You are a 420 kg brown bear in an autumn Rocky Mountain valley. Walk, sprint and wade; salmon leap a ledge in the river, an elk herd grazes up-valley, a wolf watches from the rocks and an eagle soars overhead. Keep health, hunger, thirst and stamina up, follow scent and tracks, photograph and study wildlife, and finish the tasks.
Educational model, not a field guide or wildlife-management advice. Constants marked [assumption] are typical orders of magnitude. Animals never get hurt: when the bear is exhausted it rests. Bear, elk, deer, wolf, salmon and eagle are modelled as lumped animals with simple behaviour rules.
The science
Energy. Basal metabolism follows Kleiber: BMR = 70 M0.75 kcal/day (about 6 500 kcal/day, 315 W, for 420 kg). Moving adds the net cost of transport c = 10.7 M-0.316 J per kg per metre (Taylor et al. 1982, a running law; walking is scaled by 0.6 [assumption]) times a grade multiplier [assumption]. Metabolic drain of the stores runs in game time (time compression is the slider), the cost of walking is counted per metre actually walked.
Stores. Hunger is a digestible-energy store of 25 000 kcal [assumption]; a salmon gives about 4 kg of flesh at 1.9 kcal/g and 85 % digestibility [assumption]. Surplus beyond the store becomes fat at 7 700 kcal/kg and raises the weight; starvation burns fat and then lowers health. Thirst follows a 12 L reserve and a loss rate that grows with temperature and exertion [assumption].
Stamina. Critical-power model: above CP = 4 BMR [assumption] the anaerobic reserve W′ = 180 kJ drains at P − CP (time to exhaustion W′/(P−CP), about 31 s at 10 m/s); below CP it refills at half the surplus (resting: 1.5x).
Scent. Gaussian plume with ground reflection, C = Q / (2π u σy σz) e-y²/2σy² [e-(z-H)²/2σz² + e-(z+H)²/2σz²], Briggs rural neutral spreads σy = 0.08x(1+10-4x)-1/2, σz = 0.06x(1+1.5·10-3x)-1/2. Animals smell the bear when its plume exceeds a threshold at their position, so approaching downwind gets you detected much earlier than approaching upwind. Flight-initiation distances (elk 95 m, deer 75 m, wolf 55 m [assumption]) are multiplied by your noise (sprint x2, sneak x0.5, rest x0.4) and by visibility (fog, night).
Salmon leaps. Without drag, a fish leaving the water at speed v and angle θ reaches h = v² sin²θ / 2g, so it needs v = √(2gh) / sinθ. Launch speed is drawn from N(6.0, 0.8) m/s [assumption]; the 0.9 m ledge (plus a 0.3 m margin) is passed by about 80 % of attempts, the 4.5 m falls by practically none, so fish crowd the plunge pool. A swipe catches each fish in reach with p = 0.45 [assumption]; at least one of n: 1 − (1 − p)n.
Sun and weather. Latitude 52°N, late October: declination (Spencer series) and hour angle give elevation and azimuth, which light the scene; temperature is 18.3 + 5 cos(2π(h−15)/24) − 6.5 K/km · Δz plus a weather offset. Photo score blends angular size, centring, light and visibility.
Habitat. Wolf-elk dynamics dE/dt = rE − aEW, dW/dt = −mW + bEW with RK4; the invariant bE − m ln E + aW − r ln W is conserved (check below). It is context for the drawn herd, not a link to the individual animals.
Honest limits. Lumped physiology (no digestion delay, no hibernation), simple herd rules, rigid-part animation, fish arrival rate and weather are illustrative, no real-time ecology; the valley is a 420 m diorama with distant mountains drawn for context.