A mathematical model of an estuarine seagrass

ELSEVIER

Ecological Modelling 98 (1997) 137-149

A mathematical model of an estuarine seagrass Joanne Wortmann a,., John W. Hearne a, Janine B. Adams b a Department of Mathematics and Applied Mathematies, University of Natal, Pietermaritzburg, Private Bag XO1, Scottsville, Pietermaritzburg 3209, South Africa b Department of Botany, University of Port Elizabeth, Box 1600, Elizabeth 6000, South Africa

Accepted 11 September 1996

Abstract

A discrete simulation model for the dynamics of a submerged macrophyte, Zostera capensis SetcheU, is presented. The model describes the vegetative spread of Zostera sp. which occurs through runners. The model can be used to analyse the response of Zostera sp. to various freshwater-related scenarios. The model shows how reduced freshwater inflow and associated stable salinities have contributed to the increased Zostera sp. population. The effect of floods and dry conditions are simulated. The dynamics of Zostera sp. was investigated for various mouth breaching scenarios. © 1997 Elsevier Science B.V. Keywords: Discrete model; Freshwater-related scenarios; Mouth breaching scenarios; Spread; Submerged macrophyte

1. Introduction

The role o f freshwater in South African estuaries today differs from what it would have been in the past when river catchments were free of dams and industrial and agricultural pollution were absent (Adams and Bate, 1994c). Today, over 40% o f the total river runoff is already impounded (Adams et al., 1992). This can be expected to threaten estuarine ecosystems (Jezewski and Roberts, 1986) since the flora and fauna of estuaries are uniquely adapted to varying freshwater * Corresponding author.

inputs. Reduced freshwater inflow has increased the water column salinity to the extent that submerged marine macrophyte communities have encroached to the upper reaches and displaced brackish communities. Reduced freshwater inflow also increases the frequency of mouth closure due to increased sediment stability. The amplitude and frequency of floods is attenuated with less freshwater inflow. Zostera capensis Setchell is a submerged macrophyte that is common in many South African estuaries. Submerged macrophyte communities are important as they provide a substantial amount of primary productivity, nutrient

0304-3800/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3800(96)01910-2

138

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

storage and nursery habitats in shallow estuarine waters (Hanekom and Baird, 1984; Talbot and Bate, 1987). Zostera sp. occupies the intertidal and shallow subtidal zone in South African estuaries. It is dominant in permanently open tidal estuaries because of its ability to survive daily periods of exposure (Adams and Bate, 1994b). Zostera sp. thrives under saline conditions (30 parts per thousand (ppt)). With the probability of increases in freshwater impoundment of river systems, the model in this paper was developed to determine the long term effects of these impoundments on the growth dynamics of Zostera sp. communities. The model describes the vegetative spread of Zostera sp. This occurs via runners. Although Zostera sp. also grows from a seed bank, this aspect of Zostera sp. growth is not modelled as our purpose is to model the dynamics of existing Zostera sp. beds. In a survey of the Swartkops estuary, South Africa, Talbot and Bate (1987) found that Zostera capensis area expansion between summer and winter appeared to be via existing runners because no new beds were observed in the area. Most of the recovery of Zostera sp. in the Kwelera estuary (Talbot et al., 1990) after the flood in November 1985 came from regrowth and enlargement of existing beds. It is this phenomenon which we model in this paper. Deterministic, first-order differential equations were chosen to describe the growth dynamics and spatial spread of the Zostera sp. community.

2. The model

The growth of aquatic plants is controlled by physical factors (e.g. light, temperature, sediment quality and changes in water level fluctuations) and physiological characteristics of the plant (e.g. nutrient requirements and sediment preference). Models of submerged macrophytes appear in Titus et al. (1975), Scheffer et al. (1993) and Bach (1993). These models represent macrophytes in one-dimension with differences predicted in the vertical direction by segmenting the water column into layers. Hara et al. (1993) developed a model of an emergent estuarine macrophyte. They apply

a diffusion model to the growth dynamics of individual shoots of the plant during one growing season. Collins and Wlonsinski (1989) use a two dimensional model based on a set of rectangular grid cells to simulate the growth of macrophytes in reservoirs. In their model however, neighbouring plants do not interact: Macrophytes occupy the sediment surface and if biomass of a cell exceeds a certain volumetric density factor, the macrophyte only grows upward into the next higher cell. Weiner (1981) argues that a plant's reproductive output should be affected by the presence and behaviour of neighbours. His model of plant competition is based on the individual level that looks at the number, distance and species of neighbours. This type of model is known as a neighbourhood model, e.g. Brisson and Reynolds (1994, 1996), Pacala (1986a,b). The model developed in this paper is kept relatively simple in that it does not consider physiological processes, e.g. photosynthesis, respiration, as in the models of Titus et al. (1975), Scheffer et al. (1993) and Bach (1993). The forcing functions are related to factors affected by freshwater inflow and are discussed later. Growth, 1 ........ =

o

0.8 0.6

"O O

0.4

E 0.2 0

0.2 0.4 0.6 0.8 biomassdensi~(g/sqrm) fl

--f2

1

--f3, f4

Fig. 1. Graphs of the model functions. The functions are dimensionless, lie between 0 and 1 and depend on biomass density. The function fl (Eq. (2)) represents biomass growth from a cell. The function f2 (Eqs. (2) and (3)) determines how much cell growth contributes to expansion to adjacent cells. The functions f3 (Eq. (3)) and f4 (Eq. (4)) account for competition for space in spread to the adjacent cells (f3) and competition within a cell (f4).

139

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

= 0.8 .9 '~ 0.6

hl

-~'0.4

gl

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, 10

,

, - ", , , , 20 30 40 salinity (ppt)

I 50

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1

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~ 0.8

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>~ 0.2 0 0

0.2

0.4 0.6 0.8 velocity (m/s)

1

~ 1.2

I

0 3

5

I•° 7

9

11

exposure time (hours)

Fig. 2. Graphs showing the forcing functions of the model. The h (g) functions are growth (death) functions. Zostera grows optimally for salinities between 15 and 30 ppt. The exposure functions show that Zostera growth is reduced if exposed above the water level for more than 6 h a day. Growth of Zostera is significantlyreduced at 0.5 m/s and Zostera will not persist in estuaries where the current velocityconsistentlyexceeds 1 m/s (which would represent high flow conditions in most South African estuaries). mortality and expansion are related to biomass density and the forcing functions.

3. Model structure The present model is grid-cell based. The grassland model of (Hobbs and Hobbs, 1987) is constructed on a grid of squares that each represent an area of grassland. Van Tongeren and Prentice (1986) use a grid-cell based model to simulate the recovery and spatial spread of plants after fire damage. The spatial model in Busing (1991) describes the growth of individual trees that occupy grid cells. Regeneration, growth and mortality of each tree are influenced by other individuals within a fixed neighbourhood radius.

Kenkel (1990) model of plant competition is based on a spatial structure of grid cells. Cellular automation models are also based on grid cell structures. A cellular automation is an approach that explores how simple rules of local cell processes can generate complex behaviours in space and time (e.g. Hogeweg, 1988; Caswell and Etter, 1993; Ermentrout and Edelstein-Keshet, 1993). In the present model hexagons were chosen as the cell shape because adjacent cells are exposed to the same surface area. The cells are chosen so that macrophyte biomass is distributed uniformly within each cell. Like Van Tongeren and Prentice (1986) we assume that there is a maximum amount of biomass that a cell can support. For Z o s t e r a sp. this value is approximately 300 g/m 2 (Adams and Talbot,

140

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

~'300

~ 250 "~'~200 150 x~ (D 100 (/}

E 5O ._o " 0

1

~

I

I

I

I

I

20 30 40 distance from mouth (m)

0

10

~- 300

~'300

~ 250

~ 250

"~200

,~_~200

15o

~5o

100

100 (tJ

=m 50

~ 5o

--~

.g e~ 0

, 0

._o I

10

t

I

20

p

I

t

30

I

~

40

.0

0

i

0

distance from mouth (m)

I

i

I

i

I

i

I

10 20 30 40 distance from mouth (m)

Fig. 3. Graphs showing the initial biomass distribution of Zostera for the model simulations. Biomass distributions are shown at the high (top graph), average (bottom left) and low (bottom fight) tide marks. Since Zostera is able to survive short daily periods of exposure, there is some biomass at the high and average tide marks. A longitudinal salinity gradient is assumed and so Zostera biomass decreases away from the estuary mouth.

1992), although this value will vary for different systems. Biomass change is modelled as d T t ( z u ) = a o - z),j

(1)

where, • represents the /jth cell; Z,j represents Zostera sp. biomass (g) in the/jth cell, and G,7 and D U represent rates of growth and mortality (g/ day) in the/jth cell. Cell growth is density dependent, and is given by

where, EGR is the specific growth rate (g/gl/day), K is the carrying capacity of a cell (g) and fl and f2 are dimensionless density-dependent functions (Fig. 1). The function fl is used to describe possi-

ble biomass growth from the/jth cell: macrophyte increment is at first linearly related to it's biomass, but is discounted by a factor that increases with biomass, ensuring that growth reaches a minimal rate when a cell is full. Biomass growth is not zero when a cell is full because there is the possibility of expansion to adjacent cells. The function f2 is used to determine how much biomass growth is expansion. When a cell is empty, any biomass growth is cell growth only, and when a cell is full, any biomass growth is expansion. Van Tongeren and Prentice (1986) assume that growth is anisotropically distributed to adjacent cells up to a maximum rate. We assume that potential growth is distributed isotropically to adjacent grid cells, i.e. that cell biomass attempts to grow to all adjacent cells equally, and that

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

141

~-300

~ 250

~ 200 == 15o -o 100

~ 50 o

x~

0

I

I

I

I

I

q

]

10 20 30 40 distance from mouth (m)

o

~'300 ~ _ _

~,300 ~-250 200

~-250

~ 200

~

15o

~ 1oo +

-8 loo

~- 5o o

~

Eo 5° T

0

i

0

I

i

I

~

P

~

I

q

10 20 30 40 distance from mouth (m)

"Q

0

i

0

I

4

I

I

I

i

I

10 20 30 40 distance from mouth (m)

Fig. 4. Graph showing how Zostera dies back towards the estuary mouth when the mouth is closed for 5 months. Biomass distributions are shown at the high (top graph), average (bottom left) and low (bottom right) tide marks. effective or realised expansion depends on the density of the adjacent cells. This objective is achieved by using the simple formula,

e~/= PGij x f2

×f3 --zT~] x n

(3)

where: e~t is the actual growth from the/jth cell to the adjacent klth cell, f3 is a dimensionless density-dependent function (Fig. 1); and n is the number of adjacent cells. If a cell is partly surrounded by high density cells, the use of Eq. (3) means that some potential expansion growth can be lost; if a cell is completely surrounded by high density cells then all potential expansion growth is lost to competition for space (fs = 0). Background mortality is high when competition for space is strong,

/Zo\ Dij = EDR x Zo. x f4~--~ )

(4)

where, EDR is the specific mortality rate (g/gl/ day), and f4 is a dimensionless density-dependent death function (Fig. 1). The simultaneous action of several environmental factors upon growth is usually modelled using one of two classical laws: the law of multiplicative action of factors or Liebig's minimum law. The assumption of the law of multiplicative factors is that salinity, water level and flow velocity, for example, act independently on growth, for example, resulting in multiplying the factors (Swartzman and Bentley, 1979). Liebig's minimum law implies multiplication by the minimum of the salinity, water level and flow velocity factors. With this law only one factor is allowed to act at a time. The law of multiplicative factors has been chosen for the present model where various factors act independently on a rate. This approach has

142

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

been successful in modelling submerged macrophytes with combined light, temperature and nutrient gradients (Bach, 1993; Collins and Wlonsinski, 1989; Scheffer et al., 1993; Titus et al., 1975). The effect on growth of the two factors, salinity and water level, is expressed by two dimensionless functions hi(S) and ha(W), where E G R = E G R max × hi(S) × h2(W) and EGRma x is the maximum growth rate (0.005 g/g/day), h~(S) the dimensionless salinity growth function and h2(W) the dimensionless water level growth function. These physical functions are based on data from Adams and Bate (1994c) and are shown in Fig. 2. The salinity function is averaged over a period of 60 days. The water level function combines the individual effects of exposure above the water level and depth below the water surface, i.e. h2(W) = h2~(exposure time) × h22 (time below 2.5 m). The mortality rate varies with salinity, water level and flow velocity. These three factors are assumed to act independently, implying that the use of the multiplicative factors approach is reasonable, and E D R = EDRmax x g~(S) x gE(W) x g3(V) where EDRmax is the background mortality rate (0.005 g/g/day), g~(S) the dimensionless salinity death function, g2(W)= g2~(exposure time)x g22 (time below 2.5 m) the dimensionless water level death function and g3(V) the dimensionless sloughing function expressing loss of biomass due to current velocity (Fig. 2). Although wave impact decreases with depth, Zostera sp. grows in shallow intertidal and sudtidal waters and we assume that velocity is uniform with depth. The growth and death water level depth functions are not shown in Fig. 2: they depend linearly on the daily time Zostera sp. is submerged below 2.5 m. Salinity has a considerable effect on aquatic plant life. In small temporarily closed estuaries where there is lack of freshwater input, high salinities ( > 4 5 ppt) have been observed to cause impoverishment of the estuarine flora (Adams et al., 1992; Adams and Bate, 1994a). In addition to salinity stress, submerged macrophytes are sensitive to water level fluctuations. Reduced freshwater inflow may lead to a drop in the water level and this may result in the exposure and die back of the plants. The depth below the water surface

~: 100

/

m 80 ca o

"6 60

"6 m 40

E

ao 0

~

0

I

35

1.5

I

I

I

I

~

I

I

55 75 9.5 closure time (months)

I

11 5

Fig. 5. Graph showing the relationship between mouth open time and mouth closure time for the survival of Zostera in a temporarily closed estuary. For a specific mouth closure time, if the mouth open time is at least the value from the graph, Zostera will survive in the mouth.

is important. Zostera sp. cannot survive below 2.5 m due to insufficient light for photosynthesis. Submerged macrophytes will not persist in estuaries where the current velocity consistently exceeds 1 m/s (which would represent high flow conditions in most South African estuaries) and at 0.5 m/s growth would be significantly reduced (Reed, 1994). By simulating model runs at different time steps and different cell sizes, we found that a daily time step required a cell size of between 1 and 1.3 m 2 to give stable solutions (i.e. to give bounded 140 o~ 120 ~: 100 .o_ 80 .~ 60 ¢_ 40 2O LI

I

4

I

8

I

I

J

I

I

I

:

12 16 20 time (months)

- - natural

I

24

~,

28

post-dam

Fig. 6. The overall response of Zostera to a flood in a permanently open estuary. The flood occurs at the beginning of the first year. The graph shows how the presence of dams attenuates floods and reduces the dynamic nature of the system.

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

~" 300

-~"300

~ 250

2so

143

.._~200 Q)

150

15o

100

100

O0

¢o

E 5O

E 5O .9

"~

0

q

0

10

~

I

20

I

i

i

30

i

~

-Q

0

40

i

0

I

10

distance from mouth (m)

i

I

20

i

I

~

30

I

40

distance from mouth (m)

Fig. 7. The response of Zostera to a dry period of 1 year (initial biomass distribution given in Fig. 3). Water levels drop and submerged macrophytes are exposed and die-back. Biomass distributions are shown at the previous average (left) and previous low (right) tide marks.

biomass values). For these runs, an ideal environment for Zostera sp. growth was assumed; i.e. the forcing growth (death) functions had values of 1 (0). This means that salinity was kept constant at 30 ppt, the current velocity was less than 0.1 m/s, and the area modelled was below the low tide mark so that Zostera sp. was always submerged but not below a depth of 2.5 m.

4. Results Results were obtained for a grid of 20 by 20 cells, with a cell size of 1.2 m 2. Input data is a time series of daily salinity, water level and current velocity readings which is based on output from a physical model (Slinger, 1994) which was applied to a permanently open estuary and a temporarily closed estuary, representative of two categories of South African estuaries. Zostera sp. is found in permanently open estuaries where salinities are between 15 and 30 ppt. Our model was used to determine the effect of various mouth breaching scenarios on Zostera sp. Input data was based on results from the physical model of Slinger (1994) for a temporarily closed estuary. Fig. 3 shows the initial biomass distribution of Zostera sp. for these model simulations. Biomass distributions are shown at the high, average and low tide marks. Since Zostera sp. is able to survive short periods of exposure ( < 6 h/day, Adams and Bate, 1994b), there is some biomass at

the high and average tide marks. A longitudinal salinity gradient is assumed and Zostera sp. biomass therefore decreases with distance from the mouth. Fig. 4 shows the long term effect on Zostera sp. when the mouth is kept closed for 5 months and open for 4 months. Zostera sp. dies back towards the mouth because of lower salinities when the mouth is dosed. Other model simulations for different mouth breaching scenarios were used to determine what combinations lead to the survival of the Zostera sp. community in the mouth. We found the relationship % open time 0.12 x closure time + 0.2 if closure time < 4.5

m°nths0.7 if closure time > 4.5 months

(5)

where % open time is the minimum open time (in units of % of closure time) required for the survival of Zostera sp. in the mouth and closure time is in units of months. A shorter mouth open time resulted in the disappearance of Zostera sp. This relationship is shown in Fig. 5. Zostera sp. fluctuates in response to episodic floods (Palmer, 1980; Talbot and Bate, 1987; Hanekom and Baird, 1988). Decreasing or disappearing with the onset of major floods, these populations show rapid recovery after a lag of 1- 3 years (Talbot et al., 1990). The impoundment

144

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

~'300

~ 250 -~m200

.._>,

15o ¢/)

100

E 50 .9

.o

0

~

0

i

10

I

I

20

I

i

30

I

40

distance from mouth (m)

~- 300

~- 300

¢:~"250

~ 250

~ 200

.~_~200

150

15o

"o u) 100

100

(/) ¢6

E 5O

E 50 0

.o

0

i

0

I

I

I

i

I

I

20 30 40 distance from mouth (m)

10

"~

0

i

0

i

20 30 40 distance from mouth (m)

10

Fig. 8. Graph showing the initial distribution of Zostera for model simulation results in Figs. 9 and 10. Biomass distributions are shown at the high (top graph), average(bottom left) and low (bottom right) tide marks. A longitudinal salinity gradient is assumed and so Zostera biomass decreases away from the estuary mouth. of freshwater can be expected to alter this influence of floods on Zostera sp. populations. Our model showed that a pristine (i.e. no freshwater impoundment) estuary showed a 100% loss in Zostera sp. biomass at the onset of a flood (Fig. 6). In contrast to this, there is a 50% difference between pre- and post-flood biomass values for estuaries with freshwater impoundment (Fig. 6). (Input data for the flood scenarios were determined from the physical model of Slinger (1994)). The worst case scenario for submerged macrophytes is dry conditions which result in low water levels. This would lead to the exposure of the submerged macrophytes, and consequent die back. The graph in Fig. 7 shows the die back of Zostera sp. (initial biomass distribution given by Fig. 3) after a dry period of 1 year.

In South Africa the impoundment of freshwater from river systems to meet ever-increasing demands for freshwater has altered the longitudinal salinity gradient of estuaries. Salinities of 35 ppt may be found in the upper reaches of some South African estuaries. This has favoured Zostera sp. colonisation in the upper reaches. Fig. 8Fig. 9Fig. 10 show the encroachment of Zostera sp. upstream when freshwater inflow is reduced. The model predicts that after 3 years, Zostera sp. has spread 20 m upstream. Diversity is lost in the system as brackish submerged macrophyte species are absent in the upper reaches. In some estuaries freshwater macrophyte areas have been colonised by Zostera sp. beds. This has occurred in the upper reaches as a result of freshwater impoundment. The model showed that an increase in freshwater inflow by 5% was not

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

145

~" 300

~ 250 .~__~200

~= 150 100 t~

E 50 ._o .a 0

i

0

I

q --'-=,f

i

I

10 20 30 40 distance from mouth (m)

~- 300

~- 300

~ 250 ~ 200

~'250 "~200

.I

15o

?: 15o

100

x~ 100 it} O~

E 5O .9

"

0

,

10 20 30 40 distance from mouth (m)

E 50 ._o .o 0 0

10 20 30 40 distance from mouth (m)

Fig. 9. Graph showing the encroachment of Zostera upstream after a reduction in freshwater inflow for 1 year. Initial biomass distribution is given in Fig. 8. Biomass distributions are shown at the high (top graph), average (bottom left) and low (bottom right) tide marks.

enough to initiate the die back of Zostera sp. (salinities did not decrease sufficiently) in these areas, whereas an increase in freshwater inflow by 10% lead to the die back of Zostera sp. beds in these areas (Figs. 11 and 12). 5. Discussion

It is only during the last decade that attention has been paid to seagrasses anywhere along the South African coastline (e.g. Hanekom, 1982; Talbot and Bate, 1987; Hanekom and Baird, 1988; Talbot et al., 1990; Adams, 1991; Adams and Talbot, 1992; Adams and Bate, 1994a,b). Talbot and Bate (1987) surveyed the distribution and biomass of Zostera sp. in the Swartkops estuary, South Africa. Historical evidence, to-

gether with their winter 1981 (following the flood)-summer 1981 survey indicated a short term variability in biomass within the estuary. Such changes were probably in response to flooding. (Hanekom (1982) showed Zostera sp. biomass fluctuations were linked to episodic floods rather than to seasons). Talbot and Bate (1987) found that the average winter (post-flood) Zostera sp. biomass was half that of the summer biomass. While the present model results are general in the sense that they do not apply to a particular estuary, the post-dam scenario developed for Fig. 6 closely resembles the situation in the Swartkops estuary during 1981. Salinities are high throughout the estuary (Edgcumbe, 1980). The model predicts that average biomass is halved after the flood (Fig. 6).

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

146

~- 300

~ 250 .~_~200 15o 100

E 50 .g -~ 0 0

20 30 40 distance from mouth (m)

10

~" 300

~'300

0-250

~'250

~200

.~_~200

15o

15o

100

-o (/) 100

E 5O ._o

E 50 .o

(/)

0

'

20 30 40 distance from mouth (m)

10

~

0

,

0

10 20 30 40 distance from mouth (m)

Fig. 10. Graph showing the encroachment of Zostera upstream after a reduction in freshwater inflow for 3 years. Initial biomass distribution is given in Fig. 8. Biomass distributions are shown at the high (top graph), average(bottom left) and low (bottom right) tide marks. Talbot et al. (1990) recorded the variability in the distribution of Zostera capensis in the Kwelera estuary, South Africa. At the time of their study there were no dams on the Kwelera river. After a flood in November 1985, Zostera sp. took 3 years to recover to 64% of the pre-flood Zostera sp. biomass. The model in this paper (Fig. 6) predicts a slow recovery of Zostera sp. in an undisturbed estuary. The flood in November 1985 in the Kwelera estuary was heavy, whereas the flood simulated in the model was moderate, which explains the longer recovery time in the Kwelera estuary. There is complete removal of beds in response to major floods, moderate floods often lead to intensive deposition of fine muddy sediments which can either result in the smothering of beds or temporarily impair growth, but some of the rhizomes remain rooted (Talbot et al., 1990).

It is difficult to compare the long-term behaviour of Zostera sp. in Talbot and Bate (1987) and Talbot et al. (1990) with model output because of the lack of physical information on these estuaries. Validation of the encroachment rate predicted by the model should be tested experimentally. We discuss below some qualitative observations that agree with model output, and how the model may be used to assist in decision making in the management of the mouth condition and freshwater inflow. In South African estuaries where mouth closures are occurring more frequently due to reduced freshwater inflow, Zostera sp. communities may start to die back if the mouth remains closed for too long. This is not beneficial in terms of the substantial amount of primary productivity, nutrient storage and habitat shelter provided by this

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

147

~'300

15o

i,,~

~1oo i E 5or

-~

0 0

10 20 30 40 distance from mouth (m)

~" 300

~'300

~'250

~- 250

200

"~200

15o

15o

~100

100

O)

~= 5o

E 50 .g .o

.o

0

,

0

r

~

I

d

I

i

I

i

10 20 30 40 distance from mouth (m)

t'~

0

,

0

I

~

I

p

I

~

P

10 20 30 40 distance from mouth (m)

Fig. 11. Graph showing the initial distribution of Zostera for model simulation results in Fig. 12. Biomass distributions are shown at the high (top graph), average (bottom left) and low (bottom right) tide marks. Uniform high salinities are assumed throughout the estuary and so Zostera is present away from the mouth.

seagrass. If a management aim was to maintain Zostera sp. beds in the mouth, then the relationship given by Eq. (5) may be used to assist in determining the frequency and duration of mouth breaches. The model may be used to assess the effect of a disturbance on Zostera sp. For example, after a heavy flood in a particular estuary the model could predict the recovery time of Zostera sp. This would indicate whether other species that need Zostera sp. beds for survival or reproduction would die because of a long absence of the Zostera sp. habitat. In some South African estuaries (e.g. Kromme estuary, Adams and Talbot (1992), Slinger (1994) freshwater macrophyte areas have been colonised by Zostera sp. By testing various freshwater-related scenarios, the model may be used to deter-

mine whether it is possible to initiate a die back of Zostera sp. in these areas and what volume of freshwater should be released to achieve this goal (e.g. Figs. 11 and 12).

6. C o n c l u s i o n

The model developed in this paper describes the growth of the submerged aquatic macrophyte Zostera capensis Setchell. The model was used to explore the response of Zostera sp. to various freshwater-related scenarios. It was shown how the model can assist in managing mouth breaches and freshwater inflow. Zostera sp. is absent from most temporarily closed estuaries in South Africa (Adams and Bate, 1994c). This may be due to the fact that mouth closures are occurring more fre-

J. Wortmann et al./ Ecological Modelling 98 (1997) 137-149

148

~'300 ~'250 .~_~200 150 100 E 50

._o •~

0

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:

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~

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I

I

10 20 30 40 distance from mouth (m)

~-300

~" 300

~c~250

~ 250

~ 200

~200 Q)

150 Q}

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50

E 50

o'}

E

.o .o

15o

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o

0

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0

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t

*

10 20 30 40 distance from mouth (m)

.15

0

i

0

I

10 20 30 40 distance from mouth (m)

Fig. 12. Graph showing the die-back of Zostera (initial biomass distribution given in Fig. 11) after increasing freshwater inflow for 2 years. Biomass distributions are shown at the high (top graph), average (bottom left) and low (bottom right) tide marks. quently. A n o t h e r possibility is that the s u b m e r g e d m a c r o p h y t e Ruppia cirrhosa G r a n d e that is comm o n in m a n y South A f r i c a n estuaries o u t competes Zostera sp. Ruppia sp. has a wide range o f salinity tolerance, b u t c a n n o t survive n e a r the m o u t h o f p e r m a n e n t l y o p e n estuaries because of strong tidal currents. M o d e l l i n g the c o m p e t i t i o n between these two s u b m e r g e d m a c r o p h y t e s is in progress.

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