Clock-

Air-

Grass-

Pond-

Mean core-

Drag: orbit · wheel/pinch: zoom · the green carpet thins where the herd has grazed · red-tinted animals are overheating

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Capybara Herd Pond Lab: Wallowing Heat Refuge, Grazing and Logistic Pasture Regrowth

A herd shares a 30 m pasture with a pond. Heat sends the animals into the water, hunger sends them to the grass, and the grass regrows only as fast as a logistic curve allows.

Live measurements

What the herd is doing- Weather- Core temperature- Pond visits- Grass eaten today (average animal)- Grass on the pasture- Daily growth and grazing- Best regrowth (max sustainable yield)- Sustainable herd size (prediction)-

Grass on the pasture, % of the carrying capacity (orange: the 50 % point where regrowth is fastest)

Herd core temperature (red: hottest animal, orange: mean)

Herd, grass and weather

Herd size

Regrowth r

Capacity K

Day peak

Night low

Pond water

Sun strength

Sim speed

Camera

The run starts at 06:00 with 80 % grass. Capybaras are active from 04:30 to 21:30 and rest by the pond at night; whenever the core temperature passes 38.6 C an animal walks into the water and stays until it has cooled to 37.0 C. Changing a slider or preset restarts the run.

Experiment: how many capybaras can this pasture feed?

Runs the current pasture for 30 days with eight herd sizes and reports the grass left and the grass each animal eats per day, then compares the point where animals go hungry with the logistic prediction.

Independent numerical checks

Check	Theory	Measured

Each check runs the simulator headless at start-up and compares with a closed form that does not use the simulator.

The science

Logistic grass. Each 1.5 m cell holds grass biomass G (g dry matter per m2) growing as dG/dt = r G (1 - G/K), with the closed form G(t) = K / (1 + ((K - G0)/G0) e^(-r t)). Growth is fastest at G = K/2 where it equals r K / 4 per m2, so a pasture of grass area A can supply at most r K A / 4 grams per day indefinitely (the maximum sustainable yield). A herd that eats more than that sends the grass towards zero.

Grazing. An animal bites from the cell it stands on at a Holling type II rate I = Imax G / (G + h) (Imax = 100 g/h, half-saturation h = 60 g/m2), moves to the richest nearby cell when its own cell is thin, and stops when it has eaten 120 % of its daily need (1000 g dry matter, roughly 2 % of body mass). Capybaras graze mostly in the cool parts of the day, so the herd is active from 04:30 to 21:30.

Heat and the pond. The core temperature obeys C dTb/dt = M + G_fur (T_air + dT_sun - Tb) - E on land and C dTb/dt = M - G_w (Tb - T_w) in water. Here C = 50 kg x 3470 J/kg/K; M is 0.8 x Kleiber (3.4 m^0.75 W) times an activity factor of 1.0 resting, 1.3 grazing, 1.8 walking; G_fur is the fur-plus-boundary-layer conductance of 1.6 m2 of skin; dT_sun = alpha S f / h is the sol-air excess of the sun-warmed coat; and G_w = 0.7 x 1.6 m2 x 30 W/m2/K for the submerged skin. In water the core relaxes exponentially with time constant tau = C / G_w (about 1.4 h) towards T_w + M / G_w, so cooling from 38.7 to 37.0 C takes tau ln((Th - Tinf)/(Tc - Tinf)) (about 14 minutes with a 26 C pond). Sweating is weak (a small ramp above 38.2 C); the pond is the real radiator.

What is simplified. One lumped core temperature per animal, no shade, no mud, no social structure beyond mild spacing, no predators, no seasons for the grass. The coat, skin conductance in water, the 38.6 and 37.0 C thresholds, the grass parameters and the 1000 g/day need are rounded typical or illustrative values chosen to give plausible wallowing bouts of 10-20 minutes and a pasture that supports about ten animals; they are not measurements and should be spot-checked against the literature before being quoted. The animals are rigid walking models, not a gait simulation.

Checks on this page. (1) Grass regrowth over ten days against the closed-form logistic curve in every cell; (2) the duration of a wallowing bout against tau ln(...); (3) the steady core temperature of a resting animal on land against Ta + 0.85 M / G_fur; (4) exact mass conservation: change in grass = growth minus eaten over three days with ten animals. The sweep compares the herd size at which animals first go hungry with r K A / 4 divided by the daily need.