Energy landscapes, stopover networks and reproductive constraints: a mathematical framework in the Arctic bird migration under Climate Change

Arctic-breeding waterbirds depend on fat stores gained at stopover sites during spring migration, and climate change is altering the winds, food timing and wetland quality along their routes. We present a compact mathematical model of spring migration from a wintering area to an Arctic breeding site, built to test five hypotheses about how these changes act on migration energetics and reproduction. The model combines a fat-dependent flight equation with wind, a stopover module in which food availability follows the spring green wave, probabilistic route choice over a network of eight wetlands, and a reproductive module limited by fat, calcium and arrival time relative to snowmelt. Energetic outcomes are linked to population growth rate (λ) through a three-stage projection matrix. We simulated a generic goose-sized bird of about 2 kg under seven scenarios. Single perturbations (weaker tail-winds, an earlier spring, or degraded western wetlands) were buffered, reducing arrival probability by about 1 percentage point and λ by 1–2%. Combined, they reduced arrival probability from 0.99 to 0.79 and λ from 1.00 to 0.78, about five times the sum of the single effects. Degrading the western corridor shifted the mean initial heading by 15° and concentrated birds at a previously minor eastern site. Calcium-poor northern staging sites reduced reproduction by 20% without affecting arrival. Advancing departure by 10 days compensated for a spring up to 20 days earlier, whereas a 10% decline in fat deposition reduced expected reproduction by 15%. All parameters are assumed, so results are comparisons between scenarios rather than predictions.