Body condition B (0–1, fraction of maximum fat reserve) is integrated day-by-day over a 20-year span. Each simulated year has a consolidated ice season and an ice-free (open-water) season whose length grows with the warming-trend slider:
iceFreeDays(year) = baseIceFree + warmingTrend·year
c(t) = ice concentration in [0,1] (ramps over the 15-day
freeze-up/break-up margins, 1 at full consolidation,
0 through the ice-free season)
while ice present (c > 0):
dB/dt = huntGain·c·sealDensity·(1−B) − restingLoss
while ice-free (fasting):
dB/dt = −fastLoss
Hunting success scales with ice concentration c — seals are caught from the ice edge, so fragmented margin ice yields partial success while consolidated mid-season ice yields the full rate; the (1−B) term models satiation, since a bear near maximum fat gains reserve more slowly. During the ice-free season bears cannot hunt seals efficiently from open water at all and lose reserve at a steady fasting-metabolism rate, consistent with field studies of Arctic polar bears (e.g. Molnár et al. 2010; Robbins et al.) showing hunting success collapses with ice concentration and fasting mass-loss accumulates roughly linearly with fast duration. A longer ice-free season — the direct effect of a warming trend — leaves less time to rebuild reserve and a longer fast to survive, so body condition trends downward across years once losses outpace the ice-season gain. The dashed line marks an approximate survival/reproduction threshold; a year whose minimum dips below it is flagged as a stress year.
- Top strip — ice extent (white/blue) vs. ice-free (green) over time, with a moving playhead.
- Bear pane — the bear icon sits on ice while hunting (blue = healthy) and swims/rests on land while fasting (colour shifts toward red as reserve drops).
- Bottom chart — body-condition trajectory across all 20 years against the survival threshold.