Modelling the consequences of duck migration patterns on the genetic

Acta Oecologica 23 (2002) 205–212
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
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
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
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
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
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
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
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
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
Body mass
Wing span
Migration strategy:
0.185–1.57 kg
0.58–0.98 m
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
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-
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
20.69° *
118.14° *
329.49° *
139.64° *
219.00° *
274.95° *
74.20° *
88.64° *
Spring migration
Mean angle (µ)
95% confidence interval (–/+) for µ
Length of mean angle (r)
Autumn migration
Mean angle (µ)
95% confidence interval (–/+) for µ
Length of mean angle (r)
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
Spring migration
Autumn migration
Females Males
Females Males
Mean angle (µ)
95% confidence interval (–/+) for 39.44°
Length of mean angle (r)
214.09° 213.41°
212.36° 211.53°
215.82° 215.28°
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
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
Body mass
Wing span
2.69 NS
13.6 **
0.07 NS
0.42 NS
1.92 NS
–108.4 ***
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
Body mass
Wing span
0.80 NS
–0.13 NS
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-
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.
P.W.W. Lurz et al. / Acta Oecologica 23 (2002) 205–212
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. We are also grateful for the comments made by
the two anonymous reviewers. This research was funded by
the European Commission as part of the Framework Programme 5 LAKES project.
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