For pasture-based production systems, the goal is to calculate an animal's nutrient requirements for maintenance, growth, reproduction and lactation considering its age, sex, physiological status and environment and then to determine the daily allowances of alternative feedstuffs that would cover the shortfall of seasonal pastures. Unraveling the complicated interactions between animals (intake levels, productive processes, seasonal metabolism) and feeds (physicochemical characteristics) requires numerous balance trials with animals of various production levels offered a spectrum of common feedstuffs. Models reduce the numbers of combinations and permutations by allowing optimally interpolation among the empirical trials.

There are, of course, many gaps in our understanding of nutrient requirements of wapiti and other farmed game. Much less research has been done and the needs are somewhat more complex. The particular challenge for this project was to link bioenergetics and behaviour in order to capture the considerable ability of wild ruminants to capitalize on opportunities and offset stresses of seasonal environments. Necessarily, this model provides only a framework to condense the growing body of knowledge.

A model of seasonal energetics and growth of wapiti (BION, Hudson and White 1985) has been available for some time. However, it has become dated in research content and computer implementation (originally programmed in FORTH to achieve sufficient speed on 80s vintage microcomputers). BION was extended in some ways and simplified in others to improve performance and make best use of what is known about nutrient requirements of wapiti.

STELLA was selected as the modeling language for its simplicity, strict adherence to systems dynamics conventions, and availability of a free player for both MS-Windows and Mac OS. STELLA derives from DYNAMO, the language used for the MIT/Club of Rome study on limits to world growth. A new version (STELLA 5.0) which allows subscripted variables simplified programming and offered new scope for dealing with distributed systems.

This model is part of the collaborative Digital Deer project which serves as a clearinghouse for information on the nutrition, bioenergetics and behaviour of deer. It features background papers and eventually regional reviews of feeding practices. At the present time, two models are under development: BION simulates daily energy exchanges and provides a means to evaluate performance of deer on pastures. ACTIVE in an 'animat' which simulates minute by minute decisions and energetic transactions of deer in natural environments and is used to study the response to disturbance.

The model (BION) simulates bioenergetic transactions of individual female wapiti of any age from weaning to maturity which may or may not be pregnant and/or accompanied by a calf. Because of complications of antler growth and the rut, the current version does not provide a good representation of the bioenergetics of adult males. The model is designed to simulate changes over one year with a daily time step but can be cycled to reconstruct lifetime performance.

Interaction is via a control panel (Fig. 2). The model invites inputs in several ways. Graphical parameters such as seasonal patterns of temperature, precipitation and forage digestibility can be sketched to represent the year beginning 1 September. Numerical parameters describing the animal, pasture and management are entered in a tabular form with a page tab. There also is a switch to establish pregnancy.

Major tracking variables are summarized in graphic pads monitoring general parameters (weight, intake, conceptus weight, and milk production), activity budgets, feeding constraints, digestive kinetics, body composition and energy and nitrogen balance.

The seasonal environment experienced by wapiti is defined by temperature, precipitation, snow pack and forage biomass and quality. Temperature influences both thermoregulation and pasture dynamics. Snow influences pasture availability and pools of green forage, dry forage and litter determine foraging rates and diet quality.

Animals are assumed to have access to two habitats or pasture types each with different parameters. Default settings assume that these are open and wooded habitats in the aspen parkland of western Canada.

Soil moisture within the rooting zone, a driving factor in plant growth, is modeled simplistically as the balance of precipitation, percolation, and evapotranspiration. Soil fertility and the influence of animals on it is not explicitly programmed. However, the general productivity of the site is established by parameters defining plant growth.

The dynamics of pastures grazed by wapiti was the subject of an unfunded proposal to AARI so this important information gap remains unfilled. However, some preliminary work to calibrate the following rudimentary model was available the Ministik Wildlife Research Station in the southern edge of the boreal aspen forest so default parameters describe a volunteer Bromus/Poa sward in open or aspen forest. Other forage resources of the aspen forest such as browse and leaf litter are not considered in this version despite their importance in the seasonal round of resource use (Gates and Hudson 1983).

Wapiti are able to select diets both by selecting feeding habitats and green/dry pools within each habitat. Selection of feeding stations within each habitat was not modeled mechanistically because it requires fine spatial resolution and unreasonably sophisticated pasture resource inventory (Jiang and Hudson 1993).

Spatial behavior of wapiti on seasonal pastures responds largely to foraging opportunities (Watkins et al. 1991; Wilmshurst et al. 1995). Time spent grazing in each of two habitats is considered linearly proportional to the relative green forage pools.

Grass swards offer modest opportunity for selection within a feeding patch because green and dry forage are intermixed. Selectivity is allowed by assigning a preference factor for green:dry pools and applies this to the size of the respective forage pools. From these rules regarding resource use, seasonal diets are composed and asymptotic digestibilities and protein concentrations are computed.

Like other wild ruminants, wapiti on pasture spend 90-95% of their day either grazing or resting/ruminating. They increase grazing time to narrow the difference between requirements and pasture supply and therefore increase grazing times when requirements increase or grazing efficiency declines. The limit to this adaptive behaviour is the time required for rumination which can be as high as 12 h/day. Rumination time is considered proportional to rumen dry matter which must be cleared to free rumen capacity for additional forage intake.

The daily nutritional requirement is the sum of costs associated with physiological maintenance, thermoregulation, activity, growth and, if a fecund female, gestation and lactation. Work on the nutrition of deer has been limited largely to energy requirements. This is justified because energy usually is the most important factor limiting animal productivity. However, protein is a close second and, because protein is required by rumen micro-organisms to unlock energy by the fermentation of cellulose, protein and energy nutrition are closely linked.

Daily requirements for energy and protein are determined by the factorial approach summing costs for maintenance, gestation, lactation and gain. Shortfalls in energy intake stimulate mobilization of body tissues and "negative gain".

Ecological maintenance represents the costs of free existence. Until recently, these costs had to be calculated, assuming various productive efficiencies, from fasting metabolic rate, and energy costs of activity and thermoregulation. Jiang and Hudson (1992, 1994) developed techniques for evaluating energy budgets of free ranging animals and provided the estimates for maintenance and gain used to parameterize this model.

Published estimates for minimum winter requirements of red deer and wapiti are in the order of 450-550 kJ/kg^0.75/day (Fennessy et al. 1981, Suttie et al. 1987, Jiang and Hudson 1994, Cool and Hudson 1996). Summer and autumn values increased to 720 and 876 kJ/kg^0.75/day (Jiang and Hudson 1994).

Based on this work, BION multiplies 550 kJ/kg^0.75 as the winter nadir by the appetence cycle, a scalar ranging seasonally from 1 to 1.5. This cycle can be interpreted as a photoperiodic neuroendocrine response. The cycle is modulated by the nutritional environment but this is not known in a quantitative way. Relevant results will come from current studies supported by AARI (Christopherson and coworkers).

The incremental costs of free-existence increase this by about 200 kJ/kg^0.75/day (Jiang and Hudson 1992, Wairimu et al. 1992) but the value varies with resting metabolism. Activity is better represented as a fixed scalar (1.15) rather than a fixed cost per unit activity. Although summer activities probably do not range widely, winter costs are expected to vary with snow cover and supplemental feeding. If supplement is available ad libitum, heavy snow forces animals to camp near the feeder and costs appear to decline. Under other conditions, they are eager to continue foraging despite supplementation and activity costs increase. The relationships are not known in a quantitative way.

In the original model, thermoregulatory costs were calculated as the difference between net thermal loss to the environment and the heat produced from tissue and food-related metabolism. Some of this information is provided by Parker and Robbins (1984). However, factors such as posture and activity have such a profound effect on tissue and external insulation that a more direct approach was adopted. Adult wapiti protected from wind are very resistant to temperatures as low as -25°C when standing quietly. Although calves have lower critical temperatures of -20°C when bedded, it rises to -5°C when they are standing or active (Fig. 3). Standing values were used in this version.

Energy requirements for gestation are calculated from Adams et al.'s (1990) equation for red deer adjusting for the different birth weights and gestation lengths of wapiti (250 vs 233 days)(Fig. 4). From work on other ruminants, metabolizable energy was assumed to be used for gestation with an efficiency of only 13%.

Birth weights of healthy elk calves range from 15-22 kilograms (Hudson et al. 1991). Male calves are slightly heavier than female calves. Birth weights are directly related to maternal age and size (Blaxter and Hamilton 1980, Hudson et al. 1991). Good nutrition increases birth weights slightly (Hamilton and Blaxter 1980).

Birth weights of wapiti conform to interspecies allometric relationships and this may even hold for wapiti of different sizes (Robbins 1993):

BW = 0.2143 LVWT^0.79

Conceptus weight (fetus plus associated uterine tissues) at any stage of gestation is estimated:

CW = 1.54 BW e^{(0.0195 DP -5.122)}

Daily energy retention (PR) is:

PR = 4.184 BW e ^{(0.0193 DP -1.7938)}

Several studies have been conducted on lactation in Cervus elaphus. Arman et al. (1974) studied the composition and yield of milk from red deer. Robbins (1981) and Hudson and Adamczewski (1990) provided comparable data for wapiti. Fitting the lactation curve to data for well-fed wapiti, potential milk yield (Milk, kg/d) is calculated from days lactating (DL)(Fig. 5):

Milk = 0.022*(DL+25)^1.55*+exp(-.0195*(DL+25))

Although the effect of body size and condition is not known precisely, the following correction was made by multiplying the above equation by EBWsum/Mature_Wt.

The energy content of milk (EVl, kJ/kg) varies with the stage of lactation. Using data from Arman et al. (1974):

EVl = 4327 DL ^0.096

Unsupplemented wapiti hinds on aspen ranges produce less but more concentrated milks so the energy supply to the calf is about the same (Hudson and Adamczewski 1990). This milk supports calf gains of 800-1000 g/d.

Liveweight is calculated from empty body weight by adding the weight of digesta pools and, for pregnant females, the developing conceptus. Empty body weight is determined by integration of daily gains. Daily gains can be determined either from direct estimations of the costs of gain or from information on the energy content and composition of gain and the expected efficiencies of utilisation of metabolizable energy. The current version uses new information on seasonal costs of gain in wapiti; namely, 27,000 kJ/kg during winter increasing by 1.5 at peak metabolic activity in early summer (Jiang and Hudson 1994). Where nitrogen is limiting, surplus energy is deposited solely as fat.

The growth impetus of northern wild ruminants varies seasonally. These target gains have been established by regressing summer weight gains against spring weight and winter weight changes against peak autumn weights (Fig. 6, Hudson et al. 1985 and unpublished data). The interesting observation is that growth at all ages is dictated linearly to the deviation from asymptotic weight although different slopes apply in summer and winter. These relationships were manipulated to predict daily gains and to merge summer and winter relationships into a single expression modified by the seasonal appetence cycle.

Maintenance requirements for protein (Nx6.25) must minimally cover endogenous urinary and fecal excretion, and (negligible) dermal losses. The constant endogenous component is assumed to arise from the degradation and replacement of protein and simple nitrogenous components of tissues.

Mould and Robbins (1981) estimated EUN to be 0.16 gN/W^0.75 while metabolic fecal nitrogen was 5.58 gN/kg dry matter intake. In ruminants, these two quantities are not strictly independent and perhaps cannot simply be added to give total maintenance requirements. However, in the absence of relevant data for wapiti, the factoral approach is adopted (Robbins 1993).

Nitrogen required for development of the conceptus is:

NP = BW e ^{(0.01969 DP-1.7274)}

Nitrogen required for lactation is calculated using a value of 0.97% (6.2% protein) for the nitrogen content of wapiti milk. Protein requirements for growth are calculated assuming that lean tissue is 23% protein.

Feed protein to meet this net requirement is calculated by dividing by the digestibility of dietary protein and its biological value. Both are strongly influenced by dietary protein concentration and the two terms often are multiplied to obtain an overall efficiency called Net Protein Value (NPV). Over the range of typical diets, NPV varies little from 0.40-0.45 and is similar for most ruminants (Fig. 7).

There is some suggestion that digested protein, like energy, is not used equally efficiently for maintenance and various productive functions. Attempts at refinement define metabolizable protein as the proportion of digested protein absorbed as amino acids. This metabolizable protein is used with an efficiency of about 0.67 for maintenance, 0.50 for growth and gestation, and 0.65 for lactation.

This "black-box" approach does not distinguish the protein requirements of rumen microbes and host tissues and therefore does not address the issue of optimal ruminal degradation.

The advantage offered by wild ruminants is that most of their seasonal nutrient requirements can be met by grazing. Of course, the adequacy of the nutrient supply from forage depends on both its quality and availability and how it is influenced by stocking rate.

Regulation of intake on pasture can be visualized as the minimum of 3 interacting constraints: metabolic demand (Illius and Jessup 1996), digestive capacity (Allen 1996) and logistics of foraging (Wickstrom et al. 1984, Forbes 1996).

Animals eat to meet nutrient requirements for maintenance, growth and reproduction. Intake is therefore limited ultimately by this demand. The target dry matter intake from pasture (metabolic constraint) is calculated as this metabolizable energy required to meet requirements for seasonal maintenance and production divided by the metabolizable energy concentration of the feed.

Within limits, ruminants can compensate for deteriorating diet quality simply by consuming more. But, low quality forages ferment and pass from the rumen slowly and intake becomes limited by gut fill. Although not quantified, rumen capacity seems to increase under these circumstances and also during lactation to accommodate higher intakes. Potential daily dry matter intake limited by the digestive constraint is determined as the difference between digesta mass and rumen capacity.

This parameter is sensitive to the integration interval. Animals can increase daily intakes through frequent short feeding bouts rather than a single large one. The simplest solution was to adjust rumen capacity to work with a daily time step.

Nutrient intakes on pasture are influenced by logistic as well as digestive factors. Pasture biomass/structure and snow cover are most important. The feeding rate on foliage and browse is not very sensitive to biomass because of the clumped distribution of these forages. However, intake on grass pastures is determined largely by standing crop although different maximum feeding rates occur on green and dry forage. The feeding rate of wapiti is reduced to 50% at about 500 kg/ha (Fig. 8). Wapiti compensate by grazing longer but reach an upper limit of about 12 h/day because of pre-emptive activities and the rumination requirement.

The model determines maximum forage intakes by multiplying feeding times (mins) by feeding rates (g/min). Maximum feeding rates are varied from 11 to 22 g/min in proportion to the relative proportion of dry and green pools.

Ingested forage is subjected to the competing processes of digestion and passage. BION simulates this competition explicitly for soluble, potentially digestible and completely indigestible fractions. Estimating digestion and passage rates from Westra and Hudson (1981) and especially Jiang and Hudson's (1996) study of wapiti on seasonal pastures in Alberta, parameters were related to forage digestibility.

Physical properties of feed rather than specific morphophysiological adaptation explain most seasonal variation in digestive parameters. Among domestic ruminants, passage rates are influenced by intake level, forage type and forage quality. However, the relationship appears weak in deer (Milne et al. 1978, Renecker and Hudson 1990, Domingue et al. 1991 a,b 1992, Sibbald and Milne 1993). The simplest explanation is that digesta fill increases either by changing distension set-points or digestive tract dimensions. Evidence for the former comes from Sibbald and Milne (1993) who did not find differences in the weight of gut tissues but did find higher dry matter proportions and weights of digesta and water-filled capacity of the rumen when voluntary feed intake by red deer was high. Domingue et al. (1991a,b) also found that higher feed intake was accommodated by higher digesta loads.

Although wild wapiti and other deer are superbly adapted to smooth out the seasonality of nature, by stocking heavily and limiting their choices of habitats and foods, supplementary feeding becomes necessary. Shortfalls in pasture can be made up with a variety of conventional feedstuffs although attention to quality and palatability is more important than it is for beef cattle. Tables of ME values of feeds intended for sheep seem to work well with wapiti and red deer.

The amount of supplement to offer is determined by the shortfall of pasture intake. Although the requirements of animals for energy and protein are known rather precisely, the proportion obtained from pasture can only be very crudely estimated as discussed above. Also, heavy supplementation with palatable feeds reduces dependence on pasture forage and apparently reduces the efficiency of winter energy conservation (Kozak et al. 1994, 1995).