Aquatic Botany 81 (2005) 245–251
Growth limitation of Lemna minor
due to high plant density
Steven M. Driever, Egbert H. van Nes *, Rudi M.M. Roijackers
Department of Environmental Sciences, Aquatic Ecology and Water Quality Management Group,
Wageningen University, P.O. Box 8080, NL-6700 DD Wageningen, The Netherlands
Received 4 March 2004; received in revised form 11 October 2004; accepted 6 December 2004
The effect of high population densities on the growth rate of Lemna minor (L.) was studied under
laboratory conditions at 23 8C in a medium with sufﬁcient nutrients. At high population densities, we
found a non-linear decreasing growth rate with increasing L. minor density. Above a L. minor biomass
of ca. 180 g dry weight (DW) mÀ2, the net growth rate became negative. At a density of 9 g DW mÀ2,
a maximum relative growth rate of ca. 0.3 dÀ1 was found. At very low densities (<9 g mÀ2), we
observed an inverse density dependence (or Allee effect). Probably, this lower growth rate was due to
lower local temperatures within such partly covered L. minor decks. On the basis of these
experimental results and literature data, a simple model was created. To test the model, the density
of duckweed in three different Dutch ditches was monitored for 9 weeks in spring. Within this period,
full coverage of the ditches by duckweed was reached. The maximum density increased with rising
air temperature. The model described the ﬁeld data well, suggesting that crowding is an important
factor in limitation of duckweed growth.
# 2005 Elsevier B.V. All rights reserved.
Keywords: Lemnaceae; Crowding; Biomass; Growth rate; Model; Inverse density dependence
In eutrophic ditches and ponds, duckweeds (Lemnaceae) often form dense ﬂoating mats
(Landolt, 1986). The biodiversity of such systems is usually low, as the water under
* Corresponding author. Tel.: +31 317 482733; fax: +31 317 484411.
E-mail address: email@example.com (E.H.van. Nes).
0304-3770/$ – see front matter # 2005 Elsevier B.V. All rights reserved.
246 S.M. Driever et al. / Aquatic Botany 81 (2005) 245–251
Lemnaceae mats often becomes too anoxic for ﬁsh and macrofauna to survive (Janse and
Van Puijenbroek, 1998). Due to competition for light, also submerged macrophytes usually
cannot coexist with Lemnaceae. The duckweed mats may be persistent and it is suggested
that Lemnaceae dominance is a self-stabilizing state (Scheffer et al., 2003). In (sub)tropical
areas, other free-ﬂoating plants such as water hyacinth (Eichhornia crassipes Solms) can
form an even larger threat to biodiversity (Mehra et al., 1999).
To control free-ﬂoating Lemnacea, insight in the growth dynamics is necessary. Several
abiotic factors have been studied intensively such as nutrients and temperature. Lemnacea
need high phosphorus and nitrogen loadings (Portielje and Roijackers, 1995). With
increasing temperature, the growth rate increases approximately linearly up to an optimum
(Landolt, 1986). Duckweed may deplete nutrients (Scheffer et al., 2003) and can change
conductivity and pH of the water (McLay, 1976). This way they change their own growth
conditions (Landolt and Kandeler, 1987). Relatively little attention has been paid to cause
of intraspeciﬁc competition within mats of Lemnacea and the effect on their growth.
We studied the effect of crowding on the growth rate of Lemna minor in the laboratory.
L. minor was grown in different densities, varying from low to high, in a medium with
sufﬁcient nutrients. From the results of this experiment, a simple model was constructed to
explore the factors involved in growth of L. minor. To validate the model, we monitored
three Lemna-dominated ditches near Wageningen (The Netherlands) for 9 weeks.
2. Materials and methods
2.1. Crowding experiment
The growth rate of L. minor was determined under laboratory conditions (23 8C, a 14-h
photoperiod and an irradiance of 180 mmol mÀ2 sÀ1 PAR). The plants were grown on a
liquid medium based on Smart and Barko (1985), optimised for Lemnacea by Szabo et al.
(2003). A series of different densities was used (5.5, 9.5, 90, 180 and 915 g dry weight
(DW) mÀ2). For each treatment, six replicates were applied. The initial biomass was
determined as fresh weight. The plants were placed in vertical cylinders (height 10 cm,
diameter 5.9 cm), which were placed in 2-l aquaria ﬁlled with medium (Szabo et al., 2003).
After day 4, the cylinders were placed in a basin with fresh medium. After day 7, the
experiment was stopped and the fresh weight and dry weight (24 h at 70 8C) of L. minor
were measured. The initial dry weight was calculated using the dry weight to fresh weight
ratio at the end of the experiment. The relative growth rate was calculated assuming
A simple model was constructed to describe the effect of crowding, temperature and
¼ B r f ðT; B; N; PÞ À l B (1)
S.M. Driever et al. / Aquatic Botany 81 (2005) 245–251 247
The variation in time of the biomass of L. minor (B in g DW mÀ2) was modelled as the
function of the maximum growth rate (r). The gross production was modiﬁed by a
limitation function ( f(T, B, N, P)), which was a function of air temperature (T), biomass (B)
and nutrients (N and P). Furthermore, the production was corrected for the loss (l), which
included mortality, predation and respiration.
The limitation function ( f(T, B, N, P)) was deﬁned as:
T À Tmin N P hB
f ðT; B; N; PÞ ¼ (2)
Topt À Tmin N þ hN P þ hP B þ hB
Temperature (T) limitation was assumed to be linear from the minimum temperature
(Tmin, 5 8C) up to the optimum temperature (Topt, 26 8C) (Landolt, 1986; Landolt and
Kandeler, 1987). Nutrient limitation of ammonia and nitrate (N) and ortho-phosphate (P)
were modelled as Monod-type functions, with the following half saturation values:
hN = 0.04 mg N lÀ1 and hP = 0.05 mg P lÀ1 (Luond, 1980). The limiting effect of biomass
was simply assumed to be another Monod-type function dependent on biomass B and with
a half saturation hB, which was determined during this study.
2.3. Field observations
Three ditches in the surroundings of Wageningen, The Netherlands, were selected. In all
ditches L. minor was present at the start of the monitoring period. For a period of 9 weeks
(April–July 2003) biomass was measured in approximately 14-days intervals using
stratiﬁed sampling. The water surface of the ditch was divided by eye into three strata, i.e.
0–20%, 21–80% and 81–100% coverage. The strata were drawn on a map and within each
stratum, 10 random sampling coordinates were drawn. The biomass in the stratum with 0–
20% coverage was neglected.
Duckweed was sampled using a method after McLay (1974). A 10 cm Â 10 cm gauze
covered iron square was positioned horizontally under the L. minor cover. The square was
lifted up through the cover of plants. All biomass not accounting for L. minor was removed
by hand and dry weight was determined (24 h at 70 8C).
Water samples for chemical analyses of N and P were taken at the last three sampling
dates. N–NO3À + N–NO2À, N–NH4+ and P–PO43À were analysed using a Technicon Auto-
analyser II. Air temperature data were obtained from a nearby weather station.
Growth rates of L. minor decreasing with increasing density (Fig. 1). The highest growth
rate of 0.30 dÀ1 was observed at a biomass of 10 g DW mÀ2. Remarkably, the lowest
biomass (5 g DW mÀ2) had a signiﬁcantly lower growth rate of 0.23 dÀ1 (Mann–Whitney
P < 0.008). The highest densities of 180 g DW mÀ2 and 915 g DW mÀ2 showed a negative
net growth rate of À0.02 and À0.08 dÀ1, respectively. These experimental data were used
to calibrate the model, assuming no nutrient limitation. The maximum growth rate, r, was
248 S.M. Driever et al. / Aquatic Botany 81 (2005) 245–251
Fig. 1. Growth rate as a function of the initial biomass of L. minor (g DW mÀ2). Dots indicate the measured
growth rate. The solid line represents the curve described by the model at a constant temperature of 23 8C.
obtained by extrapolation and was corrected for the optimum temperature of 26 8C
(0.41 dÀ1). The half saturation constant, hB, (26 g DW mÀ2) was calculated from the
equilibrium biomass. The resulting model was used to describe the net relative growth for
different biomasses (Fig. 1).
Fig. 2 shows the ﬁeld data and model prediction for each ditch. Growth rate, r, was ﬁtted
for each ditch separately assuming different limiting factors for each ditch. With an
increase in air temperature (day 42–47; Fig. 2), the duckweed biomass in all ditches
increased, as the model predicted.
For f N (N) and f P (P), the assumption was made that nutrients were not limiting
(Table 1), supported by the fact that L. minor was present at the start of the sampling period.
Using a combination of a laboratory-scale experiment and a simple model, we obtained
insight in the growth dynamics of L. minor in the ﬁeld. The laboratory experiment showed
the relation between crowding and growth rate. We were able to model ﬁeld growth in
Dutch ditches, suggesting that we captured the main processes in the model.
Yet several processes were neglected or oversimpliﬁed in the model. For instance, the
model assumed that the plants were homogenous distributed over the ditch. In reality, this
is usually not true because of the inﬂuence of birds and wind (Dufﬁeld and Edwards, 1981).
Indeed the distribution of L. minor in the sampled ditches was very heterogeneous, also
within the three strata.
In the model the loss, l, was assumed to be constant for all ditches (0.05), which equals a
lifetime of about 35 days, a realistic value for individual fronds (Landolt, 1986). The loss
included respiration, grazing and mortality implicitly. It was neglected that respiration is
S.M. Driever et al. / Aquatic Botany 81 (2005) 245–251 249
Fig. 2. Biomass (g DW mÀ2) of L. minor in three ditches and maximum air temperature (8C) from day 0 (17 April
2003) to day 63 (18 June 2003). Field data are indicated as black squares, open triangles and black dots for
Opheusden, Zetten and Sinderhoeve, respectively with standard errors (N = 10). Model output is shown as a
dashed and dotted line, dashed line and solid line for Opheusden, Zetten and Sinderhoeve, respectively. Maximum
air temperature is indicated by the dotted line.
strongly dependent on temperature. Differences between ditches in grazing pressure by
birds and invertebrates were not known and could not be accounted for in the mortality
rates. The inﬂuences of temperature, crowding and decomposition on mortality are
unknown. In our model, we used air temperature instead of water temperature. It is known
that temperature can vary widely between water, air and within ﬂoating mats (Dale and
Gillespie, 1976), so we assumed that the temperature of the fronds in the upper layers is
better described by the maximum air temperature than by the water temperature.
Despite these simpliﬁcations, the negative effect of crowding on growth rate was
accurately described in the model. The density dependent reduction of growth rate was
Characteristics of the ditches
Characteristic Sinderhoeve Zetten Opheusden
Length (m) 40.0 45.5 48.0
Width (m) 3.0 1.8–3.0 0.7
Depth (m) 1.6 0.5 0.4
Sediment Sand Clay Clay
N–NH4+ (mg lÀ1) 0.07 (Æ0.03) 0.08 (Æ0.01) 0.14(Æ0.10)
N–NO3À (mg lÀ1) 0.05 (Æ0.05) 0.04 (Æ0.03) 0.99(Æ1.38)
P–PO43À (mg lÀ1) 0.42(Æ0.56) 0.51 (Æ0.68) 1.62 (Æ0.65)
The nutrient levels are mean values for the last three sampling dates.
250 S.M. Driever et al. / Aquatic Botany 81 (2005) 245–251
clearly not linear, like in logistic growth, but it decreased approximately logarithmically. It
could well be described as a Monod-type growth limitation by biomass. The mechanism
causing this density dependency is not completely clear. In a dense mat, fronds are piled up
in several layers. One could expect that in such case layers can be subdivided into two
parts: an upper part with nutrient limitation and a lower part with light limitation
(Clatworthy and Harper, 1962) or CO2 limitation. However, since we observed only
decompositon in the lower parts, it seems not very likely that nutrient limitation of the
upper part was a major factor.
The laboratory experiments suggested that there is an inverse density dependence at low
densities. In waters partly covered by L. minor (biomass below 9.5 g DW mÀ2), the relative
growth rate increased signiﬁcantly with increasing Lemna density. A likely explanation for
this effect seems to be the increase of temperature in a closed deck, due to solar radiation
(Dale and Gillespie, 1976). In this way, there is facilitation at low densities once there is full
coverage, i.e. the higher temperature within the mat will increase the relative growth rate.
For other ﬂoating plants, a similar facilitation may occur. For instance, the tropical ﬂoating
Salvenia molesta is known to increase temperature locally (Room and Kerr, 1983).
We thank Gertie Arts and Dick Belgers from Alterra (Wageningen, NL) for useful
suggestions and discussions and Frank van Herpen, who helped a great deal with the
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