Can landscape-scale characteristics be used to predict plant invasions along rivers?
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<ul><li><p>Can landscape-scale characteristics be usedto predict plant invasions along rivers?G. S. Campbell1*, P. G. Blackwell2 and F. I. Woodward1 1Department of Animal and Plant</p><p>Sciences, University of Sheffield, Sheffield, UK, and 2Department of Probability and Statistics,</p><p>University of Sheffield, Sheffield, UK</p><p>Abstract</p><p>Aim To determine whether the invasions of hydrochorus plants, that is those which canmake use of rivers to transport their propagules, can be predicted using informationderived at the landscape scale. This is desirable to avoid the need for the difficult tomeasure parameters required by detailed invasion models.</p><p>Methods A model for plant propagule dispersal was developed that simulated bothlocal dispersal (autochory) and aided dispersal along river corridors (hydrochory). Thisprovided the simulated invasion behaviour that was to be predicted by the simpleanalytical method. This latter was based on readily available river network character-istics. The analytical summary was then tested for its ability to predict the results of aseries of simulation experiments.</p><p>Results Predicted dispersal rates derived from the analytical summary method werestrongly correlated (R2 of 0.8941) to the mean seed displacement simulated by the plantdispersal model.</p><p>Main conclusion The simple analytical summary of the river networks provides a goodprobabilistic description of the simulated invasion process. This means that readilyavailable information might be able to be used to predict real invasions by alien plantspecies. This method should now be tested against observed invasions by alien plants.</p><p>Keywords</p><p>Hydrochory, invasion, simulation, landscape.</p><p>INTRODUCTION</p><p>This paper describes the development of a model for theinvasion of the UK by alien plant species, specifically thosethat are associated with riparian habitats. There are manywell-documented examples of invasion by alien plant speciesin the UK (see for example Ellis, 1993; Beerling & Palmer,1994; Dawson, 1994; Perrins et al., 1993). In the ecologicalcontext an invasion is the dispersal of a non-endemic speciesand its subsequent spread into a new environment (Cousens& Mortimer, 1995). The term dispersal is used here to meanthe movement of propagules away from the parent (Speller-berg & Sawyer, 2000) and migration is used for the advanceof a species from one area to another (Allaby, 1992). An alienis a species, which has arrived because of human activity(Clement & Foster, 1994) and in the British context may be</p><p>defined as a species which was not present in the area nowforming the British Isles, at the end of the last Ice age (Ellis,1993). Modelling such invasions is made difficult by thediscrepancy between the scale at which the mechanisms ofinvasion occur, i.e. at the scale of individual plants and that atwhich its progress is recorded nationally, generally at aresolution of 10 km. This paper reports an approach to themodelling of plant invasions that attempts to reconcile thehighly random nature of the processes involved with theavailable spatial and autecological data.</p><p>Much work has been aimed at developing predictivemodels of the spatial response of plants to natural andanthropogenic environmental disturbances (see Higgins &Richardson, 1996 for a review). Such disturbances includeclimate change, edaphic alteration and, perhaps mostdramatically, the introduction of plants to novel environ-ments. The reactiondiffusion approach adopted in theclassic work by Skellam (1951) assumed that the rate ofspecies spread was a constant given that the asymptotic rate</p><p>*Correspondence: Department of Plant and Soil Sciences, University of</p><p>Aberdeen, Aberdeen AB24 3UU, UK. E-mail: email@example.com</p><p>Journal of Biogeography, 29, 535543</p><p> 2002 Blackwell Science Ltd</p></li><li><p>of spread has been reached. The central assumption in thismodel that dispersal is effectively a random process exhib-iting Brownian motion, does not allow for a non-uniformlandscape or for more than one mode of dispersal. In fact, itwas the underestimation of the post-glacial migration byoak trees in England, using this model which lead Skellam(1951) to the conclusion that aided dispersal in the form ofornithochory (dispersal by birds) must have played a part inthe migration (Higgins & Richardson, 1996). Similarpalaeoecological evidence for hazel (Corylus avellana L.)(Huntley, 1993) and alder (Alnus glutinosa L.) (Chambers& Elliot, 1989) is indicative of a post-glacial migration rategreater than that, which would be expected from autochorusdispersal alone.</p><p>Another approach to modelling plant invasions, which hasproved partially successful, is spatio-phenomenologicalmodelling, that is the use of historical data to determinemathematical relationships between elapsed time and areainvaded (see for example Perrins et al., 1993; Pysek &Prach, 1993). However for some species, such modelsproduce estimates of the mean rate of invasion thatunderestimates the observed invasion rate by an order ofmagnitude (Andow et al., 1990). An example of such aspecies is Himalayan Balsam (I. Glandulifera), which has anobserved maximum invasion rate 38 km year)1, whereas thedehiscent (explosive seed pod) dispersal alone should give aninvasion rate of 23 m year)1 (Williamson, 1996). As withthe post-glacial migration of tree species this discrepancy inpredicted and observed invasion rates is attributed to thephenomenon of aided dispersal (Higgins & Richardson,1996) whereby organisms make use of secondary dispersalvectors to augment autochorus mechanisms. A furtherweakness of spatio-phenomenological models is that theydo not consider the heterogeneous nature of the landscapewhen estimating dispersal rates.</p><p>A contrasting and in many ways complementary approachis that taken in spatio-mechanistic models, which useempirically derived growth and dispersal functions todeterministically model the behaviour of plant populations.Unlike spatio-phenomenological models, spatio-mechanisticmodels such as MIGRATE (Collingham et al., 1997) canallow for biological differences between species. The spa-tially explicit, spatio-mechanistic model allows for landscapeheterogeneity and can incorporate functions for modellingmultiple dispersal vectors, including occasional long-dis-tance dispersal of propagules. These models perform well atcertain landscape scales, providing a platform for sensitivityanalysis and invasion rate prediction (see for example Williset al., 1997). However, such models deal with the fate ofindividual propagules in a probabilistic, albeit biologicallyrealistic manner, consequently the resulting populationinvasion predictions, whilst being entirely feasible, repre-sents just one of the many possible scenarios. The resultsfrom such models need careful interpretation as the effect ofone or more rare and long-distance dispersal events on theoverall pattern of propagule dispersal can be substantial(Perrins et al., 1993).</p><p>An alternative modelling approach is not to attempt tomodel the fine scale mechanisms of the invasion process butrather to use analytical methods to model the process at alandscape and population scale. This approach parallels thatused by Yves et al. (1998), to investigate the ability of simpleanalytical summaries of landscape characteristics (spatialarrangements of habitats) to predict population dynamics.The predictions of a simple analytical description of habitatsuitability were regressed against the results from a demo-graphic simulation to test the predictive ability of the former.The strong relationship between the values predicted by theanalytical method and those simulated by the demographicmodel (R2 0.88, where R2 is the proportion of variation inthe observed values explained by the model) suggest thatsuch analytical approaches could be used to study landscape-scale population dynamics in the absence of detailedecological and geographical data. This type of analyticalmodel was developed to predict the invasion of hydrochorusalien plants in the UK and is described here.</p><p>For species that are able to use rivers as agents of aideddispersal it was hypothesized that the contribution toinvasion rate made by hydrochorus dispersal is such thatfor certain plants, predictions based on this alone willexplain the observed pattern of invasion (Campbell, 2001).To assess the potential of such an analytical summarymethod the following approach was adopted.</p><p>1. Construct a model of plant propagule dispersal, whichsimulates local, plant-mediated (autochorus) and long-range aided dispersal by rivers (hydrochory).</p><p>2. Carry out a series of simulation experiments to developrelationships between a relevant landscape characteristic(river network distribution) and simulated rates ofdispersal.</p><p>3. Assess the capacity of the analytical summary method topredict the dispersal rate of an independent series ofsimulation experiments.</p><p>4. If step 3 is successful, apply the analytical summarymodel to historical plant invasions in the UK and assessits predictive ability in real world situations.</p><p>The first three stages are designed to develop a relationshipbetween river network characteristics and plant dispersalrates and to assess the ability of the analytical method toexplain the behaviour of a simulated invasion using onlyvery limited input data. The important point about this inputdata is that unlike the multiple parameters required fordetailed mechanistic models, it is readily available at thenational scale for the UK. The fourth step, as describedabove, is designed to see if this model can predict realinvasions using only this minimal input data. This paperreports on the first three stages of this process, the modeldevelopment and testing against simulated invasions.</p><p>LANDSCAPE GENERATION PROGRAM</p><p>The experimental landscapes were generated using aprogram written in C and were represented by a grid of</p><p> 2002 Blackwell Science Ltd, Journal of Biogeography, 29, 535543</p><p>536 G. S. Campbell et al.</p></li><li><p>cells arranged in a two-dimensional array forming thedispersal surface. The grid dimensions were set by a user-defined parameter at the start of the simulation. Each cellwas assigned a code, which dictated the direction a simu-lated propagule that moves into that cell takes in thesubsequent iteration. For the purposes of description com-pass directions will be used to describe the movements acrossthe two-dimensional landscapes, with north being towardsthe top of the dispersal area. A directional code of zerorepresents dry land in the simulation model with no pre-determined dispersal direction, i.e. with an equal probabilityof movement in any of the eight allowable directions. Thedispersal surface was initialized with an array of zero values;this represented a landscape containing no rivers to aidpropagule transport. This homogeneous dispersal surfacewas then overlain with a simulated river network in whicheach cell has a downstream movement direction code,corresponding to the directionalized network function ofthe ARC/INFO Geographical Information System (ESRI,1998). This code determines the direction of the nextpropagule move, for example, a code of two would meana downward diagonal move to the southeast and a code of16 would mean a horizontal movement to the west (Fig. 1).</p><p>THE EXPERIMENTAL LANDSCAPES</p><p>To determine the relationship between dispersal efficiencyand drainage characteristics, a series of random networkswere generated with drainage densities (area of river cellsas a percentage of the total area) ranging from 0 to 25%.These were consistent with observed drainage characteris-tics of the UK river network at a 0.5-km resolution. Arange of networks was generated with 0, 1, 2, 4, 8, 16, 32,50, 64, 100, 128, 200 and 256 stream heads (the upstreamend of the river) to provide a range of drainage densities,which produced realistic-looking river networks (seeFig. 2). The number of stream heads was based on ageometric progression with the addition of three values(50, 100 and 200) to avoid extended breaks in thecontinuum of generated densities. The second characteristicof the simulated river networks, which was experimentallyvaried, was the directional bias as determined by thenetwork generation program. The experiments describedhere were carried out on 325 simulated river networks thatranged from those with very meandering rivers (series 5) tothose with a strong westeast bias (series 1) via intermediatedegrees of directional bias (series 2, 3 and 4). Each seriescontained five replicates each of a range of thirteennetwork densities with between 0 and 256 stream heads.This gave a total of 325 simulated landscapes but forreasons of space, only nine examples of these networks areshown (Fig. 2).</p><p>To assess the predictive ability of the model, two furtherseries of networks were generated. Series X, having riverswith a directional bias intermediate between those of series 3and 4; and series Y with completely random river networks(Fig. 3). Neither of these network series (X and Y) was usedin the regression analysis described below but was rather</p><p>used as an independent data set to test the predictive abilityof the relationships derived for series 15. For the experi-ments described here, all simulated dispersal landscapeswere 200 by 200 cells in extent.</p><p>SIMULATION MODEL</p><p>A simulation program was written in the C language inwhich plant propagules (seeds) disperse across the experi-mental landscapes in a random manner, with all land-basedmoves being one cell in any of the eight directions (Fig. 1).Each move made by a seed represents one generation, i.e.from seed to adult, which then reproduces, before dying. Thepropagule produced by the previous generation then makessubsequent moves, until the requisite number of generationshas been simulated. The model simulates the dispersal of alarge number of individuals each producing a singleoffspring before themselves dying, i.e. they are annualplants. The offspring, which are produced during oneiteration, are able to disperse during the subsequent iter-ation, and so a single line of descent is followed in each case.One of the fundamental features of dispersal is the random</p><p>Figure 1 An example of a section of a simulated landscape withsimulated river flow direction indicated by the codes correspondingto those in the key. For clarity, the zero codes of terrestrial cells arenot shown.</p><p> 2002 Blackwell Science Ltd, Journal of Biogeography, 29, 535543</p><p>Landscape-scale characteristics 537</p></li><li><p>nature of the trajectory of each propagule in the absence ofexternal vectors such as wind, gravity or as in this caseflowing water. What is required to simulate such randomdispersal behaviour is a model that captures the essential</p><p>properties of this sequence of independent steps (i.e. themovement of propagules away from the parent plant). Onesuitable model for this purpose is the random walk, a wellstudied mathematical process (for example Renshaw, 1993).</p><p>Figure 2 Examples of random drainage net-works generated with different numbers ofstream heads and direction code prob...</p></li></ul>
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