1How climatic changes affect migratory birds remains difficult to predict because birds use multiple sites in a highly interdependent manner. A better understanding of how conditions along the flyway affect migration and ultimately fitness is of paramount interest.
2Therefore, we developed a stochastic dynamic model to generate spatially and temporally explicit predictions of stop-over site use. For each site, we varied energy expenditure, onset of spring, intake rate and day-to-day stochasticity independently. We parameterized the model for the migration of pink-footed goose Anser brachyrhynchus from its wintering grounds in Western Europe to its breeding grounds on Arctic Svalbard.
3Model results suggested that the birds follow a risk-averse strategy by avoiding sites with comparatively high energy expenditure or stochasticity levels in favour of sites with highly predictable food supply and low expenditure. Furthermore, the onset of spring on the stop-over sites had the most pronounced effect on staging times while intake rates had surprisingly little effect.
4Subsequently, using empirical data, we tested whether observed changes in the onset of spring along the flyway explain the observed changes in migration schedules of pink-footed geese from 1990 to 2004. Model predictions generally agreed well with empirically observed migration patterns, with geese leaving the wintering grounds earlier while considerably extending their staging times in Norway.
Predicting the impact of climate change on migratory birds constitutes a particular challenge since birds use chains of sites during their annual cycle, and the use of a single site cannot be viewed in isolation from the use of all other sites. Climate change may alter stop-over site conditions by changing temperatures and precipitation regimes, and such variations might affect birds both directly, by changing energy expenditure, and indirectly, by changing food availability and/or quality. Furthermore, climate change is not a uniform, linear phenomenon and changing conditions on the locations along the flyway may thus differ in both their nature as well as their magnitude.
Therefore, we aimed to investigate the influence of stop-over site conditions on migration schedules and fitness of a long-distance migrant bird using a modelling approach. We paid particular attention to parameters that are likely to change with climate, namely energy expenditure, intake rate, stochasticity in intake rate and onset of spring. Energy expenditure varies with ambient operative temperatures. The intake rate is an aggregate function of the amount and quality of food consumed; it has an upper limit as set by the bird's processing capacity (Prop & Vulink 1992) and, for herbivores, an external limit is set by vegetation growth, energy and nutrient content, which is highly dependent on local climatic conditions. The onset of spring indicates the date when food becomes available. This is not only dependent on vegetation development but also on frost and snow cover. Stochasticity in intake rate describes how much the intake rate on a given site varies around its mean value on a day-to-day basis; if stochasticity = 0, the site offers a stable and predictable food supply. If climate change causes more extreme weather events (Kharin & Zwiers 2005; Barnett et al. 2006), stochasticity is likely to increase.
Given the complexity in determining the optimal behavioural solutions in this spatially and temporally extensive system, we developed a stochastic dynamic model for migrating birds using discrete stop-over sites. We used this model to evaluate the influence of the mentioned parameters and generated temporally and spatially explicit predictions of an optimally behaving migrant under a specific set of environmental conditions. Such models are particularly useful for investigating environmental conditions that range beyond those presently found in nature, and where interdependencies in response or input variables make it difficult to separate the individual effects.
We parameterized the model for the pink-footed goose Anser brachyrhynchus, which migrates in spring from its wintering grounds in Belgium, the Netherlands and Denmark via mid and north Norwegian stop-over sites to Arctic breeding grounds on Svalbard (see underlying map in Fig. 4). There is extensive ecological knowledge of this species, which allowed us to parameterize the model (Klaassen et al. 2006b; Madsen & Klaassen 2006). A resighting database of neck-banded individuals from 1990 onwards provided the opportunity to compare model predictions explicitly with the empirical data. We thus tested whether the model correctly predicted changes in site use by the geese over a period of 15 years between 1990 and 2004, in relation to changes in spring phenology.
We developed a stochastic dynamic model to find the sequence of migratory decisions that would maximize the fitness of the female pink-footed goose. The basic dynamic program has been described in detail elsewhere, together with its parameterization (Bauer, Madsen & Klaassen 2006; Klaassen et al. 2006b); however, to facilitate understanding of our results and to clearly indicate the changes made to the model since the two earlier publications, we provide a brief outline of the model in the following, and a full description in Appendix S1 in the Supplementary material.
The model covered the spring migration to the breeding grounds. Birds were characterized by their body stores and location, i.e. site, at a particular day. We considered the following stop-over sites in the model: Denmark, Mid-Norway, and North-Norway. Sites were characterized by energy expenditure, predation risk and food-availability – the latter being described by average intake rate, day-to-day variability in intake rate (i.e. standard deviation of intake rate) and onset of spring (i.e. the time at which intake rate becomes > 0·0). Within each time-step, i.e. 1 day, a bird decided either to remain and forage on its present site or to continue migration to one of the next stop-over sites. Decisions depended on the bird's current state (i.e. body stores), time of the year and expected conditions on the present and subsequent sites.
Once the bird has reached the breeding grounds, we no longer model its decisions but assume that its current reproductive success is determined by arrival time and body reserves at arrival. For many breeders in seasonal environments, it has been shown that successful breeding is only possible if the birds arrive within a rather short time-window (e.g. Bety, Giroux & Gauthier 2004; Both, Bijlsma & Visser 2005; Madsen et al. 2007). This may be especially pronounced for Arctic breeders, where early arrival is detrimental and late arrival jeopardises successful reproduction. Furthermore, for several species of geese reproductive output is also related to the amount of reserves at arrival (for review see Klaassen et al. 2006a). When birds fail to reach the breeding grounds in time, arrive outside this time-window, or arrive with insufficient body reserves, they are unlikely to reproduce in the present but only in subsequent year(s).
With the dynamic programming equations (see Bauer et al. 2006; Klaassen et al. 2006b; and Appendix S1 in Supplementary material) and the errors-in-decision-making approach (McNamara et al. 1997), the (nearly) optimal migratory behaviour was calculated for all combinations of body stores, dates and stop-over sites. The errors-in-decision-making approach allows for deviations from perfectly optimal behaviour, given that such deviations have very little cost. Consequently, probabilities are calculated for alternative actions, which depend on their fitness consequences. These probabilities are then used in subsequent simulations to follow individual birds during their journey and to generate predictions of individual migratory behaviour, i.e. departure and staging times and, more importantly, to quantify the fitness consequences of given environmental circumstances.
We here extended the analyses of an earlier study (Bauer et al. 2006), which investigated the impact of certain aspects of food availability on staging decisions. Although we re-ran these analyses with the altered model, the results for intake rates and stochasticity were qualitatively similar and, therefore, we present these results briefly. Instead, we focus on expenditure as a newly incorporated factor and onset of spring as an important determinant of stop-over site use.
We independently varied the site-specific parameters most likely to be affected by climate: energy expenditure, onset of spring, intake rate and stochasticity in intake rate on each site in a range that goes beyond the empirically known values. Specifically, energy expenditure was varied between 0·3 and 1·7 MJ day−1, onset of spring between day 90 and 140 (31 March and 20 May, respectively), intake rates between 1·3 and 4·0 MJ day−1, and stochasticity in intake rate between 0 and 8·5 MJ day−1 (to avoid negative intake rates under high stochasticity, they were truncated at 0·0). The parameter under consideration was varied step-wisely and independently on all sites such that all combinations possible were tested. Except for the focal parameter in a scenario, other parameters were kept constant on all sites at values in the range of their empirical estimates (see Klaassen et al. 2006b): intake rates = 2 MJ day−1, energy expenditure = 1·3 MJ day−1, onset of spring in Mid-Norway = day 100 and North-Norway = day 120. No such empirical estimate existed for stochasticity, which was therefore set at an intermediate value of 3 MJ day−1.
Varying environmental parameters independently identified onset of spring to be the key parameter for determining staging times. Therefore, in the second part of our analyses, we used ‘real’ onset-of-spring values derived from Normalized Difference Vegetation Index (NDVI) satellite data (see Appendix S2 in Supplementary material for details) as model input. The spring-migration itineraries thus predicted between 1990 and 2004 were compared with empirical data obtained from individually marked pink-footed geese.
empirical migration data
During the springs of 1990–2004, a total of 2100 pink-footed geese were individually marked with neck collars (see http://pinkfoot.dmu.dk) and resighted on their staging sites during systematic re-sighting campaigns (Madsen 2001). We calculated minimum stop-over durations as a conservative estimate of individual stop-over periods from individual resightings using the difference between the first and last date at which a bird was seen on a particular site, mainly because this method needs no further parameters (compared to SODA models, e.g. Schaub et al. 2001) and because we were mainly interested in variations in stop-over site use between years. The population average (± SE) resulted from these individual staging times.
Model birds adjusted to varying levels of energy expenditure by avoiding sites where expenditure was high. Instead, sites with comparatively low expenditure were visited longer (as shown for variations of energy expenditure on the Mid-Norwegian site in Fig. 1). When increasing expenditure in Mid-Norway, for instance, the model predicted staging time on this site to shorten, whereas staging times were prolonged considerably on the Danish and slightly on the North-Norwegian site. Such behaviour is comparable to the reaction of model birds to varying levels of stochasticity in intake rates (Bauer et al. 2006): sites with comparatively high stochasticity were avoided in favour of site(s) with more constant, predictable food supply.
Intake rates influenced the model geese’ staging times in general much less than the other parameters (Appendix S3 and Fig. S1 in Supplementary material). As found by Bauer et al. (2006), there were only minor variations in departure and staging times over large ranges of intake rates, and these were mainly attributable to changes in intake rates in North-Norway.
Onsets of spring crucially determined staging times in all sites. Departure from Denmark was markedly affected by the onset of spring in the Norwegian sites (Fig. 2a). Staging times in Mid-Norway were mainly determined by the difference in onsets of spring between the two Norwegian sites (Fig. 2b), e.g. long staging when spring in North-Norway started much later. In contrast, staging times in North-Norway were only determined by the onset of spring in this site (Fig. 2c) with long staging times when spring started early and skipping if spring started very late in the season (day 140).
The fitness consequences of these parameter changes differed between the parameters themselves, but were highly dependent on the site at which they occurred. While fitness remained unchanged over a major part of the parameter ranges, high energy expenditure or high stochasticity on either site led to decreasing fitness (Fig. 3a,b). Similarly, very low intake rates or very late springs decreased fitness in general but the effect was most pronounced for changes on the North-Norwegian site (Fig. 3c,d).
When using onset of spring data from 1990 to 2004, the model predicted that the geese would leave Denmark progressively earlier (Fig. 4a), such that they departed on day 110 (20 April) in 2004, approximately 2 weeks earlier than in 1990. This prediction is supported by empirical departure times, which also advanced by 2 weeks during this period. For the same period, staging times in Mid-Norway were predicted to increase – a trend that is also supported by the empirical data, which showed an increase from around 10 days in 1990 to more than 3 weeks in 2004 (Fig. 4b).
On average, predicted and empirical staging durations for North-Norway were very similar, but empirical data seem much more stable than the predicted data, which show large year-to-year variations. Staging times were predicted to decrease in the early 1990s, to remain relatively low and constant in the late 1990s (with some birds predicted to skip the site), increasing again in the last few years of the study period.
Model predictions and empirical data are highly correlated for Denmark and Mid-Norway (r = 0·81 and r = 0·79, respectively, both P < 0·001); however, there was no significant correlation between model and reality for North-Norway (r = 0·35, P = 0·20). When comparing trends over time, we found that the model predicted for Denmark a change in departure dates of –1·09 days year−1, which was not statistically different from the trend in empirical departure dates (–0·96 days year−1, GLM: F1,26 = 0·094, P = 0·76). An extension of staging times of 1·3 days year−1 was predicted for Mid-Norway, which also corresponded well to the empirically found trend of 1·1 days year−1 (GLM: F1,26 = 0·753, P = 0·39). In contrast, no trend was detected for North-Norway, neither in the model nor in reality (GLM: F1,26 = 0·385, P = 0·54).
We additionally predicted the fitness consequences of the variation in onset of spring over the study period. As predicted by the model, the expected fitness varied considerably over the years between an almost unchanged expected fitness and, in some years, a reduction of up to 12% (Fig. 5). The pattern in the fitness-reduction follows the pattern of onset of spring in North-Norway (r = 0·89, P < 0·001) – late springs there tending to be detrimental to the geese. Interestingly, these findings are supported by a survival analysis (Kery, Madsen & Lebreton 2006) that, over most of the study period, corresponds to our predictions (Fig. 5): if we omit the outlier-value of 1999, the correlation is significant (r = 0·83, P = 0·001); otherwise it is slightly non-significant (r = 0·52, P = 0·086).
The migrants in our model adjusted the use of stop-over sites to changes in all parameters that we varied, but to varying degrees. Furthermore, the fitness consequences of these changes were highly dependent on the location at which they occurred.
Within the range of tested energy expenditures, the birds tended to avoid sites that required high metabolic rates. In experimental studies on barnacle geese, a temperature decline of 10 °C increased energy expenditure by c. 40% (S. van der Gaaf & J. Stahl, pers. comm.); high windspeed and high temperature variations were additional factors that substantially increased expenditure (Pendlebury, MacLeod & Bryant 2004; McKinney & McWilliams 2005). Although such dramatic (sustained) changes in temperature are not expected to occur, more frequent extreme weather events might increase energy expenditure at least temporarily and/or locally and thus lead to behavioural adjustments, as suggested by our study. A similar behaviour followed from increasing stochasticity in model intake rates: birds behaved in a risk-averse manner by favouring sites with predictable food supply – a reaction that has been suggested earlier in both theoretical (Weber et al. 1998; Bauer et al. 2006) and empirical studies (Katti & Price 1999; Schaub & Jenni 2001; Bayly 2006).
Intake rates had surprisingly little impact on staging times, indicating that geese may adjust feeding time or intensity under variable food supply, which has indeed been found in empirical studies (Riddington, Hassall & Lane 1997; Therkildsen & Madsen 2000). Moreover, most of the variation in predicted staging times was caused by varying intake rate in North-Norway, indicating the paramount importance of this site. Indeed, North-Norway is the last site before the breeding grounds – detrimental conditions cannot be compensated for on subsequent sites and will thus result in significant fitness consequences (Fig. 3). These finding are supported by empirical studies, which found a strong correlation between the body reserves with which geese leave North-Norway and the number of young produced (Drent et al. 2003; J. Madsen & M. Klaassen, pers. comm.). The importance of North-Norway suggested by this may seem at odds with the model predictions of birds skipping North-Norway completely in some years (Fig. 4). However, for these years, fitness of the model-geese was also predicted to be low, which is supported by empirical survival rates (Kery et al. 2006).
Migration schedules were mostly determined by the phenology of stop-over sites. According to model predictions, the geese commenced spring migration as soon as the following sites became available and continued to follow the development of spring along their route – a phenomenon referred to as the green-wave hypothesis (Drent, Ebbinge & Weijand 1978; van der Graaf et al. 2006). This suggests that herbivores in particular follow the spring development of the vegetation. Our study thus supports earlier findings that migrants advance their spring migration in correlation with an early climate signal (e.g. Walther et al. 2002; Hüppop & Hüppop 2003; Ahola et al. 2004; Sparks et al. 2005). Using past onset of spring data as model input for the phenology of the stop-over sites from 1990 to 2004, we found good agreement between predicted and observed values for departure dates from Denmark and staging times in Mid-Norway. However, staging times in North-Norway were less well predicted on a year-to-year basis. This may relate to the scaring campaigns that have intermittently taken place in this area in the periods 1993–95, 1999–2002. Consequently (a part of) the goose population may have reduced their use of this site, as was theoretically predicted by Klaassen et al. (2006b). Generally, it seems that the geese are more gradual in their responses to environmental change than predicted in our model which, by definition, shows immediate responsiveness.
However, the agreement between predictions and observations for a large part of the spring migration may be surprising in the light of the rather strong model assumptions; namely, that model-geese always behave optimally and have full knowledge of conditions on all sites. Since the ‘real’ geese appeared to behave near-optimally, they must have had such knowledge and adapted to the new conditions very fast. This hypothesis is supported by observations of geese changing migration schedules and site use between years, and the fact that geese with poor body condition in one spring were most likely to change in the subsequent spring (Madsen 2001). Alternatively, the geese may have used relatively simple behavioural rules that have not required a change. Such a rule might be to leave a site when vegetation has developed to a certain ‘threshold’ stage, this threshold being correlated with the conditions on the subsequent site. Indeed, earlier studies have shown that such local cues exist and that climate is correlated over medium distances (e.g. Hurrell & van Loon 1997). As long as the relation between local and distant circumstances is not revoked, changes in the phenology of sites do not require substantial adaptations. However, this notion also implies that birds migrating over longer, uninterrupted distances should experience many more difficulties under changing climatic conditions (reviewed in Visser & Both 2005). This also holds for species where local cues may lose reliability (e.g. day length, Coppack et al. 2003; Frederiksen et al. 2004; Helm & Gwinner 2005; Marra et al. 2005). For example, in trans-Sahara migrants, it has been suggested that signals in the wintering grounds strongly determine departure dates and, consequently, arrival dates in their European breeding grounds. However, given the diverging climatic developments in Europe and Africa, the arrivals are now too late and the birds experience a mismatch between peak food availability and peak requirements (Gordo et al. 2005; Sanderson et al. 2006). Although adjustments have been observed, e.g. by advancing egg-laying, they do not suffice to regain lost time (Visser & Both 2005). However, species with different life-expectancies may differ considerably in their potential to cope with changes: longer-lived species have predominantly culturally determined migration routes, so they are more likely to adapt than species in which migratory behaviour is genetically determined – as reviewed by Sutherland (1998), none of the ‘cultural’ species used a suboptimal migration route.
Our study species may be considered a representative for long-lived species migrating in relatively short hops rather than jumps. Our modelling approach, with its strong assumption of optimal behaviour, may be particularly useful to assess the consequences of long-term climatic trends on the migration fate of such species.
We thank Bart A. Nolet and two anonymous referees for comments on an earlier draft of this manuscript, and Ingunn M. Tombre and Per Ivar Nicolaisen for the coordination of observations of banded pink-footed geese in Norway. The analysis was carried out under the 5th EU framework project FRAGILE (EVK2- 2001–00235). This is publication 4222 of the Netherlands Institute of Ecology (NIOO-KNAW).