Studies of animal movement behaviour have identified general optimal movement strategies based upon the spatial distribution of resources (32, 36, 46). Using a similar analytical approach, we show that general optimal dispersal strategies can be identified for plants based purely on the shape of the entire seed dispersal kernel in relation to the spatiotemporal distribution of the plant habitat. Earlier studies have shown how dispersal propensity may evolve in response to landscape structure, cost of dispersal and other (density-dependent) processes (13, 25–27, 47). We here show that the entire shape of the dispersal kernel can be seen as a multi-scale search strategy that needs to balance incentives to disperse over short-distances, long distances and everything in between.
The model used in this study is very simple, with individual plants being identical except for differences in dispersal strategies. Competition is not explicitly parameterized in the model, but implicitly there is some form of density dependence due to the role of kin avoidance. Multi-scale dispersal strategies emerge as optimal in a wide range of landscapes even within this simple and straightforward framework, suggesting that they are of importance as a baseline in the natural setting where more processes play a role in spatial population dynamics. The reference framework following from our results is visualised conceptually in Fig. 6. The main hypotheses for real plant data generated from our findings are: (1) In static, but patchy habitats, short-distance dispersal (e.g. µ > 3) dominates multi-scale dispersal strategies, due to the importance of optimizing habitat encounter. Particularly when patches are small and inter-patch distances are large, there is a strong selection in favour of extremely short-distance dispersal. (2) In contrast, extreme long-distance dispersal (µ → 1, or even uniform dispersal kernels) is favoured in both stable, continuous habitats as well as in unpredictable and dynamic landscapes. These dispersal strategies are driven by avoidance of kin competition and need to colonize newly formed patches. (3) In patchy and dynamic environments, a complex trade-off between finding habitat, avoiding kin competition and colonizing new patches results in multi-scale dispersal strategies with µ correlated to average patch size, inter-patch distance and, most importantly, patch turnover rate. Our results suggest that multi-scale kernels similar to Lévy flights (µ ~ 2) would be selected for in patchy landscapes with intermediate patch sizes (~ 2 to 100 times the plant size), intermediate inter-patch distances (~ 5 to 100 times the plant size) and relatively high patch turnover rates of around 50% per generation.
Some aspects of our findings are in line with well-known patterns observed in plant communities: Plant species in patchy and highly dynamic habitats typically have dispersal strategies dominated by long-distance dispersal and species from patchy but highly static landscapes tend to display predominantly short-distance dispersal that promotes the chance of success in ‘winning the home patch’ (22, 48–50). Yet, such hypotheses are not trivial. For example, in static but patchy landscapes, short-distance dispersal strategies may rapidly evolve. Colonization has been followed by rapid loss of long-distance dispersal in plants on islands and patches in urban environments (51–53). Such species are extremely vulnerable to habitat loss and fragmentation, as their dispersal strategy is not adapted to colonizing new areas (54). With ongoing global change, such dispersal-limited species are under great threat of extinction – an example of such a case is the endemic and highly threatened Centaurea corymbosa which is adapted to long term persistent, but isolated rocky outcrops (55).
Some hypotheses generated within our study may appear counterintuitive. For example, species in homogeneous habitats are suggested to have uniform dispersal kernels. This hypothesis would explain why, indeed, many species of large-scale, more or less continuous habitats, such as primary forest (56) and heathlands (57), have adaptations for very long-distance dispersal. Previous studies may have suggested that these adaptations serve to avoid density-dependent mortality close to the parent (16, 58, 59), but this would not explain dispersal over more than a few tens of m (the decay rate of pest-induced mortality, (24)). Our results suggest that selection for kin avoidance may explain these long-distance dispersal syndromes, although escaping density-dependent mortality may be an additional, enforcing factor.
Our analyses also lead to interesting untested hypotheses: species subjected to patchy environments should have multi-scale dispersal strategies that vary in the fatness of their tail in relation to patch size and inter-patch distances, but primarily in relation to patch turnover rates. This means that mid-range scales may become more or less prominent depending on habitat distribution characteristics. Analyses of measured plant dispersal kernels across real landscapes should reveal whether these hypotheses indeed reflect reality. It is, however, difficult to obtain complete dispersal kernels from field measurements, as long-distance dispersal events are extremely difficult to measure and at the same time form a vital component of the dispersal strategy. For wind dispersal, mechanistic models have been developed that simulate complete dispersal kernels (including long-distance dispersal events), and these have withstood tests against field tracking and trapping data (e.g., CELC, (60); and WALD, (61)). Simulations of tree dispersal kernels using WALD indicate that forest trees such as Liriodendron tulipifera in oak-hickory forests, one of the largest and most continuous forest habitats in temperate regions, could have tails with power laws of µ ~ 1.5 (61); species such as Pinus taeda are likely to have even fatter tails (56). These kernels are close to the long-distance dominated dispersal kernels that would be expected for species in continuous habitats. Simulations of wind dispersal using the CELC model for herbs characteristic of patchy and temporary wet grasslands ((60); data from (62)) generate dispersal kernels that are best fitted by 2D-Pareto distributions with µ ~ 2 (1.9 for Cirsium dissectum, 2.0 for Hypochaeris radicata). These values match the Lévy-like multi-scale dispersal kernels expected for species in successional, patchy habitats. For species typical of highly disturbed sites, such as Tussilago farfara in disturbed open sites, extreme long-distance dispersal has been reported - up to 4000 m in one generation (63), with a roughly estimated µ of 0.59 (64). Another species typical of disturbed sites is Cecropia obtusifolia, a pioneer tree colonizing forest gaps. Seed trap data of this species in young forests are best fit by a 2D-Pareto distribution with µ = 1.1 (data from (65)). We summarize these first lines of evidence in Fig. 6.
The occurrence of multi-scale dispersal strategies in nature becomes particularly apparent in species that combine multiple dispersal vectors that transport seeds across different scales. For example, Cakile maritima produces two different types of seeds that are either dispersed by water or as tumble weed attached to the maternal plant (66). In other species, the same seed types are intended to be dispersed by different vectors, such as plants with seeds in fleshy fruits (dispersed by a range of animal species with varying dispersal capacities, (67)) and wetland plants (dispersed by water or by waterbirds, (68)). Investments in seed morphology to optimize dispersal come at widely varying costs (47), which may also be driven by post-dispersal processes. Such investments have therefore not been included in our simple model (but see below).
By proposing to analyse seed dispersal as a plant search strategy for finding suitable habitat and using kernels with different scaling behaviour to compare dispersal strategies across different landscape dynamics, we break with the tradition of investigating dispersal propensity or focusing only on a single scale of plant dispersal kernels such as the tail or modal distance. With methodological hurdles to the study of long-distance dispersal being overcome (56, 69), much research has focused on quantifying the tail of the dispersal kernel (5, 69–71). This has resulted in rapid progress in our understanding of, and ability to predict, the connectivity of plant populations in fragmented landscapes (72, 73) and has helped to explain species’ abilities to track climate change (3, 74) or become invasive (75). At the same time, other studies have focused on the mode of the dispersal distribution to facilitate cross-species comparisons (76). The mode represents the distance where most seeds end up, which is a far easier measure and therefore an attractive parameter to study. We however stress that the entire dispersal kernel defines the movement strategy of plants, and as such is relevant for local, landscape-scale, and global species survival. Such an integrated approach to plant dispersal has also been advocated in the general ‘movement ecology paradigm’ (77), and an important first step in making large cross-species comparisons of entire dispersal kernels has recently been taken (11). The simplicity of our approach, which uses a flexible dispersal function parameterized by a single parameter, µ, facilitates further comparisons across large numbers of species with widely differing dispersal strategies, while also allowing for the exploration of relations between species’ dispersal strategies and their traits, life history strategy, or habitat characteristics.
As a final point, we hope our framework facilitates plant ecological research to benefit from conceptual advances in animal movement ecology. Promising future directions for plant ecological research include exploring how different costs of dispersal (e.g. due to investments in traits) modify the optimal search strategy (cf. (36)) and examining plant dispersal kernels for the existence of ‘composite walks’, which combine multiple movement types into one dispersal strategy, not necessarily showing scaling properties (cf. (78)). The latter would be relevant in species with dispersal dimorphisms or species using multiple dispersal vectors, as discussed above. Another interesting direction would be to explore to what extent plant searches can be considered as ‘informed searches’. There is a growing body of evidence that plants dispersed by animals, water, and wind utilize ‘directed dispersal’ strategies, in which they use environmental cues or select specific vectors that result in disproportionate arrival of seeds at more suitable sites (79–81). In a recent study, ‘informed dispersal’ has been suggested as a strategy to escape competition and environmental stress (82). Thus, future research could explore these strategies in the light of ‘informed searches’ in plants, similar to how animals use cues to guide their search towards suitable sites (cf. (83)). Insights in how these factors shape the evolution of dispersal strategies, and progress in knowledge of dispersal mechanisms, can mutually inspire each other, and thereby improve the understanding and quantification of dispersal in plants.