In this study, we test two hypotheses. First, in deciduous broad‐leaved forests, which are the main habitat for Asian black bears, spring provides a sufficient food supply from simultaneous leaf‐flush of deciduous broad‐leaved trees, whereas autumn provides extensive hard mast. Thus, we expect that the daily energy balance of bears will exhibit a two‐peak pattern, rising temporarily in spring, dropping to the lowest point in summer, and peaking in autumn. Second, in poor mast years, bears must obtain substitute food items by expanding their home range and activities, which in turn increases their energy expenditure, ultimately lowering the energy balance in poor mast years for both sexes.

In this study, we estimated the daily energy balance of Asian black bears during different periods of the year. Because the bears’ food items change seasonally, we estimated the daily energy balance for each month separately. The energy balance in autumn may vary widely depending on masting conditions, so for the period from September to November we made separate estimations for years of good and poor mast.

The amount of hard mast such as nuts and acorns—the main food sources for many Asian black bear populations in autumn—fluctuates widely among years (Shibata et al. 2002 ). Studies suggest that bears adjust their food habits and behavior in accordance with the amount of hard mast available, and the degree of behavioral change differs between the sexes with the increase in daily movement distance being greater for females than for males (Koike 2009 , Kozakai et al. 2011 , Koike et al. 2012 ). Therefore, the energy balance likely varies widely between good and poor mast years and between males and females. Although the amount of energy bears can accumulate prior to hibernation is assumed to be less in poor mast years compared to good mast years, the degree of the difference has yet to be clarified.

Asian black bears ( Ursus thibetanus ) are omnivores that are difficult to observe directly. Relying heavily on plant food items, bears seasonally shift their diet. They consume herbaceous and woody plants in spring, social insects and soft mast in summer, and hard mast and soft mast in autumn (Koike 2010 ). Therefore, it is possible that the energy balance of Asian black bears also fluctuates seasonally. A study by Yamanaka et al. ( 2011 ) suggested that the nutritional state of bears is lowest in summer, based on the low‐fat accumulation in the femur. Thus, Asian black bears may not even satisfy their base metabolism, with ants as the main source of food in the summer (Yamazaki et al. 2012 ). In addition, although bears hibernate during winter, a certain amount of energy is still necessary for survival, and fat accumulated prior to hibernation is the energy source consumed during hibernation (Nelson et al. 1983 ). Thus, bears must obtain more energy during autumn than in other seasons. In fact, previous studies have indicated that wild brown bears ( U. arctos ) and American black bears ( U. americanus ) do have increased body mass and fat in autumn and have decreased body mass and fat in spring after hibernation (Hilderbrand et al. 2000 , Schwartz et al. 2014 ). However, the seasonal change in the energy balance of Asian black bears and other Ursidae species is unknown.

Previous studies devised a formula that can be applied to all mammals for estimating energy consumed during activity states such as resting, traveling, or feeding, based on the body mass (Kleiber 1961 , Taylor et al. 1974 ). For primates and ungulates that can be observed directly, energy intake has been estimated by determining the food item type, time spent feeding, and amount of food items consumed per unit time, as well as the energy content of each food item ( Macaca fuscata , Nakagawa 1997 ; Cervus canadensis , Gedir and Hudson 2000 ; Gorilla beringei beringei , Wright et al. 2014 ). Because of the inherent difficulties in conducting field studies of large carnivores that are not directly observable, few studies have attempted to convert estimated energetic requirements of wild carnivores to prey requirements (Powell 1979 ). However, in the case of carnivores with simple diets that primarily hunt ungulates, energy intake or balance has been determined by estimating the number of ungulates hunted based on location data from GPS collars mounted on individuals. Such GPS tracking studies have allowed researchers to obtain empirical estimates of activity and movement costs and to estimate annual kill and consumption rates for many carnivores ( Puma concolor , Knopff et al. 2010 ; Canis lupus , Metz et al. 2012 ; Panthera tigris altaica , Miller et al. 2013 ). Estimating the energy balance remains a challenge, however, for species that are not easily observed, those for which it is difficult to calculate the proportion of time spent on each activity, and omnivores.

Energy obtained from food resources forms the fundamental basis of biological activity; thus, energy intake is an essential factor in evaluating an animal's nutritional state (Robbins 1992 ). It is also crucial, however, to consider the energy balance: energy intake minus energy expenditure (Barboza et al. 2009 ). Few studies to date have directly examined the energy balance in wildlife (Nakagawa 1997 , Gedir and Hudson 2000 ), instead using models to predict potential energetic costs or requirements (Oftedal and Gittleman 1989 ), because, unlike with domestic animals, accurately measuring these values in free‐ranging animals poses several difficulties.

Because Q. crispula is the most dominant species across a wide elevation range and is reportedly an autumn staple food resource of bears in this area (Kozakai et al. 2011 ), we defined the poor and good mast years based on the acorn production of Q. crispula . Based on this information, we identified 2006, 2010, and 2012 as poor mast years and 2007, 2008, 2009, 2011, 2013, and 2014 as years with above‐average yield and thus good mast years (Tochigi et al. 2018 ). Tochigi et al. ( 2018 ) quantitatively assessed the seed production of 241–304 individual Q. crispula trees over several years in this study area and estimated individual tree energy values and regional mast energy values.

The study area is in the Ashio‐Nikko Mountains, in the central part of Honshu Island, Japan (36.54°–36.80°N, 139.22°–139.49°E). Elevations range between 400 and 2400 m a.s.l., and the area is characterized by steep terrain. From 2006 to 2017, annual precipitation was 2236 mm and annual mean temperature was 7.2°C (Japan Meteorological Agency 2018 ). Up to 1600 m a.s.l., the natural vegetation of this area is deciduous broad‐leaved forest composed of Quercus crispula , Quercus serrata , Acer spp., and Fagus crenata . In general, Q. serrata is dominant below 1000 m a.s.l. and Q. crispula is dominant above this elevation. Above 1600 m a.s.l. are mixed forests of conifers ( Tsuga spp.) and birch ( Betula spp.), and below 1000 m a.s.l. are conifer plantations of Cryptomeria japonica and Chamaecyparis obtusa .

Methods

Estimation of energy intake was based on the energy content (kcal/g) of major food items, their average ingestion rate (g/min), and daily feeding time (min). To estimate energy expenditure, we used data on average daily resting time, average traveling time, average feeding time, average travel distance, and mass of each individual to calculate the costs of resting, traveling, and feeding (Fig. 1). Because there are no parameters or equations that are specific for bears, we made a number of assumptions in applying energetic equations that were not specifically developed for bears, such as adjusting body mass by month and using surrogate values for some parameters.

Identification of major food items We conducted a fecal analysis to identify major food items of Asian black bears in the study area. We collected bear feces opportunistically during food surveys and radio‐tracking between May and November in each year from 2006 to 2012. Collected feces were frozen prior to analysis. All fecal samples were washed through a series of sieves to extract the food items. We separated food items of good mast years and those of poor mast years in samples collected from September to November, and we then determined the percent frequency of occurrence (100 × [number of scats containing a food type/total number of scats]) and percent volume (total percent volume of items/total number of scats). Food items accounting for <10% were not considered major food items and were excluded from the analysis.

Nutritional analysis of major food items Based on previously reported values (Masaki et al. 2012, Yamazaki et al. 2012), we determined the dry weight per single unit (e.g., one fruit, one leaf) and the gross energy content of major food items identified from the fecal analysis. Gross energy content for carbohydrates, crude protein, and fat were estimated at 4.2, 4.8, and 9.5 kcal/g dry weight, respectively, based on values provided by the Association of Official Analytical Chemists (Williams 1984). We also measured dry weight and gross energy content per unit for food items without known values. After collecting major food items in the study area, we dried collected samples for 2 h at 135°C and then measured dry weight per unit. Gross energy content was measured with a cylindrical calorimeter (C5000 Calorimeter system; IKA‐WERKE, Staufen im Breisgau, Germany). Because a portion of the food items’ gross energy is excreted as feces and urine, we estimated digestible energy content in the current study. Using the study by López‐Alfaro et al. (2015) as a reference, we determined digestible energy content by multiplying the proportion of digestible energy (%) to gross energy content (kcal/g). The proportions of digestible energy have only been examined for some foods (e.g., ants, 18.7%), so we substituted values of similar foods for items that had no values available. In particular, we substituted the values of spring vegetation (41.3%) for green vegetation in May, summer vegetation (35.3%) for green vegetation in June–August, autumn vegetation (24.3%) for green vegetation in September–November, pine nuts (49.7%) for acorns or nuts, and berries (60.0%) for soft mast.

Calculating intake per food item per unit of time Bears were observed visually at close range or were sought after with binoculars. A digital camera (Model XLH1; Canon, Tokyo, Japan) was used to video record the foraging behavior of bears. Bears were observed twice per week from May to November in 2006 to 2015. Based on video recordings, we calculated the quantity consumed in one bite for each food item (e.g., the number of fruits consumed in one bite, hereafter “one unit”) and the number of bites taken per minute (hereafter “unit rate”). We define the mass consumed in one bite for each food item as unit mass (g/unit). We also defined the mass of food consumed per minute as ingestion rate (g/min), which was calculated as unit mass (g/unit) × unit rate (unit/min). The ingestion rate of ants could not be determined from the video recordings, so we counted the number of stones that bears turned over per minute. We drew on the existing literature (Yamazaki et al. 2012, Fujiwara et al. 2013) and calculated this as average weight of ants per stone (89.9 mg/stone) × stones/min. We expected that the ingestion rate of Q. crispula acorns would differ substantially when bears feed in treetops versus when they feed on the ground because bears make the effort to climb trees to consume acorns and there is a great abundance of acorns in the crowns of the trees; therefore, we calculated the ingestion rate separately for these situations. Because signs of bears foraging for Q. crispula acorns in treetops have been observed in October (Nakajima et al. 2012, 2018), the ingestion rate for consumption in treetops was used for September and October, while the ingestion rate for consumption on the ground was used for November.

Calculating daily activity times and travel distance of bears We captured Asian black bears by using barrel traps between 2005 and 2014. Captured bears were immobilized before handling. After basic body measurements and premolar extraction for age determination were performed, bears that were more than three years old were equipped with microchips and GPS collars (GPS3300S and GPS4400S, Lotek, Ontario, Canada; FollowitAB, Followit, Lindesberg, Sweden) with activity sensors. Collars were programmed to record one location every 2 h. Because the energetic costs for females nursing and caring for young may be significantly higher than the energetic costs for males or single females, in this study we used the movement data of single individuals not including adult females with cubs or yearlings. Bear capture and handling methods were performed in accordance with the guidelines for animal research established by the Mammal Society of Japan (2009). For Lotek collars, we classified the activity sensor values following Kozakai et al. (2008), who used the total number of X‐ and Y‐acts in each 5‐min interval to define areas with activity (number of acts ≥ 14) and inactivity (number of acts ≤ 13). For Followit collars, we classified the activity sensor values following Arimoto et al. (2014), who used the activity rates in each 5‐min interval to define areas with activity (number of acts ≥ 12) and inactivity (number of acts ≤ 11). To calculate daily travel distance and travel speed based on the linear distance between GPS measurement locations and total daily travel distance, we calculated average daily travel distance of each individual for each month. We calculated all daily travel distances using ArcGIS 9.3 (ESRI, Redlands, California, USA) and its extension, Geospatial Modeling Environment. To calculate daily resting time, traveling time, and feeding time, a switching state‐space model (below, SSSM; Jonsen et al. 2005), modified for positioning data whose positioning interval is regular (Arimoto et al. 2014), was applied to the positioning data to smooth defects and errors of location data and classify the behavior classification as movement or stay. SSSMs estimate unobserved true positions based on an observation equation that explains the observation error of the positioning data and the state equation that explains the dynamics of the movement process (Jonsen et al. 2005). Location error for two‐dimensional fixes was larger than that for three‐dimensional fixes (Yamazaki et al. 2008). Therefore, we estimated the parameters of the t distribution separately for three‐dimensional and two‐dimensional fixes, which were related to the magnitude of location error. To interpolate missing location data, the linear interpolated position was used as an initial value for Bayesian estimation. The state equation of the SSSM consists of two‐state equations prepared for two behavioral states of movement and stay. The state equation is defined by the parameter θ of the average rotation angle, the velocity, and the autocorrelation parameter γ of the direction. That is, in the moving state, θ is close to 0 and γ is expected to be close to 1; in the staying state, θ is close to π and γ is expected to be close to 0. Prior distributions of θ and γ are provided by beta distribution (parameters α = 1 and β = 1) as noninformative priors because there is no prior information that can be referred to in the GPS data of the bears. To estimate the posterior distributions of the parameters in the model, we used Markov chain Monte Carlo (MCMC) methods. There were two chains in this model. The model sampled a total of 20,000 MCMC iterations, with the first 15,000 discarded as burn‐in and thinning to every 10th sample to reduce autocorrelation. Convergence was determined when the Gelman‐Rubin convergence diagnostic statistic ( R ^ ) fell below 1.1 for each chain (Gelman et al. 2003). If convergence did not occur, the MCMC was increased by 10,000 iterations until convergence was achieved. We used the R packages R2WinBUGS and WinBUGS for the MCMC analysis for SSSMs. Based on the median of the posterior distribution (take values 1 and 2) of the parameter bt representing the difference in behavior, the behavior of each location point was classified as movement or stay. Furthermore, after classifying movement and stay with SSSM, based on the activity sensor values for each location point, each location point was classified as stay in active, stay in inactive, or movement. Arimoto et al. (2014) conducted a field survey at most continuous location points of stay in active, and there were a lot of feeding signs, suggesting it is possible that feeding behavior occurred at the area of some continuous location points. Therefore, in this study, we classified staying in active as feeding and staying in inactive as rest. We categorized each measurement location point into resting, traveling, or feeding states and, in turn, calculated average daily values of rest, travel, and feeding of each individual for each month, based on the 12 daily measurements and the proportion of each state. Because we use only 12 measurements per day, there is the possibility of underestimating or overestimating each activity category. Because most bears emerge from the den site by May and enter the den site by November (Koike and Hazumi 2008), we used the GPS data from May to November and considered the sexes separately.

Estimating the proportion of feeding time for each food item For each major food item identified through fecal analysis, we calculated the proportion of feeding time within the daily feeding time, as described above, for each individual. Fecal analysis results are the proportion of indigestible residue. Therefore, for food items with poor digestibility such as herbs, fecal analysis content tends to be inflated compared to the actual proportion of volume consumed. To correct for this discrepancy, we used the correction factor (CF: g dry matter consumed/mL residue in feces) used for brown bears (Hewitt and Robbins 1996) to estimate the actual consumption amount. In particular, we calculated the approximate proportion of dry matter consumed for each food by multiplying CF by percent volume of major food items, as calculated in the fecal analysis. For items without known CFs, we substituted a CF of similar foods: that of crickets (0.91) for ants, clover (0.33) for green vegetation, nuts (1.54) for acorns, and blueberries (0.54) for all soft mast. In addition, bears spend a larger proportion of time‐consuming food items with a slower ingestion rate, even if the proportion of consumption volume is small. Thus, to calculate the proportion of feeding time for each food item, we divided the proportion of dry matter consumed of each food item by its ingestion rate (g/min), converted the value to a percentage, and estimated the proportion of feeding time of each food item for each month. Data for autumn (September–November) were analyzed separately for good and poor mast years.

Estimating daily energy balance of bears Daily energy balance (kcal/d) is determined by subtracting daily energy expenditure (kcal/d) from daily digestible energy intake (kcal/d). In this study, we estimated the daily energy balance of each individual for each month. Although the bears were weighed when captured, their seasonal body mass change thereafter is unknown. To estimate body mass change after capture for each month, we adjusted the measured body mass with known proportions of seasonal change in Asian black bears (Hashimoto and Yasutake 1999). The calculations were carried out under the assumption that body mass of mature bears does not vary between years. Daily digestible energy intake of each individual for each month was estimated by using the following formula: daily digestible energy intake (kcal/d) = Σ digestible energy content i (kcal/g) × ingestion rate i (g/min) × feeding time i (min/d), where i denotes food items consumed each month. Feeding time i was obtained by multiplying the proportion of feeding time for food item i (%) by the feeding time of each individual (min/d). Daily energy expenditure of each individual for each month was estimated with the following formula: daily energy expenditure (kcal/d) = energetic cost of resting (kcal/d) + energetic cost of traveling (kcal/d) + energetic cost of feeding (kcal/d). Daily energetic cost of resting, also called the basal metabolic rate, was calculated as follows (McNab 2008): energetic cost of resting (kcal/d) = 61.9 × W0.77 × t 1 /24, where W denotes estimated body mass in each month (kg) and t 1 denotes average daily resting time of each individual for each month (h). The intercept and the exponent of 0.77 were specialized for carnivores and were derived from measurements of 61 species of carnivores, ranging from 77‐g least weasels (Mustela nivalis) to 388‐kg Weddell seals (Leptonychotes weddelli). Although McNab (2008) used metabolic rates measured during hibernation in polar bears, brown bears, and black bears in his original allometric equation, those metabolic rates were not used in the above equation (Robbins et al. 2012). For daily energetic cost of traveling, metabolic rate generally increases in direct proportion to the travel distance and traveling time and increases in inverse proportion to body mass (Taylor et al. 1970). In this study, we estimated energetic cost of traveling with the following formula: energetic cost of traveling (kcal/d) = (5.8 × W0.75 × t 2 ) + (2.6 × W0.6 × d), where W denotes estimated body mass in each month (kg), t 2 denotes average daily traveling time for each month (h/d), and d denotes average total daily travel distance (km/d) for each month. All of these equations were originally from Taylor et al. (1970), who found that the steady‐state oxygen consumption of seven groups of mammals (21 g to 18 kg) increased almost linearly with running speed. They derived the equations for the energetic cost of running common to terrestrial mammals from the energetic cost of running and the predicted standard metabolism. These equations have been applied to large terrestrial carnivores such as Iberian lynxes (Felis pardina), pumas (Puma concolor), and tigers (Panthera tigris; Aldama et al. 1991, Laundré 2005, Miller et al. 2013). When considering the daily energetic cost of feeding, energy expenditure from feeding is higher than the basal metabolic rate (Barboza et al. 2009). Based on previous work, we defined the energetic cost of feeding to the same as the energetic cost of traveling, when bears travel at an average speed (Ackerman et al. 1986, Aldama et al. 1991, Miller et al. 2013). Using average travel speeds, we replaced d in the equations above with the product of speed and time and estimated the energetic costs of feeding (kcal/d) = (5.8 × W0.75 + 2.6 × W0.6Ts) × t 3 , where W denotes estimated weight in each month (kg) and t 3 denotes average daily feeding time for each month (h/d). Average travel speed of bears was calculated for each month using average values of daily travel distance (km)/daily travel time (h). Ts represents the average travel speed (km/h), and we used 0.9 (km/h) as Ts based on the GPS collar data.

Estimating change of accumulated energy balance due to masting For males and females, we calculated the accumulated energy balance from autumn to the following summer (i.e., from September to August) for each masting condition. First, we averaged the body mass of males and females, respectively, in September each mast year. Second, we averaged the resting time, feeding time, traveling time, traveling distance, and energy intake of males and females, respectively, in September each mast year. Finally, we calculated the resting cost, feeding cost, traveling cost, energy expenditure, and energy balance by using the above formulas with these averaged data in September. In October and November, we used body masses estimated by considering the rate of change from previous months (Hashimoto and Yasutake 1999) and averaged the resting time, feeding time, traveling time, traveling distance, and energy intake each month for each mast year and for each sex. December to April corresponds to the hibernation period, and daily energy expenditure during hibernation was estimated by referring to the formula of Farley and Robbins (1994): y = 50.96W0.78, where y denotes daily energy expenditure during hibernation (kcal) and W denotes body mass (kg). For data from December to April, we used estimated body mass by considering the rate of decrease from November to May. Energy intake during hibernation was assumed to be 0 kcal. We assumed the cumulative energy balance from the previous season is 0 kcal in September. In May, we used average body mass in years following a good mast year or a poor mast year, and in June and August, we used body mass estimated by using the changing rate from the previous month (Hashimoto and Yasutake 1999). We then averaged the resting time, feeding time, traveling time, traveling distance, and energy intake each month in each mast year. Finally, we summed the estimated energy balance from September to the following August for males and females, respectively, each mast year.