Application of Population Dynamics Modeling to Habitat Evaluation – Growth of Some Species of Attached Algae and Its Detachment by Transported Sediment

Hydroécol. Appl. (2004) Tome 14 Vol. 1, pp. 161-174

Application of Population Dynamics Modeling to Habitat Evaluation – Growth of Some Species of Attached Algae and Its Detachment by Transported Sediment –

Tetsuro Tsujimoto(1), and Takashi Tashiro(2)

Abstract. – Mathematical population dynamics modelling has been employed to simulate and predict habitat situation of living species. It is introduced to description of botani- cal growth in aquatic ecosystem by setting the growth and decay rate. Although the PHABSIM technique also can discuss habitat situation, it cannot evaluate the habitat with dynamical changes efficiently. Population dynamics is applied for developing habitat evaluation method in the paper. By investigating the algal habitat in the middle reach of the Yahagi River, the net growth rate is changed spatially corresponding to velocity and water-depth. According to the field observation and conventional hydraulic modeling, the growth rate and the detachment rate of attached algae is estimated. By applying the simulation, population dynamics modeling can be identified as one of the necessary angles for habitat evaluation.

Key words. – Population dynamics modelling, attached algae, algal habitat, growth rate, detachment rate, Yahagi River

INTRODUCTION 1995) is often performed where the investigated area as habitat is mea- The study on the river ecosystem sured by physical properties such as provides the understanding of the velocity, water-depth and the compo- suitability of the situation of each area sition of bed materials. This method- as habitat for each species. The ology was developed initially for PHABSIM (Physical Habitat Simula- predicting suitability of fish habitat tion, Bovee 1982; Stalnaker et al. condition. Although this conventional

(1) Professor, Dept. of Civil Engineering, Nagoya University. Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan. (2) Post doctoral fellow, Aqua Restoration Research Center, Public Works Research Institute. Kasada-cho, Kawashima-cho, Hashima-gun, Gifu pref. 501-6021, Japan. 162 Tetsuro Tsujimoto and Takashi Tashiro model guarantees the suitable area, ory of population dynamics as one of but we often experience that the pop- the essential viewpoints for habitat ulation or biomass in the place with evaluation. Firstly, field-data investi- the highest habitat suitability does not gation has been conducted in the necessarily show the highest value, middle reach of the Yahagi River to particularly, investigated when the estimate the growth rate and the envi- species having low mobility is tar- ronmental capacity of algae ash-free geted. weight. Then, with the use of the field- Recently, the population dynamics observation data, the growth-detach- (Teramoto 1996) is one of the attrac- ment dynamics model for algae has tive researches of ecology. It has been carried out. The simulation has been employed to simulate the devel- demonstrated that the nuisance opment of living species by using growth of algae is caused by the mathematical models. When the pop- shortage of sediment transport. ulation dynamic model is applied, the growth and decay rate of target species are investigated. The most im- FIELD INVESTIGATION IN THE portant characteristic of this model is YAHAGI RIVER that it can describe temporal change in the habitat situation. Conse- Study area quently, we can discuss inhabitant condition of organisms despite of The main stem of the Yahagi River their mobility. However, there is an has a length of 117 km, and a catch- ambiguity related to the selection of ment area of 1,830 km2 in the central objective spatial scale in this model. area of Japan. Seven dams in the In other words, the population dynam- main stem have been constructed, ics have not been discussed by envi- and the Yahagi Dam (river km (Rkm) ronmental change. 80.0; Figure 1) is the largest one. In the present study, an attempt However, all of the dams but the was done to combine a habitat suit- Yahagi Dam are not sufficient enough ability evaluation with a population to control discharges during strong dynamics model that describes flood events. Though the middle response of organisms. From the reach of the Yahagi River was a sand viewpoint of river ecosystem conser- river before constructing the dams, it vation, it is important to grasp dy- displays the characteristics of a cob- namic condition of growing attached ble river at present (picture in Fig- algae adequately because it feeds ure 1). The change has been the other species in river. Therefore, produced by shortage of sediment by discussing about the dynamics of supply from the upper reach due to algal growth and the habitat suitability the dams, it also have caused eco- of algae in the middle reach of the system degeneration such as bloom- Yahagi River, we can identify the the- ing of attached algae (Tashiro et al. Application of Population Dynamics Modeling to Habitat Evaluation 163

Fig. 1. – Study area location in the Yahagi River

(b)

Fig. 2. – (a) Bed elevation contour and (b) Distribution of exposure height of substratum cobble, where No.1 to 4 provide the different bed type to investigate 164 Tetsuro Tsujimoto and Takashi Tashiro

2003). The study area showed the average value of 2 samples in the fig- typical situation of the ecosystem de- ure. Table 1 shows the result of water generation, which located in the mid- quality measurements during the in- dle reach of the river, in Toyota City vestigation period. The parameters of (Rkm 42.0; Figure 1). attached algae biomass had the same trends for the 4 quadrates which started to increase from the fall Collection and analysis data season (September 2002) and exhib- ited the maximum value in the winter The investigated channel was de- season (November or December fined to include one of the reaches 2002). The trends also correspond and to include continuous sets of riffle well to the previous study in a and pool. A GPS (Global Positioning different location of the Yahagi River System) receiver and the levelling (Rkm 53.0, Uchida 1997). These were used for the investigations. Fig- common characteristics depend on ure 2 shows the contour of relative low frequency of disturbance during bed elevations and the distribution of the algal growth phase. Furthermore, exposure height of the substratum the community dynamics of attached cobbles (Tashiro et al. 2003). algae in the investigated reach sug- Riverbed type is distributed in the gested to be related to the change in channel with the pool section in the water temperature. upper region and riffle section in the lower region. According to the change in riverbed type, the points were set as four quadrates (each 1m2) in Figure 2a to investigate algal habitat conditions. Riverbed type of No.1 to No.4 can be described as fol- Table 1. – Results of water quality measure- lows: pool section, transition section ment in the channel. between pool and riffle, riffle section and rapid section, respectively. The biomass fluctuation of attached algae in each quadrate was examined for about half of a year. Hy- draulic conditions in each quadrate and water quality were also investigated. Figure 3 shows the change in ash-free weight and chlorophyll-a, which implies the biomass of attached algae on cobbles of each quadrate. The each plot means the Application of Population Dynamics Modeling to Habitat Evaluation 165

Fig. 3. – Ash-free weight (g/m2) (upper figure) and Chlorophyll-a (mg/m2) (lower figure) of attached algae on the cobble in each quadrate

MODELLING OF GROWTH- namics of attached algae, the effect DETACHMENT DYNAMICS OF of algal detachment is added to the ATTACHED ALGAE conventional Logistic Equation as follows: d  N(t) (1) Model concepts N(t)= ε 1– N(t) – pN(t) dt  K  Logistic Equation can be utilized in where N(t) denotes ash-free weight order to explain population dynamics (g/m2); ε / p represent growth / de- of organisms (Verhulst 1838). In this tachment rate (day-1) and K means modelling of growth-detachment dy- environmental capacity. 166 Tetsuro Tsujimoto and Takashi Tashiro

Integrating Eq.(1) and giving N0 as (4) Detachment rate of attached al- an initial ash-free weight, the follow- gae is amount to be neglected during equation is derived. ing the growth phase because the N(t) = (2) growth rate is dominant the de- ε tachment rate in low disturbance N0Kp(– ) εεε+ ε condition; N0 {}{}KpN(– )–0 exp–(–) pt (5) Nutrient concentration in the in- Furthermore, this equation is vestigated reach is stable during turned into discrete type for the simu- the growth phase. lation of growth-detachment dynam- In the assumption (2), the common ics of attached algae as follows: initial ash-free weight in the each = 2 Nj+1 (3) quadrate is assumed 3.62g/m N Kp(–ε ) which is the averaged value of the j 4 quadrates on 2002/9/26 (Figure 3). εεεN + {}KpN(– )– exp–(–){} ε∆ pt j j The environmental capacity of the each quadrate in the assumption (3) 2 in which the subscript j is the variable is as follows: No. 1 = 24.1g/m ; No. 2 2 2 at the time step j; ∆t denotes time in- = 24.1g/m ; No. 3 = 46.8g/m ; and 2 terval. No. 4 = 35.4g/m . Under these assumptions, the conventional Logistic Equation (Verhulst 1838) is utilized. Estimation of growth rate and Figure 4 shows fitted Logistic Curves environmental capacity of to each observed datum in the each attached algae quadrate (No.1~4)fortheestimation of growth rate and environmental capacity of attached algae community In this study, growth rate and envi- on cobbles in the each quadrate. ronmental capacity of attached algae are estimated by using the field inves- Generally, the algal blooming de- tigation. The following assumptions pends on nutrient condition and light are employed to support the estima- environment. The effect of nutrient tion: condition should be divided into nutrient concentration and supply rate in (1) Growth phase of attached algae water (Borchardt 1996). Nutrient sup- started on 2002/9/26 (t=0) (Fig- ply rate is often more important for ure 3); growth of attached algae, and the ve- (2) Cobbles of each quadrate have locity is related to the nutrient supply the same initial ash-free weight of in the current water (Peterson 1996; attached algae (Figure 3); Stevenson 1996). It is also known (3) The maximum ash-free weight of that light exploitation of attached al- attached algae can be varied on gae depends on water-depth and tur- cobbles of each quadrate as well bidity. Consequently, the relationship as the environmental capacity; between hydraulic conditions, the Application of Population Dynamics Modeling to Habitat Evaluation 167

Fig. 4. – Logistic curve fitting to ash-free weight (g/m2) of the attached algae growth rate and environmental ca- (n=20kg–1m2 in the case) and turbidity pacity of attached algae is discussed. T (kg/m3). The daily data of turbidity Firstly, the growth rate estimation is are predicted by referring to the ob- expressed as follows: served data (Table 1) and water-clar- εε= ity test results in the Yahagi River. 00(/)IIh (4) On the other hand, the environ- εε=×fU() g () h (5) 0 max εε mental capacity is estimated as fol- ε where 0 represents the growth rate in lows: clear water; ε represents the maxi- =× max KKmax fUghKK() () (7) mum growth rate of investigated data –1 where K represents the maximum (0.1day ); fε and gε denote the func- max 2 tions of velocity (U) and water-depth environmental capacity (46.8g/m ); fK (h) about the growth rate, respec- & gK denote the functions of velocity (U) and water-depth (h) about the en- tively; and Ih/I0 means the remaining light rate at water-depth h, estimated vironmental capacity, respectively. by employing the following equation That is to say, we apply the equations (Reynolds 1994). (Eqs. (5) & (7)) involved the meaning of the preference curves which esti- II/=ω exp(– h ) (6) h 0 mated habitat suitability in the in which ω(m–1) is the coefficient of PHABSIM to evaluate magnitude of monochromatic light extinction. This the growth rate and the environmen- coefficient is estimated by multiplying tal capacity of the attached algae in the correction coefficient n (kg–1m2) the present study. 168 Tetsuro Tsujimoto and Takashi Tashiro

Fig. 5. – Relationship between velocity / water-depth and normalized growth rate (a) / environmental capacity (b) of the attached algae and described preference curves

Figure 5 shows the relationship be- Estimation of detachment rate of tween hydraulic conditions (velocity attached algae due to bed-load and water-depth) and the parameters transport about the growth of attached algae ε ε (normalized growth rate ( 0/ max) and Because detachment rate of at- normalized environmental capacity tached algae depends on disturbance

(K/Kmax)) on cobbles in the each conditions, evaluation of the distur- quadrate. The each plot is estimated bance effect is needed. Therefore, by using the parameters (ε,K)ofthe the modelling that deals with the rela- each quadrate (No. 1 ~ 4) in Figure 4 tionship between the detachment rate and the relationship of Eqs. (4) – (7). and bed-load transport (Kitamura et The each line is described according al. 2000) is utilized in this section. By to these data plots. The growth rate is the way, frequent floods, caused by larger in the shallow water with high ordinary rainfall, cannot transport the velocity, and the environmental ca- large cobbles on the substrates in the pacity is larger in the medium magni- investigated channel, the cobbles tude of velocity and depth, relatively. serve as roughness against water Application of Population Dynamics Modeling to Habitat Evaluation 169

flow, and only fine bed-materials are fective shear velocity on sandy sub- transported. The exposed cobbles on stratum. The detachment rate p can the substrates reduce the sand be determined by using the following tractive force among the exposed equation at last. cobbles (Fujita et al. 2000). Hence, p=(24x3600)αW (day–1) (10) when the bed-load transport in cobble x in which α is the resistant coefficient rivers is estimated, the following of algae detachment (1.23×10–4N–1m equation is set up to express the shel- for Cladophola glomerata, Kitamura tering effect due to the exposed cob- et al. 2000). bles on the substrates (Tashiro et al. 2003). fu()δ 2 τδτ==f() * ,()–f δδ =1 SIMULATION OF GROWTH- **e σρ (/–)1gds DETACHMENT DYNAMICS OF (8) ATTACHED ALGAE τ where ∗(e) expresses the non-dimensional (effective) tractive force; δ (= In order to model growth-detach- ∆ ∆ ment dynamics of attached algae, C/dC, c is the exposure height of the cobble) means the non-dimensional NHSED2D, 2DH flow computation exposure height of cobbles normal- (Pornprommin et al. 2002) is employed for the expression of hydraulic ized by and the cobble diameter (dc); f signifies the function of sheltering ef- condition. The governing equations of fects due to the roughness condition; the depth-averaged 2D flow fields for σ ρ surface flow can be written as follows: u* is the shear velocity; and denote the density of the sand and water re- The momentum equations spectively; g implies the gravitational ∂q  T  x + q x = div q x –  acceleration; and ds implies the sand ∂ρt  h  diameter. According to the Ashida & ∂ζ  C  Michiue’s Formula (Ashida & Michiue ––gh  f  q q ∂  2  x (11) 1972), bed-load discharges qB are es- x h τ timated by adopting the *e values. ∂   q y q Ty + div q –  = When a particle of sand in motion ∂ρt  y h  collides with substratum cobble, the ∂ζ  C  workload of the collision per unit area ––gh  f  q q ∂  2  y (12) and time Wx is estimated by referring y h to the analysis of Ishibashi (1983) as The continuity equation follows: ∂ζ + =γ 13/ 23/ divq =0 Wqdux B se* (9) ∂t (13) γ where represents the coefficient re- where qx and qy are unit discharges in lated to material property of cobble each x– and y– direction; q is vector of 5 -4 2/3 ζ (4.94×10 Nm s ); u*e denote the ef- unit discharge; is water surface ele- 170 Tetsuro Tsujimoto and Takashi Tashiro

vation; h is water-depth; Tx and Ty are In the present model, the boundary vectors of momentum fluxes due to fitted non-orthogonal grid system is horizontal turbulent diffusion, g is employed, and the FVM (Finite Vol- gravitational acceleration; ρ is den- ume Method) is employed to disperse

sity of water; and Cf denotes resis- the governing equations (Ferziger & tance coefficient of bed-surface. Peirc 1997). The dispersed momen- When the two kinds of diameters to tum equations are solved by the frac- examine for the roughness estimation tional step method (Ferziger & Peirc were determined, the real riverbed 1997) by solving Poisson equation on conditions in the channel were con- water-surface elevation. First the sidered. Therefore, the large cobbles equations, which exclude the terms / fine sands were set at a 10 cm / related to the gradient of water sur- 1 mm diameter. Eq. (14) is employed face elevation, are integrated with fi- as the resistance law by using the nite time step to calculate the in-term

equivalent sand roughness (ks) that unit discharge. Poisson equation on varies according to the exposure water-surface elevation, which is de- height of cobbles (determined by the rived by substituting the in-term unit ∆ expression ks= C+ds). discharge into the continuity equa- U 11110. h tion, is solved. The unit discharge is ==ln finally revised by calculated water- uCκ k (14) * f s surface elevation. By repeating these where U denotes the depth-averaged processes, converged solution of flow velocity. field can be obtained. The momentum fluxes due to horizontal turbulent diffusion are mod- Daily discharge and turbidity in the ν eled by using eddy viscosity T as reach are given in Figure 6. The hori- follows: zontal time scale is equal to the one in ∂  q  Figure 4. Because the annual maxi- = ρν x Thxx T   mum discharge in the reach is about ∂x  h  (15) 800m3/s (Tsujimoto et al. 2002), there  ∂  q  ∂  q   is no disturbance during the investi- ==ρν   x  +  y   TTxy yx T h gated period. The daily turbidity is es-  ∂y  hx ∂  h   timated by the relationship between (16) the observed data (Table 1) and the ∂  q  daily discharge. According to the flow Th= ρν  y  computation model (NHSED2D model, yy T ∂   (17) y h Pornprommin et al. 2002) and the The eddy viscosity is modeled with daily discharge (Figure 6), we can shear velocity u and water-depth h. compute the distribution of daily hy- * draulic condition in the investigated να= uh (18) T * reach (Figure 2), and then can simu- where αis empirical constant (α=0.1). late the growth-detachment dynamics Application of Population Dynamics Modeling to Habitat Evaluation 171

Fig. 6. – Discharge (m3/s) and turbidity (g/m3) in the investigated channel of attached algae community in the ible result is found in the simulation of each quadrate. quadrate No.1, the detachment effects of attached algae are overval- Initial distribution of ash-free ued in the other quadrates. By weight of attached algae set to be uni- discussing the results, the problem is form (N =3.62g/m2) except at the veg- 0 in phenomena of riffle or rapid sec- etated area (Figure 2). In the tion. In other words, the following simulation, the following condition is effects possibly cause the disagree- assumed: (1) if some sections were ment: (1) biological effect due to the exposed to the atmosphere, a half of nest made by caddisfly larvae in the the ash-free weight of attached algae substrates; (2) disturbance efficiency could be reduced on the sections per of small amounts of attached algae. day by referring to Burns & Walker Firstly, about the (1) effect, high den- (2000); and (2) also, if some sections sities of caddisfly population inhabit didn’t have any ash-free weight of at- in the substrates in the riffle or rapid tached algae, 1% ratio of the initial section of the Yahagi River (Uchida variable (0.0362g/m2) could be pro- 1997) and their high density can de- vided in the sections at the next time crease the movability of the sub- step. strates (Statzner et al. 1999). And Figure 7 shows the simulation re- then, because the modelling of algae sult of the growth-detachment dy- detachment due to bed-load transport namics of attached algae on cobbles aims at the condition of extremely of each quadrate. The effect of algae blooming algae (Kitamura et al. detachment estimated by using Eqs. 2000), the detachment of small (9) & (10) can be examined by setting amounts of attached algae may not bed-load discharge qB as a parameter be applied due to the detachment effi- of a calibration. Although a reproduc- ciency. In order to apply this kind of 172 Tetsuro Tsujimoto and Takashi Tashiro

Fig. 7. – Simulation results of the growth-detachment dynamics of attached algae community on cobbles in the each quadrate by employing bed-load discharge (qB) as a parameter of calibration simulation to actual rivers, bed-load ciently by considering real phenom- discharges in riffle and rapid section, ena as well as geomorphologic fea- i.e., sand transport on highly exposed tures. In other words, the algal cobble bed must be estimated suffi- blooming in the Yahagi River is Application of Population Dynamics Modeling to Habitat Evaluation 173 caused by shortage of bed-load dis- REFERENCES charge in riffle or rapid section. Ashida, K., M. Michiue. 1972. Study on Hydraulic Resistance and Bed-load Transport Rate in Alluvial Streams, Proceedings of The Japan Society of CONCLUSION Civil Engineers, Japan Society of Civil Engineers, No.206, pp.59-69. (in Japa- nese) Borchardt, M.A. 1996. Nutrients, Algal Ecology, edited by R.J. Stevenson et In the present study, we attempted al., Chapt.6, Academic Press, pp.375- to construct new methodology for 402. habitat evaluation by combining the Bovee, K. D. 1982. A guide to stream ha- two kinds of different techniques, i.e. bitat analysis using the instream flow habitat suitability evaluation and Lo- incremental methodology. FWS/OBS- gistic equation. We could exhibit the 82/26. U.S Wildl. Serv., Coop. Instream Flow Serv. Grp., Fort Collins, efficiency of the proposal methodol- CO. 248p. ogy that understood the temporal Burns, A., K. Walker. 2000. Effects of wa- change and the environmental char- ter level regulation on algal biofilms in acteristics of habitat condition. the River Murray, South Australia, Re- gulated Rivers: Research & Manage- Concretely, the growth-detachment, 16, pp.434-444. ment dynamics of attached algae was Ferziger, J.H., M. Peirc. 1997. Computa- modelled and was applied to the in- tional method for fluid dynamics, vestigated channel in the middle Springer, 364p. reach of the Yahagi River. By investi- Fujita, M., T. Sawada, T. Mizuyama, A. Ki- gating the habitat of attached algae in noshita. 2000. Movement of Sediment Removed from a Sabo Dam and Its the channel, the characteristics of Impact on River Environment, Annual growth rate and environmental ca- Journal of Hydraulic Engineering, Vol. pacity of attached algae can be ex- 44, Japan Society of Civil Engineers, plained. On the other hand, by pp.1215-1220. (in Japanese) employing the hydraulic modelling Ishibashi, T. 1983. A Hydraulic Study on such as algae detachment due to Protection for Erosion of Sediment bed-load transport and bed-load Flush Equipments of Dams, Procee- dings of The Japan Society of Civil transport on exposed cobble bed, the Engineers, Japan Society of Civil Engi- detachment rate related to bed-load neers, No.334, pp.103-112. (in Japa- transport was described. Finally, the nese) simulation aimed at description of Kitamura, T., M. Kato, T. Tashiro, T. Tsuji- phenomena in actual river is going on moto. 2000. Experimental Study on developing, the proposed methodol- Detachment of Attached Algae Clado- phola glomerata Due to Bed-load, ogy can explain the cause of habitat Advances in River Engineering, Vol.6, degeneration due to algal blooming Japan Society of Civil Engineers, and reveal current problems. pp.125-130. (in Japanese) 174 Tetsuro Tsujimoto and Takashi Tashiro

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