatures (e.g. the mean of temperatures measured at relevant microsites or at Weather stations (WSs), during any given period, Hillman, 1969; Asplund 1974; Sinervo et al., 2011, reviewed in Graae et al., 2012). This is problematic because microsites with similar mean temperatures may reach temperature extremes that overwhelm the thermal tolerance of the organisms under study (e.g. Fig. 1). Thus, mean temperatures potentially hide relevant thermal variation that may be responsible for the processes which thermal ecologists study. The thermal environment of a specific organism is best represented by the distribution of its operative temperatures (OT). OT represent the temperatures that a body may attain in its natural environment (Porter et al., 1973; Stevenson, 1985; Bakken, 1989; Hertz et al., 1993; Seebacher and Shine, 2003; Bakken and Angilletta, 2013). They can be obtained from temperature sensors installed in models that imitate key biophysical characteristics of the organism’s body (e.g. size and color, Geiger, 1950; Porter, 1973; Christian et al., 1984; Hertz et al., 1993, Helmuth and Hofman, 2001, Seebacher and Shine, 2003; Bakken and Angilletta, 2014). OT can also be deduced from biophysical and mathematical principles (Porter et al., 1973; Kearney and Porter 2004, Denny et al., 2006). Other authors have described the thermal environment of ectotherms locally, using thermal images (Chapperon et al., 2011) or using the worldclim database (e.g. Worldclim, Hijmans et al., 2005), which consists in an interpolation of WS data (e.g. Deutsch et al., 2008; Clusella-Trullas et al., 2011). In a different case, the body
4 temperatures of non basking lizards have been estimated from air temperatures measured at the nearest WS (Huey et al., 2009). Nevertheless, how WS data relates to OT is a highly relevant topic because WS are often far-away from where focal organisms live (Geiger, 1950) and can misrepresent the thermal environment of these organisms (e.g. Buckley et al., 2013). Recently, several authors have called for studies aiming to enhance our understanding of this problem (Suggit et al., 2011; Graae et al., 2012; Navas et al., 2013). We argue that the Extremes of Operative Temperatures (EOT) can solve problems derived from using mean temperatures. EOT are referred here as any maximum or minimum of OT measured at a single microsite or across several ones, along any period of time relevant for a study. Such extreme values can be analyzed as quantiles of data distributions, an approach that is gaining recognition in ecology, climatology, and ecophysiology (Cade et al., 1999; Cade and Noon 2003; Marengo et al., 2009; Huey et al 2009; Clusella-Trullas et al., 2011; and Kingsolver et al., 2013). EOT present several utilities. For example, they inform on which microhabitats provide thermal refuges for a given ectotherm, they can also show how WS temperatures relate to operative temperatures in the field. The biological interpretation of EOT is simple: organisms can only occupy microsites experiencing EOT within their tolerated range of temperatures (e.g. Porter et al., 1973; Kearney et al., 2009; Suggit et al., 2011; Teixeira et al., 2013). If the most buffered of available microsites for a population of organisms surpasses the organisms’ tolerated range of temperatures, then the population will necessarily experience thermal stress (e.g. Huey et al., 2009; Kingsolver et al., 2013). Despite their simplicity, EOT are still not as well examined as other parameters used for study
5 thermoregulation. Examples of these other parameters are the extent of thermoregulation (Hertz et al., 1993), null models of temperature distribution (Christian et al., 2006), or the daily amount of time precluding thermoregulation (Sinervo et al., 2010). To instigate researchers to consider carefully the use of mean temperatures in future studies, we quantify how much mean OT misrepresent available OT for organisms in a tropical semiarid region. After that, we test whether EOT are more sensitive to thermal differences among microsites than mean OT. Finally, we show how descriptors of EOT allow to: 1) infer on the spatial distribution of a theoretical ectotherm; 2) understand the relationship between WS data and field OT.
2. Material and methods 2.1.
Temperature sampling
Our database of OT comes from four localities in the Brazilian Caatinga, a tropical semiarid biome. Three localities are situated at Bahia state: Alagoado (9º20'14''S, 41º22'22''W, 400 m a.s.l., sampled during 6 days in February 2010); Vacaria, (10°40'38.22"S, 42°37'46.30"W, 450 m a.s.l, sampled during 3 days in September 2011); and Gameleira de Assuruá (11°18'2.86"S, 42°39'27.74"W, 880 m a.s.l, sampled during 9 days in September 2010). We sampled one additional site at Pernambuco state: Catimbau (8°35'29.23"S, 37°14'44.32"W, 760 m, a.s.l., during 6 days in February 2010). The obtained database contains temperatures measured during the dry and wet seasons, along a large segment of the altitudinal range of the Caatinga biome. Vegetation at our study sites
6 typically consisted of small bushes (typically less than 5 m diameter) or scattered small trees lower than 5 m, separated by sand banks. Within each sampling site, we recorded OT at 6 microsites per day using 3 “Logbox A” data loggers (error ± 1 ºC), each one carrying two registering sensors. These microsites consisted of three different depths under vegetation (surface, 5 and 10 cm depth) and three in the exposed sand (surface, 5 and 10 cm depth). Within each site, we repositioned sensors daily to avoid systematic effects of local nuances (i.e. a branch shading the logger always at the same hour). Each day, data loggers were deployed to record temperatures at 10 min intervals during 24h. The measurement sensor was inside a hollow cylindrical cap, with its single opening sealed by the sensor. The cap, made of shiny aluminium color, is not painted and measures 3.5 cm long and 0.3 cm wide (weight = 0.5 g). The physical properties of operative temperature models need to be adequated to each question and small and hollow metallic tubes with very low heat capacity have been used to estimate operative temperatures of small lizards and insects” (Bakken 1992). The probes of our dataloggers have been validated for very small lizards of diverse colors and body shapes (Camacho et al. 2014). We sampled 21 days, three to nine days for each site (13975 measurements in total). This dataset cannot fully describe the thermal dynamics of microsites within the caatingas, but is enough for the methodological questions addressed herein and constitutes a sample size comparable to previous approaches (Porter et al., 1973, Bakken and Angilletta, 2014). The local weather during the sampling period was daily categorized as clear (no or few clouds), cloudy (totally or almost totally overcast), or rainy. Due to the rarity and unpredictability of rainfall in the Brazilian Caatinga (Streilein, 1982), the
7 influence of rain could only be estimated from two days, one at Alagoado and another at Catimbau. We also obtained a WS dataset of air temperatures measured hourly and during the same periods at the nearest WSs from our field localities. These WSs belong to Brazil’s national meteorological service (INMET), which uses the “Stevenson screen” and measures temperatures at 1.5~2 m above the ground. The utilized WS were always within 150 m in altitude and at less than 100 km from their respective localities, common for studies that estimate OT through WS data (e.g. Sinervo et al., 2010, 2011; Clusella-Trullas et al., 2011). The nearest WS for the sampling localities listed above, respectively, were: Petrolina (at 80 km from Alagoado), Barra (at 70 km from Vacaria), Irecê (at 84 km from Gameleira) and Garanhuns (at 85 km from Catimbau). In total, we obtained 534 air temperature measurements from those WSs. 2.2 Analyses All our analyses can be reproduced using the supporting file 2 and the dataset
used
for
this
study.
The
dataset
is
stored
at
github:
(https://github.com/AgustinCamacho/temperature-datasetjot/blob/b640a4d1e37ff20585742b7c8846849cebdd11de/temperature.csv).
Comparison of mean OT and EOT To show how the daily mean OT hides thermal variation, we regressed the daily mean OT on the daily maximum OT range. The latter parameter represents the maximum daily error for behavioral thermoregulation options. It is calculated as the maximum difference between OT simultaneously measured each day.
8 Secondly, we tested whether extreme percentiles of OT (i.e. EOT) predict intermicrosite differences in OT better than central quantiles. Central quantiles represent central tendency of the measured temperatures and thus would have analog behavior to the mean. We examined this prediction calculating 100 percentiles for the data loggers’ temperature dataset. For each percentile, we calculated the F-value of an ANOVA model with OT as dependent variable and two categorical factors relevant for microsite description: type of vegetation (covered and exposed) and depth (surface, -10cm, and -5cm). The obtained Fvalue represents the magnitude of the differences in temperatures among microsites and it was calculated by fitting each model by permutation (R package “lmPerm”, Wheeler, 2010). Next, we recoded the percentiles so that they ranged from the most central (i.e. percentile 50 = rank 1) to the most extreme (first and last percentile = rank 50). Finally, F-values were regressed against the percentile ranks. By definition of the F-value, percentiles leading to greater F-values will necessarily better detect differences among microsites. Demonstrations of the use of EOT Herein, we first exemplify how knowing the distribution of EOT across different microsites and at the nearest WS helps understanding the local distribution of an ectotherm. To show this, we compared the daily minimum and maximum OT measured at the local microsites and the respective nearest WSs. We did this using an honest multiple comparison procedure, based on mixed linear models that fitted, separately, either the daily minimum or maximum OT (Hothorn et al., 2008). Our argument is that an ectotherm will avoid places in which EOT reach harmful levels. Thus, to infer on the effects of temperature on an ectotherm’s local distribution it is only necessary to compare the obtained
9 EOT and the animal’s thermal tolerance. For this example, we assumed that our sensors represent the OT of an imaginary lizard. The thermal tolerance of an ectotherm can be given by its critical maximum temperature (CTMAX), a temperature that immediately leads to immobility and then death (Cowles and Bogert, 1944). For this example, we used 46°C, the mean CTMAX of 10 species of small lizards with similar characteristics to our loggers and that inhabit the study sites (Camacho et al. 2014). In a second example, we determine the predictive power of WS over EOT. To do that, we fitted four ANCOVA models in which local EOT (dependent variables) were represented by different descriptors derived from WS. These were: the daily maximum, the daily minimum, the highest daily maximum OT and the lowest daily maximum (i.e. the warmest microsite available at the coldest moment of the day). We modeled each dependent variable using WS derived factors, a local weather factor (categorical with three levels: sunny, cloudy, rainy) and a random factor (sampling site). WS derived factors were the daily maximum temperature (Tamax) and the daily temperature range (TaR). These factors have shown significant predictive power in previous global studies on thermal challenges for ectothermic animals (e.g. Huey et al., 2009; Clusella-Trullas et al., 2011). In this case, we assessed the predictive power of WS factors over EOT looking at changes in model fit derived from excluding those factors from the model. We evaluated model’s fits comparing their respective values of Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) (Wang and Liu, 2006). All model comparisons are summarized within the supporting file 1 (tables S hereafter), and were generated using the script in the supporting file 2.
10 Control of temporal autocorrelation during analyses. Temperature data are often temporally autocorrelated due to temporal variation of the factors acting on temperatures (e.g. along a given sampling trip or during a day) and also due to measuring repeatedly at the same place (e.g. sensors being shaded at the same time of the day). In our first test, correcting for temporal autocorrelation was unnecessary because the ranked percentiles and F-values regressed do not keep the temporal structure of the original temperatures. In all the subsequent tests, we used linear mixed models (R package “lme4”, Bates et al., 2012), in which “site” was included as a random factor controlling temporal autocorrelations of measurements across sites. Finally, temporal autocorrelation at the within day scale was controlled by calculating variables on a daily basis. None of the models fitted herein showed visual signs of temporal autocorrelation in the residuals.
3. Results Comparison of mean OT and EOT The daily mean of OT significantly explained the daily error (ΔAIC= 21.82 and ΔBIC= 20.68 compared to a model without mean OT, table S1). The maximum daily error reached maximum values of 41°C, error of 25°C were already present for daily mean OT of 26°C (Fig.2B). Thus, at our study sites, higher daily mean OT leads to a very high loss of information about the range of available OT. Extreme quantiles led to higher F-values than central quantiles (R2= 0.4904, F-statistic: 16.82, DF: 97, p
