The total dispersal kernel: a review and future directions

Abstract

The distribution and abundance of plants across the world depends in part on their ability to move, which is commonly characterized by a dispersal kernel. For seeds, the total dispersal kernel (TDK) describes the combined influence of all primary, secondary and higher-order dispersal vectors on the overall dispersal kernel for a plant individual, population, species or community. Understanding the role of each vector within the TDK, and their combined influence on the TDK, is critically important for being able to predict plant responses to a changing biotic or abiotic environment. In addition, fully characterizing the TDK by including all vectors may affect predictions of population spread. Here, we review existing research on the TDK and discuss advances in empirical, conceptual modelling and statistical approaches that will facilitate broader application. The concept is simple, but few examples of well-characterized TDKs exist. We find that significant empirical challenges exist, as many studies do not account for all dispersal vectors (e.g. gravity, higher-order dispersal vectors), inadequately measure or estimate long-distance dispersal resulting from multiple vectors and/or neglect spatial heterogeneity and context dependence. Existing mathematical and conceptual modelling approaches and statistical methods allow fitting individual dispersal kernels and combining them to form a TDK; these will perform best if robust prior information is available. We recommend a modelling cycle to parameterize TDKs, where empirical data inform models, which in turn inform additional data collection. Finally, we recommend that the TDK concept be extended to account for not only where seeds land, but also how that location affects the likelihood of establishing and producing a reproductive adult, i.e. the total effective dispersal kernel.

Keywords: Defaunation; dispersal vector; frugivore; mathematical modeling; seed dispersal; seed dispersal effectiveness; total dispersal kernel; total effective dispersal kernel; wind.

Figure 1.

Seed dispersal of one plant species by different vectors (A), methods to assess seed dispersal (B) and the TDK resulting from seed dispersal kernels of different vectors (C). (A) Seeds from a plant can be dispersed naturally by different biotic and abiotic vectors, resulting in varying densities of seeds transported over varying distances. This can include higher-order dispersal, where already dispersed seeds are moved by a subsequent dispersal vector (e.g. scatter-hoarding rodents). Human-mediated dispersal (e.g. by hikers or vehicles) can contribute to seed dispersal, but dispersal distances become more unpredictable since the vector’s travel distances cannot be inferred from its biology alone. The size of icons and thickness of arrows correlate with the number of dispersed seeds—the larger the icon, the more seeds the vector disperses. Different lengths of arrows symbolize varying dispersal distances. (B) Seed trap data combined with inverse modelling incorporates all aerial vectors but does not allow identification of individual vectors and often ignores secondary seed dispersal. Scat sampling with genetic identification allows identification of individual vectors but ignores gravity and secondary dispersal. Both methods may underestimate long-distance dispersal unless genetic approaches are used to match seeds to adult plants across larger areas. Gut-passage time combined with movement data, or tracking of individual seeds from a source plant, can characterize where mobile vectors or wind move seeds but ignore other vectors (e.g. gravity, ants). These three broad approaches need to be combined with seed fate-focused studies to understand seed dispersal effectiveness. Methods that combine genetic data of established seedlings to adult plants can be used to characterize the total effective dispersal kernel (at least to the seedling stage), but do not allow vector identification. Ultimately, a combination of methods will lead to the best representation of the TDK, but also bring challenges associated with integrating different types of data. (C) Conceptualized TDK, including the seed dispersal kernels of all potential dispersal vectors for a given plant species/population. The contribution of each dispersal vector to the TDK depends on its importance, i.e. how many seeds it disperses and how far. Solid lines represent dispersal kernels of vectors where there is empirical evidence for the kernel shape and their contribution to the TDK can be calculated. Dashed lines represent dispersal kernels that have so far rarely been described or studied and their contribution to the TDK is unknown (for example secondary dispersal or human-mediated dispersal), increasing the uncertainty of TDK calculations and illustrating the need for more empirical studies on neglected dispersal vectors. The black dashed line represents the TDK based on all dispersal vector contributions, where contributions of primary vectors are summed and multiplied for secondary vectors. The probabilities densities are scaled such that the area under the TDK is one.

Figure 2.

Schematic representation of the modelling cycle for parameterizing and selecting total dispersal kernel models. It includes (i) data sampling and preparation, (ii) model building and (iii) simulations, for example projections of spread (Neubert and Caswell 2000) or different management scenarios (Shea et al. 2014). Simulations can be used for improving the sampling design (iv) using a virtual ecologist approach (Zurell et al. 2010), thereby restarting the cycle.