ReviewConverging approaches for modeling the dispersal of propagules in air and sea
Introduction
Denny (1995) published an inspiring book on the comparative physics of air and water and the consequences for life in these two media, including movement. Movement is fundamental to life and therefore widely studied to determine why, when, where, and how organisms move (Holyoak et al., 2008). How organisms move depends on their own internal state drivers (such as gain energy or look for safety) and navigation ability but also on external factors such as the media in which they move (Nathan et al., 2008a). External factors may have predominant impact on the movement, as, e.g., for terrestrial seed dispersal in the air and larval dispersal in the water. Terrestrial plant seeds, spores, pollen, fungi and insects are typically dispersed by wind (Bakker et al., 1996) together with other bioaerosols (Fröhlich-Nowoisky et al., 2016) but can also be dispersed by water or animals. Similarly, most aquatic organisms have planktonic early life stages (eggs and larvae) which are transported by oceanic currents from spawning to nursery habitats during the larval dispersal stages (Pineda et al., 2007; Secor, 2015). There are many natural parallels between aerial and aquatic dispersal. In both cases dispersal occurs in three dimensions and is largely influenced by a physical process, wind or ocean currents, respectively. However, until recently it was believed that one of the significant differences between dispersal of plants and fish was the spatial scale at which dispersal occurs. According to Kinlan and Gaines’s (2003) comparative review of propagule dispersal in marine and terrestrial environments, the genetically-estimated dispersal scales of demersal fish species (in the range 1–1000 km) is typically orders of magnitude larger than the estimated dispersal scale of terrestrial plants species (0.1 m – 10 km). This lead to the view of marine systems tending to be “open” and terrestrial systems being more “closed” (Carr et al., 2003). This view was challenged (Dawson and Hamner, 2008) and direct estimates of fish dispersal gave a more nuanced view (Levin, 2006). For example, Buston et al. (2011) reported a five-fold decrease of successful dispersal over a distance from 0 to 1 km for clown anemone fish larvae. Similarly, Almany et al. (2013) showed that 50% and 95% of coral grouper larvae settled within ∼10 and 30 km of the spawning aggregation, respectively. D’Aloia et al. (2015) found that the spatial scale of dispersal for a reef fish was one order of magnitude smaller than previously thought. There are several other examples reported in Bode et al. (2018).
The modeling approaches being developed to simulate propagule dispersal in air and sea have also become similar. As an illustration of these converging approaches, the schematic views proposed by Lett et al. (2009) and by Trakhtenbrot et al. (2014) for modeling larval and seed dispersal, respectively, are essentially the same. In both cases, outputs of a Eulerian model simulating the main physical forcing mechanism (currents or wind) serve as inputs to a Lagrangian model that include biological components (e.g., larval vertical movement, seed terminal velocity). In the Eulerian model the set of equations governing the dynamics of the ocean or the atmosphere are solved numerically on a spatially-discrete domain to provide velocity fields of water or air in (generally) three dimensions over time. In the Lagrangian (or individual-based) model the biological entities (eggs and larvae or seeds) are represented as distinct virtual individuals. These individuals are tracked over space and time while being transported by the simulated currents or wind. The main biological parameters and processes potentially interacting with the physical transport are also explicitly considered in the Lagrangian model. The resulting Eulerian-Lagrangian (or biophysical) model is used to simulate the trajectories of the larvae or seeds over the spatial domain (Fig. 1). In this study, we reflect on these converging modeling approaches by first putting them into an historical perspective, and then by comparing the physical and biological processes represented in marine larva vs. terrestrial seed dispersal models, the data used for the models output corroboration (sensu Augusiak et al., 2014), and the tools available to perform simulations. We finally discuss the opportunity that this convergence offers to bridge the gap between two scientific communities which are currently relatively disconnected. More broadly, we also see our comparison across systems as a useful way to strengthen the links between aquatic and terrestrial ecology (Stergiou and Browman, 2005) by sharing knowledge, methods, tools, and concepts, highlighting similarities and differences against which each system can be better evaluated (Rotjan and Idjadi, 2013).
Section snippets
Historical perspective
Theoretical developments in terrestrial and marine ecology started from the same general concepts that internal ecological dynamics (such as density-dependent relations and competitive interactions) determined the persistence of populations and communities (Steele, 1991a,b). But the large and rapid fluctuations observed in fish stock abundance and fish recruitment lead to the alternative view that external physical processes (such as advective and mixing processes in the ocean) could actually
Physical processes and models
Lagrangian dispersal of organisms are simulated by wind or current velocity fields. These velocity fields are obtained by solving the Geophysical Fluid Dynamics (GFD) equations on a discretized spatio-temporal grid. GFD equations include (EOM.1-EOM.4, Vallis, 2006):
- the mass continuity equation, which is the mathematical derivation of mass conservation of a fluid parcel;
- the momentum equation, which is the derivation of Newton’s second law for a fluid. It is based on the Navier-Stokes
Lagrangian particle dispersion models
Lagrangian dispersion models were first introduced and studied by the atmospheric community with the aim of predicting the evolution of plumes of pollutants in the atmosphere. First well-known references for Lagrangian stochastic models (LSM) include Wilson et al. (1981); Sawford (1985); De Baas et al. (1986), and the classic landmark paper Thomson (1987). The reader is also referred to Rodean (1996) for a comprehensive review of works and improvements in LSM for atmospheric purposes.
Biological processes and models
Once the wind or current velocity fields are available from the atmospheric or oceanic model simulations, the minimum information required to set up a biophysical model of terrestrial seed or marine larva dispersal is the time and location of individuals release and the duration of their tracking. For terrestrial seeds, the duration of transport is the “seed passage time” (Nathan et al., 2008b), which depends on seed terminal velocity and atmospheric stability (see below) but is often fixed in
Biophysical model outputs corroboration
A direct corroboration of simulated dispersal trajectories is still challenging because it is currently possible to track in situ only a limited number of seeds on land (Skarpaas et al., 2004) and even less larvae in the sea (Leis et al., 2006). The physical part of the biophysical models can be evaluated by comparing trajectories of real vs. simulated oceanographic drifters in the sea (e.g. Fossette et al., 2012) and atmospheric balloons in the air (e.g. Riddle et al., 2006). The complete,
Conclusion
Our analysis shows that the methods used to model and measure marine larva and terrestrial seed dispersal are converging largely independently of each others. More broadly, similar biophysical modeling approaches are now largely applied to simulate aquatic and aerial dispersal. The physical parts of these models are similar to the extent that the main equations that approximate the circulation of the ocean and the atmosphere are very much alike. Hence, the geostrophic balance between the
Author contributions
CL analyzed and interpreted the WoS citations data, NB was the major contributor of the “Physical processes and models” section of the manuscript, MB was the major contributor of the “Lagrangian particle dispersion models” section, CL was the major contributor of the “Historical perspective”, “Biological processes and models” and “Biophysical model outputs corroboration” sections. All authors read and approved the final manuscript.
Declarations of Competing Interest
None.
Acknowledgements
We thank the Marine Connection (iMarCo; https://wwz.ifremer.fr/gdrmarco/) group members for their feedback and encouragement, and David Kaplan and Ran Nathan for comments on an earlier version of this manuscript.
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