Elsevier

Ecological Modelling

Volume 137, Issue 1, 1 February 2001, Pages 61-75
Ecological Modelling

A model of the development of a periphyton community: resource and flow dynamics

https://doi.org/10.1016/S0304-3800(00)00432-4Get rights and content

Abstract

An ecological model of periphyton dynamics was designed to approach the development of a periphyton community under the effects of surrounding nutrient concentration and light intensity. The model simulated the vertical heterogeneities of biomass, light irradiance, and nutrients within the periphyton mat. To determine the competition for resources between species, a Monod-type relationship was used to relate external nutrient concentration to periphyton uptake rate, and ‘Liebig's law of the minimum’ was used to combine light and nutrient effects on growth rate and tension strength of the algal cell. The effect of the periphyton community to the vertical distribution of water velocity was also numerically investigated. To confirm the validities, the developed model was verified using several cases: the external concentration was constant or was varied with different diffusion coefficients. Reasonable responses of the periphyton community to the ambience nutrient concentrations, light intensity and, in turn, temporal variation of nutrients during the development of a periphyton community strongly encouraged further application of the model. Variation in the water velocity in a vertical direction intensively contributed to the results of the model.

Introduction

Studies of stream ecosystems have focused on periphyton communities, because benthic algae usually dominate planktonic communities. Many experimental studies have concentrated on the dynamics of the essential resources for periphyton growth. Although several studies have been made on the photosynthesis–irradiance relationship (Sand-Jensen and Revsbech, 1987, Boston and Hill, 1991, Dodds, 1991, Graham et al., 1995, Hill, 1996), only a few studies have evaluated the relation between light inside a matrix and the algal response.

The relation between periphyton and nutrients has been intensively studied. Borchardt (1994) found different optimum N:P ratios for Spirogyra fluviatilis at different velocities. Newbold et al., 1981, Newbold et al., 1983 examined the horizontal heterogeneities 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, Bothwell, 1988, Bothwell, 1989).

Several models have been devised to clarify the relations among the periphyton community, nutrient concentration in the overflowing water, and the nutrient availability for periphyton growth (Kim et al., 1992, Mulholland et al., 1994, DeAngelis 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 resources for periphyton growth, indicating the possibility of a nutrient-limited condition for periphyton communities (Horner et al., 1990, Dodds, 1991, Borchardt, 1996). However, the vertical 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 community structure and producing higher uptake rates by removing the community from the surface in the experiment (Kim et al., 1992), in this study we used models to: (1) simulate the process of periphyton 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.

Section snippets

Model description

All processes are given in the appendix to compute the thickness of the periphyton mat, light resource, growth, settlement and detachment of periphyton (Asaeda and Son, 2000). Table 1 lists the symbols.

An important concept underpinning algal resource kinetics is the single resource limitation (Hamilton and Schladow, 1997), or the growth of a species being limited by only one resource at a time, ‘Liebig's law of the minimum’. Thus, the resource index, which is defined as the indicator of the

Numerical procedure

A system of differential equations was solved numerically by coding in FORTRAN90, including 23 subroutines of ∼2300 command lines. Additional graphic subroutines authorized by Microsoft corporation permitted the main program to simultaneously show the results. The model was also programmed with highly flexible running options. For accuracy, the fourth-order Runge-Kutta method was initially used to solve a system of the first-order differential equations. To increase the computational stability

Verification and discussion

In the verification, the major nutrients of concern were nitrogen, and phosphorous because they are essential for aquatic organism. Other nutrients, such as carbon and silicon, were assumed to be sufficient for periphyton growth. Boundary values of the phosphorous and nitrogen concentrations (e.g. EN0 in Eq. (9)) were tentatively assigned at 2 and 15 μg l−1, respectively. The water depth, depth-average water velocity, and the light intensity at the water surface were assumed to be constant as 6

Application

Observations made at a stream facility at the University of Louisville, Kentucky, USA (Peterson and Stevenson, 1990, Peterson and Stevenson, 1992) were used to validate the model. To provide a water velocity of 0.29 and 0.12 m s−1, water depths of 2.5 and 6.0 cm, respectively, were used. Despite fluctuations were expected in the experiments, phosphorous and nitrogen concentrations were kept constant at the entrance of the channels throughout the simulation at 2.0 and 15.0 μg l−1, respectively,

Concluding remarks

This study numerically indicated the importance of the diffusion process in nutrient exchange between the periphyton community and overflowing water. The model showed reasonable behavior of periphyton communities, such as light reduction in the periphyton mat, variation of the internal 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

Acknowledgements

The study was made while the second author, Duong Hong Son, was receiving a scholarship from the Japanese Ministry of Education, Culture 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 Foundation. These supports are gratefully acknowledged. We also acknowledge V.T. Ca for his valuable comments on the flow dynamics part of the study.

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