Measuring plant dispersal: an introduction to field methods and experimental

design

James M. Bullock1,*, Katriona Shea2 and Olav Skarpaas2,31NERC Centre for Ecology and Hydrology, Winfrith Technology Centre, Dorchester, Dorset, DT2 8ZD, UK;2Department of Biology and IGDP in Ecology, The Pennsylvania State University, 208 Mueller Laboratory,University Park, PA, 16802, USA; 3Centre for Ecological and Evolutionary Synthesis, Department ofBiology, University of Oslo, PO Box 1066, Blindern, N-0316, Oslo, Norway; *Author for correspondence(e-mail: jmbul@ceh.ac.uk; phone: +44-1305-213591; fax: +44-1305-213600)

Received 9 December 2005; accepted in revised form 14 February 2006

Key words: Dispersal kernels, Dispersal mechanism, Long-distance dispersal, Model fitting, Optimisation,Simulation models

Abstract

The measurement of plant dispersal is vital for understanding plant distribution and abundance at differentscales. However, dispersal is difficult to measure and there is a lack of guidance for researchers new to thesubject. In this paper we provide advice on methods for measuring dispersal in the field and approaches toexperimental design. First, we encourage clear exposition of the aims of the dispersal study and the ultimateuse to which the data will be put (e.g. local dynamics, invasion processes, etc). We outline the types ofdispersal exhibited by plants and emphasise that many species are dispersed by multiple processes, whichare not necessarily related to putative adaptations. Few studies properly address the full range of processesby which a species is dispersed. We review methods for measuring plant dispersal, summarising the type ofdispersal measured and problems with each method. We then outline the major questions about effort to beconsidered in sampling protocols and present an optimisation algorithm for designing dispersal studiesgiven a suite of options, and biological and resource constraints. We propose and demonstrate a simulationmodelling approach to comparing the data quality obtained by alternative experimental designs. Inte-grating simulation models with pilot studies offers a rapid route to improved estimation methods. We thendiscuss functions commonly fit to dispersal data and recommend caution as none is a priori the bestdescription of the dispersal process. Finally, we call for a better description and understanding of dispersalkernels by: a more rigorous approach to designing dispersal measurement; better targeting of dispersalstudies to particular questions; and achieving a deeper understanding of the mechanisms underlying dis-persal, so that we can move from descriptions of pattern to a grasp of process.

Introduction

The aim of this paper is to provide researcherswith an introduction to the methods available forstudying plant dispersal and guidance on how to

design dispersal experiments. The distribution andabundance of species are determined by thedynamics of individuals at a location (demogra-phy) and the movement of individuals betweenlocations (dispersal). Although both processes are

Plant Ecology (2006) 186:217 –234 � Springer 2006

DOI 10.1007/s11258-006-9124-5

equally important, methods and protocols forstudying demography are far better developed andmore commonly used (Menges 2000; Caswell andKaye 2001; Stokes et al. 2004) than those for dis-persal, because movement of individuals is muchharder to study. Researchers have tried a range ofingenious approaches to overcome these difficul-ties, and the study of plant dispersal would bemuch aided by a synthetic overview of approachesto experimental design. Furthermore, many dis-persal experiments are designed in an ad hocmanner with little consideration of the full rangeof issues. Two recent papers provide some help.Nathan et al. (2003) review methods for measuringlong-distance dispersal, with examples takenmostly from the animal kingdom. In general, thereappears to be a relative lack of plant studiescompared to animal dispersal and migrationstudies, possibly because moving animals areusually larger and hence easier to follow thandispersive plant stages. However, Nathan et al.(2003) provide particularly useful guides to indi-rect methods involving genetic markers andmechanistic models. Greene and Calogeropoulos(2002) mostly consider fitting parametric functionsto dispersal data and some general methods forestimating dispersal. There is a need to comple-ment these papers with more specific guidance onhow to go about designing a plant dispersal study.We aim to provide guidance in this paper byhighlighting the issues to be considered in studyingplant dispersal, assessing the range of methods forthe direct measurement of dispersal and their prosand cons (and providing key references), devising aprotocol for optimising the design of plant dis-persal studies, and considering the fitting ofmodels to dispersal data.

The need for dispersal data: objectives

Plant ecologists are interested in dispersal fornumerous reasons (Bullock et al. 2002). Withinpopulations, dispersal affects the spatial arrange-ment of individuals and thus the biotic and abioticenvironment they experience (Bolker and Pacala1999). At larger scales dispersal patterns determinethe type of regional dynamics shown by plants andthe relevance of metapopulation theory (Freckl-eton and Watkinson 2002; Ehrlen and Eriksson2003). Knowledge of dispersal is essential for

predicting the ability of species to track climatechange (Watkinson and Gill 2002), range expan-sion of non-native species (Higgins et al. 2001), orre-colonisation by endangered species (Coulsonet al. 2001).

Clearly, a dispersal study must target the type ofdata required and the ultimate question beingaddressed. Scale is a vital consideration. Anunderstanding of local population processes mayrequire detailed data on dispersal over a fewmetres whereas dispersal over hundreds of metresmay be necessary for metapopulation or invasionstudies. Model requirements for dispersal datadiffer. Mathematical models of population spread,such as those using integro-difference equations,are highly sensitive to variation in the tail of thedispersal kernel whereas variation in mean dis-persal distance has little impact (Kot et al. 1996;Shigesada and Kawasaki 2002; Caswell et al.2003). In contrast, data on mean or modal dis-persal distances are often more important in spa-tially explicit models of competition (Bolker andPacala 1999) or models of Evolutionary StableStrategies which seek to understand the optimaldispersal characteristics of a population (Geritzet al. 1999; Silvertown and Bullock 2003). Goodestimates of entire dispersal kernels may beunnecessary; metapopulation models often requireonly simple data on the number of plants movingbetween, and staying within, population patches(Thomas and Kunin 1999).

Types of dispersal

While seed and spore (of some lower plants) dis-persal is studied most commonly, some plants canalso disperse as fragments (e.g. pieces of rhizome,stolon or root), bulbils or through clonal growth.Many species disperse more than one type ofpropagule, such as seeds and rhizome fragments(e.g. Fallopia japonica Forman and Kesseli 2003)or plant fragments and spores (e.g. Undaria pin-natifida Forrest et al. 2000).

Plant fragments and bulbils are relatively largeand are usually dispersed simply in flowing water,by wind or in soil which is moved, for example, bymachinery or animals (Beerling et al. 1994;Ronsheim 1994; Forrest et al. 2000; Thomas et al.2005). Spores of lower plants are also dispersed bywind, water and soil (Sundberg and Rydin 2000;

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Gaylord et al. 2002; Spijkerboer et al. 2002).Higher plants show an impressive variety ofadaptations for seed dispersal (Ridley 1930; vander Pijl 1982; Willson and Traveset 2000) relatingto dispersal by ballistics (e.g. explosive pods), wind(pappi, samaras), water (air spaces, corky tissues),sticking to animals (spines, hooks, mucilage),being ingested by vertebrates (fleshy fruit) or beingcarried by invertebrates (elaiosomes). Dispersal ofan individual seed may be a complex process.Ballistic dispersal is followed by seed-carrying byants in many species (Ohkawara and Higashi 1994)and wind-dispersed seeds may undergo secondarydispersal after coming to rest, by being blownalong smooth substrates such as snow or sand(Greene and Johnson 1997; Schurr et al. 2005).

However, putative adaptations do not describecompletely the dispersal ecology of a species. Forexample, Rhinanthus minor has extensions to theseed coat which aid dispersal by wind, but it is alsodispersed by farm machinery, grazing animals,floods, and in earthworm guts (Bullock et al.2003). The fleshy fruits of Crataegus monogynaseem a clear adaptation to dispersal by birds, butthey also float well in rivers and are gathered byhumans (Ridley 1930). Brassica napus has noobvious dispersal mechanism but seeds are dis-persed short distances by the wind (J. Bullock,unpublished data), and longer distances in rivers(Scott and Wilkinson 1999) and by spillage duringtransport of harvested seeds (Crawley and Brown1995). These examples illustrate the importance ofhumans, who disperse seeds by many activities;e.g. on machinery and vehicles, in soil and ballastor even intentionally (Hodkinson and Thompson1997). Many dispersal studies do not consideradequately the different ways by which propagulesof a species are dispersed, often targeting solely thevector suggested by putative adaptations. Certainways of measuring dispersal are only relevant forparticular modes of dispersal (Table 1) and dif-ferent dispersal modes may result in very differentdispersal patterns (Bullock et al. 2003). Therefore,it may be necessary to use multiple measurementmethods and experimental designs to describe thedispersal kernel accurately. Later we consider howto combine data from these multiple sources into asingle dispersal kernel.

Long-distance dispersal – the extreme tail of thedispersal kernel – is receiving a lot of attention(Bullock and Clarke 2000; Nathan et al. 2003).

Some long-distance dispersal may be caused byunusual processes (Higgins et al. 2003), but muchis simply the extremity of standard types of dis-persal (Nathan et al. 2002; Tackenberg 2003).Thus, in many cases the practical solution tomeasuring long-distance dispersal is to sampleusing the protocols we describe below over fardistances or large areas, if this is possible. How-ever, for extreme long-distance dispersal, onlycertain methods, such as mechanistic models orgenetic markers, will be possible (Nathan et al.2003; Jones et al. 2005; Nathan 2005).

Options and constraints in designing a dispersal

study

Decision making

There is a wide variety of approaches for mea-suring dispersal and choosing the best approachfor a given situation involves answering three mainquestions:

(1) What is the objective of the dispersal study?(2) What are the options available for measuring

dispersal?(3) What are the constraints on the experimental

design?

If the options and constraints are weightedappropriately, the answers to these questions willallow for an optimal experimental design, giventhe aim of the study. The answer to the firstquestion, following the above, should consider theuse to which the data will be put and the differenttypes of dispersal exhibited in the study system.Below, we focus on the latter two questions anddescribe what options to consider when planningto measure dispersal, and possible constraintslimiting use of such options.

Propagule sources

Propagules may be measured following individualrelease by the researcher or following abscissionfrom plants. In the latter case single plants andisolated patches of plants (point sources) areobvious sources of propagules with little likelihoodof contamination from other seed sources (though

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Table

1.A

summary

ofpossible

methodsto

track

individualpropagules,withreferencesthatdescribetheapproaches.

Method

Forwhatpropagule

types?

Issues

andproblems

References

Tracking

Followingwind-dispersedpropagules

–abscissionin

thefield

Largeandeasily

visible

Veryslow

data

gathering–especially

waitingforabscission

None(practicaldifficulties

meannoonehastriedthis)

Difficultto

follow

over

longdistances

Followingwind-dispersedpropagules

Largeandeasily

visible

Slow

data

gathering

GreeneandJohnson(1989)

–handrelease

intheopen

orwindtunnels

Difficultto

follow

over

longdistances

GreeneandJohnson(1997)

Tunnel

length

limitsdetectionofthetail

JongejansandSchippers(1999)

Artificialabscission(see

text)

Followingants

carryingseeds

Antdispersed(elaiosomes)

Slow

data

gathering

Cain

etal.(1998)

Observer

mayaffectbehaviour

Ohkawara

andHigashi(1994)

Followingvertebratescarryingseeds

Vertebrate

dispersed

Slow

data

gathering

Murray(1988)

Maybeim

possible

tofollow

theanim

als

Jansenet

al.(2002)

Seeddepositionmaybedifficultto

observe

Observer

mayaffectbehaviour

Re-locating

Re-locatingmarked

propagules

Largeandeasily

visible

Mayneedto

searchlargeareas

Bossard

(1990)

–fluorescentpowder

Re-locationmaybedifficultin

dense

or

complexvegetation(bestin

open

habitats)

HorvitzandSchem

ske(1994)

–paint

Kalisz

etal.(1999)

–radioisotopes

Forget

(1996)

–thread

Locatinggerminants/seedlings

Any,althoughdistinctive

germinants/seedlingsare

needed

Mayneedto

searchlargeareas

GreeneandCalogeropoulos(2002)

Heterogeneousrecruitmentmeansseed

dispersal

kernel

isapproxim

atedpoorly

Difficultyin

relatingseedlingsto

aparticularparent

Methodsinvolveeither

followingpropagulesin

realtimeorre-locatingindividualdispersedpropagules.Theseprovidedata

ondistance

(andpossibly

direction)ofeach

propagule

from

thesource.

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for plant patches source geometry may affect op-tions, see Greene and Calogeropoulos 2002).However, often one is interested in dispersal withina continuous distribution of plants (e.g. a forest),where sources are more difficult to identify withcertainty. In these cases statistical methods areavailable to generate individual dispersal curvesand we discuss these below. Alternatively, indi-vidual sources (plants or plant parts) can betransplanted to simplified surroundings; e.g.shrubs into large open fields (Bullock and Clarke2000), or branches into the laboratory (Stamp andLucas 1983). However, simplification by excludingother plants which intercept seeds may alter thedispersal kernel (Bullock and Moy 2004; Greeneet al. 2004).

For wind-dispersed plants, propagules can bereleased individually in wind tunnels (Jongejansand Schippers 1999), or in open areas such asparking lots or fields (Greene and Johnson 1989;Jongejans and Telenius 2001). Individual release ofpropagules (usually seeds) is popular, but it cangive a very different kernel estimate (seed shadow)to that obtained using traps around a plant(Skarpaas et al. 2004). Such differences may arisebecause of source geometry or the effect of theseed source on wind patterns, or because theconditions during dispersal (e.g. wind speeds, airhumidity) sampled by experimenters differ fromthose during natural seed abscission (Greene andJohnson 1992; Schippers and Jongejans 2005).Wind tunnels are generally unrepresentative offield conditions and will not give good estimates ofthe field dispersal kernel, although they can beuseful for testing of mechanistic models (Jongejansand Schippers 1999).

Individual release of propagules can be usedfor other dispersal vectors, e.g., by setting updepots for propagules to be gathered by animals(Ohkawara and Higashi 1994), feeding orattaching propagules to animals (Fischer et al.1996), or putting propagules into water (Anders-son et al. 2000; Ha et al. 2003). Again, oneshould be careful that artificialities such as thetiming of release or the number of seeds put intoa depot (rates of removal are often higher with ahigher seed density (Kaspari 1993; Gorb andGorb 2000)), or even direct handling of seeds(thus leaving olfactory cues which may affectanimal behaviour (Wenny 2002)) do not affectthe measured dispersal kernel.

Clumped and directional dispersal

Many dispersal vectors may deposit propagules ina clumped fashion. Obviously, there are usuallymore propagules close to the source, but there aremany causes of clumping independent of distancefrom the source. These include animal behaviour –rodents may hoard seeds (Jansen et al. 2002), antstake them to the nest (Peakall and Beattie 1995) orbirds deposit them in particular defaecation loca-tions (Verdu and Garcia Fayos 1996) – or physicalprocesses such as trapping of seeds by other plants(Bullock and Moy 2004), or parts of rivers wherewater flow is slowed (Merritt and Wohl 2002).Factors such as a prevailing wind direction, uni-directional water flow and biased movement byanimals lead to differences in the number ofpropagules dispersing in different directions, andin the dispersal distances – anisoptropy (Bullockand Clarke 2000; Wagner et al. 2004). Bothclumping and anisotropy have consequences forboth experimental design and data analysis (e.g.fitting models). We return to these issues below.

Direct methods for measuring dispersal

Direct measurement of dispersal distances canbe done by tracking individual propagules(‘Lagrangian’ methods) or by determining howmany propagules arrive at specific locations(‘Eulerian’ methods), often in traps. Tracking canbe done by following propagules in real time or byre-locating individual propagules once they havecome to rest. Below we compare broad approachesto measuring dispersal and go into some detailabout alternative approaches. These are summar-ised in Tables 1 and 2.

Nathan et al. (2003) suggest that, in principle,tracking methods are a better option than trappingbecause the former provide exact individual dis-persal distances and should allow long-distancedispersal events to be detected, while the latter re-quire assumptions about where propagules will falland are limited by the boundaries of the trappingarena (although re-locating propagules may im-pose similar problems). Tracking will also allowone to detect clumped and anisotropic patterns ofpropagule deposition. However, tracking will oftenbe specific to a dispersal vector (e.g. wind or a birdspecies), whereas trapping quantifies propagules

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deposited at a location irrespective of the vector.This is a benefit of tracking if one is interested inspecific vectors, but it may not give the completedispersal kernel, integrated over all vectors, that issupplied by trapping. In particular, tracking ismost useful for animal-dispersed propagulesbecause the animal itself can be tracked (seebelow).

Tracking propagules

Tracking methods require that the propagule (orits vector) can be followed or re-located, so thisapproach is difficult or impossible for many plantpropagules, especially those which are small anddispersed by wind or water. Furthermore, it isoften impossible to follow propagules which travellong distances, because, e.g., landscape barriers,exhaustion or equipment limitation form barriersto the chasing ecologist (Klinkhamer et al. 1988;Tackenberg 2003). If propagules are followed inreal time then data acquisition is slow compared totrapping (Skarpaas et al. 2004), although we ad-dress this issue below. Finally, tracking of wind-dispersed propagules usually involves individualrelease which has the problems described above.For these reasons, although we agree trackingshould be done if possible, trapping methods areoften the only practicable approach for manyplants.

Some seeds are followed relatively easily by eyeand individuals can be tracked directly; such asseeds being carried by slow-moving ants (Cainet al. 1998) or large wind-dispersed seeds with

pappi or samaras (Tackenberg 2003). For propa-gules dispersed by animals or anthropogenically, itis often more straightforward to track the dispersalvector itself. Measures of general movement by thevector will, in general, be easier to obtain thanmovement with the propagule, but movement withthe propagule may be different than that without(e.g. for animals caching seeds (Vanderwall 1993)).Animals may be followed directly, but this couldeither be physically difficult or disturb the animal;in which case tracking might be done using, e.g.,radio-tags or individual markers such as birdrings, which allow location of the animal at adistance (see Kenward et al. 2002 for a review ofanimal tracking methods). Human-aided dispersal,whether by humans themselves or by vehicles,could be measured by direct observation ofmovements or a variety of methods, such asquestionnaires about distances travelled (Buchanand Padilla 1999), data on trade patterns (Mac-Isaac et al. 2002), using Geographical PositioningSystems on individuals or their vehicles (Stedmanet al. 2004), or using the highly sophisticated ap-proaches to analysing and modelling trafficmovement (Wei et al. 2005). Such methods haverarely been used to study human-aided dispersal,but Buchan and Pallida (1999) used questionnairesto assess distances moved overland by boat ownersand implications for dispersal of aquatic alienspecies. If the vector is physically followed, thendeposition of propagules may be observed directly,e.g. by observing defaecation and analysing thedung (e.g. for marked propagules) (Wehncke et al.2004). In the absence of direct observation ofdepositions, to gain a complete measure of

Table 2. A summary of methods used to trap propagules at specific locations, with references that describe the approaches.

Method For what propagule types? References

Sticky traps All (but not very large propagules) Weiblen and Thomson (1995)

Skarpaas et al. (2004)

Containers on or in the substrate All Bullock and Clarke (2000)

Bullock et al. (2003)

Netting on a frame Large (tree seeds) Dalling et al. (2002)

Netting or traps in water All Middleton (1995)

Stieglitz and Ridd (2001)

Soil in seed trays All (germinants are counted) Vickery et al. (1986)

Artificial turf to trap river or tidal sediment Not large Goodson et al. (2003)

Chang et al. (2005)

Sample substrate directly and sieve

out propagules or count germinants

All Augspurger and Hogan (1983)

Ribbens et al. (1994)

These methods provide data on density of propagules at each location.

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dispersal distances, data on the speed and distanceof vector movement should be combined with datadescribing the proportion of propagules taken andhow long they are retained (e.g. in the gut or onfur) (Murray 1988; Sun et al. 1997; Holbrook andSmith 2000; Westcott et al. 2005).

In many cases direct tracking is not possible, butlarger seeds can be marked and later relocated(using methods given in Table 1). Relocation in-volves searching an area for propagules, and so thesame problem arises as with trapping in delimitingthe area to be searched (see Sampling effort below).If this area is too large for a complete search then atrapping methodology might be used, by searchingonly part of the area (e.g. in quadrats or alongtransects) within a distance from the source.Search effort will be decreased hugely by methodswhich allow detection of propagules at a distance,e.g. fluorescence or radio-isotopes.

A simple method is to survey for seedlings/ger-minants (this can also be done as a trapping ap-proach, by searching along transects). This givesinformation about ‘realised dispersal’ (i.e. dis-persal and establishment) and is generally less timeconsuming than following or searching for prop-agules (Greene and Calogeropoulos 2002). How-ever, this method is inaccurate if the distributionof germinants is not a direct translation of prop-agule distribution; for example, if recruitment isdensity dependent or varies spatially with hetero-geneous environmental conditions.

Trapping propagules

Rather than following individuals, it is often easierto collect propagules at particular locations andthis usually involves some form of trap. Examplesinclude: sticky traps, comprising a viscous sub-stance (the non-drying, odourless adhesives usedin commercial insect traps are ideal, e.g. Tangle-foot in the USA and Oecotak in the UK) smearedover surfaces; containers on or dug into theground; netting suspended on a frame; soil in seedtrays (propagule numbers can be estimated bycounting germinants); nets in water fixed at alocation or dragged over sample areas; or pieces ofartificial turf to trap river or tidal sediment (Ta-ble 2). Alternatively, the substrate (e.g. soil or riversediment) can be sampled and propagules are

separated from the substrate or allowed to ger-minate in the substrate.

The effectiveness of this approach depends onthe area of trapping and the position of traps (seebelow). A practical drawback is the risk of con-tamination in traps by propagules from conspe-cifics other than the intended source. Ideally,sources should be isolated naturally or artificiallyor propagules from particular sources could bemarked (see methods in Table 1). Another possi-bility is to measure the location of all possiblesources in relation to the trap locations. If oneassumes a particular function is an adequatedescriptor of the dispersal kernel, maximum like-lihood methods can be used to find parametervalues for the function which best fit the relationaldata (Ribbens et al. 1994; Clark et al. 1999; Uri-arte et al. 2005). This so-called ‘inverse approach’should be used with caution. One has to assumethe function(s) used is the correct representation ofthe true kernel, the approach does not performwell in choosing between alternative functions,rare, long-distance events may be masked if thepropagule lands near another source (Greene et al.2004) and clumping of propagules or anisotropycould lead to large inaccuracies. It may be possibleto separate sources by linking individual propa-gules to the parent plant (i.e. the mother for seeds)using genetic approaches (Latta et al. 1998; Rich-ardson et al. 2002; He et al. 2004; Jones et al.2005).

Indirect methods for measuring dispersal

Genetic methods offer an alternative approach tothose involving direct observation of the fate ofpropagules. Several reviews have proposed avariety of uses of genetic markers for measuringdispersal (Ouborg et al. 1998; Cain et al. 2000;Ennos 2002; Raybould et al. 2002; Nathan et al.2003). In choosing whether to use genetic methodsthere is a need to consider: the expense and timeinvolved in finding suitable markers and in pro-cessing samples; the restrictive assumptions re-quired for the analysis of certain types of geneticdata; and the fact that the data gained may notalways be valid for the question asked (e.g. it isusually difficult to derive dispersal kernels fromthese data). Nathan et al. (2003) provide an

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overview of the potential and limitations of geneticmethods.

Recently, there have been great advances in thedevelopment of mechanistic models, which de-scribe the movement of propagules in an air flow(Nathan et al. 2002; Tackenberg 2003; Soons et al.2004). These are very exciting and have predictedreal dispersal data well. However, they have notbeen tested in a wide range of systems and do notyet offer an alternative to measuring wind dis-persal directly. In fact, field studies of wind dis-persal should include measures of relevantenvironmental variables to allow parameterisationand testing of these models. Schurr et al. (2005)have recently extended these ideas to develop amechanistic for secondary dispersal by wind.

Direct and indirect methods could be combined.Vertebrates can be followed or radio-tracked, butif they have ingested seeds it may be difficult toobserve seed deposition (see Table 1). So trackingdata may be combined with information on gutretention times and dung deposition patterns (Sunet al. 1997; Holbrook and Smith 2000). Geneticanalysis may allow propagules which have been re-located using tracking techniques or trapped to beassigned to a particular parent in the cases whenthis may be in doubt (Latta et al. 1998; Grivetet al. 2005).

Optimising the experimental design

Sampling effort and replication

Dispersal is a stochastic process, because variationamong propagules, in the behaviour of vectors andeven in the type of vector, leads to variation indispersal distances among sites and over time.Dispersal studies should aim to address this sto-chasticity, both by quantifying dispersal over arange of environmental conditions (and possiblyvectors) and by having enough samples to pick uprare events. Constraints on time and resourcescontrast with this aim and so the design of asampling approach must consider how best tomanage this trade-off. Stated generically, this is anobvious question which all experimenters face, soto provide targeted guidance we concentrate ondirect methods.

In a tracking study one should consider howmany propagules to follow and under what range

of conditions. Many tracking studies take place ononly a few occasions (often only once) through thedispersal season. We show below that one can getgood data from relatively few tracking events, butsuch data may not represent completely the vari-ation in dispersal distances. Weather conditionsaffect dispersal distances of wind-dispersed seeds(Tackenberg 2003) and the behaviour of mostother vectors, e.g. water or animals (Westcottet al. 2005). So such an approach may not repre-sent the true dispersal kernel that is realised over awhole season. We encourage doing many smallstudies (each with few tracking events) through theseason rather than a few large studies. Replicationamong sites will also provide a more generic rep-resentation of dispersal for a species. Such datamight be used in mechanistic models along withmeasurement of predictor variables to extrapolateover the whole season.

In trapping, maximising the strength of the seedsource, e.g. by using a group of plants, is a simplebut very productive way to increase the amount ofdata collected. However, larger sources becomemore like area sources than point sources (Greeneand Calogeropoulos 2002) and so interpretation ofthe dispersal data must reflect this. One must alsodecide the number and size of traps to use. Smallertraps can be approximated to precise point esti-mates, larger traps may be logistically less trou-blesome, but will generate ‘binned’ data withpoorer resolution to distance from the source. Asolution is to use larger traps at the further dis-tances, because spatial resolution can be less andthere is a need to increase trapping area to detectthe propagules at low densities. Traps are oftensquare, rectangular, circular or in strips; but thereis no theoretical reason why one shape is betterthan another per se.

Questions as to the extent of the trapping area,the arrangement of traps in space and the pro-portion of the study area sampled are difficult.Larger trapping areas and 100% of that areasampled are obviously best, but, apart from re-source constraints, at some point the cost of set-ting up and monitoring an extra trap will generatediminishing returns. Within continuous stands ofsource species, regular or random grid traparrangements are usually used (Clark et al. 1999;Dalling et al. 2002). For point sources commonarrangements are concentric annuli (rings aroundthe source) (Skarpaas et al. 2004), directional

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transects or traps arranged in sectors (which at-tempt to sample the same proportion of area orannulus at increasing distances from a source)(Hoppes 1988; Bullock and Clarke 2000).

A final consideration for trapping is the degreeof replication. In trapping, it is rare to have rep-lication because this involves repeating a trappingdesign at more than one location; often researchersprefer to maximise the number of traps in a singletrapping design. Bullock et al. (2003) showed thatreplication was essential if one is to understandvariation among dispersal kernels caused by dif-ferent dispersal vectors and that it aided thedetection of rare long-distance events.

Possible clumping of propagules should beconsidered, especially if the vector (e.g. an animal)or site characteristics (e.g. isolated bushes whichmay trap propagules) are suggestive of clumping.As discussed above, tracking should be preferred,if possible, where there is clumping. Otherwise,replication should be increased and traps could beset out in such a way as to measure this clumpingand especially to target possible areas of clumping,e.g. under bushes (seed trapping, bird defaecationlocations). Similarly, anisotropy could be dealtwith by trapping in different directions and sepa-rating data by direction (Bullock and Clarke2000).

An optimisation approach

Above we describe options for experimental de-sign, but provide few rules. Many dispersal studiesare done without sufficient consideration of thefull range of methods available or of the ways inwhich sampling design can be optimised. We sug-gest studies can be improved using two ap-proaches: (1) Carry out pilot studies to assessdirectly the dispersal vectors, where the bulk ofdispersal lies, the general shape of the dispersalkernel and potential data collection methods and(2) Use basic data to develop models of the pro-cesses which might be going on in the system inquestion. Basic data may come from the pilotstudy, from previous studies on the species ofinterest or similar species, from an assumed para-metric dispersal function (this assumption must bebased on some knowledge of the study species), orfrom estimates made using a mechanistic model ofdispersal. For well-defined problems sampling

design can then be optimised using analytical orgraphical techniques (Assuncao and Jacobi 1996)or simulation (Stoyan and Wagner 2001; Pielaatet al., 2006). This suggests the following generalalgorithm for optimising the experimental designfor trapping round a point source (a similar ap-proach could be used to define an algorithm forarea sources). This algorithm is illustrated in Fig-ure 1.

(1) Do a pilot study to generate basic dispersaldata.

(2) Choose a plausible dispersal kernel using thebasic data. If there is considerable uncertaintyabout the functional form of the dispersalkernel, one could optimise across possiblealternative kernels. As new data arrive Bayes-ian methods could be used to update under-standing of the underlying kernel distribution(Hilborn and Mangel 1997).

(3) Simulate N seeds distributed according to thatkernel (with N determined by the expectedfecundity of the point source).

(4) Simulate sampling the seeds with differentpossible methods. At this stage the constraintslisted above can be included and differenttrade-offs tested.

(5) Use the simulation model to choose theexperimental method that best recreates theoriginal kernel or the aspect of that kernel ofmost interest (e.g. the tail). Candidate modelscan be fitted to the data using maximumlikelihood or least squares. Maximum likeli-hood requires a specification of the errordistribution, and this may lead to betterestimates in some cases, especially when er-rors are non-Gaussian, and a realistic errordistribution can be assumed (e.g. Poisson forcounts) (Hilborn and Mangel 1997). Good-ness of fit to the data can be assessed usingresidual sum of squares, residual deviance orAkaike’s Information Criterion (Burnhamand Anderson 2002). Goodness of fit to theoriginal kernel can be measured, e.g., usingthe Kullback –Leibler Information (seebelow).

(6) Do a refined dispersal study.

To achieve very high quality data this process canbe iterated using the dispersal data from (6) in thealgorithm.

225

Critical to this approach is the simulation study.Here is not the place to give detail on how to dosuch a simulation, but Assuncao and Jacobi(1996), Stoyan and Wagner (2001), Skarpaas et al.(2005) and Pielaat et al. (2006) present methods.To illustrate the algorithm we used the simulationapproach developed by Skarpaas et al. (2005), inthis case to choose between seed trapping andtracking methods. One hundred thousand seeds

were dispersed from a point source according to alognormal distribution of dispersal distances (x)

fðxÞ ¼ 1ffiffiffiffiffiffiffiffiffiffiffi

2prxp exp

ln x� lð Þ2

2r2

!" #

where the mean l and standard deviation r of ln xare both 1 (which works well as a rough approxi-mation for, e.g., the wind-dispersed Carduus

Distance

Den

sity

Distance

Des

nis

ty

-30

-20

-10

0

10

50

- -10 10

x

y

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -30 -10 10 30 50

x

y

Track

-5 0

-

-30

-20

-10

0

10

20

30

50

- -30 -10 10

x

y

Trap

Track Tail

Distance

Den

sity

Pilot dispersal study

Fit a function to the data

Use the function to simulate dispersal ofN propagules

. Trap

Simulate sampling the propagules with different methods

Compare sampled data with original function

Do a refined dispersal study using the best sampling method

Figure 1. A flow chart illustrating an approach to optimising the design of experiments to describe dispersal kernels. More detail is

given in the text. The return arrow indicates that this can be an iterative process, whereby data from the refined study are used to

further improve experimental design.

226

nutans; O. Skarpaas unpub. data). The simulatedseed shadow was sampled using a sector trap lay-out sampling a constant proportion of the cir-cumference at increasing distances from the source(similar to Bullock and Clarke 2000), with a max-imum trap distance of 100 m and a total trap areaof approximately 100 m2 (these are reasonablepracticable constraints based on experience of ourCarduus system, but each study will have its ownconstraints). This design was one of the best in amore extensive simulation study comparing dif-ferent trapping designs (Skarpaas et al. 2005).Fitting the lognormal kernel to the data obtainedwith this design gives precise parameter estimatesand a good overall fit. How much effort is neededto obtain similar results using the tracking method?

We imitated tracking by taking random samplesof the 100,000 dispersal distances, for sample sizesranging from 100 to 3000, and used these to esti-mate 95% confidence intervals of parameters andgoodness of fit (Manly 1997). The estimated ker-nels were compared in terms of the precision ofparameter estimates and of overall fit to the ‘‘true’’model (i.e. the lognormal distribution), indicatedby the Kullback –Leibler information I (Burnhamand Anderson 2002)

I ¼Z

1

x¼0

f xð Þ ln f xð Þf xð Þ

dx

where x is distance travelled from the releasepoint, and f(x) and fðxÞ are the true and the fittedmodel respectively. I measures the distance be-tween the true and the fitted kernel; the lower itsvalue, the better fit (when I=0 there is no differ-ence between the kernels). The simulations suggestthat 1000 –1500 seeds must be tracked before thetracking method matches trapping in terms ofprecision of parameter estimates and overall fit (I)to the true dispersal kernel (Figure 2).

The two approaches can further be compared byestimating the cost of each of the methods, e.g. interms of money or labour. Our own experiencewith both methods (e.g. Bullock and Clarke 2000;Skarpaas et al. 2004), suggest that the number ofperson-hours needed to conduct a seed trap studyas described above is at least 200. In comparison,releasing 1500 seeds requires less than 120 person-hours, although these estimates will vary fromsystem to system.

A number of complications could be added tothis comparison (auto-correlated wind speeds anddistances in tracking studies, non-random seedabscission, the form of stochasticity, etc.). Forexample, clumped dispersal could be dealt with bysimulating dispersal according to a fitted function,but including a degree of autocorrelation in dis-persal distances, or by using an appropriatemechanistic model incorporating autocorrelationin environmental conditions (Tackenberg et al.2003; Soons et al. 2004). Wagner et al. (2004) andSkarpaas et al. (2005) deal with simulating aniso-tropic dispersal. However, this simple examplesuffices to illustrate the utility of the simulationapproach in choosing between dispersal measure-ment methods. When information on complicatingfactors is available (e.g. suggested by pilot studies),it can be incorporated into the simulations.

In a similar vein, Assuncao and Jacobi (1996)developed a procedure for optimising sampling forgene flow which is relevant to propagule dispersal.This assumes a trapping approach and deployssample stations at certain distances from thesource to gather data which best represent theunderlying dispersal curve (represented as a para-metric function, e.g. a negative exponential). Thisis useful, but has limitations, especially in that onlyone dimension (distance from source) is involved,so that one cannot try out different two-dimen-sional arrangements (which is often the mainquestion).

Pielaat et al. (2006) developed a sequentialsimulation approach to placement of traps alongtransects for optimal estimation of invasion wavespeeds in one and two dimensions. They foundthat there was a trade-off between nearby sam-pling, which gives many seeds but few long-dis-tance events, and long-distance sampling; theoptimal design for invasion wave speed estimationwill involve sampling towards the tail, and therelative sampling effort that should be placed atthe tail depends on its thickness.

Stoyan and Wagner (2001) used a simulationapproach to compare one- and two-dimensionaltrapping schemes to capture the entire dispersaldistribution for single trees and clusters of trees.For single trees, they found that some schemes areindeed better than others; they recommend thatsome traps be placed where propagules appearwith a low probability. For clusters of a few trees,the three trap layouts tested (linear, uniformly

227

random, more traps near trees) were nearlyequivalent.

Parameterisation of empirical dispersal models

A common step following the gathering of dispersaldata is to fit plausible curves to these data to allowcomparison among data sets or for use in models ofspatial dynamics (or, possibly, to follow the algo-rithm described). A number of functions are in usewhich describe the decay of seed number with dis-

tance (Table 3); exponential, Laplace, inversepower, Gaussian, lognormal, Clark’s 2Dt, negativebinomial, and several mixed distributions (e.g.double exponential, exponential combined withinverse power) (see Greene and Calogeropoulos2002; Skarpaas et al. 2004; Lewis et al. in press).Certain uses of dispersal data, such as integro-dif-ference models of population spread, require trueprobability distributions, which excludes, e.g., theinverse power model and the exponential when thescale and shape parameters differ. Although dif-ferent authors have their own favourite models

0 500 1000 1500 2000 2500 3000

0.00

0.01

Seeds released

0 500 1000 1500 2000 2500 3000

1 e

-05

1 e

-04

Seeds released

0 500 1000 1500 2000 2500 3000

0.8

0.9

.01.

11.

2

Seeds released

0.02

0.03

0.04

031

e-0

2

0 500 1000 1500 2000 2500 3000

0.8

0.9

1.0

Seeds released

1.1

1.2

11

e-

lnI

σµI

Figure 2. Comparison of seed tracking (Lagrangian) and trapping (Eulerian) methods for parameter estimation and goodness of fit to

a ‘‘true’’ lognormal kernel with parameters l and r=1. Mean (solid line) and 95% confidence intervals (dashed) of estimates for l and

r (upper panels) and Kullback –Leibler information I goodness of fit (lower panels) for 1000 simulated seed release experiments as a

function of the number of seeds released in each experiment. The mean and 95% confidence intervals obtained in a seed trap study

using a point seed source of 100,000 seeds and a sector trap design are plotted for comparison (dotted).

228

(Portnoy and Willson 1993; Clark et al. 1999;Bullock and Clarke 2000), in reality the choice of adistribution a priori is rather subjective.

However, certain distributions do suppose amechanistic process and more work needs to bedone on whether these mechanisms match thebehaviour of certain vectors. The Gaussian dis-tribution results from propagules moving byBrownian motion for a fixed length of time. TheLaplace results from propagules moving randomlyand having a certain probability of settling per unitof time. The 2Dt (Clark 1998) invokes Brownianmotion, but with a v2 variance. Katul et al. (2005)recently introduced the Wald model, which is amathematical simplification of a model describingwind dispersal under turbulent conditions (Ta-ble 3). This seemed to work well for a range ofdata sets and may prove to be the best model forwind dispersal data. The fact that certain dispersalvectors tend to produce longer tails to the kernel –e.g. in general, vertebrates disperse seeds furtherthan wind dispersal, while invertebrates andexplosive dispersal is even less effective (Willson1993; Clark et al. 2005) – might mean that certainfunctions relate better to certain vectors. There isonly limited evidence for this, with Clark et al.(2005) showing that the best fit function for ver-tebrate-dispersed seeds was the inverse power, butthe Gaussian was best for wind-dispersed seeds.

Practically, one should not choose just one func-tion, but assess the fit of alternative functions tothe data (see Clark et al. 1999; Bullock and Clarke2000; Skarpaas et al. 2004; Clark et al. 2005).

However, one should take care when fitting suchmodels to dispersal data. In some cases, the datawill not amenable to model fitting because theyshow an idiosyncratic pattern such as multiplemodes (Bullock et al. 2003). Patterns such asclumping might be dealt with by appropriate def-inition of the error structure (e.g. Bullock andClarke 2000) or anisotropy by correction duringmodel fitting (Skarpaas et al. 2005). Even if thedata are suitable, fitting usually uses least squaresor maximum likelihood methods, but both meth-ods place more confidence in the samples withhigher numbers, i.e. near the source, so the fit tothe tail can be poor (Bullock and Clarke 2000).Furthermore, fitting a putative kernel to fairlyshort-distance data may extrapolate tails far inexcess of our confidence in that tail. Replication indispersal studies (see above) should greatly im-prove the accuracy of fitted models (in relation tothe true dispersal kernel).

Earlier we recommended doing multiple exper-iments to assess dispersal by different vectors or atdifferent times of the season. If models are fitted todata derived from these different studies, then itmay be useful to combine them to get an overalldispersal kernel which describes the outcome fol-lowing dispersal by all vectors. The way to com-bine kernels will be different depending on whetherpropagules of a species have ‘alternative’ (e.g.wind or animal) or ‘sequential’ (wind then animal)modes of dispersal. In the case of alternative dis-persal modes each propagule is distributedaccording to one kernel only and the individualkernels will have the same origin, so the combinedkernel kcom is simply the sum of the individualkernels k weighted by the proportion p of propa-gules dispersed by each mode (Higgins et al. 2003).

Thus, for any number of kernels:

kcom ¼X

piki; whereX

pi ¼ 1:

In the case of sequential dispersal, propaguleswill first be distributed according to the first ker-nel, and then, from this distributed source, thepropagules will be dispersed further according tothe second kernel. Assuming the two dispersal

Table 3. Functions commonly used to describe dispersal data.

Name Function

Negative exponential a exp �bx½ �Inverse power ax)bx

Mixed (one of many

possible mixtures)

a exp �bx½ � þ cx�dx

Laplace

12b exp�

jx�ajb

h i

Gaussian (Normal)

1affiffiffiffi

2pp

h i

: exp � x�bð Þ22a2

h i

Wald (inverse Gaussian)*

a2px3� �1

2 exp � a x�bð Þ22b2x

h i

Lognormal

exp � ln x=bð Þ½ �2

2a2

� �

axffiffiffiffi

2pp

2Dt**

a

pb 1þx2b

� �aþ1

These probability density functions describe density of propa-

gules at distance x from a source. For simplicity the same

notation – a, b, c and d – is used for fitted parameters in all

functions, but they will take different values in each function.*Katul et al. (2005), **Clark (1998). NB. The Wald function is

designed for wind dispersal data (see text).

229

processes are independent, the combined kernel isnow the convolution of the two kernels (Neubertand Parker 2004), where convolution is an inte-gration approach which blends two functions. Thefirst dispersal mode moves a propagule to point xand the second moves it from x to y, so the con-volution is:

kcom ¼Z

1

�1

k1ðxÞk2ðy� xÞdx:

Summary and future directions

Given the importance of dispersal in all facets ofecology, there is a pressing need for a betterdescription and understanding of dispersal kernels.We consider the planning of a dispersal studyshould ask the following questions.

(1) What will I use the dispersal data for? Somedispersal studies are targeted to precise ques-tions, such as testing mechanistic models(Nathan et al. 2002) or modelling rates ofspread (Cain et al. 1998; Lewis et al., in press),but many simply report some aspect of dis-persal. If a researcher is clear about the aim ofa particular dispersal study, then it is easier todesign the study logically and systematically.

(2) How is my study species dispersed? Many, ifnot all, species are dispersed by more than oneprocess. If one requires a complete descriptionof the dispersal kernel (e.g. for models ofpopulation spread), it may be necessary eitherto identify all dispersal processes or to usemethods which are not specific to certain typesof dispersal (e.g. hand release of propagulestargets dispersal by wind). The former ap-proach is more difficult than the latter, but itmay be possible to identify and assess themajor types of dispersal using observation andpilot studies. Different methods may then beused to quantify dispersal by each process.This will also help achieve a more mechanisticunderstanding of dispersal (see below).

(3) How do I optimise my dispersal study? In gen-eral, the design of dispersal measurementprotocols needs more rigour. It is fairly easy toimagine excellent but logistically unfeasibleempirical protocols, but we have little under-

standing of the loss of power resulting fromsimpler, tractable designs, nor how to optimisethem. While the huge variety of dispersal typesmean that it is not possible to make generaldesign recommendations that will apply tomost situations, we are in a position to definean approach to making the best decision tai-lored to the idiosyncrasies of the system ofinterest. The optimisation procedure we havedescribed here is a simple approach whichcould be used widely. This involves pilotstudies to test different methods for measuringdispersal and to gain basic data on the dis-persal kernel followed by simulation modellingto assess the value of different samplingstrategies. To illustrate our method, we havepresented an example in which tracking rela-tively few individual propagules providedinformation of a quality comparable to thatproduced in relatively effort-intensive trappingstudies.

(4) Can I summarise my data with a dispersalmodel? All models are wrong, but some areuseful (Box 1979). There are few formal com-parisons of different models and their abilityto describe dispersal data (Portnoy and Will-son 1993; Clark et al. 1999; Bullock andClarke 2000; Skarpaas et al. 2004), but, forexample, which model is used can radicallyaffect the outcome of population spreadmodelling (Kot et al. 1996; Clark 1998). Ifmodels are to be used there should be propertesting of different options, using statisticalmethods such as those described in this paper.Replication of dispersal studies would reallyhelp with this. It may not be necessary to fitmodels; Clark et al. (2001) describe a non-parametric approach to using dispersal data inmodelling population spread.

The more rigorous approach described abovewould advance our understanding of plant dis-persal and spatial dynamics hugely. One aspect ofthis is good quantification of dispersal by differentprocesses, so that the contribution of these pro-cesses to the full dispersal kernel of a plant isunderstood. However, the methods we have dis-cussed here really generate descriptive informa-tion, although a deeper mechanistic understandingis possible. Recent developments on this front offer

230

strong synergistic possibilities. Mechanistic modelshave been devised which simulate seed movementin wind (Greene and Johnson 1989; Nathan et al.2002; Tackenberg 2003; Soons et al. 2004) basedon falling velocity, height of release, turbulence,etc, although there is controversy surroundingdifferent modelling approaches (Soons et al.2004). Validation of mechanistic models againstreal data is vital and will provide a thoroughunderstanding of the factors affecting the dispersalof species. However, such models are only welldeveloped for wind dispersal, and to some extentfor vertebrate dispersal (Nathan et al. 2003).

Acknowledgements

This paper was initiated at the NCEAS workinggroup on demography and dispersal and we thankespecially Janneke HilleRisLambers, Carol Hor-vitz and Brian Beckage for useful discussion. AndyStephenson, and the Mortensen-Shea dispersaldiscussion group provided valuable comments onearlier versions of the as did two referees. Part ofthis work was supported by NERC Grant NE/B503141/1 to J. Bullock, by USDA-CSREES(Biology of Weedy and Invasive Plants) NRIGrant #2002-35320-12289 and NSF Grant #DEB-0315860 to K. Shea, and by NRC Grant 161484/V10 to O. Skarpaas.

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