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

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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 simu- late 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 habi- tat 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 model- ing, 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 spe- cies 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 at- tached algae in each quadrate was examined for about half of a year. Hy- draulic conditions in each quadrate and water quality were also investi- gated. Figure 3 shows the change in ash-free weight and chlorophyll-a, which implies the biomass of at- tached 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 fol- lows: 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 dur- ing 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 as- sumptions, 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 ca- pacity 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.
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