The migration of birds through a stopover site may be understood as a physical process of hydrological flow through a reservoir whose water levels rise and fall over a migration period. Hydrological flow models show promise as a way of integrating information on storage (daily counts of birds), inflow/outflow (number of birds arriving/departing each day) and transit time (length of stay (LOS)) over a migration period. We used a hydrological flow model to evaluate the relationship between stopover duration and passage population sizes of migrant birds under variable wetland conditions in two case studies. First, we considered the northward migration of Common Cranes Grus grus at Gallocanta Nature Reserve in Spain. We calibrated the model with daily counts recorded in 1984 and 1985, and then used it to predict transit time distributions based on counts of cranes 30 years later (2015–17). The model was calibrated with a mean transit time of 6.5 days observed in 1984/85, consistent with observed values of LOS, and predicted a mean transit time of 5.2 days for the 2015–17 period. The model also predicted an ~6.2× increase of the total migratory passage population of cranes at Gallocanta, which qualitatively agreed with the large increase in the overall population from the 1980s to 2010s. Second, migration dynamics of Eurasian Spoonbills Platalea leucorodia were considered during southward migration at two intertidal coastal wetlands in northern Spain from 2002 to 2005. The model well captured the observed differences in transit time between Urdaibai Biosphere Reserve (median transit time of 1.1 days) and Santoña Marshes Natural Park (median transit time of 2.1 days). Transit times of both species were negatively correlated with estimates of annual population sizes. These results indicate that hydrological flow models can provide insights into the migration ecology of waterbirds (or species where regular counts during migration are available), and that LOS is a dynamic decision that can depend on the population sizes of migratory birds.

Estimating the length-of-stay, the number of days a bird can be expected to stay at a site, at stopover sites is critical to understanding the migration ecology and estimating the population sizes of birds as they move between breeding and non-breeding sites. Estimating the length-of-stay of migrating animals at stopover sites has an analogue in the hydrological concept of transit time, the amount of time that water spends in a reservoir, which can be calculated as a numerical integration of inflow and outflow rates with an underlying Storage Age Selection function. We used this approach to estimate the lengths-of-stay of migrating Western Sandpiper (Calidris mauri) and Dunlin (Calidris alpina) based on the time series of daily counts at two sites in British Columbia, Canada. The approach yielded mean transit times for Western Sandpiper during southward migration at Sidney Island that ranged between 9·6 days and 3·8 days, and showed a significant decline over time, 1992-2001, and is consistent with the estimates obtained from the capture-mark-resight studies. Transit times during northward migration at Roberts Bank, Fraser River Delta, based on the best available information ranged from 1·8 to 3·2 days for Western Sandpiper, and had a median value of 2·0 days for Dunlin, which is consistent with the estimates obtained from the radio-telemetry studies. These results indicate that the hydrological flow models may offer a means to estimate the length-of-stay from the daily counts of birds during migration. The models present an opportunity for testing the alternate hypotheses concerning the roles of behavioural- vs. habitat-related mechanisms driving shorebird population sizes.