ALMaSS  1.0 The Animal, Landscape and Man Simulation System
ALMaSS brown hare Energetics

## 1. Introduction

The aim of the energetic component of the hare model was to describe the energy balance of the hare on a daily basis throughout its lifetime. This required a consideration of energy inputs and costs at each growth stage. The energy costs can broadly be broken down into four groups: resting metabolism; reproduction; activity (movement); growth. In the description that follows each of these sections is considered as appropriate for each life stage.

## 2. Resting metabolic rate (RMR)

### 2.A Age 1-35 days

For hares under 36 days, RMR (kJ kg-1) was calculated based on Hacklander et al. (2002a) by fitting curves to their observations on RMR of captive animals assuming that the categorical relationships between RMR and temperature presented were continuous up to 35 days old. An equation to predict the slope and intercept for calculating RMR vs temperature at different ages was then used to calculate RMR as a function of age and temperature:
$$RMR = (-1.566 age + 58.487)T + 1525.4 age ^{-0.3997}$$            (eqn 1),
where T is the number of degrees drop in temperature from the thermo-neutral point.

### 2.B Age >35-days

RMR for hares at age 36 days and above was obtained from the general relationship between energy consumption per day and size. This can be expressed as:
$$e=(69.1 x 4.187)w^{0.808}$$            (eqn 2),
where w is live-weight in kg, and e is energy consumption in kJ kg -1. This equation was based on the study of 272 species of placental mammals (McNab, 1988) and covers grazers in the range of 0.14-150 kg BW. RMR was then calculated on a daily basis by assuming that b was constant at the value for 36 days (2.12 kJ kg -1) from equation 1.

## 3. Hare growth

### 3.A Age 1-35 days

Unfortunately, there is no information regarding the relative weight gain with age between 0-35 days, hence a constant daily weight gain of 26 g per day was assumed. We further made the assumption that the data provided by Hacklander et al. (2002b) on captive hares represent the maximal growth rate that could be expected in wild hares.

The energy required for the growth of hares is determined from the relationship between data points presented by (Hacklander et al., 2002a), and assuming linear interpolation between the energy requirement and age. Fitting a linear relationship to data on actual digested energy intake by leverets from milk and solid food (Hacklander et al., 2002a) provides the relationship for KJ/day consumed:

$$KJ day^{-1} = 14.5 age + 52.25$$            (eqn 3)

Hence the predicted energy expenditure (KJ) covering RMR can be compared to the actual total energy use (RMR + growth + activity + thermoregulation + food absorption), also provided by (Hacklander et al., 2002a). The difference can be used to estimate the instantaneous cost of adding one kg of weight at the different ages since the animals observed were caged animals with limited movement possibility at temperatures within the thermo-neutral zone (Hacklander et al., 2002a) (Table 1). The energetic cost of growth of leverets during lactation (KJ per kg gained BW) is a linear function of age in days:

$$BWgain KJ/Kg = 311.6 age + 3019.9$$            (eqn 4)
(R2 = 0.998, compared to Hacklander et al's data (Hacklander et al., 2002a) ).

 Age Days Weight Kg RMR KJ Energetic Intake KJ Difference KJ/day Cost of growth KJ/Kg 3.5 0.21 181.2 203.0 21.8 838.6 10.5 0.39 210.8 304.5 93.7 3604.4 17.5 0.58 249.9 406.0 156.1 6005.4 24.5 0.76 289.2 507.5 218.3 8397.0 31.5 0.94 328.8 609.0 280.2 10777.7

Table 1: Based on data from (Hacklander et al., 2002a) assuming hares at thermo-neutral temperature

Hare weight gain per unit energy decreases asymptotically with age, but never becomes zero. In the model implementation, leverets obtain energy up to the amount required to gain 26g body weight per day, based on (eqn 4).

### 3.B Hare growth from 36 days to death

As with leverets <36 days old, the approach used was to model the maximum amount of energy that the hares were allowed to use for growth from day 36. If maximum energy was available every day during the life of the hare they would reach a live weight of 5.2 kg (plus additional energy reserves as fat deposits). This level was set as the absolute maximum a free-living hare could achieve if it never experienced any non-optimal nutritional conditions. This weight should therefore never be achieved, and indeed out of 179 female hares sampled in Denmark during 2003-2008 only 4 hares reached a total live-weight of 5kg (T. Jensen, unpublished).

The growth curve used in the model was based on data presented by Pielowski (Pielowski, 1971a; Pielowski, 1971b). Pielowski gives mean growth data for individual hares characterising the growth of hares in Poland in the 1960s. The data describe a rapidly rising curve reaching an asymptote after 2 years age. We constructed four candidate growth model curves having this general shape and tested their fit using AIC criteria were used to determine the degree of explanatory power of the 4 models (Table 2). Model 2 was selected as the most parsimonious fit.

 Model 1 $$wt=(a-(b/c^{age}))$$ df = 4 AIC = 237.3 Model 2 $$wt=a+(b-a)/(1+exp((c-age)/d))$$ df = 5 AIC = 233.1 Model 3 $$wt=a age/(b+age)$$ df = 3 AIC = 274.7 Model 4 $$wt=(a/age^b))/(1+exp((c-age)/d)))$$ df = 5 AIC = 237.

Table 2: Model structure, degrees of freedom and AIC statistics for the 4 models tested.

In constructing the final age-specific energetic relationships all total wet-weight (ww) values were converted to ingesta-free and dry matter weights (dmw) and weight-gains (however RMR was still based on live-weight). In doing this we used the following estimates:

• The mean water content of Lagomorphs is 66% (Robbins, 1993 p.228)
• The mean fat-percentage of Lagomorphs is 7% (21% of dmw, (Robbins, 1993))
• The ingesta was estimated to be 600 g ww in an adult hare of 5kg, approximately 12 % of live weight (Belovsky, 1984).
• Net energetic efficiency of depositing protein was 44%, which equals a cost of 42.7 kJ/g (dmw) (Robbins, 1993).
• Net energetic efficiency of depositing fat was 59%, which is equivalent to a cost of 63.7 kJ/g (dmw).The net efficiency is our own estimate based on herbivore efficiencies in converting structural carbohydrates or protein to fat (Robbins, 1993).

Hares attain maximum body weight for the first year of life at the age of 240 days (Pielowski, 1971a), but the protein/fat ratio in weight gain varies throughout the maturation period. To calculate the energetics of growth (cost of weight gain) we therefore divided the life of the hares into three further periods (36-240 days, 241-365 days and 365+ days). At all stages the cost of gaining 1g dmw as protein, was calculated using a net conversion efficiency of protein deposits of 44% (Robbins, 1993) p.310) as 42.7KJ/g BW (18.8KJ x 100/44). The cost of deposing fat is estimated using a net efficiency of deposing fat of 59% (average between net efficiency of protein deposit and a general average of net fat deposit efficiency of 74%) - giving 63.7 kJ/g (37.6kJ x 100/59). This fat deposition efficiency estimate was based on the fact that net efficiency of fat deposition is variable - highest for fat created from protein and carbohydrates, but much lower if the fatty acids are delivered in the food.

### 3.B.I Age 36-240 days

During this period the model hares gained weight primarily by depositing protein. However, as the mean fat-percentage of Lagomorphs is 7% (21% of DM, (Robbins, 1993) we assume that body weight gain consisted of 100% protein at the age of 36 days and with a linear increase of fat deposition to being 50% protein and 50% fat at the age of 240 days.

### 3.B.II Age 241-365 days

During this period weight gain composition was assumed to change linearly from 50% fat to 100% fat.

### 3.B.III Age 366 days - death

After one year of age the body weight gain was presumed to be a result of filling up readily usable fat depots (i.e. 100% fat). Model hares obtained a daily energy intake less locomotion costs. If this intake failed to reach RMR, then the hare would burn fat reserves. If excess energy over RMR was available, the hare would use this for growth until the excess energy exceeded the maximum daily growth energy for that day. At this point further excess energy could be converted to fat, up to a maximum fat depot size of 4% of live-weight (Hacklander, pers comm.).

## 4. Reproduction Costs

### 4.A Energy Requirements for Lactation

Since (Hacklander et al., 2002a) supplies information on the amount of solid food consumed as a proportion of the total energy consumption with age, we could calculate the amount of milk required per day in kJ supplied up to day 35 (where we assume weaning is complete in the free-living population) by interpolation of the points. The energy required for maximum daily growth from milk was therefore used as a maximum energetic cost of lactation for the female per leveret; assuming her own energetic needs were met by her energy intake, then she would deliver up to this amount of energy to each of her young. Absorption efficiency of the milk by leverets was assumed to be 99% (Hacklander et al., 2002a).

### 4.B Energetic costs of milk formation

The digestion efficiency for females has been measured to be 0.6265 on a low fat diet, which is near natural composition (Hacklander et al., 2002b). However, to calculate the conversion efficiency of digested energy to milk an indirect approach was needed. The mean daily energy intake of non-parous females has been measured to be 1553kJ day-1 during the whole lactation period, and parous females nursing the same litter size as non-parous females to be 55% higher (Hacklander et al., 2002b). Since milk transfer was calculated to be a mean of 650 kJ day-1 the efficiency of conversion could be calculated to be:
$$650/((1553 x 1.55)-1553) = 0.76$$            (eqn 5)
This value was used to calculate the conversion efficiency of energy intake to milk energy for the model female hare.

### 4.C Costs of production of foetal mass

Foetal mass is assumed to consist of almost entirely of protein; therefore the energetic costs of foetal mass production are the same as adding protein as body weight. Foetal mass costs were apportioned to each day of gestation as a fixed proportion of the fat reserves each day. The total foetal mass at parturition was therefore dependent upon the energetic status of the female hare all through gestation. The number of leverets and their size was determined by fixing a leveret weight range of 95-125g live-weight, with the number leverets produced being the maximum number possible whilst keeping sizes within this range.

## 5. Activity Costs

Taylor et al. (1982) provide a relationship for the metabolic cost of transport based on a studies of 90 species:
$$COT = 10.7m^{-0.316}kJkg^{-1}$$            (eqn 6),
where COT is the cost of transport, M is body weight in kg. This relationship was used to calculate the cost of transport for all model hares.

## 6. Solid Food Intake

Intake was determined by a combination of four factors: ingestion rate, energetic content of food, digestibility of food, and accessibility of food. Energetic content of food was assumed to be fixed at 3.5 KJ/g
(mean content of perennial grasses is 3.2 KJ/g ww (Robbins, 1993)), but the digestibility to vary with season. Maximum rate of ingestion was observed to be 1.7g min-1 (Andersen, 1947), which therefore provided an energy intake of 5.94kJ min-1. This rate is comparable although lower than predicted for snowshoe hares (Belovsky, 1984). The intake rate was modified by calculating the accessibility of the forage by making the assumption that accessibility fell by 0.125% for each 1mm of vegetation above a height of 0.25m, which meant that at 1.1m accessibility was zero. Digestibility was given as 0.5 plus the square root of the proportion of new green biomass out of total biomass, with a ceiling of 0.8, giving a maximum energetic intake of 3.0kJ min-1. This assumes that the digestibility of old plant matter is 0.5 (Mowat et al., 1965), and that digestibility of young growth was 0.8, which is the in vitro digestibility recorded for young grass (Robbins, 1993). In order to prevent rapid daily fluctuations caused by changes in daily vegetation growth, the value used was constructed as the running average over the previous two weeks. Intake in kJ for a given day was therefore as:
$$Kj = \sum_v^{i=1} 1.8T_iA_iD_i$$            (eqn 7),
where v is the number of vegetation types foraged during the day, Ti is the time spent in vegetation i, Ai is vegetation i's accessibility and Di is vegetations i's digestibility. This assumes that biomass is not limiting.

## 7. References

Andersen, J., 1947. Traek af harens spiseseddel. Dansk Jagttidende, 2: 22-25.
Belovsky, G.E., 1984. Snowshoe Hare Optimal Foraging and Its Implications for Population-Dynamics. Theor. Popul. Biol., 25: 235-264.
Hacklander, K., Tataruch, F. and Ruf, T., 2002a. The effect of dietary fat content on lactation energetics in the European hare (Lepus europaeus). Physiological and Biochemical Zoology, 75: 19-28.
Hacklander, K., Arnold, W. and Ruf, T., 2002b. Postnatal development and thermoregulation in the precocial European hare (Lepus europaeus). Journal of Comparative Physiology B-Biochemical Systemic and Environmental Physiology, 172: 183-190.
McNab, B.K., 1988. Complications Inherent in Scaling the Basal Rate of Metabolism in Mammals. Quarterly Review of Biology, 63: 25-54.
Mowat, D.N., Fulkerson, R.S., Tossell, W.E. and Winch, J.E., 1965. The invitro digestibillity and protein content of leaf and stem prorportions of forages. Canadian Journal of Plant Science, 45.
Pielowski, Z., 1971a. The individual growth curve of the hare. Acta Theriologica, 16: 79-88.
Pielowski, Z., 1971b. Length of life of the hare. Acta Theriologica, 16: 89-94.
Robbins, C.T., 1993. Wildlife feeding and nutrition. Academic Press.
Taylor, C.R., Heglund, N.C. and Malony, G.M.O., 1982. Energetics and mechanics of terrestrial locomotion. I. Metabolic energy consumption as a function of speed and body size in birds and mammals. Journal of Experimental Biology, 97: 1-21.