Acta Oecologica 23 (2002) 205–212 www.elsevier.com/locate/actao Modelling the consequences of duck migration patterns on the genetic diversity of aquatic organisms: a first step towards a predictive tool for wetland management P.W.W. Lurz *, M.D.F. Shirley, S.P. Rushton, R.A. Sanderson Centre for Life Sciences Modelling, Porter Building, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK Received 1 September 2001; received in revised form 1 February 2002; accepted 23 February 2002 Abstract We have developed a spatially explicit modelling framework that links duck migration patterns with gene transport. The model is individual-based and simulates the journey of a duck from migration start locations through stopover sites to breeding or wintering sites. We investigate two different migration strategies: ‘hopper’ (where the bird makes many stopovers) and ‘jumper’ (where the bird makes few stopovers). The migration model is linked to a genetics model calculating gene frequency changes based on propagule deposition for potential duck landing sites along the European migration pathways. We present the results of a sensitivity analysis relating flight characteristics of several duck species to the resulting pattern of potential gene spread. The modelling framework is designed to develop hypotheses on the likely impact of duck migration on genetic diversity of aquatic organisms; and the predictions are discussed in relation to future empirical research and subsequent model development. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Dispersal; Gene spread; Individual based model 1. Introduction Waterfowl are abundant, have widespread distributions and may undergo both short-distance and long-distance movements often at the transcontinental scale (Owen and Black, 1990). The potential role of wildfowl-mediated transport of aquatic plants and invertebrates was recognised by Darwin (1859). Whilst there has been a long history of research which has shown the potential for transport of aquatic organisms by ducks (Schlichting, 1960; Proctor, 1964), quantification of the transport and its importance for the genetic composition of populations of these organisms in the field has been less intensively studied. Only with the development of molecular techniques has it become possible to quantify genetic differences between populations distributed in space. Determining the impacts of wildfowl populations on this genetic variation is a bigger and more complicated problem. The spatial and temporal dynamics of * Corresponding author. E-mail address: [email protected] (P.W.W. Lurz). © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 1 4 6 - 6 0 9 X ( 0 2 ) 0 1 1 5 1 - 7 the wildfowl and the organisms that they are purported to transport make fieldwork approaches difficult. Quantifying wildfowl movement in time and space and investigating this in combination with assessing what is picked up, transported and deposited and the subsequent fate of the dispersed propagules is a considerable challenge. Whilst we cannot investigate many of these ecological processes in combination, significant advances can be made by the investigation of the individual processes, e.g., gut retention times and propagule survival, followed by a synthesis which combines each component. The most obvious approach to synthesis is to develop a model which simulates the key ecological processes at the relevant spatial and temporal scales, but which also integrates all processes so that the role played by migratory wildfowl in longdistance dispersal appears as an emergent property of the model. There are two approaches that can be used for modelling organisms and genes linked to their distributions. These are associative models that attempt to relate the distribution of a species to habitat and other environmental features and 206 P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 process-based models that derive distribution patterns from of the underlying life-history processes that go on in the landscapes themselves. The two approaches differ in their underlying philosophies. Associative approaches are essentially ‘top-down’ in that pre-existing animal distribution data are overlaid on habitat information that is collected (usually) at the same time as the animals are surveyed. The overlaying procedure is then used to develop a formal mathematical linkage between incidence of the animal and the landscape which can be used to predict distributions. For example, multivariate techniques have been used extensively to simplify habitat characteristics and classify bird communities in a number of habitat types (see Hill et al., 1993, and Rushton et al., 1994, for examples of shore birds and river birds, respectively). In addition, studies on gene flow have been modelled using statistical approaches (e.g., Maltagliati, 1998; Gavrilets and Cruzan, 1998). Process-based models, in contrast, are ‘bottom-up’ in that they simulate the dynamics of populations and individual movements (dispersal, migration) in the landscape and the distribution of the species arises as an emergent property. Process-based models for modelling species distributions are based on the premise that the distribution of a species in the landscape arises from interactions between individual behavioural processes such as migration and local dispersal as well as life-history processes such as mortality. In these models the habitat data act as templates on which the populations processes occur and the distribution of organisms and thus alleles across habitats emerges as the model is run (an example is given in Lurz et al., 2001). Process-based approaches are inevitably much more complex than associative methods because they attempt to simulate individual processes. The models are spatially referenced which means that they are linked to a map of a ‘real’ landscape, which generally includes information on the location of water bodies (e.g., lakes), coastlines and geographical data (e.g., altitude). This is usually stored in a digitised format within a Geographical Information System (GIS) which allows map manipulations and data extraction. When planning a modelling framework it is necessary to consider the best approach to use. We have chosen a process-based approach to enable us to examine the effects of individual behaviour such as migration strategy, propagule transport, morphological differences between species and variation of flight paths. Environmental heterogeneity combined with these individual differences are more easily modelled using process based rather than associative approaches. It also allows the addition of more processes such as propagule survivorship during transport and germination/hatching success as these processes become more fully understood. An integrated GIS-modelling framework was developed in a first attempt to integrate bird migration behaviour, propagule transport and landscape structure. It was used to make preliminary predictions on the potential impact of European bird migrations on the genetic diversity of aquatic invertebrates and macrophytes. We have developed an initial modelling framework in which the migration model is structured to be able to compare the results for different migration options or stop-over decisions (e.g., Alerstam and Lindström, 1990; Hedenström and Alerstam, 1997). These involve predictions based on minimum energy expenditure and represents animals moving along a series of stepping stones which we termed ‘hoppers’ and predictions on minimum time, i.e., ducks completing the journey as fast as possible, which we termed ‘jumpers’. The terms jumpers and hoppers were first introduced by Piersma (1987) and we consider these to be two possible strategies likely to have different effects on genetic biodiversity in water bodies along migration routes. We describe the modelling framework and discuss preliminary findings in relation to future research. In particular, we examined the possible consequences of variation in migration behaviour and morphological characters of selected duck species on allele distribution along migration flight paths. 2. Methods 2.1. Modelling framework There are two major components to the modelling approach: a migration model and a genetics model. The whole modelling framework is co-ordinated by a series of inter-linked programs, running on Linux workstations, calling individual models and sorting file outputs and graphic displays. All models were written in the programming language ‘C’, and interact with GRASS, a Geographical Information System (Westervelt et al., 1990). As a first step in the framework, the model abstracts the location and type of wetlands along the migration flight paths from the GIS and creates a list of available landing sites. This information is then passed on to the migration model, detailed in Fig. 1. The diagram is read as a sequence of steps executed from left-to-right and top-to-bottom within each step (Dent and Blackie, 1979). The migration model is designed in such a way that it would be applicable to not just ducks, but also other species of migrating wildfowl. Bird specific characteristics are chosen using known distributions of duck weight and wingspan for each species and sex (Cramp et al., 1977). Rather than predetermine the route of migration taken by individual birds, the direction that each duck sets off in is determined by an ‘angle map’ based on an analysis of European ringing records and species-specific published migration flight paths (e.g., Crissey, 1955; Donker, 1959). This sends individual ducks towards spring or autumn flight routes. In order to determine the stopping point for an individual bird (Fig. 1, far right), two different migration strategies are currently simulated. The first strategy is that ducks will fly as far as they can on a single fat load (‘jumper’ strategy). P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 Fig. 1. Structure diagram of migration model. The diagram is read as a sequence of steps executed from left-to-right and top-to-bottom (within each step). This maximum flight distance is calculated using biometric equations (Pennycuick, 1989). When the duck has reached this maximum distance travelling in the predetermined direction, the model determines whether there is suitable habitat for stopping (i.e., lakes or coastline). If not, the model checks backwards along the travelled route for the nearest suitable stopping point. This stopping strategy will result in long-distance transport of genetic material, with no intervening gradient. The second stopping strategy (‘hopper’) works in the opposite way. In this strategy, the duck moves the equivalent of one day’s travel, and then interrogates the landscape for a suitable stopping place. If none is to be found, the subroutine moves the duck gradually forward on its projected flight path. Other migration strategies could be integrated into this system simply by altering the rules determining where a duck ends its migration journey. The jumper and hopper strategies could be used to investigate observed patterns of population structure and genetic diversity across lakes in relation to specific waterfowl species and their relative migration patterns. The hopper strategy may result, for example, in higher gene flow over short distances as the ducks will take many and frequent stops. Each modelled population follows one or the other strategy. Each time an individual duck lands in a cell, its arrival there is recorded (these data are used in the genetics section of the model), and the cell is interrogated to generate a new direction of flight. Some cells are designated ‘end cells’, based on the observed summer/winter distributions of each species; if a duck lands in one of these end cells, its migratory path has finished. At present, the influence of weather is only modelled very simply. The direction of flight could be changed due to strong winds and journey time can increase. Flight distances can also be calculated with or without head and tail winds. However, there is some indication that waterfowl species may avoid flying in adverse weather conditions. The migration model currently does not include stopovers due to water loss occurring through an imbalance where loss exceeds metabolic water production (e.g., Klaassen, 1996; Klaassen 207 and Biebach, 2000). The model currently assumes that individuals have accumulated enough energy for migration (e.g., Bairlein and Gwinner, 1994) and are able to refuel at stopover and breeding or wintering sites (e.g., Mayhew, 1988). The model therefore does not simulate the population dynamics of waterfowl species, nor life histories of individuals migrating across Europe, but potential dispersal pathways for genetic propagules. There are two stochastic components in the model. First, each bird has a random body weight and wingspan, determined from a truncated normal distribution appropriate to the duck species modelled. These two parameters affect flight energetics (Pennycuick, 1989) and therefore distances travelled. Second, mean flight angles are modified by deviates drawn from a von Mise’s (circular) distribution. In other words, the migration model simulates potential pathways between breeding and overwintering sites across Europe. 2.2. Genetics model A genetics model has been created which is directly linked to the duck migration model. This genetics model does not attempt to emulate any specific genetic system; its intent is only to demonstrate the functionality of the model. For this explanatory example we have assumed that there are two loci under examination on the chromosomes of a hypothetical organism. The first locus has five alleles that are naturally (i.e., in the absence of migration) found in five bands that correspond with lines of latitude. Similarly, the second locus has five alleles that are distributed according to the lines of longitude. Each time a duck stops in a grid cell as part of its migration cycle, its presence and its last stopping place is recorded. This allows the genetics model to determine the origin of any potential propagules that are deposited in the grid cell, and also in what quantity. The flow diagram for the genetics model (Fig. 2) shows the steps taken; it should be noted, however, that this system is generalised, and can be modified to produce output appropriate to any genetic system (e.g., microsatellites, mitochondrial alleles). The genetics model first calculates how many alleles have been carried to each grid cell of the map, based on input from the migration model. This accounts for multiple ducks originating from the same grid cell, and thus potentially depositing a duplicate ‘dose’ from that cell. Currently, no account is taken for the probability that a propagule will be carried by a duck, the probability that a propagule will survive the journey in a viable condition, or the probability that a propagule will be deposited. These processes are indicated in Fig. 2 by a dotted outline. Each duck is assumed to carry an ‘inoculum’ of genetic material of the same size. The gene frequencies of the total inoculum is calculated (assumed to be the same as in the originating lake); these frequencies are then scaled down many thousands of times, and added to the gene frequencies 208 P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 and red-crested pochard (Netta rufina). The recovery data obtained from the Spanish Ringing Office, the Copenhagen Bird Ringing Centre and Euring were collected over 69 years (from 1930 to 1999) and included all of Europe and Eurasia (approximate latitudes 72° north to 30° north, and longitudes 20° west to 60° east). Migratory journeys (consisting of birds recovered in the year following ringing, and recovered in a location different from ringing) were divided into two groups, Spring Migration (ducks heading north between January and May) and Autumn Migration (heading south between July and November). The distance travelled and the angle taken were calculated for each individual, and were grouped by species, sex and age. Analyses of flight angles were carried out using the software package Oriana (Kovach Computing Services, 1994, Version 1.0). Our analyses excluded resident birds (as they did not move between ringing and recapture). 2.4. Sensitivity analysis of the spatially explicit model Fig. 2. Flow diagram of genetics model. Dotted outlines indicate propagule-specific processes not included in the model. of the current grid cell. It is assumed that gene frequencies then return to an equilibrium before the next migration event. In addition to propagule deposition, there are no data currently included in the model on the probability that a propagule will germinate / hatch in the new environment. Related to this is the lack of data on whether or not the genes transported into the populations will be less fit than those already present. Currently, these effects have been excluded from the model (it is assumed that all propagules will survive in the new environment and that all alleles have equal fitness in all environments). These assumptions may affect the output of the model and future research should focus on parameterisation of these variables. For the species under consideration, given the assumptions of the model, the inclusion of the variables would lead to a dilution and a reduction in the speed of spread. 2.3. Parameterisation of flight direction We analysed ringing recoveries in relation to the direction and distance travelled by individuals of eight duck species: northern pintail (Anas acuta), northern shoveler (Anas clypeata), common teal (Anas crecca), Eurasian wigeon (Anas penelope), mallard (Anas platyrhynchos), gadwall (Anas strepera), common pochard (Aythya ferina) The sensitivity analysis we performed investigates the impact of four specific model parameters (duck body mass and wingspan, spread around mean flight angle and migration strategy) on predicted gene spread. Stochastic simulation models typically have a large number of input variables, and it is necessary to discover which of these parameters has the greatest influence on the outputs of the model. The results of a sensitivity analysis can be used to refine the parameterisation process, indicating which variables have significant impacts on model predictions. A Latin Hypercube Sampling strategy following the methods of Vose (1996) was used to select values for the input parameters in the model from the known or estimated ranges of the different variables in the model (Table 1). The aim was to provide a range of input values for each variable that could potentially occur under field conditions. In other words the model would be run a sufficiently large number of times to encompass the potential range of conditions that occur naturally rather than simply worst and best case scenarios (sensu Bart, 1995). In this method, sample values of the input parameters were selected using a randomisation procedure subject to constraints on the extent of correlation of input variables that were imposed by the modeller. A uniform distribution was assumed for each variable with upper and lower limits derived from the literature. Table 1 Model input parameter ranges encompassing characteristics of the eight focal duck species including both sexes. Thus body mass and wingspan ranges are the minimums and maximums found amongst all eight duck species. Range of spread around mean flight angle (kappa) and migration strategies are also given Input parameter Range Body mass Wing span Kappa Migration strategy: . 0.185–1.57 kg 0.58–0.98 m 1–20 Hopper or jumper migration P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 Kappa is analogous to the standard deviation of a Von Mise’s distribution and is a measure of the deviation from a mean flight angle. The choice of n (the number of simulations) depends primarily on the computing costs of the model. The maximum number of permutations is equal to (n!)k–1 , where k is the number of variables in the sensitivity analysis. Iman and Helton (1985) have determined that stable estimates of sensitivity coefficients can be obtained if n is greater than (4/3)k. In this case, with k = 4, the value for n was set at 100 for the sensitivity analysis. The sensitivity of the predictions of the model to the four input parameters was investigated in four separate grid cells (locations were Norway 63°N, 13°E; Netherlands 50°N, 5°E; Spain 35°N, 5°W and Italy 43°N, 10°E). Three of these locations lie on the major European flyway, while the fourth (Italy) was chosen to demonstrate differences in the intensity of travel on allele spread. Lakes in each of these regions were seeded with a particular allele at the beginning of the model and the equivalent of 1000 year periods of duck migration was simulated. The response of the model was a metric of gene spread, i.e., the number of cells to which a particular allele reached through simulated bird-mediated transport. 3. Results 3.1. Parameterisation of flight angles The majority of ringing data obtained (87%) was on mallard and teal. Table 2 gives summary statistics of flight angles for all eight duck species during the two migration periods. Results of the analysis are expressed as the mean angle (and 95% confidence interval), the length or straightness of the angle and the concentration. The most commonly used index for describing straightness for a popula- 209 tion is the ‘r’ value, which is based on the length of the mean vector of a sample of known vectors (Batschelet, 1981). ‘r’ ranges from zero to one; where there is so much dispersion that there is no common direction, r = 0; when all the data are concentrated at the same direction (i.e., the mean angle), r = 1. The concentration is a parameter specific to the Von Mise’s distribution and measures the departure of the distribution from uniform. Flight angles for the spring period suggest a general movement north-east, probably in line with a general increase in mean temperatures. Likewise, autumn migration patterns for all species (with the exception of the mallard) is in a south-westerly direction. The main difference between species is down to the concentration around the mean flight angle (Table 2). Wigeon, gadwall, teal and shoveler displayed relatively focused mean flight angles (high concentration) compared to the other species. The autumnal return journey is more diffuse for wigeon and mallard, and more directional for red crested pochard, shoveler and pintail. These movements which are very ‘scattered’ (e.g., mallard in autumn) potentially reflect the known overlap of wintering and breeding areas (Scott and Rose, 1996), which is likely to result in individuals moving along a variety of different pathways. Teal shows similar levels of concentration of flight direction for both migration journeys. This suggests that most of the birds are flying in similar directions and makes them an ideal species for developing input flight angle maps for the model described. Table 3 gives a summary statistic of the analysis and Fig. 3 gives a pictorial representation of the mean flight angle and standard deviation displayed in rose diagrams. We also investigated if the distance travelled by individual teals varied significantly in relation to age, sex and whether the birds were travelling to the breeding or wintering grounds. We found no significant difference in the distance travelled by males and females (xﬂmale = 1346.8 km, Table 2 Analysis of flight angle for the eight focal duck species. ‘r’ varies between 0 and 1, where 0 indicates no common direction, and 1 indicates that all birds follow the mean angle. Concentration indicates the variation about the mean angle, and is analogous to the variance. ‘*’ indicates that the confidence intervals are not reliable for this analysis Species Wigeon Gadwall Pochard Mallard Pintail Teal Shoveler Red-crested pochard 17 24.28° 7.67° 40.90° 0.83 3.25 71 42.49° 28.75° 56.22° 0.61 1.55 191 25.52° 10.67° 40.37° 0.37 0.8 606 11.07° 2.43° 19.70° 0.36 0.77 14 69.42° 20.69° * 118.14° * 0.45 0.85 435 47.93° 42.97° 52.88° 0.64 1.69 64 41.65° 29.01° 54.29° 0.67 1.84 47 54.57° 329.49° * 139.64° * 0.14 0.27 249 246.98° 219.00° * 274.95° * 0.18 0.36 50 232.41° 219.97° 244.86° 0.73 2.22 377 209.26° 201.89° 216.62° 0.52 1.2 7742 81.42° 74.20° * 88.64° * 0.12 0.25 210 232.08° 224.13° 240.02° 0.61 1.56 1909 213.77° 211.00° 216.54° 0.59 1.46 202 235.48° 233.24° 237.73° 0.96 12.9 87 228.24° 215.25° 241.23° 0.59 1.46 Spring migration Observations Mean angle (µ) 95% confidence interval (–/+) for µ Length of mean angle (r) Concentration Autumn migration Observations Mean angle (µ) 95% confidence interval (–/+) for µ Length of mean angle (r) Concentration . 210 P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 Table 3 Summary of results for the analysis to determine the angle of flight based on common teal ringing records. See Table 2 for explanation of length and concentration Spring migration Autumn migration Females Males Females Males Observations 165 Mean angle (µ) 46.62° 95% confidence interval (–/+) for 39.44° µ 53.81° Length of mean angle (r) 0.71 Concentration 2.08 . 199 48.10° 40.30° 617 705 214.09° 213.41° 212.36° 211.53° 55.89° 0.63 1.65 215.82° 215.28° 0.93 0.91 7.35 5.60 Fig. 3. Rose diagrams of the mean flight angles for common teal. The thick line indicates the mean angle and black lines give an indication of the number of birds heading in different directions. Data shown are for all teal records combined and for females and males separately. xﬂfemale = 1402.1 km; F1, 1626 = 1.71, NS), but our findings indicate differences between juveniles and adults (xﬂadult = 1406.9 km, xﬂyearling = 1320.8 km; F1, 1626 = 4.03, P = 0.045) and suggest that the distances travelled vary significantly in relation to the two migration journeys (xﬂnorth = 1670.2 km, xﬂsouth = 1289.5 km; F1, 1626 = 57.60, P < 0.0001). Teal heading to the breeding grounds travel significantly further than those heading to the wintering grounds. 3.2. Sensitivity analysis Migration strategy was a highly significant variable for gene spread for each of the four locations (Norway, Netherlands, Spain and Italy; the gene spread for the two migration strategies were compared with t-tests, N = 50, Table 4 Sensitivity analysis results, summarising F-values and significance levels of an analysis relating duck body mass, wing span and kappa to gene spread using a ‘hoppers’ migration strategy. * indicates a significance of P < 0.05, ** of P < 0.01 and *** a significance of P < 0.0001. NS indicates not significant Parameter Norway Netherlands Italy Spain Body mass Wing span Kappa . –164*** 2.69 NS 10.68** 13.6 ** 0.07 NS 6.04* 33.8*** 0.42 NS 1.92 NS –108.4 *** 85.5*** 0.003 NS Table 5 Sensitivity analysis results, summarising F-values and significance levels of an analysis relating duck body mass, wing span and kappa to gene spread using a ‘jumpers’ migration strategy. * indicates a significance of P < 0.05, ** of P < 0.01 and *** a significance of P < 0.0001. NS indicates not significant Parameter Norway Netherlands Italy Spain Body mass Wing span Kappa . –114.9*** 4.02 4.70 –106.9*** 31.7*** 12.18** –136*** 0.80 NS –0.13 NS –200.6*** 0.30 NS 4.24 NS P < 0.0001 in all cases). The results of a partial correlation analysis relating duck body mass, wing span and kappa to gene spread in the four locations indicated that the most important variable was body mass (Tables 4 and 5). Wingspan was only a significant variable for Spain in the hopper migration strategy and the Netherlands of the jumper strategy. Kappa was only important for Norway and the Netherlands in the hopper migration strategy. For the hopper migration strategy (Table 4) the negative F-values for body mass in Norway and Spain indicate that smaller ducks making frequent stops might be more important for spreading genes originating in these locations; whereas larger ducks, making comparatively longer hops, could be more important for spreading genes from the Netherlands and Italy. For the long-distance (jumper) migration strategy (Table 5), the findings suggest that smaller ducks making more stops might be more important for spreading genes than bigger ducks. For alleles spreading from the Netherlands, small ducks with large wings and the direction of flight could be important. This was not the case for alleles in Norway, Spain and Italy. Based on the sensitivity analysis, we hypothesise that duck body mass and migration strategy play significant roles in influencing the pattern of allele spread in all of the four regions investigated. In addition, wingspan may have an important influence on the pattern of allele spread by ducks originating in Spain, whereas kappa may have a significant effect on allele spread from Norway and the Netherlands. Therefore, the results suggested that the factors important for simulated gene spread vary according to the point of origin of specific alleles. Based on these predictions, one might hypothesise that different duck species (each with different morphologies and migration P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 behaviour) are likely to vary in the effects they have on gene spread along migration flight paths. 4. Discussion The sustainable use of wetlands requires management approaches that incorporate the spatial and temporal interconnections of aquatic ecosystems (Amezega and Santamaría, 2000). Humans have increased the rate of change in the spatial distribution and movement patterns of many species and often there is a desire to predict the impact of these changes and how they might best be managed (South et al., in press). Spatially explicit population models (SEPMs) allow for the explicit representation of complex landscapes (South et al., in press) and can be used to inform habitat management and research options (Liu et al., 1995; Rushton et al., 2000). In this paper we have presented the results of a modelling framework in which a SEPM migration model for wildfowl was linked to a genetics model to investigate the impact of migration patterns on genetic diversity of aquatic organisms along flight paths. Unlike most SEPMs, this model does not simulate the population dynamics of waterfowl species, nor life histories of individuals migrating across Europe, but potential dispersal pathways for genetic propagules and the likely consequences of these movements on the genetic diversity in water bodies on or off the migration pathways. We contrasted two different strategies and the results of the sensitivity analysis strongly suggest that stop-over decisions made by individuals may have an important influence on gene spread. Our results predict that, both at the individual and species level, larger ducks may be important for long-distance gene spread in all regions investigated as they have the ability to travel further between stopovers. Furthermore, depending on the type of migration strategy (i.e., hopper or jumper), wing span and variation in the mean flight angle may also be important. The model simulations indicate that the contribution of different waterfowl species to dispersal is likely to differ in different parts of Europe and this should be investigated further with empirical case studies focusing on contrasting duck species. Based on these preliminary results, a conservation strategy to safeguard the biodiversity of, for example, cladocerans and aquatic angiosperms should examine carefully the existing network of European wetland sites in relation to migration pathways (see also Amezaga et al., 2002). The model framework presented in this paper constitutes a first step towards developing a predictive tool for wetland management in relation to biodiversity. The model is intended to illustrate the potential pathways along which genetic material can be distributed, and therefore currently assumes that transport and propagule survival in the new habitat occurs every time. The next developments of the model will need to address in more detail processes involved in wildfowl-mediated dispersal of aquatic organ- 211 isms. Specifically, future work needs to focus on three components of the model to improve predictions. First, there are bird-specific processes, such as alternate migration strategies, and processes that affect distances travelled such as the amount of fat accumulated by individual birds (e.g., see Gauthier et al., 1992), water constraints (Klaassen, 1996), fat and muscle burn during long-distance migration (Pennycuick, 1998). Other factors also affect dispersal behaviour such as philopatry, differences between the sexes due to moult migration and seasonal differences in distances travelled during winter movements or autumn/spring migrations (as indicated by the results of the ringing analysis in this paper and Green et al., 2002). Differences in behaviour, orientation, fuel loads and flight range (Hedenström and Alerstam, 1997; Weber and Houston, 1997) combined with the spatial distribution of water bodies along the European migration pathways are also likely to lead to a geographically articulated patterns of Anatid stopover and thus propagule deposition locations and this needs to be addressed in more detail. Clausen et al. (2002) hypothesise that the endozoochorous transport of aquatic macrophyte seeds is likely to be a rare event because long-distance migratory movements of birds are out of phase with the reproduction of these plants and migratory birds tend to void their gut contents prior to departure. Spatially explicit simulation models are particularly suited to investigating rare events such as these, and future model development could explore the importance of these events in long-distance dispersal. Second, propagule-specific processes such as the amount being transported, gut retention times and transport survival will need to be addressed. Ducks can carry propagules either on their feet and feathers or ingested in their gut (VivianSmith and Stiles, 1994; Figuerola and Green, 2002; Green et al., 2002). Charalambidou and Santamaría (2002) indicated species-specific differences in propagule survival in captive feeding experiments. In addition, temporal variation in propagule retention times and survival, mainly as a result of diet induced variation in digestive tract morphology, are also probable (Charalambidou and Santamaría, 2002). Potential dispersal distances of seeds by different duck species have been calculated by Clausen et al. (2002), based on gut retention times and flight speed. These data could be used to develop more realistic predictions of propagule spread. Finally, the population genetics of organisms being dispersed will need to be modelled more explicitly, by examining factors involved in selection of alleles, such as survival in the new habitat, competition with pre-existing fauna and flora, and colonisation of virgin habitats. De Meester et al. (2002) suggest that aquatic organisms have a high dispersal potential, but local adaptation could provide a powerful buffer against newly invading genotypes, and therefore, may result in low gene flow. This hypothesis reinforces the need for modelling a more comprehensive genetic system with case studies of specific aquatic organisms. 212 P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212 Acknowledgements We would like to thank Francisco F. Cantos (Spanish Ringing Office, Ministry of Environment) and Kjeld Pedersen (Copenhagen Bird Ringing Centre) for access to their data and Andy Green, Jordi Figuerola and Elmar Stoll for their help. 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