35 SPATIAL AND TEMPORAL HETEROGENEITY IN THERMAL CONDITIONS FOR WILDLIFE Nicholas J. DeCesare1, Richard. B. Harris2, Jesse R. Newby3, and Collin J. Peterson4 1Montana Fish, Wildlife and Parks, Missoula, Montana 59804, USA; 2Montana Fish, Wildlife and Parks, Helena, Montana 59620, USA; 3Montana Fish, Wildlife and Parks, Dillon, Montana 59725, USA; 4Montana Fish, Wildlife and Parks, Kalispell, Montana 59901, USA. ABSTRACT: Temperature is an important component of climatic conditions that drive animal evolu- tion, niche space, and life history traits. We used field-deployed temperature sensors and generalized linear mixed-effects models to quantify the spatiotemporal variation of ambient temperatures in three study areas of western Montana, in support of concurrent studies of moose ecology and population dynamics. We found substantial potential for thermal refuge for moose; temperature ranges observed simultaneously among sites within study areas averaged 7.0°C during summer and 6.1°C during win- ter. We considered 6 site variables hypothesized to affect local temperatures (elevation, topographic position, aspect, land cover type, forest canopy cover, and the interaction of land cover and solar radiation), and all contributed to model performance. However, the direction and magnitude of effects varied in a cyclic fashion during the 24-hour diel cycle, and in many cases, exhibited reversed effects between day and night. Although spatial heterogeneity in temperature during summer was only slightly higher than during winter, our ability to explain such pattern was much better during summer (average R2 = 0.51–0.56) than during winter (average R2 = 0.09–0.23). We encourage researchers and managers to explore field collection and spatiotemporal modeling of temperature sensor data for cost-effect description of thermal environments for wildlife in local settings. ALCES VOL. 59: 35–51 (2023) Key words: Alces alces, ambient temperature, climate change, diel cycle, habitat, iButton, Montana, moose, spatial, summer, thermal cover, winter Temperature is an important component of climatic conditions that drive animal evolu- tion, niche space, and life history traits (Magnuson et al. 1979). Wildlife responses to variation in temperature can include spa- tial and temporal shifts in behavior (Heide- Jørgensen et al. 2020), physiological costs (Haroldson et al. 1998), and effects on growth and demography (Frishkoff et al. 2015, Pérez-Barbería et al. 2020). Although the sensitivity of ectotherms to spatial varia- tion in microclimatic conditions is well established (Woods et al. 2015), evidence in the literature is mixed regarding the relative importance of thermal conditions for ungu- lates. Ungulates in temperate regions commonly exhibit behavioral responses to temperature such as shifts in habitat selec- tion towards areas of thermal cover to miti- gate warm conditions (Bowyer and Kie 2009, DelGiudice et al. 2013, Wiemers et al. 2014). These findings emphasize thermal cover as a component of ungulate habitat, and habitat management practices for spe- cies such as elk (Cervus canadensis) com- monly include thermal cover prescriptions (Smith and Long 1987). However, Cook et al. (1998) argued the positive energetic benefits of thermal cover are outweighed by negative reduction of forage in such envi- ronments when managing habitat for elk, while Long et al. (2014) suggested the HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 36 relative importance of forage and thermal conditions are context-dependent. Among ungulates, the cold-adapted moose (Alces alces) has received particular attention with regards to impacts of tempera- ture on physiology, habitat selection, and fit- ness. Heat can increase metabolic costs for moose at lower temperature thresholds than observed for other sympatric ungulates (Renecker and Hudson 1986). Although pop- ulation performance has been negatively cor- related with temperature (Lenarz et al. 2009; but see Mech and Fieberg 2014), no empiri- cal data exist to link population performance to ambient temperature, unlike indirect impacts related to habitat change (Monteith et al. 2015, Holmes et al. 2021) and parasit- ism (Pekins 2020). In addition to intrinsic adaptations to thermal stress (Thompson et al. 2019, 2020), moose commonly employ thermoregulatory behavior through micro- and macro-habitat use at high summer tem- peratures (Schwab and Pitt 1991, Dussault et al. 2004, Broders et al. 2012, van Beest et al. 2012, van Beest & Milner 2013, Melin et al. 2014, Street et al. 2015, McCann et al. 2013, Ditmer et al. 2018, Alston et al. 2020, Borowik et al. 2020) and during winter (Burkholder et al. 2022). A notable exception was found in Ontario, where the general lack of moose behavioral response to temperature was attributed to low underlying variability in temperature across the study area (Lowe et al. 2010). The importance of thermal conditions in driving wildlife behavior in any local system likely depends upon the heterogeneity of micro-climates (Long et al. 2014, Londe et al. 2020). Spatial variation in the thermal environment is often ignored in wildlife man- agement (Elmore et al. 2017). However, the spatial and temporal variation of thermal con- ditions can be complex functions of broad- scale climate context and fine-scale heterogeneity in vegetation type and structure, topography, hydrology, season, and time of day (Lookingbill and Urban 2003, McGraw et al. 2012, Olson et al. 2014, Londe et al. 2020). Elmore et al. (2017) suggested that heterogeneity in thermal conditions be assessed prior to conducting studies of the relative importance of thermal conditions on wildlife behavior and demography. For cold- adapted species such as moose, predicting spatial and temporal variation in temperature across habitats may be particularly important at the species’ range periphery. Relatively cool locations may serve as a crucial compo- nent of habitat in such settings where high temperatures may impose metabolic costs if unmitigated (McCann et al. 2013, Ditmer et al. 2018). Under these circumstances the influence of land management decisions on thermal refugia may become a relevant con- cern, along with forage and security cover, in managing habitat for moose or other species (Elmore et al. 2017). We measured spatiotemporal variation in ambient temperatures during both winter and summer within three study areas of western Montana (USA) in support of concurrent studies of moose ecology and population dynamics. Our objectives were to assess the thermal conditions available to wildlife in these areas, to understand the effects of envi- ronmental covariates on temperature across time and space, and to predict thermal land- scapes as a function of those covariates. METHODS Study Areas We investigated factors affecting local tem- peratures in 3 three areas of western Montana, USA where long-term studies of moose ecol- ogy and demography were ongoing (Newby and DeCesare 2020). The Cabinet Mountains study area (48.2°N, 115.5°W) was character- ized by dense forest of diverse conifer species, ranging in elevation from 660 to ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 37 2,494 m with mean January temperatures of −8.1 to −0.8°C, mean July temperatures of 7.7 to 25.0°C, and mean annual precipitation of 91.4 cm. The Big Hole study area (45.4°N, 113.5°W) was a higher elevation valley including willow- (Salix spp.) riparian habi- tat surrounded by forested mountains, rang- ing in elevation from 1,842 to 3,232 m with mean January temperatures of −12.0 to −2.2°C, mean July temperatures of 5.4 to 22.9°C, and mean annual precipitation of 63.8 cm. The Rocky Mountain Front study area (47.9°N, 112.7°W) included areas of riparian and fen habitat and rugged moun- tainous forests, ranging in elevation from 1,200 to 2,803 m with mean January tem- peratures of −10.2 to −0.9°C, mean July tem- peratures of 7.1 to 22.6°C, and mean annual precipitation of 71.4 cm. Field Methods To quantify relationships between biophysi- cal variables and local air temperatures, we used temperature sensors (iButton Model DS1921G-F5; Maxim Integrated, San Jose, California) to measure ambient temperature at selected, non-random loca- tions within each of the 3 study areas. Sensors (n = 96; 32 per study area) were deployed a minimum of 1 km apart during one winter and one summer session lasting 85 days each, as dictated by memory limita- tion of the sensors. We programmed sensors to take temperature readings during the same hourly schedule within each study area and season. Season dates were not identical across study areas as certain sensors initiated or ended a few days apart. Overall, winter sampling occurred during 18 November 2013–16 February 2014 in the Cabinet Mountains, 14 December 2013–9 March 2014 in the Big Hole, and 19 November 2014–13 February 2015 in the Rocky Mountain Front. Summer sampling occurred during 9 July–3 October, 2014 in the Cabinet Mountains, 3 July–27 September, 2014 in the Big Hole, and 17 July–11 October, 2014 in the Rocky Mountain Front (Fig. 1). We anchored sensors at a height of 2 m above ground to the stems of trees or shrubs where available, or to existing wooden fence struc- tures in open areas (Lundquist and Huggett 2008), and shielded sensors from solar radi- ation using custom radiation shields follow- ing Holden et al. (2013). We subjectively selected sampling sites to include shrubland and forested vegetation cover types (MNHP 2017) across a gradient in elevation that aligned with areas used by radio-collared moose in a related study (Newby and DeCesare 2020; 858–1,444 m in the Cabinet Mountains, 1,847–2,263 m in the Big Hole, and 1,330–1,764 m in the Rocky Mountain Front). Temperature was recorded at hourly intervals (i.e., 0:00, 1:00, 2:00, …) throughout the 24-hr diel cycle. To represent ambient conditions generally in each study area, we developed reference val- ues from data collected at Remote Automatic Weather Stations (RAWS) administered by the National Interagency Fire Center. Range in Temperature as Metric of Potential Thermal Refuge We first used descriptive comparisons of temperature data across sites within each study area and season to evaluate the degree of spatiotemporal variation. Because tem- perature sensors were collecting concurrent temperature measurements during the same day and hour within each area, we used the range (maximum – minimum) in tempera- tures at each sensor during each day-hour as a metric of potential for thermal refuge among environmental conditions at a given time. We used scatter density plots to visual- ize the variation in temperature ranges within each season and estimated the average range per hour for each site and season. This estab- lished the degree of variation which we then HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 38 sought to explain with environmental covari- ates and generalized linear models. Environmental Covariates To quantify site characteristics affecting temperature, we first estimated metrics of topography using a digital elevation model from the USGS 3D Elevation Program (USGS 2019). From the DEM we estimated elevation, aspect, and a topographic position index (TPI). TPI generally discriminated the gradient of landforms from drainages (nega- tive values) to ridges (positive values) and was estimated as the difference in elevation between any given pixel and the average ele- vation of the surrounding neighborhood, 1-km in radius (Weiss 2001). We used a trigonometric transformation of aspect (cos[aspect-45]; McCune and Keon 2002) that indexed heat load received according to variation in slope aspect. This transforma- tion of aspect ranged from −1 to 1 along a southwest to northwest gradient. We also quantified vegetation conditions at each site according to available raster lay- ers for land cover type (MNHP 2017) and percent forest canopy cover (Homer et al. 2015). Lastly, we accounted for the effect of variable solar radiation during daytime using measurements of solar radiation (W · m-2) recorded at RAWS stations. In final stages of model-building we tested 2 interactions between solar radiation (recorded at a single RAWS site in each study area) and both land cover and aspect to assess whether the effects of these variables depended upon the rela- tive solar radiation across days. Statistical Analyses We quantified spatiotemporal variation in temperature as the site- and hour-specific difference between ambient temperatures recorded by each iButton sensor and the temperature recorded simultaneously at RAWS stations located within each study area (Cabinet Mountains FIRM8; Big Hole Fig. 1. Locations of study areas, temperature sensors, and Remote Automatic Weather Station (RAWS) sites for monitoring ambient temperature, western Montana, 2013–2015. ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 39 SLCM8, Rocky Mountain Front GSNM8; Fig. 1). We built models that predicted Δt (defined as tsite – tRAWS) based on environ- mental covariates measured at each site. Treating Δt as the response variable in our models instead of tsite itself did not affect covariate patterns (because tRAWS was a con- stant across all sites for a given day-hour), but served to link our models to widely available RAWS data and ensure that we could make predictions both in- and out-of- sample for any given location and date-time using GIS-measured variables and available RAWS data. Modeling variation in Δt also focused our analyses specifically on spatial variation in temperature by adjusting all data relative to the temporally varying measure of temperature at the RAWS sites. This effectively removed temporal (i.e., daily) variation in temperature data and left us to model spatial differences alone. We modeled effects on Δt separately by 8 separate hours of the day (0, 3, 6, 9, 12, 15, 18, 21) to better illuminate the dynamics of how site factors varied in their effects on local temperatures during the daily cycle. Preliminary examination of data indi- cated that Δt readings recorded at the same time-of-day on successive days were highly autocorrelated. To minimize the effects of such serial correlation on estimates of devi- ance, we modeled all relationships using the function lme within the R package nlme (Pinheiro et al. 2022), treating sample site as a random variable and with autocorrelation structure modeled using corARMA within sample sites. We used maximum likelihood (rather than restricted maximum likelihood) throughout, as this has been recommended for model selection in cases where the ran- dom factors remain the same in all models within the suite but various combinations of putative explanatory variables are examined (Zuur et al. 2009). For each combination of study area (i.e., region), season (summer vs. winter), and hour of the day, we began by evaluating uni- variate patterns of each environmental vari- able and Δt. We first centered and standardized all continuous covariates (Schielzeth 2010) and then fit univariate models for canopy, land cover type, eleva- tion, aspect, and TPI to explore patterns in the data. We then fit global main effects models including all 5 of these same envi- ronmental covariates as hypothesized driv- ers of Δt for each study area, season, and hour. We were less concerned about poten- tially problematic effects of multicollinear- ity among covariates for two reasons. First, correlations among these covariates were all <0.6, and second, the underlying goals for these models were more rooted in predic- tions than parsimony; thus, we fit global models to all subsets of data rather than per- forming model selection for each study area, season, and hour. Lastly, in addition to the 5 main effects covariates, we also included the interaction of solar radiation and land cover type in all daytime models. We conducted preliminary assessment of this interaction using AIC to compare main effects models with those including the interaction, and models were improved in the majority of cases (78%, 90%, and 60% of data subsets by season and hour in the Big Hole, Cabinet Mountains, and Rocky Mountain Front study areas, respectively). We evaluated the conditional R2 value from each model to assess the relative amount of variation explained (Nakagawa and Schielzeth 2013) and used standardized coef- ficients to assess the relative importance of each covariate (Galipaud et al. 2017). Lastly, to understand the relative importance of each covariate across all times of day, we averaged the absolute values of standardized coeffi- cients for each covariate across hour-specific HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 40 models per study area and season to compare relative variable importance. RESULTS Ambient Temperature Data We deployed sensors in 96 different locations, equally distributed across the 3 study areas and retrieved data from all 96 sensors during summer and 93 sensors during winter (Table 1). Restricting our interpretations to temperatures gathered at the 8 focal hours of the day analyzed here, these yielded 124,653 temperature readings for comparison with temperatures at their respective RAWS sites (Table 1). Elevations of sensors were lowest in the Cabinet Mountains study area and highest in the Big Hole study area. A higher proportion of sensors were located in forested cover types in the Cabinet Mountains than at the other two study areas; forest canopy was higher in the Cabinet Mountains (Table 1). Across all sensors and times-of-day, tempera- tures recorded by field sensors were, on aver- age, 0.95–2.35°C colder than that at RAWS stations in the Cabinet Mountains and Big Hole study areas across both seasons, but more similar to that at the RAWS station on the Rocky Mountain Front (Table 1). There was substantial potential for ther- mal refuge according to the temperature ranges observed among sites per study area, season, and hour (Fig. 2). On average, sites varied by 7.0°C during summer (Big Hole 6.1°C, Cabinet Mountains 7.6°C, Rocky Mountain Front 7.3°C) and by 6.1°C during winter (Big Hole 6.1°C, Cabinet Mountains 5.0°C, Rocky Mountain Front 7.4°C; Fig. 2). However, we observed considerable hetero- geneity in the magnitude of temperature variation among sites on a given day and hour (Fig. 2), ranging from 0°C (e.g., identi- cal temperatures across all sites in a given area) to maximum temperature ranges of 19, 20.5, and 22.5°C observed among sites at a single time in each study area, respectively. Environmental Drivers of Thermal Refuge Considered in isolation (i.e., via univariate coefficients), predictor variables not only var- ied in a cyclic fashion during the 24-hour diel cycle, but in many cases, exhibited reversed effects between day and night (Fig. 3). Such patterns were most pronounced during sum- mer in the Cabinet Mountains, where condi- tions such as high canopy cover, forest land Table 1. Summary of ambient temperature data, site attribute data for mean elevation, mean percent canopy closure, mean transformed aspect (TA), proportionate forest land cover, and the mean difference between temperatures measured at each site and Remote Automatic Weather Station (RAWS) sites in close proximity to each study area (Δt), from 3 study areas in western Montana during summer and winter seasons, 2013–2015. Study area Season Sensors (n) Temperature readings (n) Mean (SD) elevation, m Mean (SD) percent canopy Mean (SD) TA Proportion forested Mean (SD) Δt Cabinet Mountains Summer 32 21,142 1,135 (164) 71 (37) −0.04 (0.68) 0.91 −2.14 (3.83) Winter 32 21,048 −0.95 (2.79) Big Hole Summer 32 20,459 2,061 (121) 36 (27) 0.09 (0.56) 0.59 −2.35 (2.35) Winter 31 19,713 −1.23 (2.54) Rocky Mountain Front Summer 32 21,856 1,518 (122) 32 (26) 0.10 (0.72) 0.69 0.08 (2.88) Winter 30 20,435 −0.43 (3.15) ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 41 cover type, high elevation, northerly aspects, and convex topographic positions (i.e., ridges) tended to yield cooler temperatures during the day, but warmer temperatures at night (Fig. 3). Univariate results also showed stronger ability to explain spatiotemporal variation in temperature with our covariates during sum- mer than winter across all study areas (Fig. 3). When pooling covariates into multivari- able models, all six variables (5 main effect terms and an interaction between land cover and solar radiation) made relatively similar contributions to model performance. We used average absolute values of standardized coefficients to evaluate relative importance of covariates and found forest land cover and elevation to be among the most consistently high, though canopy, aspect, and TPI were also comparable in some seasons and study areas (Fig. 4). Conditional R2 values showed considerably higher ability to explain varia- tion in the data with models for summer tem- perature (average R2 = 0.51, 0.55, 0.56 among study areas) compared to those Fig. 2. Scatter density plot and average (dashed line) of the maximum range in ambient temperature measured concurrently across days at hourly intervals among sensors within 3 study area 2 seasons, western Montana, 2013–2015. HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 42 Fig. 3. Univariate coefficients and standard errors for the effects of spatial covariates and season on ambient temperature variation by time of day in the Big Hole, Cabinet Mountains, and Rocky Mountain Front study areas of western Montana, 2013–2015. ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 43 estimated for winter (average R2 = 0.09, 0.23, 0.14 among study areas). Lastly, global models facilitated the spatial prediction of ambient temperature across each study area, which also revealed differences in thermal environments between seasons and times (Fig. 5, Tables 2 and 3). DISCUSSION In contrast to McGraw et al. (2012) who found no differences > 2°C in radiant tem- perature using black globe sensors in Minnesota (minimal elevation range), we found average differences in ambient air temperatures of 6–7°C at all 3 study areas during both seasons. Under the most extreme conditions, differences between locations potentially available to moose approached 20°C, depending on study area, season, and time-of-day. Surprisingly, spatial heteroge- neity in temperatures was somewhat consis- tent across both time of day and baseline temperature (N. DeCesare, unpublished data). The refuge effect of relatively cool sites appears consistently available; how- ever, animal responses to temperatures, and their dependence on thermal refugia, may be accentuated during particularly extreme conditions (Pigeon et al. 2016, Robertson et al. 2022). Furthermore, drivers of spatial pattern in these differences were not static, and covariates associated with cool condi- tions varied widely by study area, season, and time of day (Fig. 3). Moose selection of sites as thermal refugia may therefore be conditioned temporally and spatially accord- ing to shifting patterns of heterogeneity that dictate where and when cooler conditions are available. Combinations of biophysical variables generating cooler microclimates typically reversed between early-morning and late-af- ternoon time periods. Similar to studies else- where, we found that both forested vegetation types and increased canopy closure within forested vegetation provided cooling (rela- tive to grass-shrub types) during midday but retained warmth at night (Olson et al. 2014, Li et al. 2015). Elevation-temperature rela- tionships were more complex, with decreases in temperature at high elevation in some study areas and seasons, but inversion pat- terns of cooler temperature at low elevation in some situations (e.g., summer nighttime temperatures in Cabinet Mountains). Such summer inversion patterns have been observed previously in mountain study areas, where radiatively cooled air can accu- mulate in drainage bottoms during night (Holden et al. 2011). Diurnal cycles of moose movement and habitat use consistent with some of these time-varying patterns of Fig. 4. Average importance of 6 variables (canopy, forest land cover, elevation aspect, topographic position index [TPI], interaction of forest land cover forest and solar radiation), in explaining spatial variation in ambient temperature in 3 study areas and 2 seasons, western Montana, 2013–2015. HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 44 temperature have been noted by Dussault et al. (2004), Borowik et al. (2020), and Burkholder et al. (2022). Where moose have been shown to increase nighttime activity in response to warm ambient temperatures (Montgomery et al. 2019), spatial variation in temperature conditions may induce behav- ioral effects during both daytime and nighttime. While spatial heterogeneity in tempera- ture during summer was only slightly higher compared to that during winter (Fig. 2), our Fig. 5. Predicted ambient temperature from global generalized linear models in an example portion of the Cabinet Mountains study area during two times and seasons and relative to the average recorded temperature at Remote Automatic Weather Station (RAWS) sites during the study period, 2013–2015. ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 45 Ta bl e 2. G lo ba l m od el c oe ffi ci en ts (a nd st an da rd e rr or s) p re di ct in g Δt d ur in g su m m er , a cc or di ng to sp at ia l v ar ia tio n in c en te re d an d st an da rd iz ed c ov ar ia te s i n th re e st ud y ar ea s o f w es te rn M on ta na , 2 01 3– 20 15 . St ud y ar ea H ou r in te rc ep t C an op y Fo re st la nd c ov er El ev at io n A sp ec t TP I Fo re st * so la r ra di at io n B ig H ol e 0 −4 (0 .3 2) 0. 08 (0 .2 3) 2. 01 (0 .4 4) −0 .5 5 (0 .2 9) −0 .0 6 (0 .1 6) 0. 35 (0 .2 2) 3 −3 .7 (0 .3 4) 0. 16 (0 .2 5) 1. 78 (0 .4 7) −0 .4 5 (0 .3 1) −0 .1 3 (0 .1 8) 0. 33 (0 .2 4) 6 −3 .3 2 (0 .3 2) 0. 17 (0 .2 3) 1. 6 (0 .4 4) −0 .4 2 (0 .2 9) −0 .2 (0 .1 7) 0. 28 (0 .2 2) 9 −0 .8 6 (0 .5 7) −0 .2 6 (0 .4 2) 0. 64 (0 .7 8) −0 .5 5 (0 .5 2) −0 .3 6 (0 .3 ) 0. 32 (0 .3 9) −0 .0 9 (0 .0 4) 12 −1 .5 7 (0 .3 2) 0. 05 (0 .2 3) 0. 41 (0 .4 3) −0 .8 6 (0 .2 9) −0 .3 3 (0 .1 6) 0. 04 (0 .2 2) −0 .2 9 (0 .0 4) 15 −2 .8 8 (0 .2 9) −0 .0 2 (0 .2 1) 0. 85 (0 .4 ) −1 .2 8 (0 .2 7) −0 .1 3 (0 .1 5) −0 .0 3 (0 .2 ) −0 .3 8 (0 .0 5) 18 −4 .2 1 (0 .3 1) −0 .1 5 (0 .2 3) 0. 74 (0 .4 3) −0 .9 2 (0 .2 9) −0 .1 3 (0 .1 6) 0. 14 (0 .2 2) −0 .3 7 (0 .0 4) 21 −4 .6 6 (0 .3 4) −0 .0 6 (0 .2 5) 1. 95 (0 .4 7) −0 .6 1 (0 .3 1) 0. 03 (0 .1 8) 0. 37 (0 .2 4) −1 .0 2 (0 .0 5) C ab in et M ou nt ai ns 0 0. 02 (0 .7 7) 1. 14 (0 .2 3) −0 .5 (0 .8 2) 0. 57 (0 .3 3) −0 .2 1 (0 .2 3) 0. 79 (0 .3 1) 3 0. 67 (0 .7 6) 1. 07 (0 .2 3) −0 .2 4 (0 .8 1) 0. 98 (0 .3 2) −0 .1 5 (0 .2 2) 0. 69 (0 .3 1) 6 0. 79 (0 .6 9) 1 (0 .2 1) −0 .1 7 (0 .7 3) 1. 14 (0 .2 9) −0 .1 2 (0 .2 ) 0. 59 (0 .2 8) 0. 3 (0 .0 5) 9 0. 28 (0 .5 9) −0 .0 9 (0 .1 8) −0 .1 6 (0 .6 2) 0. 75 (0 .2 5) 0. 09 (0 .1 7) 0. 45 (0 .2 4) −0 .3 8 (0 .0 5) 12 −3 .5 5 (0 .5 8) −0 .6 8 (0 .1 8) −0 .4 6 (0 .6 2) −0 .2 1 (0 .2 5) 0. 06 (0 .1 7) 0. 02 (0 .2 4) −0 .6 5 (0 .0 4) 15 −4 .9 6 (0 .5 9) −0 .3 2 (0 .1 8) −0 .7 8 (0 .6 2) −0 .9 3 (0 .2 5) −0 .5 1 (0 .1 7) 0. 22 (0 .2 4) −0 .8 2 (0 .0 3) 18 −4 .7 4 (0 .8 1) −0 .1 1 (0 .2 4) −1 .1 5 (0 .8 6) −1 .0 9 (0 .3 4) −0 .8 3 (0 .2 4) 0. 59 (0 .3 3) −0 .7 9 (0 .0 4) 21 −2 .2 6 (0 .5 8) 0. 79 (0 .1 7) −0 .5 2 (0 .6 1) −0 .3 1 (0 .2 5) −0 .3 (0 .1 7) 0. 79 (0 .2 3) −0 .4 (0 .0 5) R oc ky M ou nt ai n Fr on t 0 0. 75 (0 .3 4) 0. 04 (0 .3 ) 0. 66 (0 .5 1) −0 .4 5 (0 .2 4) −0 .2 6 (0 .2 3) 0. 9 (0 .2 6) 3 0. 71 (0 .3 3) −0 .0 4 (0 .2 9) 0. 5 (0 .5 ) −0 .4 7 (0 .2 3) −0 .2 6 (0 .2 2) 0. 96 (0 .2 5) 6 0. 17 (0 .3 6) −0 .2 2 (0 .3 1) 0. 4 (0 .5 4) −0 .3 6 (0 .2 5) −0 .2 4 (0 .2 4) 0. 98 (0 .2 7) 0. 24 (0 .0 7) 9 −1 .6 5 (0 .3 ) −1 .1 4 (0 .2 6) −0 .2 (0 .4 5) −0 .6 7 (0 .2 1) 0. 14 (0 .2 ) 0. 93 (0 .2 3) −1 .6 4 (0 .0 6) 12 −0 .9 8 (0 .2 3) −0 .4 7 (0 .2 ) 0. 22 (0 .3 4) −0 .6 4 (0 .1 6) 0. 19 (0 .1 5) 0. 17 (0 .1 7) −0 .4 3 (0 .0 5) 15 −0 .5 3 (0 .1 7) −0 .3 1 (0 .1 5) 0. 65 (0 .2 6) −1 .0 2 (0 .1 2) −0 .0 3 (0 .1 2) 0. 19 (0 .1 3) −0 .0 3 (0 .0 4) 18 −0 .6 5 (0 .1 9) −0 .2 9 (0 .1 7) 0. 7 (0 .2 8) −1 .2 3 (0 .1 3) −0 .4 6 (0 .1 3) 0. 35 (0 .1 4) −0 .3 6 (0 .0 4) 21 0. 66 (0 .3 ) 0. 32 (0 .2 6) 0. 84 (0 .4 4) −0 .6 2 (0 .2 1) −0 .3 4 (0 .2 ) 0. 78 (0 .2 3) −0 .0 3 (0 .0 6) HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. ALCES VOL. 59, 2023 46 Ta bl e 3. G lo ba l m od el c oe ffi ci en ts (a nd s ta nd ar d er ro rs ) p re di ct in g Δt d ur in g w in te r, ac co rd in g to s pa tia l v ar ia tio n in c en te re d an d st an da rd iz ed c ov ar ia te s in th re e st ud y ar ea s o f w es te rn M on ta na , 2 01 3– 20 15 . St ud y ar ea H ou r in te rc ep t C an op y Fo re st la nd c ov er El ev at io n A sp ec t TP I Fo re st * so la r ra di at io n B ig H ol e 0 −1 .5 6 (0 .1 6) 0. 12 (0 .1 2) 0. 81 (0 .2 3) 0. 18 (0 .1 5) −0 .3 (0 .0 8) 0. 11 (0 .1 1) 3 −1 .5 5 (0 .1 6) 0. 15 (0 .1 2) 0. 81 (0 .2 3) 0. 19 (0 .1 5) −0 .3 2 (0 .0 9) 0. 02 (0 .1 2) 6 −1 .7 5 (0 .1 9) 0. 06 (0 .1 4) 0. 9 (0 .2 6) 0. 33 (0 .1 8) −0 .3 4 (0 .1 ) 0. 07 (0 .1 3) 9 −1 .5 (0 .1 6) 0. 02 (0 .1 2) 0. 7 (0 .2 2) 0. 41 (0 .1 5) −0 .3 8 (0 .0 8) 0. 18 (0 .1 1) −0 .0 1 (0 .0 7) 12 −1 .7 7 (0 .2 4) 0. 14 (0 .1 8) −0 .0 5 (0 .3 4) 0. 06 (0 .2 3) −0 .2 (0 .1 3) 0. 17 (0 .1 7) −0 .2 7 (0 .0 7) 15 −1 .6 2 (0 .2 ) 0. 07 (0 .1 5) −0 .1 3 (0 .2 8) −0 .3 (0 .1 8) −0 .1 1 (0 .1 ) 0. 11 (0 .1 4) −0 .0 7 (0 .0 7) 18 −1 .3 8 (0 .1 ) 0. 16 (0 .0 7) 0. 47 (0 .1 4) −0 .0 6 (0 .0 9) −0 .1 4 (0 .0 5) 0. 15 (0 .0 7) −0 .4 9 (0 .0 5) 21 −1 .5 3 (0 .1 5) 0. 11 (0 .1 1) 0. 79 (0 .2 1) 0. 12 (0 .1 4) −0 .2 2 (0 .0 8) 0. 15 (0 .1 ) C ab in et M ou nt ai ns 0 −0 .2 9 (0 .2 2) 0. 38 (0 .0 7) −0 .0 7 (0 .2 3) 0. 07 (0 .0 9) −0 .1 3 (0 .0 6) 0. 11 (0 .0 9) 3 −0 .1 8 (0 .2 3) 0. 35 (0 .0 7) −0 .0 6 (0 .2 4) 0. 05 (0 .1 ) −0 .1 3 (0 .0 7) 0. 07 (0 .0 9) 6 −0 .1 5 (0 .2 4) 0. 35 (0 .0 7) −0 .0 2 (0 .2 5) 0. 11 (0 .1 ) −0 .1 (0 .0 7) 0. 05 (0 .1 ) 9 −0 .1 7 (0 .2 5) 0. 25 (0 .0 7) 0. 01 (0 .2 6) 0. 11 (0 .1 ) −0 .0 9 (0 .0 7) 0. 05 (0 .1 ) −0 .0 8 (0 .0 5) 12 −1 .7 (0 .3 1) −0 .3 (0 .0 9) −0 .1 9 (0 .3 3) −0 .2 6 (0 .1 3) −0 .2 2 (0 .0 9) −0 .0 8 (0 .1 3) −0 .4 3 (0 .0 5) 15 −2 .3 8 (0 .3 2) −0 .1 5 (0 .1 ) −0 .3 9 (0 .3 4) −0 .5 3 (0 .1 4) −0 .2 9 (0 .0 9) −0 .0 3 (0 .1 3) −1 .0 1 (0 .0 5) 18 −1 .2 5 (0 .2 1) 0. 18 (0 .0 6) −0 .1 (0 .2 2) −0 .3 2 (0 .0 9) −0 .1 5 (0 .0 6) 0. 02 (0 .0 8) −0 .1 8 (0 .0 5) 21 −0 .5 1 (0 .2 1) 0. 39 (0 .0 6) −0 .2 1 (0 .2 2) 0. 01 (0 .0 9) −0 .1 4 (0 .0 6) 0. 08 (0 .0 8) R oc ky M ou nt ai n Fr on t 0 −0 .7 9 (0 .1 9) −0 .3 2 (0 .1 6) 0. 69 (0 .2 7) −0 .4 3 (0 .1 2) −0 .3 (0 .1 2) 0. 42 (0 .1 4) 3 −0 .4 1 (0 .2 ) −0 .3 7 (0 .1 7) 0. 7 (0 .2 9) −0 .3 4 (0 .1 3) −0 .2 8 (0 .1 3) 0. 39 (0 .1 5) 6 −0 .6 4 (0 .1 9) −0 .4 1 (0 .1 7) 0. 72 (0 .2 8) −0 .2 6 (0 .1 2) −0 .2 8 (0 .1 2) 0. 31 (0 .1 4) 9 −0 .9 1 (0 .1 7) −0 .5 2 (0 .1 4) 0. 5 (0 .2 4) −0 .2 5 (0 .1 1) −0 .2 3 (0 .1 ) 0. 34 (0 .1 2) −0 .0 6 (0 .0 9) 12 −1 .4 9 (0 .1 9) −0 .6 7 (0 .1 6) 0. 34 (0 .2 7) −0 .4 9 (0 .1 2) −0 .1 6 (0 .1 2) −0 .0 2 (0 .1 4) −0 .3 3 (0 .0 8) 15 −0 .5 2 (0 .1 2) −0 .2 9 (0 .1 ) 0. 37 (0 .1 7) −0 .7 3 (0 .0 8) −0 .2 (0 .0 7) 0. 16 (0 .0 9) −0 .3 8 (0 .0 6) 18 −0 .5 4 (0 .1 6) −0 .0 3 (0 .1 4) 0. 69 (0 .2 3) −0 .4 5 (0 .1 ) −0 .2 8 (0 .1 ) 0. 31 (0 .1 2) −0 .0 6 (0 .0 7) 21 −0 .9 8 (0 .1 8) −0 .2 3 (0 .1 5) 0. 72 (0 .2 5) −0 .4 4 (0 .1 1) −0 .2 8 (0 .1 1) 0. 37 (0 .1 3) ALCES VOL. 59, 2023 HETEROGENEITY IN THERMAL CONDITIONS – DECESARE ET AL. 47 ability to explain such pattern was much bet- ter during summer (average R2 = 0.51–0.56) than winter (average R2 = 0.09–0.23). To the contrary, another study directed at predicting monthly maximum and minimum tempera- tures over space using covariates similar to ours found equivalent model fit during sum- mer and winter (Estevo et al. 2022). There are likely other unmeasured drivers of spatial variation in temperature during winter for which we were not able to account. Studies of moose behavioral responses to heat have emphasized summer conditions (e.g., Melin et al. 2014), though relatively warm tempera- tures can also induce physiological costs during winter (Renecker and Hudson 1986). We don’t fully understand animals’ ability to anticipate or detect heterogeneity in the ther- mal environment, but it’s possible that such ability may also vary between seasons. Measures of ambient temperature are not equivalent to the operative or effective temperature (Bakken 1981) that better describes the thermal conditions experi- enced by an animal by accounting for the additional and potentially more impactful effects of solar radiation and wind (Mitchell et al. 2018). Heterogeneity in operative tem- perature in our study areas may be higher than ambient temperature alone (Dzialowski 2005, Elmore et al. 2017). Furthermore, we did not sample additional variation in real- ized temperatures in accordance with the ground, water, or snowpack which may mit- igate thermal conditions for wildlife (McCann et al. 2013, Thompson et al. 2021). We used a relatively modest sample size of temperature sensors and were able to find a variety of complex relationships between temperature and topographic and vegetation conditions. While spatiotemporal tempera- ture data are already available at coarse scales from various remote-sensing or inter- polated data sets, multiple studies have shown that models using locally-derived empirical temperatures outperform general models (Macek et al. 2019, Estevo et al. 2022). We encourage researchers and man- agers to explore field collection and spatio- temporal modeling of temperature sensor data for cost-effect and baseline description and prediction of thermal environments for wildlife (Fig. 5). The physiological effects of thermal environments are multi-faceted and complex, and improving our understanding and management of thermal environments is an important challenge for future conserva- tion (Mitchell et al. 2018). ACKNOWLEDGEMENTS We thank Z. Holden for assistance with design of this study and supply of thermal radiation shields. 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