APPENDICES
FOR ONLINE PUBLICATION ONLY
1
Appendix A: Model processes
t
S t ,i  Fwind ,t ,i   ( Ft 1,i  c )(1  p)(1  rt 1,ts )
ts 1
eq. A.1
In equation A.1, the number of mobile seeds St,i, in source water cell i at time step t is
given by the number of seeds dispersed by wind into cell i at time step t ( Fwind ,t ,i ) plus
the additional number of mobile seeds in cell i at time step t (which depends on the
number of hydrochorous seeds entering the cell at time step t-1). The latter seeds
originate from wind dispersal at previous time steps. These can be calculated by
multiplying the number of mobile seeds entering cell i from an upstream water cell at
time step t-1 (that is, Ft-1,i) with the capture probability c, resulting in the number of
captured seeds in cell i at time step t-1. The number of captured seeds is then
multiplied with 1 minus the proportion of captured seeds that remain permanently in
cell i (p) to get the number of seeds in cell i that are mobile again. Then, mobile seeds
are multiplied with 1 minus the proportion of mobile seeds that sink (rt-1,ts) to obtain
the number of mobile seeds (that were already in the water at time step t-1) in cell i at
(the beginning of) time step t. The proportion of seeds that sink is dependent on the
residence time of the seeds (that is, time since seeds entered the water: t minus ‘time
starting’ ts). Therefore, mobile seeds in cell i at t-1 should be calculated for all seed
packages (see section hydrochory module) separately, and then added up, resulting in
the total number of mobile seeds in cell i at the end of t-1 and thus in the beginning of
2
t
time step t (  ( Ft 1,i  c )(1  p )(1  rt 1,ts ) ) (except those originating from wind
ts1
dispersal at time step t).
3
Appendix B: Parameterization
B1: Capture probability c
To parameterize the proportion c of seeds that remains in a water cell i during
transport through a cell, we used the seed release and retrace experimental design
described in Soomers and others (2010). Five out of eight experiments, executed in
2008 and 2009 in an 810 m long ditch in the Westbroekse Zodden (the Netherlands,
N:52°9'43", E:5°7'1"), were used for parameterization, three for validation of the
model. For these experiments, 1000 painted seeds were released in the ditch that was
divided into sections of 2 meters each, which corresponds to the cell size in the model.
For parameterization, the number of captured seeds in each section, 3 hours after
release was registered and transformed to the percentage of the total number of
retraced seeds. We used the location of the captured seeds three hours after release
because this time span allowed the seeds to reach the end of the ditch, given the speed
with which they were transported. Furthermore, the explanatory variables helophyte
cover 0-50 cm from the bank, the slope of the bank, the wind speed vector
perpendicular to the ditch and the presence or absence of 1) floating coarse plant
material (mowing remnants/aquatic plants) and 2) fine material such as algae,
duckweed or an ‘oil’ film on top of the water caused by iron-oxidizing bacteria, were
registered. Because of excess zero’s in the dependent variable (that is, percentage of
captured seeds in a section, multiplied with 100), a zero-inflated Poisson regression
analysis was used to investigate the relation between seed percentage and explanatory
variables. Zero-inflated models are two-component mixture models, in which a point
mass at zero is combined with a count distribution (Atkins and Gallop 2007). Only
4
independent variables that were significant in both regression model components were
selected as explanatory variables in the final model. This procedure resulted in the
following regression equations (eq. B1.1 and B1.2) for the zero-component α and the
count-component β of the zero-inflated regression model:
α=
1
1 e
 ( 2.14 0.036H 1.36 F 1.42 M )
eq. B1.1
β= e 3.980.018H  2.06 F  2.23M
eq. B1.2
c=((1-α)*β)/10000
eq. B1.3
from which the seed proportion that remains in a cell when transporting through it,
and thus the parameter value for capture probability, c (eq. B1.3), can be calculated. H
is the percentage of helophyte cover in a section, 0-50 cm from the ditch bank, F is
the presence (1) or absence (0) of fine organic material and M the presence (1) or
absence (0) of coarse organic material. The resulting regression model was
significantly better than the 0-model (P<0.001, Likelyhood Ratio Test). The
denominator of equation B1.3 is 10000 because the dependent variable in the
regression model was the percentage of seeds that were captured in a cell times 100,
whereas the parameter value for c is the ratio of seeds that are captured in a cell.
For model validation, a special simulation landscape, in which every model cell
corresponded to a ditch section of the experiment ditch, was created. To calculate c
5
for each model cell of this model validation landscape for each of the three model
validation runs, values for the independent variables, such as measured in the ditch
section corresponding to the considered model cell during the three experiments that
were kept separate, where used as input for these eq. 5 and 6.
For the real model simulations, for which the simulation landscapes visualized in
Figure 1 were used, two scenarios of ditch roughness were distinguished: 1)
roughness scenarios in which helophyte abundance along the bank (0-50 cm from the
ditch bank) was 25.6% per cell (the average abundance in our experiments) and where
no other obstructions were present in the ditch (called the highway scenario, H), and
2) roughness scenarios in which helophyte abundance was 50%, and fine floating
material was present in the cells (called the increased roughness scenario, IR). For
both scenarios, helophyte abundance was assumed to be 5% in winter (1st of
November-31st of March). Filling in these values for the independent variables in
equations B1.1-B1.3 results in a capture probability c of 0.002 for the highway
scenarios in the summer season and 0.0007 in the winter season and in a capture
probability c of 0.078 in the increased roughness scenarios during the summer season
and of 0.016 in the winter season. In these scenarios, c was assumed to be equal for
each cell (in contrast to the validation runs).
B2: Permanent capture probability p
After seed transport and capture, part of the captured seeds remain permanently in the
cell in which they were captured, whereas the rest of the captured seeds becomes
mobile again. To parameterize the proportion of captured seeds that are deposited
permanently, a long term seed mimic experiment was executed as follows.
6
Two hundred and fifty individually marked flat, round, cork seed mimics with a
diameter of 4 cm were released in each of two ditches in the Westbroekse Zodden (the
Netherlands, N:52°9'43", E:5°7'1"). A pilot study in which both seed mimics and
Carex pseudocyperus seeds were released and retraced in a ditch divided into 10-m
sections, revealed that seed deposition one day and three days after release was well
represented by seed mimic deposition (Spearman correlation, r=0.933, P<0.001 and
r=0.963, P<0.001 respectively). Every week, the xy coordinates of each individual
mimic that could be retraced was registered. Thereby, it could be determined whether
seed mimics had moved over the week. Seed mimics in ditch 1 could be followed
during 9 weeks, after which the ditch was cleaned, and mimics in ditch 2 could be
followed during 16 weeks. In both ditches, part of the mimics did not move anymore
after they had reached their first deposition location the day after release, which
confirms the assumption that part of the captured seeds stay at their capture location
permanently. Unfortunately it is almost impossible to execute such an experiment for
a whole year. Therefore, we had to assume that mimics that had not moved for several
weeks would not become mobile again. Because only 12 mimics of ditch 2 could be
retraced every week, we only used the data retrieved in ditch 1 to determine the
percentage of seeds that are deposited permanently after capture (56 mimics). For
week 1-5, we calculated the percentage of the mimics captured in that week that were
still at the same location at the last observation day (after 9 weeks). We used a
solution of a negative exponential growth equation (eq. B2.2), to determine the ratio
of the captured seeds per day that remains at this location until the end of the
experiment.
Z (t )
  pZ (t )
t
eq. B2.1
7
Z (t )  Z 0  e  pt
eq. B2.2
Equation B2.1 represents the negative exponential growth equation for which
equation B2.2 is the solution for continuous time. Z(t) refers to the number of seed
mimics still floating after 7 days (t=7), Z0 is the initial number of floating seed mimics
in a certain experiment week and t is the number of days after which the location of
the mimics was registered again (7). For each week (week 1-5), the proportion of
captured seeds that are captured permanently each time step, p, was calculated using
equation B2.3, which follows from equation B2.2.
p
ln( Z 0 )  ln( Z (t ))
t
eq. B2.3
The weighted average of these proportions that were calculated for experiment week
1-5 was used as the parameter value for the proportion of captured seeds that are
deposited permanently each time step (p=0.168 (SD: 0.11)).
B3: Capture probability of culverts cculvert
An experiment was performed to determine the effect of culverts on seed transport.
We released 200 painted C. pseudocyperus seeds in front of 3 different culverts in the
Westbroekse Zodden and placed a net behind the culvert. This experiment was
executed fifteen times in total. On average, only 4% (SD: 4.9) of the seeds had been
8
transported through the culvert one day after release. Therefore, the ratio cculvert of
seeds captured in or before a culvert when transporting through it was set to 0.96.
B4: Sinking ratio rt,ts
Data of Van den Broek and others (2005), who measured seed buoyancy of seeds of
wetland species during 210 days, were used to determine the proportion of floating
seeds that sunk each day, for both species. Van den Broek and others determined for
both of our model species the days at which 10%, 25%, 50%, 75% and 90% of the
seeds had sunk. We used these data points to determine a linear regression line
relating percentage of sunken seeds to number of days after release. When the
intercept was positive, the regression line was forced through the origin to avoid a
situation in the hydrochory module in which seeds start sinking before they are
actually released. The data points of Van den Broek and others (2005), and the fitted
regression lines are plotted in Figure B4.1. Equations for the regression lines are given
in the caption of Figure B4.1.
9
Figure B4.1. Percentage of sunken seeds plotted versus the number of days after release, for
Carex pseudocyperus and Phragmites australis. Data points (diamond symbols connected by
dashed lines) taken from Van den Broek and others (2005), for stagnant water. Equation of
the fitted linear regression line (solid lines) for C. pseudocyperus: y=0.61x-20.1, R2=0.99.
Equation of the fitted linear regression line, forced through the origin, for P. australis:
y=0.90x, R2=0.63
The regression equation given in Figure B4.1 can be written as
S=a(t-ts) + i
eq. B4.1
for both species, in which S is the percentage of sunken seeds, a is the regression
coefficient (a=0.61 for C. pseudocyperus, a=0.90 for P. australis), t is the time step, ts
is the time step at which the considered seeds were shed (thus: t-ts is the number of
days after release of the considered seeds, x), and i is the intercept (i=-20.1 for C.
pseudocyperus and i=0 for P. australis) of the regression lines.
To determine each time step the ratio of the still floating seeds that sink, equation
B4.2, that follows from equation B4.1, is used in the hydrochory module:
rt,ts = a / [100 - a ((t - ts)-e) + a]
eq. B4.2
10
rt,ts in equation B4.2 is the ratio of the seeds that are still floating that sink at time step
t and were shed into the water at time step ts, e represents the number of days after
release at which seeds start sinking. For both species, e is calculated by calculating the
value for t-ts in equation B4.1 for which S equals 0 (e=33.1 for C. pseudocyperus,
e=0 for P. australis). If t-ts<e, rt,ts was regarded to be zero.
To be able to calculate rt,ts at each time step for each seed, the model kept track of the
time since release for each seed.
11
Appendix C: Model validations
C1: Details on model validation procedure
Seed release and retrace experiments (described in appendix B1 and in Soomers and
others 2010), were used to validate the hydrochory module. Three out of eight
randomly chosen repetitions of the experiment described in appendix B1 were kept
separate, to use them for model validation. We measured (or obtained from databases)
in one ditch the variables that drive seed transport via water in the model. These
variables were obtained for each experiment section (that is, a 2 meter long part of the
ditch) which corresponds with one model cell.
The variables were wind speed and direction on the days at which the experiments
were executed (read from the KNMI database (KNMI, 2011)), helophyte density
along the bank, presence of fine floating material (such as algae, a bacterial film, or
duckweed), presence of coarse floating material such as mowing remnants, presence
of a culvert, and seed buoyancy. Capture probability c varied per model cell,
according to helophyte density and presence of fine or coarse floating material (see
equations in Appendix B1). In the model, 1000 seeds were released in the ditch at the
same location as in the experiments. Because in the experiments seeds were released
at 10 am, the average daily wind speed and direction used in the model was calculated
from 10 am that day until 10 am the next day.
Because we never observed seeds in the nets, which were placed at the end of the
ditch for five out of the eight experiments, we could assume that seeds we did not find
back were not lost because they had been transported over longer distances than we
could trace. Therefore, we assumed that the proportion of retrieved seeds in a cell of
12
the total number of retrieved seeds would be the same as the proportion of retrieved
seeds of the total number of released seeds if all seeds had been retrieved.
The model was run with the settings of each experiment [that is, wind speed of the
days of the experiment, helophyte density etc. for each model cell (corresponding to a
ditch-section) at the days of the experiment] for 2 time steps. The percentage of
released seeds located in each model cell after 2 time steps of hydrochorous dispersal
(48 hours) was compared with the percentage of retrieved seeds in the experimentsections 48 hours after release. To assess model performance, seed percentages in the
model cells were related to seed percentages in the experiment sections using a
Spearman correlation test for all experiments together. Furthermore, cumulative seed
percentages for both the model and experimental results were plotted against distance
from release point for the three experiments separately.
13
C2: Model validation: observed versus simulated distances
Figure C2.1: Cumulative percentages of released C. pseudocyperus seeds plotted against
transport distance for three independent release experiments (solid lines) and for the
corresponding model simulations (dashed lines). Model settings correspond to actual wind
speed and direction of the days of the experiment and actual helophyte cover and presence or
absence of fine or coarse organic material per experiment section (see Appendix B1).
Permanent capture probability according to Appendix B2. Observed and simulated
percentages per distance two days after release are plotted.
14
Appendix D: Model simulation results
Figure D.1: The contribution of each dispersal mode (1) wind or 2) water after
entering via wind (for scenario SW-HD-IR) to the total number of Phragmites
australis seeds that deposited at a certain distance class from the centre of the seed
source. SW-HD-IR: majority of the ditches southwest-northeast oriented, high ditch
density, increased roughness (see Appendix B1 and Figure 1).
15