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Population genetics, molecular markers and the study of


Journal of Ecology 1999, 87, 551±568

ESSAY REVIEW

Population genetics, molecular markers and the study of dispersal in plants
N. J. OUBORG*{, Y. PIQUOT{ and J. M. VAN GROENENDAEL*
*Department of Ecology, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, the Netherlands; and {Laboratoire de Ge?ne?tique et Evolution des Populations Ve?ge?tales, URA CNRS 1185, Universite de Lille 1, Ba?timent SN2, F-59655 Villeneuve d'Ascq, Cedex, France

Summary 1 Long-distance dispersal events are biologically very important for plants because they a?ect colonization probabilities, the probabilities of population persistence in a fragmented habitat, and metapopulation structure. They are, however, very di?cult to investigate because of their low frequency. We reviewed the use of molecular markers in the population genetics approach to studying dispersal. With these methods the consequences of long-distance dispersal are studied, rather than the frequency of the dispersal events themselves. 2 Molecular markers vary, displaying di?erent amounts of variation and di?erent modes of inheritance: they may be either dominant or codominant, and may or may not be subjected to genetic recombination. Use of markers has inspired the development of maximum likelihood techniques that take the evolutionary history of alleles into account while estimating gene ?ow. 3 Inferring seed dispersal rates from indirect measurements of gene ?ow involves three steps: (i) quantifying genetic di?erentiation among populations and using this to estimate the rate of gene ?ow; (ii) producing a genetic dispersal curve by regressing geographical distance among populations against the amount of gene ?ow; and (iii) separating seed-mediated from pollen-mediated gene ?ow, by comparing di?erentiation in nuclear vs. cytoplasmic molecular markers. In this way, potentially very low levels of gene ?ow can be detected. 4 The indirect approach is based on a number of assumptions. The validity of each assumption should be assessed by independent methods or the estimates of gene ?ow and dispersal should be mainly used in a comparative context. In metapopulations, with frequent extinction and colonization, the relationship between genetic di?erentiation and gene ?ow is not straightforward, and other methods should be used. 5 Highly variable molecular markers, especially microsatellites, have facilitated a direct genetic approach to measuring gene ?ow, based on parental analyses. 6 The population genetic approach provides di?erent information about dispersal than ecological methods. Thus population genetic and ecological methods may supplement each other, and together lead to a better insight into the dispersal process than either of the methods on its own. Keywords: coalescence, gene ?ow, isolation by distance, paternity analysis, pollento-seed-migration ratio Journal of Ecology (1999) 87, 551±568

# 1999 British Ecological Society

Correspondence: Joop Ouborg (fax + 31 24 3652134; e-mail joopo@sci.kun.nl).

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Introduction
Dispersal is one of the central processes in the dynamics and evolution of plant populations. The spatial dynamics of plant populations are determined to a large degree by the movement of seeds. At regional scales, seed dispersal ranges will set the possibilities for colonization of new sites, and will in?uence the probability of extinction of local populations (the rescue e?ect; Brown & Kodric-Brown 1977). Among-population dispersal is also an important determinant of metapopulation structure and will de?ne the units within which we consider dynamics and evolution (Husband & Barrett 1996). For example, can we regard the local population as the unit of dynamics, or do we need to consider the dynamics of neighbouring populations if we are to achieve a complete understanding of the local dynamics? If we observe a disequilibrium at the local population level, can we understand this in the light of metapopulation dynamics and regional equilibria (Olivieri et al. 1990; Antonovics et al. 1994; Husband & Barrett 1996)? Furthermore, dispersal is an important issue for several applied topics, including viability analysis for populations of fragmented species (Ellstrand 1992; Ellstrand & Elam 1993; Ouborg 1993), evaluation of the risks of escape of genetically modi?ed organisms into natural populations (Ellstrand & Ho?man 1990) and control of epidemic diseases and invasions of exotic species (Hengeveld 1989; Williamson 1996). If we are to ?nd answers to the questions within this diverse array of topics, some quanti?cation of dispersal is vital. However, quantifying dispersal, and especially long-distance dispersal, has always been one of the more di?cult tasks in plant population biology. Several approaches can be found in the literature. Many studies measure the actual distance over which individual propagules disperse and construct a frequency distribution. Dispersal distances are measured by trapping seeds at various distances from the source (Huiskes et al. 1995; Ruckelshaus 1996; Thiede & Augspurger 1996), by recapturing marked and released propagules (Johansson & Nilsson 1993) or by using arti?cial analogues of dispersal propagules (Nilsson et al. 1991). Another approach tries to predict dispersal distances by measuring the aerodynamic properties of seeds in wind tunnel experiments (Van Dorp et al. 1996) and making di?usion models (Greene & Johnson 1996; Cain et al. 1998). Both these approaches typically yield leptokurtic dispersal curves, with the majority of seeds dispersing over very short distances and only a very small proportion dispersing over longer ranges. For instance, in a seed trap experiment with Lupinus texensis 95% of the seeds dispersed less than 2 m, less than 0.5% of the seeds dispersed between 3.2 and 3.4 m, and no dispersed seeds were detected beyond 3.5 m (Schaal

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1980). While the maximal detected dispersal distance may vary between species and experiments, the general rule is that long-distance dispersal is very rare. However, comparison of observed colonization rates with rates predicted from dispersal curves drawn up using the methods described above suggests that the magnitude of long-distance dispersal is frequently underestimated (Van Dorp 1996; Cain et al. 1998). At the same time these rare long-distance dispersal events have great biological relevance. They determine both the possibilities of colonization of new sites and the structure of metapopulations, and may also contribute to gene ?ow among populations and thus in?uence the distribution of genetic variation. Although conventional population genetic wisdom says that the exchange of one migrant per generation is enough to prevent strong di?erentiation among two populations (Ellstrand & Elam 1993) (although allele frequencies may still be quite di?erent; Wright 1978), the methods available to study dispersal are generally insu?ciently sensitive to measure this low-frequency dispersal rate reliably, thus illustrating the limitations of such methods. The search for a solution to this problem led Silvertown (1991) to suggest that the study of dispersal would greatly bene?t from integration of ecological and population genetic approaches. The argument was that if it is very di?cult to estimate long-distance dispersal rates by following individual propagules, then we should approach the problem from the other end, by studying the (population genetic) consequences of dispersal, rather than dispersal events themselves. Part of Silvertown's plea was based on the potential o?ered by the use of sophisticated molecular marker techniques, which at that time were emerging rapidly. The question then was: `How can these techniques help us understand dispersal, and, especially, will they lead to qualitatively new insights?' The central question addressed in this paper is the way in which the population genetic approach, through the use of molecular markers, may indeed be able to help the study of dispersal. Any attempt to integrate ecological and population genetic approaches to study dispersal should start with a de?nition of dispersal, as distinct from gene ?ow. Dispersal and gene ?ow, although clearly related, have di?erent meanings, which could be confused. Therefore, throughout this paper dispersal will refer to the dispersal of seeds (or other propagules able to establish themselves), while gene ?ow will refer to the movement of genes and thus may involve both seed and pollen migration. We begin this review by discussing a few characteristics of molecular markers that are relevant to the study of dispersal. We then discuss the two basic population genetic approaches to this topic: the indirect and direct methods. In the indirect method,

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gene ?ow is inferred from the distribution of genetic variation among (sub)populations, and dispersal rates are then calculated from gene ?ow levels. Speci?c applications are needed to achieve this and two, genetic dispersal curves and separation of seed dispersal from pollen ?ow, are presented here. The direct method of estimating gene ?ow and dispersal, and the help of molecular markers in this approach, is then discussed. We conclude with a comparison of the type of information that can be obtained from ecological and the two population genetic approaches, and discuss prospects for the application of molecular markers in dispersal research.

Molecular markers
Gene ?ow in plants has been studied intensively with the use of allozyme markers, where gene ?ow is estimated from the distribution of allozyme variation over populations. The results of these studies have been reviewed in several papers (Hamrick 1987; Govindaraju 1988; Hamrick & Godt 1990; Ellstrand 1992; Gray 1996). The use of allozymes has provided a wealth of information with respect to pollen- and seed-mediated gene ?ow in plants. Allozymes exhibit Mendelian inheritance, have mutation rates in the order of 10±6 (Voelker et al. 1980) and can be applied without extensive technical development. Because of these properties allozymes are in many cases still a good choice in terms of the information they provide and their cost-e?ectiveness. Nevertheless, there may be reasons to apply other types of markers. For instance, attempts to measure gene ?ow in a direct way at small spatial scales, by following allozyme alleles in space and time, are frequently frustrated by the often limited variability that allozymes express (Barrett et al. 1993). Also, because allozymes (like nuclear DNA markers) are transmitted through both seeds and pollen, a maternally or paternally inherited marker is needed to separate seed dispersal from pollen ?ow. Finally, there is the unresolved debate about whether allozyme polymorphisms are selectively neutral, at least some allozyme data suggesting that selection may a?ect polymorphisms (reviewed by Kreitman & Akashi 1995). The development of molecular markers has provided the study of dispersal with new, potentially powerful tools that may o?set these limitations. Nowadays many types of molecular marker techniques are available, the most widely used including RAPD (random ampli?ed polymorphic DNA), RFLP (restriction fragment length polymorphism), AFLP (ampli?ed fragment length polymorphism), minisatellite ?ngerprints and microsatellites or SSR (simple sequence repeats). These markers di?er in the type and amount of variability they express, in their suitability for each particular question and in

# 1999 British Ecological Society Journal of Ecology, 87, 551±568

the ease and costs of their development and application. Detailed descriptions of techniques and type of data yielded by each marker type are not presented here but can be found elsewhere (Bruford et al. 1992; Avise 1994; Olmstead & Palmer 1994; Weissing et al. 1995; Jarne & Lagoda 1996). Estimating gene ?ow with genetic markers essentially involves assessing the distribution of alleles in space. This distribution is, broadly speaking, in?uenced by seed- and pollen-mediated gene ?ow, random genetic drift, di?erent forms of natural selection, mutational divergence and genetic recombination. While markers may di?er in their mutation rates, may be selectively neutral or subject to di?erent selective pressures (see below), and may or may not be subject to recombination, gene ?ow and genetic drift should a?ect all markers in a similar way (leaving aside the fact that haploid markers have lower e?ective population sizes and are more subject to drift than diploid markers). Thus when several types of diploid nuclear markers yield the same distribution pattern, this supports interpretations of observed distributions in terms of gene ?ow and drift. From the array of di?erences among the various marker types, we highlight ?ve aspects here that are particularly relevant for the use of molecular markers in the study of seed- and pollenmediated gene ?ow. First, most molecular markers represent variation in non-coding DNA regions. Although there may be cases where markers are non-neutral, for instance markers linked to quantitative trait loci (QTL) (Tanksley 1993) or microsatellites associated with neurological disorders in humans, where the number of repeats is correlated with the severity of the symptoms of the disease (Ashley & Warren 1995), it is generally assumed that variation expressed by these markers is essentially selectively neutral. By applying a random set of markers a signi?cant in?uence of selection on the results is cancelled out. Most plants are homoplasmic for haploid organelle genomes [mitochondrial (mt) and chloroplast (cp) DNA], meaning that all copies of mtDNA or cpDNA within an individual are identical. No recombination occurs, the organelle genome is in complete linkage disequilibrium and it is essentially inherited as a single gene. Selection may therefore in?uence cpDNA marker polymorphisms. On the other hand, cpDNA genes are highly conserved within species, which makes them suited for higher order phylogenetic inferences (Olmstead & Palmer 1994). If no variation is present in these structural genes, then cpDNA marker variation, representing non-coding intron variation, could be selectively neutral. Data pertaining to this issue are still lacking (McCauley 1995). Secondly, molecular markers di?er in the amount of variability they display. For the study of gene

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?ow it is important to adjust the variability of the marker to the spatial scale of investigation and the questions asked. For instance, at spatial scales of within or between populations, the presence or absence of structure in the distribution of highly variable markers, such as microsatellites, would give us insight into the amount of gene ?ow. However, using these same markers for the study of populations at large geographical scales may reveal one set of alleles in one population and another, non-overlapping, set in another, distant, population, indicating that these populations are completely di?erentiated. Although some speci?c assumptions about the evolutionary history of microsatellite alleles (e.g. of stepwise mutation; Jarne & Lagoda 1996) would allow reconstruction of the amount of divergence among these populations, the validity of these assumptions is still under debate. Thus, little can be said about the e?ect of distance on the amount of di?erentiation. In fact, di?erentiation at such spatial scales is determined almost completely by genetic drift and mutational divergence (setting aside possible di?erences in mating system among the populations). At these spatial scales we are interested in relatedness and phylogeny of populations rather than in the level of gene ?ow (which is probably very low if it exists at all). Less variable markers, like slowly evolving cpDNA or mtDNA markers, are then more suited. Thus choosing the right marker, with the right amount of variability for the spatial scale of the study, is a key part of each study of gene ?ow or dispersal. Although the ranking of markers according to their variability may di?er among species (Lonn et al. 1995), the gen? eral trend is that allozymes are less variable than RAPD or RFLP markers, which are less variable than microsatellites or minisatellite ?ngerprints. Markers in some regions of the cpDNA are even less variable than allozymes (Olmstead & Palmer 1994). Thirdly, markers can be classi?ed as either codominant, meaning that banding patterns of homozygotes can be distinguished from the patterns of heterozygotes, or dominant, where banding patterns of heterozygotes are identical to the patterns of one of the homozygotes and thus homo- and heterozygotes cannot be distinguished. Codominant markers (e.g. allozymes, microsatellites and most RFLP) allow easy estimation of allele frequencies in populations. Dominant markers (e.g. RAPD, AFLP), on the other hand, allow estimation of genotype but not of allele frequencies. Minisatellite ?ngerprints are codominant but, because of the large number of bands that typically result from this technique, it is often very di?cult to calculate allele frequencies. The amount of gene ?ow is often inferred from quanti?cation of the amount of di?erentiation among populations, in terms of FST (Wright 1978).

The calculation of this, and related parameters (e.g. GST, Nei 1973; RST, Slatkin 1995), is based on allele frequencies. Alternative estimation procedures, for example methods based on similarity of multilocus pro?les rather than those based on allele frequency, will have to be used for calculating FST-values from dominant marker data. Fourthly, markers di?er in their mode of inheritance. Nuclear DNA is bi-parentally inherited and is transmitted through both seeds and pollen. Organelle DNA (mtDNA and cpDNA) is often uniparentally inherited; in angiosperms organelle DNA is exclusively transmitted through seeds, in gymnosperms exclusively through pollen. Thus comparing patterns of di?erentiation in nuclear markers with di?erentiation patterns in cpDNA or mtDNA markers opens the possibility in several species of estimating the ratio of pollen vs. seed ?ow. While uniparental inheritance is the rule for cpDNA (Mogensen 1996), various examples exist of at least partial bi-parental inheritance or of paternal leakage of cpDNA (Corriveau & Coleman 1988; Mogensen 1996; Stewart & Prakash 1998). Fifthly, while nuclear DNA is subjected to recombination during the process of sexual reproduction, organelle DNA that is uni-parentally inherited is not. This means that patterns of cpDNA or mtDNA di?erentiation are not confounded by variation among populations in mating structure. These points illustrate the important di?erences in characteristics among marker types. It is important to choose the right marker for the particular scale and question being evaluated. Table 1 summarizes the di?erences in characteristics and gives an overview of the suitability of the various marker types for the di?erent methods and scales of study. However, because of species-speci?c di?erences in polymorphism and inheritance of markers, and because the unavailability of markers may force one to take a pragmatic approach, the actual choice of markers in a less than perfect world may deviate from the ideal presented in this table.

The indirect approach to measuring dispersal
To study dispersal with population genetic methods we need (i) to estimate gene ?ow from data on the distribution of genetic variation and (ii) a means of inferring dispersal from gene ?ow. Here we will consider the methods, including their limitations, of both steps.

GENETIC CHARACTERIZATION OF GENE FLOW

The rate of gene ?ow is inferred from the amount of genetic di?erentiation among populations. The spatial distribution of alleles is quanti?ed, and a popu-

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Table 1 A summary of the di?erent attributes of various marker types, and a ranking of their suitability for an indirect population genetic approach to the study of dispersal within and between populations, for a direct approach and for phylogenetic inferences at large spatial scales and long time frames. RAPD, random ampli?ed polymorphic DNA; AFLP, ampli?ed fragment length polymorphism; nucl. RFLP, nuclear restriction fragment length polymorphism; cyto. RFLP, cytoplasmic (i.e. mitochondrial or chloroplast) restriction fragment length polymorphism. Suitability ranking for applications: ±, not suitable; ±/+ , to be avoided if possible; +, suitable; + +, well suited; + + +, very well suited

Microsatellites

+++ Codominant Bi-parental Yes High

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lation genetic model is then applied to estimate what amount of gene ?ow would result in a similar distribution. The theory and application of the indirect estimation of gene ?ow is a large ?eld within population genetics, and many papers have addressed one or several aspects of the approach (Wright 1978; Weir & Cockerham 1984; Slatkin 1985a, 1987, 1993; Slatkin & Barton 1989; Cockerham & Weir 1993; Neigel 1997); here we do no more than summarize its basic outline. The approach is built on four components (Neigel 1997): a demographic model, a genetic marker system, a population genetic model and a parameter estimator. The demographic model describes the way in which dispersal takes place, and the in?nite island model (Wright 1978; Slatkin 1985a), where an in?nitely large source population sends migrants to a ?nite set of subpopulations at a constant rate, is the most frequently used. A genetic marker system, most often allozyme markers, is used to establish the pattern of genetic di?erentiation among populations. The level of genetic di?erentiation is quanti?ed in a parameter, FST (Wright 1978), which is the standardized among-population variance in allele frequency. A key concept in the indirect approach is application of the classical population genetic equation (Wright 1978):

Minisatellite ?ngerprints

+++ Codominant Bi-parental Yes High + (Haploid) Uni-parental No Intermediate ++ Codominant Bi-parental Yes Intermediate +++ Dominant Bi-parental Yes High

Cyto. RFLP

Nucl. RFLP

± /+ ± /+ +++ ±

++ ++ ++ ± /+

± ++ ++ +++

± /+ ± /+ +++ ± /+

+++ +++ +++ ± /+

AFLP

FST ?

1 1 ? 4Ne m

?1?

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where Ne is the e?ective population size, m is the proportion of individuals that are immigrants, and thus Nem is the number of migrants. This equation states that, in the absence of selection, and at equilibrium between drift and gene ?ow, the genetic differentiation between populations is inversely related to the rate of gene ?ow among them. Many variations of the indirect approach can be applied in preference to the classic form just described. In some, other demographic models are used, including (in order of increasing realism) the ?nite island model (i.e. migration is equally likely among a set of populations with equal e?ective population sizes; the distance between populations is not taken into account; Wright 1931), one- and twodimensional stepping stone models (i.e. the migration rate is constant and de?nes the rate of exchange from one neighbouring population to the next; Kimura 1953), continuum models (i.e. the migration rate is a ?xed function of distance; Wright 1940) and migration matrix models (i.e. migration rates may be di?erent and are de?ned for each pair of populations in a migration matrix; Bodmer & Cavalli-Sforza 1968). There is a trade-o? between the realism of the model and its mathematical tract-

++ Dominant Bi-parental Yes Low + Codominant Bi-parental Yes Low

RAPD

Allozymes

Polymorphism Dominance Mode of inheritance Recombination Costs (development and application) Applications Indirect, within populations Indirect, between populations Direct Phylogeography

++ +++ + +

± /+ ± /+ ++ ±

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ability and most approaches therefore use less realistic but more tractable models. Other models to describe the relationship between observed distributions of alleles in space and the rate of gene ?ow expected to give rise to a particular pattern include estimation of gene ?ow from genetic distances (Nei 1972), from the frequency of private alleles (i.e. alleles exclusively present in a single population; Slatkin 1985b) and from the use of spatial autocorrelation methods (Epperson 1993). These provide alternative methods for estimating the number of migrants. Although in its essential form FST is de?ned as a parameter describing the distribution of allele frequencies among populations, it can also be treated as a statistic. Crow & Aoki (1984) suggest that GST, a parameter that can be derived from information from multiple loci (Nei 1973) and has the same relationship to Nem as FST, should be used as an estimator for FST, whereas Weir & Cockerham (1984) and Cockerham & Weir (1993) o?er an alternative estimator y, which can be calculated from the variance between populations and the variance within populations components, derived from an ANOVA. A comparison showed that y is a less biased estimator than GST, and moreover is independent of the number of populations involved in the estimation (Cockerham & Weir 1993). Standard errors of y can be obtained by a jack-kni?ng procedure (Weir & Cockerham 1984). The signi?cance of the estimated FST can be tested, by permutation analysis of the null distributions, under the assumption that genotypes are randomly distributed among populations (Exco?er et al. 1992; Goudet 1995). Once a value for FST has been estimated, equation 1 is applied to estimate Nem, the number of migrants per population. The indirect method can potentially detect very low levels of gene ?ow. The exchange of only one migrant, be it a seed or a pollen grain fathering a seed, would lead to a GST value of 0.20; in a review of 610 allozyme studies in plants an average GST of 0.265 was found, corresponding to 0.69 migrants per generation (Hamrick 1983). As for any sample statistic, the sampling error associated with the estimate decreases as more samples are taken. For example, Giles & Goudet (1997), in an allozyme study of genetic di?erentiation among populations of Silene dioica, found FST estimates of as low as 0.030 to be signi?cantly di?erent from zero, but their sample size was around 3200 individuals.

ASSUMPTIONS OF THE INDIRECT APPROACH

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The indirect approach is based on a number of assumptions, both implicit and explicit, that have been discussed at length in several papers (Slatkin

1985a; Slatkin & Barton 1989; Porter & Geiger 1995; Giles & Goudet 1997; Neigel 1997). In an extensive simulation study, Slatkin & Barton (1989) demonstrated that the indirect method gives reasonably accurate gene ?ow estimates for both island and stepping stone models. Estimates are una?ected by the number of populations in the study, providing y is used to estimate FST. When mutation rates are much lower than migration rates, as would in general be the case when using allozymes as markers, estimates of gene ?ow are una?ected by mutation. Although both stabilizing and diversifying selection, as may occur when markers are not completely neutral, will a?ect estimates of gene ?ow, the e?ect is relatively small (Slatkin & Barton 1989). The approach outlined above has been used in many situations and as yet none of the alternative indirect methods can clearly outperform it (Neigel 1997). Nevertheless, the method should be used cautiously. No direct observations on gene ?ow are used in the method and inferences are necessarily limited by the assumptions of the model. Unless the various assumptions of the model are veri?ed by direct observations, there may be little basis for distinguishing between the e?ects of migration and other evolutionary forces that could lead to the same allele frequency distribution (Cockerham & Weir 1993). A central position in the indirect approach is taken by the equilibrium assumption. Strictly speaking equation 1 only holds for situations where an equilibrium between genetic drift and gene ?ow has been reached in a large number of populations that are constant in size and never go extinct. Although equilibrium values for y and GST are reached quite rapidly in population genetic terms (Birky et al. 1989), this will still take tens of generations. Therefore population history should be taken into account when applying the indirect method. It may be expected that more accurate estimates of gene ?ow will be obtained for species with short generation times and for situations where no disturbance has occurred for many generations than for species with long generation times and for situations with recent or regular disturbance. It is the likely violation of the demographic equilibrium assumption that renders the indirect approach unsuitable for application in metapopulation studies. Metapopulations, with frequent extinctions and (re)colonizations, are subject to constant perturbation away from this equilibrium. In fact, although the appreciable genetic di?erentiation present among local populations may suggest limited gene ?ow, gene ?ow may actually be considerable, as shown by McCauley et al. (1995) in a study of the genetic structure of a metapopulation of Silene alba. Evidence from previous ?eld studies showed that

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both extinction of local populations and colonization of empty sites occurs frequently in this metapopulation (Antonovics et al. 1994): McCauley et al. (1995) showed that the FST-value was greater among recently founded than among longer established populations. Thus in a system with high extinction± colonization dynamics, and consequently a high level of dispersal and gene ?ow, FST-values were higher, suggesting lower levels of gene ?ow than in less dynamic situations. The amount of di?erentiation among populations that are part of a metapopulation is not a simple function of the rate of gene ?ow but will also be in?uenced by spatial and temporal factors, such as frequent extinction and recolonization (i.e. metapopulation dynamics) (Slatkin 1977; Whitlock 1992), variation in age among populations, with more differentiation being observed among younger than older populations (Whitlock & McCauley 1990; Giles & Goudet 1997), spatial and temporal variation in population size, resulting in increased di?erentiation (Whitlock 1992), the degree of common origin of immigrants (Wade & McCauley 1988; Whitlock & McCauley 1990; Giles & Goudet 1997) and the size of the colonizing group (Wade & McCauley 1988; Whitlock & McCauley 1990). Giles & Goudet (1997) investigated genetic di?erentiation among populations in metapopulations of the red campion Silene dioica on an island archipelago in the Gulf of Bothnia, Sweden. About 100 islands are present within a 20-km2 area. Because there is a constant rate of land uplift in this area, the age of the islands can be estimated from their height above sea level. Knowledge of the time required before islands can be colonized by plants was used to estimate the ages of S. dioica populations. Gene ?ow among islands occurs by seeds, which move by wind and water, and by pollen transported by bumblebees. Giles & Goudet (1997) scored six polymorphic allozyme loci in 58 populations, and analysed the data to investigate the e?ects of population age and spatial arrangement of populations on FST-values. Values were signi?cantly different among age groups, from 0.057 in the youngest age group, to 0.030 in the intermediate age group to 0.066 in the older populations. The higher di?erentiation among young populations than among intermediate populations was attributed to founder e?ects and genetic drift. Young populations were not at drift±migration equilibrium. While estimating gene ?ow from an indirect approach is not possible in metapopulations, an indirect approach may still provide insight into other aspects of dispersal in metapopulations. McCauley et al. (1995) followed an approach based on models by Whitlock & McCauley (1990) to investigate the common origin of colonizers. Whitlock & McCauley (1990) de?ned two extremes: the migrant

pool mode, where colonizers originate at random from all possible source populations, and the propagule pool mode, where all colonizers originate from the same source population. They developed a model where the FST value among newly colonized sites (FSTo) is expressed as a function of the number of colonizers k, the FST value among old established populations (FSTc) and a parameter F (which will be 0 for the complete migrant pool mode and 1 for the complete propagule mode). In a Silene alba metapopulation, census data allowed McCauley et al. (1995) to estimate the number of founders (k) to be on average 4.12. By calculating FSTo for a set of newly founded populations and FSTc for a set of old established populations they estimated F to be 0.73 for nuclear markers (allozymes) and 0.89 for cpDNA markers. This suggests that most founders have a common population of origin.

THE INDIRECT APPROACH AND MOLECULAR MARKERS

Studies of gene ?ow in plants based on calculation of FST values from allozyme data are abundant (reviewed by Hamrick 1987; Hamrick & Godt 1990), but so far only a limited number of studies has been based on molecular marker data. The question is whether the application of molecular markers as opposed to allozymes may yield di?erent results. In a study of the genetic structure of Beta vulgaris ssp. maritima (sea beet) populations, the application of RFLP markers resulted in di?erent conclusions about the patterns of gene ?ow from those obtained when allozyme markers were applied to the same populations (Raybould et al. 1996, 1997). The di?erence could be explained by assuming that balancing selection in?uenced the allele frequencies in at least some of the allozyme loci. When using molecular markers in the indirect method the estimator for FST has to be adjusted to allow for the underlying evolutionary model for each type of marker. For instance, while the y and GST statistics are based on the in?nite allele model of evolution (Slatkin 1991; Weir 1996), microsatellite evolution does not comply with this model. Evidence is accumulating that microsatellite evolution follows a stepwise mutation model, where each mutation event leads to an increase or decrease of one size unit (Weber & Wong 1993; Estoup et al. 1995; Amos et al. 1996; Jarne & Lagoda 1996). Slatkin (1995) has therefore proposed a descriptor, RST, as a microsatellite-speci?c parameter of population di?erentiation, which can be estimated as described by Michalakis & Exco?er (1996). Microsatellites have been used in a further study of genetic structure of Beta vulgaris ssp. maritima populations (Raybould et al. 1998). The results showed that gene ?ow patterns for RFLP and

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microsatellite data were similar when RST estimators, but not when FST estimators, for microsatellite data were used. For restriction site data obtained from RFLP analyses, Lynch & Crease (1990) proposed the statistic NST, which partitions nucleotide diversity into within- and between-population components, and thus is a FST analogue at the DNA level. Dominant markers, like RAPD and AFLP, do not allow estimation of allele frequencies, making estimation of FST values di?cult. Several solutions have been suggested to circumvent this problem. Lynch & Milligan (1994) provided unbiased estimators of FST from RAPD data, but at the same time argued that their estimators do not solve the problem completely. Another approach is known as AMOVA (Analysis of MOlecular VAriance) (Exco?er et al. 1992). This approach is based on comparing multilocus pro?les between individuals. The genetic variance is divided into a between- and a withinpopulation component, by a hierarchical analysis of molecular variance, directly from the matrix of squared distances between pairs of haplotypes. A signi?cant between-population variance component would indicate restricted gene ?ow. This method, although developed for RFLP data, seems to work equally well for RAPD data (Wol? et al. 1997). Application of the indirect method using data from molecular markers may require adjustment to be made to the population genetic model as well as to the estimators of FST. Some molecular markers, more speci?cally microsatellites and multilocus ?ngerprints, are subject to relatively high mutation rates. Mutation rates for allozymes are in the order of 10±6, while for microsatellites they may be in the order of 10±3 (Jarne & Lagoda 1996), and mutation rates of up to 10±2 have been found for minisatellite ?ngerprints (Bruford et al. 1992). Mutation may thus become a major factor shaping FST-values, and equation 1 then changes to (Hartl & Clark 1989): FST ? 1 1 ? 4Ne m ? 4Ne m ?2?

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where m is the mutation rate. As is evident from this equation, the same distribution of genetic variation could be explained by either (or both) mutation or gene ?ow. Neigel (1997) argues that a coalescent approach, i.e. an approach where the evolutionary history of alleles is taken into account, would be able to separate the e?ects of migration and drift from the e?ects of mutation. Slatkin (1991) has worked out a relationship between FST and the average coalescent time of alleles (i.e. the number of past generations that separates two alleles from a common ancestor). The availability of DNA markers and DNA data has inspired the development of new data analysis

techniques. These techniques take into account the extra information contained in molecular markers compared with allozymes. While allozyme data are generally analysed as presence and absence of alleles (i.e. allele frequencies), for molecular markers the relatedness between alleles can be worked out. Thus the underlying evolutionary history of the observed spatial distribution pattern of alleles can be taken into account. This provides opportunities for more accurate estimates. Slatkin & Maddison (1989) introduced a measure of gene ?ow inferred from the phylogeny of alleles. This approach was further developed by Slatkin & Maddison (1990; Slatkin 1991, 1993) and is now at a point where integration of maximum likelihood estimation and coalescent inferences can be attempted. Beerli (1998) introduced a Markov Chain Monte Carlo (MCMC) method to extract the genealogy that ?ts the observed data with maximum likelihood. This MCMC method can be shown to be superior to methods based on FST estimates (Beerli 1998). In addition the method can deal with variability in mutation rates, with unequal population sizes and with asymmetrical migration between populations, such as might occur with hydrochorous dispersal of seeds in rivers. The gene ?ow estimates increase in accuracy, with increasing numbers of unlinked loci having independent coalescent trees, and also with increasing variability of the data, so that the more polymorphic loci that are included the better the estimate. Tufto et al. (1996) presented a maximum likelihood method that can be used to estimate parameters for any migration pattern from observed patterns of allele frequencies. By conditioning the likelihood on the observed mean frequency of alleles, the maximum likelihood estimator becomes independent of equilibrium allele frequencies. This method may therefore be less dependent on the validity of the equilibrium assumption that is otherwise necessary for the indirect method. Rannala & Hartigan (1996) developed another pseudomaximum likelihood estimator (PMLE) that may be applied to species with either discrete or continuous generation times, and gives more accurate estimates of Nem than FST-based estimates. The availability of highly variable molecular markers also makes other approaches to the study of aspects of dispersal possible. Rannala & Mountain (1997) presented a statistical method for detecting immigration by using multilocus genotype data. The method is based on a Bayesian statistical inference technique, with the probability of observing an allele being conditional on the observed alleles in other populations. The method allows identi?cation of immigrants even when overall di?erentiation among populations is low.

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These methods, which represent some of the new indirect approaches to inferring gene ?ow, have yet to be applied to ?eld data.

GENETIC DISPERSAL CURVES

Several theoretical studies, following the original paper by Wright (1943), have shown that when gene ?ow is restricted by distance, genetic di?erentiation among populations will increase as a function of the distance between them. Slatkin & Maddison (1990) and Slatkin (1993) have explored this process, known as isolation by distance, in detail. They showed that in equilibrium situations, and under (one- or two dimensional) stepping stone models and continuum models, a negative linear relationship will exist between the log of the estimated num? ber of migrants M (= Nem from equation 1) and the log of the geographical distance D will exist. This isolation by distance concept can be used to evaluate the validity of gene ?ow interpretations derived from the indirect approach. The method essentially involves the following steps. Gene frequency data from a number of populations are used to estimate y for all pairs of two populations. y is well suited, because it is an FST estimator that is independent of the number of populations involved ? in its estimation (Cockerham & Weir 1993). M is ? calculated from y using equation 1. Log(M) is plotted against log(D) and a least squares regression line can be ?tted, described by: ? log(M) = a ± b log(D) (3)

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A signi?cant negative relationship indicates isolation by distance, and the steepness of the slope b indicates how quickly gene ?ow declines with distance. The intercept of the regression line serves as an estimator of gene ?ow, or (in continuum models) the number of individuals in an area of panmixis (Slatkin & Maddison 1990; Slatkin 1993). Strand et al. (1996) argue that using the intercept as an estimator of Nem is not correct, because the intercept gives an estimate at unit distance, which may be different from the actual distance among populations in the system. However, standardizing Nem estimates by distance may help comparison of gene ?ow between situations where spatial distribution of populations di?ers. The regression includes all pairwise combinations of populations. Therefore data points are not independent and standard tests for signi?cance of slope cannot be applied. Instead, randomization procedures will have to be used to construct a null distribution that represents random association between ? log(M) and log(D). If the observed slope falls outside this null distribution, then signi?cant isolation by distance is shown to exist. Alternatively a Mantel test, to test the signi?cance of the association

? between the matrix of M-values and the matrix of geographical distances, can be applied (Mantel 1967). Equation 3 describes the relationship between the estimated number of migrants and distance, and can thus be regarded as a genetic dispersal curve. These curves and the isolation-by-distance procedure may help the study of dispersal in two distinct ways. First, isolation by distance will only be detectable at equilibrium (Slatkin 1993). Any situation where gene ?ow is restricted should lead to isolation by distance at equilibrium. Thus, if isolation by distance can be detected, this increases the likelihood that the system is at equilibrium and therefore the con?dence one can have in the gene ?ow estimate obtained from the indirect approach. If no isolation by distance is detected, then either dispersal is not distance dependent (which is, apart from very small spatial scales, unlikely in plants) or no equilibrium exists. Slatkin (1993) formulated a few non-equilibrium expectations, under a radiation model (i.e. a single ancestral population gives rise to all of the extant populations). He distinguished two results: (i) no isolation by distance detected and overall low estimates of Nem, and (ii) no isolation by distance detected and overall high estimates of Nem. Under the radiation model the ?rst result would indicate absence of ongoing gene ?ow, while the second result would indicate recent colonization of populations. It should be stressed, however, that such interpretations depend strongly on the underlying demographic model. For instance in a metapopulation absence of isolation by distance may be expected to be associated with low Nem estimates, even though colonization is continuing. The isolation by distance approach has been applied to a limited number of plant species. In some studies isolation by distance was detected (Potamogeton pectinatus: Hollingsworth et al. 1996; Mader et al. 1998; Silene dioica: Giles & Goudet 1997; Lonicera periclymenum: Grashof-Bokdam et al. 1998) but in other species no such pattern could be demonstrated (Cecropia obtusifolia: Alvarez-Buylla & Garay 1994). Strand et al. (1996) used the isolation-by-distance procedure in a study of Aquilegia populations in the south-western United States and Mexico. They used ? cpDNA haplotype variation to construct a log(M) ± log(D) plot. No signi?cant relationship was detected and Nem estimates were low, suggesting the absence of ongoing gene ?ow. Slatkin (1993) had previously shown that under complete isolation the Nem estimate depends on the e?ective population size Ne and the number of generations since isolation t, so that drift alone would lead to Nem = Ne/t. When t was estimated from paleaobotanical data and Ne was estimated from census data from populations to give a range of Nem values that could be explained

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by drift and isolation alone, the population estimates fell well within this range, supporting the interpretation that the observed di?erentiation patterns indicated an absence of ongoing gene ?ow. The second way the isolation-by-distance procedure may help is by comparing genetic dispersal curves. If gene ?ow is more distance-restricted in situation A than in situation B, then regression line A should be steeper than regression line B. This can be tested by jack-kni?ng procedures where random samples are omitted from the analyses, to construct con?dence limits for each of the slopes. Mader et al. (1998) investigated genetic di?erentiation in a world-wide collection of Potamogeton pectinatus, Sago pondweed, using RAPD and cpDNA methods. The species reproduces predominantly by vegetative propagation (tubers) but also produces a limited amount of seed. The tubers are consumed by Bewick's swans, Cygnus columbianus bewickii, that migrate from their wintering grounds in western Europe to breeding grounds in Siberia, and may play a role in the long-distance dispersal of the species. A highly signi?cant correlation between pairwise genetic distances and pairwise geographical distances was found. The association between genetic and geographical distance was signi?cantly higher in non-swan visited populations than in swan-visited populations, resulting in a steeper slope of the regression line for non-swan visited populations. While the data set did not allow separation of historical from current processes, this result suggests that swan-mediated dispersal reduces the amount of genetic di?erentiation.

POLLEN-TO-SEED RATIO ESTIMATES

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A second application of the indirect approach where the use of molecular markers is very informative, is based on the potential of these markers to separate seed from pollen ?ow. This is often an important distinction. For instance, if a high level of gene ?ow is measured among existing populations, that does not necessarily mean that the colonization probability of new sites is high. Gene ?ow might be mainly pollen mediated, while seed ?ow is in fact restricted. As nuclear markers are transmitted through both seeds and pollen, while cpDNA markers are often transmitted only in seeds (in many angiosperms), comparison of the level of di?erentiation in the two types of markers provides information on the relative contribution of pollen and seed ?ow to the total gene ?ow. The identi?cation and application of cpDNA polymorphisms was greatly facilitated by the description of universal cpDNA polymerase chain reaction (PCR)-primers (Demesure et al. 1995). Previously, cpDNA had mainly been used at the interspeci?c level, for establishing phylogenies. It

was generally believed that the chloroplast genome was too conserved to be of use at the intraspeci?c level. However, it has been reported that intraspeci?c cpDNA polymorphisms are more widespread than once believed (Olmstead & Palmer 1994; McCauley 1995; see also Table 2). The level of polymorphism depends on the taxa investigated and on the chloroplast region used. Some regions in the chloroplast genome are highly conserved and display an absence of polymorphism, whereas other regions, like intergenic spacer and intron regions, are more variable and may even be variable at the (meta)population level (Gielly & Taberlet 1994). Formal models that allow calculation of the pollen-to-seed ?ow ratio, based on the values of FST for nuclear and cpDNA markers, have been published for island models (Petit et al. 1993a; Ennos 1994) and for isolation-by-distance models (Hu & Ennos 1997). Application of these models to existing data has resulted in ratios that agree with those which might have been predicted from knowledge of the biology of the species (Table 3). Thus in a windpollinated plant with very large seeds (Quercus petraea; Kremer et al. 1991) pollen dispersal contributes much more to gene ?ow than seed dispersal does, while in a sel?ng species with small seeds (Hordeum spontaneum; Brown 1979; Nevo et al. 1979; Neale et al. 1988) a more even pollen-to-seed dispersal ratio was found (Table 3). The approach has been explored in some detail by McCauley (1994, 1997) and McCauley et al. (1995) in their study of spatial patterns in North American populations of the dioecious species Silene alba. They measured population structure of nuclear markers by using seven polymorphic allozyme markers, while di?erentiation among populations in cpDNA was measured by using restriction analysis of a particular part of the chloroplast genome. FST values were about ?ve times higher for the chloroplast haplotypes than for the allozymes (McCauley 1994), leading to a pollen-to-seed ?ow ratio of 11.4 [according to the Ennos model (Ennos 1994)]. Thus gene ?ow in this species is predominantly pollenmediated and seed ?ow is much more restricted. In a study at three di?erent spatial scales, at kilometres, tens of metres and metres, it was demonstrated that the ratio of pollen to seed ?ow changes with the spatial scale (McCauley 1997). Pollen-toseed movement ratios of 3.4, 9.2 and 124.0 were found at the large, intermediate and small scales, respectively. Thus within populations gene ?ow is mainly pollen mediated, while between populations the contribution of seed and pollen ?ow to dispersal is more equal. This is in agreement with the putative metapopulation structure, as suggested by data on extinction and colonization of local populations (Antonovics et al. 1994). The rate of local extinction must be balanced by the rate of colonization, and

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# 1999 British Ecological Society Journal of Ecology, 87, 551±568 Number of populations FST 20 32 8 8 8 1 1 3 3 3 8 58 22 11 6 5 3 19 10 35 40 30 5 3 2 7 8 8 1 1 80 470 171 81 104 71 98 90 123 180 188 245 262 95 55 191 380 365 13 4 3 3 7 6 3 11 4 8 8 3 1 1 1 3 8 6 1±3 1±2 1±2 1±2 1±3 1±4 1±2 1±3 1±4 ± 1±4 1±3 ± ± ± 2±3 3±6 2±5 Number of individuals Number of tested enzymes Number of haplotypes 0.621 0.905 0.925 0.769 ± ± ± 0.600 0.674 ± 0.430 ± ± ± ± ± ± ± Number of haplotypes per populations References Byrne & Moran (1994) Petit et al. (1993b) Petit et al. (1993b) Petit et al. (1993b) Mason-Gamer (1995) Mason-Gamer (1995) Mason-Gamer (1995) El Mousadik & Petit (1996) McCauley (1994) Forcioli et al. (1994) D. Forcioli (unpublished data) Neale et al. 1988 Wang & Szmidt (1994) Wang & Szmidt (1994) Wang & Szmidt (1994) Wang & Szmidt (1994) Dong & Wagner (1994) Dong & Wagner (1994)

Table 2 Evidence for within-population variability in chloroplast DNA markers

Species

Eucalyptus nitens (Myrtaceae) Quercus petraea (Fagaceae) Q. robur Q. pubescens Coreopsis grandi?ora var. grandi?ora (Asteraceae) Coreopsis grandi?ora var. harveyana (Asteraceae) Coreopsis grandi?ora var. saxicola (Asteraceae) Argania spinosa (Sapotaceae) Silene alba (Caryophyllaceae) Beta vulgaris ssp. maritima Beta vulgaris ssp. maritima Hordeum vulgare Pinus tabulaeformis Pinus yunnanensis Pinus massoniana Pinus densata Pinus densata Pinus contorta

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Table 3 Results of application of the Ennos model (Ennos 1994). Pollen-to-seed ?ow ratios are calculated from FST and FIS values, which are estimated independently. FST nuclear refers to genetic di?erentiation in nuclear markers; FST cytoplasmic refers to genetic di?erentiation in cytoplasmic markers; FIS is the inbreeding coe?cient Species Silene alba Silene alba, large scale Silene alba, intermediate scale Silene alba, small scale Silene vulgaris Quercus petraea Pinus contorta Pinus radiata Pinus attenuata Pinus muricata Hordeum spontaneum FST nuclear 0.134 0.128 0.051 0.027 0.13 0.037 0.0608 0.13 0.13 0.22 0.49 FST cytoplasmic 0.674 0.613 0.546 0.875 0.62 0.884 0.66 0.833 0.833 0.882 0.735 FIS 0 0.047 0.056 0 0 0 0 0 0 0 1 Pollen-to-seed ?ow ratio 11.4 3.4 9.2 124.0 8.9 196 28 31 44 24 4 Reference McCauley (1994) McCauley (1997) McCauley (1997) McCauley (1997) McCauley (1997) Ref. in Ennos (1994) Ref. in Ennos (1994) Ref. in Ennos (1994) Ref. in Ennos (1994) Ref. in Ennos (1994) Ref. in Ennos (1994)

thus seed ?ow must be of importance for the system. While the method is an elegant extension of the indirect approach, it does have some limitations. It is important to remember that the whole approach relies on strict uni-parental inheritance of cpDNA markers, and would be seriously compromised by even small amounts of paternal leakage. A practical limitation is that measures of the FST-values cannot be replicated across cytoplasmic markers. The chloroplast (or mitochondrial) DNA does not recombine, and all markers are therefore completely linked so that no independent measures can be made (Ennos 1994). More generally, no statistical procedure has so far been designed to test the signi?cance of pollen-to-seed ?ow ratios. It remains to be investigated whether the resampling strategies used to evaluate the signi?cance of FST estimates can be applied to testing of pollen-to-seed ?ow ratios. Despite these limitations, the approach is promising and could lead to new insights into the dispersal process.

Direct measurements of gene ?ow
The basic approach used in direct measurement is to determine the genotypes of all reproductive adults in the population and compare them with the genotypes of a representative sample of seedlings. By means of maximum likelihood methods (Meagher & Thompson 1987) or forms of paternity exclusion analysis (Devlin et al. 1988; Devlin & Ellstrand 1990) it may be possible to achieve the ideal that the parents of each o?spring can be identi?ed. A frequency plot of the physical distance between parent and o?spring describes the realized gene ?ow within the population. The frequency of individuals that carry alleles found in the o?spring, but not in the parent, population is an estimate of the realized seed dispersal into the population. Discrepancies between indirect and direct gene ?ow estimates have been

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found in several cases (Campbell & Dooley 1992; see summary in Rousset 1997) but may be expected because the two approaches di?er in the information they provide: while the indirect approach gives the equilibrium level of gene ?ow over the past generations, the direct method gives the actual gene ?ow in the present year. One of the problems in the past with the direct approach has been the lack of su?ciently variable markers, leading to foreign and local gametes (cryptic gene ?ow) being indistinguishable, and thus underestimation of actual gene ?ow. With the development of highly variable markers, especially microsatellites, this problem is alleviated to a large extent, as is illustrated in a study of gene ?ow in oak trees (Dow & Ashley 1996). In a stand of Quercus macrocarpa, 62 adult trees and 100 random saplings were screened at four hypervariable microsatellite loci. Of the 100 saplings, 71 had only one parent within the population, indicating that gene ?ow, most likely through pollen, was extensive. Fourteen of the saplings had no parent in the population and thus must have arrived in the population through the dispersal of acorns. The results illustrated that long-distance seed dispersal may be more common than was previously thought and that long-distance pollen dispersal in this species is extensive. The same approach was followed in a study of pollenmediated gene dispersal in the tropical tree Gliricidia sepium (Dawson et al. 1997), where long-distance dispersal events, although rare, could be identi?ed. Arens et al. (1998) analysed dispersal of black poplar, Populus nigra L., along Dutch rivers, using AFLP markers. This species is rare along the Dutch Rhine, where the genotypes of 33 and 61 seed-producing mature trees in two populations were determined. Thirty-?ve young trees were sampled in the vicinity of the two populations and in three patches downstream and were also genotyped, and possible parents were assigned through exclusion analysis,

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i.e. pairs of mature trees where both lacked one or more bands that were present in a young individual were discarded as possible parents. Nineteen young trees had no parent among the 94 mature trees, leading to the conclusion that they must have been established from seeds that came from populations upstream. Because AFLP markers are dominant, no inclusion analysis, i.e. when a mature tree shares a band with a young individual it can be assigned as a possible parent, could be performed. Thus dominant markers like AFLP provide less discriminative power in these types of analyses than codominant markers such as microsatellites. These studies illustrate the great potential of highly variable markers, and especially of microsatellites, in the direct measurement of gene ?ow and dispersal. Because of the high variability of microsatellites, the amount of cryptic gene ?ow that has to be estimated is reduced. The large number of low frequency alleles that is typical of microsatellites greatly increases the probability of excluding all but the true parents. Even though some attributes of microsatellites, such as homoplasy (identical alleles with di?erent evolutionary histories) and relatively high mutation rates (Jarne & Lagoda 1996), might sometimes lead to biased assessments of parent±o?spring relationships, their usefulness for parental analysis and direct measurements of gene ?ow and dispersal is obvious. Studies using microsatellites will certainly contribute to our knowledge of plant dispersal in the (near) future. The direct estimation of dispersal in plants has some problems of its own. First, in species with a long-lived seed bank, seedlings that apparently have no parents within the population might have emerged from the seed bank. Secondly, in shortlived species, for instance annuals, parents may have died before their seedlings emerge. In both cases seed and pollen ?ow level would be overestimated. Therefore, the method is most appropriate for longlived species and species without a seed bank. A more general limitation of the method is that it can only be applied to relatively small populations. In large populations the method would soon become impractical. However, with the development of automated laser-detection equipment and ?uorescent-labelled microsatellite primers, the number of samples that can be screened for microsatellite variation within a given time span is increasing, thereby stretching the limits of the practical feasibility of the method.

Conclusions and prospects
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In this paper we have addressed the question of how the population genetic practice of estimating gene ?ow can aid in the study of seed dispersal in plants. The basic approach outlined in this paper is the fol-

lowing: population genetic methods allow quanti?cation of the amount of genetic di?erentiation among populations, and subsequently estimation of the rate of gene ?ow. This ?ow is comprised of a seed dispersal and a pollen dispersal component, and the contribution of pollen movement to the rate of gene ?ow must therefore be estimated. Seed dispersal is equivalent to overall gene ?ow minus the contribution due to cross-pollination. A major role in this approach is played by the availability of molecular markers. Where studies of population structure using allozymes were often frustrated by insu?cient variability, molecular markers can almost always be found with a suitable amount of variation. Because many di?erent markers exist, and even more are being developed (Strand et al. 1997), it may be possible to ?ne-tune the amount of variation to the question asked and the spatial scale of study. Screening di?erent markers in the same set of individuals allows us to test interpretations of the patterns of di?erentiation. Furthermore, because nuclear and cytoplasmic markers have become available, separation of seed from pollen ?ow has become possible, thus allowing a separation of the amount of gene ?ow from the opportunities of (re)colonization. Highly variable microsatellite markers have made the direct approach to the measurement of gene ?ow more feasible. The application of markers in the indirect approach allows the potential to estimate the importance and frequency of rare long-distance dispersal events, because it focuses on the consequences of dispersal rather than on following dispersing propagules through space. However, the interpretation of the data obtained in the indirect method is based on a number of important assumptions. For many of these assumptions it has been shown that although deviations will cause bias, estimates will still be in the right order of magnitude. The equilibrium assumption may be the most critical of all. As it is unknown what percentage of populations is near equilibrium, incorporating information about the history of populations is therefore an important aspect of interpreting results of the indirect approach. Other methods of studying dispersal are, of course, also based on assumptions. For instance, in seed trap experiments often one central isolated individual is used as seed source (Thiede & Augspurger 1996) and the results are then assumed to be representative of whole populations. In di?usion modelling approaches, assumptions are made about the distribution of wind speed, about the in?uence of turbulence and about the shape of the landscape (Greene & Johnson 1996). For all methods the results are valid only for as long as the assumptions are valid. Thus when applying any method its assumptions should be made explicit,

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and additional research, testing whether assumptions are likely to hold in the speci?c study situation, is needed to evaluate the validity of dispersal estimates. Bearing this in mind, the population genetic approach to the study of dispersal will be helpful in many cases. The indirect method allows the measurement of low levels of gene ?ow and thereby enables speci?c questions to be tested. These include the e?ect on dispersal of di?erent spatial arrangements of populations, an exercise very relevant for landscape planning and conservation issues. Similarly the question of whether populations are e?ectively isolated can be addressed, hypotheses about migratory pathways in the landscape can be investigated by comparing the ?t (R2) of a genetic dispersal curve with the distance axis de?ned as-thecrow-?ies with a genetic dispersal curve where distance is expressed according to the supposed migratory pathway (e.g. dispersal through road verges, rivers), and maximum likelihood methods within the indirect approach allow investigation of speci?c hypotheses, such as whether dispersal in rivers is uni-directional. Many more examples could be given. Although some, or all, of these aspects have been studied with allozymes, the development of the seed vs. pollen ?ow ratio approach made possible by the availability of cytoplasmic molecular markers may be particularly useful in allowing closer approximation of the seed dispersal part of gene ?ow. Many questions are awaiting further application of this method, including construction of pollen vs. seed dispersal curves (McCauley 1997), comparison between species with di?erent modes of dispersal (Ennos 1994) and assessment of the extent of metapopulation structure (McCauley 1997). Although indirect methods unfortunately cannot be used to estimate the amount of dispersal in metapopulations, they can, in conjunction with data on the history of the populations, still give insight into other aspects of dispersal, such as the degree to which migrants have a common origin. Direct methods can be used to test the e?ect of the establishment of a corridor on the connectivity among populations, and may provide particular insight into how local within-population processes, such as allocation to sexual reproduction, and frequency and percentage of ?owering, will in?uence regional dynamics. There is no hope that a notoriously di?cult to trace process like long-range seed dispersal, with its often complicated spatial and temporal dimensions, will prove measurable using one single, easy-toapply method that is applicable in any situation. Perhaps the biggest merit of the population genetic approach is therefore that it supplements the ecological approach. Clear di?erences exist between the information provided by ecological compared with

indirect and direct population genetic approaches. While ecological methods measure dispersal, population genetic methods measure the sum of dispersal and establishment. While the indirect method gives an estimate of average dispersal over past generations, the ecological and direct population genetic methods measure actual dispersal in the present year. These di?erences, which should be kept in mind when comparing results of the di?erent approaches, also give a combined approach great value. Molecular markers and the population genetic approach should not be seen as a replacement for ecological methods. Instead, both types of information should supplement each other. Applying di?erent methods to the same material will give us more insight into the dispersal process than can be obtained from either of the approaches on its own. For instance, comparing ecological estimates of dispersal with estimates based on a direct population genetic approach will give information about the contribution of germination and establishment to the colonization process. Comparing ecological and genetic dispersal curves gives information about the possible deviation of current dispersal levels from past gene ?ow levels. In that respect, molecular markers provide a tool for an independent test of hypotheses that were formulated based on ecological data, and ecological studies may test interpretations of observed distributions of genetic variation. Silvertown (1991) asked whether the use of molecular markers would lead to qualitatively new insights. Our review suggests we may expect new and exciting insights into the process of dispersal using molecular markers. The most obvious studies to start with would be making comparisons between ecological and genetic dispersal curves. This will tell us whether our view of plant dispersal has been biased, and by how much, in the past. Another potentially fertile area is the application of the pollen-to-seed ratio methods: the markers are available, the models are ready for application. For instance, comparing seed ?ow with pollen ?ow in a number of landscape structures using this method may shift our perception of the e?ect of landscape fragmentation on seed dispersal and the e?ciency of establishing dispersal corridors, and will help in identifying groups of species that are susceptible to fragmentation, based on their pollen-to-seed ?ow ratios. At the moment these approaches are very promising and may guide us to a better understanding of dispersal in plants.

Acknowledgements
We would like to thank Michael Cain, Richard Ennos and David McCauley for providing us with

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preprints of their papers, and Alan Gray, Alan Raybould and two anonymous referees for constructive criticism of earlier versions of this paper. This work was supported by an EC-TMR grant to N. J. Ouborg.

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