Table 3 Bioenergetic modeling to estimate the theoretical energy expenditure of reproductive female bats using the Classic and Ncube PH1 bat boxes.

Mass (Mb)

8.47 g

⁸⁷

Basal metabolic rate (BMR)

1.44 ml O2 g⁻¹ h⁻¹

⁸⁸

Minimal torpid metabolic rate (TMR_min)

0.03 ml O2 g⁻¹ h⁻¹

^{20,89,90,91,92}

Normothermic temperature (T_norm)

35 °C

^20,90,91,92

Lower critical temperature (T_lc)

32 °C

^20,90,91,93

Upper critical temperature (T_uc)

37 °C

^20,28

Minimal torpid temperature (T_tor-min)

2 °C

^20,85,86,87

Normothermic conductance below the lower critical temperature (C_lnorm)

0.2638 ml O2 g⁻¹ °C⁻¹

^20,86,87,89

Normothermic conductance above the upper critical temperature (C_unorm)

0.4978 ml O2 g⁻¹ °C⁻¹

⁸⁵

Torpid conductance (C_tor) or (C_lct)

0.055 ml O2 g⁻¹ °C⁻¹

^20,86,87,88

Change in torpid metabolic rate (TMR) over a 10 °C change in Ta (Q₁₀)

1.6 + 0.26T_a − 0.006 T_a²

^20,89,90,91

Specific heat capacity of tissue (S)

0.131 ml O2 g⁻¹ °C⁻¹

^20,90,91,92

Gestating mean torpor duration per day

133 min

^20,73

Lactating mean torpor duration per day

334 min

^20,73

Gestation period

May 15–June 30. We used a 2 weeks delay for cooler sites

³²

Lactation period

June 16–August 1. We used a 2 weeks delay for cooler sites

³²

Gestation activity budget

Foraging: 2 bouts of 20 min, resting in the roost: 1080 min, resting outside: 120 min

³²

Lactation activity budget

Foraging: 3 bouts of 105 min, resting in the roost: 2 bouts of 60 min and 1 bouts of 1080 min, resting outside: 0 min

³²

Foraging flight during gestation by 8.47 g little brown bat

4.20 kJ h⁻¹

⁷⁷

Foraging flight during lactation by 8.47 g little brown bat

3.90 kJ h⁻¹

⁷⁷

Typical diet for little brown bat

71.2% protein, 18.4% fat and 8.8% carbohydrate

⁷⁷

(1) Calculating normothermic energy expenditure (E_norm)

The normothermic energy expenditure varies with ambient temperature, T_a, according to a metabolic response curve using the following equations^20,88,89,90

when T_a > T_lc; E_norm = BMR + (T_lc − T_a)*C_lnorm

when T_a < T_uc; E_norm = BMR + (T_a − _uc)*C_unorm

when T_a ≥ T_lc ≤ T_uc; E_norm = BMR

where BMR is the basic metabolic rate, T_lc is the lower critical temperature, T_uc is the upper critical temperature, C_lnorm is the thermal conductance in normothermia below the lower critical temperature, and C_unorm is the thermal conductance in normothermia above the upper critical temperature

(2) Quantify predicted energy expenditure during torpor depending on whether T_a was lower or higher than T_tor-min

During torpor, metabolic rate, TMR, and body temperature decline with T_a until a lower ambient set-point temperature, T_tor-min, is reached, after which torpor body temperature is defended (that is, remains constant) and consequently TMR increases. Thus, TMR varies with temperature according to^20,90,91,92

when T_a > T_tor-min; E_tor = TMR_min*Q₁₀^((T_a − T_tor-min)/10)

when T_a ≤ T_tor-min; E_tor = TMR_min + (T_tor-min − T_a)*C_t

where Q₁₀ represents the change in torpor metabolism resulting from a 10 °C change in T_a, and C_t represents torpor conductance below T_tor-min

Cooling phase = 67.2% of active arousal

(3) Calculating predicted energetic cost for active arousal

The energetic cost of arousals E_ar is a simple function of the required increase in body temperature from T_tor to normothermic levels, T_norm, and the specific heat capacity S of the bat’s tissues^89,90,91

E_ar = (T_norm -T_tor)*S

(4) Conversion from mass-specific Vo2 into SI (energy expenditure)^20,94

Heat Production = (17.71P + 20.93C + 19.55L)*mass-specificVo₂