82 Introduction A fundamental aspect of flight behavior is how an organism responds to varying external factors such as wind. The relation between wind and flight behavior has important implications for migration, orientation, foraging behavior and flight energetics. Unlike many seeds, for example, that are passively dispersed by wind, intuitively we know that many flying organisms must react to wind, otherwise they would not reach their goal, whether long distance such as a wintering or breeding site, or short distance such as a foraging location. In this paper, we select birds as our topic of discussion, although many of the ideas presented below are equally relevant for insects, bats and other flying organisms. Furthermore, we focus on the analysis of air speed, but our approach can be extended to analyze heading as well. A bird’s air speed and heading, movement in relation to the air, are determined by the bird’s behavior, whereas ground speed and flight direction, the movement relative to the earth’s surface, are determined by both the flight behavior and the corresponding winds. During powered, flapping flight a bird’s air speed is directly related to the metabolic cost of flight, which can be estimated using the power curve for flight (e.g. Pennycuick, 1989; Rayner, 2001; Tucker, 1975). A bird’s ground speed and flight direction are relevant for calculations of distance and duration of travel. Therefore, the relationship between wind, flight and fuel, may change with different objectives. Numerous field and theoretical studies have tried to measure or predict how birds and insects react to wind (e.g. Liechti, 2006; Riley et al., 2003; Srygley and Oliveira, 2001). One hypothesis regarding migratory flight is that birds should maximize the distance traveled for a given amount of fuel. In order to fulfill this hypothesis birds are predicted to increase their air speeds in headwinds and decrease their air speeds in tailwinds (Liechti, 1995; Pennycuick, 1978). Pennycuick (Pennycuick, 1978) further proposed that this prediction could be tested by comparing the relationship, initially assumed to be non-linear, between air speed (V a ) and the difference between ground speed (V g ) and V a , both scalar quantities. It is noteworthy that this difference is generally represented in the literature as V g –V a and termed the ‘speed increment due to wind’ or the ‘wind effect’, where positive values of V g –V a represent tailwinds and negative values represent headwinds. Pennycuick states “A ‘tail wind’ is conventionally defined as the scalar difference between ground speed and true air speed. The ‘wind effect’ means that a bird whose ground speed is less than its air speed will normally respond by increasing its air speed, resulting in a negative correlation between the air speed and ‘tail wind’” [(Pennycuick, 2001) p. 3288]. Perhaps as a result of the simplicity of this particular approach, the linear relationship between V a and V g –V a has been tested in the literature numerous times for birds (Alerstam et al., 1993; Alerstam and Gudmundsson, 1999; Green and Alerstam, 2000; Gudmundsson et al., 2002; Hedenström and Alerstam, 1996; How flying organisms alter their air speed in response to wind is important in theories of flight energetics. Numerous studies have investigated the relationship between air and wind as a function of ground speed and air speed. This study shows that this approach can lead to erroneous results, due to spurious correlations. An alternative way to analyze air speed is proposed that overcomes the problems of one-dimensional linear models. The new model is non-linear and has two explanatory variables. Using two synthetic data sets with known properties and a data set with real observations of migratory bird tracks and wind observations, we illustrate the weaknesses of the conventional analysis as well as the strengths of the newly proposed model. This leads to the conclusion that for many studies a reanalysis of the effect of wind on air speed is desirable. Supplementary material available online at http://jeb.biologists.org/cgi/content/full/210/1/82/DC1 Key words: compensation, flight, model, spurious correlation, wind. Summary The Journal of Experimental Biology 210, 82-90 Published by The Company of Biologists 2007 doi:10.1242/jeb.02612 Analyzing the effect of wind on flight: pitfalls and solutions Judy Shamoun-Baranes 1, *, Emiel van Loon 1 , Felix Liechti 2 and Willem Bouten 1 1 Computational Biogeography and Physical Geography, Institute of Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands and 2 Swiss Ornithological Institute, 6204 Sempach, Switzerland *Author for correspondence (e-mail: shamoun@science.uva.nl) Accepted 19 October 2006 THE฀JOURNAL฀OF฀EXPERIMENTAL฀BIOLOGY