Module 4

Reproduction & Denning

Polar-bear reproduction combines delayed implantation, an 8-month ice-to-den gestation window, altricial 0.6 kg neonates born into a snow cavern, and 28% fat mother’s milk that drives ~10× cub mass growth inside four months. This module traces the cycle.

1. Delayed Implantation

Mating in April–June; blastocyst arrests in the uterus until October, when implantation resumes and active gestation begins. The mechanism — shared with other ursids, mustelids, roe deer — is thought to allow the female to assess body condition before committing metabolic resources. Ramsay 1988 measured minimum-body-condition thresholds (~190 kg, ~20% fat) below which implantation fails.

2. Maternal Den Thermodynamics

In October–November the pregnant female digs a snow den 1–3 m below the surface. Snow is an excellent insulator (k ≈ 0.05–0.15 W m^-1K^-1); den interior remains near 0 °C even at −40 °C ambient, a gradient of ~40 °C across a few decimetres of snowpack. The cubs are born in November–December at 600–700 g, altricial, with closed eyes and sparse natal fur. Maternal body heat maintains the 0 °C + den interior.

3. Milk Composition & Cub Growth

Polar-bear milk is ~33% fat — among the most calorically dense mammalian milks — at 4–5 kcal g^-1. Derocher 1993 analysed seasonal composition changes; protein is ~11%, sugars ~2%. Cubs emerge from the den in March–April weighing ~10–12 kg, a ~20× mass increase fuelled entirely by fat stored in the mother.

Simulation: Cub Growth & Den Thermal

Python

script.py49 lines

import numpy as np, matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Cub growth in den: 0.6 kg at birth -> 12 kg at emergence (4 months)
t = np.linspace(0, 120, 200)
# Exponential-ish growth on calorie-dense milk (33% fat, 11% protein)
mass = 0.6 * np.exp(0.025 * t)

# Milk energy density (kcal/g)
milk_E = 4.5
# Daily intake scales with mass
intake_g = 80 + 5.5 * mass

# Snow-den thermal profile: outside -30 C, den 0 C, near mother +34 C
pos = np.linspace(0, 1, 100)
T_profile = -30 + (0 - (-30)) * np.exp(pos * 3)

fig, axes = plt.subplots(1, 3, figsize=(17, 5), facecolor='#0a0a1a')
for ax in axes:
    ax.set_facecolor('#111827'); ax.tick_params(colors='#cbd5e1')
    for s in ax.spines.values(): s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.3)

ax = axes[0]
ax.plot(t, mass, color='#38bdf8', lw=2.6)
ax.set_xlabel('Day in den', color='#cbd5e1'); ax.set_ylabel('Cub mass (kg)', color='#cbd5e1')
ax.set_title('Cub growth 0.6 -> 12 kg', color='#bae6fd', fontweight='bold')

ax = axes[1]
ax.plot(mass, intake_g, color='#fbbf24', lw=2.6)
ax.set_xlabel('Cub mass (kg)', color='#cbd5e1')
ax.set_ylabel('Milk intake (g/day)', color='#cbd5e1')
ax.set_title('Milk 33% fat, 4.5 kcal/g', color='#bae6fd', fontweight='bold')

ax = axes[2]
ax.plot(pos*100, T_profile, color='#60a5fa', lw=2.6)
ax.fill_between(pos*100, -40, T_profile, color='#60a5fa', alpha=0.1)
ax.axhline(0, color='#38bdf8', ls='--', label='Den interior 0 C')
ax.axhline(-30, color='#f87171', ls='--', label='Outside -30 C')
ax.set_xlabel('Distance from mother (% of den)', color='#cbd5e1')
ax.set_ylabel('Temperature (C)', color='#cbd5e1')
ax.set_title('Den thermal gradient', color='#bae6fd', fontweight='bold')
ax.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print('Hedberg 2011: cubs gain ~100 g/day in the first month on fatty milk')
print('Den interior 30-40 C warmer than outside air')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

4. Maternal Energy Budget

The denning female fasts for 5–8 months, losing 30–40% of body mass while producing several hundred kilocalories per day of milk. Stirling & Derocher 2012 showed body-condition at den entry is the single strongest predictor of cub survival to weaning (~2 years). Climate-driven earlier ice breakup (M6) directly reduces hunting time and therefore maternal fat reserves.

Key References

• Ramsay, M. A. & Stirling, I. (1988). “Reproductive biology and ecology of female polar bears.” J. Zool., 214, 601–634.

• Derocher, A. E. et al. (1993). “Milk composition in polar bears.” J. Mammal., 74, 93–103.

• Hedberg, G. E. et al. (2011). “Milk composition in free-ranging polar bears.” Zoo Biol., 30, 550–565.

• Stirling, I. & Derocher, A. E. (2012). “Effects of climate warming on polar bears.” Glob. Change Biol., 18, 2694–2706.

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