Behavior underpins the predictive power of a trait‐based model of butterfly movement

Abstract Dispersal ability is key to species persistence in times of environmental change. Assessing a species' vulnerability and response to anthropogenic changes is often performed using one of two methods: correlative approaches that infer dispersal potential based on traits, such as wingspan or an index of mobility derived from expert opinion, or a mechanistic modeling approach that extrapolates displacement rates from empirical data on short‐term movements. Here, we compare and evaluate the success of the correlative and mechanistic approaches using a mechanistic random‐walk model of butterfly movement that incorporates relationships between wingspan and sex‐specific movement behaviors. The model was parameterized with new data collected on four species of butterfly in the south of England, and we observe how wingspan relates to flight speeds, turning angles, flight durations, and displacement rates. We show that flight speeds and turning angles correlate with wingspan but that to achieve good prediction of displacement even over 10 min the model must also include details of sex‐ and species‐specific movement behaviors. We discuss what factors are likely to differentially motivate the sexes and how these could be included in mechanistic models of dispersal to improve their use in ecological forecasting.

A detailed understanding of how exactly body size impacts dispersal through the effects on observable small-scale movement behavior is currently missing. Further, the extent to which mechanistic understanding can improve predictive power by comparison to a correlative approach is not well-understood.
To inform comparison of correlative and mechanistic approaches, we here evaluate the effect of a trait often related to mobility, wingspan (Sekar, 2012), on measuring and forecasting movement in four species of butterfly in the south of England. We also present a random-walk model of butterfly movement behavior that incorporates relationships between wingspan and the key aspects of the movement process, including flight speed, turning angle, and the proportion of time spent flying. We parameterize the model with newly collected data on butterfly flight paths. Though the number of species is limited, the collection of high-precision movement and behavioral data allow us to closely evaluate the success of the two approaches and to explore why traits, such as body size or wingspan, may break down when predicting movement over longer timescales.
The predictive success of the mechanistic approach is found to be strongly influenced by the inclusion of sex-specific behavior, and we detail why the correlative approach is less successful.

| Study species and sites
The study was conducted on four species of grassland butterfly: Aricia agestis (Dennis & Schiffermüller, 1775), Maniola jurtina (Linnaeus, 1758), Pyronia tithonus (Linnaeus, 1758), and Melanargia galathea (Linnaeus, 1758). All four species are commonly found in southern England and range in average wingspan from around 28 to 58 mm (Thomas, 2010). The brown argus, A. agestis, is the smallest with a wingspan of between 25 and 31 mm (Newland, Still, Swash, & Tomlinson, 2015). It is a bivoltine species with adults found first on the wing in June and then again in August. In contrast, the other three species are univoltine, are found on the wing through June to  (Newland et al., 2015). In this study, we take the mid-value published values of wingspan as body size trait measure in further analyses. Sex was identified on the wing for all species except A. agestis, which required close inspection of caught individuals.

| Movement and behavioral observations
The behavior of individual butterflies was recorded in the field at a distance from observers of approximately 3 m for a maximum of 10 min between the hours of 10:00 and 16:00. During this observation period, the position of each individual was recorded by planting a sequentially numbered marker flag, either at each landing site or after every 15 s during continuous flight, following established methodology (Schultz, 1998;Turchin, 1991). To accurately record the movement of the butterflies, observations relied on two observers one placing the flags and the other constantly following and recording behavior.
The precise location of each flag was retrospectively mapped using Records of precise location, time, and behavior were later processed to calculate the distance between successive flags, hereafter referred to as a step distance.
Step speed was calculated as step distance/step duration.
Step speed was used as our measure of flight speed as step distances depend on both step duration and flight speed. Turning angle was calculated as the absolute subtended angle between successive steps (i.e., +40° and −40° were both recorded as Finally, displacement rate is calculated as the Euclidean distance between positions at the start and the end of the observation period.
Aricia agestis could only be sexed by catching the butterfly after the observation, reducing the number of observations in which sex was confirmed. Because of this, the sexes were pooled for comparison of step speeds, turns, and any displacement predictions in A. agestis.

| Statistical analysis
Linear mixed effects models (LMERs) with a Gaussian error structure were used to evaluate the effect of wingspan, sex, and air temperature on the movement components. Butterfly ID was included in models of flight duration, step speed, and turning angle as random intercepts to account for repeated measures. Linear models were used for proportion of time in flight and displacement rate since in these analyses there was just one observation per individual. A single mean value of wingspan as reported in the literature was used for each sex x species combination and entered as a covariate in the analysis as a species/sex trait, alongside air temperature and sex as a fixed factor. Note that the focus of this study is to evaluate relationships to wingspan across groups and not the response to intraspecific variation in this particular trait. Model diagnostics were used to check the conformation of the data to the assumptions of the error structure, and suitable transformations were used when residuals were skewed.
Step speed was square-root transformed, displacement rate and flight durations were both log-transformed, while proportion of time flying was logit-transformed. To display the effects of circular concentration, a von Mises circular distribution was fitted to the turning angles and the parameter k, a reciprocal measure of the dispersion, was estimated with confidence intervals derived from a boot-strapping procedure (Lund & Agostinelli, 2011). All analyses were conducted in R 3.6.1 (R Core Team, 2019).

| Mechanistic random-walk model
The effects of movement components on displacement rate and their relationship to wingspan were investigated in three scenarios differing in the distributions from which flight components were drawn. In the first scenario, step speeds were drawn from sex-and species-specific distributions, but turning angles and proportion of time in flight were drawn from distributions of pooled data. In the second scenario, both step speed and turning angles were drawn from sex-and species-specific distributions, while proportion of time flying was selected from a pooled distribution. In the third scenario, all distributions were sex-and species-specific. For each scenario, the success of the model was evaluated by plotting the observed against the predicted mean displacement distances (Piñeiro, Perelman, Guerschman, & Paruelo, 2008). In each scenario, we conducted 50 repeats of the movement of 1,000 butterflies for each sex and species combination. For comparison with a trait-based approach, we compare these results against the success of a simple regression of observed displacement against wingspan.  Table 1. Movement was affected by the predictor variables in all cases except that sex had no effect on step speed or turning angle.

| RE SULTS
Step speed over 15 s was roughly proportional to wingspan  Figure 1c for air temperatures between 18 and 21°C, the temperature window for which most data are available. Males flew much longer than females, more than three times longer in M. jurtina, and the largest species flew two to three times longer than the smallest. The effects of sex and wingspan on proportion of time flying are shown in Figure 1d. Males spent more time flying than females. There was variation between the sexes in the effects of wingspan but some tendency for larger species to spend more time flying. Displacement rate is the total displacement observed during an observation bout (usually 10 min) divided by the bout duration and therefore gives the combined effects of all three movement components. Displacement rate was affected by air temperature, wingspan, and sex (Table 1)

| D ISCUSS I ON
The full mechanistic model, which included sex-specific movement behaviors, outperformed simpler models containing only the effects of changing step speeds and turning angles and dramatically outperformed the correlative approach in predicting displacement rate, as shown by comparing Figure 2b,e. In building the mechanistic model, we took into account that the distance moved by an individual is a combination of movement capacity, behavior, and environmental influence (Nathan et al., 2008), so we began by looking at each of these components to understand how a widely used species trait for approximating movement, wingspan, relates to small-scale individual movement. We then explored the subsequent effects of these including these components in mechanistic models predicting longer-term displacement. Movement capacity was strongly related to wingspan. Larger butterflies had a greater capacity for movement than smaller butterflies as they flew faster and straighter irrespective of sex ( Figure 1). Behavior was also related to wingspan with larger butterflies found to have longer flights than smaller butterflies, though sex ( Figure 1c) and air temperature were also important (Table 1) The relationship between wingspan and flight speed (Figure 1) is expected from first-principle scaling arguments assuming isometry with changing size (Norberg & Rayner, 1987). Previous intraspecific comparisons based on temperate species have found flight speed correlates well to wingspan (Berwaerts et al., 2002), but interspecific comparisons conducted on a large sample of neotropical species, where isometry is likely violated, have found mixed results (Dudley, 1990;Dudley & Srygley, 1994. Wingspan alone provided a good predictor of flight speed in our study based on four related species living in a shared habitat; however, extrapolation of these results to multiple species will also need to account more directly for traits such as wing loading, aspect ratio, and momentum of inertia arising from differences in wing shape and proportions (Betts & Wootton, 1988).
The relationship between wingspan and directedness of flights for butterflies has not received much attention even though turning TA B L E 1 Coefficients from LMERs and linear models (±standard errors) predicting the four components of the movement process and displacement rate from wingspan, sex, and air temperature Step speed (m/s) ±SE

Note:
Step speed was measured as distance moved in 15 s, turning angle is the change in heading between adjacent 15 s steps. Proportion of time flying and displacement rate were measured over 10 min. Non-significant (p > .05) predictors are omitted from display. angles are commonly reported. We found that the larger butterflies had straighter flights ( Figure 1b) and that inclusion of species/ sex-specific turning angles improved displacement predictions considerably ( Figure 2d). Size might influence directedness if the higher inertia of larger butterflies leads to decreases in maneuverability producing fewer or shallower turns as is the case for bats (Norberg & Rayner, 1987). Detailed studies of butterfly movement in real-time conducted using harmonic radar suggest turning angle also varies within a species among habitats (Cant, Smith, Reynolds, & Osborne, 2005), likely reflecting a change in foraging strategy in response to resource density and/or landscape features (Delattre et al., 2010;Fownes & Roland, 2002;Odendaal, Turchin, & Stermitz, 1989;Roland, Keyghobadi, & Fownes, 2000;Schtickzelle, Joiris, Dyck, & Baguette, 2007;Zalucki & Kitching, 1982). It remains to be determined to what extent turning angle varies between species and how it subsequently influences displacement rates. Further, it is not well explored how variation in turning relates to sex-and species-specific search strategies (Root & Kareiva, 1984) for the location of different resources.
Larger butterflies flew for longer than smaller butterflies though there was a strong effect of both sex and temperature. The influences of size and temperature on flight durations are consistent with previous studies (Cormont et al., 2011;Heinrich, 1986) and theoretical predictions based on the physics, anatomy, and posture of Colias species (Kingsolver, 1983;Tsuji, Kingsolver, & Watt, 1986). However, the substantial behavioral differences between the sexes demonstrate the limitations of using a single trait, such as wingspan, to predict mobility. Male flight behavior may primarily reflect a search for females and repeat matings, a behavior termed "patrolling" (Brakefield, 1982;Shreeve, 1984), whereas females are primarily focused on locating suitable egg-laying sites and avoiding the unwanted attentions of males. Flight durations and inter-flight periods are also likely subject to the spatial distribution of nectar resources and egg-laying sites (Odendaal et al., 1989;Root & Kareiva, 1984), which suggests the extent of differences among the sexes and species may also be dependent on the resources in the immediate environment. These factors altogether likely explain why in practice traits such as wingspan are only weak predictors of mobility.
However, by accounting for these differences we demonstrate that it is possible to predict displacement rates with a higher degree of accuracy ( Figure 2). F I G U R E 2 Observed and modeled mean displacement rates for each sex x species combination. Upper panel (a) shows relationship of displacement rates with wingspan as observed, bars show standard errors; lower panels show observed versus predicted displacement rates. Lines indicate perfect prediction. Symbols indicate modeling scenarios. (b) The correlative approach, fitting a regression line to the data in a; (c-e) mechanistic models. (c) Assuming only step speed is sex-and species-specific; (d) assuming turning angle and step speed are sex-and species-specific; (e) assuming all three movement components are sex-and species-specific Observed displacement rate (m/s)

Linear model
Step speed Turning angles

P(time in flight)
While it is clear that wingspan provides an important trait-based approach to modeling dispersal potential, the accuracy of model pre- in movement (Morales & Ellner, 2002) which is less directly related to morphological traits such as wingspan. Further, though our study measured local movements within homogenous habitat, the discrepancy between trait and dispersal is likely further uncoupled across different quality habitat patches which have been shown to have strong effects on butterfly behavior (Conradt, Bodsworth, Roper, & Thomas, 2000;Delattre et al., 2010;Odendaal et al., 1989;Roland et al., 2000;Schtickzelle et al., 2007). This is particularly relevant for understanding the role of rarer long distances movements in connecting populations which, though likely influenced by a capacity for movement, may be crucially influenced by behavior and interactions with the landscape structure (Nowicki et al., 2014). This context-dependency demonstrates a common weakness of the mechanistic approach, as it necessitates the collection of detailed behavioral information of the target species across different many circumstances.
A useful contribution of mechanistic models of movement is therefore in explaining the basis of motivational differences in relation to resource density, habitat structure, and foraging strategies, such that they provide better prediction for dispersal for species across varying landscape structures (Doherty & Driscoll, 2018;Johnston et al., 2019;Patterson, Thomas, Wilcox, Ovaskainen, & Matthiopoulos, 2008;Pauli et al., 2013;Urban et al., 2016).
In conclusion, we have shown that the reason wingspan can serve as a proxy for dispersal in butterflies is that it correlates well with flight speed and the tortuosity of butterfly movement. However, the most accurate predictions of displacement depend on sex-and species-specific parameterizations of flight and inter-flight durations, which decouple the relationship between wingspan and movement rate. Since these behaviors likely reflect motivation to move, substantive improvements in model predictions will require an understanding of how species view and utilize resource availability in complex landscapes. Demonstrating the extent to which behavior can improve predictive power over simple correlative approaches suggests that there is both scope and strong justification to develop process-based models as a practical tool for ecological forecasting.

ACK N OWLED G M ENTS
L. Evans was supported by a BBSRC CASE/Syngenta PhD studentship award. Access to sites was granted by the Earth trust, The University of Reading and Jealott's hill Syngenta. We are grateful to additional research assistance in the field provided by undergraduate students: Andrew Tarbie, Felix Townsend, Ginny Crouch, and Arron Watson.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
LE collected the data, conducted the analysis, and developed code for the individual-based model. LE, RS, and RW led the writing of the manuscript with contributions from TO, IS, and PT.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data from the study and the app used for the project are archived at Mendeley Data: http://dx.doi.org/10.17632/ kpcgk fmpv8.1. Full data description is provided by .