Rapid shifts in dispersal behavior on an expanding range edge

Abstract

Dispersal biology at an invasion front differs from that of populations within the range core, because novel evolutionary and ecological processes come into play in the nonequilibrium conditions at expanding range edges. In a world where species’ range limits are changing rapidly, we need to understand how individuals disperse at an invasion front. We analyzed an extensive dataset from radio-tracking invasive cane toads (Rhinella marina) over the first 8 y since they arrived at a site in tropical Australia. Movement patterns of toads in the invasion vanguard differed from those of individuals in the same area postcolonization. Our model discriminated encamped versus dispersive phases within each toad’s movements and demonstrated that pioneer toads spent longer periods in dispersive mode and displayed longer, more directed movements while they were in dispersive mode. These analyses predict that overall displacement per year is more than twice as far for toads at the invasion front compared with those tracked a few years later at the same site. Studies on established populations (or even those a few years postestablishment) thus may massively underestimate dispersal rates at the leading edge of an expanding population. This, in turn, will cause us to underpredict the rates at which invasive organisms move into new territory and at which native taxa can expand into newly available habitat under climate change.

Many populations are shifting their range edges in response to climate change (1, 2) and other anthropogenic stressors (3, 4), and invasive species are spreading rapidly worldwide (5, 6). We need to predict rates of range shift to manage these changes, but (despite sophisticated theory on the processes underlying range shift), models routinely underestimate the rate of spread (7) because they underestimate the frequency of long-distance dispersal. Not only are rare long-distance dispersal events difficult to document (8, 9), but populations in the spreading vanguard are subject to powerful ecological and evolutionary forces not experienced by conspecifics within the range core. On the expanding range edge, individuals mate assortatively by dispersal ability (“spatial sorting”) (10, 11); deleterious mutations can surf to fixation (12, 13), and parasites and pathogens may get left behind (14, 15). These differences could all affect dispersal rates and mean that to predict rates of range shift, we need to actually measure dispersal at the invasion front.

Understanding the differences in dispersal rates at and behind an invasion front also may clarify the roles of plasticity, evolution, and ecology. For example, covariation of dispersal rates with conspecific or pathogen density implies a role for plasticity (e.g., density-dependent dispersal) or ecology (the effect of parasites and pathogens) rather than evolutionary processes in driving dispersal-rate variation. In contrast, higher dispersal rates at the invasion front versus further back in the range core, uncorrelated with ecological factors, would suggest an underlying signal of ongoing spatial sorting. There are two ways that we could measure such a shift: by comparing populations (invasion front versus postinvasion) through space or by comparing those populations in the same area, through time. Neither approach is ideal: the former is confounded through space (local landscape features may change dispersal rates), whereas the latter is confounded through time (differences in weather among years may change dispersal rates). The second potential complication is easier to quantify (and thus, to control for), so we measured dispersal rates at a single site, from the first arrival of an invasive species until several years later.

To analyze movements across a heterogeneous landscape, we need new methods as well as new data. On the analytical front, we need to acknowledge differences among individuals (16, 17) as well as an individual’s ability to switch from one behavioral mode to another (18–20) (Fig. 1). In the present paper, we develop a hierarchical Bayesian model to analyze animal dispersal at both individual and population levels and apply it to an extensive radio-tracking dataset on the movements of invasive cane toads (Rhinella marina) as they first arrived at our study site in tropical Australia, and over the subsequent 8 y. Cane toads are large, toxic American amphibians that were brought to Australia in 1935 to control insect pests, and have been spreading ever since. The rate of toad invasion has accelerated dramatically during the toads’ Australian expansion across northern Australia, partly due to rapid evolutionary shifts in dispersal and population growth rates (21–23). Here, we investigate whether the toads that first arrived at our field site (pioneers) were more dispersive than postinvasion toads tracked in the same area.

Fig. 1.

Movement paths of three radiotracked cane toads, illustrating the diversity of modes of dispersal and our method of classifying every movement probabilistically as one of two modes: either “dispersive” or “encamped.” The color of each overnight displacement (step), and associated color box below it, correspond to the estimated probability of each move being in dispersive mode. Crossed out sections indicate days of missing data. The toad whose movements are shown on the Left, made a single long dispersal (in red) between two periods of primarily encamped movement (blue). Center and Right show toads staying in dispersive and encamped mode, respectively, throughout the tracking period.

Results

Toads in the invasion vanguard showed strikingly different patterns of movement than did conspecifics that we tracked at the same site a few years postinvasion. Fig. 2 compares the two groups of toads with respect to the movement parameters that most influence long-term displacement rate (SI Appendix, Fig. S19), the aspect that is most obviously critical to the rate of range expansion and that has evolved rapidly upwards during the toads’ Australian invasion (24). Although the tendency to switch from encamped to dispersive mode was similar between populations (Fig. 2A), pioneer toads remained for longer in dispersive mode (Fig. 2B) and consequently spent a larger proportion of time in dispersive mode. They also showed higher directionality (Fig. 2C) and longer daily displacement (Fig. 2D) when in dispersive mode than did postinvasion toads. The coefficient of variation of movement distances (an estimate of “tail fatness,” important for invasion speed) (25, 26) was similar in dispersive-mode pioneer versus postinvasion toads.

Fig. 2.

Pattern of switching between encamped and dispersive modes, and movement parameters within the dispersive mode, for free-ranging cane toads. Estimates are shown for pioneer and postinvasion toads (Left shows median values and 95% central credibility limits for both sets of toads, and Right shows the difference between the two groups (posterior predictive distribution of difference between populations); the filled areas under the curves show the probability that the pioneer toads were more dispersive in terms of: (A) probability of remaining in encamped mode, (B) probability of remaining in dispersive mode, (C) dispersive directionality, (D) dispersive mean movement distance, and (E) dispersive coefficient of variation of movement distances.

Movement parameters within encamped mode would, a priori, be expected to have less influence on overall displacement rates. Counterintuitively, pioneer toads were more likely to remain sedentary (use the same shelter in successive nights, rather than relocating) while they were in encamped mode (Fig. 3A), but also to move farther while they were in encamped mode (Fig, 3C). The coefficient of variation in movement distance during encamped mode (but not dispersive mode) thus was higher for pioneer toads (Fig. 3D). More variable displacement distances within encamped mode reflect occasional long-distance moves by pioneer toads, perhaps aborted attempts to switch into dispersive mode. Directionality in encamped mode did not differ between pioneer and postinvasion toads (Fig. 3B).

Fig. 3.

Movement parameters of radiotracked cane toads while they were in encamped mode. Estimates are shown for pioneer toads and postinvasion toads. Left shows median values and 95% central credibility limits for both sets of toads, and Right shows the difference between the two groups (posterior predictive distribution of difference between populations); the filled areas under the curves show the probability that the pioneer toads were more dispersive in terms of: (A) probability of unchanged location when in encamped mode, (B) encamped directionality, (C) encamped mean movement distance, and (D) encamped coefficient of variation of movement distances.

Discussion

Our switching model allows us to delineate movement modes and to look at changes in dispersal behavior over the years immediately following establishment. The analyses showed no difference between pioneer and postinvasion toads in the probability to shift from encamped to dispersive modes, indicating similar intervals of time spent within the encamped mode. However, having shifted, pioneers remained dispersive for longer periods, traveled farther per unit time, and moved in a more consistent direction. All of these changes increase overall displacement. The evolved behavioral modifications that have accelerated the toad invasion front through tropical Australia (11, 21, 23, 24) thus are manifested over very short periods following arrival and establishment of the invasion front.

We were able to make this observation because of the sensitive analytical tool we used. The hierarchical Bayesian framework allows us to compare populations, while acknowledging parameter uncertainty at the individual level (27). In combination with the hidden states model, this approach avoids confusing differences between individuals with different behavioral modes within an individual. For example, comparing one individual in encamped mode with another in dispersive mode is misleading; valid comparisons at the population level must be based on individuals in the same mode. Because an individual can switch from one mode to the other, any given dataset may not reflect the long-term behavior of that individual. For example, the individuals in Fig. 1 Center and Right (that were tracked for relatively short periods) remained within the same mode for the entire period of tracking, whereas the data on the Fig. 1 Left come from a toad that was tracked for a longer period, and (as a result) displayed periods of both modes. Our model allows us to compare individuals that were tracked for different durations. Importantly, it also clarifies what aspects of toad behavior change rapidly near the invasion front and influence long-term displacement. Separating between the two movement modes reveals substantial differences in directionality during dispersive mode but not during encamped mode. If we ignore those movement modes, and simply combine all of the data for a single analysis, we would substantially underestimate the differences between pioneer and postinvasion toads (Fig. 4, Left).

Fig. 4.

Turning angles (Left) and daily displacement distance (Right) of cane toads radiotracked at the invasion front (pioneers, Upper) compared with toads in the same area a few years later (postinvasion, Lower). Frequency distributions are separated into encamped (white) and dispersive (black) modes of movement (as probabilistically estimated). A movement with probability κ of being dispersive contributes with κ to the black bar and (1 − κ) to the white. While in dispersive mode, invasion-front toads were more directional and traveled farther per night.

Researchers are increasingly recognizing the impact of different movement modes on an individual’s rate of dispersal (28–30). In our study, sharp turning angles and short step lengths resulted in short displacements while toads remained in encamped mode, whereas the shift to dispersive mode involved long-distance moves in a consistent direction (Fig. 1). This autocorrelation in behavior results in greater long-term displacement distances than would a simple correlated random walk with the same step lengths and turning angles (31). Longer periods in dispersive mode increased overall displacements of pioneer toads relative to their postinvasion conspecifics. However, why would toads exhibit different movement modes? Studies of movement in a metapopulation setting have shown that movement behavior inside patches commonly differs from that exhibited in the matrix (32), so animals are clearly capable of responding to extrinsic environmental cues. A metapopulation framework may be an appropriate model for cane toad dispersal during the dry season, when toads are largely confined to small, isolated patches of damp habitat (33). However, the wet season (the time when toads disperse and when we conducted our studies) offers a far more homogeneous hydric environment, with few constraints on toad movements. Thus, in the wet season, a toad’s switch from one movement mode to another may be driven mainly by its internal state, e.g.,physiological and psychological factors (32, 34), rather than habitat heterogeneity. Thus, the shift in the length of dispersive periods between pioneer and postinvasion toads (Fig. 2B) might reflect a difference in physiological attributes (more athletic toads near the front), and/or endocrine triggers for mode switching. Indeed, a high incidence of spinal arthritis in invasion-front toads (35) suggests that some individuals in the pioneer population may disperse at rates so high as to approach the upper limits of their physiological or biomechanical tolerance.

Even within a single population, individuals differ in patterns of movement. If all animals moved with the same parameters, their long-term displacement would tend to a Gaussian distribution (ref. 28 and references therein). However, substantial variation among individuals in movement parameters (SI Appendix, Figs. S1 and S2) indicates that some toads were far more dispersive than others, generating a leptokurtic distribution of movement distances (36, 37). Leptokurtic displacement kernels yield faster and (if the tail is not exponentially bounded) accelerating invasion speed, even if dispersal abilities do not evolve (25, 26, 38). If differences in dispersal abilities have a genetic basis, the resultant spatiotemporal variation generated by evolutionary change may require more than a single kernel to accurately describe dispersal rates across the range of an invasion (24).

The more extensive movements of pioneer toads fit well with a priori predictions if this system has been under evolutionary pressure toward an accelerated invasion speed through spatial sorting (progressive accumulation of genes for faster dispersal) (10). Whereas previous analyses have revealed an evolutionary shift in dispersal behaviors over the course of the toads’ invasion (21, 23), our analysis appears to demonstrate the ongoing nature of the spatial sorting operating on the invasion front. The work was conducted at the same site (eliminating landscape features as a confounding effect), and the study area experienced consistent thermal conditions and rainfall through time (SI Appendix, Fig. S5). The dispersal rates of the toads that we radiotracked were not correlated with a toad’s sex (SI Appendix, Fig. S21) or body size (SI Appendix, Figs. S6–S13) or with our measures of conspecific density (even when allowing for a range of potential time lags in such effects: SI Appendix, Figs. S14–S18). Other local conditions most likely to have facilitated rapid dispersal at the invasion front include more food (39) and escape from native-range parasites (15). It is unlikely that toads would choose to disperse more when encountering areas of high food availability and even harder to imagine how it would make them move in a more directional manner (Fig. 2C). If parasite load drove the annual shift in rates of toad dispersal, we would expect to see a massive shift in movement distances from 2007 to 2008 [when 16% of toads were infected with lungworms (40)] to 2009–2010 [when 70% of toads were infected (40)]. No such shift in dispersal rates was evident (SI Appendix, Fig. S20). Thus, none of these proximate factors correlate with the clear shifts in dispersal behavior (length of dispersive periods, directionality, and movement distance) in our data (Figs. 2 and 3).

Although it remains possible that toad movements were influenced by some unmeasured factor, the observed shifts are consistent with what we would expect from spatial sorting. That is, movement behaviors shift rapidly following the arrival of toads simply because it is the most dispersive individuals in the invasion vanguard that arrive first. As individuals representing the slower end of the standing variation in dispersal behavior arrive, mean dispersal rates drop. A similar shift occurred in relative leg length of toads (21). Relative leg length was a proxy for displacement rate in that case, with longer-legged (faster dispersing) toads arriving first. Here, we observe the same phenomenon in the behavioral traits directly responsible for dispersal.

Overall displacement rates in these toads are heritable (24, 41), suggesting that the underlying movement behaviors that determine displacement rates are also heritable. If there remains genetic variation in these traits in the population near the front, ongoing spatial sorting will promote further evolution toward more dispersive individuals. Whether or not this system evolves toward higher dispersal rates will depend on other factors, such as the fitness consequences of more rapid dispersal. Regardless of these evolutionary considerations, however, such large shifts in movement parameters have important consequences for range-shifting populations. Noticeably, dispersal parameters shifted rapidly; individuals at the invasion front differed dramatically from conspecifics in the same study area only a few years later. Thus, measures made in areas behind the actual invasion front may underestimate the dispersal rates of individuals in the invasion vanguard, and thus, rates of range expansion also. Indeed, this underestimation of dispersal rate through sampling may partly explain why previous models of spread rate in toads have underestimated observed spread rates (11). The differences in behavior we observed here, for example, may allow pioneer toads to disperse more than twice as far in a wet season than their postinvasion counterparts (median 2.19 times as far, 95% predictive central credibility interval between 1.34 and 3.74 times as far: SI Appendix, section S9). Similar patterns likely will occur at expanding range edges in other species: certainly, rapid increases in dispersal during invasion have now been observed in organisms ranging from pine trees (42) to butterflies (43), and these increases in dispersal rate are almost certainly due, in part, to spatial sorting. Thus, models may routinely underestimate spread rates not only because rare long-distance dispersal is difficult to observe (7, 9), but also because sampling has been conducted at inappropriate times and places: dispersal rates on an invasion front are, by dint of spatial sorting, higher than those in the range core. Whether the species in question is an invader moving into new territory, or a native species moving into an area where the climate has suddenly become favorable, the only robust basis for understanding how individuals move about at the range edge will come from studies that explicitly focus on that nonequilibrium situation.

Materials and Methods

We have radiotracked cane toads on the Adelaide River flood plain in tropical Australia each wet season (December to March) over an 8-y period, beginning with the first toads to arrive at this site in 2005. This dataset enables us to explore how the movement patterns of individuals at an invasion front differ from those of conspecifics in longer-colonized areas. As well as tracking the toads, we also recorded conspecific density and environmental covariates, and so can assess the influence of these proximate factors on the dispersal behavior of free-ranging toads. All telemetry procedures were carried out under approval of the University of Sydney Animal Ethics Committee (permit L04/11-2005/3/4252).

To analyze daily displacements by radiotracked toads, we formulated a statistical movement model in a hierarchical Bayesian framework, expressing distributions at both individual and population levels by intuitively meaningful parameters. Similar to hidden Markov models, movement modes were included as hidden states and we probabilistically allocated each overnight displacement into one of two modes (encamped vs. dispersive). Within each mode, toads were assumed to move with correlated random walks, with the modes differing in directionality (given by mean cosine of turning angles) and mean and coefficient of variation of daily displacement. We also included the probability of not relocating at all (i.e., displacement distance equal to zero) as a special case of encamped behavior. At the hierarchical level, we describe the distributions of parameter estimates by population means and scale-free measures of variability; we use posterior predictive differences to identify presence and magnitude of population differences. In dispersive mode, individuals are expected to move in a more directed manner and travel farther. We used these expectations, simulations, and previous studies to construct a set of vague priors. Methods are described in detail in the SI Appendix, where section S1 describes the movement data, section S2 describes the movement model at individual and population level, section S3 describes prior elicitation, section S4 describes MCMC details, and section S5 describes prior sensitivity. We further provide additional analysis of weather data (section S6), correlation between movement parameters and individual characteristics (section S7), correlation between movement parameters and population density (section S8), long-term displacement prediction (section S9), cutoff between pioneers and postinvasion toads (section S10), and sex difference in movement parameters (section S11).