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.
What the paper shows and why it matters
(AI-generated)
Plants spread through their seeds, and ecologists describe where a seed lands relative to its parent with a dispersal kernel, a probability density over distance. Seeds are carried by several vectors (wind, animals, water, humans), often one after another. For a plant with a single vector, that vector’s kernel is the total kernel, although closer examination usually reveals further vectors. Yet many studies still cover one vector where several act. The total dispersal kernel, which combines all vectors, describes where seeds end up and is needed to predict how a plant population responds if a vector is lost. The concept is simple, but few well-characterised examples exist. The paper addresses the problem of estimating such a kernel from real data.
The paper argues that the total dispersal kernel of a plant, the pattern of where its seeds land once all vectors are counted, can be built from the kernels of individual vectors and fitted in an iterative modelling cycle, in which data inform models and models direct further data collection. Vectors acting side by side combine as a weighted mixture of their kernels; vectors acting in sequence combine by composition, typically a convolution rather than a simple multiplication. Fitting raises five statistical issues, among them sequential dispersal and seed fate (what happens to a seed after it lands). The paper holds that separating vector contributions from the observed total alone is very difficult, so robust prior information on single-vector kernels is needed. Two boxes, on musk thistle and on the fruit-eating animals of Guam, show systems where parts of the kernel have been explored.
The paper recommends extending the kernel to the total effective dispersal kernel, which adds how a landing site affects the chances that a seed establishes. It hypothesises that the total and the total effective kernel rarely resemble each other, because of distance-dependent mortality, uneven habitat and the effect of gut passage on germination, so measuring where seeds land is not enough. It also proposes “total dispersal kernel” as the common term instead of “complete” or “full”. The aim is to support predictions of how plant populations respond to losing or changing vectors under global change. The paper is a review with recommendations, not a test of the cycle.