Ó Springer-Verlag 1999
Behav Ecol Sociobiol (1999) 46: 280±286
ORIGINAL ARTICLE
Thomas P. Weber á Thord Fransson á Alasdair I. Houston
Should I stay or should I go? Testing optimality models of stopover decisions in migrating birds
Received: 3 April 1999 / Received in revised form: 22 April 1999 / Accepted: 26 April 1999
Abstract Time-minimizing migrants should leave a stopover site if the instantaneous speed of migration drops to the average speed of migration in the environment. This argument has been used in two dierent ways: either there is local variation in the fuel deposition rate and a ®xed expected speed or there is global variation in the fuel deposition rate, i.e. locally experienced variation represents global variation along the route. The ®rst case leads to a far steeper relationship between departure load and fuel deposition rate than the second case. So far, data on departure loads have mainly been analysed within the concept of local variation of the fuel deposition rate and the result that the observed slopes are much lower than predicted has been explained by changes in the expected speed along the route or by individual dierences in the expected speed. We show here that the observed relationships generally fall close to the predictions for global variation. We propose that migrants use a behavioural rule which projects the current experience into the future and therefore interprets local variation as global variation. Key words Fuel deposition á Fuel loads á Luscinia svecica á Selasphorus rufus á Sylvia communis
T.P. Weber (&) Department of Animal Ecology, Ecology Building Lund University, S-22362 Lund, Sweden e-mail:
[email protected] Tel.: +46-46-2223789, Fax: +46-46-2224716 T. Fransson Department of Zoology, Stockholm University S-10691 Stockholm, Sweden and Swedish Museum of Natural History, Bird Ringing Centre Box 50007, S-10405 Stockholm, Sweden A.I. Houston School of Biological Sciences, University of Bristol Woodland Road, Bristol BS8 1UG, UK
Introduction During migratory journeys, many birds cover distances that exceed their maximum ¯ight range. They therefore stop at several intermediate sites where they replenish fuel reserves. Many passerine species migrating through Scandinavia and mainland Europe have the possibility of landing and feeding nearly everywhere along the route. But how should such a migratory journey be organized? Should the birds make many stopovers and ¯y short distances before refuelling or should they make a few long ¯ights? Alerstam and LindstroÈm (1990) argue convincingly that patterns of stopover site use provide insight into selective pressures faced by migrants and that an optimality approach can elucidate the factors aecting migratory strategies. They identify time of arrival at the migratory endpoint as a crucial factor shaping migratory strategies, but also discuss energy and mortality as alternative currencies. For time-minimizing migrants, Alerstam and LindstroÈm (1990) identify a simple rule for when to depart from a stopover site: a migrant should leave when the current speed of migration drops to the average speed for the environment. Implicit in their formulation of the model and a subsequent application in the analysis of ®eld data (LindstroÈm and Alerstam 1992) are two distinctive forms of variation experienced by migrants: local variation, i.e. the fuel deposition rate experienced at a site does not aect the fuel deposition rate at future sites, and global variation, i.e. locally experienced variation represents variation along the entire migratory route (Houston 1998). These two situations give dierent values for the expected speed for the rest of the environment. Both models predict a positive relationship between the fuel deposition rate and the departure load but for the ®rst case the relationship is much steeper. In their analysis of experimental and natural variation in fuel deposition rates of bluethroats (Luscinia svecica) and rufous hummingbirds (Selasphorus rufus), LindstroÈm
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and Alerstam (1992) assumed local variation in the fuel deposition rate and found a shallower relationship than they expected. They postulated a changing expected speed of migration and individual variation in the expected speed as possible explanations for the observed discrepancy. Klaassen and LindstroÈm (1996) oer an explanation for the discrepancy based on an increase in rate of energy expenditure with increasing fuel load. For a review of various explanations of the discrepancy, see Alerstam and HedenstroÈm (1998). Here we will follow up the suggestion made previously by Houston (1998) and reanalyse in more depth the two datasets on bluethroats and hummingbirds and a combination of previously published data (Fransson 1998) and new data on whitethroats (Sylvia communis) while keeping the distinction between local and global variation in mind. We support a hypothesis which is based on a simple behavioural rule that migrants might use. This rule interprets local variation as global variation, or gives high priority to current experience at the expense of a ®xed expectation of the future. Such a hypothetical decision rule results in a close match to the data without the need to invoke a sophisticated knowledge of the future.
The models Flight ranges
rived ¯ight range equations can be written in a form similar to Eq. 1, diering in their value for the exponent and the variables that are included in the constant c. Time-minimization models of departure fuel loads Central to model of Alerstam and LindstroÈm (1990) is a cost of stopover paid by the birds. With time-minimization as the optimization criterion, this cost is most commonly modelled as a time cost: birds arriving at a stopover site cannot start fuel deposition immediately. There are a number of mechanisms that could impose a time cost, such as territory establishment (Rappole and Warner 1976; Moore and Yong 1991) or switching from metabolizing fuel to depositing fuel (Klaassen and Biebach 1994; Hume and Biebach 1996; Karasov and Pinshow 1998). The two scenarios of local and global variation can both be analysed by using the general rule that it is optimal to leave a site when the instantaneous speed of migration dY/dt falls to the overall speed of migration S (Alerstam and LindstroÈm 1990). This criterion is illustrated for local and global variation in Fig. 1, in which dY/dt is plotted against fuel load. We also show in this ®gure the instantaneous speed of migration if the energy expenditure increases with fuel load (Klaassen and LindstroÈm 1996). The ®gure shows clearly that with global variation, the departure load is higher than with local variation of the fuel deposition rate. We now look
The ¯ight range equation ± a relationship determining how far a bird can ¯y with a certain fuel load in still wind conditions ± is central to the analysis of migratory strategies (Weber and Houston 1997). Let Y(x) be the ¯ight range in kilometres as a function of relative fuel load x, which is de®ned as the fuel load divided by a constant reference lean body mass (Alerstam and LindstroÈm 1990): ! 1 Y
x c 1 ÿ
1
1 x0:5 The constant c has the unit of km and depends on the bird's lean body mass, M0)0.5, the lift-to-drag ratio and the energy equivalent of the fuel stores. This equation is derived from Pennycuick's theory of bird ¯ight (Pennycuick 1975, 1989) and assumes that parasite and induced drag are aected by increasing body mass. The power of )0.5 in the ¯ight range Eq. 1 arises partly from the assumption that the eective lift : drag ratio decreases with increasing fuel reserves in proportion to M)0.5, where M is the total body mass. If the eective lift : drag ratio is less aected by increasing body mass than assumed ± as pointed out by Alerstam and LindstroÈm (1990) ± dierent values for the exponent in Eq. 1 can arise. Weber and Houston (1997) have furthermore demonstrated that many empirically de-
Fig. 1 Speed of migration against fuel load. Curve i shows k(dY/dx) where the fuel deposition rate is independent of fuel load and curve ii where the fuel deposition rate is aected by the energy costs of high fuel loads (Klaassen and LindstroÈm 1996). The upper horizontal line is the overall speed assuming global variation and the lower line, the overall speed assuming local variation. The two curves for the instantaneous speed and the line for the overall speed under global variation were calculated using k=0.02. In curve ii, the realized fuel deposition rate is dependent on the fuel load: k ± bx; we use a value for b of 0.0158 as derived by Klaassen and LindstroÈm (1996) for bluethroats. The overall speed assuming global variation was calculated with x*=0.29 and the overall speed assuming local variation with k*=0.011 and x*=0.14
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in more detail at the two cases of global and local variation. (Although we do not analyse the eects of fuel load on the fuel deposition rate, we note that the basic distinction between optimal fuel loads under local and global variation persists ± see Fig.1.) Constant expected fuel deposition rate independent of current experience: local variation Birds should leave the site when the instantaneous speed of migration drops to the overall migration speed, which is independent of the current site. All future sites have the same expected fuel deposition rate k* and hence optimal departure fuel load x*. Both fuel deposition rate and fuel load are measured relative to lean body mass; fuel deposition rate has units of day)1 and fuel load is dimensionless. The criterion for the time-minimizing fuel load is now (LindstroÈm and Alerstam, 1992): dY
x dY
x k
2 k dx dx xx Using ¯ight range Eq. 1 in Eq. 2 we arrive at 2=3 k x
1 x ÿ 1 k
3
Birds update expected fuel deposition rate to currently experienced value: global variation The criterion for the time-minimizing departure fuel load x* as given by Alerstam and LindstroÈm (1990) if the fuel deposition rate is constant along the migratory route is: Y
x dY
x k x=k te dx
4
where k is the fuel deposition rate in days)1 and te is the establishment cost in days. Equation 4 gives the condition for maximising the rate of gain of ¯ight distance. This condition essentially assumes that the migratory journey covers an in®nite distance. Figure 2 gives a graphical example of how to ®nd the optimal stopover time t*. We can then ®nd x* from x*=kt* (Alerstam and LindstroÈm 1990). In both Eqs. 2 and 4, the constant c from the ¯ight range Eq. 1 cancels out. Therefore we need no estimate for this parameter to analyse the data.
Results Bluethroats (L. svecica) in Sweden Bluethroats at a stopover site in central Sweden were supplied with supplementary food ad libitum (Lind-
Fig. 2 The graphical solution to Eq. 4 using ¯ight range Eq. 1, giving the optimal staging time t* in days as a function of fuel deposition rate (day)1) with an in®nite migration distance. The range is dimensionless and given relative to the parameter c in Eq. 1. The daily fuel deposition rate k=0.04 and the establishment time te=2 days, plotted on the negative x-axis. The dimensionless optimal departure fuel load is x*=kt*
stroÈm and Alerstam 1992). At this stopover site, the ®rst substantial fuel deposition occurs after leaving the breeding grounds. The closed circles in Fig. 3 show the departure fuel load as a function of fuel deposition rate. There is a signi®cant positive relationship between the two variables (r=0.808, P=0.012). LindstroÈm and Alerstam ®t a model to their data in which the birds leave a site when the instantaneous speed of migration drops to the expected speed of migration for the rest of the journey, i.e. the birds have a ®xed expectation of the conditions at future stopover sites (local variation). The predicted relationship [see curve (i) in Fig. 3] for an expected fuel deposition rate of k*=0.011 and a departure load of x*=0.14 further along the route is much steeper than the observed pattern; the predicted line is completely determined by k* and x*. LindstroÈm and Alerstam (1992) argue that an increase in the expected speed of migration along the route or individual variation in the expected speed could explain the observed pattern. Curves (ii)±(iv) in Fig. 3 show the expected relationship if global variation is assumed; for the establishment cost we use values of 1 day (ii), 3 days (iii) and 5 days (iv). The observed values all lie close to the predicted line for global variation with an establishment time cost of 3 days. Lower values for the establishment time cost shift the line downwards to some degree, higher values upwards. From the expected fuelling rate and departure load (see above) we can estimate the establishment time cost by using ¯ight range Eq. 1 in Eq. 4 and solving for te. Using k*=0.011 and x*=0.14 we arrive at a value of 1.3 days. We conclude from this analysis that the bluethroats in the study of LindstroÈm and Alerstam (1992) do not seem to base their departure decisions on a ®xed expectation of the conditions at future sites. The data are
283 Fig. 3 Departure fuel load (closed circles) as a function of daily fuel deposition rate of bluethroats at a stopover site in central Sweden. The birds had access ad libitum to a supply of mealworms. Curve i is the predicted relationship if local variation is assumed; the values used in Eq. 3 to calculate this line are k*=0.011 and x*=0.14. Curves ii±iv are calculated using Eq. 4 assuming global variation with establishment time costs of 1 day (ii), 3 days (iii) and 5 days (iv)
consistent with a rule that projects the current experience into the future, which leads to a shallow relationship between departure load and fuel deposition rate. Rufous hummingbirds (S. rufus) in California LindstroÈm and Alerstam (1992) also used data on migrating rufous hummingbirds (Carpenter et al. 1983) to test the time-minimization hypothesis. Because the birds were not provided with supplementary food, the average values for staging duration, departure loads and fuel deposition rates were used to calculate the estimates for k* and x* in Eq. 3; the values obtained are k*=0.059 and x*=0.63. The predictions for migrants operating under the assumption of a ®xed future characterized by these values is shown by curve (i) in Fig. 4. The relationship predicted under global variation is calculated with establishment costs of 1, 3 and 5 days and is shown by curves (ii)±(iv) in Fig. 4. The slope of the predicted line is similar to the trend shown by the Fig. 4 Departure fuel load (closed circles) as a function of daily fuel deposition rate of rufous hummingbirds at a stopover site in California without supplementary food. All the calculations were done with ¯ight range Eq. 1. Curve i is the predicted relationship if local variation is assumed; the values used in Eq. 3 to calculate this line are k*=0.059 and x*=0.63 and are obtained by averaging the values from the individual birds. Curves ii±iv are calculated using Eq. 4 assuming global variation with establishment time costs of 1 day (ii), 3 days (iii) and 5 days (iv)
data points. In this case, a value of 5 days for the establishment time cost gives a reasonable ®t to the data, although most of the points lie below this line. From the expected fuelling rate and departure load we arrive at an establishment time cost of 4.6 days, which corresponds well with the value above. Whitethroats (S. communis) on Gotland/Sweden Fransson (1998) conducted an experiment using a feeding station with ad libitum supply of mealworms to attract resident juvenile whitethroats preparing for autumn migration. Estimates from birds under natural conditions and additional data on fuel deposition rates and departure loads for four juvenile individuals carrying radio transmitters served as controls (T. Fransson, unpublished data). Small radio transmitters (0.6 g) were glued on the back of four ®rst-year whitethroats preparing for migratory departure. Birds with transmitters were followed intensively and trapped on several occasions during a short time period before they departed.
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The fuel deposition rate under natural conditions was estimated from ten short-time retraps (between 3± 9 days) of birds that were de®nitely in a state of premigratory body mass gain (>1 g/day increase). The departure loads of whitethroats under natural conditions at the study site were estimated as the mean fuel load of the heaviest quartile of birds with completed post-juvenile moult (see Alerstam and LindstroÈm 1990 for the logic behind this approach). For the birds using the feeding station there is no relationship between fuel load at departure and fuel deposition rate (r=0.001, P=0.99; Fig. 5, closed circles). All the individuals using the feeder were juvenile birds. If we include data from the juvenile birds carrying radio transmitters (Fig. 5, open circles) and one data point representing the fuel deposition rate and departure load estimated from recaptured birds (Fig. 5, diamond) the correlation between fuel deposition rate and departure load is now barely signi®cant (r=0.475, P=0.053). If we distinguish between manipulated and unmanipulated birds we ®nd that the two groups dier signi®cantly in their fuel deposition rate and departure fuel load (Hotelling's T2-test ± a multivariate test for dierences in means between two groups ± with logarithmically transformed data: T2=26.897, F2,14=12.552, P
