28 Jul 2003 18:48 AR AR200-ES34-21.tex AR200-ES34-21.sgm LaTeX2e(2002/01/18) P1: GCE AR REVIEWS IN ADVANCE10.1146/annurev.ecolsys.34.011802.132428 (Some corrections may occur before final publication online and in print) R E V I E W S I N A D V A N C E Annu. Rev. Ecol. Evol. Syst. 2003. 34:575���604 doi: 10.1146/annurev.ecolsys.34.011802.132428 Copyright c 2003 by Annual Reviews. All rights reserved THE ECOLOGY AND EVOLUTION OF SEED DISPERSAL: A Theoretical Perspective Simon A. Levin Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544 email: slevin@princeton.edu Helene C. Muller-Landau National Center for Ecological Analysis and Synthesis, 735 State Street, Santa Barbara, California 93101 email: hmuller@nceas.ucsb.edu ���Ran Nathan Department of Life Sciences, Ben-Gurion University, Beer-Sheva 84105, Israel email: rnathan#bgumail.bgu.ac.il ���J�� er �� ome Chave Evolution et Diversite�� Biologique, CNRS, Universite�� Paul Sabatier, batiment �� IVR3, F-31062 Toulouse, France email: chave@ckt.fr Key Words spatial ecology, long-distance dispersal, mechanistic models, invasion speed, population dynamics Abstract Models of seed dispersal���a key process in plant spatial dynamics��� have played a fundamental role in representing dispersal patterns, investigating disper- sal processes, elucidating the consequences of dispersal for populations and commu- nities, and explaining dispersal evolution. Mechanistic models of seed dispersal have explained seed dispersion patterns expected under different conditions, and illuminated the circumstances that lead to long-distance dispersal in particular. Phenomenological models have allowed us to describe dispersal pattern and can be incorporated into models of the implications of dispersal. Perhaps most notably, population and com- munity models have shown that not only mean dispersal distances but also the entire distribution of dispersal distances are critical to range expansion rates, recruitment pat- terns, genetic structure, metapopulation dynamics, and ultimately community diversity at different scales. Here, we review these developments, and provide suggestions for further research. ���Order of the last three authors was determined by a random-number generator. 1543-592X/03/1215-0575$14.00 575 First published online as a Review in Advance on August 6, 2003

28 Jul 2003 18:48 AR AR200-ES34-21.tex AR200-ES34-21.sgm LaTeX2e(2002/01/18) P1: GCE AR REVIEWS IN ADVANCE10.1146/annurev.ecolsys.34.011802.132428 576 LEVIN ET AL. INTRODUCTION Dispersal is defined as the unidirectional movement of an organism away from its place of birth. In sedentary organisms such as all plants and some animals, dispersal is mostly confined to a short early stage of the life cycle. In higher plants, individuals move in space mostly as seeds. Many plant species can also move through vegetative growth, but this kind of movement is not as common and typically induces relatively minor spatial change. Although nonvegetative dispersal units can be diverse and can be more appropriately described by more specific botanical terms (cf. van der Pijl 1982), here we use the term seed dispersal as a general expression for the dispersal of the reproductive unit of a plant. To understand dispersal, we need to measure its spatial patterns, to explore the mechanisms that generate them, and to examine their consequences. We thus start with an overview of the empirical evidence for patterns and processes of dispersal and then discuss models describing these. The theoretical implications and explanations of dispersal are discussed in subsequent sections, starting with population spread, briefly through other aspects of population and community dy- namics, to the evolution of dispersal. We end with a synthesis of main conclusions and directions for future research. SEED DISPERSAL PATTERNS AND PROCESSES Dispersal Mechanisms The great variety of dispersal-aiding morphologies attracted the attention of natu- ralists as early as Aristotle (384���322 BC) and Theophrastus (371���286 BC) (Thanos 1994). For a long time, the study of seed dispersal was either anecdotal or spec- ulative, with attempts to explain the selective value of each and every detail of a dispersal unit (Ridley 1930, van der Pijl 1982). The most commonly used classifi- cation system of dispersal syndromes is based on the agent or vector of dispersal, typically inferred from seed morphology. The principal agents of dispersal are either abiotic (wind and water) or biotic (animals and the plant itself), and the dispersal syndromes are termed, respectively, anemochory, hydrochory, zoochory, and autochory (van der Pijl 1982). The vector-based method, and similarly any other classification of dispersal morphologies, can be refined to account for more subtle differences in the morphol- ogy of the dispersal unit, its potential dispersers, and adaptive features (van der Pijl 1982). However, as the level of detail in classification increases, the promise of the- oretical generalization recedes. Furthermore, general classification methods tend to miss, and even misconstrue, important characteristics of the seed dispersal process. A key point is that dispersal is seldom mediated by a single dispersal agent and is not confined to the primary movement of seeds from the plant to the surface (Phase I dispersal) (Chambers & MacMahon 1994, Watkinson 1978). Rather, it also entails subsequent movements (Phase II dispersal) that can be mediated by other dispersal

28 Jul 2003 18:48 AR AR200-ES34-21.tex AR200-ES34-21.sgm LaTeX2e(2002/01/18) P1: GCE AR REVIEWS IN ADVANCE10.1146/annurev.ecolsys.34.011802.132428 ECOLOGY AND EVOLUTION OF DISPERSAL 577 agents. The common practice of using the morphological dispersal syndrome to distinguish short- from long-distance dispersal is therefore questionable. In fact, the actual processes responsible for long-distance dispersal (LDD) are only loosely correlated with those interpreted from seed morphology (Higgins et al. 2003). A second major limitation of traditional classification schemes stems from the ambiguous relationships between the morphological dispersal syndrome and the contribution of the dispersal process to plant fitness (disperser effectiveness sensu Schupp 1993). Dispersal agents, even within restrictively classified groups, differ markedly in their effectiveness both quantitatively (numbers and distances of dis- persed seeds) and qualitatively (treatment and deposition of seeds) (Schupp 1993). An extreme example for the importance of the quality of the dispersal agents is directed dispersal, or the disproportionate arrival of seeds to favored establishment sites in which survival is relatively high (Howe & Smallwood 1982). Wenny (2001) provides many examples and a thorough discussion of this phenomenon, which seems to be more common than previously believed. Spatial Patterns Dispersal is encapsulated in the seed dispersion pattern (Nathan & Muller-Landau 2000), most commonly measured in a two-dimensional setting, though it can also be measured in one (e.g., Thebaud & Debussche 1991) or three spatial (Nathan et al. 2002b, Tackenberg 2003) dimensions. Seed dispersion patterns depend on adult dispersion patterns, their geometry and fecundity, and on the variation in the direction and distance of dispersal events. As such, they can be very complex, hence difficult to quantify. The most common practice utilizes a ground network of seed traps (Greene & Calogeropoulos 2002) direct observations (e.g., Watkinson 1978) and genetic analyses (e.g., Godoy & Jordano 2001) are used much less frequently. Dispersal studies usually cover an area where most, but not all, dispersal occurs. Quantifying seed dispersion patterns at increasingly large scales is exceedingly more difficult because more uncertainty is associated not only with the fate of rare events but even with the identity of the mechanisms operating at these scales (Higgins et al. 2003). The seed trap method soon becomes unfeasible because of the extremely huge sampling area required to detect rare LDD events (Greene & Calogeropoulos 2002). Thus, the quantification of LDD is extremely challenging (Cain et al. 2000, Nathan et al. 2003). Unconventional methods that focus on individual movements and methods that couple modeling and empirical tools are the most promising ways to estimate LDD see Greene & Calogeropoulos (2002), Nathan et al. (2003), Wang & Smith (2002) for recent reviews. Seed dispersion patterns reflect the totality of all individual dispersal events in a population, whereas the dispersal curve summarizes the distribution of distances traveled by seeds. Dispersal curves can in principle form any kind of distribution cases of directed dispersal discussed above, for example, may generate complex multimodal dispersal curves (Schupp et al. 2002). The majority of empirical seed

28 Jul 2003 18:48 AR AR200-ES34-21.tex AR200-ES34-21.sgm LaTeX2e(2002/01/18) P1: GCE AR REVIEWS IN ADVANCE10.1146/annurev.ecolsys.34.011802.132428 578 LEVIN ET AL. dispersal data, however, fit a relatively simple, unimodal leptokurtic distribution, characterized by a peak at or close to the source, followed by a rapid decline and a long, relatively ���fat��� tail (Kot et al. 1996, Willson 1993). In the following section, we define relevant terms and discuss the mathematics of dispersal curves. Many studies evaluate dispersal based on postdispersal (seedlings, young plants, or even adults) dispersion patterns. Although this kind of data can be collected in a cost-effective manner, it may not provide a reliable way to reconstruct disper- sal. This is because data interpretation should address uncertainties involved not only with dispersal, but also with predispersal (e.g., pollination, seed production, and predispersal seed loss), and postdispersal (e.g., seed predation, germination, and seedling competition) processes (Nathan & Muller-Landau 2000, Schupp & Fuentes 1995). Such coupling is especially challenging for large-scale studies with virtually no information on establishment processes that follow LDD (Nathan 2001) despite their crucial importance for plant population dynamics. THEORETICAL MODELS OF SEED DISPERSAL Phenomenological Models Ultimately, we will argue that understanding of dispersal requires the development of mechanistic models that can explain observed pattersn. We begin, however, with a characterization of those patterns through purely phenomenological models. SEED DISPERSAL CURVES Data on dispersal can be represented either by the fre- quency distribution of dispersal distances or by the two-dimensional distance func- tion of postdispersal seed densities. The two types have been coined, respectively, distance distribution and dispersal kernel (Nathan & Muller-Landau 2000), or one- and two-dimensional probability density functions (Cousens & Rawlinson 2001). Mathematically, a dispersal kernel is expressed in Cartesian coordinates by P(x, y)dxdy, the probability that a seed released at point (0, 0) lands in a square of size dxdy centered at the deposition site (x, y). Given the symmetries in this problem, it is easier to deal with polar coordinates r, ��, where r = x 2 + y2 is the distance between the release point and the deposition site, and �� is the radial angle. If dispersal is isotropic, the probability of landing in an annulus of width dr at a distance r from the point source is 2��rP(r)dr. In certain cases, dispersal is directed along one preferential direction, and it can be suitably modelled as a one-dimensional process. Then, P(x)dx is the probability that a seed starting at point 0 lands in the segment of length dx centered at x. It is assumed throughout this section that one-dimensional kernels are functions of x, while two-dimensional kernels are functions of r. The seed shadow N(x) is the product of the dispersal kernel P and the total number of seeds dispersed . Dispersal curves can be estimated from seed dispersion patterns by taking into account the location, geometry, and fecundity of adults, and the directionality of the dispersal process, though the latter is usually ignored. A general problem with

28 Jul 2003 18:48 AR AR200-ES34-21.tex AR200-ES34-21.sgm LaTeX2e(2002/01/18) P1: GCE AR REVIEWS IN ADVANCE10.1146/annurev.ecolsys.34.011802.132428 ECOLOGY AND EVOLUTION OF DISPERSAL 579 such estimation is the identification of the specific source location of dispersed seeds. This has led researchers to select isolated individuals so that the seed source location is not ambiguous (e.g., Lamont 1985). However, more generally, adult plants tend to form conspecific aggregations hence, seed shadows of neighboring individuals typically overlap. Methods for resolving the overlapping seed shadow problem are discussed in Clark et al. (1998b), Nathan & Muller-Landau (2000), and Ribbens et al. (1994). Traditionally, three functional forms for the distance distribution were com- monly fitted to dispersal data: the Gaussian, the negative exponential, and the inverse power law. The Gaussian distribution is well defined but does not fit the leptokurtic distributions that are commonly observed. The negative exponential, probably the most commonly used functional form, has a fatter tail, but not fat enough to accommodate many LDD data. The inverse power law has a fat tail, but P(r) = a/r�� goes to infinity as r goes to zero (if �� 0) hence only functions such as P(r) = a/(1 + br)�� can be used as general forms for dispersal kernels. A general parametric formulation encompassing all these models is P(r) = a r�� exp(���br�� ) = a exp(���br�� ��� �� ln(r)), (1) where a, b, ��, and �� are parameters (Turchin 1998, p. 200). Recent studies have proposed fat-tailed distributions such as the (two-dimensional Student t) 2Dt (Clark et al. 1999) P(r) = a(1 + br 2)����� . (2) For �� = 1, this is the Cauchy distribution (Shaw 1995). These dispersal kernels are strongly leptokurtic, with a disproportionately large fraction of the seeds dispersed far. Short- and long-distance dispersal can be associated with different dispersal mechanisms (see Seed Dispersal Patterns and Processes above), hence the overall distribution of dispersal distances in a population may be best represented by stratified modelling, i.e., mixing several dispersal kernels such as two exponential distributions (Higgins & Cain 2002). MOTIVATION OF MODEL FORMS Phenomenological models are chosen mainly��� if not entirely���on their ability to fit the data. However, particular modelling forms can also be justified by general assumptions about the dispersal process. The sim- plest example rests on a homogeneous deposition model, which implies an ex- ponential dispersal kernel. In one space dimension, assume that a fraction �� of the dispersed seeds that have not yet settled are deposited between x and x + dx, while the remaining fraction are dispersed further. This yields a differential equa- tion for P(x), dP(x)/dx = ����� P(x), whose solution on the half-line x ��� 0 is the exponential P(x) = �� exp(�����x). (3) with mean dispersal distance L equal to 1/��.