a model of the development of a periphyton community

8/8/2019 A Model of the Development of a Periphyton Community

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T. Asaeda, D. Hong Son /Ecological Modelling 137 (2001) 617562

flu6iatilis at different velocities. Newbold et al.

(1981, 1983) examined the horizontal heterogenei-

ties of nutrients due to a spiraling process using

both models and experiments. In natural streams,

the saturation concentration of nutrients on a

periphyton community seems to depend strongly

on the density of the community (Bothwell, 1985,

1988, 1989).

Several models have been devised to clarify the

relations among the periphyton community, nutri-

ent concentration in the overflowing water, and

the nutrient availability for periphyton growth

(Kim et al., 1992; Mulholland et al., 1994; DeAn-

gelis et al., 1995). The vertical variation of oxygen

produced in photosynthesis (Carlton and Wetzel,

1987; Sand-Jensen and Revsbech, 1987; Carlton

and Wetzel, 1988; Bott et al., 1997) implies a

vertically varying concentration of nutrient re-

sources for periphyton growth, indicating the pos-

sibility of a nutrient-limited condition forperiphyton communities (Horner et al., 1990;

Dodds, 1991; Borchardt, 1996). However, the ver-

tical variation of the resources for periphyton

growth, such as light and nutrients, has not been

quantitatively examined by either models or

experiments.

As a number of problems have been pointed

out in experiments, such as altering the commu-

nity structure and producing higher uptake rates

by removing the community from the surface in

the experiment (Kim et al., 1992), in this study weused models to: (1) simulate the process of periph-

yton development under the effects of essential

resources such as nutrients and light; and (2) in

turn, model the resources and water flow in the

development of the periphyton community.

2. Model description

All processes are given in the appendix to com-

pute the thickness of the periphyton mat, lightresource, growth, settlement and detachment of

periphyton (Asaeda and Son, 2000). Table 1 lists

the symbols.

An important concept underpinning algal re-

source kinetics is the single resource limitation

(Hamilton and Schladow, 1997), or the growth of

a species being limited by only one resource at

time, Liebigs law of the minimum. Thus, th

resource index, which is defined as the indicato

of the health condition and the reproduction abi

ity of the cell, is given as:

Rn, k, i( j)=min[NRn, k, i( j), IRn, k ,i( j)] (

Although the multiplication form of these compo

nents is an alternative for the resource index, Eq(1) seems to provide better results (Haney an

Jackson, 1996). Particularly, the multiplicatio

form becomes problematic when a number

resources increase.

Some periphytic algae grow within the viscou

sub-layer, where the flow is substantially lamina

(Horner et al., 1990); however, filamentous alga

are found mainly outside the viscous sub-lay

(Dodds and Gudder, 1992). Fig. 1 shows the ma

processes in the water column and their direction

of influence.

2.1. Detritus

The amount of detritus is simply assumed to b

produced only from dead cells in a periphyto

mat, and is given as a result of mortality, decom

position, and detachment as:

(DCk, i( j)

(t=%

n

GmortalCn, k, i( j)

(qT20Gdecomp

+Gdetach

)DCk, i( j) (

2.2. Nutrients

Although the process of the internal nutrie

concentration during reproduction is biological

greatly complex, the changing rate is thought t

depend on the reproduction rate (Haney an

Jackson, 1996). In the reproduction process of

cell, some nutrients inside the parent cell a

assumed to conservatively succeed to new daugh

ter cells. Thus

(IN C)n, k, i( j)=(INnew Cnew)n, k, i( j) (

If the reproduction rate is a function of tempera

ture, maximum reproduction rate, and resour

sufficiency (Eq. (4A)), excluding the subscrip

from Eq. (3) yields:


3/15


Table 1

Glossary of symbols

Symbol Unit Definition

mm3 mm2B Total biomass

C cell mm2 Cell density

Drag coefficientCdDC cell mm2 Dead cell density

EN External nutrientmg l1

concentration

Upstream nutrientmg l1ENoconcentration (boundary

condition)

Bottom friction coefficientf

Fcr Threshold strength of theN

filament

m s2g Acceleration due to gravity

Detachment rate forday1Gdetachnon-filamentous species

Gdiv Reproduction rateday1

Grazing rateday1GgzMortality rateday1GmortalRespiration rateday1GresDepthmH

Ik Light irradiance at k-layermE m2 s1

IN Internal nutrientmg cell1

concentration of the cell

Minimum internal nutrientmg cell1INminconcentration for

reproduction

mE m2 s1 Saturation irradiance forIsatreproduction

Von Karman constantK

(=0.4)

Kdiff m2 s1 Diffusion coefficient

Half-saturation nutrientmg l1

KNconcentration for the uptake

process

Viscosity coefficientKvis m2 s1

Calibration constantm s2Kz

l Longitudinal distancem

Length of filamentcell filament1L

Day, layer, and filamentousn,k,i(j)

(non-filamentous) species

index

Ndetach filament day1 Detachment rate for

filamentous species

NR, IR Nutrient and light resource

index

Q Temperature constant

SI m2 Surface area of filamentous

cell

Snor m2 Trapping efficiency

CT Water temperature

t day Time

m s1U Water velocity

Table 1 (Continued)

Unit DefinitionSymbol

mg cell1 day1UNmax Maximum rate of nutrient

uptake

m3Vi Biovolume of filamentous cel

m Distance from the bottomZ

mDz Thickness of k-layer

m1

Abiotic and biotic attenuatiopw, pcconstant

z, za Water, algal specific densitykg m3

Bottom shear stress~bottom N m2

(=zfU2/H)

IN C=INnew Cnew=INnew(C+DC)

6

=INnew(C+CqT20GdivRDt) (

or:

INnew=

IN

1+qT20GdivRDt (

Thus, the loss rate of the internal nutrient concen

tration due to the reproduction is given by

(IN

(t=

INnewIN

Dt=

INqT20GdivR

1+qT20GdivRDt(

In this study, the reduction of internal nutrie

concentration due to the respiration process

assumed simply as a function of the respiratio

rate, the internal nutrient concentration, and th

temperature as GresINq

T-20

(Hamilton anSchladow, 1997).

Benthic algal communities usually comprise a

outer layer of actively growing cells that remov

nutrients from the overflowing water and an inn

layer of older, metabolically inactive cells (Mu

holland, 1996). In the study, however, all cells o

a species in each layer were assumed to have th

same characteristics in nutrient uptake. The inte

nal nutrient concentrations and the maximum up

take rates were selected according to the size o

algal species (Borchardt et al., 1994).

The nutrient uptake rate of a cell is assumed t

correlate inversely with the internal nutrient con

centration, being zero when the cell saturates, an

to positively correlate with the nutrient con

centration in the surrounding water by a Micha

lis-Menten-type relationship (Hamilton an


4/15


Fig. 1. A schematic diagram shows the main processes inside the periphytic mat. Filled boxes are simulated constituents, rounde

boxes are related processes, hexagon and pentagons are controlling factors, and arrows are influencing directions.

Schladow, 1997). Endogenous requirements for

nutrients are the main cause of thresholds for

growth, and thus the minimum concentration of

internal nutrients is often defined as the concen-tration to stop the reproduction. Combining these

relations with the losses due to reproduction and

respiration provides the expression for the ex-

change rate of the internal nutrient concentration:

(INn, k, i( j)

(t

=UNmaxi( j)qT20

INmaxi( j)INn, k, i( j)

INmaxi( j)INmini( j)

ENk

KNi( j)+ENk

INn, k, i( j)qT20Gdivi( j)Rn, k, i( j)

1+qT20Gdivi( j)Rn, k, i( j)Dt

GresINn, k, i( j)qT20 (7)

The nutrient resource index is defined as

NRn, k, i( j)=INn, k, i( j)INmini( j)

INn, k, i( j)(8)

Overflowing water exchanges nutrients contin

ously with the periphyton mat. The diffusion pro

cess through the top boundary layer of th

periphyton mat, regardless of molecular or turbulent diffusion, controls the supply of nutrien

markedly (Mulholland et al., 1994). If nutrie

exchanges from the sediment and other process

were negligible, the conservation of the extern

nutrient concentration in the k-layer is given as

(ENk

(t+U

(ENk

(x=Kdiff

(2ENk

(z 2

+103

DV

qT20Gdecomp

%i( j)DCn, k, i( j)INn, k, i( j)

103

DV%n

%i( j)

UNmaxi( j)qT20

INmaxi( j)INn, k, i( j)

INmaxi( j)INmini( j)

ENk

KNi( j)+ENkCn, k, i( j) (


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The ratio of 103/DV is used to convert theuptaken and decomposed nutrient rate (mg day1)

to the exchange rate of the nutrient concentration(mg l1 day1) in the layer. In Eq. (9), the left

terms indicate the unsteadiness and the advectivetransport of the nutrient concentration, and the

right terms are the diffusion, the decomposition ofdetritus, and the loss due to algal uptake. The left

hand side and the first term on the right hand sideare well-defined for mass transport in fluid me-

chanics and the remaining terms are sources andsinks inside the layer.

Although excluding nutrients released from thesubstrate, the model considers nutrient cycling

through dead cells (detritus). This assumption issatisfactory for most laboratory experiments on

periphyton development, where the substrate isusually made from ceramic, plastic, and clay tilesand no nutrients are released from bottom. Fur-

thermore, nutrient exchanges in nature betweenthe sediment and over-flowing water are so com-

plicated that they may be represented by anotherindependent sub-model (Asaeda and Bon, 1997).

If nutrient flux from the air and from thesediment is assumed to be negligible, the

boundary conditions for Eq. (9) are:

(EN

(z

)surface

=0(EN

(z

)bottom

=0 (10)

Provided that the amount of a nutrient is con-served in the water column regardless of its forms

and that the main processes in the nutrient ex-change occur as in Fig. 1, Eqs. (1), (7)(10) are

repeatedly applied for all concerned nutrients. Inthis study, these equations were used to evaluate

temporal variations of phosphorous and nitrogenconcentrations. More detailed processes in the

cycling of the specific nutrient can be coupled tothe governing Eqs. (7) and (9).

2.3. Flow dynamics

The algal mat lies from the viscous sublayerthrough the overlying outer boundary layer, and

thus, the local Reynolds number varies widely. Ifa steady and longitudinally homogeneous current

is assumed, the friction at the bottom and thedrag force on the periphyton mat balances with

the longitudinal pressure gradient as:

0=1

z

(P

(x+Kvis

(2U

(z 2CdU

2B2/3

DV(1

where (P/z(x is the longitudinal pressure grad

ent and is given by the vertical integration of E

(11):

1

z

(P

(x

=~bottom

z

CdU2

B2/3

DV

(1

The last term in Eq. (11) represents the resistanc

due to the periphyton mat, and is similar to th

equation used for a terrestrial plant canop

(Kondo and Watanabe, 1992).

Inside the viscous sublayer, the kinetic viscosi

of water and the linear velocity distribution we

used. Outside the viscous layer, turbulent viscosi

and diffusivity were calculated from the velocit

profile and the mixing length, lm, as:

Kvis=Kdif= lm2

)(U

(z ) where lm=Kz1z

H1/

(1

3. Numerical procedure

A system of differential equations was solve

numerically by coding in FORTRAN90, inclu

ing 23 subroutines of 2300 command line

Additional graphic subroutines authorized by M

crosoft corporation permitted the main progra

to simultaneously show the results. The modwas also programmed with highly flexible runnin

options. For accuracy, the fourth-order Rung

Kutta method was initially used to solve a system

of the first-order differential equations. To i

crease the computational stability of the diffusio

process and to save computation time, an implic

scheme was finally used for the external nutrien

concentrations and vertical profile of velocity.

Thomas algorithm was used to solve a tri-diago

nal matrix (Fletcher, 1991), while an explic

scheme was used to integrate all the remaininvariables. The stability condition of the vertic

diffusion, DtBDz2/4Kdiff, was satisfied (Vreu

denhil, 1994). Thus, a few seconds of the time ste

was used in our model, while several hours

time step was used in previous models (EPA

1985). To deal with high biomass environments


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small time step is a prerequisite condition to reduce

errors caused by numerical integration. If a large

time step was chosen, for instance, a dense periph-

yton in a thin layer would exhaust the whole

nutrient even within a period less than the time step.

The velocity was calculated upwards immedi-

ately from the viscous sublayer, while the interpo-

lation of linear velocity distribution was adopted

inside the boundary layer. The water depth was

divided into a number of layers, their thickness

gradually increasing from the bottom to the water

surface. A resolution of one-third of the sublayer

thickness was always applied to the bottom layer.

The vertical resolution of the overlying mesh was

strongly related to the hydraulic conditions. In each

layer, the relationships of the periphyton biomass,

internal and external nutrient concentrations, irra-

diation, and the hydraulic regime of the overflow-

ing water were established.

Although this study is one dimension (vertical),

the advective transport of nutrients can not be

neglected because nutrients in a water column are

limited compared with the requirements of the

periphyton community. If the position of a consid-

ered area is in the middle of a stream and the

nutrient gradient is linear along the stream, the

contribution of nutrients from a convection, the

second term of Eq. (9), is numerically represented

as

UEN0ENk0.5l

,

where EN0 is the boundary condition for nutrien

and l is the length of a stream. In this aspec

considering one more dimension (e.g. longitudina

certainly provides results closer to reality than th

study.

4. Verification and discussion

In the verification, the major nutrients of concer

were nitrogen, and phosphorous because they ar

essential for aquatic organism. Other nutrient

such as carbon and silicon, were assumed to b

sufficient for periphyton growth. Boundary valu

of the phosphorous and nitrogen concentration

(e.g. EN0 in Eq. (9)) were tentatively assigned at

and 15 mg l1, respectively. The water dept

depth-average water velocity, and the light intensi

at the water surface were assumed to be constana s 6 c m , 2 0 c m s1, and 150 mE m2 s

respectively. Table 2 lists the biological paramete

of filamentous and non-filamentous species. Th

resource index for periphyton species was calc

lated from Eqs. (1), (8) and (3A).

4.1. Constant external nutrient concentration

The first verification was made under constan

external nutrient concentrations or, in other word

an infinite diffusion coefficient. The verificatioconsisted of three cases: (a) the condition

Table 2

Biological parameters used in the model (nutrient-related parameters are for either phosphorus or nitrogen)

Symbol Unit Filamentous i-species Non-filamentous j-species

day1Gdecomp 0.02 0.02

day1Ggz 0 0

Gres 0.1day1 0.1

INmin 0.610710107mgP cell1

mgN cell1 200107 4.2107

INmax mgP cell1 70107 4.2107

mgN cell1 1400107 29.4107

mE m2 s1Isat 200 200

2.0mgP l1 10.0KN30.0 4.0mgN l1

0.05105mgP cell1 day1 1105UNmax0.3510514105mgN cell1 day1


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Fig. 2. Cell density of filamentous (solid lines) and non-filamentous (dashed lines) species in three cases: a, b, and c (refer to the text

Fig. 3. Temporal variation of the internal phosphorous concentration of filamentous (solid lines) and non-filamentous (dashed line

cell in the bottom layer in three cases: a, b, and c (refer to the text).

were as described in Table 2; (b) the minimum

and the maximum internal nutrient concentra-

tions of case (a) were reduced by 50%; and (c) the

nutrient uptake rates of all species of case (a) were

reduced by 50%. The time step of 60 s was used.

Fig. 2 shows the cell density of filamentous and

non-filamentous species in three cases. In case (a),

the peak biomass of filamentous and non-filamen-

tous species was 8000 and 20 000 cell mm2

ondays 19 and 17, respectively (Fig. 2, case (a)). At

the peak biomass, however, the non-filamentous

community was dislodged and its density gradu-

ally decreased, while the filamentous community

notably fluctuated because remaining filaments

detached intermittently. As these detached

filaments were considerably long, consisting

many cells, their detachment markedly affecte

the total density of the community.

The decrease in the maximum and minimu

internal nutrient concentrations by 50% slight

shifted the peak values of both filamentous an

non-filamentous biomass to the earlier days (1

and 14), because the decrease in the maximu

and minimum nutrient concentration consquently increases the uptake rate in Eq. (7) an

eventually the growth rate (Fig. 2, case (b)). Thu

the periphyton community becomes more vulne

able to the drags and resource depletion.

With decreasing uptake rates, the biomass

non-filamentous species in case (c) did not i


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crease as fast as cases (ab). Consequently,

filamentous and non-filamentous biomass started

being dislodged later: on day 27 and day 16 (Fig.

2, case (c)). Especially, the extended high biomass

period of non-filamentous species delayed the in-

tensive growth of filamentous species by nearly 10

days.

Fig. 3 shows the variation of the internal phos-

phorous concentration, as an example of the in-

ternal nutrients concentration, where both

phosphorous and nitrogen had similar trends. The

value of a cohort settled at the beginning is repre-

sented for a non-filamentous species, whereas fo

a filamentous species, the value of an individu

filament is used. Reducing concentration to zer

shows the detachment of concerned filament.

Notably, the internal nutrient concentratio

was reduced markedly for both filamentous an

non-filamentous species within the first few day

after settling, because of the lower ambient nutr

ent condition than the cell experienced before. A

the uptake rate depends on the ambient nutrien

concentration, if a cell settles on a nutrient-poo

substratum, the internal nutrient concentratio

decreases rapidly. After that, a markedly stab

level of the internal nutrient concentration las

for both species (Fig. 3). As the external nutrien

remains constant regardless of the biomass, th

uptake rate of an individual cell balances with th

loss due to reproduction and respiration once th

internal nutrient concentration level satisfies th

condition until the limiting factor changes to thirradiance. The markedly stable level of the inte

nal nutrient concentration lasts for 15, 10, an

22 days in cases (ac), respectively (Fig. 3). Th

internal nutrient concentration increased slight

before the filament detachment.

Fig. 4 shows the temporal variation of resourc

indices of phosphorous nitrogen and light,

these cases. Generally, when a species switch

from being nutrient-limited to light-limited, th

nutrient resource indices increase. In due cours

an increasing biomass consequently decreases thlight index (Eq. (3A)), growth rate (Eq. (4A)), an

the reproduction loss (Eq. (5)), and finally i

creases the internal nutrient concentration (E

(6)). Thus, immediately after the light condition

limiting and further worsens with increasin

filamentous algal biomass, the internal nutrie

concentration recovers.

Fig. 4 also shows that filaments detach earlie

in case (b) and latest in case (c). A higher resourc

index of a single cell implies a healthier filamen

and, thus, the filament is more difficult to bdetached. The result indicates, however, th

filaments with a higher resource index were d

tached sooner. The drag force increases exponen

tially with an increase in resource index, while th

tension strength of a cell increases only linear

with an increase in resource index. The bioma

Fig. 4. Temporal variation of the phosphorous (solid lines),

nitrogen (dashed lines), and light (dotted lines) resource index

of filamentous (left) and non-filamentous (right) cell in three

cases: a, b, and c (refer to the text). Arrows indicate detach-

ment of filaments.


9/15


Fig. 5. Cell density of filamentous (solid lines) and non-

filamentous (dashed lines) species in two cases: d and e (refer

to the text).

required in the computation without a diffusio

process. In this verification, the time for the 30-da

simulation was 2 h using PC 586/550 MHz.

The results indicate that the non-filamentou

biomass transitions of the two cases have a simila

pattern, differing only by 10% (Fig. 5). Althoug

the transport is extremely hampered inside th

viscous sublayer, nearly a sufficient amount

nutrients is supplied for periphyton growth at

diffusion coefficient of 5109 m2 s1.

However, a temporal variation of the intern

nutrient concentration distinguished cases (d

(Fig. 6). With Kdiff=5109 m2 s1 (Fig. 6, ca

(e)), the nutrient flux is not sufficient to rapid

increase the filamentous algal biomass from day 1

thus showing a reduction in the internal nutrien

concentration. A similarity between Fig. 3(case (a

and Fig. 6(case (d)) implies that at a diffusio

coefficient of 1106 m2 s1, the rate of nutrien

flux is sufficient for each cell regardless of thcommunity density.

Fig. 7 shows marked differences in the nutrien

resource indices at different diffusion coefficients

Fig. 6. Temporal variation of the internal phosphorous con-

centration of filamentous (solid lines) and non-filamentous

(dashed lines) cell in the bottom layer in two cases: d and e

(refer to the text).

Fig. 7. Temporal variation of the phosphorous (solid lines

nitrogen (dashed lines), and light (dotted lines) resource inde

of filamentous (left) and non-filamentous (right) cell in tw

cases: d and e (refer to the text). Arrows indicate detachmen

of filaments.

fluctuation of a filamentous community causes

fluctuations in the light resource index of bothspecies (Fig. 4, cases (ab)). A comparison of Figs.

2 and 4 implies an exact inverse correlation between

the filamentous algal biomass and the light resource

condition.

4.2. Varied external nutrient concentration

The second verification was made with two

values of the diffusion coefficient inside the viscous

sublayer: (d) 1106 m2 s1, which was in the

same order with the molecular viscosity; and (e)5109 m2 s1, which is comparable with the

molecular diffusion coefficient for oxygen of 2

109 m2 s1 (Sand-Jensen and Revsbech, 1987).

Eq. (13) was used to calculate the diffusion coeffi-

cient outside the viscous sublayer. The time step

was 5 s, which was much smaller than the value


10/15


Fig. 8. Vetical profile of velocity on day 5 (d5), day 15 (d15),

and day 25 (d25).

5. Application

Observations made at a stream facility at th

University of Louisville, Kentucky, US

(Peterson and Stevenson, 1990, 1992) were used t

validate the model. To provide a water velocity o

0.29 and 0.12 m s1, water depths of 2.5 and 6

cm, respectively, were used. Despite fluctuationwere expected in the experiments, phosphorou

and nitrogen concentrations were kept constant

the entrance of the channels throughout th

simulation at 2.0 and 15.0 mg l1, respectively, an

the water temperature was 17.8C.

Fig. 9 shows the simulated results on ce

densities of these current regimes compared wit

observations. Generally, a community subject to

high flow rate experienced a markedly small

increasing rate and a lower peak biomass than

community subject to a low flow rate. In the slocurrent regime, the peak biomass of A

minutissima was 9500 cell mm2 on day 6 an

again occurred on day 14 with a higher value

12 000 cell mm2, while in the fast current regim

it was only 3200 cell mm2 on both days 15 an

30 due to the lower initial density and the highe

net emigration rate.

The Spirogyra spp. biomass started dislodgin

on day 25 with its high biomass of 15 000 ce

mm2 and fluctuated in the last 10 days of th

experiment in the slow current regime, while in thfast current regime the dislodgment was delaye

until day 30 with 4000 cell mm2. The low

biomass of Spirogira spp. in the fast curre

regime was mainly because of the low

immigration rate than in the slow current regim

Due to the low biomass, the time of dislodgmen

was delayed 5 days in the fast current regime.

Fig. 10 shows the variations in the resour

index of three species at the bottom. Having a hig

light saturation level, Spirogyra growth w

always subject to the light limitation of bocurrent systems. Although slightly higher in th

fast current due to the lower biomass density, th

light resource index of Spirogyra was maintaine

at 0.2 until its biomass increased and shade

itself. In the later stage of the experiment, how

ever, all species suffered from light limitation nea

the viscous sublayer. The phosphorous resource

index of filamentous species was stable at 0.5

with Kdiff=1106 m2 s1, exactly the same

as with the infinite diffusion coefficient, while it

gradually decreased to 0.4 on day 18 with

Kdiff=5109 m2 s1. This difference, how-ever, did not affect much the biomass (Fig. 5).

The similarity between cases (a) and (d) in the

biomass (Figs. 2 and 5), the internal nutrient

(Figs. 3 and 6), and the resource indices (Figs. 4

and 7) indicates that the diffusion coefficient of

1106 m2 s1 is still high enough to support

the dense community. As the nutrient require-

ment of filamentous species was higher than

non-filamentous species (Table 1), the nutrient

resource index of filamentous species was always

smaller in both cases than non-filamentous spe-cies.

Fig. 8 shows the vertical velocity distributions

on days 5, 15, and 25. The periphyton commu-

nity built on short turfs of filaments markedly

modifies the vertical profile of velocity such that

it de-creased near the bottom, but compensated

for this by increasing above the middle of the

depth on day 15. With further increasing

biomass as much as to form a mat on the sur-

face (on day 25), however, the surface velocity

decreases and the depth of the maximum valuereduces until at about two-thirds of the total

velocity (38 mm). The final velocity profile

agrees generally with the experimental observa-

tion that most of the water flow occurs in the

middle of the floating mat of zygnematalean and

the bottom (Peterson and Stevenson, 1990).


11/15


the bottom, which was again more serious in the

slow current regime.

From the initial values, the nutrient indices of

algae tended to decrease because of the high algal

consumption of nutrients under sufficient irradia-

tion. After Spirogyra arrived at the water surface,

the high floating biomass interrupted the penetra-

tion of solar irradiation into the water column,

and thus the nutrient concentration gradually re-

covered at the bottom layers. As a result, in the

final stage of growth, nutrient resources were

nearly satisfactory for all species shifted from

having nutrient-limitation to light-limitation. In

both flows, the light resource index of all species

temporarily fluctuated because of the dislodge-

ment of Spirogyra at the later stage of the

experiments.

Because Spirogyra has a high nutrient require-

ment, its internal nutrient concentration varied

largely according to the ambient concentrationcompared with that in diatom cells, especially in

the slow current. For A. minutissima and Synedra

spp., however, the ambient nutrient concentra-

tions were relatively sufficient and thus the nutri-

ent resource indices of these species were stable at

0.50.8 and 0.60.8, respectively, in both curren

regimes.

After reaching the water surface, Spirogy

filaments started to extend along the stream. A

increase in density of filaments near the surfa

reduced markedly the external nutrients in bo

current regimes (Fig. 11). In the surface layer

phosphorous and nitrogen concentrations wereduced from the initial values to 1.2 and 2.0 m

l1 in the slow current on day 24 and to 1.8 an

10.0 mg l1 in the fast current on day 28. With

high Spirogyra biomass in the final stage, th

nutrient concentrations in the water fluctuate

with the frequent detachment of algal communit

At the bottom, the external nutrient concentr

tion decreased with the increasing biomass un

0.5 mg l1 in phosphorous and 1.5 mg l1

nitrogen on day 15 in the slow current and on

until 1.0 and 3.5 mg l1 on day 30 in the facurrent. In the slow current regime, howeve

nutrients at the bottom quickly recovered aft

the floating filamentous mat formed on day 1

because the growth rate and the nutrient uptake

of diatom species declined.

Fig. 9. Comparison of cell density between computed (lines) and observed (symbols) results in the slow flow (left) and fast flo

(right) regime. SP, Spirogyra; AM, Achnanthes minutissima; SYN, Synedra spp.; Dead, Dead Achnanthes minutissima.


12/15


Fig. 10. Resource indices of three algal species at the bottom layer in the slow flow (left) and fast flow (right) regime: P, Phophorou

N, Nitrogen; L, Light.

The benthic algal biomass temporally varied

with successive rate, autogenic dislodgment, and

disturbance of the surrounding environment. Both

physiological and morphological characteristics

determine the competitiveness of algal species in

the benthic mat. Competitive dominants under

favorable environmental conditions are species

that have the highest intrinsic increasing rates toallow them to proliferate over other taxa. Despite

prominent differences in the nutrient concentra-

tion between the bottom layer and the overlying

water and between the fast and slow currents,

nutrient resource index of the diatom, A. minutis-

sima and Synedra, was relatively stable. In other

words, A. minutissima appeared to have adapte

to exploit relatively low levels of dissolved nutr

ents. This agreed with the findings of Pring

(1990).

A Spirogyra recession occurring at the end o

both currents was reproduced fairly well by th

study, implying that light availability to cells

the lower layers of periphyton matrices regulatebiomass accumulation by affecting the strength o

attachment of the bottom cells to the substratu

(Boston and Hill 1991; Peterson, 1996). Sever

pieces of evidence suggest that Spirogyra is no

capable of tolerating prolonged exposure to e

tremely low or no light (Graham et al. 1995


13/15


Fluctuations of diatom biomass and A. minutis-

sima dead cells coincided with the Spirogyra re-

cession due to the secondary detachment of

non-filamentous cells inhabiting the interstices of

the filamentous mat. Also, it shows that, a consid-

erable number of dead cells were settled from the

overlying water and were trapped on top of the

benthic mat and then detached with filaments.

6. Concluding remarks

This study numerically indicated the impor-

tance of the diffusion process in nutrient exchange

between the periphyton community and overflow-

ing water. The model showed reasonable behavior

of periphyton communities, such as light reduc-

tion in the periphyton mat, variation of the inter-

nal nutrient concentration, and the transition

process of a vertical velocity profile.As several effects were minimized in this study,

such as the respiration effect on the cell cytoplasm

volume, nutrient releases from the sediment, or

biological acclimation of the benthic algae to re-

sponses of resource-limited environments, erosio

of the viscous sublayer due to the existence of th

biomass, etc. this model should be applied wi

some cautions. In the model of this stud

biomass loss due to grazing was simply treated a

a constant rate though it should be varied wit

herbivorous species and density. The fact is wort

emphasizing that taxonomic and physiognom

structures of periphyton community species a

markedly affected by the presence of invertebrat

(Mulholland et al., 1994). All these factors bein

taken for granted, however, the model is conside

ably useful to study the response of a periphyto

community to a particular environmental factor

Finally, to deal with the diffusion process of

high biomass concentration, a time step of min

utes or even smaller should be used.

Acknowledgements

The study was made while the second autho

Duong Hong Son, was receiving a scholarsh

from the Japanese Ministry of Education, Cultu

Fig. 11. Temporal variation of nutrient concentration in the slow flow (left) and fast flow (right) regime.


14/15


and Sports. This study was financially supported

by the Japanese Ministry of Education, Culture,

and Sports, Foundation of River and Watershed

Management, and the Maeda Engineering Foun-

dation. These supports are gratefully acknowl-

edged. We also acknowledge V.T. Ca for his

valuable comments on the flow dynamics part of

the study.

Appendix A

The following formulae are used in the model.

Incline angle of filaments, h:

tan h:Buoyancy

Drag=

(zza)gVi

zCdU2Vi

2/3=

Kz

Vi1/3

U2where

Kz=

(zza)g

zCd

(1A)

where: Periphyton settlement:

Cn, k, i( j)initial =max

0,

Cn, 0 , i( j) %k1

kk=1

Cn, kk, i( j)initial

Bk

DVkSnorDz

n(2A)

The light attenuation constant and light resource

index:

pk=pw+pc

Bk

DVk and

IRn, k, i( j)=Ik

Isati( j)exp

1

Ik

Isati( j)

(3A)

Non-filamentous biomass, Cn,k,j as cell mm2:

(Cn, k, j

(t=Cn, k, j[q

T20GdivjRn, k, jGmortalj

GdetachjGgz

j] (4A)

Filamentous biomass, Ln, k, j. Nn, k, j as cell

mm2

:(Ln, k, i

(t=Ln, k, iq

T20GdiviRn, k, i and

(Nn, k, i

(t= [Gmortali+Ggzi]Nn, k, iNdetach

(5A)

Detachment condition for the bottom-attache

filaments:

Ndetach=) Nn, k, iDt1

0if: zCdU

2SiLn, i)

]

RFcr1BRFcr1

(6A

Detachment condition for the laterally attache

filaments:

Ndetach=

FNn, k, iDt

1

0if: zCdU

2SiLn, i

F]

B

DVFcr2

BB

DVFcr2

(7A

Detachment rate non-filamentous community:

Gdetachj=G0

Fdetach

F0+Fdetachwhere

Fdetach=zCdU

2Sj

B/DV

(8A

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