Figure 2: Method to estimate changes in litter size under earlier on-shore arrival.
From: Predicting climate change impacts on polar bear litter size
The logic of our analyses is illustrated for a female with straight-line body length L=1.9 m that hunted on the sea ice until 1 August and came ashore with body mass MA=350 kg on that date (solid square). We first establish her body masses before and after on-shore arrival, subject to the constraint MA=350 kg. Before on-shore arrival body masses (1 June to 1 August) are estimated by projecting MA backwards in time under the Early (green dashed line, EFS) and Late Feeding (blue dot-dashed line, LFS) scenarios, respectively. After 1 August, body mass is lost because of on-shore fasting in both scenarios (green-blue dashed line), resulting in a den entry (1 October) body mass of 311.1 kg. Energy density at den entry is thus 30.25 MJ kg−1, implying an expected mean litter size X=2.86 (equations (1)–(3)). Next, on-shore fasting is initiated at an earlier date (1 July in this example; arrows) with on-shore arrival body mass equalling the body mass obtained for that date under Early and Late Feeding, ME and ML, respectively. In this example, ME=350 kg (solid circle) and ML=313.1 kg (solid diamond). Mass loss due to fasting then results in den entry body masses 292.4 kg and 259.6 kg, den entry energy densities 28.64 MJ kg−1, and 25.50 MJ kg−1, and expected mean litter sizes XE=2.49 and XL=1.88, under the Early (dashed line) and Late (dot-dashed line) Feeding scenarios, respectively.
